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diff --git a/17576-t/17576-t.tex b/17576-t/17576-t.tex new file mode 100644 index 0000000..2300757 --- /dev/null +++ b/17576-t/17576-t.tex @@ -0,0 +1,16170 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Project Gutenberg's A Rudimentary Treatise on Clocks, Watches and %% +%% Bells, by Edmund Beckett. %% +%% %% +% This eBook is for the use of anyone anywhere in the United States and % +% most other parts of the world at no cost and with almost no restrictions% +% whatsoever. You may copy it, give it away or re-use it under the terms % +% of the Project Gutenberg License included with this eBook or online at % +% www.gutenberg.org. If you are not located in the United States, you % +% will have to check the laws of the country where you are located before % +% using this eBook. % +%% %% +%% %% +%% Packages and substitutions: %% +%% book.cls: Standard LaTeX documentclass. %% +%% makeidx: Required to generate index. %% +%% If unavailable, remove, see below. %% +%% graphicx: Required for PNG illustrations. %% +%% If unavailable, use graphics package or see below. %% +%% wrapfig: Used to wrap text around narrow figures. %% +%% If unavailable, try floatflt or see workaround below. %% +%% multirow: Used in tables on 219.png, 365.png. %% +%% If unavailable, see below. %% +%% longtable: Used to make one very long table break across pages. %% +%% If unavailable, remove, see below. %% +%% rotating: Used for landscape figures and table. %% +%% If unavailable, see workaround below. %% +%% color: Used to define grey background for corrections. %% +%% If unavailable, see workaround below. %% +%% hyperref: Required to create PDF hyperlinks. %% +%% If unavailable, remove, see below. %% +%% %% +%% All of the above were already in my distribution (tetex, 2004). %% +%% %% +%% %% +%% Producer's Comments: %% +%% %% +%% Since there are PNG illustrations, it is best to compile using %% +%% pdflatex. Running pdflatex once, then makeindex, then pdflatex 3 %% +%% more times should be sufficient. (Check that the ToC and index %% +%% numbers are present, and that the long table near the end is %% +%% correctly aligned and starts at Moscow and ends with Gloucester.) %% +%% %% +%% If pagination is altered, check that the wrapfigs (figs 5, 9, 12, 16, %% +%% 20, 60 and 70) are present and in sequence with other figs. Some %% +%% manual adjustment (moving the figures to a different spot in the %% +%% tex file) may be needed. %% +%% %% +%% The file can be compiled using latex instead of pdflatex, but only %% +%% if the \includegraphics lines are removed, or if the PNG files are %% +%% converted to EPS. In that case, the pdftex option in graphicx and %% +%% hyperref should be changed to dvips. %% +%% %% +%% %% +%% Things to Check: %% +%% %% +%% Spellcheck: OK %% +%% LaCheck: OK (false positives: @s, \refs and decimal points.) %% +%% Lprep/gutcheck: OK %% +%% PDF pages, excl. Gutenberg boilerplate: 313 %% +%% PDF pages, incl. Gutenberg boilerplate: 322 %% +%% ToC page numbers: OK %% +%% Index: OK %% +%% Longtable: Aligned. %% +%% Images: 77 PNG (in /images), 4 LaTeX (embedded). %% +%% Wrapfigs: Figs. 5,9,12,16,20,60,70: Present and in sequence. %% +%% Fonts: OK %% +%% Pound signs: OK (Some fonts turn them into dollar signs!) %% +%% %% +%% %% +%% Compile History: %% +%% 9th January 2006: LW compiled with pdflatex (tetex under MacOSX) %% +%% pdflatex clocks %% +%% makeindex clocks %% +%% pdflatex clocks %% +%% pdflatex clocks %% +%% pdflatex clocks %% +%% 22nd January 2006: jt compiled with pdflatex (MikTeX/WinXP) %% +%% pdflatex 17576-t %% +%% makeindex 17576-t %% +%% pdflatex 17576-t %% +%% pdflatex 17576-t %% +%% pdflatex 17576-t %% +%% %% +%% 30 April 2023: okrick. %% +%% MiKTeX Console 4.9, Windows 10 Home %% +%% TeXworks 0.6.7 used to generate PDF output. %% +%% %% +%% %% +%% First two pages give a pdfTeX warning - this is a known issue and is %% +%% safe to ignore. 96 Overfulls, but of these only 8 are in body text, %% +%% the rest from unavoidably wide tables or in the index. 6 Underfulls. %% +%% %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass[a4paper,oneside,11pt]{book}[2001/04/21] + +\listfiles + +\usepackage{makeidx}% If unavailable, the following line makes the file +% compile. Do not run makeindex. Document will have no index. +\providecommand{\printindex}{} + +\usepackage[pdftex]{graphicx}% If unavailable, use "graphics" in place of +% "graphicx". If both are unavailable or if PNGs are absent, +% add the option "draft" into the documentclass. Figures will not appear, +% but nor will hyperlinks. Or, don't use draft mode but manually remove all +% the figures; hyperlinks will still work. + +\usepackage{wrapfig}% If unavailable, change all lines starting +% begin{wrapfigure} (e.g. begin{wrapfigure}{o}{111pt}) to \begin{figure}, +% and all \end{wrapfigure}s to \end{figure}. Figures will appear but not +% with text wrapped round them. Or, use the floatflt package, whose syntax is +% (for example) \begin{floatingfigure}{111pt} ... \end{floatingfigure}. +% It is very likely that manual adjustment of the placement of these figures +% would be necessary to ensure they appear and are in sequence. + +\usepackage{multirow}% If unavailable, the following line makes the file +% compile, although two tables (219.png and 365.png) will be hard to read. +\providecommand{\multirow}[3]{#3} + +\usepackage{longtable}% If unavailable, you might remove the only table that +% uses it, or find a way to split it into several tables that each fit +% on one page. Or, CTAN lists a number of alternative packages for long +% tables. + +\usepackage{rotating}% If unavailable, replace every instance of +% {sidewaysfigure} with {figure} and {sidewaystable} with {table}. +% Figures should display but smaller; the table will be partly cut off. +% Or, try using the landscape environment from the lscape package. + +\usepackage{color}% If unavailable, the file will compile if the 2nd +% newcommand below is uncommented and the one above it commmented out. +% Textual corrections will be underlined instead of highlighted in grey. +\providecommand{\definecolor}[3]{} +\providecommand{\colorbox}[2]{#2} +\definecolor{corr}{rgb}{0.85,0.85,0.85} +\newcommand{\correction}[1]{\colorbox{corr}{#1}} +%\newcommand{\correction}[1]{\underline{#1}} + +\usepackage[pdftex,plainpages=false,pdfpagelabels=true,colorlinks,linkcolor=blue]{hyperref} +% If unavailable, the following lines ensure the file compiles, but +% the document will not have hyperlinks. +\providecommand{\hyperlink}[2]{#2} +\providecommand{\hypertarget}[2]{#2} +\providecommand{\phantomsection}{} +\providecommand{\pdfbookmark}[3][0]{} +\providecommand{\hypersetup}[1]{} + +%%%%%%%%%%%%% Fix hyperref page links %%%%%%%%%%%% +\makeatletter +\AtBeginDocument{\def\pageref#1{% + \expandafter\@pagesetref\csname r@#1\endcsname\@empty{#1}}} +\makeatother + +%%%%%%%%%%%%%%%%% Hyperref setup %%%%%%%%%%%%%%%%% +\hypersetup{ +pdfauthor = {Edmund Beckett}, +pdftitle = {A Rudimentary Treatise on Clocks, Watches and Bells +for public purposes.} +} + +%%%%%%%%%%%%%%% Styling of headings %%%%%%%%%%%%%% +\makeatletter +\def\@makechapterhead#1{% +\phantomsection \vspace*{50\p@}% + {\parindent \z@ \centering + \normalfont + \interlinepenalty\@M + \Huge \bfseries #1\par\nobreak + \setlength{\unitlength}{1cm} + \begin{picture}(5,1)(-2.5,0) + \put(-2.5,0){\line(1,0){5}}\put(-2.5,-0.1){\line(1,0){5}} + \end{picture} + \vskip 40\p@ + }} +\def\@makeschapterhead#1{% +\phantomsection \vspace*{50\p@}% + {\parindent \z@ \centering + \normalfont + \interlinepenalty\@M + \Huge \bfseries #1\par\nobreak + \setlength{\unitlength}{1cm} + \begin{picture}(5,1)(-2.5,0) + \put(-2.5,0){\line(1,0){5}}\put(-2.5,-0.1){\line(1,0){5}} + \end{picture} + \vskip 40\p@ + }} +\renewcommand{\indexname}{\protect\label{index}\protect\pdfbookmark[0]{INDEX.}{index}\protect\plainindexname{}INDEX.} +\newcommand{\plainindexname}{\gdef\indexname{INDEX.}} +\renewcommand\section{\@startsection {section}{1}{\z@}% + {-3.5ex \@plus -1ex \@minus -.2ex}% + {2.3ex \@plus.2ex}% + {\normalfont\Large\bfseries\centering}} +\renewcommand\subsection{\@startsection{subsection}{2}{\parindent}% + {0ex \@plus1ex \@minus.2ex}% + {0em}% + {\normalfont\normalsize\bfseries}} +\renewcommand{\fnum@figure}{\textsc{Fig.~\thefigure}} +\makeatother +\pagestyle{headings} +\setcounter{secnumdepth}{-1}% No numbering of sections, starred or not. + + +%%%%%%%%%%%%%%%% Alter float rules %%%%%%%%%%%%%%% +\renewcommand\floatpagefraction{.60} +\renewcommand\topfraction{.85} +\renewcommand\bottomfraction{.65} +\renewcommand\textfraction{.15} +\setlength{\abovecaptionskip}{0pt} +\setlength{\belowcaptionskip}{10pt} + + +\providecommand{\therefore}{\mathrel{{.}\kern-.05em\raise.40em\hbox{.}\kern-.05em{.}}} %could use amssymb to get this. +\hyphenation{iso-chro-nous} +\makeindex + + + +%%%%%%%%%%%%%%%% Start of Document %%%%%%%%%%%%%%% +\begin{document} + +\thispagestyle{empty} +\small +\begin{verbatim} +Project Gutenberg's A Rudimentary Treatise on Clocks, Watches and +Bells, by Edmund Beckett. + +This eBook is for the use of anyone anywhere in the United States and +most other parts of the world at no cost and with almost no restrictions +whatsoever. You may copy it, give it away or re-use it under the terms +of the Project Gutenberg License included with this eBook or online at +www.gutenberg.org. If you are not located in the United States, you +will have to check the laws of the country where you are located before +using this eBook. + + +Title: A Rudimentary Treatise on Clocks, Watches and Bells + +Author: Edmund Beckett + +Release Date: January 22, 2006 [eBook #17576] +Revised: April 30, 2023 + +Language: English + +Character set encoding: TeX + +*** START OF THIS PROJECT GUTENBERG EBOOK CLOCKS, WATCHES, BELLS *** + + + + +Produced by Robert Cicconetti, Laura Wisewell and the +Online Distributed Proofreading Team at https://www.pgdp.net +Revised by Richard Tonsing + + + +\end{verbatim} +\normalsize +\newpage + +\frontmatter + + +\framebox{% +\begin{minipage}{0.9\textwidth} +\label{transnotes}\pdfbookmark[0]{Transcriber's Notes.}{transnotes} +\textbf{Transcriber's Notes:} +The original of this book had its table of contents, running headers, +and headings in the text all independent. The table of contents given +here is as in the original, as are the headings in the text. However, +the PDF bookmarks reflect the structure of the headings in the text, +and, owing to repagination, it has proved very difficult to match the +running headers, although I have aimed to as far as possible. Some of +the book's headers seemed to refer to a figure on the page; these are +preserved here as figure captions, which did not appear in the +original.\medskip + +All page references, including those in the index, have been +re-generated to point to anchors placed in the source text; in some +cases their placement was ambiguous, but every effort has been made to +place them directly beside the text referred to. Phrases such as ``this +figure'' or ``on the next page'' have been left as in the original, but +may no longer be accurate after repagination. However, I have ensured +that a hyperlink is always given.\medskip + +Two pages of the original copy used had corners missing, therefore the +words ``see'' on page~\pageref{corner1} and ``They'' and ``where'' on +page~\pageref{corner2} are uncertain, and there could be another word +following ``languished'' on page~\pageref{corner3}. In an equation on +page~\pageref{correction1} the $l$ in the denominator had been printed +as a /. The word ``scrapewheel'' on page~\pageref{correction4} has been +changed to ``scapewheel''. Finally, the word ``explored'' on +page~\pageref{correction2} had been printed as ``exploded''. All of +these words have been highlighted in the text \correction{like this}, +and also in the source file with two asterisks (**). + +\end{minipage} +} + + + +%-----File: 001.png---------------------------------------------- +%-----Folio: i ---------------------------------------------- +\title{\label{titlepage}\pdfbookmark[0]{Title Page.}{titlepage} +{\small A RUDIMENTARY TREATISE\\ +ON}\\[4ex] +{\Huge CLOCKS, WATCHES, \& BELLS}\\[2ex] +FOR PUBLIC PURPOSES% +} + +\author{{\small BY}\\ +EDMUND BECKETT, LORD GRIMTHORPE\\ +LL.D. K.C. F.R.A.S. \\[3ex] +\small PRESIDENT OF THE BRITISH HOROLOGICAL INSTITUTE,\\ +\small AUTHOR OF `ASTRONOMY WITHOUT MATHEMATICS,' ETC. +} + +\date{% +\textit{EIGHTH EDITION, MOSTLY REPRINTED FROM THE SEVENTH +EDITION OF} 1883, \textit{WITH A NEW PREFACE AND NEW +LIST OF GREAT BELLS, AND AN APPENDIX +ON WEATHERCOCKS} \\[3ex] +\textsf{WITH NUMEROUS ILLUSTRATIONS}\\[6ex] +LONDON\\ +CROSBY LOCKWOOD AND SON\\ +7 STATIONERS' HALL COURT, LUDGATE HILL\\ +1903\\[3ex] +\textit{All Rights reserved by the Author}\\[3ex] +D. VAN NOSTRAND COMPANY. +} +\maketitle +%-----File: 002.png--------------------------------------------------- +%-----Folio: ii --------------------------------------------------- +\thispagestyle{empty} +\vspace*{\fill} +\begin{center} +PRINTED BY\\ +WILLIAM CLOWES AND SONS, LIMITED,\\ +LONDON AND BECCLES. +\end{center} +\vspace*{\fill} + +\newpage +%-----File: 003.png----------------------------------------------- +%-----Folio: iii ----------------------------------------------- +\chapter{PREFACE TO THE EIGHTH EDITION.} + +There have been so many editions or reprints of this +book (including the articles on Horology in two editions +of the \textit{Encyclop\ae dia Britannica}) that I cannot count +them rightly, especially as several were issued under +my former names of Denison and Beckett (Lord Grimthorpe +since 1886). At least, I suppose so. This is +certainly, in substance, at least the tenth issue. The +book led to my designing, either directly or indirectly, +not only the Westminster and St.~Paul's clocks, and +the great peal of bells there, but those of many other +Cathedrals and Churches, as well as Town-hall, Railway-station, +and others in several of our Colonies, by special +request. As I did all that work gratuitously, I have +no means of tracing them, or probably remembering +the names of them all. I know that I once counted +above forty. +%-----File: 004.png----------------------------------------------- +%-----Folio: iv ----------------------------------------------- + +The Publishers have received from my friend Canon +Nolloth, of Beverley Minster, some further information +about Bells, which (as it could not be inserted in the +stereotype plates) has been inserted, with some remarks +of my own, as Addenda, at pp.~\pageref{addenda_start}--\pageref{addenda_end}. Canon +Nolloth has also completed (pp.~\pageref{longtable1}--\pageref{longtable2}) my own last +list of large bells in various countries. + +I have also added a short Appendix (p.~\pageref{appendix}) on +Weathercocks. + +\hspace*{\fill}GRIMTHORPE. +\begin{tabbing} +\hspace*{0.1\textwidth}\=\hspace*{0.1\textwidth}\=\kill +\textsc{Batch Wood, St.~Alban's.}\\ +\>\textit{May}, 1903. +\end{tabbing} +%-----File: 005.png----------------------------------------------- +%-----Folio: v ----------------------------------------------- + + +\chapter{PREFACE.} + +As this is not unlikely to be the last time that I shall +revise this book, considering my age and the number +of copies printed in each edition of late (3000), and as +I have had more leisure than for many years, I have +endeavoured to make it as complete as possible, and +have introduced more new matter and alterations than +in any edition since the fourth. + +This was one of the first `Rudimentary Treatises,' +undertaken with great spirit by the late Mr.~Weale, at +the suggestion of my friend and connection, Colonel +Sir W.~Reid, K.C.B., the author of the `Law of +Storms,' and the chief manager of the Exhibition of +1851, at the request of the Prince Consort; and 7000 +copies were printed of the first edition. The articles +on Clocks and Watches, but not on Bells, in the eighth +and ninth editions of the \textit{Encyclop\ae{}dia Britannica}, were +abridgments of this book, and therefore make this +edition practically the ninth written by me. + +It should be understood that this professes to be a +rudimentary treatise in the sense of teaching the +principles of horology, and so much practical knowledge +as may be useful both to clockmakers and to +%-----File: 006.png--------------------------------------------- +%-----Folio: vi --------------------------------------------- +amateurs who wish to make, or direct the making of, +their own clocks of superior character; and I have had +abundant information that it has been useful in that +way, besides vastly improving the general character of +public clocks especially, in all the English-speaking +world, and wherever large English clocks go. + +Nobody can learn the details of watchmaking from a +book, and at any rate in no such space as could be +given to it in a volume like this. There have been, +from time to time, useful letters on various details of +the art in the \textit{English Mechanic} and the \textit{Horological +Journal.} I have never heard of any amateur taking +up watchmaking as many do the making or designing +of clocks; and it depends much more on manual +dexterity and practice. Therefore that part of the +book deals more with principles than with working +details. + +I leave the chapter on Bells to speak for itself, as the +only English treatise on their proper construction, +shape, composition, and the best modes of hanging; +and as the result of long experience and many special +experiments, to revive an art which had sunk to a +lower ebb thirty or forty years ago than it had ever +reached in the thousand years or more since large bells +were first made. + +\hspace*{\fill}E.~B.\nopagebreak +\begin{tabbing} +\hspace*{0.1\textwidth}\=\hspace*{0.1\textwidth}\=\kill +\sc Batch Wood, St.~Alban's, and\\ +\>\sc 33, Queen Anne Street, W:\\ +\> \>\textit{Jan,} 1883. +\end{tabbing} + + +%-----File: 007.png--------------------------------------------- +%-----Folio: vii --------------------------------------------- + +\chapter{CONTENTS.} +\begin{tabbing} +\hspace*{0.1\textwidth}\=\hspace*{0.75\textwidth}\=\hspace*{0.15\textwidth}\kill + +\>\>\` \sc page \\ +MEASURES OF TIME \` \pageref{chap:ON_THE_MEASURES_OF_TIME.} \\ +\>Sidereal day \` \pageref{subsec:Sidereal_day} \\ +\>Solar day and transit instrument \` \pageref{subsec:Solar_day} \\ +\>Mean time and year \` \pageref{subsec:Mean_time} \\ +\>Equation of time \` \pageref{equation_of_time} \\ +\>Astronomical and civil day \` \pageref{astronomical} \\ +\>Table of equation of time \` \pageref{timetable} \\ +\>Sidereal time \` \pageref{sidereal_time} \\ +\>Table of local time \` \pageref{localtable} \\ +\>Sidereal and mean dials useless \` \pageref{useless} \\ +Sun-dials \` \pageref{sec:INSTRUMENTS_FOR_MEASURING_TIME} \\ +\>Meridian dial simplest \> \textit{fig.}~\ref{fig01}\'\` \pageref{fig01} \\ +\>Dipleidoscope \> \textit{fig.}~\ref{fig02}\'\` \pageref{fig02} \\ +\>Water and sand clocks \` \pageref{sec:WATER_AND_SAND-CLOCKS.} \\ +\\ +\textbf{Clocks, History of} \` \pageref{sec:CLOCKS.} \\ +\>Early English ones \` \pageref{early} \\ +\>Common clock train \> \textit{figs.}~\ref{fig03} and \ref{fig04} \'\` \pageref{fig03}, \pageref{fig04} \\ +\>Fan-fly instead of pendulum \` \pageref{fanfly} \\ +\>Conical pendulum, or governor \` \pageref{subsec:Conical_Pendulum.} \\ +\>Relation of length to gravity \` \pageref{lg} \\ +\>Barker's mill governor \` \pageref{barker} \\ +\>Revolving pendulum \> \textit{fig.}~\ref{fig05}\'\` \pageref{fig05} \\ +\>Balance-wheel, earliest \> \textit{fig.}~\ref{fig06}\'\` \pageref{fig06} \\ +\\ +\textbf{Pendulums,} history of \` \pageref{sec:PENDULUMS.} \\ +\>Crown-wheel escapement \> \textit{fig.}~\ref{fig07}\'\` \pageref{fig07} \\ +\>Cycloidal theory \> \textit{fig.}~\ref{fig08}\'\` \pageref{fig08} \\ +\>Cheeks, a failure \` \pageref{cheeks} \\ +\>Circular error \` \pageref{subsec:Circular_error.} \\ +\>Mathematics of pendulum theory \` \pageref{maths} \\ +%-----File: 008.png--------------------------------------------- +%-----Folio: viii --------------------------------------------- +\>Lengths of various pendulums \` \pageref{lengths} \\ +\>Centre and radius of oscillation \` \pageref{subsec:Centre_of_oscillation.} \\ +\>Moment of inertia \` \pageref{moi} \\ +\>Standards of length \` \pageref{standard} \\ +\>French metre a bad measure \` \pageref{metre} \\ +\>Egyptian and Jewish cubits \` \pageref{cubit} \\ +\>Short and slow pendulums \` \pageref{subsec:Short_and_slow_pendulums.} \\ +\>Shape and material of pendulums \` \pageref{subsec:Shape_of_pendulums.} \\ +\>Suspension of them \> \textit{fig.}~\ref{fig09}\'\` \pageref{fig09} \\ +\>Where they may be \` \pageref{where} \\ +\>Pendulum springs \` \pageref{subsec:Pendulum_springs.} \\ +Regulation of clocks \` \pageref{subsec:Pendulum_regulation.} \\ +\\ +\textbf{Compensated pendulums} \` \pageref{subsec:Compensation_of_pendulums.} \\ +\>Table of expansions and specific gravities \` \pageref{sgtable} \\ +\>Zinc and steel pendulum \` \pageref{zincsteel} \\ +\>Weights of some \` \pageref{weightstable} \\ +\>A mistake about compensation \` \pageref{misled} \\ +\>Wood and lead compensation \` \pageref{subsec:Wood_and_Lead.} \\ +\>Wood, zinc, and lead \` \pageref{subsec:Wood,_zinc,_and_lead_compensation.} \\ +\>Smeaton's glass pendulum \` \pageref{subsec:Smeaton's_pendulum.} \\ +\>Compound bar compensation \> \textit{fig.}~\ref{fig10}\'\` \pageref{fig10} \\ +\>Homogeneous and Ellicott's \> \textit{fig.}~\ref{fig11}\'\` \pageref{fig11} \\ +\>Mercurial; Baily's mistake \` \pageref{subsec:Mercurial_compensation.} \\ +\>A new kind of jar \> \textit{fig.}~\ref{fig12}\'\` \pageref{fig12} \\ +\>Cast-iron jars best; calculation for \` \pageref{subsec:Cast_iron_jars} \\ +Barometric error and compensation \` \pageref{subsec:Barometric_compensation.} \\ +\>Westminster pendulum fully compensated \` \pageref{fully} \\ +\>Air-tight clock cases \` \pageref{airtight} \\ +\>Compensation by thermometer tube \` \pageref{therm} \\ +\>Greenwich plan \` \pageref{grenplan} \\ +\\ +\textbf{Anchor pallets} \>\> \textit{fig.}~\ref{fig13}\'\` \pageref{fig13} \\ +\>Harrison's recoil escapement \` \pageref{subsec:Harrison's_recoil_escapement} \\ +Clocks out of beat \` \pageref{subsec:Clock_out_of_beat.} \\ +\\ +\textbf{Dead escapements}\>\>\textit{fig.}~\ref{fig14}\'\` \pageref{fig14} \\ +\>General theory of \` \pageref{dead} \\ +\>Importance of dead friction \` \pageref{friction} \\ +\>Sir G.~Airy's calculations \` \pageref{gairycalc} \\ +\>His conclusion erroneous \` \pageref{gairyerr} \\ +\>Proper construction \` \pageref{folio90} \\ +\>Half-dead escapement \` \pageref{subsec:Half-dead_escapement.} \\ +%-----File: 009.png--------------------------------------------- +%-----Folio: ix --------------------------------------------- +\>Loseby's isochronal spring fails \` \pageref{subsec:Loseby's_isochronal_spring.} \\ +\>Large and small arcs \` \pageref{subsec:Large_and_small_arcs.} \\ +\>Value of firm fixing of pendulum \` \pageref{subsec:Importance_of_firm_fixing.} \\ +\>Materials for scapewheels \` \pageref{subsec:Aluminium_bronze.} \\ +\>Weight of them \` \pageref{subsec:Weight_of_scapewheel.} \\ +\>Pallets should be short \` \pageref{subsec:Length_of_pallets.} \\ +\>Rules for construction \` \pageref{palletrules} \\ +Pin-wheel dead escapement\>\>\textit{fig.}~\ref{fig15}\'\` \pageref{fig15} \\ +\>Pin pallets \` \pageref{subsec:Pin_pallets.} \\ +\>Single-pin escapement\>\textit{fig.}~\ref{fig16}\'\` \pageref{fig16} \\ +\>Sir E.~Beckett's three-legged one\>\textit{fig.}~\ref{fig17}\'\` \pageref{fig17} \\ +\>Another form of it\>\textit{fig.}~\ref{fig18}\'\` \pageref{fig18} \\ +Detached escapements, Airy's\>\>\textit{fig.}~\ref{fig19}\'\` \pageref{fig19} \\ +\>Beckett's\>\textit{fig.}~\ref{fig20}\'\` \pageref{fig20} \\ +\>Single-beat escapements waste no force \` \pageref{singlebeat} \\ +\\ +\textbf{Gravity escapements}, value of \` \pageref{sec:REMONTOIRE.} \\ +\>Mudge's\>\textit{fig.}~\ref{fig21}\'\` \pageref{fig21} \\ +\>Sir G.~Airy's calculations \` \pageref{gairycalc2} \\ +\>Proper conclusion therefrom \` \pageref{conclusion} \\ +\>Effect of a close case \` \pageref{closecase} \\ +\>Failure of early gravity escapements \` \pageref{failure} \\ +\>Cumming's and Hardy's \` \pageref{subsec:Cumming's_escapement.} \\ +\>Kater's, Gowland's, Gannery's \` \pageref{subsec:Kater's_escapement.} \\ +\>Bloxam's\>\textit{fig.}~\ref{fig22}\'\` \pageref{fig22} \\ +\>Correction of Airy's mistakes \` \pageref{gairyerr2} \\ +\>Beckett's gravity escapements \` \pageref{subsec:Sir_E.Beckett's_Gravity_Escapements.} \\ +\>Four-legged\>\textit{fig.}~\ref{fig23}\'\` \pageref{fig23} \\ +\>Banking pins, useful \` \pageref{banking} \\ +\>Fly to be light and large \` \pageref{fly} \\ +\>Double three-legged\>\textit{fig.}~\ref{fig24}\'\` \pageref{fig24} \\ +\>Most successful for large clocks \` \pageref{large} \\ +\\ +\textbf{Going part of clocks}, generally \` \pageref{sec:GOING_PART.} \\ +\>Section of one\>\textit{fig.}~\ref{fig25}\'\` \pageref{fig25} \\ +\>Dial work \` \pageref{subsec:Dial_work.} \\ +\>Regulator clocks \` \pageref{reg} \\ +\>Winding keys should be long \` \pageref{subsec:Winding_keys} \\ +Year clocks \` \pageref{subsec:Year_clocks.} \\ +\>Clock cases and Moon dials \` \pageref{subsec:Clock_cases} \\ +\>Day of the month clocks\>\textit{fig.}~\ref{fig26}\'\` \pageref{fig26} \\ +\>Chronoscopic dials without hands \` \pageref{chronoscopic} \\ +%-----File: 010.png--------------------------------------------- +%-----Folio: x --------------------------------------------- +\>Equation of time clocks\>\textit{fig.}~\ref{fig27}\'\` \pageref{fig27} \\ +Maintaining powers \` \pageref{sec:MAINTAINING_POWERS_OR_GOING_BARRELS.} \\ +\>Endless chain\>\textit{fig.}~\ref{fig28}\'\` \pageref{fig28} \\ +\>Spring-going barrel\>\textit{fig.}~\ref{fig29}\'\` \pageref{fig29} \\ +\>Bolt and shutter \` \pageref{subsec:Bolt_and_shutter.} \\ +\>Beckett's improved one \` \pageref{subsec:Improved_bolt_and_shutter.} \\ +\>Sun-and-planet power\>\textit{fig.}~\ref{fig30}\'\` \pageref{fig30} \\ +Spring clocks \` \pageref{subsec:Spring_clocks.} \\ +American clocks and Austrian \` \pageref{subsec:American_clocks.} \\ +Improved French clocks \` \pageref{subsec:Improved_French_clocks.} \\ +Self-winding clocks \` \pageref{subsec:Self-winding_Clocks} \\ +Water clocks \` \pageref{subsec:Water_clocks.} \\ +Electrical, Bain's \` \pageref{subsec:Electrical_clocks} \\ +\>Shepherd's \` \pageref{shep} \\ +\>Jones's controlled \` \pageref{jones} \\ +\>Ritchie's\>\textit{fig.}~\ref{fig31}\'\` \pageref{fig31} \\ +\>His pendulums\>\textit{fig.}~\ref{fig32}\'\` \pageref{fig32} \\ +\>Lund \& Blockley's \` \pageref{lund} \\ +\>Timeballs and guns \` \pageref{subsec:Time_balls_and_guns} \\ +\\ +\textbf{Striking Clocks}, for one only\>\>\textit{fig.}~\ref{fig33}\'\` \pageref{fig33} \\ +\>Common striking part\>\textit{fig.}~\ref{fig34}\'\` \pageref{fig34} \\ +\>Repeating method \` \pageref{repeat} \\ +\>New French form of it \` \pageref{newfrench} \\ +\>Strike and silent \` \pageref{subsec:Strike_and_silent.} \\ +\>Locking plate\>\textit{fig.}~\ref{fig35}\'\` \pageref{fig35} \\ +\>Half-hour striking one \` \pageref{subsec:Half-hour_striking.} \\ +\>With rack movement \` \pageref{subsec:Half-hours_with_Rack_Movement.} \\ +\>Quarters on two bells \` \pageref{quart} \\ +\>Quarter chimes \` \pageref{subsec:Quarters--Tunes.} \\ +\>Best construction for them\>\textit{fig.}~\ref{fig36}\'\` \pageref{fig36} \\ +Tell-tale clocks, and musical \` \pageref{subsec:Tell-tale_clock} \\ +\\ +CHURCH OR TURRET CLOCKS \` \pageref{sec:CHURCH_OR_TURRET_CLOCKS.} \\ +Pendulums long and heavy \` \pageref{subsec:Pendulum.} \\ +\>Position of clock \` \pageref{subsec:Position_of_clock.} \\ +\>Frame, old form \` \pageref{subsec:Frame.} \\ +\>Some of the largest clocks \` \pageref{folio_182} \\ +\>Small turret clock with gravity escapement\>\textit{fig.}~\ref{fig37}\'\` \pageref{fig37} \\ +\>Clock towers and architects \` \pageref{architects} \\ +\>Wire ropes \` \pageref{subsec:Wire_ropes.} \\ +\>Striking from great wheel \` \pageref{subsec:Striking_from_the_great_wheel} \\ +%-----File: 011.png--------------------------------------------- +%-----Folio: xi --------------------------------------------- +\>Two hammers \` \pageref{2hammer} \\ +\>Stops for weights \` \pageref{subsec:Stops_for_weights.} \\ +\>Number of lines and pulleys \` \pageref{lines} \\ +\>Bushes, various forms\>\textit{fig.}~\ref{fig38}\'\` \pageref{fig38} \\ +\>Four-wheeled train clock\>\textit{fig.}~\ref{fig39}\'\` \pageref{fig39} \\ +Size of fly important \` \pageref{subsec:Size_of_fly.} \\ +\\ +\textbf{Large clocks with quarters} \` \pageref{sec:LARGE_CLOCKS_WITH_QUARTERS.} \\ +\>Best pattern of one\>\textit{fig.}~\ref{fig40}\'\` \pageref{fig40} \\ +\>Number of cams and teeth \` \pageref{nocams} \\ +\>Discharge of striking \` \pageref{disch} \\ +\>Two-quarter hammer\>\textit{fig.}~\ref{fig41}\'\` \pageref{fig41} \\ +\>Cambridge and Westminster quarters \` \pageref{subsec:Cambridge_and_Westminster_chimes.} \\ +\>Doncaster quarters \` \pageref{subsec:Doncaster_quarters.} \\ +\>Worcester \` \pageref{subsec:Worcester_and_Chester_Cathedral_quarters.} \\ +\>Arrangement of chime barrel \` \pageref{barrel} \\ +\>Proper interval for chimes \` \pageref{interval} \\ +\>Lifting off hammers \` \pageref{lift} \\ +\>Quarters on two bells \` \pageref{subsec:Quarters_on_two_bells.} \\ +Striking at exact time \` \pageref{subsec:Time_of_striking.} \\ +\\ +\textbf{Chime tunes} \` \pageref{subsec:Chime_tunes.} \\ +\>New method\>\textit{fig.}~\ref{fig42}\'\` \pageref{fig42} \\ +\>Large and small bells together bad \` \pageref{lsbad} \\ +Clock hammers\>\>\textit{fig.}~\ref{fig43}\'\` \pageref{fig43} \\ +\>Fixed above bell\>\textit{fig.}~\ref{fig44}\'\` \pageref{fig44} \\ +\>Cranks for them\>\textit{fig.}~\ref{fig45}\'\` \pageref{fig45} \\ +\>Weight of hammers \` \pageref{subsec:The_weight_of_hammer} \\ +\\ +\textbf{Dials of turret clocks} \` \pageref{sec:DIALS.} \\ +\>List of some large ones \` \pageref{largedial} \\ +\>Materials for \` \pageref{dialmat} \\ +\>Concave \textit{v.} convex \` \pageref{subsec:Concave_dials.} \\ +\>Hands, construction of \` \pageref{subsec:Hands.} \\ +\>Illumination of dials \` \pageref{subsec:Illuminated_dials.} \\ +\>Dial-wheels \` \pageref{subsec:Dial_wheels.} \\ +\>Universal joints and friction\>\textit{fig.}~\ref{fig46}\'\` \pageref{fig46} \\ +\>Weathercocks and ventilation \` \pageref{subsec:Ventilation_of_clock-room.} \\ +\\ +\textbf{Train remontoires} \` \pageref{sec:TRAIN_REMONTOIRES.} \\ +\>Bevelled-wheel remontoire\>\textit{fig.}~\ref{fig47}\'\` \pageref{fig47} \\ +\>Continuous motions \` \pageref{subsec:Continuous_motion_remontoire.} \\ +\>Telescope drivers \` \pageref{telescope} \\ +%-----File: 012.png--------------------------------------------- +%-----Folio: xii --------------------------------------------- +\>Royal Exchange remontoire\>\textit{fig.}~\ref{fig48}\'\` \pageref{fig48} \\ +\>Simplest train remontoire\>\textit{fig.}~\ref{fig49}\'\` \pageref{fig49} \\ +\>Spring remontoire, Sir G.~Airy's \` \pageref{subsec:Spring_Remontoire.} \\ +\>Sir E.~Beckett's\>\textit{fig.}~\ref{fig50}\'\` \pageref{fig50} \\ +Cast-iron wheels \` \pageref{subsec:Cast-iron_wheels.} \\ +\>Decay of brass in bad air \` \pageref{decay} \\ +Jobbing in public clocks \` \pageref{jobbing} \\ +Specifications for them \` \pageref{sec:SPECIFICATIONS_FOR_PUBLIC_CLOCKS.} \\ +\>Degree of error to be allowed \` \pageref{degerr} \\ +\\ +\textbf{The Westminster clock} (see frontispiece) \` \pageref{sec:CONSTRUCTION_OF_THE_WESTMINSTER_CLOCK.} \\ +\>Double-barrelled crab there\>\textit{fig.}~\ref{fig51}\'\` \pageref{fig51} \\ +\>Another form of it\>\textit{fig.}~\ref{fig52}\'\` \pageref{fig52} \\ +\>Mode of regulating \` \pageref{subsec:Regulation.} \\ +\>Pendulum and escapement \` \pageref{subsec:The_double_three-legged_gravity_escapement} \\ +\>Maintaining power \` \pageref{subsec:Maintaining_power.} \\ +\>The dials and hands \` \pageref{subsec:The_dials} \\ +\>Quarters \` \pageref{subsec:Quarters.} \\ +\>Hour striking part \` \pageref{subsec:Hour-striking_part.} \\ +\>Mode of discharging exactly\>\textit{fig.}~\ref{fig53}\'\` \pageref{fig53} \\ +\>Winding of striking parts \` \pageref{subsec:Winding_of_striking_parts.} \\ +\>Its rate \` \pageref{subsec:Rate.} \\ +\>History of it \` \pageref{subsec:History_of_the_clock.} \\ +\>Sir C.~Barry's hands for it \` \pageref{barryhands} \\ +\>Mr.~Cowper Temple about it \` \pageref{ctemple} \\ +\>The bells and their history \` \pageref{sec:THE_WESTMINSTER_BELLS.} \\ +\>Sir G.~Airy's report on them \` \pageref{gairyreport} \\ +\>Mr.~Cowper Temple again \` \pageref{ctemple2} \\ +\>Cost of clock and bells, and of the dials and bell-frame \` \pageref{cost} \\ +\\ +\textbf{Teeth of wheels} \` \pageref{sec:TEETH_OF_WHEELS} \\ +\>Helix teeth\>\textit{fig.}~\ref{fig54}\'\` \pageref{fig54} \\ +\>Epicycloidal\>\textit{fig.}~\ref{fig55}\'\` \pageref{fig55} \\ +\>Drivers and runners\>\textit{fig.}~\ref{fig56}\'\` \pageref{fig56} \\ +\>Lantern pinions\>\textit{fig.}~\ref{fig57}\'\` \pageref{fig57} \\ +\>Depthing tool \` \pageref{depthing} \\ +\>Internal wheels \` \pageref{subsec:Internal_wheels} \\ +\>Bevelled and skew-bevelled \` \pageref{subsec:Bevelled_wheels.} \\ +\>Cams \` \pageref{subsec:Cams} \\ +\>Calculation for them \` \pageref{camcalc} \\ +\>Simplest construction\>\textit{fig.}~\ref{fig58}\'\` \pageref{fig58} \\ +Oil for clocks \` \pageref{subsec:Oil_for_clocks.} \\ +%-----File: 013.png--------------------------------------------- +%-----Folio: xiii --------------------------------------------- +\\ +WATCHES AND CHRONOMETERS \` \pageref{chap:WATCHES_AND_CHRONOMETERS.} \\ +History of early watches \` \pageref{History_of_early_watches} \\ +Mainsprings \` \pageref{subsec:The_main-spring} \\ +American Spring Barrel\>\>\textit{fig.}~\ref{fig59}\'\` \pageref{fig59} \\ +Tipsy key \` \pageref{tipsy} \\ +American watch\>\>\textit{fig.}~\ref{fig60}\'\` \pageref{fig60} \\ +English\>\>\textit{fig.}~\ref{fig61}\'\` \pageref{fig61} \\ +Winding stops \` \pageref{subsec:Winding_stops.} \\ +Up-and-down dial\>\>\textit{fig.}~\ref{fig62}\'\` \pageref{fig62} \\ +Dial wheels \` \pageref{subsec:The_dial_wheels} \\ +Balance spring \` \pageref{subsec:Balance_spring.} \\ +Balance free from gravity \` \pageref{free} \\ +Regulation of watches\>\>\textit{fig.}~\ref{fig63}\'\` \pageref{fig63} \\ +\>Old plan\>\textit{fig.}~\ref{fig64}\'\` \pageref{fig64} \\ +\>Glass balance springs \` \pageref{subsec:Glass_balance_springs} \\ +Timing for position \` \pageref{subsec:Timing_for_position.} \\ +\>Gimbals\>\textit{fig.}~\ref{fig65}\'\` \pageref{fig65} \\ +\>Ship timepieces \` \pageref{subsec:Ship_time-pieces.} \\ +\\ +\textbf{Compensated balances} \` \pageref{sec:COMPENSATION_OF_BALANCES.} \\ +\>Harrison's and Le Roy's \` \pageref{harrleroy} \\ +\>Common plan\>\textit{fig.}~\ref{fig66}\'\` \pageref{fig66} \\ +\>Chronometrical thermometer \` \pageref{subsec:The_chronometrical_thermometer} \\ +\>Secondary compensation \` \pageref{subsec:Secondary_compensation.} \\ +\>Mathematical theory of \` \pageref{2ndmath} \\ +\>Greenwich trials \` \pageref{subsec:Greenwich_trials.} \\ +\>Eiffe's compensation \` \pageref{subsec:Eiffe's_compensation_balance} \\ +\>Dent's\>\textit{fig.}~\ref{fig67}\'\` \pageref{fig67} \\ +\>Loseby's\>\textit{fig.}~\ref{fig68}\'\` \pageref{fig68} \\ +\>Kullberg's\>\textit{fig.}~\ref{fig69}\'\` \pageref{fig69} \\ +\>Dent's prismatic\>\textit{fig.}~\ref{fig70}\'\` \pageref{fig70} \\ +\\ +\textbf{Escapements}, vertical\>\>\textit{fig.}~\ref{fig71}\'\` \pageref{fig71} \\ +\>Lever\>\textit{fig.}~\ref{fig72}\'\` \pageref{fig72} \\ +\>Horizontal\>\textit{figs.}~\ref{fig73}, \ref{fig74}, \'\` \pageref{fig73}, \pageref{fig74} \\ +\>Duplex\>\textit{fig.}~\ref{fig75}\'\` \pageref{fig75} \\ +\>Chronometer\>\textit{fig.}~\ref{fig76}\'\` \pageref{fig76} \\ +\>Lever chronometer\>\textit{fig.}~\ref{fig77}\'\` \pageref{fig77} \\ +\>Tourbillons \` \pageref{subsec:Tourbillons.} \\ +Remontoires useless \` \pageref{subsec:Remontoires.} \\ +Repeaters \` \pageref{subsec:Repeaters} \\ +Keyless watches\>\>\textit{fig.}~\ref{fig78}\'\` \pageref{fig78} \\ +%-----File: 014.png-------------------------------------------- +%-----Folio: xiv -------------------------------------------- +Pedometers and stop watches \` \pageref{subsec:Pedometer.} \\ +Recording watch\>\>\textit{fig.}~\ref{fig79}\'\` \pageref{fig79} \\ +Dials and cases \` \pageref{dialcase} \\ +Watch factories \` \pageref{subsec:American_watch-factories.} \\ +\\ +BELLS \` \pageref{chap:BELLS.} \\ +History of bells \` \pageref{chap:BELLS.} \\ +Founders, past and present \` \pageref{founders} \\ +Foreign and English \` \pageref{foreign} \\ +Old bell metal \` \pageref{Old_bell_metal} \\ +Notes and sizes \` \pageref{subsec:Notes_of_bells.} \\ +Notes and weights \` \pageref{subsec:Weight_of_bells.} \\ +Scales of thickness \` \pageref{thickness} \\ +Exeter, York, and Bow peals \` \pageref{EYB} \\ +St.~Paul's and Worcester \` \pageref{SPW} \\ +Bradford and Manchester \` \pageref{Bradford_and_Manchester} \\ +Bad modern towers \` \pageref{Bad_modern_towers} \\ +Doncaster and Burton peals \` \pageref{DB} \\ +Headingley and Gainford \` \pageref{HG} \\ +Thickness of large and small bells \` \pageref{thicknessls} \\ +Maiden bells \` \pageref{maiden} \\ +Sizes for peals \` \pageref{subsec:Sizes_of_peals.} \\ +\\ +\textbf{Shape of bells}, rules for \` \pageref{subsec:Shape_of_bells.} \\ +\>Section or sweep\>\textit{fig.}~\ref{fig80}\'\` \pageref{fig80} \\ +\\ +\textbf{Composition,} best \` \pageref{subsec:Composition_of_bell-metal.} \\ +\>Atomic proportions \` \pageref{atomic} \\ +\>Cast steel, bad \` \pageref{subsec:Steel_bells.} \\ +\>Silver a vulgar error \` \pageref{subsec:Silver.} \\ +Moulding, two modes of \` \pageref{subsec:Moulding.} \\ +Mending cracked bells impossible \` \pageref{subsec:Mending_cracked_bells.} \\ +New bell crown, Sir E.~Beckett's\>\>\textit{fig.}~\ref{fig81}\'\` \pageref{fig81} \\ +\>Taylor's \` \pageref{taylor} \\ +Clapper bolt independent \` \pageref{bolt} \\ +Tucking up in stock \` \pageref{tuck} \\ +Tolling levers and gudgeons \` \pageref{subsec:Tolling-levers.} \\ +\>Great Paul's hanging \` \pageref{gphang} \\ +Bell ropes \` \pageref{subsec:Bell-ropes.} \\ +Ellacombe's chiming hammers \` \pageref{subsec:Ellacombe's_chiming_hammers.} \\ +Stays and sliders \` \pageref{subsec:Stays_and_sliders.} \\ +Gudgeons should be long \` \pageref{subsec:The_Gudgeons,} \\ +%-----File: 015.png-------------------------------------------- +%-----Folio: xv -------------------------------------------- +Clappers and iron stocks \` \pageref{subsec:Clappers} \\ +Bell frames \` \pageref{subsec:Bell-frames,} \\ +\>Bottom should fit walls \` \pageref{walls} \\ +\>Arrangement of frames \` \pageref{framearrange} \\ +\>Folly of some constructions \` \pageref{folly} \\ +Clappering cracks bells \` \pageref{subsec:Clappering.} \\ +\\ +\textbf{Specifications} for peals \` \pageref{subsec:Specifications.} \\ +Bell towers, proper size of \` \pageref{subsec:Bell-towers.} \\ +\>Proper plan of bells in \` \pageref{bellplan} \\ +\>Architects destroy belfries \` \pageref{archdestroy} \\ +\>Windows in \` \pageref{windows} \\ +The great bells of Europe \` \pageref{subsec:The_great_bells_of_Europe} \\ +\>List, with weights and sizes \` \pageref{longtable1} \\ +\\ +\textbf{Addenda} \` \pageref{chap:ADDENDA.} \\ +\\ +\textbf{Appendix.}---Weathercocks \` \pageref{chap:APPENDIX.} \\ +\\ +\textbf{Index} \` \pageref{index} \\ +\end{tabbing} +%-----File: 016.png-------------------------------------------- +%-----Folio: 1------------------------------------------------- + +\mainmatter +\chapter{ON THE MEASURES OF TIME.}\label{chap:ON_THE_MEASURES_OF_TIME.} +\phantomsection +\addcontentsline{toc}{section}{Measures of Time.} + +Before considering the construction of horological machines +it is desirable to understand what it is they have to measure. +It is easy to reply, days and their subdivisions. But there +are various kinds of days, all meaning one rotation of the +earth, with reference to the stars, or the equinoctial point $\Upsilon$, +or the sun, or an imaginary sun going with the average speed +of the real sun in its apparent annual motion round the earth. + +\subsection[Sidereal day]{A sidereal day}\label{subsec:Sidereal_day}\index{Day!sidereal}\index{Sidereal!day}\markright{SIDEREAL, SOLAR, AND MEAN TIME.}\ is the first or the second of these, or +is one absolute rotation of the earth, or the time between +two successive passages of the same star over any given +meridian; for the stars are so far off that the whole width +of the earth's orbit does not make a difference of $1''$ in the +apparent place of the nearest star: much, less does the +motion of the earth in one day make any sensible difference. + +And as this rotation is the only period that is measurable by +any object which is both fixed and visible, all clock time\index{Clock time, all regulated by sidereal time} is +ultimately regulated by sidereal time\index{Sidereal!time}, which is daily taken at +observatories by observing when certain stars pass the +meridian. + +This is done by having a telescope fixed at right angles +across a stiff axis with pivots at the ends, which is laid +exactly east and west and horizontal on very firm supports, +so as to be free from all vibration and disturbance. The +%-----File: 017.png-------------------------------------------- +%-----Folio: 2------------------------------------------------- +telescope can then only move in the plane of meridian and +is called a \textit{transit instrument}\index{Transit instrument}, and is the primary horologic +instrument for measuring whole days, while clocks measure +their subdivisions. Some very fine wires are stretched vertically +across the focus of the telescope, or the place where an +image of the star is formed by the object-glass,\index{Astronomy without Mathematics@`Astronomy without Mathematics'!referred to}\footnote{See my +`Astronomy without Mathematics,' p.~399, 7th ed.} one of the +wires being in the middle or meridian: the others are useful +to measure the distance of the star as it approaches and +leaves the meridian; and the magnifying power increases the +apparent motion, and makes it so much easier to observe +accurately. + +But this is not strictly true: $0$ or $24$~o'clock by sidereal +time is not when any particular star passes the standard +meridian of the country (here of Greenwich), but when that +imaginary point called $\Upsilon$ passes, where the sun is at the +vernal equinox, or the intersection of the ecliptic and the +celestial equator. And that recedes $50{''}.1$ a year among the +stars; which is equivalent to $3\frac13$~sec.\ of time in the earth's +rotation, but to $20\frac13$~min.\ in the annual revolution, which is +the difference between the sidereal and the equinoctial or +common year. Therefore a clock going rightly by the stars +would be $3\frac13$~sec.\ slow at the end of the year by $\Upsilon$ or by what +is called sidereal\index{Sidereal!time} but is really equinoctial time. The place +of $\Upsilon$ is always known, because the distance of every considerable +star from it in sidereal time, or Right Ascension, is +given in the Nautical almanac; and so clock time is actually +measured by the stars at last, but with this correction, which +you see is only the $110$th of a second a day. + +\subsection[Solar day]{A solar day}\ \label{subsec:Solar_day}\index{Day!solar}\index{Solar day!defined}is the interval between two successive +transits of the middle of the sun over the meridian; and +before that can happen the earth must make more than one +absolute rotation, because the sun is going (apparently or +relatively) round it in the same direction as the earth rotates---\textit{i.e.}, +from west to east; for the apparent motion of all the +%-----File: 018.png-------------------------------------------- +%-----Folio: 3------------------------------------------------- +heavenly bodies westward is only the consequence of the +earth's rotation eastward. Therefore there is one\label{1more} more +sidereal day in the year than there are solar days; or a +sidereal day is a $366$th, or nearly $3$m.~$56$s.\ shorter than a +solar day; or they are in the proportion of $1.00274$ to $1$, or +$1$ to $.99727$. A small wheel of $8$ teeth revolving round a +fixed large one of $2922$ makes $366\frac14$ absolute rotations, +but $365\frac14$ relatively to the large one: this is called a sun +and planet motion accordingly. + +The length of a solar day is continually varying a little +from two causes.\index{Solar day!why it varies} One is that the earth's orbit is an ellipse +with the sun in one focus, and the earth moves slowest when +it is farthest off---\textit{i.e.}\ in July. The other, and much the +larger cause is, that the sun moves in the ecliptic, and not +in the equator; and if you bring each successive $10^\circ$ (say) +of the ecliptic on a globe up to the brass meridian, you will +see that they seldom correspond to exactly $10^\circ$ of the equator, +which is the hour circle of the globe. The consequence is +that the days are a minute longer in December, and half a +minute longer in June than they are in April or September; +and if a good clock is set with the sun-dial in November, it +will be half an hour before the sun in February. Hence it is +that the afternoons are so much darker in November than +they are at the same number of days after Christmas. It +was the fashion in France, as late as 1826, to make the +public clocks show solar time, either by some complicated +machinery or by altering them nearly every day. + +\subsection[Mean time]{Mean time}\label{subsec:Mean_time}\index{Mean time}---that is, a mean solar day---is the average +length of all the solar days in the year; which is no +exact number of days; for the sidereal year, or time of +the sun's return to the same place among the stars, is +$365.25634$ mean days, and the equinoctial or common +year, or mean time of the earth's return to $\Upsilon$ is fixed by +astronomers at $365.242216$ mean solar days, or $365$~days, +$5$~hours, $48$m.~$49\frac12$~s. The difference between true and mean +%-----File: 019.png--------------------------------------------- +%-----Folio: 4-------------------------------------------------- +solar time for each day is called the \label{equation_of_time}\textit{Equation of time}\index{Equation of time}.\markboth{EQUATION OF TIME.}{SIDEREAL, SOLAR, AND MEAN TIME.} It is +usually given in almanacs in the form of `clock before' or +`after sun.' But the following table, at p.~\pageref{timetable}, shows the time +which a clock in the longitude of Greenwich, Boston, Louth +and Grimsby (for they are all in longitude $0^\circ$), ought to show +when the sun is on their meridian. It is easily adapted to +any place west of those, by adding to the time in the table +$4$m.\ for $1^\circ$ of longitude, and so on; and for the few places +in England east of Greenwich you must subtract at the +same rate from the time in the table. + +The equation is not quite the same every year, but moves +on nearly a quarter of a day yearly, till \index{Leap-year, how it affects the equation of time}leap-year comes +and puts it very nearly back again. The reason why it +does not do so quite is, that the year is not quite $365\frac14$~days. +That is the error which is attempted to be corrected by +dropping the leap-day of every century except those divisible +by $4$. I have shown in my `Astronomy'\index{Astronomy without Mathematics@`Astronomy without Mathematics'!referred to} that a much more +complete correction would be made by simply dropping every +$32$nd leap-day, or that of every $128$th year; and that dropping +the leap-day of every century except the fifth would +better than the fourth. + +The table at p.~\pageref{timetable} is made for the first year after leap-year; +and it will practically serve for a long time to come +(in case you have not an almanac with an equation table), if +in the second year you subtract the difference between the +equation for any given day and the next, when the time +is increasing, and add when it is decreasing. Thus on +1~January 1881 the clock was $3$m.~$58$s.\ before sun, and +$4$m.~$26$s.\ on 2~January---the difference being $28$s. Therefore +subtract $7$s.\ for 1~January 1882, which makes the +clock $3$m.~$51$s.\ before sun. Again, for 1~January 1883, +the third year after leap, subtract $14$s.\ from the time in the +table, and you get $3$m.~$44$s.; for leap-year up to February~11, +where the equation turns, subtract three quarters of the difference. +From thence to the end of the month, as the time +%-----File: 020.png-------------------------------------------- +%-----Folio: 5------------------------------------------------- +is decreasing, you must add the three quarters of difference, +treating the 29th as March~1. + +And generally, when the time is decreasing, you must add +the proper fraction of the difference. Thus the time on +1~October 1881 is $11.49.38$, and on 2~October is $11.49.19$. +For 1882 add a quarter of the difference (say $5$s.) and you +have the time on 2~October $11.49.24$. For the third year +after leap add $10$s.\ for 2~October; but for leap-year itself +back to 29~February, or the day before 1~March, subtract +a quarter of the difference when the time is decreasing. +Thus for 1~March of leap-year it is $0.12.30$, and for +29~February it is $0.12.42$; while for 28~February, beginning +from the other end of the year, it became $0.12.54$ by adding +three quarters of the difference. I find by looking back at +old almanacs that this always gives the equation as nearly +right as you can observe the sun by any kind of dial: if +you want to be more exact you must get an almanac with +the equation for every day in the year. + +In setting a mean time\index{Mean time!how got from sidereal observations} clock by sidereal observations you +have nothing to do with the equation of time, which only +relates to the sun. Some almanacs besides the Nautical +give the mean time at which certain stars and planets pass +the meridian of Greenwich, and then the operation of setting +the clock is simple and obvious enough. Whitaker's\index{Whitaker's almanack, sidereal time of noon in} almanac +gives the sidereal clock time at each mean solar noon. But +it should be observed that astronomers'\label{astronomical} mean time has no +\textsc{a.m.}\ and \textsc{p.m.}, but is reckoned up to 24~hours from the noon +after the midnight at which the civil day is considered to +begin. Thus $11$h.~\textsc{a.m.}\ 1~January 1880 of common life was +$23$h.\ 31~December 1879 with astronomers. Without some +of the data which are only to be found in such an almanac +it is of no use attempting to find the time from sidereal +observations, and therefore it is not worth while to give any +less simple modes of doing it from other data than those just +mentioned. +%-----File: 021.png----------------------------------------------- +%-----Folio: 6---------------------------------------------------- + +{\setlength{\tabcolsep}{1.5pt} +\begin{sidewaystable}[p]\index{Equation of time!table of the}\label{timetable}\index{Table!equation of time}\markboth{TABLE OF THE EQUATION OF TIME.}{TABLE OF THE EQUATION OF TIME.} +\caption{TABLE OF THE EQUATION OF TIME, +FOR THE FIRST YEAR AFTER LEAP YEAR\@.\newline +Showing Greenwich clock time when the Sun +is on the meridian, after correcting for the longitude of the place.} +\centering +\small +\begin{tabular}{|r|rrr|rrr|rrr|rrr|rrr|rrr|rrr|rrr|rrr|rrr|rrr|rrr|} +\hline +Month & \multicolumn{3}{c|}{\textsc{January.}} & +\multicolumn{3}{c|}{\textsc{February.}} & +\multicolumn{3}{c|}{\textsc{March.}} & +\multicolumn{3}{c|}{\textsc{April.}} & +\multicolumn{3}{c|}{\textsc{May.}} & +\multicolumn{3}{c|}{\textsc{June.}} & +\multicolumn{3}{c|}{\textsc{July.}} & +\multicolumn{3}{c|}{\textsc{August.}} & +\multicolumn{3}{c|}{\textsc{September.}} & +\multicolumn{3}{c|}{\textsc{October.}} & +\multicolumn{3}{c|}{\textsc{November.}} & +\multicolumn{3}{c|}{\textsc{December.}} \\ +\hline + & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. & +\sc h. &\sc m. &\sc s. \\ +1 &$0$ &$3$ &$58$ &$0$ &$13$ &$55$ &$0$ &$12$ &$33$ &$0$ &$3$ &$55$ &$11$ &$56$ &$57$ &$11$ &$57$ &$31$ &$0$ &$3$ &$30$ &$0$ &$6$ &$2$ &$11$ &$59$ &$50$ &$11$ &$49$ &$38$ &$11$ &$43$ &$43$ &$11$ &$49$ &$19$\\ +2 & &$4$ &$26$ & &$14$ &$3$ & &$12$ &$21$ & &$3$ &$37$ & &$56$ &$50$ & &$57$ &$40$ & &$3$ &$41$ & &$5$ &$58$ & &$59$ &$31$ & &$49$ &$19$ & &$43$ &$42$ & &$49$ &$42$\\ +3 & &$4$ &$54$ & &$14$ &$9$ & &$12$ &$8$ & &$3$ &$19$ & &$56$ &$43$ & &$57$ &$50$ & &$3$ &$52$ & &$5$ &$53$ & &$59$ &$11$ & &$49$ &$0$ & &$43$ &$42$ & &$50$ &$6$\\ +4 & &$5$ &$21$ & &$14$ &$15$ & &$11$ &$55$ & &$3$ &$1$ & &$56$ &$37$ & &$58$ &$0$ & &$4$ &$3$ & &$5$ &$48$ & &$58$ &$52$ & &$48$ &$42$ & &$43$ &$43$ & &$50$ &$30$\\ +5 & &$5$ &$48$ & &$14$ &$20$ & &$11$ &$41$ & &$2$ &$43$ & &$56$ &$31$ & &$58$ &$10$ & &$4$ &$13$ & &$5$ &$43$ & &$58$ &$32$ & &$48$ &$24$ & &$43$ &$45$ & &$50$ &$55$\\[2ex] +6 & &$6$ &$15$ & &$14$ &$24$ & &$11$ &$27$ & &$2$ &$25$ & &$56$ &$26$ & &$58$ &$20$ & &$4$ &$24$ & &$5$ &$36$ & &$58$ &$12$ & &$48$ &$6$ & &$43$ &$47$ & &$51$ &$20$\\ +7 & &$6$ &$41$ & &$14$ &$27$ & &$11$ &$12$ & &$2$ &$8$ & &$56$ &$21$ & &$58$ &$31$ & &$4$ &$33$ & &$5$ &$29$ & &$57$ &$52$ & &$47$ &$49$ & &$43$ &$50$ & &$51$ &$46$\\ +8 & &$7$ &$6$ & &$14$ &$29$ & &$10$ &$57$ & &$1$ &$51$ & &$56$ &$17$ & &$58$ &$42$ & &$4$ &$43$ & &$5$ &$22$ & &$57$ &$31$ & &$47$ &$32$ & &$43$ &$55$ & &$52$ &$12$\\ +9 & &$7$ &$31$ & &$14$ &$30$ & &$10$ &$42$ & &$1$ &$34$ & &$56$ &$14$ & &$58$ &$51$ & &$4$ &$52$ & &$5$ &$145$ & &$57$ &$11$ & &$47$ &$16$ & &$44$ &$0$ & &$52$ &$39$\\ +10 & &$7$ &$55$ & &$14$ &$31$ & &$10$ &$26$ & &$1$ &$17$ & &$56$ &$11$ & &$59$ &$5$ & &$5$ &$0$ & &$5$ &$5$ & &$56$ &$50$ & &$47$ &$0$ & &$44$ &$6$ & &$53$ &$6$\\[2ex] +11 & &$8$ &$19$ & &$14$ &$31$ & &$10$ &$10$ & &$1$ &$1$ & &$56$ &$9$ & &$59$ &$17$ & &$5$ &$9$ & &$4$ &$56$ & &$56$ &$29$ & &$46$ &$45$ & &$44$ &$12$ & &$53$ &$34$\\ +12 & &$8$ &$42$ & &$14$ &$30$ & &$9$ &$54$ & &$0$ &$45$ & &$56$ &$7$ & &$59$ &$29$ & &$5$ &$16$ & &$4$ &$46$ & &$56$ &$9$ & &$46$ &$30$ & &$44$ &$20$ & &$54$ &$2$\\ +13 & &$9$ &$5$ & &$14$ &$29$ & &$9$ &$37$ & &$0$ &$29$ & &$56$ &$6$ & &$59$ &$41$ & &$5$ &$24$ & &$4$ &$36$ & &$55$ &$48$ & &$46$ &$16$ & &$44$ &$28$ & &$54$ &$31$\\ +14 & &$9$ &$27$ & &$14$ &$27$ & &$9$ &$20$ & &$0$ &$14$ & &$56$ &$6$ & &$59$ &$54$ & &$5$ &$30$ & &$4$ &$25$ & &$55$ &$27$ & &$46$ &$2$ & &$44$ &$38$ & &$55$ &$0$\\ +15 & &$9$ &$48$ & &$14$ &$24$ & &$9$ &$3$ &$11$ &$59$ &$59$ & &$56$ &$6$ &$0$ &$0$ &$7$ & &$5$ &$37$ & &$4$ &$14$ & &$55$ &$6$ & &$45$ &$49$ & &$44$ &$48$ & &$55$ &$29$\\[2ex] +16 & &$10$ &$8$ & &$14$ &$20$ & &$8$ &$46$ & &$59$ &$44$ & &$56$ &$7$ & &$0$ &$19$ & &$5$ &$43$ & &$4$ &$2$ & &$54$ &$44$ & &$45$ &$36$ & &$44$ &$59$ & &$55$ &$58$\\ +17 & &$10$ &$28$ & &$14$ &$16$ & &$8$ &$28$ & &$59$ &$30$ & &$56$ &$8$ & &$0$ &$32$ & &$5$ &$48$ & &$3$ &$49$ & &$54$ &$23$ & &$45$ &$24$ & &$45$ &$11$ & &$56$ &$28$\\ +18 & &$10$ &$48$ & &$14$ &$11$ & &$8$ &$11$ & &$59$ &$16$ & &$56$ &$10$ & &$0$ &$45$ & &$5$ &$53$ & &$3$ &$36$ & &$54$ &$2$ & &$45$ &$13$ & &$45$ &$24$ & &$56$ &$57$\\ +19 & &$11$ &$6$ & &$14$ &$5$ & &$7$ &$53$ & &$59$ &$2$ & &$56$ &$12$ & &$0$ &$58$ & &$5$ &$58$ & &$3$ &$23$ & &$53$ &$41$ & &$45$ &$2$ & &$45$ &$37$ & &$57$ &$27$\\ +20 & &$11$ &$24$ & &$13$ &$58$ & &$7$ &$35$ & &$58$ &$49$ & &$56$ &$15$ & &$1$ &$11$ & &$6$ &$2$ & &$3$ &$9$ & &$53$ &$20$ & &$44$ &$52$ & &$45$ &$51$ & &$57$ &$57$\\[2ex] +21 & &$11$ &$41$ & &$13$ &$51$ & &$7$ &$17$ & &$58$ &$37$ & &$56$ &$19$ & &$1$ &$25$ & &$6$ &$5$ & &$2$ &$55$ & &$52$ &$59$ & &$44$ &$42$ & &$46$ &$7$ & &$58$ &$27$\\ +22 & &$11$ &$57$ & &$13$ &$43$ & &$6$ &$58$ & &$58$ &$25$ & &$56$ &$23$ & &$1$ &$38$ & &$6$ &$8$ & &$2$ &$40$ & &$52$ &$39$ & &$44$ &$33$ & &$46$ &$23$ & &$58$ &$57$\\ +23 & &$12$ &$13$ & &$13$ &$35$ & &$6$ &$40$ & &$58$ &$13$ & &$56$ &$28$ & &$1$ &$51$ & &$6$ &$10$ & &$2$ &$25$ & &$52$ &$18$ & &$44$ &$25$ & &$46$ &$39$ & &$59$ &$27$\\ +24 & &$12$ &$27$ & &$13$ &$26$ & &$6$ &$22$ & &$58$ &$2$ & &$56$ &$33$ & &$2$ &$4$ & &$6$ &$11$ & &$2$ &$9$ & &$51$ &$57$ & &$44$ &$17$ & &$46$ &$57$ & &$59$ &$57$\\ +25 & &$12$ &$41$ & &$13$ &$17$ & &$6$ &$3$ & &$57$ &$51$ & &$56$ &$38$ & &$2$ &$17$ & &$6$ &$12$ & &$1$ &$53$ & &$51$ &$37$ & &$44$ &$11$ & &$47$ &$15$ &$0$ &$0$ &$27$\\[2ex] +26 & &$12$ &$54$ & &$13$ &$7$ & &$5$ &$45$ & &$57$ &$41$ & &$56$ &$44$ & &$2$ &$29$ & &$6$ &$13$ & &$1$ &$37$ & &$51$ &$16$ & &$44$ &$5$ & &$47$ &$34$ & &$0$ &$57$\\ +27 & &$13$ &$7$ & &$12$ &$56$ & &$5$ &$26$ & &$57$ &$31$ & &$56$ &$51$ & &$2$ &$42$ & &$6$ &$13$ & &$1$ &$20$ & &$50$ &$56$ & &$43$ &$59$ & &$47$ &$54$ & &$1$ &$27$\\ +28 & &$13$ &$18$ & &$12$ &$45$ & &$5$ &$8$ & &$57$ &$22$ & &$56$ &$58$ & &$2$ &$54$ & &$6$ &$12$ & &$1$ &$3$ & &$50$ &$36$ & &$43$ &$54$ & &$48$ &$14$ & &$1$ &$56$\\ +29 & &$13$ &$29$ & & & & &$4$ &$49$ & &$57$ &$13$ & &$57$ &$6$ & &$3$ &$6$ & &$6$ &$10$ & &$0$ &$45$ & &$50$ &$17$ & &$43$ &$50$ & &$48$ &$35$ & &$2$ &$25$\\ +30 & &$13$ &$38$ & & & & &$4$ &$31$ & &$57$ &$5$ & &$57$ &$14$ & &$3$ &$18$ & &$6$ &$8$ & &$0$ &$27$ & &$49$ &$57$ & &$43$ &$47$ & &$48$ &$57$ & &$2$ &$54$\\ +31 & &$13$ &$47$ & & & & &$4$ &$13$ & & & & &$57$ &$22$ & & & & &$6$ &$5$ & &$0$ &$8$ & & & & &$43$ &$45$ & & & & &$3$ &$23$\\ +\hline +\end{tabular} +\end{sidewaystable} +} +%-----File: 023.png-------------------------------------------- +%-----Folio: 8------------------------------------------------- +\markboth{SIDEREAL AND MEAN TIME.}{SIDEREAL AND MEAN TIME.} +But you may \textit{regulate}\index{Clocks!regulate by sidereal observations} the rate or going of a mean clock\index{Mean time!how got from sidereal observations} +from sidereal observations without the aid of any tables or +astronomical data, though you cannot \textit{set} it to the actual +time. The mean day is $3$m.~$56.5554$s.\ sidereal longer than +a sidereal day; and therefore sidereal\label{sidereal_time} hours, minutes, \&c., +may be turned into mean ones by multiplying them by +$.99727$, or by subtracting $9.83$~seconds from every hour, +and $1$~second from every $6$m.~$6$s. And as the +$3$m.~$56.55$s.\ sidereal = $3$m.~$56$s.\ mean, the mean clock ought to show so +much less at the second transit of a star than the time it +showed at the first transit. + +This operation may also be performed with sufficient +accuracy without a transit instrument. For if you make a +small eye-hole in a thin plate, fixed looking south, and set +up or find anywhere due south of it a perfectly vertical +straight edge, the occultation or emergence of any given +star against that straight edge will be seen through the eye-hole +at exactly every 24 sidereal hours, or at every +$23$h.~$56$m.~$4$s.\ of mean time. And it is not necessary for merely +regulating a clock, that the hole and the edge should be very +exactly in the meridian, if you only use it for observing stars +not far from the equator. But if you aim at using it for +setting as well as regulating your clocks, with the help of +astronomical tables, then you must take care to have the hole +and the edge exactly in the meridian. Probably the best +way of doing this is to fix the plate by carrying the time +by two or three chronometers of known rate from the +nearest observatory, using the almanac time of the `southing' +of one or more stars. + +In all operations for setting clocks from any kind of celestial +observations, you must remember the difference between +your own longitude and that which is the standard of the +country, which is here the Royal Observatory at Greenwich.\index{Greenwich!mean time and local time} +The meridian you use must be the true one of the place, and +not a false one adapted to Greenwich beforehand, unless the +%-----File: 024.png-------------------------------------------- +%-----Folio: 9------------------------------------------------- +longitude is very small; in which case the error arising from +the change in the sun's declination between summer and +winter will be insignificant. \hyperlink{localtable}{Here} is a table\markboth{LOCAL TIME.}{LOCAL TIME.} of some forty +towns, showing how much the clock ought to be before +or behind the sun if it is to agree with Greenwich mean +time; which the railways had long adopted; and it is now, +by an Act of 1880, the only legal time for all Great Britain, +and Dublin time for Ireland. There is a longer list in +Britten's `Watchmaker's Hand-Book'. + +\begin{table}[!hbt] +\centering\index{Greenwich!mean time and local time!table for forty-two towns}\label{localtable}\hypertarget{localtable}{}\index{Table!difference of forty-two towns from Greenwich mean time} +\begin{tabular}{|lrr|lrr|} +\hline +\multicolumn{6}{|c|}{GREENWICH TIME BEFORE LOCAL.}\\ +\hline + &M. &S. & &M. &S. \\ +Westminster Palace\dotfill &$0$ &$30$ &Carlisle\dotfill &$11$ &$38$\\ +Peterborough\dotfill &$1$ &$0 $ &Liverpool\dotfill &$11$ &$53$\\ +Hull\dotfill &$1$ &$8 $ &Edinburgh\dotfill &$12$ &$43$\\ +Lincoln\dotfill &$2$ &$4 $ &Exeter\dotfill &$14$ &$18$\\ +Doncaster\dotfill &$4$ &$12$ &Plymouth\dotfill &$16$ &$30$\\ +York\dotfill &$4$ &$24$ &Glasgow\dotfill &$17$ &$0 $\\ +Portsmouth\dotfill &$4$ &$24$ &Holyhead\dotfill &$18$ &$36$\\ +Leicester\dotfill &$4$ &$33$ &Cardigan\dotfill &$18$ &$40$\\ +Oxford\dotfill &$5$ &$1 $ &Falmouth\dotfill &$20$ &$12$\\ +Southampton\dotfill &$5$ &$36$ &Dublin\dotfill &$25$ &$22$\\ +Derby\dotfill &$5$ &$52$ & & & \\ +\cline{4-6} +Leeds\dotfill &$6$ &$4 $ & & & \\ +Newcastle\dotfill &$6$ &$24$ &\multicolumn{3}{|c|}{LOCAL TIME}\\ +Lichfield\dotfill &$7$ &$18$ &\multicolumn{3}{|c|}{BEFORE GREENWICH.}\\ +\cline{4-6} +Birmingham\dotfill &$7 $ &$33$ &Grimsby\dotfill &$0$ &$0 $\\ +Berwick\dotfill &$8 $ &$0 $ &Louth\dotfill &$0$ &$0 $\\ +Aberdeen\dotfill &$8 $ &$23$ &Boston\dotfill &$0$ &$0 $\\ +Worcester\dotfill &$8 $ &$41$ &Cambridge\dotfill &$0$ &$23$\\ +Manchester\dotfill &$9 $ &$0 $ &Colchester\dotfill &$3$ &$32$\\ +Bath\dotfill &$9 $ &$26$ &Ipswich\dotfill &$4$ &$38$\\ +Bristol\dotfill &$10$ &$12$ &Norwich\dotfill &$5$ &$13$\\ +Shrewsbury\dotfill &$10$ &$56$ &Dover\dotfill &$5$ &$16$\\ +Chester\dotfill &$11$ &$32$ &Paris\dotfill &$9$ &$21$\\ +\hline +\end{tabular} +\end{table} +%-----File: 025.png-------------------------------------------- +%-----Folio: 10------------------------------------------------ + +Though such contrivances are of no real use\label{useless}, for they +would certainly not answer as well as independent sidereal +and mean time clocks beating their own seconds, yet it +may save calculators some trouble if I add here that the +late Astronomer Royal in 1849 communicated to the +R.A.S.\ three different arrangements of trains which he had received +from a Dr.~Henderson\index{Henderson's sidereal and mean time clocks combined}\markboth{SIDEREAL AND MEAN TIME DIALS.}{SIDEREAL AND MEAN TIME DIALS.} for enabling one clock to show sidereal +and mean time on two different dials. +\begin{enumerate} +\item Let the $24$-hour arbor of the mean solar clock carry a +wheel of $247$, driving one of $331$ on an arbor which carries +also a wheel of $43$, driving one of $32$ (only I should put these +two smaller wheels first, the mean clock driving). The last of +these three arbors will carry a hand showing sidereal hours, +but, remember, hours only; and you must descend again to +sidereal seconds by a train of the usual numbers, so as to +get the $86,400$ in a day. Of course the same train reversed +would give mean time from a sidereal clock. + +\item Let the $24$-hour arbor carry a wheel of $96$, driving one +of $79$ on an arbor which carries a wheel of $157$, driving one +of $133$ on an arbor which carries a wheel of $72$, driving one +of $103$. A hand on this fourth arbor will show sidereal hours. + +\item Let the $24$-hour arbor carry a wheel of $50$, driving one +of $30$ on an arbor which carries a wheel of $182$, driving one +of $211$ on an arbor which carries a wheel of $196$, driving +one of $281$. This fourth wheel will show sidereal hours +with an error of a second in rather less than a thousand +years, the sidereal day being equal to $86164.0906$ mean +seconds. The errors of the other two trains are a little +greater, but still quite insignificant. But Sir G.~Airy\index{Airy, Sir G.~B.} and +Dr.~Henderson did not notice, or perhaps know, as I do by +experience, that all attempts to run the time down from the +slow hands or wheels of a train to the fast ones, instead of +putting the fast ones nearest to the pendulum as usual, +invariably fail and show very large errors; and therefore +such a combination of dials would be quite useless except +%-----File: 026.png-------------------------------------------- +%-----Folio: 11------------------------------------------------ +for the roughest approximation, which could be of no value +to any one who wanted to reduce one kind of time to the +other accurately, or to use the secondary dial for observations +of any kind. +\end{enumerate} + +Moreover, there is this fatal objection to all contrivances +for showing sidereal and mean time by hands depending ultimately +on one pendulum, that the secondary clock, whichever +it may be, cannot in any way beat or show accurately +its own seconds, as there is a difference of $16$~seconds to be +spread over the day, or something more than $.6$ an hour. +I am only surprised that Sir G.~Airy\index{Airy, Sir G.~B.}, who must have been +quite aware of this, though he might have no experience of +the other difficulty, should have thought it worth while to +make that communication to the Royal Astronomical Society, +as if it could be of any use to astronomers, or to anybody +else that I can see. + +There are some other clocks\index{Clocks with dials for many places}\markboth{CLOCKS FOR MANY LONGITUDES.}{CLOCKS FOR MANY LONGITUDES.}, however, which may possibly +be useful to telegraph-offices where they want to know the +local\index{Local time, clocks for} time at which messages arrive, or the English time +when they were sent. They consist of a single common +clock movement driving as many dials as you please, say for +the capitals of all the principal countries, the hands being +set just as much before or behind English time as the +respective longitudes require; and of course they always +keep their distance, and so show the local time of each +country corresponding to whatever is the present Greenwich +time. + +We shall see presently some of the methods of finding local +time, or at least the time of noon at any place; and though +it belongs rather to astronomy than horology, it is not out of +the way to mention that the longitude of any place is best +found by carrying thither chronometers with Greenwich time +and comparing it with the local time, except where the +Greenwich time can be telegraphed direct without the need +of carrying chronometers. +%-----File: 027.png--------------------------------------------- +%-----Folio: 12------------------------------------------------- +\section{INSTRUMENTS FOR MEASURING TIME.}\label{sec:INSTRUMENTS_FOR_MEASURING_TIME} +\index{Sundials}\index{Time, measures of!sun-dials}\markboth{SUN-DIALS.}{SUN-DIALS.} +At the head of these of course stand the oldest of them +all, sun-dials. But it would be a waste of time to say much +about them, except in the forms in which they may be made +subservient to the more useful and accurate machines by +which they have been superseded. The principal feature +of all sun-dials which have to indicate other hours besides +noon is a \textit{gnomon}\index{Gnomon, its position on sundials}, with a straight edge, or pair of edges, +parallel to the earth's axis, and therefore inclined to the +horizon at an angle equal to the latitude of the place, with a +plate for the gnomon to throw a shadow on. Thus an Indian +sun-dial has its gnomon nearly level, and it should be +elevated above the plate, while a polar one would be +quite upright. If the plate of the dial is part of a cylinder +of which the gnomon is the axis, all the hour divisions +will be equal, but not otherwise. The divisions before and +after noon are equal whenever the plate is equally inclined +to east and west. Sometimes they are set in other fanciful +positions; in whatever position the plate is, the same hour +marks are right for all times of the year, if the gnomon is +parallel to the earth's axis. But all that belongs to the art +of \textit{dialling}, which may be found in any of the encyclop\ae dias, +and is of no use to us, as sun-dial observations cannot +be relied on except when the sun is near the meridian, +by reason of refraction which bends the sun's rays. + +\subsection[Meridian dial.]{Meridian dial.}\ \label{subsec:Meridian_dial.}\markboth{MERIDIAN DIAL.}{MERIDIAN INSTRUMENTS.}\index{Meridian dial}\index{Time, measures of!meridian dials}A solar meridian mark or sun-dial for +noon only is intelligible and usable by many persons who +cannot or will not undertake sidereal observations, and is so +easily made that everybody ought to have one who cares +about having accurate time, and has not the means of +getting it from some other source. The simplest of all ways +of fixing such a mark is to set up a plate facing the south +with a narrow vertical slit in it, reaching down to the +bottom, upon a horizontal slab of smooth stone, and mark +%-----File: 028.png--------------------------------------------- +%-----Folio: 13------------------------------------------------- +\begin{figure}[htb] +\centering +\caption{\sc Meridian Dial} +\includegraphics[width=0.8\textwidth]{images/fig01.png} +\label{fig01} +\end{figure} +the line of brightness on the stone at the time of solar noon +by a chronometer or a good watch carrying the time from +some accurate source. The best way of making\index{Meridian dial!method of constructing one} these +gnomons is to screw a pair of thin zinc or copper cheeks on +a cast iron upright piece, without attempting to make a +sufficiently narrow slit in the iron itself. It should have a +thick polygonal lump at the bottom screwing on to an iron +rod or `lewis' let into the stone, and lead or cement run +round it after it is set upright and as near the meridian as +possible. The octagon in the drawing shows the shape of +this base and the section across the middle of the gnomon. +I\index{Beckett, Sir E.!meridian dial} fixed the first of these, +without a chronometer, in the +garden of a vicarage near Cambridge in 1838, by the following +method; and as it was afterwards tested by Professor +Challis and found as right as can be practically +observed, the method +may be safely followed. +$\mathrm{AC}$ is the slit, +which I have generally +had about $9$ +inches high. About +an hour before noon, +on a fine day in +summer, when the +shadow is short +enough to lie within +the slab, mark with +a pencil where the +top of the bright +line, or centre of the +little hole at $\mathrm{A}$ falls, say at $\mathrm{S}$, and draw the arc of a circle +$\mathrm{S}s$ with radius $\mathrm{CS}$\@. Mark again two other spots, $\mathrm{S}^\prime$ and $\mathrm{S}^{\prime\prime}$, +at about $11.15$ and $11.30$~\textsc{a.m.}, and draw the corresponding +arcs, $\mathrm{S}^\prime s^\prime$ and $\mathrm{S}^{\prime\prime}s^{\prime\prime}$. +Then watch for the times when the +end of the bright line again falls on each of the three circles, +%-----File: 029.png--------------------------------------------- +%-----Folio: 14------------------------------------------------- +and mark the places $s$~$s^\prime$~$s^{\prime\prime}$. Bisect all the arcs, and if a +straight line $\mathrm{CB}$ will run through all the bisections, you +may be pretty sure that is the true meridian; if not, some +mistake has been made, and you must try again another day. + +As you will probably begin to fix the slab and gnomon by +the compass, it may be as well to mention that the apparent +magnetic north in England is about $18^\circ$ west of real north +at present; for it decreases now slightly with time, and is +different in different parts of the world. + +\begin{figure}[htb] +\centering +\hypertarget{fig2}{\caption{\sc The Dipleidoscope}} +\setlength{\unitlength}{0.7cm} +\begin{picture}(8,18.5)(-4,0) +%Thick triangle +\multiput(-4,6)(0,0.025){11}{\line(1,0){8}} +\multiput(0,0)(0.025,-0.016666){10}{\line(2,3){4}} +\multiput(0,0)(-0.025,-0.016666){10}{\line(-2,3){4}} +%Lines +\put(1,1.5){\line(-1,4){4.25}} +\put(-2,3){\line(1,6){2.583333}} +\put(-2,3){\line(2,-1){3}} +\put(-0.1875,6.25){\line(1,4){3.0625}} +%labels +\put(0,0.3){\makebox(0,0)[b]{A}} +\put(-3.6,5.8){\makebox(0,0)[tl]{B}} +\put(3.6,5.8){\makebox(0,0)[tr]{C}} +\put(1.1,1.8){\makebox(0,0)[b]{$\beta$}} +\put(0.8,1.5){\makebox(0,0)[tr]{$\beta$}} +\put(-2.1,3.2){\makebox(0,0)[b]{$\gamma$}} +\put(-1.7,2.7){\makebox(0,0)[tl]{$\gamma$}} +\put(-3.5,18.5){\makebox(0,0)[t]{S}} +\put(1,18.5){\makebox(0,0)[t]{$\mathrm{R}_2$}} +\put(3.25,18.5){\makebox(0,0)[t]{$\mathrm{R}_1$}} +\put(-1.3,6.4){\makebox(0,0)[bl]{$\alpha$}} +\put(-1.7,5.9){\makebox(0,0)[tr]{$\alpha$}} +\put(-0.1875,6.7){\makebox(0,0)[b]{I}} +\put(0.5,6.4){\makebox(0,0)[b]{$\mathrm{A}-\delta$}} +\end{picture} +\label{fig02} +\end{figure} + +\subsection[Dipleidoscope]{The Dipleidoscope}\ \label{subsec:Dipleidoscope}\index{Dipleidoscope,the|(}\index{Time, measures of!dipleidoscope}\markboth{THE DIPLEIDOSCOPE.}{MERIDIAN INSTRUMENTS.}is another meridian instrument, +which was invented by +the late Mr.~J.~M.~Bloxam\index{Bloxam!invented the dipleidoscope}, +a barrister in +considerable practice +whose name I shall +have to mention again +with some clock inventions. +He took a patent +for it (long ago expired) +and assigned it to the +late Mr.~Dent, by whom +only they were made. +Its name, compounded +of $\delta\iota\pi\lambda\acute{o}o\varsigma$ double, $\epsilon\hat{\textrm{'}\!\!\iota}\delta o\varsigma$ +an image, and $\sigma \kappa o\pi\acute{\epsilon}\epsilon\iota\nu$ to see, indicates the +principle of it; because +in all positions but one +you see a double image +of the sun reflected in +it; and if it is so fixed +that the single image---\textit{i.e.}\ the +coincidence of the two---occurs at solar noon, it +evidently becomes a meridian instrument. It has the advantage +also of reflecting the sun when it is just too cloudy +%-----File: 030.png--------------------------------------------- +%-----Folio: 15------------------------------------------------- +%**Transcriber's note: A small part of the top right corner of this page was missing, so the word "see" is a guess. +\label{corner1}for a shadow to be distinct, and in fact you can only \correction{see} +it through darkened glass when the sun is bright. + +The instrument consists of three small plates of glass put +together at their edges in a brass box about $2$~inches wide +and high, so as to form a hollow prism of any convenient +angle, no precision being necessary in this. $\mathrm{ABC}$ in \hyperlink{fig2}{this +figure} is the section of it at right angles to the axis of the +prism. The front glass $\mathrm{BC}$ is plain; the other two are +blackened behind to form reflectors. But though the front +glass is transparent, it also reflects, because there are dark +ones behind it. $\mathrm{SI}$ and $\mathrm{IR}_1$ are sections of the planes of +incidence and reflection of the sun's rays from the glass $\mathrm{BC}$, +those planes being all parallel to the axis of the prism, +which should be approximately parallel to the earth's axis. +Part of the rays passes through that glass, and is reflected +by glass $\mathrm{AC}$ to $\mathrm{AB}$, and again reflected there and +sent through $\mathrm{BC}$ to $\mathrm{R}_2$. Now let the angle of incidence, +and therefore of first reflection at I, be called $\mathrm{A}-\delta$ (A being +the angle between the two reflecting glasses), and let the other +angles be designated as in the figure. It requires no +mathematics beyond the knowledge that the three angles of +every triangle =~$180^\circ$, commonly called $\pi$ to see that the +angle $\beta = \pi-(\mathrm{C+A}-\delta)$ in the small triangle near $\mathrm{C}$; +and in the one near $\mathrm{A}$, $\gamma = \pi-(\mathrm{A} +\beta) = \mathrm{C}-\delta$; and in +the triangle near $\mathrm{B}$, $\alpha=\pi-(\mathrm{B} + \gamma)= \pi-(\mathrm{B + C} -\delta) +=\mathrm{A} + \delta$. That is to say, the angle $\alpha$, made by the plane of +emergence of the twice reflected rays with the front glass, +differs from that of the once reflected by $2\delta$. Therefore, if +the prism is so placed as to make $\delta=0$, which it will be if +the angle of incidence $=\mathrm{A}$, the twice reflected rays will +come out parallel to the once reflected, and the two images +of the sun will coincide. In fixing the instrument however, +we have nothing to do with the angles; but simply to adjust +it by trial with a chronometer (for it cannot be done without), +so that the images do coincide at solar noon. +%-----File: 031.png-------------------------------------------- +%-----Folio: 16------------------------------------------------ +%**Transcriber's note: A small part of the top left corner of this page was missing, so the words "They" and "where" are guesses. +\label{corner2}\correction{They} were at first made so as to be fixtures on the stone +\correction{where} they were set, and so they were always exposed to +the weather, and besides, if cemented in wrongly, they were +wrong for ever. To avoid both these evils, I suggested the +making of a brass plate to be fixed on the stone, with a +raised slip adjustable by screws, against which the instrument +is to be laid closely when used, but at other times it +may be kept in the house. Some of them are made +to turn on an axis parallel to the earth's axis, and then +they can be presented to the sun at other hours besides +noon, but only for the given latitude like a sun-dial. Some +are made adjustable for latitude also. They are moreover +made for star observations with the reflectors silvered instead +of blackened, on account of the greater feebleness of star +light. A table was published to be used with them, +showing the time of first and last contact of the two +images of the sun for every day in the year, as that +observable perhaps more accurately than the time of coincidence; +at any rate it gives three chances of observation +instead of one. But many people prefer my meridian slit.\index{Dipleidoscope,the|)} + +\section{WATER AND SAND-CLOCKS.}\label{sec:WATER_AND_SAND-CLOCKS.} +\index{Time, measures of!water clocks}\index{Water clocks}\markboth{WATER AND SAND-CLOCKS.}{WATER CLOCKS.} +The earliest time-keeping \textit{machine} is the clepsydra\index{Clepsydr\ae{} of Greeks and Romans} or +water clock of the Greeks and Romans\index{Water clocks!used by the Greeks and Romans}, which was no doubt +made in various ways. Vitruvius mentions one made as a +water wheel, which would probably be very irregular. This +simplest in construction is a graduated cylindrical vessel +with a hole in the bottom, and this appears to have been the +most commonly used: but they must surely have discovered +that the water in that case by no means runs out +with uniform velocity, though they did not know, and some +of the modern writers on antiquities apparently do not either +that the velocity varies as the square root of the height of +the water above the hole. But if a trough is kept full by a +%-----File: 032.png-------------------------------------------- +%-----Folio: 17------------------------------------------------ +stream, and a hole made anywhere in it, the water will then +run uniformly into, and rise uniformly in, another cylindrical +vessel in which its height may be marked on the sides, if it +is of glass, or else by a floating index, and that will make a +very fair clock. I do not however find any notice of such a +one in books on Greek and Roman antiquities. Various +other forms of clepsydra are described in them, which it is +not worth while to copy here. + +The case is different with \index{Sand clocks}\markboth{WATER AND SAND-CLOCKS.}{SAND CLOCKS.}\index{Time, measures of!sand clocks}sand. If a column of dry sand +ever so high stands over a small hole, the sand will run out +no faster than if it is a very moderate height, for the same +reason that a pile or cone of sand on a given base will stand +up to a certain height and angle only, which depends on the +amount of friction between the particles. The angles of the +waist of an hour-glass ought to agree with that natural angle +of the sand in order that it may run out uniformly to the end---if +that is of any consequence, which it hardly is for the +boiling of eggs, or even for the old use of limiting the length +of sermons; which object might sometimes be advantageously +accomplished now by a descending sounding-board, or as +sounding-boards are gone out of fashion, by a pulpit bottom +or `drop' let down by clock work after $25$~minutes. + +The burning of graduated candles\index{Candles graduated, for marking time}\index{Time, measures of!graduated candles} was another mode of +marking time, and if the candles were of wax, as they +probably were, and sheltered from wind, and the wicks +uniform throughout, the measure would be accurate enough +for any purpose for which it was likely to be used. The +consumption of oil in a lamp might also be marked and used +in the same way. + +This seems the proper place to notice a genuine water +clock, invented and used by Lord \index{Rosse, Lord, his water clock}\index{Water clocks!Lord Rosse's}Rosse for the important +purpose of driving an equatorial telescope\index{Telescope-driving clocks} so as to keep it +pointed to a star, against the earth's rotation, for which +there are various contrivances. It is described in the R.A.S.\ \textit{Monthly Notices}, +vol.~xxvi., and the principle of it is that the +%-----File: 033.png-------------------------------------------- +%-----Folio: 18------------------------------------------------ +water is let out slowly from a box by an india rubber tube +carried by a float, so that its mouth is always at the same +small depth below the surface of the water; and as the +pressure depends only on that depth the outflow is uniform +and the descent of the float with it, and that has a cord attached +to it, and at the other end attached to the wheel which +drives the telescope. The great equatorial at Greenwich\index{Water clocks!the one at Greenwich} is +driven by another kind of water clock, which will be notified +farther on, as it is combined with a revolving pendulum, and +we will now proceed to what are properly called + +\section{CLOCKS.}\label{sec:CLOCKS.} +\markboth{HISTORY OF CLOCKS.}{HISTORY OF CLOCKS.} +The invention\index{Clocks!invention of} of clocks driven by a weight has been +generally attributed to Pacificus, Archdeacon of Verona, in +the ninth century; and also to Gerbert, afterwards Pope +Silvester II., who made a clock at Magdeburg in 996, when +he was an Archbishop. But there does not seem to be any +contemporary proof that either of these were weight clocks; +nor is it certain that Gerbert's was a clock at all; for it is +described by an old writer quoted in Beckmann's `History of +Inventions' (4th ed.~1846) thus:---`Magdeburg horological +fecit, illud recte constituens considerate per fistulam stella +nautarum duce'---\textit{i.e.}\ `he made a time-piece at Magdeburg, +setting it by looking at the pole-star through a tube.' Beckmann +thought William, Abbot of Hirshaw in the eleventh +century, had the best claim to the invention; of whom it was +said, `Naturale horologium ad exemplum c\oe lestis hemisph\oe rii +excogitavit;' and soon after, certain monks had the +duty `horologium dirigere et temperare, et signa pulsare;' +which however looks rather like their directing the clock +than the clock them, or as they say at sea, `\textit{making it} ten +o'clock,' rather than learning from the clock that it is so. + +But he also says that in those times the day and the +night were each divided into twelve hours, between sunset +%-----File: 034.png-------------------------------------------- +%-----Folio: 19------------------------------------------------ +and sunrise; and if so, such hours could not be shown by +any clocks; for we may be sure that no clocks of those +days were able to adapt themselves to hours of such varying +length. And all this seems to me very insufficient evidence +of the existence of clocks, as we now understand the word; +which, by the way, appears not to have driven out the older +word `horologe,' until the time of Henry VIII., having been +long used for a bell (cloche). + +But it may be safely concluded from the various allusions +to horologia, and to their striking spontaneously, in the +twelfth century, that genuine clocks had been invented +before then, though there is no surviving description of the +construction of any clock until the thirteenth century, when +it appears that a certain `horologium' was sent by the Sultan +of Egypt in 1232 to the Emperor Frederic II\@. `It resembled +internally a celestial globe in which the sun, moon, and +planets moved, \textit{being impelled by weights and wheels,} so that +they pointed out the hour, day and night, with certainty.' +The oldest clock mentioned in England\index{Clocks!ancient clocks in England}\label{early} is that which +was put up in a former clock-tower of Westminster, with +some great bells, in 1288, out of a fine imposed on a corrupt +Lord Chief Justice, of which a memorial survived near the +same spot in a sun-dial which stood on a house in Palace +Yard, pulled down within my time, with the inscription +\textit{`Discite justitiam moniti.'} In 1292 a clock is mentioned in +Canterbury Cathedral, costing \pounds 30; and the old striking +part of the original one in Exeter Cathedral was at work not +long ago, and perhaps is still, though the going part had +been replaced; and the same at Peterborough, probably of +about the same date. That of Glastonbury Abbey, afterwards +at Wells Cathedral, dated 1325, is now in the South +Kensington Museum, going. One by Richard Wallingford, +Abbot of St.~Albans, made in 1326, is said to have been +such as there was not in all Europe, showing various +astronomical phenomena. There was also one at Dover +%-----File: 035.png-------------------------------------------- +%-----Folio: 20------------------------------------------------ +Castle, with the date 1348 on it. That also was exhibited +going in 1876. + +\markboth{OLD CLOCKS.}{OLD CLOCKS.}A description and picture of the clock made by Henry de +Vick for Charles~V.\ of France in 1370 may be seen in old +editions of the \textit{Encyclop\ae dia Britannica,} whether authentic +or made up from some other I do not know. I did not +think it worth repeating in the eighth edition, for which I +wrote the article on clocks\index{Beckett, Sir E.!on `Clocks' \&c., in the \textit{Encyclop\ae dia Britannica}}. It\index{Clocks!construction of} was very like our common +clocks now, except that it had only an hour hand, and a +vibrating balance (but no balance spring) instead of a +pendulum. It is impossible that such a clock could go well, +and it seems strange that the apparently simpler contrivance +of a pendulum should not have come till four centuries +after clocks were first invented; and yet that is the +general tradition. I suppose therefore that the pendulum +in the old Peterborough, and Exeter, and other church +clocks were added long after their original construction. +Those clocks were wound up by long spikes or handles +sticking out of the wooden barrel over which the rope goes +which carries the weight. In many old church clocks the +weight is only a large stone. It is not until quite modern +times that church clocks had minute hands besides the hour +ones, but in other respects there is surprisingly little difference +in principle between the oldest of these machines and +most turret clocks of the present day. + +The going part of a clock is, and always has been, nothing +but a train\index{Wheels for clocks!train of}\markboth{CLOCK TRAIN.}{CLOCK TRAIN.} of some number of wheels and pinions, of which +one turns in $12$~hours, and another in $1$~hour, if there is a +minute hand. The first, or slowest, or `great' wheel, is +turned by a weight hanging by a rope wound round a barrel +on that wheel's axis\index{Arbors, or axes, of wheels}, or \textit{arbor,} +as it is called in clock-making; +and the last or quickest wheel drives a fan-fly, or a fly-wheel, +or a pair of vibrating arms, called a `balance,' or a pendulum, +to regulate the velocity of the train. A spring clock is +merely a compound of a large watch and a common clock. +%-----File: 036.png-------------------------------------------- +%-----Folio: 21------------------------------------------------ +\begin{figure}[htb] +\centering +\caption{\sc Pinions} +\includegraphics[width=\textwidth]{images/fig03.png} +\label{fig03} +\end{figure} + +Any one who has looked at the inside of a clock---and it is +useless to read this book until you have---knows it consists +of a few\index{Train of wheels!in clocks} large wheels with a good many teeth, and that +the teeth of every large wheel, except the highest, are +engaged in or drive some much smaller +wheels fixed on the axes or arbors of all the large ones +except the largest. These small wheels are called pinions\index{Pinions of clocks}\label{pivots}, +and their teeth are called `leaves' for distinction. This +figure~\ref{fig03} shows a set of pinions of from $6$ to $16$ leaves, +the lowest and the highest numbers used. It also +shows the kind of steel plate which is used +for drawing \textit{pinion wire}. For it is cheaper to make +the arbors of such wire, turning off the projections +all along the arbor except where they form the pinion itself, +than to cut the pinions out of the solid. But they are not +so good as cut ones, and I believe are not used in +the best clocks. + +\begin{figure}[htb] +\centering +\caption{\sc Common Clock Train} +\includegraphics[width=252pt]{images/fig04.png}\index{Train of wheels!in clocks}\markboth{COMMON TRAIN.}{COMMON TRAIN.} +\label{fig04} +\end{figure} + +The largest wheel in the train, which is called `the great wheel,' +\textit{appears} to be stuck on the end of the barrel which +carries the string and +%-----File: 037.png-------------------------------------------- +%-----Folio: 22------------------------------------------------ +the weight attached to it---whether with a moving pulley or +not, does not signify as a matter of principle, which is all we +are considering at present. The only effect of the pulley\index{Pulleys} in +to take a double string of twice the length of a single one in +the same clock case, which enables a larger barrel to be +used and also prevents the string from untwisting. + +But if the great wheel were really fixed to the barrel there +could be no winding up, except by an endless chain contrivance, +which we need not now consider. Accordingly the +real arrangement is that the great wheel rides freely on the +arbor of the barrel, and is connected with it by a ratchet\index{Ratchet wheels} +and click; the ratchet being a saw-toothed wheel on the +end of the barrel, and the click being on the great wheel +with a spring to keep it in the ratchet teeth, which pass +under it in winding, but cannot return, except with the +great wheel itself. You will see a \hyperlink{fig29}{picture} of it under +`Maintaining Powers,' farther on in the book. And it is all +the same whether the barrel is turned in the old way by +spokes, or in the modern way by a key or `winder' put on +the squared end of the arbor; only in the former case the +barrel rides loose on the arbor, and in the latter is fixed +to it and the wheel rides loose. Consequently the weight +is always acting on the train, except at the time of winding; +and in all good clocks there are contrivances for keeping the +force on even then, called maintaining powers. + +Now suppose the great wheel has \index{Wheels, numbers of teeth}$120$ teeth, and the +pinion which it drives has $10$; then if that pinion and its +arbor and the wheel stuck on to it turn in one hour, the +great wheel will evidently turn in $12$~hours. The wheel +which turns in an hour is called the centre wheel in house +clocks, because that arbor comes through to the centre of +the dial and carries the minute hand. Suppose that wheel +has $64$ teeth and drives a pinion of $8$; then that pinion and +the wheel on its arbor will turn in $8$~minutes; and if that has +$60$ teeth and drives another pinion of $8$, that pinion and +%-----File: 038.png--------------------------------------------- +%-----Folio: 23------------------------------------------------- +arbor will turn in a minute, and the wheel on that arbor is +the scape-wheel, which drives the pendulum vibrating in a +second, as we shall see presently. Not that there is any +virtue in these particular numbers of teeth and leaves, or +that the pendulum need vibrate seconds; most church clock +pendulums are slower, and all short spring clock pendulums +are faster. All that is requisite theoretically is, that the +numbers of the teeth of all the wheels multiplied together, +and divided by the numbers of the leaves of all the pinions +multiplied together, should give the proper velocity-ratio +between the slowest wheel and the quickest. Thus, if the +scape wheel has to turn $60$ times as fast as the centre wheel, +and there is one between them, which may turn in any time, +the product of the teeth divided by that of the leaves must += $60$, and subject to that, you may distribute the numbers +as you please---theoretically; but practically other considerations +come in, such as that the slower wheels must be larger +than the quicker ones, or they could not clear the arbors +below them; that if the leaves of the pinions are very +few they do not drive easily, and if they are many the +teeth must be many and small, and more expensive to cut, +and so forth; and the result is that, in the common long +house clocks the numbers are usually what I gave just now; +but in astronomical clocks or \textit{regulators} they are higher, +sometimes twice as much; in turret clocks they vary more, +according to circumstances, as will be seen hereafter. + +The simplest of all the methods of regulating the velocity +of the train, and one which certainly existed before De Vick's +time, is the fan fly\label{fanfly},\markboth{FLIES AND FLY WHEELS.}{FLIES AND FLY WHEELS.} or a pair of arms with vanes which are +resisted by the air. I think it by no means improbable, +though it is never likely to be ascertained now, that some of +those earlier clocks were trains of wheels with a fly to regulate +their velocity, instead of a balance, which De Vick used in +his going part, though he had a fly in the striking part, as +the earlier English clocks have, and exactly as it is used to +%-----File: 039.png---------------------------------------------- +%-----Folio: 24-------------------------------------------------- +\index{Continuous motion clocks}%**Transcriber's note: I could not find this index reference in this page so have simply placed it at the page boundary.% +this day. So long as the force and friction of the train are +uniform the velocity of the fly will be uniform, as the variation +of density of the air is too small to affect it materially; +and it should be observed, that a long fly with a rather slow +motion is less affected by variations of force than a short and +quick one; but as far more accurate methods are now used, +it is unnecessary to go further into this. + +A fly wheel\index{Fly-wheel clocks, earliest}, which is either a wheel with a heavy rim or +a pair of weighted arms at right angles to the axis which +carries them, is another method; but not so good, because, +not being resisted by the air nearly so much as fans, +it is much more affected by a change of force, which in +clock work nearly always means a change of friction in the +train. It acts simply by its moment of inertia, which is +constant, and therefore the velocity cannot be constant if +the force varies. In fact there is theoretically no limit to +the velocity of a fly wheel driven by a weight, so long as +the weight can go on falling, though practically a terminal +velocity is soon reached, when the friction and the increasing +resistance of the air balance the force; but of course this +balance is disturbed and the velocity changes as soon as +the force varies. + +\subsection[Conical Pendulum.]{Conical Pendulum.}\ \label{subsec:Conical_Pendulum.}\index{Conical pendulum}\index{Pendulum2@Pendulum!conical or revolving}\markboth{CONICAL PENDULUM.}{CONICAL PENDULUM.}A +pair of weighted arms attached +to a revolving vertical axis by horizontal hinges, so +that they can fly farther out as they go, will regulate the +velocity more completely than a fly wheel or arms rigidly +fixed, and still better if it has fans attached to it, but +not completely enough to keep it uniform if the force +varies much. They are like the `governor' of a steam +engine in appearance, but no further; for the governor arms +work a lever which opens more or less of the throttle valve +of the steam pipe, according as the engine is going too slow +or too fast. A single ball or pair of balls hung in this way +and driven by a clock train form what is called a \textit{conical +pendulum}, because each arm describes a cone, and the time +%-----File: 040.png---------------------------------------------- +%-----Folio: 25-------------------------------------------------- +of its revolution may easily be determined as follows, except +so far as it is affected by friction and resistance of air:--- + +Let\label{lg} $l$ be the length of each arm, and $\phi$ the angle at which +it happens to be inclined to the vertical axis, which of course +depends on the rate of revolution or angular velocity, which +is usually called $\omega$; then the centrifugal force of each ball +$=\omega^2 l\sin\phi$; and as that is the force which keeps the balls +away from the vertical, it must balance the force which +draws them to it, which is $g \tan\phi$ ($g$ being the usual symbol +for the force of gravity, or twice the number of feet which a +body falls in the first second of time, and $g$ in this latitude +is $32.2$); therefore $\omega$ or the angular space moved over by +the arms in one +\begin{wrapfigure}{o}{111pt} +\centering\index{Pendulum2@Pendulum!conical or revolving} +\caption{\sc Revolving Pendulum} +\includegraphics[height=500pt]{images/fig05.png} +\label{fig05} +\end{wrapfigure} +second $=\surd{\frac{g}{l\cos \phi}}$, and the time of +a complete revolution through $360^\circ$ or $2\pi$, is $\frac{2\pi}{\omega} = +2 \pi \surd{\frac{l\cos \phi}{g}}$. +If you wish to know what that means in +figures, you must express $l$ in feet, as $g$ is, and write the +numerical value $3.14159$ for $\pi$, and take the numerical +value of $\cos \phi$ from a table of sines and cosines; and the +result, after extracting the square root and dividing, is the +number of seconds in which the revolution is performed. +We shall see hereafter that it is just so much less than the +time of a common vibrating pendulum of the same length as +$\surd{\cos \theta}$ is less than $1$. And as the cosine varies least when +an angle is small, a clock of this kind will go better when +the length of the arms and the weight of the balls are such +that they make only a small angle with the axis when the +clock weight is driving them. But again it must be +remembered that these results are very much modified in +actual working by the resistance of the air, which acts +more strongly on the balls as they fly farther out, and +thereby tends to regulate the velocity, as it does with a +fan fly. +%-----File: 041.png---------------------------------------------- +%-----Folio: 26-------------------------------------------------- + +A clock of this kind is often used\index{Conical pendulum!its uses} to turn the reflectors or +coloured lenses of revolving lighthouses\index{Light-house clocks}, and also for the +more accurate purpose of driving large equatorial telescopes\index{Telescope-driving clocks}, +to keep them pointed to a star notwithstanding the revolution +of the earth. For the earth does not move by jerks, as a +clock with a vibrating pendulum and escapement necessarily +does. A revolving pendulum\index{Pendulum2@Pendulum!conical or revolving} alone will not do without some +contrivance to equalise the force upon it, or to check the +pendulum itself by friction. + +The simplest form of it is setting the revolving balls +within a conical ring, which they can graze slightly, and it +is better if they are furnished with slight grazing springs. +And if the cone is also made raisable by a handle within +reach of the observer, so that he can regulate the friction, +probably this is enough in all ordinary cases. + +But for telescopes of great importance superior contrivances +are used. The chronograph at Greenwich\index{Chronograph at Greenwich}, which +drives a barrel covered with paper, on which the times of +various observations are pricked by galvanic communication +from the observers, is an ordinary clock with a revolving +pendulum, driven by an arm which also carries round a kind +of spade, dipped a little into an annular trough of water; +and the farther out the pendulum swings the deeper it pushes +the spade into the water, by a simple lever arrangement +which can easily be imagined. + +The great equatorial\index{Equatorial telescope at Greenwich, its driving apparatus}\index{Greenwich!equatorial driving clock} telescope there has a similar pendulum +and trough; but besides that, the clock is itself driven by a +`Barker's mill\label{barker},' or a pair of revolving horizontal arms on a +vertical axis, all hollow and receiving water at the top of +the axis. The arms have holes near their ends, on opposite +sides, and the water flowing out there drives the arms the +other way. The pendulum also works a throttle valve as +the governor of a steam engine does, and so regulates the +flow of water through the mill. + +A revolving pendulum may be hung by a single wire, as +%-----File: 042.png---------------------------------------------- +%-----Folio: 27-------------------------------------------------- +there is no tendency to twist, and +they are so made in bedroom clocks, +which have the advantage of being +silent. But it is difficult to get +a wire strong enough for a heavy +pendulum which would not also be +too stiff. The Greenwich ones are +hung by a kind of universal joint, +made of two pairs of suspension +springs in stirrups, set across each +other, one turned upwards and the +other downwards, with a cross between. + +We shall have to notice afterwards +some other clocks for this purpose, +in which a revolving continuous\index{Greenwich!revolving pendulum} +movement is combined with a vibrating +pendulum and escapement; but +I must describe escapements first. + +It is perhaps worth mentioning +that any point in a wheel revolving +uniformly has always the same velocity +in a horizontal direction as some +point in a pendulum which makes +a double vibration in the same time +as the wheel revolves; and therefore, +theoretically, a constant motion of +a clock-train might be got by connecting +some point in a $1$~sec.\ pendulum +with a pin in a small disc +revolving in $2$~seconds, by a rod so +long as to be practically horizontal. +But it would probably be impracticable +to keep the force constant +enough to give just proper impulse +%-----File: 043.png--------------------------------------------- +%-----Folio: 28------------------------------------------------- +to the pendulum; and if too much was given, there would +be a jerk at the end of every beat, and if too little, the +pendulum and the clock would stop. + +\section{BALANCE-WHEEL ESCAPEMENTS.}\markboth{BALANCE-WHEEL ESCAPEMENTS.}{BALANCE-WHEEL ESCAPEMENTS.}\label{sec:BALANCE-WHEEL_ESCAPEMENTS.}\index{Balance-wheel clock escapements}\index{Escapements of clocks} + +Before we go into the theory of pendulums we should +notice the one other mode of regulating the motion of a +clock-train which existed long before pendulums were +applied. The earliest +escapement of which +there is any known +description is that +which De Vick's\index{De~Vick's clock escapement} clock +had, and which is +called the \label{crown}crown-wheel +escapement. The object +of that, as of all +the later escapements, +was to let a tooth of +the quickest wheel in +the train escape past +some stops called +\textit{pallets}\index{Pallets} at every vibration +of the balance, +and that wheel is +thence called the +scape-wheel, and a +crown-wheel from its +shape. The pallets $\mathrm{A}$, +$\mathrm{B}$, in fig.~\ref{fig06}, are pieces +\begin{figure}[htbp] +\centering +\caption{\sc Balance Wheel Escapement} +\includegraphics[height=0.7\textheight]{images/fig06.png} +\label{fig06} +\end{figure} +of steel fixed to the +axis or arbor of the +balance $\mathrm{C}$ in planes at +right angles to each +other, one of them set so as to be pushed one way by +%-----File: 044.png--------------------------------------------- +%-----Folio: 29------------------------------------------------- +the front teeth $\mathrm{D}$ of the wheel, and the other the other way +by the back teeth. As one tooth escapes past its pallet, the +other pallet is in a position to receive and stop the opposite +tooth. But as the balance has then acquired a swing in the +direction in which it has been pushed by the escaping tooth, +it does not stop immediately, but swings a little farther and +so drives the wheel back again a little, producing what is +called the recoil. This is just the same as the old `vertical'\index{Vertical watch escapement} +watch escapement, which remained in use until a few years +ago, with this important exception, that the time of vibration +of a watch balance is regulated by a thin spiral spring fixed +to it and to the frame, whereas this had none, and so its +regulating power over the train depended solely on its +moment of inertia, and on its swinging farther for any +increase of force, which by no means makes it isochronous. + +The same thing is still to be found in bottle-jacks\markboth{BOTTLE-JACK ESCAPEMENT.}{BOTTLE-JACK ESCAPEMENT.}\index{Bottle-jack escapement}; the +piece of meat to be roasted forms the balance, and the noise +at each change of its motion is the `ticking' of the escapement. +It is true the meat makes several turns for one tick, +while De Vick's balance made only half a turn, but that is +because there is a wheel on the pallet arbor in the jack, +worked by a pinion on the meat arbor, as in the rack lever +watch escapement; but otherwise the bottle-jack escapement +is precisely the same as in De Vick's clock, in which the +axis of the balance was vertical, and not horizontal as in +fig.~\ref{fig06}. + +\section{PENDULUMS.}\label{sec:PENDULUMS.}\markboth{PENDULUMS.}{PENDULUMS.} + +Pendulums, like many other things, may have been\index{Pendulums!invented} +invented several times over in different ages, or even in the +same. In an old edition of the \textit{Encyclop\ae dia Britannica} it +is said that `the ancient astronomers of the east employed +pendulums in measuring the times of their observations, +patiently counting their vibrations during the phases of an +eclipse or the transit of the stars, and renewing them by a +%-----File: 045.png--------------------------------------------- +%-----Folio: 30------------------------------------------------- +little push of the finger when they \correction{languished.} %**Transcriber's note: The top right corner of this page was missing, so the full-stop after "languished" is a guess. +\label{corner3}Gassendi, Riccioli, and others, in more recent times +followed their example.' If so, it is plain that this knowledge +had itself languished and died, before the making of +what has long been called Galileo's discovery in the church +at Florence, that a chandelier, and therefore any other +pendulum, vibrated different arcs in the same time, provided +they were none of them large ones. When we consider the +vast number of pendulums of various kinds that there are +swinging about the world, it certainly is difficult to imagine +that nobody ever made that observation before the sixteenth +century. The application of it to the regulating of clocks +however is a different thing, as that required invention as +well as observation. To be sure, all that was needed was to +omit one of the weights in De~Vick's\index{De~Vick's clock escapement} balance, and set it in +a vertical instead of a horizontal plane, and it is strange +enough that this slight but valuable alteration should have +waited three centuries to be made. It would then assume +this form (fig.~\ref{fig07}), which is the same as the other in all but +the position of the parts and the omission of one arm and +weight of the balance. The bent end of the arm (called the +\textit{fork}\label{fork}) is substituted for a weight in this drawing, because it +was afterwards found better to hang the pendulum independently, +and connect it with that arm, called the \textit{crutch}, by +means of the fork. But I have seen small clocks of the +last century, and even some modern French ones, with the +crutch itself made into a pendulum by merely putting a ball +at the end of it. + +There seems no doubt however that the first person who +investigated and established the mathematical theory and +properties of the pendulum was Huyghens\index{Huyghens!theory of the pendulum}\label{huyghens}, the Dutch philosopher, +in the seventeenth century; but it seems equally +certain that the first pendulum clock was made for St.~Paul's +Church in Covent Garden, by Harris, a London clock-maker +in 1621, though the credit of the invention was claimed also +%-----File: 046.png-------------------------------------------- +%-----Folio: 31------------------------------------------------ +by Huyghens himself, and by Galileo's son, and Avicenna, +and the celebrated Dr.~Hooke\index{Hooke, inventor of the balance-spring of watches}, the undoubted inventor of +the balance spring of watches, and the discoverer of its +theory. +\begin{figure}[htbp] +\centering +\caption{\sc Crown-Wheel Escapement} +\includegraphics[width=0.9\textwidth]{images/fig07.png}\markright{CROWN-WHEEL ESCAPEMENT.} +\label{fig07} +\end{figure} +The main point of Huyghens's discovery seems at first sight +a long way off any connection with what we now understand +by a pendulum, viz., a weight or \textit{bob}\index{Bobs for pendulums}\index{Pendulum!bobs} at the bottom of a long +rod, which is hung by a string or a thin spring at the top, +and the bob therefore swinging in a circular arc, or something +very near it. For he proved that the curve in which +a bob hung by a string of insensible weight must move in +%-----File: 047.png-------------------------------------------- +%-----Folio: 32------------------------------------------------ +order to be isochronous in its vibrations, is \textit{not} a circle, but +a cycloid, or the curve traced out by a point in the rim of a +circle rolling upon a straight line, \textit{e.g.}, a nail in the tire of a +carriage wheel rolling on a smooth road, or $\mathrm{P}$ in circle +$\mathrm{DEP}$ rolling on $\mathrm{BGC}$ in fig.~\ref{fig08}; and he showed how a +certain other property of the cycloid might be made use of +to enable a pendulum bob to describe a cycloidal\index{Cycloidal!theory}\markright{CYCLOIDAL CHEEKS.} instead of +a circular arc. It is not worth while to fill these pages with +demonstrations which may be found in any mathematical +treatise on mechanics, especially as I must assume the reader +to have some of the knowledge which is only to be got from +such books, in order to understand the demonstrations if I +gave them. Therefore we may as well begin at this +point, that a body moving by gravity in a cycloid (with +the curve downwards, as $\mathrm{BPFC}$ in fig.~\ref{fig08}) does describe +\begin{figure}[htbp] +\centering\index{Pendulums!cycloidal theory} +\caption{\sc Cycloidal Theory} +\setlength{\unitlength}{1.5cm} +\begin{picture}(6.283184,4.5)(0,-2.25) +\put(0,0){\line(1,0){6.283184}} +\put(3.141592,-2){\line(0,1){4}} +\qbezier(0,0)(0,-0.429204)(0.570796,-1) +\qbezier(0.570796,-1)(1.570796,-2)(3.141592,-2) +\qbezier(5.712388,-1)(4.712388,-2)(3.141592,-2) +\qbezier(6.283184,0)(6.283184,-0.429204)(5.712388,-1) +\qbezier(3.141592,2)(3.141592,1.570796)(3.712388,1) +\qbezier(3.712388,1)(4.712388,0)(6.283184,0) +\qbezier(2.570796,1)(1.570796,0)(0,0) +\qbezier(3.141592,2)(3.141592,1.570796)(2.570796,1) +\put(3.712388,1){\line(1,-1){2}} +\put(4.712388,0){\line(0,-1){2}} +\qbezier(4.712388,0)(5.126603,0)(5.419496,-0.292893) +\qbezier(5.419496,-0.292893)(5.712388,-0.585821)(5.712388,-1) +\qbezier(5.419496,-1.707107)(5.712388,-1.414179)(5.712388,-1) +\qbezier(4.712388,-2)(5.126603,-2)(5.419496,-1.707107) +\put(3.141592,2.1){\makebox(0,0)[b]{A}} +\put(0,0.1){\makebox(0,0)[b]{C}} +\put(6.283814,0.1){\makebox(0,0)[b]{B}} +\put(3.141592,-2.1){\makebox(0,0)[t]{F}} +\put(4.712388,0.1){\makebox(0,0)[b]{D}} +\put(4.712388,-2.1){\makebox(0,0)[t]{E}} +\put(5.762388,-1){\makebox(0,0)[tl]{P}} +\put(3.101592,-0.1){\makebox(0,0)[tr]{G}} +\end{picture} +\label{fig08} +\end{figure} +both large and small arcs in the same time; the reason +of which is that the force may be proved to be always in +proportion to the distance along the curve from its lowest point +point, $\mathrm{F}$. +%-----File: 048.png-------------------------------------------- +%-----Folio: 33------------------------------------------------ + +But how is a pendulum bob, hung by a string or wire +from a fixed point, to be persuaded to describe a cycloid?\index{Pendulums!cycloidal theory|(} +It so happens that if a cycloid $\mathrm{BFC}$ is cut in two, and one +half $\mathrm{BF}$ removed as a solid with a convex edge to $\mathrm{AC}$ +(making $\mathrm{AG=FG=DE}$), and the other half to $\mathrm{AB}$, the +end $\mathrm{P}$ of a string $=\mathrm{AF}$, fixed at $\mathrm{A}$, and moving between +those `cycloidal cheeks' will redescribe the old cycloid +$\mathrm{BFC}$\@. This is mathematically expressed by saying that +the \textit{involute} of a cycloid is another equal cycloid, and therefore +also the \textit{evolute} is; the evolute being the cheeks, and the +involute the curve described from them: the proof of this +belongs of course to geometry, not mechanics, and is of no +consequence to us at present. Huyghens therefore proposed +to hang clock pendulums by a string or a thin spring between +cycloidal cheeks, and that was for some time thought a very +superior method of making clocks. I have no doubt there +are some still in existence, as I have seen them. + +But after a time it was found that clocks went rather +worse with these cheeks\index{Cycloidal!cheeks useless}\label{cheeks} than without them; and then it +occurred to somebody that the cycloidal theory is only true +for what is called in mathematics a simple pendulum, or one +in which not only the bob, but the centre of the bob, is +alone supposed to have any weight; and of course there is +no such thing possible, for the rod must have some thickness, +or it is not stiff enough to work, or to be driven by the +clock, and if you make the bob very heavy, with the view of +rendering the weight of the rod insignificant, then the bob +itself must be large, and differs considerably in its mechanical +effect from a single imaginary heavy point at its centre. And +besides that, the spring or string cannot be made to act +against the cheeks without friction and other disturbing +causes; all which things are said to have been proved to +produce greater deviations from isochronism than a variation +of several degrees in the arc. Indeed we shall see hereafter +that the common clock escapements tend to produce an error +%-----File: 049.png-------------------------------------------- +%-----Folio: 34------------------------------------------------ +of their own, which the deviation from cycloidal vibration +(commonly called the \textit{circular error\index{Circular error of pendulum}) }is actually useful in +counteracting. + +Nevertheless the cycloidal theory is valuable to this +extent: it shows why a common pendulum is very nearly +isochronous for different \textit{small} arcs; for the string $\mathrm{AP}$ will +evidently describe very nearly the same curve near the +bottom $\mathrm{F}$, whether the cheeks are there or not: in other +words, a bob vibrating in a small circular arc is almost +identical with one in a cycloidal arc described by a string of +the same length. The actual time of a circular vibration +cannot be calculated without the aid of the higher branches +of the integral calculus, and even then it can only be exhibited +in the form of a rather awkward series, which would +be little better than useless, except for small arcs; and for +them it is quite sufficient to take only the two first terms of +it.\index{Pendulums!cycloidal theory|)} The whole calculation may be found in \textit{Pratt's Mechanics, +} or in the 8th edition of the \textit{Encyclop\ae dia Britannica,} under +article \textit{Pendulum.} The first term is simply the expression +for a cycloidal vibration, $t=\pi\surd{\frac{l}{g}}$ the letters of which +I have already explained at p.~\pageref{lg}, for the conical pendulum, +whose time of vibration you now see is less than that of a +plane pendulum of the same length in the proportion of +$\surd$cosine of the angle which the conical one makes with the +vertical axis. + +\subsection[Circular error.]{Circular error.}\label{subsec:Circular_error.}\markright{CIRCULAR ERROR.}\index{Circular error of pendulum}\index{Pendulums!circular error of}---The next term in the series (omitting +all the later ones which are still smaller) constitutes the +circular error $\mathrm{K}$, or the excess of the time of vibration in a +circular arc over that in the cycloidal one belonging to the +same length of pendulum; and it is accurate enough for all +practical purposes to say that $\mathrm{K}=\pi\frac{a^2}{16}\surd{\frac{l}{g}}$; and therefore +for a whole day, $\mathrm{K}= 5400 a^2$ in seconds, whatever the +length of the pendulum is; the amount of which you may +%-----File: 050.png-------------------------------------------- +%-----Folio: 35------------------------------------------------ +easily calculate from the fact that if $a=2^\circ$, as usual in +clocks its numerical value is $.035$, and therefore $\mathrm{K}$ = about +$6$~seconds. But this is more than what is called the circular +error in a clock pendulum; for we need not care what is the +difference between the time of a cycloidal arc\index{Arcs of vibration in clocks} and the actual +circular arc which the pendulum describes, but only between +two small circular arcs, $a$ and $a_1$, as the pendulum is +likely to describe in different states of the clock. This +quantity, which we may call $\Delta\mathrm{K}$, is only $5400 (a^2 \sim a_1^2)$; +and if we assume the larger of the two arcs to be as much +$2\frac12^\circ$ and the smaller $2^\circ$, the circular error between them +will be rather less than $4$~seconds a day. This is a very large +variation of arc for a tolerably good clock, and when it is as +small as it generally is, the circular error may be expressed +by differentiating the expression $5400 a^2$, and we may say (so +long as both the arc and its variations are small, remember) +that $\Delta\mathrm{K}=10800a\,da$ ($da$ being the variation of the arc). +Thus if $a=2^\circ$ and $da=10^\prime$, $\Delta\mathrm{K}$ will be very nearly +$1$~second: \textit{i.e.}\ the clock will lose a second a day for such an +increase of the arc, independently of any other increase or +counteraction of the circular error, which may be produced +by the escapement at the same time. + +For the common purpose of finding the length of a pendulum +to beat seconds, or any other required time, we need +not trouble ourselves with anything beyond the equation\label{maths} +$t=\pi\surd \frac{l}{g}$ in which $t$ is the number or fraction of seconds, +and $l$ is expressed in feet, because $g$ means $32.2$~feet (in this +latitude), and $\pi$ is $3.1416$ or the numerical value of $180^\circ$. +Therefore in order that $t$ may be $1$~second, you will easily +find by a little calculation that $l$ must be $39.1393$~inches; +and having got that fixed, you may find the length of +pendulum for any other time of vibration very easily by +multiplying $39.14$~inches by the square of the ratio of the +%-----File: 051.png-------------------------------------------- +%-----Folio: 36------------------------------------------------ +intended time to $1$~second. But to save trouble I will put +down a few of the lengths\index{Pendulums!lengths of}, omitting small fractions. + +\begin{table}[!hbtp] +\centering\index{Pendulums!lengths of}\label{lengths}\markboth{LENGTHS OF PENDULUMS.}{LENGTHS OF PENDULUMS.} +\begin{tabular}{r@{}lrl|cr@{}l} +\multicolumn{2}{c}{\sc seconds}&\sc ft. &\multicolumn{1}{c|}{\sc in.}&\sc seconds.&\multicolumn{2}{c}{\sc inches.}\\ +\phantom{\sc sec}$4$&&$52$ &$2$ &$1\frac14$ &\phantom{\sc in}$61$& \\[1ex] +$3$ & &$29$ &$4$ &$1$\phantom{$\frac14$}&$39$ &$.14$ \\[1ex] +$2$ &$\frac12$ &$20$ &$5$ &$\frac34$ &$22$ & \\[1ex] +$2$ & &$13$ &$0\frac12$ &$\frac23$ &$17$ &$.4 $ \\[1ex] +$1$ &$\frac12$ &$7 $ &$4$ &$\frac12$ &$9 $ &$.78$ +\end{tabular} +\end{table} + +These seconds, and the second used as the unit of time in +all mathematical formulas, are seconds of mean time; and as +a sidereal day is shorter than a mean one in the ratio of +$.99727$ to $1$, a sidereal pendulum must be shorter than a +mean one in the square of that ratio, which makes the +sidereal seconds pendulum at Greenwich $38.87$~inches. I +have met with persons who could not understand how an +increasing gravity can make pendulums go faster; and +others, with a little mathematical knowledge, think that the +force varying as the distance from zero (in small arcs) is +opposite to the fundamental law of gravity varying inversely +as the square of the distance. The answer to the second of +these is, that the zero, or middle, or lowest position of a +pendulum is not an attracting body like the earth (which +attracts as if it were all condensed into its centre); and the +tendency towards zero is only a mathematical consequence of +that law of gravity. The stronger the tendency to zero, or the +stronger gravity is, the faster the pendulum will evidently +fall; and the sooner gravity will bring it again to rest in rising. +The time of rising always = the time of falling, under any +force which is equal at equal heights during the rise and fall. + +\subsection[Centre of oscillation.]{Centre of oscillation.}\label{subsec:Centre_of_oscillation.}\index{Centre of oscillation of pendulums}\index{Oscillation, centre of}\index{Pendulums!centre of oscillation of}---It must be remembered that +these are only the theoretical lengths of \textit{simple pendulums} +with all the weight concentrated in the centre of the bob, and +that this theoretical length by no means coincides with the +actual length down to the centre of gravity\index{Pendulums!relation to gravity} of the pendulum, +but is always longer. This length may properly be called +%-----File: 052.png----------------------------------------------- +%-----Folio: 37--------------------------------------------------- +the \index{Radius of oscillation of pendulums}\textit{radius of oscillation,}\markboth{RADIUS OF OSCILLATION.}{RADIUS OF OSCILLATION.} as the lower end of it is always +called the centre of oscillation; which is not a fixed point in +the body, like the centre of gravity, but a relative one, every +axis of suspension having a radius and centre of oscillation +of its own. It is not always a simple process to calculate +this length (which we may as well call $l$) for any given +pendulum as it requires either the integral calculus or some +rules deduced from it; but it will be easy to explain the +nature and meaning of the quantities on which it depends. +Let $m$ be the mass of each particle of the pendulum, which +in these calculations must not be confounded with the +weight, which is written $mg$ ($g$ being the force of gravity), $r$ +the distance of $m$ from the axis of suspension, and $\mathrm{M}$ the +mass of the whole pendulum; then the radius of oscillation +$=$ the sum of each particle multiplied into the square of its +distance from the axis, divided by the sum of each particle +multiplied into its distance simply; that is to say, +$l = \frac{\sum m r^2}{\sum m r}$ +($\sum$ being used to indicate this kind of summation, which can +only be performed by integration). + +The numerator in this fraction is called the \textit{moment of +inertia} of the body with reference to that axis of suspension. +Of course there is some quantity $k^2$ which +$= \frac{\sum m r^2}{\mathrm{M}}$, and $k$ +is then called the \textit{radius of gyration} for that axis, and $\mathrm{M}k^2$ is +obviously the moment of inertia again. In like manner +some quantity $h = \frac{\sum m r}{\mathrm{M}}$, and $h$ is then the distance of the +centre of gravity of the whole pendulum (not of the bob, +remember) from the same axis, which is easy enough to +find in bodies of the shape commonly used for pendulums. +It appears then that the effective length $l$ of a pendulum +always $= \frac{k^2}{h}$; and it is only when the rod is very thin and the +%-----File: 053.png----------------------------------------------- +%-----Folio: 38--------------------------------------------------- +bob itself small but heavy, that $k$ and $h$ can be assumed to be +even approximately identical, and therefore both $= l$, as they +are in a simple pendulum. But it does conveniently happen +that the centre of oscillation in small pendulums of the usual +forms is generally near the centre of gravity of the bob, and +sometimes coincides with it, as we shall see. + +This quantity $\mathrm{M}k^2$, the moment of inertia\label{moi}\markboth{MOMENT OF INERTIA.}{CENTRE OF OSCILLATION.}, always appears +in mathematical formulae as the resister of forces of rotation +or vibration on an axis, and of all disturbances of such forces +after they have set the body in motion, and therefore +we see at once why long and heavy pendulums are better +than short and light ones. There are a few other simple propositions +relating to the centre of oscillation and the theory +of pendulums, which it will be appropriate to notice here. + +Draw a pendulum of any shape you like, supposed to be +vibrating in the plane of the paper, and call its centre of +suspension $\mathrm{S}$, and its centre of gravity $\mathrm{G}$, and the distance +between them $h$. All bodies have this property, that their +moment of inertia round any axis through $\mathrm{G}$ (which we call +$\mathrm{M}k_1^2$) is less than round any other axis parallel to that, and +we are not concerned with any but parallel axes; and +further, if the other axis is distant $h$ from the centre of +gravity, the $k^2$ round that new axis $= k_1^2 + h^2$. Therefore if $\mathrm{O}$, +somewhere below $\mathrm{G}$, is the centre of oscillation corresponding +to $\mathrm{S}$, $l$ or $\mathrm{SO} = \frac{k_1^2+h^2}{h}$; and $l-h$, or +$\mathrm{GO} = \frac{k_1^2}{SG}$; or the +centres of suspension and of oscillation are \label{reciprocal}reciprocal. In +fact, if the pendulum is wide enough, you may draw two +circles round $\mathrm{G}$ with radii $\mathrm{GS}$ and $\mathrm{GO}$, and if you stick an +axis through the pendulum, at right angles to the same plane +of vibration, anywhere in either of those two circles, it will +vibrate in the same time as on the original $\mathrm{S}$\@. Consequently, +if you construct a pendulum (symmetrical on both +sides of its middle plane of vibration, to prevent it swinging +with a twist) with one fixed axis $\mathrm{S}$, and another adjustable +%-----File: 054.png---------------------------------------------- +%-----Folio: 39-------------------------------------------------- +one for $\mathrm{O}$, and a movable weight to adjust the time by, you +can make it vibrate in the same time on both axes; and by +adjusting the movable weight also, the pendulum can be +made to agree with the vibrations of a clock pendulum +which is beating seconds; and then the distance between $\mathrm{S}$ +and $\mathrm{O}$, or the two knife edges which represent them, being +measured, we shall know that that is the length of the +simple seconds pendulum. It has also been proved that if +round axes are used instead of knife edges, the distance +between them (not their centres) equally represents the +radius of oscillation, provided the axes roll on a plane. + +If all the standard \index{Pendulums!standard lengths}\label{standard}\markboth{PENDULUMS.}{PENDULUMS.}yard measures in the kingdom should +ever be lost, they could only be restored by this process, +according to an Act of Parliament, 5 Geo.~IV.~c.~74, which +declared that a yard is $\frac{36}{39.1393}$ of the length of the pendulum +which vibrates mean seconds in London at the level of the +sea, in a vacuum. The force of gravity decreases so much +towards the equator that an English pendulum would lose $2\frac14$ +minutes a day there. The following rule for the length +of the seconds pendulum in any latitude has been deduced +from observation, near enough for all practical purposes: +$l = (1-.0027 \cos 2 \mbox{ lat.})\,39.1156$~inches; that number of +inches being the length of the pendulum at lat.~$45^\circ$. When +the latitude is more than $45^\circ$, $\cos 2 \mbox{ lat.}$ becomes $-$, and +so $l$ exceeds its length at $45^\circ$, as of course it ought to do. +Another still simpler formula is $l = 39.017$ [the length of a +seconds pendulum at the equator] $+\, .2 \sin^2$ of latitude. + +That Act however has been repealed, and some standard +weights and measures are deposited in various public places +under an Act of 18 \& 19 Vic.~c.~72. The late Astronomer +Royal provided a set, open to anybody, at the Observatory +gate. But if they all happened to be destroyed, new ones could +be made from the old pendulum ratio. Indeed Mr.~Johnson +of Wilmington Square had one ready for that calamity. A +%-----File: 055.png----------------------------------------------- +%-----Folio: 40--------------------------------------------------- +simple pendulum $36$~in.\ long would vibrate in a time which +is to $1$s.\ as $36^2$ to $39.14^2$, or $.846$ of a second, or $70.92$ times +in a minute; and he has made a clock with a reversible +pendulum vibrating in that time, and consequently $36$~inches +between the two knife edges. + +The length of a seconds pendulum so nearly resembles the +French \index{Metre, the French, a bad measure}\label{metre}\markboth{BADNESS OF THE FRENCH METRE.}{BADNESS OF THE FRENCH METRE.}metre of $39.371$~in., that some persons may fancy +that that most ridiculous and mischievous revolutionary +measure had an origin even as rational as being the length +of a seconds pendulum in some latitude. But it has not. +It was intended to be the $40$ millionth part of a meridian of +the earth---about as rational a standard as if we enacted that +the yard should be the $420$ millionth of the mean distance of +the moon, which it is very nearly; and astronomers know +the moon's distance within a less fraction than the difference +of the metre from what it pretends to be, but is not.\footnote{% +See the essay `On Celestial Weights and Measures,' in Sir J.~Herschel's +\textit{Familiar Lectures,} condemning the metre strongly. +} Yet +there are people who want to force on all the world this +absurd, inconvenient, and useless measure, invented by a +nation whose language is declining over all the world; while +the English language, with that standard of measures which +every man carries in his arms, his legs, and in his head, is +spreading over all the world, so that it will soon be the +only universal language to be found everywhere, if it is not +so already. Doctrinaires of this kind may cram penny-school +girls with French metres, and centimetres, and +kilograms; but our yard grew and will remain as the +natural standard of length until the stature of the human +race alters. For it is the length of a good stride of a man +of what is generally considered the best height, and that +height is two such lengths, and so is the stretch of his arms, +and a yard is the natural length of his walking-stick. A +metre would be the yard of a nation of giants. With the +yard too goes the equally natural and still older measure of +%-----File: 056.png----------------------------------------------- +%-----Folio: 41--------------------------------------------------- +a foot, which all nations had, with such small variations as +would occur in times when they had no scientific provisions +for preserving exact standards. Some great authorities +believe inches to have been the oldest measure of all; and +the Egyptian cubit\index{Cubit of Pyramid, and Jewish}\label{cubit}, which was unquestionably used in +building the Pyramids, from the many simple multiples of it +which occur there, confirmed by the discovery of one +accidentally built up in a wall at Thebes, was probably $20$ +of their inches, being a little more than $20$ of ours; and +the `sacred cubit' of the Jews was $25$, according to Sir +Isaac Newton. Probably the authors of the new $25$~inch +to a mile Ordnance survey of England little thought that +they were reverting to that ancient standard. At the same +time, I do not accept the theory of the Scotch Astronomer +Royal,\footnote{% +See an amusing pamphlet on it by Mr.~F.~D.~Wackerbarth, and the +remarks on the Pyramid in my `Book on Building.' (Lockwood \& Co.)} +that the $25$~inch cubit was embodied in the +Pyramid dimensions, besides the one of $20.7$~inches, or +$20$ of some of the old continental inches. A variation of one +thousandth is practically nothing in unscientific ages, and +is less than the variation of many foot-rules now, and it is +singular that if our inch were a $1000$th longer, the earth's +polar axis would be just $500$ million inches. + +\subsection[Short and slow pendulums.]{Short and slow pendulums.}\label{subsec:Short_and_slow_pendulums.}\index{Pendulums!short and slow}\markboth{SHORT AND SLOW PENDULUMS.}{SHORT AND SLOW PENDULUMS.}---There is a kind of +pendulum which is properly enough used in the instrument +called a \textit{metronome}\index{Metronome, the}, for counting the time in music lessons in +a way that requires no particular accuracy, and occasionally, +but very improperly, used for small clocks. It follows from +the propositions I have been explaining, that if a pendulum +with a heavy rod is set vibrating on an axis very little above +its c.g.\ it will vibrate slowly, like a scalebeam; and +consequently you may have a $2$~seconds pendulum in the +compass of a few inches. But even if the weight of it were +equal to that of a large pendulum, its regulating power, or +power to resist \label{resist}disturbance, would be very much less, +%-----File: 057.png----------------------------------------------- +%-----Folio: 42--------------------------------------------------- +because that is measured by the moment of inertia $\mathrm{M}k^2$, +which is the sum of the weight of each particle $\times$ its distance$^2$ +from the axis, and that of course must be small in a short +pendulum, though its time may be long if $h$ is very small. +The time of a metronome pendulum is adjusted by a small +sliding weight on the rod above the axis of vibration, the +bob being of course below it. Moving the weight up brings +the c.g.\ of the whole nearer to the axis, and also increases +the $\mathrm{M}l^2$ of the whole, and so in both ways makes it go +slower, and \textit{vice vers\^a}. It is kept going by a roughly made +watch movement and a common recoil escapement, such as +I shall describe presently for clocks. + +\subsection[Shape of pendulums.]{Shape of pendulums.}\label{subsec:Shape_of_pendulums.}\index{Pendulums!shape of}\index{Shape!of pendulums}\markboth{SHAPE OF PENDULUMS.}{SHAPE OF PENDULUMS.}---Whatever the shape of a pendulum +is in other respects, it is essential that the back and +front should be alike both in weight and shape; or to speak +mathematically, that it should be symmetrical on each +side of the middle plane of its vibration, or it will \textit{wobble,} +and vary its time in some irregular and incalculable way. +It does not signify +however, if one side of the bob is larger +than the other in the direction of vibration; but as that +would look ugly and the other does not, one never sees the +ugly but innocent deviation, but frequently the other; for +the pendulums of common clocks are often unsymmetrical +in the back and front, and are therefore bad ones, though +perhaps as good as the clocks they belong to. For this +reason the old fashioned lens-shaped bob, or the flat cheese +shape which some clockmakers use for church pendulums, +are not good ones, because it requires great care to fix them +with their own middle plane coinciding with the middle +of the rod. It is true that a lens moves through the air +with less resistance than any other shape; but then it +must be very large to be of the same weight as a sphere or a +thick cylinder with the axis vertical, and we shall see afterwards +that nearly all clock errors are inversely as the weight +(and length) of the pendulum. But there is a shape which +%-----File: 058.png----------------------------------------------- +%-----Folio: 43--------------------------------------------------- +would probably be found to combine some of the advantages +of both though Baily's experiments (in \textit{Phil. Trans.} for +1932) showed some results which no one could have +foreseen; I mean a cylinder of elliptic section, or one having +the same horizontal section as a lens, but thicker; or of +the section formed by two arcs of a circle of $120^\circ$, which +would make the horizontal length and thickness as $12\frac18$ +to $7$~inches---a very convenient size for a large bob\index{Bobs for pendulums}\index{Pendulum!bobs} $13$~in.\ high; +which would weigh about $188$~lbs.\ in cast iron and +$288$ in lead, and is equal to a round cylinder of $8\frac14$~inches +diameter. But such figures are only approximate, the +weight depending on the density of the casting; and I have +neglected the hole for the rod, as that would be compensated +and more by the rod's own weight. A spherical bob is not so +good as this shape, because a slight error or looseness in the +hole would throw much more of the weight on one side and +increase the tendency to \textit{wobble}, a very serious defect. For +all practical purposes a cylinder is probably the best shape, +and is used now in all the best large clocks. I also +introduced the plan of making the top slightly domical, to +prevent bits of dirt resting on it, which would accelerate the +pendulum, as we shall see presently under `regulation.' + +Bobs for large clocks are generally made of cast iron, +partly because it is cheaper than lead, and also because very +heavy lead bobs are liable to be bruised out of shape in +moving about before the pendulum is hung. But there can +be no doubt that lead is best, as its specific gravity is half as +much again as iron, and therefore it is less resisted by the +air, which we shall see afterwards affects pendulums by no +means insensibly. For the same reason it is a mistake to put +lead bobs in brass cases, as is usually done in `regulators' or +astronomical clocks, as it increases the bulk much more +than the weight. The lead looks very well japanned. It is +equally absurd to case lead weights in brass, though it does +no actual harm as it does in the bob. +%-----File: 059.png----------------------------------------------- +%-----Folio: 44--------------------------------------------------- + +\subsection[Suspension of pendulums.]{Suspension of pendulums.}\label{subsec:Suspension_of_pendulums.}\index{Pendulums!suspension}\index{Suspension of pendulums}\markboth{SUSPENSION OF PENDULUMS.}{SUSPENSION OF PENDULUMS.}---Pendulums +are generally suspended +by a spring, for the obvious reason +that they then swing without any +friction---except of the air\index{Air!resistance of to pendulum}. Some +French pendulums are still hung +by a string, but that has some +friction. The spring is not designed +to act with any force as a spring, +though it does very slightly, and +therefore is not at all analogous to +the balance spring of a watch, which +is thus the substitute for gravity. +The spring is enclosed in a slit, or +between two pieces called chops at +the top of the pendulum, which also +carry the rod, except in the American +clocks, where the wire itself is +flattened out into a spring. The top +of the spring is also riveted between +two smaller pieces in common clocks, +so as to make a lump which holds +up the spring in the cock, which is +a fixed piece with a slit in it +just wide enough to hold the +spring. In clocks of the higher +class the two upper chops are much +thicker and firmly screwed together, +and a large pin put through them, +\begin{wrapfigure}{o}{113pt} +\centering +\hypertarget{fig09}{\caption{\sc Suspension of Pendulums}} +\includegraphics[height=500pt]{images/fig09.png} +\label{fig09} +\end{wrapfigure} +and the chops themselves go through +the cock tightly and are held up +by the pin which lies in $\mathrm{V}s$. This +will be better understood by \hyperlink{fig09}{this +picture} of a heavy pendulum and its +suspension. We are not concerned +%-----File: 060.png--------------------------------------------- +%-----Folio: 45------------------------------------------------- +with the lower part just yet. The nearly square plate is +a cast iron plate bolted to the wall, out of which project +the two thick pieces on which the pin lies. The pin itself +is like a bolt with a tail projecting backwards through the +head, and the piece corresponding to the head, on the right +side in the figure, is the nut. The chops of the pendulum +itself are shown a little below, and the way I introduced +of making them for `regulator'\index{Regulation!of pendulums} or astronomical clock +pendulums which have the steel rod screwed into a solid +piece, is to file out a slit wide enough to hold the spring\index{Pendulum!springs} +and a piece of brass on each side of it, and the whole is +pinched together by a screw. You cannot cut a slit thin +enough for the spring alone. This will be shown in the +figure of the four-legged gravity escapement hereafter. + +A \label{fixing}perfectly firm\index{Pendulums!importance of firm fixing} suspension is essential to good performance +of any clock, and the heavier the pendulum the +firmer its support must be. It is well known that clocks +will influence\index{Clocks!influence one another} each other when fixed against a wooden wall, +however firm it may appear, and that one pendulum will +thus actually set another of equal length vibrating. Consequently +a free pendulum can be kept swinging from an +apparently immovable support which has an invisible +vibration or twist imparted to it by a clock below beating +in the same time. All good regulators have the pendulum +cock\index{Pendulum!cocks} screwed to the back of the case, and that firmly +screwed to a strong wall; or, better still, the cock is cast +with a cast iron back or bracket which also carries the +movement, and that is screwed directly to the wall, the +whole front of the case lifting off. In the Westminster\index{Pendulum2@Pendulum!of the Westminster clock} +clock the pendulum cock is a large iron frame built in right +through the wall with a flange behind, and the cocks of +many other large clocks are fixed with bolts through the +wall. With a firm suspension the pendulum swings farther +than with a weak one, and we shall see afterwards that +(other things being equal) the errors of clocks vary inversely +%-----File: 061.png--------------------------------------------- +%-----Folio: 46------------------------------------------------- +as the square and sometimes as the cube of the +arc. + +It is hardly necessary to say that the whole of the pendulum +suspension should be so adjusted that the bend of the +spring may be exactly opposite the pivot of the pallet arbor, +in order that the fork\index{Forks of pendulums} which embraces the pendulum, as +described at page~\pageref{fork}, may have as little friction as possible. +It must \label{shake}not however be tight, for the reason just now given, +viz.\ that no point in the pendulum describes quite a circle, +and the difference is sensible enough generally to stop the +clock if the fork fits the pendulum rod too tightly. It is +equally necessary that the plane of vibration of the pendulum +should be exactly at right angles to the pallet arbor, or +else there will be a sliding motion of the pendulum backwards +and forwards in the fork. But obvious as these +things are, they are all constantly neglected, especially in +large clocks, where the friction of all the parts is also the +greatest. The fork indeed is seldom left too tight, because +that mistake tells its own story directly; but, by way of +making up for it, it is very often so loose that you hear the +shake of it from one side to the other at every beat. There +ought to be a drop of oil there, as that is just enough +to keep a steady hold without either shake or tightness, +since oiled surfaces are not really in metallic contact. + +In old church clocks a long pendulum was often \label{where}put for +convenience a good way off the clock, but so as to swing +in the same plane as the crutch\markboth{CONNECTION WITH CRUTCH.}{CONNECTION WITH CRUTCH.}, which is connected with it +by a light horizontal wooden bar, no heavier than an organ +`tracker.' The pendulum top too was often higher than the +pallet arbor, so that the pallets moved through a larger arc +than the pendulum. There is no advantage in that; but if +the pivots at the ends of the horizontal bar fit closely, there +may be less loss of power by `shake' than there generally +is between the fork and the pendulum. Indeed I have seen +old regulators made in that way, even with the pendulum in +%-----File: 062.png--------------------------------------------- +%-----Folio: 47------------------------------------------------- +the usual place, by using two short horizontal arms thus, +$\mathrm{D}${\raisebox{.5ex}{\Huge{$<$}}\raisebox{.5ex}{\parbox[1em]{2ex}{$\mathrm{C}$\\[.5em]$\mathrm{P}$}}}, $\mathrm{C}$ +being the pivot in the crutch, $\mathrm{P}$ the pivot +in the pendulum, and $\mathrm{D}$ the one at the junction of the two +arms $\mathrm{DC}$, $\mathrm{DP}$\@. But this is decidedly inferior to the other +plan of putting the pendulum on one side of the clock, since +that requires only two pivots instead of three, and there is +no twisting action on the pendulum. If the horizontal bar +were attached by slight springs it would be better still, for +there would then be neither shake nor friction, and the springs +would no more impede the action than the pendulum spring +does, for any moderate arc. There is yet in existence one +great London clock of the last century with fans on the pendulum +just above the bob (like the wings on the ankles of +Mercury) to prevent it swinging too far, and they are +actually placed obliquely, of which the effect of course is to +make it swing with a twist. The late Mr.~Vulliamy told me +he removed fans from the pendulum of the Horse Guards +clock. Sometimes heavy pendulums are hung by two +narrow springs instead of one broad and thin one, to secure +the vibration in the proper plane; but it is a bad plan, +because it is difficult to get the two springs equal in all +respects. The springs of `regulator' pendulums of $14$ or +$15$~lbs.\ are generally about $\frac12$ an inch broad and $2$~inches +long; I mean clear of the chops of course; that of the $6$~cwt.\ +pendulum at Westminster is $3$~in.\ by $5$ and $\frac{1}{60}$~in.\ thick. + +There should always be a degree plate\index{Degree plate for a pendulum}, with a pointer to +it on the pendulum wherever it can be most conveniently +seen. The length of $4^\circ$ on the plate is always $.07\times$ its +distance from the top of the pendulum; and as the only use +of the degree plate is to see that the pendulum keeps the +same arc, or to see how it varies, no very great accuracy is +required in the degrees. + +\subsection[Pendulum springs.]{Pendulum springs.}\markboth{PENDULUM SPRINGS.}{PENDULUM SPRINGS.}\label{subsec:Pendulum_springs.}\index{Pendulums!springs of}---Various opinions have been propounded +on the proper strength for them, but none on any +%-----File: 063.png--------------------------------------------- +%-----Folio: 48------------------------------------------------- +solid grounds, and some on altogether mistaken ideas of the +duty of the spring. Probably the thinner it is the better, +provided it is thick enough not to be bent too sharply or +strained by the weight of the pendulum. Every now and +then a clock is troubled with the disease of spring-breaking +over and over again. Sometimes this proceeds from the +lower edges of the upper chops being left sharp, which in +time cut the spring; and perhaps more frequently from +some unseen inequality in the fixing; and it is better to let +the pendulum hang at first with the lower chops a little +loose, and only to screw them up after the pendulum has got +a square bearing, and to take care not to put it out in +doing so. It is wonderful how much more trouble people +will take to do things wrong than would serve to do them +right, and it is almost incredible that some clock-makers +send out their best clocks with the lower edges of the upper +chops not horizontal but rounded into a circular arc. +The slightest reflection would show anybody that springs so +fixed must tend to `buckle,' or bend not in a straight line, +at every vibration. And others make the upper chops, +which have the strain of vibration, thinner and weaker than +the lower ones which have no strain. There should always +be a block of wood close under the bob of a heavy pendulum, +to prevent the top from breaking the crutch and pallets if it +falls from the spring breaking. + +A spring does not bend only at one point as a string does; +and therefore a pendulum bob hung by a spring does not +move exactly in a circle, but in something more like a +cycloid described with that radius of curvature, as in fig.~\ref{fig08}, +p.~\pageref{fig08}; and it has often been attempted to make springs +which would render the pendulum absolutely isochronous +for all such arcs as it is likely to swing. Possibly the thing +could be done, if it was worth doing; but both I and some +other persons who have spent a great deal of time on experiments +have come to the conclusion that it is not, for reasons +%-----File: 064.png--------------------------------------------- +%-----Folio: 49------------------------------------------------- +will appear when we come to consider the effect of the +escapement on the time of vibration. Indeed I may say at +once, with respect to the only escapement I have yet described +and all others on the recoiling principle, that the +circular error\index{Circular error of pendulum}\index{Pendulums!circular error of}, which it is the object of these spring contrivances +to correct, is already more than corrected by those +escapements: for the clocks never lose, but gain, when the +arc of the pendulum increases; so that the circular error is +actually useful for counteracting the escapement error, and +the clock goes better than it would with a perfect cycloidal +pendulum, or any equivalent contrivance. + +\subsection[Pendulum regulation.]{Pendulum regulation.}\markboth{PENDULUM REGULATION.}{PENDULUM REGULATION.}\label{subsec:Pendulum_regulation.}\index{Pendulums!regulation of}\index{Regulation!of pendulums}---Though pendulums can be +made by calculation and experience very nearly of the +proper length, they always require some adjustment afterwards, +besides regulating from time to time, according to +the state of the clock. The usual way of doing this is by a +screw cut at the lower end of the rod, with a nut on which +the bob rests, and by which it can be raised or lowered to +make the pendulum go faster or slower. The lower part of +the rod is always made into a square or some shape on +which the bob cannot turn, except in certain compensated +pendulums, as we shall see; for otherwise the bob would +twist round with the nut. By that means you can hold the +bob and the rod steady while you turn the nut. It is convenient +to have the thread of the screw such that one +complete turn of the nut will make a minute a day difference +in time; and the better class of pendulums have a large +round nut divided by marks which mean a second a day, +with an index fixed to the bob. + +It is easy to find what should be the width of the thread +for one turn to do a minute a \label{marks}day. Let $l$ be the length of +the pendulum, and $dl$ a small increase of $l$, and $dt$ of $t$. Then +we know that +\[ +\frac{t+dt}{t}=\frac{\sqrt{l+dl}}{\surd{l}}\textnormal{; or, } 1+\frac{dt}{t}=\sqrt{1+\frac{dl}{l}} +\] +%-----File: 065.png-------------------------------------------- +%-----Folio: 50------------------------------------------------ + +There is a result of the binomial theorem which we shall +often have occasion to use in pendulum problems, which +may be stated thus:---When a quantity is of the form $1 + m$, +$m$ being a \textit{small} fraction, $(1 + m)^n$ practically, or as astronomers +say, sensibly = $1+nm$ whether $n$ is $+$ or $-$, a +fraction or an integer; and it may be as well to mention +for those who do not know it that $(1+m)^{-n}$ means +$\frac{1}{(1+m)^n}$. \label{p50calc}Consequently here $\frac{dt}{t} = \frac{dl}{2l}$; and multiplying +by all the seconds in a day, $86400$, and calling $d\mathrm{T}$ the +daily increase, $d\mathrm{T}=\frac{43200 dl}{l}$~sec. So if we want $d\mathrm{T}$ to be +a minute for one turn of the nut, $dl$ or the width of the +thread must $= \frac{l}{720}$, or about $\frac{1}{18}$~inch, a very convenient +size for a fine screw. + +But this mode of regulating is inconvenient for large +clocks with very heavy bobs, and it is better to fix a collar +on the rod at some convenient height, on which \label{smallweights}small +weights can be laid to accelerate the clock, and taken off to +retard it. The place where a given weight is most effective +is at the middle of the length, but it does practically as well +to put it somewhat higher, and the higher it is the less risk +there is of shaking the pendulum in putting the weight on or +off, by which any accurately going clock is seriously disturbed. +The proportion and position of these regulating +weights are determined as follows:---Let $m$ be a little weight\markboth{REGULATION BY SMALL WEIGHTS.}{REGULATION BY SMALL WEIGHTS.} +added to the pendulum at a distance $d$ below the top, and $l$ +above $\mathrm{O}$ the centre of oscillation; then--- +\[ +\frac{t+dt}{t}= +\frac{1}{\surd{l}}\cdot +\frac{\sqrt{\mathrm{M}l^2+md^2}} +{\sqrt{\mathrm{M}l+md}}= +\frac{\sqrt{1+\frac{md^2}{\mathrm{M}l^2}}} +{\sqrt{1+\frac{md}{\mathrm{M}l}}} +\] +%-----File: 066.png----------------------------------------------- +%-----Folio: 51--------------------------------------------------- +and since $\frac{m}{\mathrm{M}}$ is very small this practically +\[ += \left( 1 + \frac{md^2}{2\mathrm{M}l^2} \right) +\left(1-\frac{md^2}{2\mathrm{M}l^2} \right) +\] +which again for the same reason +$= 1-\frac{m}{2\mathrm{M}} \left( \frac{d}{l}-\frac{d^2}{l^2} \right)$. +From which you see at once, that if $d = \frac{l}{2}$, $-d\mathrm{T}$ or the +daily acceleration $= \frac{10800m}{\mathrm{M}}$; or the $10800$th part of $\mathrm{M}$ +laid on the pendulum half way from the top will \label{accelerate}accelerate it +a second a day; and if $d =$ either $\frac{l}{3}$ or $\frac{2l}{3}$, $m$ must +$= \frac{\mathrm{M}}{7200}$ +to do a second a day. + +We shall get exactly the same result for $b$ if we reckon +from $o$; for if you substitute $l-b$ for $d$ in this last equation, +the result is that +$\frac{dt}{t} =-\frac{m}{2\mathrm{M}}\left(\frac{b}{l}-\frac{b^2}{l^2}\right)$; +as might have +been foreseen from the fact that the centres of suspension +and oscillation are reciprocal (p.~\pageref{reciprocal}). You will easily see +too that the worst mode of regulating is by a sliding weight +near the middle of the pendulum; for the acceleration by +moving the weight upwards from $b$ to $d$ is measured by +$\frac{dl-bl+b^2-d^2}{l^2}$, which is $o$ when $d = b$, and very +little while they are anything near equal. In short the +middle of the pendulum is the place of maximum effect for the +weight, and of minimum effect for moving it. + +\subsection[Temporary regulation ]{Temporary regulation }\markboth{TEMPORARY REGULATION.}{TEMPORARY REGULATION.}\label{subsec:Temporary_regulation_}\index{Pendulums!temporary regulation} is also sometimes required in +the best clocks: \textit{i.e.}\ they want putting on or back a few +seconds or less, though the pendulum may not want permanently +altering. Stopping the pendulum and setting it +off again so disturbs it for some time that it must be always +avoided if possible. One way of altering the clock a very +%-----File: 067.png----------------------------------------------- +%-----Folio: 52--------------------------------------------------- +little is to put on or take off a small regulating weight for a +certain number of hours. Another mode now resorted to in +very fine clocks is to apply a temporary magnet\index{Magnet used for regulating clocks}, which can +be made and unmade for any required time, so as to act +on the pendulum either with or against gravity, and so to +accelerate or retard the clock, until it shows the proper +time. Other methods have been tried which all disturbed +the pendulum too much. The first is used at Westminster, +where it is easy to put on small weights without disturbing +that slow and heavy pendulum. I regulate my best regulator +with a gravity escapement by bits of card laid on the bob of +about $40$~lbs.: that is, for permanent regulation. + +Some common clocks are regulated by a nut at the +top, above the cock, which pulls up the spring through +the slit in the cock; but this is thought unfit for +fine work, because the spring ought to be tighter in the +cock than is possible if it is to be capable of being pulled +down by the weight of the pendulum. But I rather doubt +that, if it is made carefully. + +\subsection[Compensation of pendulums.]{Compensation of pendulums.}\markboth{COMPENSATION OF PENDULUMS.}{COMPENSATION OF PENDULUMS.}\label{subsec:Compensation_of_pendulums.}\index{Compensation of pendulums}\index{Pendulums!compensation}---All substances of which +pendulums can be made expand by heat, and consequently +every pendulum naturally goes slower in hot weather than +in cold; and though the lengthening of the rod is far too +small to measure, except by most delicate experiments, it is +enough to make a difference of a minute a week between +moderate winter and summer heat ($40^\circ$ and $70^\circ$) with a +common iron wire pendulum, and in five days with a brass +one, and a minute in three weeks even with a wooden rod, +which varies the least of all materials, but is subject +to a little uncertainty from absorption of damp. The +\hyperlink{sgtable}{following} is a table of the expansion of such materials +as can be used for pendulums, \textit{i.e.}\ of $\frac{dl}{l}$ for $1000^\circ$ (F) of +heat, which I use to get rid of unnecessary decimals, as we +are only concerned with the proportions:--- +%-----File: 068.png-------------------------------------------- +%-----Folio: 53------------------------------------------------ + +White deal, and perhaps other woods, have $.0023$ expansion +and specific gravity from $.5$ up to $.9$. +\begin{table}[!hbtp] +\centering\index{Gravity, specific, of metals}\label{sgtable}\hypertarget{sgtable}{}\index{Specific gravity!of metals, \&c.}\index{Table!expansion for compensated pendulums} +\begin{tabular}{llcl} + & & &lbs \\ +Flint glass expands\dotfill &$.0048$: & a cubic inch = &$.1166$\\ +Platinum\dotfill &$.0056$ &,, &$.76$ \\ +Steel rod, tempered\dotfill &$.0064$ &,, &$.28$ \\ +Cast iron\dotfill &$.0066$ &,, &$.26$ \\ +Iron rod\dotfill &$.0070$ &,, &$.28$ \\ +Brass\dotfill &$.0100$ &,, &$.30$ \\ +Copper\dotfill &$.0106$ &,, &$.32$ \\ +Silver\dotfill &$.0115$ &,, &$.38$ \\ +Lead\dotfill &$.0165$ &,, &$.41$ \\ +Zinc\dotfill &$.0160$ &,, &$.253$ \\ +Mercury, in bulk\dotfill &$.1000$ &,, &$.49$ \\ +\multicolumn{4}{c}{its expansion in length depending on the vessel.} +\end{tabular} +\end{table} + +These differences make it easy to devise a pendulum which +will always keep the bob at the same height. To take the +most simple example, suppose we set a brass tube $6.4$~ft.\ long +on a nut at the bottom of a steel rod of $10$~ft.; it is +evident that the top of the tube, or a bob resting on it, will +stay at the same height in all temperatures. This would be +a very inconvenient sort of pendulum, but we can do the +same thing by breaking up the long lengths into pieces, none +of which must be more than $3$~ft.\ for a $39$~inch pendulum, +and consequently a steel and brass pendulum must have +three lengths of steel and two of brass. Accordingly the +old \textit{gridiron}\index{Gridiron pendulum}\index{Harrison!gridiron pendulum} pendulum, invented by Harrison,\index{Harrison!the chronometer maker} who became +the first chronometer maker of his time from a carpenter, had +a central steel rod with a cross at the bottom carrying two +upright brass rods as columns, on the top of which was +another cross piece from which hung two steel wires, again +carrying a cross at the bottom, on which two more brass +columns stood, and from the top of them hung two more +steel wires carrying the bob. + +Another form of it, invented by Troughton\index{Troughton's pendulum}, was to substitute +alternate brass and steel tubes for each pair of rods. If +%-----File: 069.png-------------------------------------------- +%-----Folio: 54------------------------------------------------ +iron were used instead of steel, another pair of each would +be required, making thirteen rods altogether. + +But since the introduction of zinc-working\markboth{ZINC COMPENSATION OF PENDULUMS.}{ZINC COMPENSATION OF PENDULUMS.} brass pendulums +have gone out, because zinc expands enough to do the +compensation with only one zinc tube, and is stiff enough, +which lead is not. It might also be done with platinum and +brass, but that is too expensive, and zinc with steel\index{Compensation of pendulums!zinc and steel}\label{zincsteel}\index{Zinc!zinc and steel pendulums} or iron +does just as well. The figure at p.~\pageref{fig09} shows the best construction +of large pendulums of this kind, and that of small +ones is substantially the same, only short zinc tubes may be +much thinner in proportion than long tubes, which have to +carry heavy weights, acting as a column which must run no +risk of bending. For small pendulums the zinc need not be +more than $.1$~inch thick, but for $2$-sec.\ pendulums, with bobs +of suitable weight, the zinc tubes are made three-fold, all +drawn tight upon each other, and altogether $\frac38$~in.\ thick. +The tubes for somewhat lighter bobs\index{Bobs for pendulums}\index{Pendulum!bobs} and shorter pendulums +may be half that thickness, or even less. No rule can be +given for such things. For $1$-sec.\ pendulums a steel rod $\frac14$~in.\ thick + is enough, but for a heavy bob I prefer $\frac38$~in., as it has +to be tapped for screws at each end. I will give some +further directions about construction presently. + +The calculations for the proper length of zinc are not quite +so simple as you may imagine, except as a first approximation: +in fact, if you attempt it all at once it is much too complicated +to be practicable. We have seen at p.~\pageref{accelerate} in effect +that the transfer of a very small weight from the lower part +of a pendulum to the upper produces a great acceleration, +and this happens in the rising of the weight of both tubes +under expansion, yet it cannot be taken into account in any +simple calculation. I suppose it is from this cause that the +expansion of zinc, given in all other tables as $.017$ for $1000^\circ$ +of heat, gives wrong results for these calculations, as is +proved by experience. I find $.016$ is the nearest value to +produce right practical results. You must remember, too, +%-----File: 070.png-------------------------------------------- +%-----Folio: 55------------------------------------------------ +that the point which we have to keep at the same level is no +measurable one, such as the centre, or the bottom, or the +top of the bob, but the c.o.\ of the whole pendulum, and +we know nothing \textit{a priori} of its relation to the top of the tubes +of the total length of the pendulum, by which I always +mean down to the bottom of the bob; for all these have to +be found by trial. In the usual astronomical, or $1$-sec.\ pendulum +of this kind, it happens that the c.o.\ of the whole +nearly coincides with the c.g.\ of a bob of $9\times3$ or $3\frac13$ or +$4$~inches; but in large ones with heavy tubes it comes much +nearer to the top. + +Again, an iron bob may be considered as attached to the\markboth{ZINC AND STEEL COMPENSATION.}{ZINC AND STEEL COMPENSATION.} +iron tube anywhere, as they both expand equally; and +therefore, as fixed at the c.o. And a lead bob may in fact +be fixed at the c.o., and now generally is in the best +pendulums, in order to avoid the slower changes of temperature +in a thick bob than in tubes. But in commoner ones it +is hung on a flange or collar at the bottom, and then you +get the benefit of the expansion upwards of about $4\frac14$~in.\ of +lead (up to the c.g.\ or c.o.) in addition to the zinc tube, +which therefore has to be shorter than in the two other +cases. And further, if the rod is steel its expansion is at a +less rate than of the iron tube. + +Bearing in mind, then, that any practicable calculation is +only approximate, we may proceed with them as follows: +Let $l$ (as usual) be the length from the top of the spring to +the c.o.; $r$ the length to the bottom of the zinc tube, which +rests on the nut at the bottom of the rod; $z$ the zinc tube to +be found; $s$ the iron tube, which may or may not = $z$, as +just now explained; $c$ the height from the bottom to the +c.o. Then for a steel rod, and a lead bob resting on the +bottom, we must have--- +\[ +.016z + .0165 c = .0064r + .007s \qquad\ldots\mathrm{A} +\] +But now $s=z$, assuming all the bottoms to coincide, as +they always do nearly; and we know by experience $c$ to be +%-----File: 071.png-------------------------------------------- +%-----Folio: 56------------------------------------------------ +about $4$--$5$~in.\ for a $9$-in.\ bob, and $r$ about $44$ in a $1$-sec.\ pendulum, +and we may introduce them at once, bearing in +mind that the moment you translate one algebraical letter +into inches all the rest become numbers of inches only. +Then transposing all the unknown and known terms to +opposite sides, equation $\mathrm{A}$ becomes--- +\[ +(.016-.007)z=.2816-.0742=.2074, +\] +which gives $z=23$; but it is safer to begin with the tubes +a little longer, in case the compensation is not found quite +enough, as they are easy to shorten, but impossible to +lengthen. + +When the bob is fixed, or may be considered fixed, at its +c.o., the equations will be, first, for a steel rod and lead bob +fixed at its middle, +\[ +.016z=.0064r+.007s=.0064r+.007(s-c),\qquad\ldots\mathrm{B} +\] +and for iron rod and bob, +\[ +.016z=.007(r+2+c).\qquad\ldots\mathrm{C} +\] +Taking the same values as before for $r$, \&c., $\mathrm{B}$ will give +$28.3$~in.\ for $z$; which, however, is more than the length of +zinc in the Greenwich sidereal pendulum, adjusted to mean +solar time in order to compare it with others. I had my +own made full $28$~in., and I have no reason to think it is +over compensated, but I cannot say I have tried it specially +for compensation. The Greenwich one, with $z=26$ more +agrees with the tabular expansion $.017$ of zinc, but not +quite. + +The Westminster pendulum, I know by its weekly rate +for a year, is exactly compensated. It was made at first for +the $.017$ expansion, and was soon found to be under-compensated, +and we had to make new tubes. If you insert +in equation $\mathrm{C}$ the lengths given for that pendulum in the +table below, you will see that $.016$ almost exactly agrees with +the ascertained results, $c$ being of course $=r-l$. All the +heights of bobs in \hyperlink{weightstable}{this table} are reckoned to the top of the +dome, and my own, the third in the table, at Batch Wood, +St.~Albans, is slightly domed at the bottom also, and the +%-----File: 072.png--------------------------------------------- +%-----Folio: 57------------------------------------------------- +weights are those of the whole pendulum approximately, as +nothing respecting compensation turns on them. All the +measures are inches. + +\begin{table}[!hbtp] +\centering\label{weightstable}\hypertarget{weightstable}{} +\begin{tabular}{lr@{}lr@{}lr@{}lr@{$\times$}ll} +\textit{sec} & \multicolumn{2}{c}{$l$} & \multicolumn{2}{c}{$r$} +& \multicolumn{2}{c}{$z$} & \multicolumn{2}{c}{\textit{bob}\phantom{lead}} +& \parbox{6em}{Weight of\\pendulum.} \\ +$1\frac14$ & $61$ & & $68$ &$.5$&$48$ &$.5$&$14$&$8$ & \ \ $200$~lbs.\\ +$1\frac12$ & $88$ & & $98$ & &$68$ & &$15$&$9$ & \ \ $300$ \ '' \\ +$1\frac12$ & $88$ & & $96$ &$.5$&$61$ & &$14$&$8$ lead & \ \ $300$ \ '' \\ +$2$ & $156$&$.5$& $173$& &$125$& &$20$&$12$& \ \ $700$ \ '' +\end{tabular} +\end{table} + +The tube should have some holes or long slots (which +look better) on each side, to allow the air to reach the zinc, so +that both tubes may change their temperature simultaneously. +At Westminster the zinc weighs $67$~lbs., and the iron tube +$40$~lbs., and the rod $62$~lbs., out of the $700$~lbs.\ total weight. + +That is no longer the heaviest \index{Pendulums!heaviest in England}\markboth{THE HEAVIEST PENDULUMS.}{THE HEAVIEST PENDULUMS.}pendulum in England, for +Mr.~Godman, a clockmaker, organ-builder, and bicycle-maker +at St.~Albans, has put a $2\frac12$-sec.\ pendulum to the +clock which he made for St.~Peter's church there with a bob +of $9$~cwt., which he made in pieces called `shifters' in clock +weights, piled on each other like cheeses, to make it manageable +without machinery, which is practically as good as one +piece. And that has lately been exceeded by a $2$-sec.\ pendulum +of $12$~cwt.\ in St.~Nicolas's Church at Bristol, by +Mr.~Langford there. It is an odd coincidence that both +those makers had the boldness also to put the gravity +escapement a long way off the clock, because for local +reasons it could not be near the best place for the pendulum, +and with a gravity escapement that may be done very well. +I need hardly say that thin iron rods on each side of the +zinc tube may be used instead of the iron tube if you +like. + +In one or both those places there was this good reason for +so separating the escapement from the clock---and there may +be the same in others, especially where new gravity escapements +are put to old clocks---that the clock itself could not be +%-----File: 073.png-------------------------------------------- +%-----Folio: 58------------------------------------------------ +fixed firmly enough to carry the pendulum without yielding; +the importance of which has been noticed at p.~\pageref{resist}, and will +be proved farther on. But there was no difficulty in fixing +the escapement with the pendulum on iron brackets bolted +to the wall. + +Some persons appear to be misled \label{misled}\markboth{A MISTAKE ABOUT COMPENSATION.}{A MISTAKE ABOUT COMPENSATION.}by the well-known +necessity for a secondary or auxiliary compensation in +chronometer balances, which will be explained afterwards, +into supposing that no \textit{single} compensation of a pendulum +can be complete.\footnote{See \textit{Horological Journal}, April 1882} +But they depend on different principles, +and the errors of an uncompensated balance are twenty +times those of the commonest iron wire pendulum for the +same variations of heat, being $6$~sec.\ a day for $1^\circ$ of heat, +according to experiments. I may as well however explain +a little more about the matter. The complete mathematical +calculation for compensated pendulums does exhibit a very +small and insignificant error, which is never taken account of +in the ordinary calculations, and I only mention it to say +that it is so small, and is not the defect which the persons I +refer to have imagined. It is the effect on the moment of +inertia, and therefore on the time of the pendulum, of the +increase of length of all the rods and tubes, which of +course have all some weight of their own. The moment +of inertia of every such piece, say of length $z$~inches and +mass $\mathrm{Z}$ (which is $z$ times the mass of one inch long of such +rod or tube), of which the c.g.\ is $h$ from the suspension, +must then be $\mathrm{Z}\left(h^2+\frac{z^2}{3\times4}\right)$; and the moment of inertia +of the whole is the sum of all those quantities in the numerator +of the fraction $\frac{\sum{mr^2}}{\sum{mr}}$ or $l$. And to each of them has to +be added its own increment for heat, viz.\ for the rod and +the two tubes, and strictly even for the increase of length of +the bob\index{Bobs for pendulums}, and the resulting one for $h$ in each case; and the +%-----File: 074.png-------------------------------------------- +%-----Folio: 59------------------------------------------------ +squares of all these appear in the numerator, and their first +powers in the denominator. This is much too complicated for +calculation except by successive approximations. + +It is quite true that if a pendulum is not compensated at +all its errors increase more slowly than the temperature, +because the time varies only as the square root of the length, +while the length varies as the temperature. But that does +not the least affect the question of how it behaves when it is +compensated, so as to keep some point in the bob which +practically agrees with the centre of oscillation, or is at $l$ +from the top at the same level. I say `practically agrees,' +because it need not be very exact. For if the c.o., which +is at least approximately known, in the bob is kept at the +proper level, it is clear that every other point pretty near it +will be so too, since all the motions are absolutely very +small, and of course their differences are smaller still. +And that is the answer to this imaginary difficulty. I\markboth{PENDULUMS DIFFER FROM BALANCES.}{PENDULUMS DIFFER FROM BALANCES.} may +anticipate the balance compensation so much as to say that +besides the 20 times greater effect of a given change of temperature +thereon, the rate of a balance depends on an +external cause, viz.\ the varying strength of the spring, +enormously more than on the mere variation of the moment +of inertia, on which a pendulum rate depends, where also it +is partly corrected by gravity acting farther from the vertical +as the pendulum lengthens; \textit{i.e.\ }both the numerator and +denominator increase, but the numerator increases most, as +it contains squares. Gravity has nothing at all to do with a +balance, if it is balanced, as of course it should be. + +\subsection[Wood and Lead.]{Wood and Lead.}\label{subsec:Wood_and_Lead.}\markboth{WOOD AND LEAD COMPENSATION.}{WOOD AND LEAD COMPENSATION.}\index{Compensation of pendulums!wood and lead}\index{Pendulums!compensation!wood and lead}\index{Wooden!pendulums|(}---The same is the principle of the +simplest of all the compensation pendulums. According to +the tabular rates of expansion of lead and of a deal rod, it is +easily calculated that a bob $14$~in.\ high on a rod $46$~in.\ long +ought to make a compensated $39$~in.\ pendulum; for c.o.\ is +about $.4$~in.\ below c.g.\ of the bob when it is $14$~in.\ long, +so that the rod must be $39.14+6.6$, or nearly +%-----File: 075.png-------------------------------------------- +%-----Folio: 60------------------------------------------------ +$46$~in., and then we shall have $6.6\times.0016 = 46 \times.0023$, +which is right. Such a pendulum however was found to +be overcompensated, and at first one is inclined to conclude +that the expansion of deal has been overrated; but this was +with a dead escapement, and I am satisfied, for reasons +which will appear farther on, that such escapements contain +a sort of irregular compensation of their own; and I advise +no one to rely on a shorter proportion of lead bob than the +above for a wooden rod for other kinds of escapements such +as I shall describe. + +Wooden rods are generally and rightly used for large +clocks where compensated pendulums cannot be afforded: +but such clocks are exposed to great changes of temperature---often +as much as $40^\circ$ between winter and summer, +and to $30^\circ$ on the average of each; which would make a +difference of $20$~sec.\ a week with an uncompensated wooden +pendulum; whereas good public clocks ought to be guaranteed +to vary not more than $5$ or $6$~sec.\ a week at the +utmost---a much easier condition than $1$~sec.\ a day, because +one day may partially correct another. The Westminster +clock only varies $1$~sec.\ a week on the average, omitting casual +disturbances by men and thunderstorms. Wooden rods +should be as thin as will bear proper fastening at the ends, +which may be thicker for that purpose. Any thickness +which could be practically used and worked will bear ten +times the weight of any bob that would be used. They +should also be thoroughly dried and saturated with oil or +some antiseptic fluid, and varnished to keep them from +absorbing damp. Small ones are sometimes gilt; but even +then they are not to be relied on, and I believe all the best +makers agree that they are unfit for the highest class of +clocks, though they will do for all but the highest. The late +Mr.~Vulliamy used to use mahogany and teak instead of +deal, but I do not know whether it was from experience, +which alone can determine such a question. I should think +%-----File: 076.png-------------------------------------------- +%-----Folio: 61------------------------------------------------ +that the creosoting process would be a good one for wood +pendulums; but that also wants trying\index{Wooden!pendulums|)}. + +\subsection[Wood, zinc, and lead compensation.]{Wood, zinc, and lead compensation.}\label{subsec:Wood,_zinc,_and_lead_compensation.}\markboth{WOOD, ZINC, AND LEAD COMPENSATION.}{WOOD, ZINC, AND LEAD COMPENSATION.}\index{Compensation of pendulums!wood, zinc, and lead}\index{Pendulums!compensation!wood, zinc, and lead}---There are +places which invite the use of longer pendulums than can +well be made of iron and zinc only, because a very long +zinc tube requires to be very thick to be safe against bending. +If wood can be made trustworthy by creosoting it in +vacuum (as they do railway sleepers), or in any other +way a very good long compensation pendulum may be made, +with a zinc tube only about a third as long as an iron rod +requires, and only a fifth of the whole length of the pendulum. +\label{pndcalc}Suppose we want a $2\frac12$~sec.\ pendulum, of which the +simple length is $244.6$~in., with a cylindrical lead bob, say +$13\times10$~in., which will weigh $400$~lbs. The lead itself will +give us a little compensation due to the height of the c.o.\ above +the bottom of the bob. The problem can only be +solved by successive approximations, and they are too long +to go through here; but if you try the following figures +you will find them come as near as any pendulum can be +made without adjustment, especially as there is some uncertainty +about the expansion rate of wood, which I have +taken according to the above table, and also taken its specific +gravity at $.1$ of iron for simplicity or a cubic inch $= +.028$~lb., for a heavyish wood, such as teak or mahogany. +Take the total length to bottom of bob $253$~in., of which +about $240$~in.\ will be wood rod, with a section of $1\frac14$~in.\ diameter, +and it will weigh about $7\frac12$~lbs. First let us see +what length of zinc tube this will require, supposing the +bob to be hung by a pair of thin steel rods from a cross +head resting on the top of the zinc tube. There should +however be a smaller collar fitting the top of the tube, with +a slightly rounded top for the cross head to lie on, as there +would otherwise be a risk of its not bearing square on the +tube, but all on one edge. The expansion of so much of +the bob as lies below the c.o.\ of the pendulum will give us +%-----File: 077.png--------------------------------------------- +%-----Folio: 62------------------------------------------------- +some compensation; and as we have assumed that to be +the difference between $244.6$ and $253$, we have $8.4 \times .0165 += .138$, for the expansion of the lead upwards; and $240 \times +.0023 = .5552$ for that of the wood downwards. Calling +the zinc tube $z$ we have $.0172 z$ upwards. The steel rods +will be quite $2$~in.\ longer than the tube, and there are $13$~in.\ of +fastenings and spring; so that we must add at least +$(z + 15) .0064$ downwards. Equating the downward and +upward expansions, you will find that $z$ must be $50$~inches. + +\subsection[Smeaton's pendulum.]{Smeaton's pendulum.}\label{subsec:Smeaton's_pendulum.}\index{Compensation of pendulums!Smeaton's}\index{Smeaton's glass pendulums}---I have a clock with an old $1$-sec.\ pendulum +by Holmes\index{Holmes, an old clockmaker}\label{holmes}, a celebrated clockmaker of the +last century, with the following compensation, which was +invented by Smeaton, the great engineer. The rod is of +brass, $43$~inches long + $2$~inches of steel spring, and on a +collar screwed to the bottom of it rests a thin zinc tube $12\frac23$ +inches long, from the top of which is hung an iron tube of +the same length, by the end being merely turned over, and +on the bottom of that tube turned outwards rests a lead bob +also of the same length, enclosing the tubes, so that the +pendulum looks simply like a glass rod with a lead bob. +The c.o.\ of the pendulum is $6$~inches from the bottom of the +bob, and therefore the expansion of $6$~inches of lead + that +of the zinc tube upwards has to balance that of the glass +rod and the iron tube downwards, as you may calculate from +the table that it will very nearly. + +Another form of steel, zinc, and glass pendulum has been +proposed, with a glass tube instead of the iron one, which +would require a shorter length of zinc; but I see no +advantage in it over the common one. + +\subsection[Compound Bar compensation.]{Compound Bar compensation.}\markboth{COMPOUND BAR COMPENSATION.}{COMPOUND BAR COMPENSATION.}\label{subsec:Compound_Bar_compensation.}\index{Compensation of pendulums!compound bar}---Before going to the +mercurial pendulum, which requires more detailed examination, +we will dispose of a few others which require shorter +notice. This one (fig.~\ref{fig10}) is founded on the principle of the +compensated balance in watches. $\mathrm{WCW}$ is a compound +bar of brass and iron brazed together with the brass side +%-----File: 078.png-------------------------------------------- +%-----Folio: 63------------------------------------------------ +downwards. As brass expands more than iron, the bar will +bend upwards as it gets warmer and carry the weights $\mathrm{WW}$ +with it, and they may be so adjusted both by magnitude +and position as to raise the centre of oscillation as much as +the elongation of the pendulum rod lets it down. I cannot +give any details of the proportions, as this plan does not +appear to have been used in England except in experiments, +\begin{figure}[!htbp] +\centering +\caption{\sc Compound Bar Compensation} +\includegraphics[width=0.8\textwidth]{images/fig10.png} +\label{fig10} +\end{figure} +and old Mr.~Dent told me it was found inferior to the other +methods, over which I do not see that it has any advantage +except the facility of adjustment. It is said in Kater's +treatise to have answered in France, but the French seem to +prefer complicated compensations to simple ones. It might +however be used to complete the adjustment of another +compensation left imperfect for that purpose, in which case +the weights would only need to be very small. +%-----File: 079.png-------------------------------------------- +%-----Folio: 64------------------------------------------------ + +\subsection[Homogeneous compensation.]{Homogeneous compensation.}\markboth{HOMOGENEOUS COMPENSATION.}{HOMOGENEOUS COMPENSATION.}\label{subsec:Homogeneous_compensation.}\index{Compensation of pendulums!homogeneous}\index{Homogeneous compensation}\index{Pendulums!compensation!homogeneous}---All the compensations +I have yet mentioned require the use of at least two substances +of different expansibility; but there is one which +does not; and though it is practically of little or no value, +in any form in which it has yet been made or suggested, it +is worth while to describe the principle of it. If the +pendulum spring is drawn up through a close slit in the +cock as much as the pendulum lengthens by heat, its +effective length will remain the same; and this may be done +by various arrangements, of which the simplest is hanging +the spring to another cock above the slit one, set on the top +of a stiff bar long enough to expand upwards as much as the +pendulum rod expands downwards. This bar may be either +of the same or of a different metal from the pendulum rod +and its length will of course depend +on its material; or the slit +cock may be on one end of a lever, +of which the other is pulled down +by a wire of the same length and +metal as the pendulum rod. But +there is a serious objection to this +plan in every form; if the slit is +loose enough to let the spring slide +up and down through it, it is too +loose for the proper action of the +pendulum in a clock good enough +to require a compensation for temperature. +There is no other kind +practically worth describing. + +\begin{figure}[htbp] +\centering +\hypertarget{fig11}{\caption{\sc Ellicott's Compensation Pendulum}} +\includegraphics[width=0.5\textwidth]{images/fig11.png} +\label{fig11} +\end{figure} +\subsection[Ellicott's pendulum.]{Ellicott's pendulum.}\markboth{ELLICOTT'S COMPENSATION PENDULUM.}{ELLICOTT'S COMPENSATION PENDULUM.}\label{subsec:Ellicott's_pendulum.}\index{Compensation of pendulums!Ellicott's}\index{Ellicott's compensation pendulum}---There +is another bad one which is still +used in small French clocks, +though it has long ago been abandoned +in England, where it was +invented by Ellicott a clockmaker +%-----File: 080.png-------------------------------------------- +%-----Folio: 65------------------------------------------------ +in the last century. $\mathrm{AC}$ the main rod is of iron or +steel and it has a pair of levers set on a cross pin at +the bottom, of which only one $\mathrm{BCD}$ is shown \hyperlink{fig11}{here}: at +$\mathrm{A}$ there is a strong collar fixed to the rod, and between +that collar and the short arm of each lever stands a stiff +brass rod. The bob hangs by two pins, of which $\mathrm{D}$ is one, +on the long arms of the levers; and it is evident that by a +proper adjustment of the levers the bob may be made to +rise under the expansion of the brass rods just as much as +the expansion of the iron rod lets down $\mathrm{C}$, the axis of the +levers. But this action involves considerable friction at $\mathrm{D}$, +and the pressure on the ends of the brass rods must very +much exceed the weight of the pendulum, and it is said to +move by jerks, and is altogether inferior even to the old +gridiron, and much more to the zinc or mercurial pendulum, +besides being much more difficult to make properly. I +suppose they are only made because they have a kind of +scientific look to ignorant people, in clocks made to show +and to sell. + +\subsection[Mercurial compensation.]{Mercurial compensation.}\markboth{MERCURIAL COMPENSATION.}{MERCURIAL COMPENSATION.}\label{subsec:Mercurial_compensation.}\index{Compensation of pendulums!mercurial}\index{Mercurial compensation}\index{Pendulums!compensation!mercurial}---The principle of this, which +is used in all the best astronomical clocks (subject to a +remark to be made afterwards), is the same as of the wood +and lead; only, mercury being fluid requires a different mode +of calculation. For it must be in a jar which has some +sideway expansion of its own, and the rise of the mercury is +only the excess of its expansion in bulk over that which the +increased width of the jar allows it. The jars can only be +made of either glass or iron, as mercury amalgamates with +and so destroys any other metal that could be used. Although +iron is the best, glass is the most commonly used, either +from old habit or ignorance, and so we must consider both +of them, and we will take the glass first, and in both cases +neglect at first the weight of the jar itself: which by a +strange oversight was forgotten altogether by Francis Baily, +P.R.A.S., in a far more elaborate paper on this subject +%-----File: 081.png-------------------------------------------- +%-----Folio: 66------------------------------------------------ +(in vol.~i.\ of their Memoirs) than there is any need of, seeing +that after all a compensated pendulum can only be accurately +adjusted by trial, of itself or one exactly like it. It is +almost equally strange that this mistake was never discovered +for forty-four years, though the best clockmakers +and the late Mr.~Bloxam\index{Bloxam!his escapements}\index{Bloxam!corrected Sir G.~Airy}, who most thoroughly investigated +the theory of escapements in two papers in the 22nd and +27th vols.\ of the R.A.S.\ \textit{Memoirs}, had practically found that +the received height of mercury was insufficient. But they +all attributed it to the pendulum spring being stiffer in cold +than heat; which always appeared to me a most inadequate +explanation, considering the weakness of the spring in +proportion to the weight of a pendulum. In 1863 I had +to calculate the height for the iron jar of a pendulum +intended to weigh $40$~lbs., and finding the result far +beyond Baily's proportions, I looked carefully through his +paper and then found out the mistake\index{Baily, F.!his mistake on pendulum compensation}\index{Compensation of pendulums!Baily's mistake on}\markboth{BAILY'S MISTAKE ABOUT MERCURIAL COMPENSATION.}{BAILY'S MISTAKE ABOUT MERCURIAL COMPENSATION.}, and published the +correction of it in the \textit{Mechanics' Magazine}, of 5~Feb.~1864. +Another reason why it had escaped discovery was that dead +escapements, which nearly all astronomical clocks had, +contain (as I said before) an irregular kind of compensation +of their own, from the greater fluidity of the oil in warm +weather. It is remarkable that Hardy, the inventor of +another kind of escapement which I shall notice afterwards, +had calculated the height of his mercury rightly before +Baily's paper which everybody accepted. + +\begin{wrapfigure}{o}{146pt} +\centering +\hypertarget{fig12}{\caption{\sc A new kind of jar}} +\includegraphics[height=500pt]{images/fig12.png} +\label{fig12} +\end{wrapfigure} +Mercury expands $.1$ in bulk while the glass jar increases +$.0048$ in diameter, and $\therefore$ the sectional area increases as +$(1.0048)^2$ or $1.0096$ to $1$; $\therefore$ the mercury will rise $.1$--$.01$ +(say) or $.09$ of its own height. And since the c.g.\ of the +bob is very nearly at $\mathrm{O}$, let $x$ be half the height of mercury; +then $.09x$ must be $=.0066(l+x)$ for the steel rod, which is +usually carried down to the bottom of the jar in the form of +a long `stirrup,' on which the jar stands. That makes $x=3.1$~in.\ or +the height of the mercury $6.2$~in., which has to +%-----File: 082.png-------------------------------------------- +%-----Folio: 67------------------------------------------------ +be increased $.1$, or rather more for a reason which will +appear afterwards, and that is Baily's result---without +considering the weight of the jar. + +The weight of the glass jar and rod may be a $6$th of +the ultimate or corrected weight of the mercury; and about +much more height must be added for it, as it is evidently +much the same as if all the bob of pendulum were mercury, +but its rise only $\frac56$ of its real amount. And approximately +this is near enough, seeing that pendulums vary in their +proportions and must be finally adjusted +by trial; and glass jars are going out +of use for the best pendulums, which it +is now agreed ought to be much +heavier than the old two-inch wide +cylinder allows. + +The late Captain Kater\index{Kater!his mercurial pendulum}\index{Mercurial compensation!Kater's and Beckett's} used for +his experiments entirely glass pendulums, +which of course require a less +height of mercury than steel ones. +There is however no advantage in that, +but rather the contrary, as the jar must +be inconveniently wide to hold any considerable +weight, besides the difficulty +of handling a heavy glass pendulum +safely. Others have made the steel rod +go through the bottom of the jar; but +that is a bad plan, as it involves +stuffing to make the hole mercury-tight, +and allows no subsequent adjustment +without risk of destroying that +tightness. It is desirable however that +the rod should plunge into the mercury, +that they may take the same temperature, and +the best way of doing this with a glass jar would be +that shown in \hyperlink{fig12}{this drawing}. The shape of the jar speaks +%-----File: 083.png-------------------------------------------- +%-----Folio: 68------------------------------------------------ +for itself. The black ring round the neck is in two +pieces of brass, put on with a piece of thin leather to +improve the fitting, before the cap is dropped over it and +screwed to them with two or three screws to each half of the +ring. All other plans with the same object that I have seen +involved some cementing to the glass or stuffing, which is +not to be trusted. The small hole in the cap is for adjusting +the quantity of mercury according to experience. + +\subsection[Cast iron jars]{Cast iron jars}\markboth{CAST IRON JARS.}{CAST IRON JARS.}\ \label{subsec:Cast_iron_jars}are superior\index{Cast iron jars best for mercurial pendulums}\index{Mercurial compensation!Cast-iron jars for} to glass, first because they +are safer, and firmer on the rod, and the construction +simpler when done properly; secondly, because the mercury +can be heated in them to drive off any moisture or air +bubbles between the mercury and the jar, as is done with +barometers; thirdly, because (contrary to the common +notion) the extra height required for the weight of the jar is +an advantage, especially when you want a very heavy bob. +Calling the jar about a third of the mercury in weight, a +$40$~lbs.\ pendulum will have a jar only $3\frac12$~in.\ wide outside; +and one \textit{holding} $40$~lbs.\ of mercury will be $3\frac12$~in.\ inside, for +we shall find the mercury to be nearly $9$~in.\ high, and a +cubic in.\ of pure mercury weighs half a pound, and common +mercury weighs slightly less. The best construction, +and much cheaper than that generally used till lately, is +to cast the jar $\frac14$~in.\ thick, and twice as long as it need +be, in order to secure sound casting, as they do for cannon, +cutting off the `dead head;' turn the outside if you like +for appearance, or else japan it, and `enamel' the inside, +\textit{i.e.\ }coat it with glass, which stops up all the pores. The +cap is partially dropped into the top of the jar just turned +out to fit it and held by $4$ or $5$ screws through the jar. The +rim is marked out into divisions of $1$~sec.\ a day as described +at p.~\pageref{marks}, an index being fixed to the steel rod, which is +tapped and screwed through the cap exactly as in the last +figure, while the cross-head is to hold it steady when you +turn the jar for regulating. A $40$~lbs.\ pendulum made thus +%-----File: 084.png-------------------------------------------- +%-----Folio: 69------------------------------------------------ +costs less than old Mr.~Dent used to pay for the pendulum +alone without the mercury, on the old construction. This +is the construction now used by Mr.~Brock of 64, George +Street, Portman Square, who used to be with Dent, and has +done all except church clock work for me for some years. +Enamelling the jars was his idea. + +For an approximate calculation like the last, we have only +to use the expansion $.0066$ of cast iron instead of glass for +the jar, and that makes the rise of the mercury $.1-.0132$ or +$.087$ nearly. And assuming the mercury to weigh $3$ times +the jar and rod, the rise must be $\frac43$ times as much as if they +had no weight, or we may treat the rise of the mercury +relatively as $.065$, or $\frac34$ of its real amount. We know that +the height must be something over $8$~in., and the total length +of the pendulum nearly $43\frac12$, allowing the c.g.\ of the bob +to be a very little above $\mathrm{O}$\@. It is not worth while to +distinguish between the expansion of cast iron and steel for +the short length of the cylinder, and we may say that the +rise of the c.g.\ of the mercury, or the increase of $x$, or +$.065x$, must $=43.5\times.0064 =.2784$, and $\therefore x= 4.3$ +nearly. The assumption that $x$ is something over $4$~in., +for the mere purpose of finding the total length of the rod, +does not affect the result sensibly, as you will see if you try +it as an inch more or less. But this is not quite enough, +because it is not the c.g.\ but the c.o.\ that has to be kept at +the same height, and we must find how much less $h$ really is +than $l$ for we have only yet stated it approximately. If $b$ +is the radius of the cylinder when the weight of the rod is +insignificant, $lh=k^2$ or $ = k^2+\frac{x^2}{3}+\frac{l^2}{4}$.\ but $b$ is so small +compared with $h$ that that term produces no sensible effect. +Then putting $39.14$ for $l$ and either $4.3$ or $4.4$ for $x$ you +will find by solving the quadratic equation that $h=38.98$ +or $l-h=.16$~in.\ = $.036x$: $\therefore$ we must say $.964\times.065x$ +or $.0626x=.2784$ as before, and $\therefore x=4.44$, which +%-----File: 085.png---------------------------------------------- +%-----Folio: 70-------------------------------------------------- +makes the height of mercury just under $9$~in.\ in a jar which +weighs $\frac13$ of the mercury. I found mine not quite enough +compensated with $8\frac12$~in., and it is perhaps a little over +done with $9$---a widely different result from Baily's $6.6$ for +an iron jar. The calculation of compensation otherwise +than by this method of approximation runs into equations +of a high order and becomes unmanageable, and after all it +is better to adjust the height of the mercury finally by trial. +The longer the bob is, or the heavier the rod and compensation +tubes, the more the c.g.\ of the bob (not of the whole +pendulum) is below c.o. A very long bob is not desirable +on account of the increased resistance of the air\index{Air!resistance of to pendulum}, and +therefore it is not expedient to make the jar more than +about a third of the weight of the mercury, which is in every +way a convenient size. + +\markboth{MERCURIAL V.\ ZINC COMPENSATIONS.}{MERCURIAL V.\ ZINC COMPENSATIONS.}It is now thought at Greenwich that zinc and steel\index{Zinc!zinc and steel pendulums!better than mercurial} pendulums +are as good as mercurial ones. The normal sidereal +clock there has a zinc pendulum, and I am told that its daily +variation of rate is reckoned by hundredths of a second. +If this is so, it will be a considerable saving in expense, +inasmuch as there is no doubt that pendulums ought to be +much heavier than used to be the fashion. I must say that +the performance of the great Westminster clock goes far +to confirm the Greenwich opinion, for it has no discoverable +error of temperature. + +\subsection[Barometric compensation.]{Barometric compensation.}\markboth{BAROMETRIC ERROR OF CLOCKS.}{BAROMETRIC ERROR OF CLOCKS.}\label{subsec:Barometric_compensation.}\index{Barometric compensation}\index{Compensation of pendulums!barometric}\index{Mercurial compensation!Barometric}---It is evident that the +larger the bob is for its weight, \textit{i.e.\ }the less its specific +gravity, the more it will be resisted by the air, and the +smaller arc it will swing under a given force. We shall see +afterwards that all the escapement errors involve $\frac{\mathrm{W}h}{\mathrm{M}l}$ +divided by either $a^2$ or $a^3$, $\mathrm{W}h$ being the force that actually +drives the pendulum for a day, or weight $\times$ daily fall, after +deducting the friction, and $\mathrm{M}l$ the same as before, and +the arc from zero as usual. Therefore the larger $a$ is +%-----File: 086.png----------------------------------------------- +%-----Folio: 71--------------------------------------------------- +\textit{for a given weight} the better a great deal. Moreover, the +greater the density of the air\index{Air!barometric effect of} is, the more it diminishes +the effective specific gravity of the pendulum, viz., by +an amount $=$ sp.~g.\ of the air, which is variously estimated +at something near the $840$th of that of water, and therefore +about a $9000$th of an ordinary lead pendulum with +deal rod, or a mercurial one with a glass jar and the usual +appendages, which make its mean sp.~g.\ about $11$, water +being $1$. And this reduction is considerably increased in a +swinging pendulum by the air which it drags along with it. +Baily\index{Baily, F.!on barometric compensation} found, by comparing the times of free pendulums +of various kinds in vacuo and in air (see \textit{Phil.~Trans.}~of +1832), that the stationary loss of sp.~g.\ is sometimes +doubled by vibration. One specially curious result should +be noted, that a thin flat rod with a very elliptical section +was more affected in this way than a round one three times +as thick, although a lens-shaped bob was less affected than +a sphere of the same diameter and of course much heavier in +proportion to its surface, which so far gives it an advantage. +But we have no information whether the air affects a lens +more or less than a sphere of the same weight. + +Bloxam\index{Bloxam!on barometric error}\label{barerr} said in a note to his paper in the R.A.S.\ \textit{Memoirs} +of 1853 that Baily overlooked the fact that the current +produced in the descent of the pendulum prevents it from +being retarded in the ascent as much as it would have +been if the air had been at rest. He also always found the +circular error to be less than its theoretical value, and the +resistance of the air doubtless tends to produce this effect. + +Without going through Baily's various results it is enough +to say that he found pendulums of sp.~g.\ about $11$ gain +nearly $13$~sec.\ a day by being put into a vacuum; as that +was the daily increase of time ($+ \Delta\mathrm{T}$ or $-$ `rate') for an +inch rise of barometer, which is shortly called the barometric +error, apart from any circular or escapement error which +may accompany it. A small platinum ball hung by a wire +%-----File: 087.png----------------------------------------------- +%-----Folio: 72--------------------------------------------------- +gained $5$~sec.\ in vacuo, against $9\frac12$ for a lead one of the +same size (for a sphere is less affected than a cylinder); the +gain was nearly $14$ for a brass and $56$ for an ivory ball, and +$19$ for a round copper rod $.41$~in.\ thick and $5$~ft.\ long; +which last was $3$ times as much as its stationary loss of +specific gravity. But this effect on the rod as a whole +pendulum is insignificant when it carries a bob much heavier +than itself, as it usually does. + +\index{Large and small arcs}Baily\index{Baily, F.!on barometric compensation} found also by calculation that with an arc of $2^\circ\ 45'$ +the barometric error ought to be neutralized by the circular +error, \textit{i.e.\ }by the diminution of arc\index{Arcs of vibration in clocks} produced by the +increased density of the air. That result differs from the +one arrived at by Bloxam, but was verified by the performance +of the Westminster\index{Westminster clock!has no barometric error} clock during the year 1872, in +which I ascertained that the barometric error does not exist\label{fully}, +\textit{i.e.\ }is exactly neutralized, by the fact that applying any +correction, either $+$ or $-$, bearing a constant proportion to +the actual variations of the barometer, would have increased +the small average variation of the clock. I mention as a +fact, without professing to account for it, that Bloxam found +the barometric error of his clock \markboth{VALUE OF LARGE ARCS.}{VALUE OF LARGE ARCS.}less with an arc of $90^\circ$ than +with a considerably larger one. But I am decidedly in favour +of large arcs, especially for large clocks exposed to greater +variations of force than small ones, and I adopted one at +Westminster before I knew that it agreed with Baily's +calculation, which it has so remarkably verified. + +In order to avoid the barometric error,\markboth{BAROMETRIC COMPENSATION.}{BAROMETRIC COMPENSATION.} Mr.~Carrington +adopted the plan of a perfectly air-tight clock case\index{Air-tight clock-case}\label{airtight}, the +winder going through a `stuffing-box,' and then he +exhausts the air down to some given pressure a few inches +below the usual height of the barometer (see R.A.S.\ \textit{Notices} +of Nov.~1872). But this is much too troublesome for common +use. Dr.~Robinson\index{Robinson, Dr., on barometric compensation of pendulums}, of the Armagh Observatory, long ago +adopted the much simpler plan of compensating the error by +attaching a pair of very thin barometers on the right and +%-----File: 088.png----------------------------------------------- +%-----Folio: 73--------------------------------------------------- +\label{therm}left sides of the pendulum rod, above the bob (R.A.S.\ \textit{memoirs} +vol.~5). This evidently has the effect of raising a +small weight of mercury from near the bottom of the +pendulum to near the top when the density of the air +increases, and \textit{vice vers\^a}. But I shall presently point out +an inconvenience of this mode of doing it, and Dr.~Robinson +expressly says that the adjustments were troublesome. +The barometric error also varies considerably even between +clocks of nominally the same kind; so much that it is not +safe to assume any given amount beforehand, but it must be +ascertained from observation of that particular clock before +the calculations are made for correcting it. In the best +kind of astronomical clocks, with detached, or with gravity +escapements, but not dead ones, we may take the daily loss +($+\Delta\mathrm{T}$) for the present at $0.3$~sec.\ a day for an inch rise +of barometer, or that is the barometric error so far as it is +unconnected by others which attend it. + +In a paper on this subject in the R.A.S. \textit{Monthly Notices} +of 1873 I remarked that two barometers are unnecessary, +because a slight want of symmetry in (not across) the plane +of vibration cannot affect the pendulum. Moreover, with a +bob of the length required for an iron jar mercurial pendulum +there is not room to put the barometer tube entirely +above the jar. What we have to do is to find the position +and the diameter $2x$ of the barometer which fixed at some +given height will thus compensate a $39$~inch pendulum of +given weight, say $40$~lbs. It is tempting at first sight to +make the great mercury jar serve as a basin for the +barometer; but there are various practical objections to it, +and it is much better to use a syphon tube bent over the +side of the jar, in which therefore a `rise of barometer' of +$r$~in.\ will be only an absolute rise $r$ of $\frac12$~in.\ in the longer +leg, with a fall of $\frac12$~in.\ in the shorter. Let the mercury in +the long leg reach to $d$ below the top of the pendulum, and +in the short one to $b$ above the centre of oscillation: $\rho$, the +%-----File: 089.png----------------------------------------------- +%-----Folio: 74--------------------------------------------------- +specific gravity of mercury, is such that a cubic inch of +mercury is very nearly half a pound. Then, by the same +mode of calculation as at p.~\pageref{p50calc}, the little weight transferred +from $b$ to $d$ being $\pi\rho x^2 r$, +\[ +-\Delta\mathrm{T} = \frac{43200\pi\rho x^2r}{\mathrm{M}} +\frac{ld-d^2+b^2-lb}{l^2} \mbox{ sec.}, +\] +or putting $\frac14$ for $\rho r$ and $40$ for $\mathrm{M}$ we must have (nearly) +\[ +850 x^2 \frac{ld-d^2+b^2-lb}{l^2} = .3. +\] +Now $d$ must be substantially $> b$ for this to keep its sign, +and also to keep tolerably constant for different degrees of +rise. For simplicity let $b = 0$, and $\therefore d = 9$~in.: this gives +$2x$ or the diameter of the tube $.03$~in. If the barometric +error is $3$ times as much, $2x$ must be $\surd{3}$ times as much or +about $.05$; in either case rather a thermometer tube than a +barometer one. The tube, after being bent over and down +either the right or left side of the jar, had better be brought +up to the rod again, and the two branches joined there by +heat for strength, and tied to the rod by waxed thread rather +than any metal fastening. If the compensation is found to +be overdone the tube has only to be untied and raised, and +if insufficient it may be lowered, if room enough has been +left for it in the bend. + +As the barometric error never lasts long in one direction +it will very seldom be thought necessary to apply the compensation +to large clocks; and we have seen that it can be +otherwise materially reduced, if not absolutely corrected, as it +is in the Westminster pendulum, by making it swing a large +arc. If it were necessary to apply the barometric compensation +to a long pendulum the best way would be to put an +annular basin for the mercury on the top of the bob, round +the compensation tubes, and have a straight barometer +dipping into it. It may easily be calculated that the same +barometric error of $.3$~sec.\ a day with a $1\frac14$~sec.\ pendulum of +$200$~lbs., and also with a $1\frac12$~sec.\ pendulum of $300$~lbs. +%-----File: 090.png----------------------------------------------- +%-----Folio: 75--------------------------------------------------- +would be corrected by a barometer tube of about a sixth of +an inch diameter. The reason why the same tube is +enough for the heavier pendulum is that the rise of the +mercury is in a more effective place, \textit{i.e.\ }near the middle of +the pendulum. A $13$~ft.\ pendulum of $700$~lbs.\ with the +lower surface of the mercury $6$~in.\ above c.o.\ requires a +tube of $.3$ diameter for the barometric error of $.3$ sec: +another odd coincidence of figures. If the barometric error +in any particular clock is found to be $2$ or $3$ times as much +as this, $2x$ or the diameter of the tube must be $\surd{2}$ or $\surd{3}$ +as much as the above figures, and it must vary in the same +way with the $\sqrt{\textrm{weight}}$ of the pendulum. We shall have to +consider this further when we come to escapements.\index{Escapements of clocks} + +The normal sidereal clock at Greenwich\markboth{GREENWICH BAROMETRIC COMPENSATION.}{GREENWICH BAROMETRIC COMPENSATION.} has a barometric +compensation\index{Greenwich!barometric pendulum compensation at}\label{grenplan} of a more complicated kind. An independent +fixed barometer raises and lowers a \index{Magnet used for regulating clocks}magnet which attracts +the pendulum more or less according to its position. I must +say that seems to me a roundabout way of doing the +business, and I should have been inclined first to try a large +arc of $2^\circ\ 45'$ like that of the Westminster clock, and if that +is not sufficient, then the simple barometric tube compensation, +with the bottom of the tube near the bottom of the +bob. + +\section{RECOIL ANCHOR PALLETS.}\label{sec:RECOIL_ANCHOR_PALLETS.}\index{Anchor pallets}\index{Pallets!anchor}\index{Recoil!anchor pallets}\markboth{ANCHOR PALLETS.}{ANCHOR PALLETS.} + +The next important invention which followed that of +pendulums, and that very soon, was a pair of anchor-like +pallets moving in the plane of the scapewheel, instead of the +`vertical escapement' with pallets set across a crown wheel, +which pallets being very short required a long swing of +the pendulum to let the wheel escape. It is not indeed +absolutely necessary that crown wheel pallets should be +very short, and they would go with less friction if they were +long and the teeth of the wheel few; but the recoil would +be more violent, and they would require more careful adjustment, +%-----File: 091.png--------------------------------------------- +%-----Folio: 76------------------------------------------------- +and as a matter of fact they always were short. +Anchor pallets in the form in which they were first invented +either by Dr.~Hooke\index{Hooke, inventor of the balance-spring of watches}, whom I have already mentioned as +one of the claimants of the pendulum, or by Clements, a +London clockmaker of his time, had a recoil, no less than +the crown wheel pallets, but they could be made to escape at +as small an arc as you please. Fig.~\ref{fig13} is a drawing of the +recoil escapement, as it is always called, which is still used +in all the common +clocks in the world, +though it has long +been abandoned in all +that make any pretension +to great accuracy. + +\begin{figure}[hbtp] +\centering +\hypertarget{fig13}{\caption{\sc Anchor Pallets}} +\includegraphics[width=0.7\textwidth]{images/fig13.png} +\label{fig13} +\end{figure} + +In \hyperlink{fig13}{this figure} the +tooth $a$ has just escaped +from the left +pallet $\mathrm{A}$, and $b$ has +dropped on to pallet +$\mathrm{B}$; the pendulum is +therefore moving to +the left, and it will +not stop immediately +but will go on a little +farther and so make +the wheel recoil a +little, as you may see +clearly enough in any +old-fashioned house +clock with a seconds +hand: as it returns, +the wheel urges the +pendulum again to the +right and so gives the +%-----File: 092.png--------------------------------------------- +%-----Folio: 77------------------------------------------------- +\index{Escapements of clocks!recoil}\index{Recoil!escapements}% +impulse which is necessary to maintain its motion against +the resistance of the air and the friction of the escapement +itself; and then tooth $b$ escapes, and the tooth below $a$ falls +on $\mathrm{A}$ and the same action takes place there. You observe +that I have drawn the acting faces convex. For +some theoretical reasons they ought to be concave; but, +as very often happens in clockwork, the one practical reason +of friction preponderates the other way. Even if they are +made flat, the teeth always wear holes in them, though the +teeth are of brass and the pallets of steel, made as hard as +possible, and it is evident that the friction at the recoil is +much greater if the pallets are concave than convex. Moreover +it is always found that as the pendulum arc decreases +from any decrease of force in the clock, it loses and \textit{vice +vers\^a;} and concave pallets would not diminish this error, +but increase it. Some considerable persons stuck to this +escapement for some time after the dead escapement was +invented, being apparently misled by the fact that variations +of force produce less variation of the \textit{arc} in this than in the +dead escapement, because the friction of the recoil checks +the arc; but it does not follow that the variations of \textit{time} +are less: in fact it has been proved both by experience and +calculation that they are not. + +I may as well mention here that a `steady rate' means, +not necessarily that the clock is going \textit{right}, but that it is +going \textit{uniformly}, or regularly gaining or losing exactly the +same number of seconds a day or a week. The rate is +always written $+$ when the clock gains, and $-$ when it +loses; which you must remember is just the opposite of the +signs appended to the expressions for the various errors of +the time in the mathematical formulae; for when $t$ the time +of vibration of the pendulum increases, $dt$ is $+$, and the +clock loses and the \textit{rate} is too little or $-$. + +\subsection[Harrison's recoil escapement]{Harrison's recoil escapement}\markboth{A POSSIBLE RECOIL ESCAPEMENT.}{RECOIL ESCAPEMENTS.}\ \label{subsec:Harrison's_recoil_escapement}\index{Recoil!escapements!Harrison's}\index{Harrison!his clock escapement}had scarcely any friction. +It was invented by him when he was a working +%-----File: 093.png--------------------------------------------- +%-----Folio: 78------------------------------------------------- +carpenter in Lincolnshire. Any one who wants to see a +description of it will find one in the 7th edition of the +\textit{Encyclop\ae dia Britannica}; but I did not think it worth +while to repeat it in the 8th; nor here, as it is a mere +obsolete curiosity, and nobody else ever made it to answer, +even before better things were invented. If such a thing +were worth doing, it might be done much more simply by a +three-legged scapewheel, such as I shall describe as one +form of the dead escapement (at p.~\pageref{subsec:Three-legged_dead_escapement.}), but without the +horizontal or dead pallets there, and with the impulse pallets +set deeper and not in the same line, though parallel to the +pendulum. The impulse would be given with nearly as +little friction\index{Friction rollers!for clock barrel} as it is there, and the recoil would also have +very little; and if the force on the scapewheel were made +uniform, as it may be by a contrivance which I shall describe +for turret clocks, there is no reason why such an +escapement should not go very well, though the dead one +would go better. + +\subsection[Clock out of beat.]{Clock out of beat.}\markboth{CLOCKS OUT OF BEAT.}{CLOCKS OUT OF BEAT.}\label{subsec:Clock_out_of_beat.}\index{Clock out of beat, to regulate}---Most people seem to know that +the beats of a clock ought to sound equal in time, but most +people have a very erroneous notion that this depends on the +clock being set on a perfectly level surface, or standing vertically; +whereas that has nothing at all to do with it, unless +the crutch has been so adjusted that the pallets do escape at +equal angles when the clock case stands upright. No doubt +they ought to be so adjusted\index{Beat!adjustment of}, because a clock looks better +standing straight than crooked. In the best clocks the +beat is made adjustable by beat-screws at the bottom of the +crutch or fork. In common ones it is simply bent by hand +till the beats sound equal. Mr.~Dent made the fork pins +in turret-clock escapements to open with a spring, to prevent +the teeth being damaged in case they should be caught by the +escaping corner of the pallets when the clock is put back, or +the pendulum set going without the clock being wound up. +Each `prong' of the fork must have a separate spring, both +%-----File: 094.png-------------------------------------------- +%-----Folio: 79------------------------------------------------ +set against a stop between them. The crutch and everything +attached to the pallets ought to be kept as light as +possible, because they are in fact a pendulum, moving on +pivots instead of a spring, and therefore with much more +friction than the real pendulum. But a long crutch is +better than a short one, because less angular motion and +force is lost in the looseness or `shake,' which, as I explained +at p.~\pageref{shake}, must be left between the fork and the +pendulum. The proper way to try whether a clock is in +beat is to let the pendulum swing only just far enough +for the escape, and then you will easily hear if the beats are +unequal. + +When a clock with any kind of anchor escapement (which +all clocks may be assumed to have, unless the contrary is +known) sounds `out of beat,' it wants either one side lifting +or the crutch bending---which you please. If the right-hand +beat of the pendulum (\textit{i.e.\ }the blow on the left-hand pallet) +comes too quick, the right pallet escapes too soon or does +not go deep enough. Therefore the right side of the clock +wants lifting; for that is equivalent to moving the pendulum +and pallets to the left. Or it wants the fork or bottom of the +crutch bending to the right, which, remember, is making a +bend \textit{in} the crutch to the left, for that carries the pallets to +the left. Or if there is a beat screw in the fork, it wants +turning to the right or `setting up,' so as to move the +crutch to the left. And \textit{vice vers\^a}, if the left beat comes +too quick, the left side of the clock wants raising, or +the fork tending to the left, or the beat screw turning to +the left. + +I shall notice afterwards, under French clocks, a contrivance +which some of them have to make the beats gradually +adjust themselves. Recoil pallets---and dead ones too---should +only just clear the teeth, and when the points get +worn so as to allow more clearance the pallets should be +renewed. +%-----File: 095.png-------------------------------------------- +%-----Folio: 80------------------------------------------------ + + + + +\section{DEAD ESCAPEMENTS.}\label{sec:DEAD_ESCAPEMENTS.}\index{Dead escapements}\index{Escapements of clocks!dead}\markboth{THEORY OF THE COMMON DEAD ESCAPEMENT.}{THEORY OF THE COMMON DEAD ESCAPEMENT.} + +\begin{figure}[tbp] +\centering +\hypertarget{fig14}{\caption{\sc Dead Escapements}} +\includegraphics[height=0.7\textheight]{images/fig14.png} +\label{fig14} +\end{figure} +These are also of the anchor kind; but in fig.~\ref{fig14}, as in +fig.~\ref{fig13}, a tooth of the scapewheel has just escaped from +pallet $\mathrm{A}$ and another has just fallen on to pallet $\mathrm{B}$; but the +face on which it falls is very different, as the shape of the +teeth also is, but +that is only to +give room for +clearance, and in +both cases it is +only the point of +the tooth that +acts. \hyperlink{fig14}{Here}, you +see the face of the +pallet is divided +into two, and one +part is an arc of +a circle of radius +$\mathrm{CB}$ while the +other part is +much the same +as it was in the +recoil pallets. +The consequence +evidently is that +there is no recoil +here, and the +tooth lies \textit{dead} on +the circular face +$\mathrm{BE}$ (which is +therefore called the dead face) however far the pendulum may +swing, until it returns to $\mathrm{B}$, and then the tooth begins to act +on the impulse face and gives the impulse to the pendulum +exactly as in the other escapement. In the same way the +%-----File: 096.png--------------------------------------------- +%-----Folio: 81------------------------------------------------- +dead face $\mathrm{DG}$ of the other pallet is part of a circle with +radius $\mathrm{CD}$: the dotted line being the old recoil shape. + +This is the dead escapement, which was invented early in +the last century by Graham\index{Dead escapements!Graham's}\index{Graham's!dead escapement}\label{dead}, who invented also the mercurial +pendulum and the horizontal watch escapement; and +the great advantage of it is that although a slight increase +of force on the scapewheel increases the arc of the pendulum, +it does not sensibly increase the time, if the escapement is +properly made. This was first demonstrated mathematically +by Sir G.~Airy\index{Airy, Sir G.~B.!his calculations for dead escapements}, in the \textit{Cambridge Philosophical Transactions} +in 1827 (Vol.~III.\ p.~105), and it may be made tolerably +clear without any mathematics, as follows. If each tooth +could drop exactly on the corner dividing the dead and impulse +faces of the pallet, as at $\mathrm{B}$, it is clear that the impulse +on each pallet would begin and end when the pendulum is at +the same distance on each side of zero or the vertical. In other +words, as much of the impulse would be given while the pendulum +is falling as while it is rising, and therefore its gravity +would be increased on one side and diminished on the other +through equal arcs and during equal times, and therefore on the +whole the accelerating force on the pendulum, and therefore +its time of vibration, not altered. Neither would the friction +on the dead faces, if it were constant throughout, and if it +acted through the same arcs before and after zero, affect the +time directly; for while the pendulum is falling the friction +acts contrary to gravity, and with gravity while it is rising +after the escape has taken place. As it is always resisting +the motion of the pendulum it tends to diminish the arc; +and on the other hand, the impulse always tends to increase +it; so that here also there is counteraction to some extent; +but as the friction on the pallets does not vary in any +definite proportion to the force of the train, but sometimes +one way and sometimes the other, no useful relation of this +kind can be established. All we can say about the arc is +that it increases under an increased force or a diminished +%-----File: 097.png-------------------------------------------- +%-----Folio: 82------------------------------------------------ +friction, until the remaining friction on the pallets and the +resistance of the air stops the increase. + +Mr.~Bloxam\index{Bloxam!his escapements} came to the conclusion, in his elaborate +papers on escapements in vols.~22 and 27 of the \textit{Astronomical +Society's Memoirs}, that so far from the dead friction\index{Dead escapements!effects of friction on}\label{friction}\index{Friction!in dead escapements} +being a thing to be disregarded as constant and not +materially affecting the rate of the clock, as Mr.~Airy\index{Airy, Sir G.~B.!his calculations for dead escapements} had +assumed, it probably affects it more than all the other escapement +errors together in an astronomical clock\index{Astronomical clocks}\index{Clocks!astronomical} with even a +moderately good train, and in a way which it is impossible +to calculate on account of the different circumstances under +which it varies. It is evidently very improbable that the +friction can be made the same while the point of the tooth is +(as we may say) ploughing its way up the pallet during the +ascent of the pendulum and sliding down it in the descent. +Having said this I shall not attempt to deal any farther with +the dead friction, but its existence must be borne in mind as +capable of either mitigating or increasing the other errors, +as the case may be; and some idea of the magnitude of its +effects may be formed from this, that I remember the arc of +a new church clock of Mr.~Vulliamy's increasing from +$2^\circ 30^\prime$ to $30^\circ 30^\prime$ in the first year, from no other visible cause +than the self-polishing of pallets. And it afterwards fell off +again from the pins of the heavy scapewheel wearing hollows +in the pallets where they dropped. + +Now\markboth{THEORY OF DEAD ESCAPEMENTS.}{THEORY OF DEAD ESCAPEMENTS.} let us apply the same reasoning to the recoil escapement, +and we shall find that the result is just the opposite +from that in the dead. That part of the impulse which is +within the points where the teeth fall on the pallets is the +same as in the dead escapement, and therefore may be taken +not to affect the time; but in the ascending portion of the +recoil the force is acting with gravity, and so it is in the +descending portion. Whenever the force of gravity is increased +the time of a falling or swinging body is diminished; +and therefore on the whole any increase of the force of the +%-----File: 098.png-------------------------------------------- +%-----Folio: 83------------------------------------------------ +clock in the recoil escapement tends to make the pendulum +go faster. But the recoil resists the pendulum in rising as +much as it impels it in falling, and by means of the friction +resists it much more; and as the force through the other +portion of the arc, corresponding to the impulse in the dead +escapement, tends to increase the arc, they may so nearly +balance each other that an increase of clock weight may +produce no visible alteration in the arc at the very same time +that it is, as we may say, knocking the pendulum backwards +and forwards more rapidly between the same limits; whereas +the dead escapement just sends it so much faster as to make +the whole vibration take very nearly the same time while it +has to pass through a longer space---subject to the following +modifications. + +The first of them is this: the teeth cannot safely be made +to drop exactly on the corners of the pallets, but must have +a little of the dead face to fall upon; and therefore the angle +or arc of impulse before zero must be rather less than that +after zero, and therefore the tendency to increase the time +preponderates. For the same reason there is necessarily +rather more of the dead friction in the descent of the pendulum, +where it acts against gravity, than in the ascent, and so +that also tends to slowness. The greater this difference is, +or the higher up the dead faces the teeth drop, the greater +these causes of error are; and yet it is very seldom that one +sees a dead escapement whose maker appears to have had +the least idea of this fact; for I suppose if they had, they +would not make them as if they thought the right thing was +for the tooth to fall as far over the dead face of the pallets as +possible, instead of falling as near the corner as possible. + +Another modification is the circular error, which I have +already explained, and which acts in the same direction as +the one last mentioned, increasing the time with the increase +of the force and therefore of the arc. + +But there is another of the opposite kind; for when the +%-----File: 099.png-------------------------------------------- +%-----Folio: 84------------------------------------------------ +whole arc increases, that portion of the arc and of the time +during which the impulse or disturbance of the natural time +of vibration takes place becomes less in proportion to the +whole, and that diminishes the increase of time which would +otherwise be caused. + +And\markboth{EFFECTS OF FRICTION IN DEAD ESCAPEMENTS.}{EFFECTS OF FRICTION IN DEAD ESCAPEMENTS.} yet further, we have hitherto assumed that nothing +varies except the force of the scapewheel teeth on the +pallets, and the friction\index{Friction rollers!for clock barrel} which is due thereto. But the +friction on the pallets may and constantly does vary even +more than the force of the clock, and generally in just the +opposite direction; for as the clock and pallets get dirty +together, the force on the pallets decreases, which accelerates +the time, while the friction increases, which retards it; and +so on the whole it is by no means certain which result will +preponderate in the natural state of the clock, or by how +much; and the only certain way to get a steady rate out of +a dead escapement clock is to take as much care as possible +to keep the force and the friction constant; which is only to +be done, and can be done in small clocks with light wheels, +by very accurate workmanship, highly finished and hard +acting surfaces, and keeping them clean and just sufficiently +oiled, and above all a good pendulum, properly fixed. It is +necessary for this also that the two pivots of the great wheel +should be as nearly equal as possible, even at the cost of +making the back one larger than it otherwise need be. I have +frequently observed the arc to be sensibly greater at that +end of the week at which the string is at the back end of the +barrel, and therefore the weight acting principally on the +thin pivot. When a pivot has to be used for winding, it +must be made much thicker than is required for a mere +pivot, and I find it an improvement to let both the \label{largepivots}pivots +rest on friction wheels as large as there is room for. They +may both be on one arbor, but the front one must ride +loose, as they will not have quite the same velocity under +the different-sized pivots. The holes should be lengthened +%-----File: 100.png-------------------------------------------- +%-----Folio: 85------------------------------------------------ +a little downwards to make the pivots rest on the friction +wheels. + +Something more precise than the above general reasoning +is of course necessary for actually measuring the different +elements of variation of rate. \label{gairycalc}This is what Mr.~Airy\index{Airy, Sir G.~B.!his calculations for dead escapements} did, or +rather laid the foundation for doing, in the paper I have +already referred to; and taking it up at the point where his +calculations ended and his inferences began, I carried it +farther in two papers in the \textit{Cambridge Transactions} in 1848 +and 1852 (vols.~8, 9). His calculations are rather too long +and complicated to insert here, and they may be found in +\textit{Pratt's Mechanics} and perhaps some other Cambridge books; +so I will take them up at the same point here. + +The first important mathematical\index{Dead escapements!mathematical theory of}\markboth{MATHEMATICAL THEORY OF DEAD ESCAPEMENTS.}{MATHEMATICAL THEORY OF DEAD ESCAPEMENTS.} result arrived at by +Mr.~Airy was this: If $\phi$ is a disturbing angular force on a +pendulum when it is at the angle $\theta$ after zero (reckoned + +when it tends to increase $\theta$), and $\alpha$ the extreme arc, then the +increase of time of one vibration due to the disturbance, +which we will call +\[\Delta=\frac{1}{\pi g\alpha^2}\int\frac{\phi\theta\,d\theta}{\sqrt{\alpha^2-\theta^2}}\] +this integral being taken between the limits through which +the disturbing force acts. He also found a corresponding +formula for the increase of arc; but that is of no use towards +ascertaining how much the arc really will be increased by +the continual action of the disturbance, as it is soon limited +by friction and resistance of air in a way which cannot be +calculated. + +Before we can make any use of this value of $\Delta$ we must +see what $\phi$ is in the particular escapement. In order to do +this let us call the angle which the impulse face of each +pallet makes with the dead face $\delta$; then, since the tooth, +taken as a prolonged radius of the wheel, ought to be a +tangent to the dead face, $\delta$ will be also the inclination of the +%-----File: 101.png-------------------------------------------- +%-----Folio: 86------------------------------------------------ +tooth to the impulse face at the beginning of the impulse; +and for this purpose we may assume it to continue the same +throughout, though in fact it increases a little.\footnote{If $\kappa$ is the motion of the wheel on the pallet during each beat, the +angle of the tooth with the pallet face will be $\delta+\kappa+\beta+\gamma$ at the +end of the impulse on the down pallet, and $\delta+\kappa-\beta-\gamma$ on the up +pallet: $\kappa$ cannot be more than $5^\circ$ in a $30$-toothed wheel, and $\beta+\gamma$ is +never more than $1\frac12^\circ$; and as $\delta$ is generally about $60^\circ$, the variation is too small to affect these calculations materially.} Let $p$ be +the distance of each pallet from their arbor, and $\mathrm{P}g$ the +moving force of the clock-weight as it arrives at the points +of the scapewheel teeth, $\mathrm{M}l$ the mass and length of the pendulum +(which we may treat as its equivalent simple one for +this calculation); then the equation of motion will be +\[\frac{d^2\theta}{dt^2}=-\frac{g\theta}{l}+\frac{\mathrm{P}pg \tan\delta}{\mathrm{M}l^2},\] +since $g$ tends to decrease $\theta$ after zero where it is +, and $\phi$, +which represents the other term in the equation, does the +contrary. And as this term is independent of $\theta$, we have +\[\Delta=\frac{\mathrm{P}p\tan\delta}{\mathrm{M}l\pi\alpha^2}\int\frac{\theta\,d\theta}{\sqrt{\alpha^2-\theta^2}}.\] +The limits between which the integration is to be taken are +from $\theta=-\beta$, where the impulse begins before zero, to ++ $\gamma$, some rather larger angle where it ends after zero; +and the result will be +\[\Delta=\frac{\mathrm{P}p\tan\delta}{\mathrm{M}l\pi\alpha^2}\left(\sqrt{\alpha^2-\beta^2}-\sqrt{\alpha^2-\gamma^2}\right)\] +Now before going any farther we may see at once from +this, that if $\beta$ could be made $=\gamma$, \textit{i.e.\ }if the impulse could +be made to \label{impulse}begin just as much before as it ends after zero, +$\Delta$ would $= 0$, and we might save ourselves all further +trouble, and pronounce the dead escapement perfect, or +capable of being made perfect, so far as the impulse is concerned. +But it seems impossible to make $\gamma-\beta$ much less +%-----File: 102.png--------------------------------------------- +%-----Folio: 87------------------------------------------------- +than $30^\prime$ and in fact it is seldom made so little. And it will +not do to say that as $30^\prime$ only $= .00085$, that still leaves $\Delta$ +very small, and so the clock must go very well; for it must +be remembered, first that $\Delta$ only means the difference of time +of a single vibration out of the whole number $\mathrm{T}$ in a day; +and $\mathrm{T}$ is $86400$ for a seconds pendulum; and further, that +$\Delta$ is not after all the error of the clock between one day and +another, but only the difference between the time of a pendulum +swinging freely, and one kept going (or in mathematical +language \textit{disturbed}) by a clock escapement; and +therefore we shall have to go one step farther and find the +variation of $\Delta$ itself before we can know anything about the +going of the clock, since $\Delta$ cannot be made $=0$. But +before we do that it will be convenient to examine the value +of it as it stands. + +Let $h$ be the daily fall of the clock weight $\mathrm{W}g$. The drop +of the tooth at each beat, or the space through which the +moving force $\mathrm{P}g$ acts, ought to be nearly = the thickness of +the pallet $= p(\beta +\gamma)\tan \delta$; and this $\times\mathrm{T}$ (the number of +beats in the day) $\times \mathrm{P}g$ would $= \mathrm{W}gh$, but for the loss in +the friction of the train and the slight difference between the +actual drop of the tooth and its theoretical drop, which is +the thickness of the pallet. For the present purpose it is +of no consequence whether $\mathrm{W}$ is a little more or less, +and therefore we may neglect this difference and consider +$\mathrm{TP}p \tan\delta =\frac{\mathrm{W}h}{\beta+\gamma}$; and therefore the excess of time of +the clock pendulum over the free pendulum in the day, or +\[ +\Delta\mathrm{T}=\frac{\mathrm{W}h}{\mathrm{M} l \pi a^2} \frac{\sqrt{\alpha^2-\beta^2}-\sqrt{\alpha^2-\gamma^2}}{\beta+\gamma}.\label{correction1} +%**Transcriber's note: The original has a "/" in place of the "l" in the denominator; what follows makes it clear that an "l" was intended. +\] + +This is by no means a pleasant expression to deal with in +a general way; but it is not difficult to draw the necessary +conclusions from it, by assuming some particular values of +the different quantities, in accordance with what they +%-----File: 103.png--------------------------------------------- +%-----Folio: 88------------------------------------------------- +usually have in clocks. Although the error of the clock is +not represented by $\Delta\mathrm{T}$, but by the variations of it, still if we +can make $\Delta\mathrm{T}$ very small, the variations of it in the same +escapement will be smaller still; although it might happen, +and in another kind of escapement does happen, that the +variations are the least when $\Delta\mathrm{T}$ is at a maximum. But +there is no fluctuation of that kind here; and before going +any farther we may observe at once the advantage of a long +and heavy pendulum, seeing that $\mathrm{M}l$ is always fixed in the +denominator of the expression for the rate of the clock due +to the escapement. Moreover it is a fact that a long and +heavy pendulum requires very little (if any) more force $\mathrm{W}h$ +to drive it than a short and light one; the reason of which +is that the chief impediment to the motion of the pendulum +is the resistance of the air, and the resistance to the surface +does not increase in anything like the same proportion as +the weight, if the bob is of a good shape. Therefore $\mathrm{W}h$ in +the numerator need not be materially increased for a very +great increase of $\mathrm{M}l$ in the denominator, which is directly +equivalent to a very great increase in the accuracy of the +clock; and you will see that the same is true in the other +escapements. + +The next point to consider is the length of the arc of +impulse $\gamma+\beta$. As we have already seen that $\gamma-\beta$ ought +to be made as small as possible, but cannot be made less +than about $30^\prime$, let us take that difference as fixed, and see +whether the whole angle of impulse $\gamma+\beta$ ought to be large +or small compared with $a$. For simplicity of calculation, +let us try the effect of making $a$, $\gamma$, and $\beta$ in the proportions +of $8$, $7$, $5$, and $8$, $5$, $3$, and $8$, $4$, $2$, keeping $\gamma-\beta$ constant, +you observe. Substituting those values then in the above +formula for $\Delta\mathrm{T}$, you will find that it comes out in the proportions +of $20$, $14$, and $13$ in the three cases respectively. +In other words, it is better \textit{not }to make $\gamma$ nearly $= a$, or the +impulse to last nearly to the end of the arc; and it is satisfactory +%-----File: 104.png----------------------------------------------- +%-----Folio: 89--------------------------------------------------- +to know that this agrees with the conclusion which +old Mr.~Dent came to from observation, though it is contrary +to the practice of most other clockmakers, who seem to +prefer that sleepy-looking kind of escapement in which the +second-hand moves very slowly and the `excursion' of the +pendulum beyond the impulse is very little. He altered the +transit clock at Greenwich from a long to a short impulse +accordingly with good effect. + +Taking it then as proved that $\gamma$ the angle of impulse after +zero ought not to be nearly so large as $\alpha$, we shall be able +to simplify the above value of $\Delta\mathrm{T}$ by assuming that $\frac{\gamma}{\alpha}$ is so +small that all higher powers of it than the square may be +omitted. And then +$(\alpha^2-\beta^2)^{\frac12}-(\alpha^2-\gamma^2)^{\frac12}$ +may be expanded +by the binomial theorem, and only two terms of each expansion +need be taken, and the equation will assume the simple form +\[ +\Delta\mathrm{T} = \frac{\mathrm{W}h(\gamma-\beta)}{2\pi \mathrm{M}l \alpha^3}. +\] + +Mr.~Airy\label{gairyerr} concluded that the smaller $\gamma+\beta$ is, the better, +because it appeared in the numerator of his expression +for $\Delta\mathrm{T}$. But he left the expression for the force unreduced +into the terms involving the shape of the pallets, in which +we saw that $\gamma+\beta$ was lying hid, ready to come out in +the denominator of the fraction; and therefore, as it is +also in the numerator, it disappears altogether, on the +assumption that $\gamma$ is moderately small, as it ought to be; and +beyond that the above expression for $\Delta\mathrm{T}$ gives no information +as to the proper size of $\gamma$ or the length of the impulse. + +But then another consideration comes in. If you make +the impulse very short, the pallet will slip away before the +tooth has time to catch it; and the shorter the angle of +impulse is the more of it is lost by the inertia of the wheel +(which therefore ought to be light): in fact this is another +reason, besides the necessity for leaving a little of the dead +%-----File: 105.png-------------------------------------------- +%-----Folio: 90------------------------------------------------ +\label{folio90}face for the tooth to fall upon, why the angle $\beta$ at which the +impulse really begins cannot help being sensibly less than +the angle $\gamma$ at which it ends. Therefore also there is no use +in making the pallet corners sharp, for the tooth can +follow the pallet immediately, and it had better slide off +slightly rounded corner than drop on to the impulse face +with a kind of jump off a sharp corner. On the whole the +result appears to be that the escape had better take place at +something near $1^\circ$, and consequently the impulse should not +begin later than $30^\prime$ before zero, assuming $\alpha$ the extreme arc +to be $2^\circ$, which will make +\[ +\frac{\gamma-\beta}{2\pi}=\frac{1}{720},\; +\mbox{and therefore}\;\Delta\mathrm{T}=\frac{\mathrm{W}h}{720\mathrm{M}l\alpha^3} +\] +The value of $\frac{\mathrm{W}h}{\mathrm{M}l}$ varies very much according to the quality +of the clock: in the best astronomical clocks it may be +taken to be as little as $\frac{1}{30}$ to make the pendulum swing $2^\circ$. +As the force which arrives at the pallets is now represented +by $\mathrm{W}$, we must treat it as variable together with the arc; +and so, differentiating $\Delta\mathrm{T}$, we shall have +\[\label{eqp90} +d\Delta\mathrm{T}=\frac{1\,\textnormal{sec.}}{21600\alpha^3}\left(\frac{d\mathrm{W}}{\mathrm{W}}-\frac{3d\alpha}{\alpha}\right)=1^s2\left(\frac{d\mathrm{W}}{\mathrm{W}}-\frac{3d\alpha}{\alpha}\right) +\] +If there was any definite relation between the ratio of +increase of the force and the arc, this would give a very +easy calculation for the variation of rate so far as the +impulse is concerned. But there is not, as it depends on +the state of the different parts of the clock. Sometimes it +may happen that the proportionate decrease of the arc from +increased friction is just $\frac13$ that of the force which arrives +at the escapement, and then there will be no variation in the +rate. Sometimes you may increase the clock-weight considerably +without making much impression on the arc, if the +pallets are dirty; and generally in an artificial experiment +of that sort, except while the arc is smaller than $2^\circ$, $\frac{d\alpha}{\alpha}$ is +%-----File: 106.png-------------------------------------------- +%-----Folio: 91------------------------------------------------ +likely to be less than $\frac{d\mathrm{W}}{3\mathrm{W}}$ and then the clock will lose, +even independently of the circular error which tends the +same way and which we know would be $10800\,\alpha\, d\alpha$ if it +were not in great measure corrected by the pendulum +spring, though it is very difficult to say how much. On the +other hand if you clean and oil the pallets alone the arc is +sure to increase, and yet the clock will generally gain, +because the increase is chiefly due to the diminution of the +dead friction, which (as I explained before) would diminish +the time, independently of the term $-\frac{3d\alpha}{\alpha}$ belonging to the +effect of the impulse, which retards less on a long arc than a +short one. + +\subsection[Half-dead escapement.]{Half-dead escapement.}\markboth{HALF-DEAD ESCAPEMENTS.}{HALF-DEAD ESCAPEMENTS.}\label{subsec:Half-dead_escapement.}\index{Escapements of clocks!half-dead}\index{Half-dead escapements}---In order to counteract the +disposition of dead escapement clocks to gain as the arc +decreases under ordinary circumstances (which, you remember, +is the opposite of what happens in the recoil escapement), +Berthoud\index{Berthoud on escapements}\index{Half-dead escapements!Berthoud's} a celebrated French clockmaker invented +the plan of making the dead faces not quite dead, but with a +slight recoil, so as to get a sort of compromise between the +effects of the two escapements. Large clocks, which are +subject to great variation of train force, are distinctly better +when so made than with quite dead pallets. Moreover the +variations of the arc are rather checked by the half-dead +pallets. The largest variations of arc I ever saw in a good +clock, were in one of Mr.~Vulliamy's\index{Vulliamy, Mr.}, who used to take +particular pains to make his pin-wheel pallets quite dead by +cutting them out of a turned cylinder of radius equal to their +distance from the arbor. A very slight recoil, such as you +can hardly see in the motion of the wheel, is enough. But +the best authorities are of opinion that a purely dead escapement +is better in astronomical clocks, where the friction and +variations of force are much less than in turret clocks. + +\subsection[Loseby's isochronal spring.]{Loseby's isochronal spring.}\markboth{FAILURE OF ISOCHRONAL SPRING.}{FAILURE OF ISOCHRONAL SPRING.}\label{subsec:Loseby's_isochronal_spring.}\index{Isochronal spring, Loseby's}\index{Loseby's!isochronal spring}---Another plan for isochronising +%-----File: 107.png-------------------------------------------- +%-----Folio: 92------------------------------------------------ +the long and short arcs\index{Dead escapements!large and small arcs} was invented by Mr.~Loseby +a chronometer maker in London, and exhibited in +1851. A large circular loop of very thin steel wire is +on a stud from the back of the clock case, say on the right +side of the pendulum, so as to embrace the rod nearly half-way +down, just catching it as it swings to the left side of the +loop. The farther it swings of course the more it has to +stretch the loop, and the resistance increases in a high ratio +with the degree of elongation; and it seems that this can be +adjusted so as to isochronise the pendulum in a dead escapement +under great variations of the force of the train. So at +least the Astronomer Royal reported after trying some experiments +on it. But it at once occurred to me that such +experiments proved nothing as to the effect of such a spring +on an astronomical clock in its natural state, in which the +variations of the pallet friction are generally greater than +those of the train and produce the opposite effect, as is evident +from the second term of the equation at page~\pageref{eqp90}, and +then the spring would make it worse. As chairman of the +Horological Jury of the Exhibition, I wrote to this effect to +Mr.~Airy, who then made a different class of experiments, +this time by artificial variations of the pallet friction, and he +issued a fresh report in 1853, that `Mr.~Loseby's invention +was \textit{not} perfectly successful.' + +\subsection[Large and small arcs.]{Large and small arcs.}\markboth{LONG AND SHORT ARCS.}{LONG AND SHORT ARCS.}\label{subsec:Large_and_small_arcs.}\index{Arcs of vibration in clocks}\index{Large and small arcs}---There is one more point in +the theory of dead escapements which requires particular +attention. You observe that $\alpha^3$ appears in the denominator +of the expression for the variation of impulse rate, and so it +would in that belonging to the dead friction. That is, the +three resisters of disturbance of the rate are the weight of +the pendulum, its length, and the cube of its arc. But the +arc in any given clock in its normal state of friction varies in +some irregular way with the force of the train, \textit{i.e.\ }the clock-weight +and its fall; and an increase of the weight in any +given ratio may or may not increase the arc in the cube root +%-----File: 108.png----------------------------------------------- +%-----Folio: 93--------------------------------------------------- +of that ratio: but so long as the arc is small, its increase +will most likely be a great deal more than that; and if so +there is a clear advantage in increasing the weight; subject +always to this memento, that the circular error also increases +with the \label{arc}arc. I have a note of having once cleaned a regulator +and oiled it with sperm oil, and the arc increased from $1^\circ\ 45'$ +to $2^\circ\ 15'$, and yet I found no material alteration in the rate. +I am satisfied that the very small arcs which used to be the +fashion are a mistake, and that from $2^\circ$ to $2^\circ\ 40'$ is much +better. A writer in \textit{H.~J.}~xix.~125 said that, in consequence +of this advice, he had increased the weight and arc of an +Austrian clock, which had almost reduced its errors from +minutes to seconds. + +\subsection[Importance of firm fixing.]{Importance of firm fixing.}\markboth{STEEL OR BRASS SCAPE-PINS.}{STEEL OR BRASS SCAPE-PINS.}\label{subsec:Importance_of_firm_fixing.}\index{Pendulums!importance of firm fixing}\index{Suspension of pendulums}---Whatever increases the +arc without increasing the weight is obviously a great advantage; +and the principal things which do that are diminution +of friction and inertia of the train, and steadiness of suspension +of the pendulum. I cannot give a better proof of how +much the arc depends on that, than the effect of hanging the +Westminster pendulum on its proper cock, which is a large +cast iron bracket built into the wall; the arc increased full +$45'$ over what it had been in the factory, where it was hung +on what seemed a perfectly firm support, a strong timber +frame built up from the ground. Even smaller pendulums +generally increase their arc from about $2^\circ$ in the factory to +$2^\circ\ 30'$ as soon as they are properly fixed to a good wall on +stone corbels or iron beams. This shows the extreme badness +of the common way of fixing large clocks on a \label{stool}stool or +timber frame set upon a wooden floor in a tower, and +common clocks by a single nail through a thin back of the +case (see p.~\pageref{fixing}). + +The friction is of course only to be diminished by proper +shaping of all the acting surfaces and making them of the +best metals for working together. Brass wheels and steel +pinions, and also brass teeth and steel pallets\index{Dead escapements!various materials for pallets} seem to be the +%-----File: 109.png----------------------------------------------- +%-----Folio: 94--------------------------------------------------- +best in small clocks, although there are other cases where +steel and steel act better together, as in the horizontal watch +escapement. In large clocks cast iron wheels and pinions +suit each other better and wear less than anything else, as +has long been known by the great machine makers, though +scarcely any clock-makers choose to believe it, and of course +refuse to try, being what they call `practical men,' who +understand by the word \textit{experience} the constant use of one +thing or one way of doing it and absolute ignorance of any +other. Mr.~Vulliamy\index{Vulliamy, Mr.} used to think steel scapewheel teeth +or pins better than brass ones, and they have been occasionally +used by other people, but I think are now generally +disused. At the same time it is certain that steel pins do +best in my escapements which will be described presently +In the best clocks the pallets\index{Pallets!various materials for} have jewels\index{Jewelled pallets}, generally sapphires, +let in for the teeth to act upon, and it is quite ascertained +that brass teeth suit them best. + +\markboth{PALLETS AND SCAPE-WHEELS.}{PALLETS AND SCAPE-WHEELS.}When the pallets are \index{Pallets!steel}\index{Steel!pallets}steel it is scarcely necessary to say +that they ought to be as hard and as smooth as possible; +especially the former, for if they are not smooth at first the +teeth will make them so in time, but soft ones will never get +hard. They are hardened like files, by being heated red hot +and cooled suddenly, and not tempered at all. The sharp +hollow corners, which are considered by ignorant people a +sign of fine work, are apt to crack in hardening, and as such +a corner is always a weak place besides, they ought not to +be so cut out; and the same remark applies to every hollow +corner in every part of a machine, unless something else has +to fit into it. Probably it is best to heat the pallets in lead +melted red hot, and cool them in oil, which is now adopted +for some larger steel things, as I have seen pallets twisted +in the ordinary mode of hardening. The same may be said +of pivots and pinions, except that they are tempered and not +left quite hard. + +\subsection[Aluminium bronze.]{Aluminium bronze.}\markboth{ALUMINIUM BRONZE.}{ALUMINIUM BRONZE.}\label{subsec:Aluminium_bronze.}\index{Aluminium bronze}\index{Wheels for clocks!aluminium bronze for}---The alloy of copper and aluminium, +%-----File: 110.png-------------------------------------------- +%-----Folio: 95------------------------------------------------ +to which this name is given, seems to me very +superior to either brass or gunmetal for many horological +purposes. It is stronger, much more elastic, smoother, far +less liable to tarnish, \textit{i.e.\ }to decay; and for small articles, +such as the scapewheels of clocks, and all the wheels of +chronometers and watches, the excess of the cost over brass +would be insignificant. It solders well with either common +`silver solder,' or another with less silver in it. Mr.~J.~F.~Stanistreet, of +Liverpool, an amateur clockmaker, told me he +had used it; and it is used for cheap watch cases. + +\subsection[Weight of scapewheel.]{Weight of scapewheel.}\markboth{WEIGHT OF SCAPEWHEEL.}{WEIGHT OF SCAPEWHEEL.}\label{subsec:Weight_of_scapewheel.}\index{Scape wheels!bad weight of}\index{Wheels for clocks}---It is important to keep the +upper wheels in the train, and particularly the scapewheel, +as light as possible. It is certain that every blow you hear +in the working of a machine indicates some loss of force, +and wearing out of surfaces, and that the machine would be +better without it---unless it is a hammer; and the heavier +the blow is, of course the worse it is. In clock escapements +a sudden stop and a blow of some amount is inevitable; but +there is no reason why it should be increased by making the +scapewheel three or four times the necessary size and +weight, and the drop of the teeth more than is necessary to +clear the pallets. I have already mentioned also that the +greater the inertia of the scapewheel, the longer it is in +effectively catching the pallet, although you cannot see the +interval. I have seen church clocks, not merely old ones +like that of St.~Paul's Cathedral, but new ones, with scapewheels +a foot in diameter, and weighing several pounds, and +you may sometimes hear the thump of every beat in the +churchyard. Bloxam calculated that a pendulum of $15$~lbs.\ does +not require half as much force as a marine chronometer, +if a great deal of it were not wasted in having to start a +heavy train from rest at every beat; otherwise its weight +would be of little consequence. Mr.~E.~D.~Johnson has made +regulators with very light and small trains, in fact, little more +than chronometer trains, and he says they answer perfectly. +%-----File: 111.png-------------------------------------------- +%-----Folio: 96------------------------------------------------ +I may observe here that the rims of wheels (in which most +of the inertia lies), and indeed the whole wheel, may be +made materially lighter with $5$ spokes than with $4$, because +the arcs are shorter. Sometimes, in the most expensive +clocks, they are made with $6$; but $5$ spokes leave very little +more than $\frac16$ of the rim open, on account of their own +thickness, as you will see in p.~\pageref{5spokes}; and they seem to me +quite close enough for clock-wheels; and of course every +unnecessary spoke adds unnecessary work and expense; that +number is used throughout the Westminster clock and many +others now. Here too, as in the pallets, and indeed in every +possible place, the modern workman who is taught to think +`high finish'\index{Finishing@`Finishing' too much undesirable} the perfection of work, or in other words to +display as much finger work and as little head work as possible, +files or `crosses out' the corners as sharp as possible +instead of leaving them rounded a little, which would make +the wheel stronger with no appreciable increase of weight. +I believe it would be a very good rule that a sharp hollow +corner ought never to be allowed anywhere, unless something +has to fit into it, as it always makes a weak place, in +which, if anywhere, things crack in casting, fly in hardening, +or break in working, and moreover is so easy to do, that as +a proof of good workmanship it is contemptible, even if it +were not really bad besides. + +\subsection[Length of pallets.]{Length of pallets.}\markboth{LENGTH OF PALLETS.}{LENGTH OF PALLETS.}\label{subsec:Length_of_pallets.}\index{Dead escapements!length and arrangement of pallets}\index{Pallets!length of}---A French clock-maker in the +Exhibition of 1851 had an apparatus for illustrating the +superiority of moderately short pallets over long ones. It +does not require much apparatus to prove that; for assuming +the scapewheel to be of any given size, it is evident that +the farther the pallets are from their arbor the longer is the +run of the teeth upon them, and the more friction there is +affecting the pendulum. The usual proportion seems to be +to make the distance of the pallets from their centre = the +wheel's diameter (generally $1\frac78$~inches in regulators), and +embracing $10$ teeth, \textit{i.e.}\ from one dead face to the other. +%-----File: 112.png-------------------------------------------- +%-----Folio: 97------------------------------------------------ +This seems to me rather an unnecessary length, and I +should prefer $9\frac12$, or half a tooth under instead of over one +third of the number in the wheel. + +Various rules\label{palletrules} and calculations have been given in books +for the length and position of the pallets, according to the +conditions which their authors thought most important. I +think the most important of them all is to keep the dead +friction a minimum, consistently with a sufficient length of +pallets to prevent much force being wasted in clearance. +The way to do this is to make the dead faces always perpendicular +to the pressure of the teeth, \textit{i.e.}\ to the circumference +of the wheel. Assuming $10$ tooth spaces, or $\frac13$ of +the wheel, to be embraced from one under face $\mathrm{B}$ to the +other $\mathrm{A}$ (fig.~\ref{fig14}) as usual, \textit{i.e.}\ $9\frac12$ spaces from one dead face +$\mathrm{B}$ to the other $\mathrm{D}$, the pallet centre $\mathrm{C}$ will be the intersection +of two tangents to the circumference at $\mathrm{B}$ and $\mathrm{D}$\@. That makes +the distance of centres $d=1.84r$ ($r$ the radius of the wheel), +and $p$ or $\mathrm{CB}$ and $\mathrm{CD}=1.54r$ which is quite enough. As +one dead face is above and the other below, the lengths of +the pallets as a whole are unequal, the appearance of which +the clock-makers dislike, though it is of no consequence. If +you determine to have them equal, and make $d=2r$, as is +usual, and $\mathrm{BC}$ and $\mathrm{AC}=1.73r$, the pressure will be perpendicular +to the dead face $\mathrm{B}$, but not quite so to $\mathrm{D}$: if you +make $d= 1.72r$, and $\mathrm{FC}$ and $\mathrm{DC}$ each $=1.4r$, the dead +face $\mathrm{D}$ will be right and the other wrong; if $d$ is anything +between those sizes, one pallet will be rather better and the +other rather worse, supposing the lengths to be equal. + +\markboth{CONSTRUCTION OF DEAD PALLETS.}{CONSTRUCTION OF DEAD PALLETS.}The unimportance of equality of length of impulse on the +two pallets is evident from the fact that in some kinds of +escapements, as we shall see afterwards, there is only one +impulse pallet, and there is no loss of force thereby. The +only way in which force is lost, apart from friction, is in +the drop of the teeth from the end of one pallet to the face +of the other, or in other words, the clearance, which is +%-----File: 113.png-------------------------------------------- +%-----Folio: 98------------------------------------------------ +necessary to prevent the point of the returning pallet from +catching the top of the tooth which last escaped from it. +Consequently the thickness of the pallets has to be rather +less than half a tooth space. The slopes or impulse faces +may be adjusted thus: Fix an index $\mathrm{CP}$ to the pallets, and +put them and the wheel on centres without shake at the +assumed distance on a board. First file down $\mathrm{B}$ till there is +only just enough dead face to receive the tooth when the +escape takes place at $\mathrm{A}$, and leave the corner $\mathrm{F}$ at first +obviously too sharp, \textit{i.e.}\ rather too long, and $\mathrm{A}$ too blunt +or the corner $\mathrm{G}$ nearly square. Mark where the index +points at the moment of escape, and mark $2^\circ$ from that +which $= .035\ \mathrm{CP} = \frac14$~in.\ if $\mathrm{CP} = 7$~in. File away $\mathrm{F}$ +till the next escape takes place at that $2^\circ$ and then reduce +$\mathrm{G}$ till that pallet has only just enough dead face for the +tooth to fall on. This will make each escape take place at +$1^\circ$ from zero of the pendulum. + +The teeth of dead scape wheels are often made of a most +absurd shape, the weakest and heaviest possible, viz.\ with +the sides radial, and therefore thinnest at the root, and with +a heavy shoulder, and also often too long. The best form +is a simple taper. What are called \textit{club} teeth, with a lump +at the end, were supposed to hold the oil better, which is +apt to run away from the points, but they seem to be +generally abandoned. In the best clocks the pallets are +jewelled with sapphires, which require scarcely any oil. + +\subsection[Pin-wheel escapement.]{Pin-wheel escapement.}\markboth{PIN-WHEEL ESCAPEMENT.}{PIN-WHEEL ESCAPEMENT.}\label{subsec:Pin-wheel_escapement.}\index{Dead escapements!pin-wheel}\index{Escapements of clocks!pin-wheel}\index{Pin-wheel escapement}---There is a very convenient +form of the dead escapement for large clocks, which goes by +this name. It is said to have been invented by Lepaute\index{Lepaute's pin-wheel escapement} in +1753, but also by Whitehurst of Derby. The teeth are pins +of brass wire set in the face of the wheel, and the upper +half of each cylinder cut off, as it could not act and would +only waste room in the drop. But I introduced the plan of +cutting off a small slice of the under or acting side also, as +shown in fig.~\ref{fig15} (next page), because, unless that is done, +%-----File: 114.png-------------------------------------------- +%-----Folio: 99------------------------------------------------ +you must either have the wheel very large, or the pins very +thin or long pallets, or a large angle of impulse, which are +all objectionable. The advantages of this escapement are, +that it does not require so much accuracy of construction as +the other, and less is lost in the drop, and therefore you can +get many more pins than teeth to act in a wheel of given +size, which often saves one wheel in the clock. If a pin +\begin{figure}[htbp] +\centering +\caption{\sc Pin-wheel Escapement} +\includegraphics[width=324pt]{images/fig15.png}\label{5spokes} +\label{fig15} +\end{figure} +%-----File: 115.png-------------------------------------------- +%-----Folio: 100----------------------------------------------- +\index{Clocks!silent beat}\index{Escapements of clocks!silent}\index{Pallets!silent}%Could not find reference in this page +gets damaged it is easily replaced, whereas if a tooth is +damaged the wheel is ruined. The blow on both pallets +being downwards, the action is more steady than it sometimes +is in the other. The pallets are best made with their +cross section rather convex, and also `half dead.' The scapewheel +of the large clock at King's Cross\index{King's Cross clock}, by which the +Great Exhibition time was kept, and of many others made +from my design, is only $4$~inches wide, with $40$ pins in it. +The lower pallet should be the inner one, and the higher +one outside the wheel, because this makes the action of the +teeth on both of them more direct. If the pallets are on +opposite sides of the wheel with two sets of pins, they may +be alike. The pins must then be at alternate places. + +\subsection[Pin pallets.]{Pin pallets.}\markboth{OTHER DEAD ESCAPEMENTS.}{OTHER DEAD ESCAPEMENTS.}\label{subsec:Pin_pallets.}\index{Pallets!pin}\index{Pin pallets}---Some of the best small French clocks now +have an escapement which at first sight may be confounded +with the pin-wheel escapement, +but is really quite different. +The scape-wheel is like a common dead one, and it is set (merely for show) in front of the dial; +but the pallets are +made of semi-cylindrical\label{ruby} ruby pins; the effect of which is +that the half-dead part of the action is not on the points of +the teeth but on their faces. The impulse is the same as on +common jewelled pallets, only with the faces round instead +of flat. I have seen an old clock with similar pin pallets, +made of a thick bristle held at both ends, for the sake of +silence, and the fork also. + +\subsection[Single-pin escapement.]{Single-pin escapement.}\markboth{SINGLE-PIN ESCAPEMENT.}{SINGLE-PIN ESCAPEMENT.}\label{subsec:Single-pin_escapement.}\index{Single-pin escapement}\index{Escapements of clocks!single pin}---This very simple and neat-looking +escapement has been several times re-invented. But +I believe the only person who ever made it really succeed, +from better attention to the proportions, was the late +Mr.~C.~Macdowall\index{Dead escapements!Macdowall's}\index{Macdowall's!single-pin escapement}\label{macd}, a very ingenious clockmaker, who died +in 1872 at the age of eighty-two. +There is an interesting +memoir of him in the \textit{Horological Journal} of +Sept.~1873. +But, like many other uneducated inventors, he was very +difficult to convince that an \textit{independent} inventor is not +allowed by the world the credit of a \textit{first} inventor unless he +%-----File: 116.png-------------------------------------------- +%-----Folio: 101----------------------------------------------- +is so. He also invented that most useful instrument---the +spiral drill\index{Macdowall's!spiral drill, \&c.}; or rather I should say, he invented the practical +mode of making it by twisting a piece of pinion wire, +\begin{wrapfigure}{o}{126pt} +\caption{\sc Single-pin Escapement} +\includegraphics[height=500pt]{images/fig16.png} +\label{fig16} +\end{wrapfigure} +for the thing itself turned up in +wood as an old Indian invention in +the 1851 Exhibition. Another of +his independent inventions was the +`helix lever wheels,' as he called +them, but they also appeared in +some German clocks in the same +Exhibition; besides some other +things which had been published in +well known English books. He also +persuaded himself somehow or other, +that he invented the three-legged +escapement which I shall next describe; +but no one ever saw or heard +of it until it had been made from +my design, though he had shown me +all his inventions, and I had helped +him to get both a patent and an +Exhibition medal for his single pin +escapement, and old Mr.~Dent, under +my advice, had bought the patent +for a considerable sum, and gave +him an order for 500 watches on +that plan if he could make or get +them made, which he could not; +and Mr.~Dent accordingly got some +made in Switzerland. I wore one +of them long enough to see that it +answered very well, but the expense +of the two extra wheels which it +requires overbalanced the advantages, +though I hear they have +%-----File: 117.png-------------------------------------------- +%-----Folio: 102----------------------------------------------- +been also made in Paris from Macdowall's instructions, +the patent not having been taken there, and being perhaps +difficult to maintain here if it had been disputed; for the +thing had certainly been published, as we found afterwards +in a French book. Its action is evident enough from this +picture (fig.~\ref{fig16}). It has the advantage of giving a great +part, you may practically say half, of the impulse directly +across the line of centres (of the wheel and pallet arbor) +and therefore with very little friction. The pin is made of +a ruby, and should be set very near the arbor. The older +ones were put too far off. Macdowall made them with a +`neck-bearing,' \textit{i.e.}\ the pivot was behind the wheel, or the +arbor came through the frame, and had the wheel pinned or +squared onto it. The pallet piece itself forms the crutch for +the pendulum, the scape-disc being set behind the clock frame. +It should have eccentric\index{Beat pins!eccentric} fork-pins to adjust for beat. + +\subsection[Three-legged dead escapement.]{Three-legged dead escapement.}\markboth{THREE-LEGGED DEAD ESCAPEMENT.}{THREE-LEGGED DEAD ESCAPEMENT.}\label{subsec:Three-legged_dead_escapement.}\index{Three-legged!dead escapement}\index{Dead escapements!Beckett's three-legged}\index{Escapements of clocks!three-legged dead}---It occurred to me\index{Beckett, Sir E.!three-legged dead escapements} +in 1851 that all the best or most direct part of the impulse +in the single-pin escapement might be kept, the more oblique +part got rid of, and one of the extra wheels saved, by using +three pins or teeth instead of one; and the result was this +\begin{figure}[htbp] +\centering +\caption{\sc Three-legged Dead Escapement} +\includegraphics[width=\textwidth]{images/fig17.png}\index{Three-legged!dead escapement} +\label{fig17} +\end{figure} +%-----File: 118.png-------------------------------------------- +%-----Folio: 103----------------------------------------------- +\markboth{MY THREE-LEGGED DEAD ESCAPEMENT.}{MY THREE-LEGGED DEAD ESCAPEMENT.}escapement (fig.~\ref{fig17}) (for clocks only, not watches), in which +the upper tooth is shown in the act of giving the impulse. +This is a \index{Scape wheels!a very small one}\textit{full-sized} view of the escapement which drove the +Westminster pendulum of $6$~cwt.\ for half a year, until it +superseded by another modification of it invented for +the purpose of equalising the force of the impulse. That +scapewheel was of steel and weighed only $\frac16$ of an ounce +or $73$~grains, and the clock weight required for it with a +common turret clock movement was only $18$~lbs.\ falling $6$ +feet a day, and less than a quarter of what a dead escapement +had required; and considering that more force is lost +by the inertia of such a train than in small clocks, we may +say that the fraction $\frac{\mathrm{W}h}{\mathrm{M}l}$ was less than a third of its usual +amount for the best astronomical pendulums swinging the +same arc. I found also that it was possible to isochronise +the long and short arcs---at least for such variations as +actually occurred, by making the stopping or horizontal +faces half-dead, as I have drawn them. The distance of +the scapewheel from the pallet arbor should be about $24$ +times the radius of the wheel, to make it escape at $1^\circ$, allowing +a little for clearance. It requires careful adjustment, +for the greatest depth on the lower pallet is something less +than $\frac18$ of the radius of the wheel. + +It is necessary in this and prudent in all dead escapements, +of large clocks especially, to have a spring-fork\index{Forks of pendulums!with springs} to the +crutch; \textit{i.e.}\ the fork-pins attached to the crutch by springs\index{Beat pins!spring}, +so that if the scapewheel is not turning from any accident +while the pendulum is moving, and the pallets jam against +the teeth, the fork springs may give way and let the pendulum +go on without breaking a tooth, as it inevitably +will unless so relieved. The pin-wheel escapement is +specially liable to this, because the edges of the pins and +pallets are not sharp as in the common toothed wheel +escapements. +%-----File: 119.png-------------------------------------------- +%-----Folio: 104----------------------------------------------- + +\begin{figure}[!htbp] +\centering +\caption{\sc Sir E.~Beckett's Three-legged Escapement} +\includegraphics[width=0.9\textwidth]{images/fig18.png}\label{B3leg} +\label{fig18} +\end{figure} +The friction might be still more reduced and the adjustment +of the pallets made easier by making the escapement +with long stopping teeth, as in fig.~\ref{fig18}. It would also +give room for a longer swing of the pendulum, which cannot +safely be made above $2^\circ$ in the other form, or the +stopping faces will reach the scapewheel arbor. An escapement +of this kind clearly reduces the pallet friction to the +smallest amount possible in any dead escapement\index{Beckett, Sir E.!three-legged dead escapements}. It is +however not free from the variations of force in the train. +Constancy of force is only to be got by an entirely different +class of escapements, or by the addition of a train remontoire, +of which I shall speak hereafter under Turret Clocks. + +\subsection[Detached escapements.]{Detached escapements.}\markboth{SIR G.AIRY'S DETACHED ESCAPEMENT.}{SIR G. AIRY'S DETACHED ESCAPEMENT.}\label{subsec:Detached_escapements.}\index{Detached escapements!for clocks}\index{Escapements of clocks!detached}---There have been various contrivances +for clock escapements on the chronometer principle +of leaving the pendulum free or detached from the scape-wheel +%-----File: 120.png--------------------------------------------- +%-----Folio: 105------------------------------------------------ +\begin{figure}[htbp] +\centering +\caption{\sc Sir G.~Airy's Detached Escapement} +\includegraphics[width=0.5\textwidth]{images/fig19.png} +\label{fig19} +\end{figure} +except at the time of receiving the impulse and of +unlocking the wheel. There is an old French one described +in Rees's Cyclop\ae dia, and Sir G.~Airy\index{Airy, Sir G.~B.!his detached escapement}\index{Detached escapements!G.~B.~Airy's} invented another, +which is described in his before-mentioned Cambridge paper, +and has been lately adopted in the normal sidereal clock\index{Greenwich!sidereal clock escapement, Airy's} at +Greenwich. A few of them had been made before by old +Mr.~Dent, with half-second pendulums, for which this escapement +does not answer, as Mr.~Brock, of George Street, +Portman Square, has also told me. The Greenwich clock\index{Astronomical clocks!Greenwich clock} +however with a seconds pendulum of about $30$~lbs., appears +to answer remarkably well, and therefore I copy the +original picture, from which its action will be easily understood. +The single pallet $\mathrm{CP}$ is exactly like the right hand or +down pallet of a dead escapement. +$\mathrm{ABD}$ is a detent attached to a +fixed block at $\mathrm{A}$ by a slight spring, +$\mathrm{B}$ being the catch which holds +the scapewheel teeth or pins, for +it does not matter which they are. +($BD$ is the flat view of it, omitting +the stop at $\mathrm{B}$.) At $\mathrm{D}$, on the underside +of $\mathrm{ABD}$, there is a very +slight `passing spring' projecting +a little backwards, as shown in +the separate sketch; so that when +\begin{wrapfigure}{o}{100pt} +\hypertarget{fig20}{\caption{\sc Sir E.\ Beckett's Detached Escapement}} +\includegraphics[height=500pt]{images/fig20.png} +\label{fig20} +\end{wrapfigure} +the pin at $\mathrm{D}$ on the pallet goes to +the left it pushes the passing spring +down, and so passes it; but when it comes to the right it +lifts up the detent, because the passing spring being underneath +cannot yield upwards. That unlocks the tooth at $\mathrm{B}$, +and lets another tooth at $\mathrm{P}$ fall upon that pallet, and give the +impulse down its oblique face. The advantages which Sir +G.~Airy contemplated were, the abolition of the dead friction, +and the power of making the impulse begin as much before +zero as it ends after zero, the value of which we saw at p.~\pageref{impulse}. +%-----File: 121.png----------------------------------------------- +%-----Folio: 106-------------------------------------------------- + +\markboth{SIR E. BECKETT'S DETACHED ESCAPEMENT.}{SIR E. BECKETT'S DETACHED ESCAPEMENT.}But I cannot help thinking the following a better plan +because it gives the impulse without any sensible friction +as in the three-legged escapement just described, and involves +no passing spring, which is always a delicate arrangement. +I\index{Beckett, Sir E.!detached escapement}\index{Detached escapements!Sir E.~Beckett's} had this clock made and set going in November +1865, and it went till August 1873, nearly 8 years, without +being touched, even with oil, as I wished to see how long +it would go. The arc decreased a little, and it had a slightly +increasing gaining rate in the last few years; but I never +had any clock go so well for anything like that time, though +my gravity escapement clock, to be mentioned presently, has +gone as well for shorter periods. The train is +not a very fine one: with a fine train, or a +coarse one with a remontoire for a turret clock, +I have no doubt this escapement would go at +least as well as any other. But since 1873 it +has not equalled my gravity escapement clocks, +and the gravity escapement is both cheaper and +safer for large clocks than any train remontoire; +which may therefore be considered obsolete. + +\hyperlink{fig20}{This figure} shows the construction clearly +enough, except as to size. The locking teeth +of the scapewheel reach about $.6$~in.\ from the +centre, and the impulse pins $.25$~in. Their +centre is $7$~in.\ below the top of the pendulum +and crutch, and the impulse begins about $1^\circ$ +before zero, and ends $1^\circ$ after. For the scapewheel +turns $36^\circ$ before and $36^\circ$ after zero; +and therefore, if $r$ is the distance of the pins +from the centre, and $p$ the length of the crutch, +$r\sin 36^\circ$ must $= p \sin 1^\circ$ for an impulse of $2^\circ$; +which makes $p = 3.7r$. Consequently the +dimensions just now given are practically +right, allowing a little for clearance, as you +must. The pallet piece $\mathrm{P}$ is a separate piece of quite +%-----File: 122.png----------------------------------------------- +%-----Folio: 107-------------------------------------------------- +hard steel screwed on to the aperture in the crutch $\mathrm{AP}$; +and this requires care in adjustment, as the depth is less +than $\frac15$ of the radius of the wheel, being $r$ \textit{vers.} $\sin 36^\circ$; +which however is more than in the three legs, for this turns +$72^\circ$ at each beat, and that only $60^\circ$, this being a \markboth{SINGLE-BEAT ESCAPEMENTS.}{SINGLE-BEAT ESCAPEMENTS.}single-beat +escapement\index{Beat!single-beat escapements}\index{Escapements of clocks!single beat}\label{singlebeat}\index{Single-beat escapements}, which, it seems necessary to inform some +persons, wastes no power if the train does not move at the +return beat of the pendulum. + +But for that it would be better to have no crutch, but make +the action take place on the pendulum itself; it is hardly +possible however to manage that behind a clock of regulator +size, with the pendulum hung to the wall as it should be. +The wheel lies behind the clock in a long cock embracing it +and the crutch. The detent $\mathrm{DEF}$ is on a stud $\mathrm{F}$ in the back +plate, though it looks \hyperlink{fig20}{here} as if it were on the crutch, as the +click $\mathrm{CE}$ really is. When the pendulum goes to the right +(in this drawing) the click trips over the top of the detent, +and when it returns to the left the click pushes the detent +aside, and sets a locking tooth free, and then the \correction{scapewheel} \label{correction4}%**Transcriber's note: The original reads "scrapewheel". +turns and a pin gives the impulse. The shape of the pins +should be observed. It will easily be seen that the scapewheel +should be at the bottom of the clock, and the great +wheel at the top, as in my gravity escapement, and also in +the dead three-legs described at pp.~\pageref{subsec:Three-legged_dead_escapement.} and \pageref{B3leg}. $\mathrm{BB}'$ are +eccentric beat pins, by which the impulse can be made to +begin as much before zero as you like, so as to make the +angle which we called $\beta$ greater than $\gamma$ if necessary. + +\section{REMONTOIRE OR GRAVITY ESCAPEMENTS.}\markboth{GRAVITY ESCAPEMENTS.}{GRAVITY ESCAPEMENTS.} +\label{sec:REMONTOIRE.}\index{Escapements, gravity!theory of}% +\index{Escapements of clocks!remontoire}\index{Gravity escapements}\index{Remontoire escapements}% +These are not to be confounded with the thing called a +train remontoire, which I alluded to just now but shall not +explain till we come to turret clocks, as it belongs only +to them. A gravity or remontoire escapement is one in +which the impulse is not given to the pendulum directly by +%-----File: 123.png-------------------------------------------- +%-----Folio: 108----------------------------------------------- +the clock-train and weight, but by some other small weight +lifted up, or a small spring bent up, always through the +same distance, by the clock-train at every beat of the +pendulum. And the great advantage of them is that the +impulse is therefore constant; for the only consequence of +a variation in the force of the clock is that the remontoire +weights are lifted either faster or slower, which does not +signify to the pendulum, as the lifting is always done when +the pendulum is out of the way. If this can be managed +with certainty, and without exposing the pendulum to some +material variation of friction in the work of unlocking the +escapement, which it must perform, its motion and therefore +its time must be absolutely constant, since there is nothing +to disturb it. It does not look a very difficult problem; and +yet it puzzled the clockmakers to solve it in a satisfactory +way for about a century, in consequence of certain small difficulties +which nobody would guess until he had the opportunity +of seeing them in action; and after all it was not done +by the clockmakers, but by two lawyers, in different ways. + +But first it may be asked, is the gravity escapement problem +worth solving? Is not the dead or the detached escapement +proved to be good enough both by experience and by +mathematics? The answer is, that in science nothing is +good enough when it can be improved upon: that both +mathematics and experience prove that only by the most +careful and delicate and therefore expensive work, and only +on a small scale and with light weights, can clocks with +`impulse escapements' (\textit{i.e.}\ receiving direct impulse from the +train) be made to go as well as the best of them do; and +although it is possible, by the addition of a train remontoire, +to make even large and heavy dead escapement clocks go +as well as astronomical ones, yet that apparatus involves +not only some extra expense, but what is far more difficult +to provide, some extra attention and intelligence in the +people who have the care of it. We may however dispose +%-----File: 124.png-------------------------------------------- +%-----Folio: 109----------------------------------------------- +of a great number of the contrivances for gravity escapements +by the remark, that they require not less, but more +delicacy of construction and careful handling afterwards than +the finest dead escapement, even if they `perform' any +better, which scarcely any of them do. + +Before we can appreciate the merits and the difficulties of +this class of escapements, it is clearly necessary to understand +the theory\index{Gravity escapements!theory of} of them; which I shall be able to exhibit more +briefly than that of the dead escapement, as some of the +ground is common to them both, and especially that useful +formula of Sir G.~Airy's for the variation of the time caused +by any escapement, from which I shall start again. But it +will help our conception of the process if we first take some +simple form of gravity escapement as an illustration of +their principle; and it does not signify that that form was +neither the first nor the best, on account of certain mechanical +objections which we are not concerned with yet. + +\subsection[Mudge's gravity escapement.]{Mudge's gravity escapement (Fig.~\protect\ref{fig21}).}\markboth{MUDGE'S GRAVITY ESCAPEMENT.}{MUDGE'S GRAVITY ESCAPEMENT.}\label{subsec:Mudge's_gravity_escapement.}\index{Gravity escapements!Mudge's}\index{Mudge!his gravity escapement}---The pallets $\mathrm{AC}$, $\mathrm{BC}$, +are no longer fixed on one arbor, but on two, as close to the +bend of the pendulum spring as possible. The acting faces +are so shaped and placed that whenever the wheel moves +from $\mathrm{B}$ towards $\mathrm{A}$, a tooth will lift one of them until it is +stopped by the nib $a$ or $b$ at the end of each acting face. +Here the pallet $\mathrm{A}$ has just been lifted and is holding the tooth +that lifted it; as soon as the pendulum comes, moving to the +right, it will evidently push that pallet out of the way by +means of the fork-pin $\mathrm{P}$, and so free the tooth, and the wheel +will begin to turn, and the opposite tooth will immediately +lift the pallet $\mathrm{B}$ till it likewise is stopped by $b$. The pendulum +is all the time going on rising to the right and carries the +right pallet with it as far as it likes to go; when it begins to +fall the pallet falls with it, not only to the place where it was +taken up, but to a lower place, corresponding to that of the +left pallet in the picture; and the fall of the weight of the +pallet from the place where it is taken up by the pendulum +%-----File: 125.png-------------------------------------------- +%-----Folio: 110----------------------------------------------- +to the place where the pendulum leaves it, or the difference +between its rise and fall with the pendulum, constitutes the +impulse, and that difference is evidently constant, however +far the pendulum may swing.\par +\begin{figure}[htbp] +\centering +\caption{\sc Mudge's Gravity Escapement} +\includegraphics[height=0.8\textheight]{images/fig21.png} +\label{fig21} +\end{figure} +If the weight of the pallets were partly or wholly counterbalanced, +and they were fixed by springs instead of acting by +their own weight on pivots, it could no longer be called a +gravity escapement, but would have the more general French +%-----File: 126.png-------------------------------------------- +%-----Folio: 111----------------------------------------------- +name of a remontoire; but the principle would be the same, +except that the force of the springs has a law of its own, and +is more variable than that of gravity. + +It is easy to show that the effect of a gravity escapement +is to make the pendulum go faster than a free pendulum, by +exactly the same reasoning as was used to contrast the dead +and the recoil escapements; or still more simply, by considering +that the remontoire weights are in effect so much +weight added to the pendulum far above its centre of oscillation +and therefore they accelerate it. But this tells us +nothing about the variation of the rate, in case the arc increases +or decreases a little under any change of friction; +and we shall see presently that a very curious result comes +out with respect to this, which it is impossible to arrive at +except by calculation. + +\markboth{MATHEMATICAL THEORY OF GRAVITY ESCAPEMENTS.}{MATHEMATICAL THEORY OF GRAVITY ESCAPEMENTS.}To do this we must find out again what that quantity +called $\phi$ in Sir G.~Airy's\index{Airy, Sir G.~B.!for gravity escapements}\label{gairycalc2} formula at p.~\pageref{gairycalc}, is for this escapement. +Let the angle after zero at which the pendulum begins +to lift the pallet be called $\gamma$, and the angle at which it leaves +the other pallet which has been giving the impulse $\pm\beta$, according +as that takes place after or before zero: so that, as +in the dead escapement, the angle $\gamma+\beta$ is the angle of +impulse, if the descending pallet is left after zero, which we +shall see is the best arrangement. Let $\mathrm{P}g$ be the weight of +each pallet, and $p$ the distance of its centre of gravity from +its axis at $\mathrm{C}$, and $\delta$ the angle which $p$ makes with the +pendulum when they are in contact. $\mathrm{M}l^2$ represents the +moment of inertia of the pendulum as usual; strictly speaking +we ought to add to it the moment of inertia of the +pallets while they are in contact with the pendulum; but as +that makes no difference in the nature of the result, and in +the best escapements one pallet or the other is always in +contact, we may either consider that as included in $\mathrm{M}l^2$ or +neglect it altogether. Then the equation of motion will be +\[ +\frac{d^2\theta}{dt^2}=-\frac{g\sin\theta}{l}-\frac{\mathrm{P}pg\sin(\delta+\theta)}{\mathrm{M}l^2}. +\] +%-----File: 127.png--------------------------------------------- +%-----Folio: 112------------------------------------------------ +We may put $\theta$ for $\sin \theta$ and $1$ for $\cos \theta$ ($\theta$ being small), +\[ +\therefore \frac{d^2 \theta}{dt} =-\frac{g\theta}{l} \left(1+\frac{\mathrm{P}p}{\mathrm{M}l}\right)-\frac{\mathrm{P}pg\sin \delta}{\mathrm{M}l^2}. +\] + +This is of the same form as in the dead escapement; +only here the constant term involving simply $\theta$, which +always indicates isochronism, has its coefficient increased; +which shows that the pendulum will regularly go faster than +if its own gravity alone acted upon it, exactly as it is accelerated +by those small regulating weights which I described +at p.~\pageref{smallweights}. The other term constitutes the disturbing force $\phi$, +from which we are to learn what will be the disturbance of +the isochronism if the arc varies a little; and this result will +also be of the same form as before, except that the limits of +$\phi$ are different, as it does not act now through the middle of +the arc only, but from $-\alpha$ to $\beta$ and from $\gamma$ to $\alpha$; and even +if $\beta$ should be identical with $\gamma$ the action is not continuous +for the falling pallet pushes the pendulum from $-\alpha$ to $\beta$, +but the pendulum lifts the pallet from $\gamma$ up to $\alpha$. Therefore +the result of the integration will be (putting $\mathrm{W}h$ for the sum +of $\mathrm{P}p\sin \delta$ for the whole day): +\[ +\Delta\mathrm{T} =-\frac{\mathrm{W}h(\sqrt{\alpha^2-\gamma^2}+\sqrt{\alpha^2-\beta^2})}{\mathrm{M}l\pi \alpha^2(\gamma+\beta)}; +\] +which differs from the dead escapement formula only in the +signs; but we shall see that that produces another very important +difference. First however we may remark that if +$\beta$ is $-$ (that is, if the falling pallet is left before zero), or +even if it is smaller than $\gamma$ (and it cannot be larger with +safety to the locking), $\Delta\mathrm{T}$ is increased, and so will all its +variations be when there are any. Therefore let us assume +that $\beta$ is as large as it can be, \textit{i.e.}\ that one pallet is taken up +just when the other is left, or $\beta=\gamma$; and then the formula +becomes much more simple: +\[ +\Delta\mathrm{T} =-\frac{\mathrm{W}h}{\mathrm{M}l\pi \alpha^2} \sqrt{\frac{\alpha^2}{\gamma^2}-1} +\] +%-----File: 128.png----------------------------------------------- +%-----Folio: 113-------------------------------------------------- +We must differentiate this, as before, to see what the +variation of rate will be; but this time we need not consider +$\mathrm{W}$ or the force of the impulse variable, because we know it +is not---if the escapement is what it pretends to be. Then +\[ +d\Delta\mathrm{T} = \frac{\mathrm{W}hda \frac{\alpha^2}{\gamma^2}-2} +{\mathrm{M}l\pi\alpha^3\sqrt{\frac{\alpha^2}{\gamma^2}-1}} +\] + +From which this remarkable result appears,---that if the +weight of the pallets is so adjusted that the pendulum swings +through an arc $\alpha = \gamma\surd{2}$, the rate will not vary at all, even +when the arc does, except what may be due to the circular +error. Unfortunately they both have the same sign, and +therefore the escapement cannot be made to correct the +circular error\index{Circular error of pendulum}. But there happens to be a mechanical +difficulty in making $\gamma$ as large as $\frac{\alpha}{\surd{2}}$ +or $.71\alpha$, which would +be $85'$ if $\alpha = 2^\circ$; and moreover Mr.~Bloxam\index{Bloxam!his escapements} came to the +conclusion, as stated in his papers, that from other causes, +especially the variation of density of the air, it is better +to make $\gamma$ considerably smaller than $.71\alpha$. Let us see +then what the variation of rate from the escapement will +be for some such value of $\gamma$ even as far from the theoretical +value as $\frac{\alpha}{4}$. + + +In the Westminster clock I know by trial that $\frac{\mathrm{W}h}{\mathrm{M}l}$ at the +escapement is not more than $\frac{1}{45}$; taking it at that, and $\alpha$ at +$2^\circ\ 40'$, as it is, and $\gamma =\frac{\alpha}{4}$, you will see, if you take the +trouble to make the calculation, that the clock will only gain +about a second a month for a decrease of arc of $5'$, which is +larger than is likely to happen, besides what is due to the +circular error so far as it is uncorrected by the spring. +%-----File: 129.png--------------------------------------------- +%-----Folio: 114------------------------------------------------ + +In those escapements where the falling pallet is left before +zero, the expression for the variation of rate would be +\[ +d \Delta\mathrm{T} = \frac{\mathrm{W}hd\alpha}{\mathrm{M}l\pi \alpha^3(\gamma-\beta)} \left\{\frac{\alpha^2-2\gamma^2}{\sqrt{\alpha^2-\gamma^2}}+\frac{\alpha^2-2\beta^2}{\sqrt{\alpha^2-\beta^2}}\right\} +\] +in which you observe $\gamma-\beta$ instead of $\gamma+\beta$ is in the +denominator, and therefore the variation is much larger than +in the other form of the escapement. Theoretically indeed +this might also be made $= 0$ by making the three angles +satisfy this condition, +\[ +\sqrt{\alpha^2-\gamma^2}\sqrt{\alpha^2-\beta^2} = \frac{\alpha^2}{2}. +\] + +\label{conclusion}Thus $\gamma = 90^\prime$ and $\beta = 78^\prime$ would be right for $\alpha=2^\circ$; +but these small differences would be even more inconvenient +mechanically than $\gamma = 85^\prime$ in the other case. That construction +therefore is decidedly the worst, notwithstanding +the tempting appearance of the pendulum being left free +through the middle of its arc; a fact which would probably +never have been known with certainty without this kind +of investigation, as the errors would have been sure to be +attributed to any but the right cause. + +Reid mentions, at page~139 of his old book, a curious fact +bearing on this. He says he cut a hole in the side of the case\label{closecase} +of a gravity escapement clock, which increased its arc from +$1^\circ~22^\prime$ to $1^\circ~37^\prime$, and at the same time made it gain $42$~sec.\ a +day, and a larger hole increased the arc $12^\prime$ more, and I +suppose the rate. Therefore the diminished resistance, from +the pendulum being able to drive the air before it through the +hole, much more than counteracted both the circular error +and the escapement error, making the clock gain this great +amount instead of losing a little under the increased arc. +Moreover such an enormous variation of rate as this shows +that the motion of the air in the clock-case may affect the +%-----File: 130.png----------------------------------------------- +%-----Folio: 115-------------------------------------------------- +rate materially. But I must add that I have twice tried the +experiment myself in a still stronger way, by taking off the +clock case altogether from my own gravity escapement clock, +and I could not observe any increase of arc at all---certainly +not of $5'$, nor any alteration of rate. The arc was however +nearly $1^\circ$ larger than in Reid's clock before he cut the holes; +and this is another proof of the unsteadiness of very small +arcs I have since found that a small enclosure for a turret +clock pendulum bob did diminish the arc a little. + +Probably no one would foresee, without experiment, that +the simple form of escapement in p.~\pageref{fig21} would fail\markboth{FAILURE OF EARLY GRAVITY ESCAPEMENTS.}{FAILURE OF EARLY GRAVITY ESCAPEMENTS.}\label{failure}. Several +of the most elaborate French turret clocks in the Exhibition +of 1851 were on that plan, and people were very much +surprised when I showed them that you could make all those +clocks increase their arc visibly and speedily by increasing +the clock-weight, which is directly contrary to the fundamental +principle of a gravity escapement. This form of the +escapement was invented by Mudge, a celebrated watchmaker +whom I shall have to mention again, and it had long been +known here that it would not answer, on account of its liability +to \textit{trip}, or to have the pallets jerked out so far by the +motion of the wheel that the nib fails to catch the lifting +tooth, and so three or four teeth run past and the time is +altogether lost. The only way of avoiding this liability is to +use a very highly finished train with high numbered pinions +to keep the force uniform, and then to make that force only +just enough to raise the pallets; but that is inconsistent +with the clock being able to work anything but a small dial, +and if it is not kept very clean and the oil fresh, it will be +sure to stop. In short, the clock becomes too expensive and +delicate, and requires too much attention to be tolerated in +common use. + +\subsection[Cumming's escapement.]{Cumming's escapement.}\markboth{CUMMING'S AND HARDY'S ESCAPEMENTS.}{CUMMING'S AND HARDY'S ESCAPEMENTS.}\label{subsec:Cumming's_escapement.}\index{Cumming's escapement}\index{Escapements, gravity!Cumming's}---But even if all these risks +were got over, there is still another radical defect in all such +escapements, which does not appear to have been ever +%-----File: 131.png--------------------------------------------- +%-----Folio: 116------------------------------------------------ +noticed before I pointed it out with reference to those clocks +in the Exhibition. The force may easily be enough to raise +the pallets a little too high, without jerking them over the +tooth altogether, and then the pressure on the nib is quite +enough to keep them there, and so the pallet is taken up by +the pendulum at some angle greater than the proper one $\gamma$; +and as it falls down with the pendulum to a constant place, +the impulse lasts longer than it ought, and of course the arc +is increased. I gave the name of \textit{approximate tripping} to this +defect, and any escapement which is liable to it is evidently +worth nothing. It seems capable of happening even where +the impulse or sloped portion of the pallet is put on one arm +and the nib on a separate one which is not lifted at all by the +wheel, but only by the pendulum, as in Cumming's escapement, +which was invented very nearly a century ago, and +for a time was thought to answer well. I suppose this is +in consequence of the force with which the tooth strikes the +stop pallet, sometimes throwing it a little out of its place, +unless it is undercut or given a slight recoil the wrong way; +and that is objectionable too, because it resists the unlocking, +and does not always resist with the same force. + +\subsection[Hardy's escapement.]{Hardy's escapement.}\markboth{HARDY'S ESCAPEMENT.}{HARDY'S ESCAPEMENT.}\label{subsec:Hardy's_escapement.}\index{Escapements, gravity!Hardy's}\index{Hardy's escapement}---One of the objections to Cumming's +escapement was the friction of no less than $8$ pivots +of the $4$ arms which had to move with the pendulum in the +course of each vibration. Hardy avoided this by setting the +arms on springs instead of pivots; but that introduced +another and probably a worse evil, because the stiffness of +the springs varies with the temperature, which of course +disturbs the rate of the pendulum. That escapement was +consequently removed from the transit clock at Greenwich +many years ago, and a dead one substituted. There were +some very good rates of three Hardy's clocks published in +\textit{Pearson's Astronomy}; but they are practically extinct. + +\subsection[Kater's escapement.]{Kater's escapement.}\markboth{KATER'S AND OTHER GRAVITY ESCAPEMENTS.}{KATER'S AND OTHER GRAVITY ESCAPEMENTS.}\label{subsec:Kater's_escapement.}\index{Escapements, gravity!Kater's}\index{Kater!his escapement}---The late Captain Kater, who paid +great attention to the theory of pendulums, invented a +%-----File: 132.png----------------------------------------------- +%-----Folio: 117-------------------------------------------------- +gravity escapement, which is very fully described in the +130th\ vol.\ of \textit{Philosophical Transactions}, on the principle of +making the weight of the descending pallet unlock the scape-wheel +by falling upon an anchor like a pair of dead escapement +pallets without the impulse faces. He supposed that +as the inertia of the anchor would stop the pallet for a +moment, the pendulum would leave it there, and so be itself +free from the friction of unlocking. But here again it was +found that the force of the wheel was apt to displace the +anchor unless its pallets were undercut, and then the resistance +was sometimes too great for the gravity pallets to +overcome, unless they were too heavy for the pendulum; +and after many attempts to make it go, that escapement +also was taken out of the only clock to which I know of it +being applied, and came into the hands of Mr.~Bloxam, who +showed me it. The failure of it is described in his paper +before mentioned. + +\subsection[Gowland's escapement]{Gowland's escapement}\markboth{GOWLAND'S ESCAPEMENT}{GOWLAND'S ESCAPEMENT}\label{subsec:Gowland's_escapement}\index{Escapements, gravity!Gowland's}\index{Gowland's escapement}, which was in the Exhibition of +1851, was on the same principle as to the unlocking only. +He had not even pallets for the impulse, but a pair of small +weights, which hung on long arms or spikes projecting horizontally +from the locking pallets, except when they were +lifted off by similar arms projecting from the pendulum. +This prevented the friction of any pallet pivots affecting the +pendulum. The locking pallets were of Mudge's form, and +were prevented from being driven too quickly and tripping, +by paddles descending from them into a pot of oil---not a +very elegant contrivance certainly, and requiring a good deal +of extra force in the train. I heard no more of it after the +Exhibition, at which I was not surprised. + +\subsection[M.~Gannery]{M.~Gannery}\markboth{M.~GANNERY}{M.~GANNERY}\label{subsec:M.Gannery}\index{Escapements, gravity!Gannery's}\index{Gannery's escapement}, of Paris, had an escapement there also, on +the same principle as to the small weights, which were hung +by strings from the pallet arms and received in cups on the +pendulum arms, or \textit{vice vers\^a}. But instead of the oil pot, he +made the scapewheel of the usual size with only $9$ teeth of +%-----File: 133.png-------------------------------------------- +%-----Folio: 118----------------------------------------------- +very slow rise and a nib at the end, which therefore lifted +the pallets slowly and seemed to obviate the tendency to +trip, so far as I could judge by merely looking at it. I +should think however that the rigidity of the strings would +be quite enough to affect the pendulum, and the friction in +lifting was considerable. Moreover I doubt whether the +stopping of the unlocking weight in any of this class of +gravity escapements is decisive enough to make the difference +of the angles of lift and of drop quite constant; and if it is +not the escapement fails. Of that escapement also I heard +no more, and the French members of the jury evidently +thought very little of it. Nevertheless, the scapewheel with +$9$ teeth instead of $30$, which reduces the pressure of the stops +in that proportion, was a great advance in the right direction +though not absolutely new, because the same thing had been +done much better some years before in + +\subsection[Bloxam's escapement.]{Bloxam's escapement.}\markboth{FORMER GRAVITY ESCAPEMENTS.}{BLOXAM'S ESCAPEMENT.}\label{subsec:Bloxam's_escapement.}\index{Bloxam!his escapements}\index{Escapements, gravity!Bloxam's}---This is so superior to the +others that it deserves a more particular description. This +drawing (\hyperlink{fig22}{next page}) of the full size in Mr.~Bloxam's own +clock, is copied (with a little alteration for distinctness of +exhibition) from his account of it in the Astronomical +Society's Memoirs of 1853. The pallets are lifted alternately +by the small wheel or pinion with $9$ teeth, and with +scarcely any friction, as the action is only for a short distance +across the line of centres. The stopping is done by +the long teeth, and the pressure there is less than the lift in +the proportion of the radii of the small and large wheels. +The stops are $\mathrm{A}$ and $\mathrm{B}$: $\mathrm{E}$ and $\mathrm{F}$ are the fork pins which +embrace the pendulum. The pallets above at $\mathrm{C}$ are cranked, +that their centres of motion may be identical with that of +the pendulum; which is perhaps an unnecessary refinement, +especially as the pendulum spring has no one centre of +motion. The size of the wheel determines that of the pallets, +thus: if the radius of the wheel is $1$~in.\ the length of each +pallet down to the stop must be $2.8$~in., to make the angle +%-----File: 134.png-------------------------------------------- +%-----Folio: 119----------------------------------------------- +between the locking teeth and each pallet $90^\circ$. Mr.~Bloxam +made the angle $\gamma$, at which the pendulum leaves one pallet +and takes up the +other, only $20^\prime$ in +his clock, and $\alpha = +1.^\circ 40^\prime$, these being +the proportions +which he concluded +were the best to +counteract the effect +of variations of density +of the air. +\begin{figure}[htbp] +\centering +\hypertarget{fig22}{\caption{\sc Bloxam's Gravity Escapement}} +\includegraphics[height=0.8\textheight]{images/fig22.png} +\label{fig22} +\end{figure} + +The objections to +this escapement are, +that it is delicate and +expensive to make, +both in itself and in +the rest of the clock, +and if a pallet got +accidentally lifted +the wheel would run +with great velocity +and probably break +a tooth when the +pallet stopped it +again---an evil to +which most of the +previous escapements +are equally +liable, and it is a +very serious one. +It is also liable to trip unless the train is very fine, +so that no more weight need be used than is absolutely +necessary. But unless a gravity escapement will enable the +clock to do with a coarse train, it is of no real use; at any +%-----File: 135.png-------------------------------------------- +%-----Folio: 120----------------------------------------------- +rate it is quite certain not to come into use; and Mr.~Bloxam +said that he considered a fine train essential. That in his +own clock was the finest and had almost the highest numbered +pinions (18) I ever saw. And therefore after all, this +can only be regarded as a theoretical or scientific solution of +the gravity escapement problem, but hardly a practical one. +I expressed this opinion of it in early editions of this book +and stated that old Mr.~Dent and I had agreed that it would +not do for the Westminster clock, even if protected from +variations of force by a remontoire in the train. Somebody +however thought he knew better; for in the 1862 Exhibition +there appeared for a short time a small turret clock +with this escapement, and a train remontoire, which was +said in the newspapers to have been made under the direction +of the Astronomer Royal. But it could not be made to +behave properly, and after a few weeks was withdrawn. + +At the same time, Mr.~Bloxam\index{Bloxam!corrected Sir G.~Airy} deserves the credit of +having first discovered, though he did not publish the +discovery till long afterwards, that the practical conclusions +of Sir G.~Airy's Cambridge paper were \label{gairyerr2}erroneous; and that +the errors of a dead escapement cannot be made either insignificant +or constant; that the dead friction does not +correct itself before and after zero; that the acceleration of +a gravity escapement pendulum over a free pendulum does +not signify the least; but that what does signify is the +constancy of that acceleration; and that the variation is +least when the acceleration is greatest, and may be made +practically nothing by a particular arrangement of the angles +of impulse. The Astronomer Royal afterwards in effect +assented to all this, first by admitting in 1852 that my +gravity escapement, which will be described presently, +answered perfectly, and by himself communicating to the +Royal Astronomical Society Bloxam's two papers of 1853 +and 1858 sent from Madeira, the latter of them after he was +dead; and then actually going too far and assuming that +%-----File: 136.png-------------------------------------------- +%-----Folio: 121----------------------------------------------- +Bloxam's escapement was a practical solution of the gravity +escapement problem. + +\subsection[Sir E.~Beckett's Gravity Escapements.]{Sir E.~Beckett's Gravity Escapements.}\markboth{SIR E.~BECKETT'S GRAVITY ESCAPEMENTS.}{SIR E.~BECKETT'S GRAVITY ESCAPEMENTS.}\label{subsec:Sir_E.Beckett's_Gravity_Escapements.}\index{Beckett, Sir E.!four and three legged gravity escapements}\index{Escapements, gravity!Beckett's|(}\index{Gravity escapements!Beckett's four-legged}---I have now +to describe the only escapements of this kind which have ever +come into real use; and that both for large and astronomical +clocks, especially the former. The earliest form of them +need no longer be described, as it has been superseded by +two others, one with a four-legged scapewheel for small +clocks, and the other with a double three-legged wheel for +large ones. + +\subsection[The four-legged escapement]{The four-legged escapement}\markboth{THE FOUR-LEGGED ESCAPEMENT.}{THE FOUR-LEGGED ESCAPEMENT.}\ \label{subsec:The_four-legged_escapement}\index{Four-legged gravity escapement}is shown in \hyperlink{fig23}{this drawing} +of a regulator of this kind seen from behind, half the real +size. To avoid confusion, only the centres of most of the +wheels are shown, and you see the train is inverted, to save +height in the frame and clockcase. $\mathrm{G}$ is the great wheel +arbor, and the barrel is shaded; $\mathrm{C}$ the centre wheel, close to +the top of pendulum and pallet arbors, $\mathrm{B}$~second wheel, +$\mathrm{A}$~seconds-hand wheel, and $\mathrm{E}$ scapewheel. $\mathrm{DD}$ are the +brackets which come out of a large cast-iron plate or back, +from which also comes the pendulum cock, shown by +partly broken lines, to leave the pallet cock visible. $\mathrm{PP}$ are +the pillars, $\mathrm{CST}$, $\mathrm{CS}^\prime\mathrm{T}^\prime$ the pallets, and their inside pivots +(the arbors being very short) run in a flat piece or cock +between the centre wheel and the clock plate or frame. +The scapewheel speaks for itself as to the long locking +teeth; but it has two sets of lifting pins near the centre, +pointing alternately backwards and forwards, one set lifting +one pallet and the others the other, the pallets being in +different planes, before and behind the wheel, with one stop +$\mathrm{S}$ pointing forwards and the other $\mathrm{S}^\prime$ backwards. This cannot +be done otherwise with an even-numbered wheel, and +though it can with a five-legged one, that is an inferior +construction in other respects, and is much more difficult +to make rightly, and has not one advantage when it is +made. I say this from experience now, as I did before +%-----File: 137.png-------------------------------------------- +%-----Folio: 122----------------------------------------------- +\begin{figure}[p] +\centering +\hypertarget{fig23}{\caption{\sc Four-legged Gravity Escapement}} +\includegraphics[height=0.9\textheight]{images/fig23.png} +\label{fig23} +\end{figure} +%-----File: 138.png-------------------------------------------- +%-----Folio: 123----------------------------------------------- +from theory. For with the strange propensity of mankind +for taking more trouble to do wrong than it would take to +do right, some persons would persist in making the escapement +with five legs. I thought it might possibly save a +little force or weight on the train, but it does not even do +that; nor anything else, except give more trouble to adjust: +whereas the four-legged one is so easy that the very first I +had made went at once perfectly without any alteration. + +The great feature of them is the regulation of the velocity +and the avoidance of the banging on the pallets and the risk +of tripping, either actual or approximate, by putting a +common fan-fly on the scapewheel arbor. And this +becomes possible or effective only by reason of the large +motion of the wheel and fly\index{Fly, striking!for gravity escapements} at every beat: viz.\ $45^\circ$ in this +escapement, and $60^\circ$ in the three-legs. A fly would be of +very little use in Bloxam's escapement, to say nothing of +its other difficulties. In order to leave room for the fly +the seconds-wheel arbor is cut short and set in a cock within +the frame, which leaves space enough for a fly above $2$~in.\ long +in each arm, from $\mathrm{E}$ to $\mathrm{B}$. + +\markright{PROPER CONSTRUCTION.}The pallets require no beat screws, as they are only thin +pieces of steel like square wires, which can easily be bent +for adjustment; and even for a $40$~lbs.\ pendulum they +have to be made very light; they must be cut out of steel +plate, and the lifting faces hardened. The pins are found to +do better also of steel than of brass, and one set of them +should be tapped into the wheel with left-handed screws, so +that the action of lifting may not tend to loosen them. The +wheel is either screwed on the arbor up to a shoulder with a +left-handed screw, so that the action tends to tighten it, or +is `squared on' a hexagon and pinned. The scapewheels +are also generally cut out of thin steel plate; but some have +been made of a harder kind of gun-metal or softer kind of +bell-metal, and I am not certain which is best. But in either +case the stops must be as hard as possible, either steel quite +%-----File: 139.png--------------------------------------------- +%-----Folio: 124------------------------------------------------ +hard or jewels. I think steel hard enough, and I do not +believe in leaving any place where there is friction totally +dry, though the oil may be the least possible. + +Another great advantage of these escapements is that the +length of the teeth or legs, and the largeness of their motion, +make the pressure on the stops, or the work of unlocking +by the pendulum, insensible; and therefore also they are +incapable of holding up the pallets so as to cause `approximate +tripping' by any force that you can apply to the great +wheel, provided the escapement is made properly. But +with that same genius for doing things wrong when it +is as easy to do them right, some persons have made the +angle $\mathrm{CSE}$, at the stop which is struck upwards, less than +$90^\circ$, and then have said the escapement failed because +it sometimes tripped, as it was pretty sure to do. For +safety it is as well to put the up stop a little higher, and the +down stop a little lower than their proper theoretical places, +which are where both the angles would be exactly $90^\circ$. + +That determines the theoretical distance of the pallet +arbors $\mathrm{C}$ from $\mathrm{E}$ the scapewheel centre. If its diameter is +$4$~in.\ that distance is $5.2$, and that \textit{is} the proper distance of +the top of the pendulum spring above $\mathrm{E}$\@. The pallet arbors +must evidently be a little lower. Mr.~Bloxam made them +cranked (see p.~\pageref{fig22}) in order to get their common axis in a +line with the top of the spring; but that is an unnecessary +refinement, at least for these escapements, and is never done. +And as no point in the pendulum really swings quite in a +circle, I doubt if the friction of the pallets on it would be +sensibly less for their being both made to describe the same +circle by cranking their arbors: at any rate it is too insignificant +to care about. + +The distance of the lifting pins from the centre should not +be more than a $40$th of $\mathrm{EC}$, or else the angle of impulse $2\gamma$ +will be larger than is found expedient. It is difficult to +make the pallets light enough even with a small $\gamma$ and the +%-----File: 140.png----------------------------------------------- +%-----Folio: 125-------------------------------------------------- +larger it is the lighter they must be. The length of their tails +down to the beat pins is arbitrary, but I found the Westminster +clock perform decidedly better with the pallet tails +long than short. The length \hyperlink{fig23}{here shown} does very well, +and it looks neat to make the two parts reciprocally parallel. +The pins should be placed so that the lifting may take place +equally across the line of centres $\mathrm{CE}$, because then it is +done with the least friction. For this purpose the pins +which lift the lower pallet must be set on the radii which +run along the acting faces of the teeth, and the other set of +pins half way between them, with reversed screws, as I said +before. + +\markboth{FOUR-LEGGED ESCAPEMENT.}{FOUR-LEGGED ESCAPEMENT.}Any gravity escapement requires a heavier\index{Gravity escapements!require heavy weights} weight than a +dead or detached one, other things being equal, because it +must be strong enough to lift the pallets promptly and +firmly always; but the superfluous force does not reach the +pendulum, and therefore does no harm, provided the train is +good enough not to waste much force generally in order to +get over occasional weak places from bad wheel-cutting. +Nothing tests the defects of a train like a gravity escapement. +If there are bad places in a common clock train they must +be very bad indeed for the teeth not to follow the pallets, +though they may be giving no effective impulse for some +seconds; but in a gravity clock the pallets have always to +be lifted; and I have never got a train yet in which I could +not hear some weak place, recurring always at the same time +of day, and requiring at least an extra pound in the weight +beyond what was generally wanted. For that reason, +though a high numbered train is not, or ought not to be +requisite for these clocks, it should be a thoroughly good +one; and as defects of cutting affect low numbers more than +high ones, it is better to have them rather high, though they +need not be anything like what are used for first-rate dead +escapements. I have the upper pinions of $10$ and the centre +one of $12$, and if these are well cut, and still better if they +%-----File: 141.png----------------------------------------------- +%-----Folio: 126-------------------------------------------------- +are lantern pinions, they are enough; if they are not, you +will soon hear and see it by the escapement, and the train +should be rejected as a bad one. + +In gravity regulators, for the same reason, the wheel must +have a little run at the pallets before it begins to lift them +just as many clocks will not begin to strike if the hammer +tail lies on the pins: \textit{i.e.}, there must be banking \label{banking}pins $\mathrm{KK}'$ +for the pallets to rest on just clear of the lifting pins. And +in turret clocks the banking pins are useful to reduce the are +without making the pallets too thin. They may be simply +a thin piece of metal adjusted for the beat pins to fall on. + +It is better to have a full-sized barrel with three lines and a +fixed pulley for a `three-quarter length' clock than two +lines and a smaller barrel. A clock of this kind with a +$40$~lbs.\ pendulum swinging $2^\circ$ requires a weight of from $20$ +to $24$~lbs., according to the train, to lift the pallets promptly +and firmly, and loud enough for an observer. + +These clocks have also been made to strike a small bell +every minute by a pin on the minute wheel, which enables +an observer to go on for some time without looking at the +clock. Of course this requires rather more weight, and no +such extra friction could be tolerated in a dead escapement. +My clocks strike one at the hour on a rather large bell, but +that makes no sensible difference in the weight. When +there is a full striking part, the train must be arranged in the +usual position, which is inverted in the mere going clocks, to +save unnecessary height of the frame and the pendulum +being several inches above it, on account of the extra wheel +and the length of the pallets. The great wheel is also put +on the left side to keep it near the side of the case and out +of the way of the pendulum. When a pendulum imparts +vibration to the weight, as they do sometimes, the simplest +cure for it is to put a board down the side for the weight to +graze when it is near the pendulum. It has never happened +in my clocks, and three lines tend to prevent it. +%-----File: 142.png----------------------------------------------- +%-----Folio: 127-------------------------------------------------- + +Unfortunately I have no daily rate of any of these clocks +regularly taken in an observatory\index{Astronomical clocks}\index{Clocks!astronomical}, until we come to the +largest of them all; but judging of my own for long periods +by the Westminster clock, which is tested daily, I have no +difficulty in pronouncing it superior in steadiness of rate to +any dead escapement whose rate I have ever seen. And +they are made by Mr.~Brock, of George Street, Portman +Square, and I dare say by other makers, for half the price of +the old-fashioned best dead escapement regulators with only +$12$~lbs.\ pendulums. + +\markboth{SIRE E. BECKETT'S GRAVITY ESCAPEMENTS.}{INFERIOR MODIFICATIONS.}Some persons have taken a great deal of unnecessary +trouble to modify these escapements in order to avoid the fly, +as if that did any harm; and have added train remontoires, +as if that did any good to any gravity escapement which +really is a gravity escapement---\textit{i.e.}\ which has no tendency +to trip, and gives a constant impulse clear of the friction of +the train. One of these attempts to get rid of the fly was +exhibited by Dr.~Clark in 1862; but the wheel was stopped +with a bang that thrilled all through the clock, which only +tends to knock it to pieces, and keeps everything in a state +of vibration. It was also a much more delicate construction, +and I should prefer Bloxam's if I had to choose between +them; for if you have not a fly, the less the motion is at +each beat the better. Another contrivance for the same purpose, +invented by a French workman here, was used by his +employers in a few church clocks, and then abandoned, and +my original form resumed by the makers in all their turret +clocks. The fly\label{fly} should of course be as light as possible, +either of thin steel or aluminium; and the best way to put it +on is with a piece of watch spring pushed in through an +oblong hole so as to press always on the arbor, which +should \textit{not} be very thin. Some persons do not seem to +know that a long fly is more effective than a wide one of the +same area. + +Another mistake made by several of these inventors, +%-----File: 143.png------------------------------------------------- +%-----Folio: 128---------------------------------------------------- +including Dr.~Clark, was that of supposing it was better to +let the pallets unlock the wheel in falling with the pendulum, +forgetting that the pendulum is then just as much affected +by the friction of unlocking as if it did it in rising, if that +friction is sensible; and if it is not, still less can it signify +whether it is borne directly or indirectly by the pendulum. +It is still worse to keep the pallets moving in contact with the +stops during each `excursion' beyond the angle of unlocking, +for that reduces it so far to a dead escapement. But +the worst of all the `improvements' was by the late Mr.~Cooke +of York, the eminent telescope-maker, who also +made these clocks, and rounded the stops `to make the +unlocking easy;' which degraded it to an impulse escapement, +the pallets being then driven away by the teeth +with a force depending on the clock weight and friction +of the train. + +\subsection[The double three-legged escapement]{The double three-legged escapement}\markboth{THREE-LEGGED GRAVITY ESCAPEMENTS.}{THE DOUBLE THREE-LEGGED ESCAPEMENT.}\ \label{subsec:The_double_three-legged_escapement}\index{Double three-legged gravity escapement}\index{Gravity escapements!double-three-legged}\index{Three-legged!gravity escapement} (fig.~\ref{fig24} next +page) is so called because it has two three-legged wheels, +$\mathrm{ABC}$ and $a~b~c$, in different planes, with one set of +$3$ lifting pins between them. Here the two wheels must +be squared on the arbor, and the lifting pins need only +be shouldered between them. The pallets also lie in +one plane between the wheels, but one stop $\mathrm{S}$ points +forward to receive the $\mathrm{ABC}$ teeth, and the other $\mathrm{S}'$ +backward to receive the $a~b~c$ teeth alternately. The reason +for two wheels is that with one three-legged wheel you +cannot have the pallets far from upright, which is evidently +the worst position for them, as it requires much more dead +weight to be moved at every beat in order to have weight +enough for effective impulse. It should be understood that +there is no particular mechanical advantage in the two wheels +being set with the alternate teeth equidistant, appearing like +a six-legged wheel. They may be set with one set of legs at +$90^\circ$ and $30^\circ$ to the other set---or at any other angles to get +any greater inclination of the pallets if desired. However the +%-----File: 144.png------------------------------------------------ +%-----Folio: 129--------------------------------------------------- +\begin{figure}[htbp] +\centering\index{Beckett, Sir E.!four and three legged gravity escapements} +\hypertarget{fig24}{\caption{\sc Double Three-legged Escapement}} +\includegraphics[height=0.9\textheight]{images/fig24.png}\index{Three-legged!gravity escapement} +\label{fig24} +\end{figure} +%-----File: 145.png------------------------------------------------ +%-----Folio: 130--------------------------------------------------- +equidistant arrangement is the natural one, and is generally +used, though not invariably. I need hardly say that a pair of +wheels of this kind are very different from a six-legged wheel +which would only move $30^\circ$ at each beat, while this moves +$6^\circ$, besides other differences. + +In this case the distance of the pendulum top from the +scape-wheel centre evidently = diameter of scape-wheel. The +lifting pins should not be farther from the centre than a $36$th +of this, or the pallets have to be inconveniently light and +thin: the pins and arbor may be solid as a three-leaved +pinion. They should be so placed that the one which is +holding up a pallet and the one which is going to lift next +may be vertically over each other, the third being on a level +with the centre---\textit{i.e.}, they will stand on the radii which form +the acting faces of the teeth of one wheel, as you see \hyperlink{fig24}{here}. + +This escapement is the best for large\index{Gravity escapements!best for large clocks} clocks, which must +have plenty of superfluous force to drive the hands in all +weathers (which superfluous force all reaches the pendulum +in clocks of the old kind, varying immensely); but the fly\index{Fly, striking!for gravity escapements} +must, on that account, be much larger in proportion +than in regulators, and care must be taken in planning +the clock to leave room for it. In the smallest turret clocks +I have always had the fly a foot long altogether and $1\frac14$in.\ wide, +and in large ones considerably more. When the fly +is very large, as at Westminster, the friction of a spring on +the arbor is not enough, and there must be a larger `roller' +or blank-wheel pinned on the arbor for the spring to act on. +At the same time it was very satisfactory to find that when +the men had once forgotten to screw up the spring after +doing something to the fly, the clock had never tripped in +the days which had elapsed; and I have tried the same +experiment elsewhere; but the four-legs will trip if the fly is +loose. The greater obliquity of the pallets, $30^\circ$ against $22\frac12^\circ$, +is the cause of this superiority of the three-legs; and this +obliquity may be increased still more if you like by altering +%-----File: 146.png---------------------------------------------- +%-----Folio: 131------------------------------------------------- +the relative position of the two scapewheels. But I by no +means advise the omission of the fly, even then. + +In very large clocks\label{large} the pallet tails are too thick to bend +for adjustment of the beat, and then eccentric beat pins are +used, which require no description. They are usually +made of brass, even in small clocks; but I think it would be +better to cover them with hard wood\index{Beat pins!ivory and wooden}\index{Wooden!beat pins}\markright{WOODEN BEAT-PINS.}. The finest clock of +this kind I have seen was a regulator with four-legged escapement +made by an amateur, Mr.~George Salt, of Saltaire; +and it had ivory beat pins, which certainly had less chatter +than brass ones. The pendulum weighed nearly $40$~lbs., +and yet the clock weight was only $15$~lbs., with about $4$~ft.\ fall. +This shows that a gravity escapement really requires +very little more force than a dead one with as good a train +as possible, though practically I should always make the +weight abundant. One thing must be specially attended to, +as a distinction between these and dead escapements: the +beat pins must on no account be touched with oil or grease +of any kind, but left absolutely dry, whatever they are made +of; for the slightest adhesion to the pendulum is fatal; though +in dead escapements the fork should always have a drop of +oil, to keep it as close as possible without being tight. Moreover, +care should be taken to make one pallet begin to lift +simultaneously with the resting of the other, and neither +before nor after. + +The best evidence of the performance\index{Gravity escapements!rate of some}\index{Rate!of some other gravity escapement clocks} of these escapements +is the annual report of the largest of them all at Westminster, +of which I shall have more to say afterwards.\footnote{And I have read in the \textit{English Mechanic} that one under the +charge of Professor Waldo, of Yale College Observatory, had gone for +several months on a rate of only $.47$~sec.\ a week.} My own have +often gone for months together without any difference from +Westminster for which I could venture to correct, or to +regulate the pendulum. I have never found on close inquiry +that the rate of the very best dead escapement regulators +%-----File: 147.png---------------------------------------------- +%-----Folio: 132------------------------------------------------- +approached that of Westminster and several other public +clocks of this kind, of which I have occasionally had reports. +I have had accounts of some that had been altered from +other escapements to this, with the effect of reducing errors +of minutes to seconds. The last was from a gentleman +who said that his turret clock, made from this book by a +man who had never made one before, has a better rate +than any astronomical clock he had ever known.\index{Escapements, gravity!Beckett's|)}\label{gravend} + +\section{CONSTRUCTION OF THE GOING PART OF CLOCKS.}\label{sec:GOING_PART.}\index{Clocks!going part of}\index{Going part of clocks}\markboth{GOING PART OF CLOCKS.}{GOING PART OF CLOCKS.} + +Fig.~\ref{fig25} (p.~\pageref{fig25}) shows the arrangement of the going part of +a common regulator, or a house clock of superior character, +except that the pendulum in a clock of that kind ought to be +hung by a cock on the back of the case; but I have already +given a drawing showing that at p.~\pageref{fig09}; so I show another +mode of suspension here. In the common recoil escapement +clocks the pendulum only weighs a pound, or less, and is +hung from a cock merely screwed to the back plate of the +frame, which is a much weaker plan than this. $\mathrm{A}a$ is one of +the pallets on the arbor $a$ and $\mathrm{E}f$ the crutch and fork; +which generally embraces the pendulum, but sometimes goes +through it, especially when it is a wooden rod. The weight +is not hung by the single line, but by a double line going +through a pulley, sometimes in the weight itself, but more +frequently hung to it by a hook. This prevents the string +from untwisting, and enables you to do with a thinner string, +and it requires a barrel of twice the diameter which a single +string would, and that is worth something when the pivots +of the barrel are as large as they usually are, of which I have +spoken already at p.~\pageref{largepivots}. But it must be remembered that +every pulley in a machine, and especially every moveable +pulley, wastes power very sensibly by the friction and stiffness +of the rope, especially when the moving power is at the +slow end of the system of ropes. Theoretically it makes no +%-----File: 148.png---------------------------------------------- +%-----Folio: 133------------------------------------------------- +difference whether a given weight with a given fall in a week +is hung by one rope without any pulleys or by half a dozen; +but practically you will find the weight has to be increased +in a very high ratio for every additional pulley you add. +You might soon reach a number at which no weight whatever +would do the required work, but would all be wasted in +overcoming the friction and stiffness of the ropes. This +remark is chiefly important with reference to turret clocks, +since not one architect in a hundred ever consults a clockmaker +before he plans either dial-holes or clock-room or +place for the weights to fall, and then people think it is the +clockmaker's fault if the clock does not perform as well as if +it had plenty of room for the weights to fall and other things +to act properly. + +The barrel is fixed to its arbor, of which the back end is a +common pivot, but the front is carried through to the dial $\mathrm{K}$ +and is squared for the key to take hold of it. The great +wheel $\mathrm{G}$ rides loose on the arbor between the barrel and a +collar shown just above $\mathrm{G}$ and it is connected with the +barrel by the ratchet and click, of which a front view and +description has been already given at page~\pageref{fig04}. (There are +in fact two ratchets $\mathrm{R}$ and $r$ in fig.~\ref{fig25}, but we need not +inquire into the functions of the second at present: it will +be explained at p.~\pageref{2ratchets}.) The great wheel $\mathrm{G}$ drives the +centre pinion $c$, which always turns in an hour, and its arbor +goes through to the dial and carries the minute hand in the +way I will describe presently. The centre wheel $\mathrm{C}$ drives +the second pinion $d$, on whose arbor is a wheel $\mathrm{D}$ which +drives the scapewheel $\mathrm{E}$ by its pinion $e$. In moderately good +clocks the pinions have all generally \index{Wheels, numbers of teeth}$8$ teeth or leaves, and +the wheels in that case have $96$, $64$, and $60$ teeth, if the +scapewheel turns in a minute as usual: in the best clocks +the pinions are occasionally as high as $16$; Mr.~Bloxam's +and Mr.~Salt's are the only ones I ever saw with higher +numbers. Of the scape-wheel, pallets, and pendulum, I +%-----File: 149.png----------------------------------------------- +%-----Folio: 134-------------------------------------------------- +\begin{figure}[htbp] +\centering\index{Clocks!arrangement of common}\index{House clock, common} +\caption{\sc Common House Clock} +\includegraphics[height=525pt]{images/fig25.png} +\label{fig25} +\end{figure}\markright{COMMON HOUSE CLOCK.} +%-----File: 150.png----------------------------------------------- +%-----Folio: 135-------------------------------------------------- +have said enough already. In the best clocks, and sometimes +in common ones, the scapewheel arbor comes through +the dial and carries a seconds hand. + +Short clocks with half second pendulums are best made +with a scapewheel of the usual number of $30$ teeth, as +either a large and heavy wheel, or teeth very closely set, are +objectionable. In that case the scapewheel will of course +turn twice in a minute, and the product of the numbers of +the teeth of the centre and second wheels must $= 120 \times +8 \times 8$ if the pinions are of $8$, which is best satisfied by $96$ +and $80$. In very inferior clocks the scapewheel pinion is +only $7$, and then $84$ and $80$ teeth will do. The American +clocks\index{American clocks}\index{Clocks!American} have lantern\index{Lantern pinions for clocks} pinions, in which $6$ pins are as good +as $8$ or $9$ common teeth, and therefore the centre and +second wheels need only have $72$ and $60$ teeth for a half-seconds +pendulum. It is not worth while to go on with +the calculation for $\frac23$~seconds pendulums or others, as the +principle of it is perfectly obvious. + +\subsection[Dial work.]{Dial work.}\markboth{COMMON DIAL WORK AND SPRING.}{COMMON DIAL WORK AND SPRING.}\index{Dial work!of house clocks}---If the minute hand were fixed rigidly to the +centre arbor, the clock could never be altered; and therefore +the way in which it is fixed and yet alterable is this: there +is a wheel $\mathrm{M}$ (in fig.~\ref{fig25}) set on a hollow arbor or pipe which +fits easily on the centre arbor, and has its own end squared +for the hand to fit it. A small bent spring with a hole in the +middle fits on the centre arbor, and the hole rests against a +shoulder which is turned on the arbor just in front of the +clock frame; the ends of the spring press against the back +of the wheel $\mathrm{M}$ when it is pressed back, as it is after the +hand is put on, and it is kept there by a collar and a small +pin put through the end of the centre arbor. + +And in this small matter there is room for a very common +mistake: the hand is kept steady by the friction of this +spring at one end and the collar at the other, and it will evidently +be much steadier for the same amount of pressure if +the spring fits the arbor tight, and so the friction is between +%-----File: 151.png----------------------------------------------- +%-----Folio: 136-------------------------------------------------- +the ends of the spring and the back of the wheel, than if it +is loose on the arbor, simply on account of the difference of +leverage at which the friction acts when you turn the hand +with your own finger. In mere regulators without any striking +part, this does not matter, because there is nothing to +disturb the hand; but when the wheel $\mathrm{M}$, or the equal wheel +$\mathrm{N}$ which is driven by it, has to lift a lever every hour to discharge +the striking part, it matters a great deal, because a +great deal more friction is then required to hold it in its +place against the pressure of the lever; and yet it seems to +be the fashion in London to make the hole in the spring +round instead of \label{squaring}squaring it on to the arbor; which would +take about ten minutes to do. The consequence is that a +clock will sometimes take to losing unaccountably in this +way, which I only first discovered by seeing the minute +hand gradually lag behind the seconds hand; and that defect +can only be permanently cured by making the \label{strong_spring}spring very +much stiffer than it need be if it is put on properly, \textit{i.e.}\ with +a square instead of a round hole. + +Over the minute-wheel $\mathrm{M}$ and its hollow arbor there is +fixed a thing called the \textit{bridge,} which is shown at $\mathrm{ML}$ (fig.~\ref{fig25}), +and has another pipe enclosing that of the wheel $\mathrm{M}$ but not +touching it; and the hour-wheel $\mathrm{H}$ with another hollow +arbor still larger rides upon the bridge pipe, and is driven by +a pinion $n$ of $1$-$12$th its own number of teeth, which is fixed +to the wheel $\mathrm{N}$ of the same number as $\mathrm{M}$\@. That wheel $\mathrm{N}$ is +generally set upon a stud or pin screwed into the front plate, +but is better with pivots in the frame and a cock. The hour +hand is set on the end of the hour-wheel socket either with +a small screw or pins. The thing marked $\mathrm{Y}$ in front of +the hour-wheel has nothing to do with the going part of +the clock, but is the \textit{snail} which regulates the number of +hours struck by the striking part, as will be explained +therewith. + +The hour hand in astronomical\index{Clocks!astronomical} clocks generally has a +%-----File: 152.png---------------------------------------------- +%-----Folio: 137------------------------------------------------- +small circle to itself in the lower half of the dial, to prevent +its hiding the seconds hand in the upper half, which it is +important that an observer should always be able to see. +Besides it moves with much less friction when so placed, as +it then turns on a thin stud fixed on the front plate of the +clock, instead of a very wide socket. It may either be +driven by an intermediate wheel and pinion from the centre +arbor, in order to make it go the right way round, or directly +by the great wheel, which involves less friction and no inconvenience +except the perfectly insignificant one of having +to move the hour hand separately from the minute hand +when you want to alter the clock much, which cannot happen +once a year in any good clock. + +\subsection[Dial.]{Dial.}\markboth{REGULATOR DIAL WORK.}{REGULATOR DIAL WORK.}\label{subsec:Dial_work.}\index{Astronomical clocks!dial work of}\index{Dial work!of house clocks}---Two different ways of fixing a dial are shown in +fig.~\ref{fig25}, and both of them different from the common one, in +which four separate pillars are screwed permanently into the +dial and the other ends go through the front clock plate and +are pinned behind it, the main pillars of the clock itself +being only long enough to connect the two plates, and +having nothing to do with the dial. Either of the two plans +in the figure seems to me to be better than this, though it is a +matter of very little consequence. The dials of the best +clocks are made of brass plates polished and silvered: the +common ones are of sheet iron: the American and Dutch of +wood. The hands\index{Hands of clocks and watches!the best colours for} are always of black steel in regulators\label{reg}, +but in common clocks they are of brass gilt, which is a very +bad colour on a white face, though very good on a black +face. The same remark applies to watch faces. I never +could understand how such an absurd thing as gold hands +on white faces---and still worse on gilt faces---came into +existence, especially as gold hands of that small size have +not even the vulgar merit of being dearer than steel +ones. + +\subsection[Winding keys]{Winding keys}\markboth{WINDING KEYS SHOULD BE LONG.}{WINDING KEYS SHOULD BE LONG.}\ \label{subsec:Winding_keys}\index{Key!for clocks}\index{Keys, winding}\index{Winding keys!for clocks}are generally made too \index{Winding keys!should be long}short in the stalk +or leverage, which makes the clock harder to wind and tends +%-----File: 153.png---------------------------------------------- +%-----Folio: 138------------------------------------------------- +to strain the arbor besides, as you may see from considering +that if the stalk was very short indeed, any force applied to +it would be chiefly consumed in trying to bend the arbor. +As there is absolutely no advantage in a short key, this is +one of the many instances of doing wrong for the pleasure of +it, when it would be quite as easy to do right and the effect +much more pleasant. All my seconds pendulum clock keys +are from $3$ to $5$~inches long, according to the weights. +The French spring clocks without fusees, in which the winding +is very hard towards the end, have keys like a very +large watch key or a piano-tuner, to prevent the strain +upon the arbor. But this makes the winding a much longer +operation and a very unpleasant one, as you have to stop +at every half turn. Sometimes such keys are given with +small English fusee clocks, for which there is no excuse. +You should take care that the wood or ivory on the handle +of a key is quite loose, or it increases the resistance materially +in winding. + +\subsection[Year clocks.]{Year clocks.}\markboth{YEAR CLOCKS.}{YEAR CLOCKS.}\label{subsec:Year_clocks.}\index{Clocks!year}\index{Year clocks}---Clocks without striking parts are sometimes +made to go a month, and occasionally even a year. +For a month they only require one more wheel and pinion +with a multiplier of $4$, between the centre and great wheels. +Year clocks require $3$ wheels below the centre, and the +pinions ought to be of $10$, $10$ and $12$ at least, on account of +the great weight required, which will have to be still greater +if the pinions are of low numbers. Assuming the clock to +go $380$~days, and the barrel to have $16$ turns as usual, the +product of the $3$ wheels must $= \frac{380.24.12.10.10}{16}$, for which +$100$, $90$, and $76$ will be the best numbers. This is far better +than trying to do it with only two wheels of $192$ and $190$ +(the lowest possible numbers), and pinions of $8$, in which +the friction will be very much greater. The best way is to +have two barrels and great wheels acting on one long pinion +of $12$, with the weight hung by the same string from both +%-----File: 154.png--------------------------------------------- +%-----Folio: 139------------------------------------------------ +barrels by a pulley which only turns while you are winding +up; and there must be a winding stop to each barrel. + +\subsection[Clock cases]{Clock cases}\markboth{CLOCK CASES.}{CLOCK CASES.}\ \label{subsec:Clock_cases}\index{Clock-cases}are necessarily connected with the construction +of the clock. The old tall case with a base as big as +the top, standing on the floor instead of screwed to the wall, +is sufficiently \correction{explored}\label{correction2} %**Transcriber's note: The original reads "exploded". +to require no more to be said against +it. The case need be no longer than is required for the +pendulum, as the weights can have $3$ lines, or smaller barrels, +or larger great wheels, of which the second is the worst. The +weights themselves of course have to be half as heavy again +as with the fall one half longer. The best case for a superior +clock is one of which the front and sides take off together. +There need be no door to the face, but only small brass or +white metal shutters over winding holes in the plate glass +front, which enables you to lock up the clock completely and +leave anybody to wind it up. Ornamental case making I +have nothing to do with, and it is not much of an exaggeration +to say that the value of the inside of a clock generally +varies inversely as the decoration of the outside. + +\subsection[Moon dials.]{Moon dials.}\markboth{MOON DIALS.}{MOON DIALS.}\label{subsec:Moon_dials.}\index{Dials!moon}\index{Lunar clocks}\index{Moon dials}---There is an old calculation that if a pinion +of $6$ is put on the hour arbor of a clock---\textit{i.e.}\ the centre +one---and drives a wheel of $91$ with a pinion of $9$ on its +arbor driving another wheel of $91$ with a pinion of $37$ driving +a wheel of $171$, that last wheel will turn in $29$d.~$12$h.~$44$m, $3.4$s., which is only about half a second more than an +average lunation. A pinion of $6$ does very well for a driving +one, though it is much too low a number for a driven pinion, +except of the fly of the striking part. But if the centre +pinion is $12$ and the great wheel $182$, those two will do for +the first pair of such a lunar train. In that case, as the +arbor of the great wheel must turn for winding, it would be +necessary to fix the $37$ wheel on the back of the great wheel, +and let that drive either the $91$ or the $171$ as may be convenient; +for the order in which wheels and pinions are +arranged is immaterial as to the velocity-ratio between +%-----File: 155.png-------------------------------------------- +%-----Folio: 140----------------------------------------------- +the first and the last. The common moon dials of old-fashioned +clocks are only driven by a single tooth on the +hour arbor driving a wheel of $59$ teeth by jumps twice a +day, leaving an error of $44$~m.\ in a month, to be set right by +hand every now and then. + +A simpler moon train, quite exact enough for this purpose +may be made by a pinion of $15$ on a $24$-hour wheel of the +clock driving a $98$ wheel with a pinion of $25$ driving a wheel +of $113$, which will turn in $708.736$~hours, which is only an +excess of $7$~seconds over one lunation of $708.73415$~h., or $3$ +minutes in $2$ years, which would be quite imperceptible in +any dial. But nobody seems to remember that no flat moon +dial can possibly imitate more than one phase of the moon, +either just half-moon, or else the narrowest possible crescent; +for the \textit{terminator}, or boundary of light and shade on the +moon, is always a semi-ellipse, varying continually from +the nearest visible approach to a semicircle down to a +straight line and then back again. The only way in which +real phases can be shown is by a globe half white or gilt and +the other half black, turning on an axis in the plane of the +dial in a hole just fitting the globe. And that only will look +like the moon when seen right in front and from a considerable +distance, as the moon is. Practically a vertical +axis will do, though I need not say that the diameter which +joins the `horns' of the terminator is seldom quite upright, +and sometimes leans a good deal either way (see my `Astronomy,' +p.~140 of 7th ed.). The axis must be turned by +a bevelled wheel, of which half will come through the dial---or +above, if you want to hide it. But all such contrivances +are mere playthings, and show the moon's phases much less +distinctly than an almanac. + +\subsection[Day of the month dials]{Day of the month dials}\markboth{DAY OF THE MONTH DIALS.}{DAY OF THE MONTH DIALS.}\label{subsec:Day_of_the_month_dials}\index{Clocks!day of the month}\index{Day of the month dials}\ have to be dealt with rather +differently, because the move must take place only once in +the $24$~hours, at some time in the night. Consequently the +wheel which carries either a small dial with figures showing +%-----File: 156.png--------------------------------------------- +%-----Folio: 141------------------------------------------------ +through a hole, or a hand pointing to figures, must have +ratchet teeth driven by a lever or click or tooth moved once +a day. There must also be a slight spring or `jumper' somewhere +on the ratchet teeth to keep them exactly in the proper +place for the click to catch next time. In the old-fashioned +clocks the month wheel simply had $31$ teeth, and you had to +move it on by hand in February, April, June, September, and +November. + +\begin{figure}[hbtp] +\centering +\hypertarget{fig26}{\caption{\sc Day of the Month Dials}} +\includegraphics[width=\textwidth]{images/fig26.png} +\label{fig26} +\end{figure} + +I doubt if such clocks, however completely automatic, are +really of much use, for this reason if for no other, that the figures +of the day of the month are always too small to be seen at such +a distance as clocks usually are when you are writing and +want the date. Large cards, changed every day, are infinitely +more used. Nevertheless, as the machinery is, or may +be, much simpler than you would suppose beforehand, I may +as well indicate the nature of it, on what seems to me the +simplest of the various ways of doing it. But for the present +foolish arrangement of months, which the world seems impotent +to set aside, we should only want six months of $30$ +%-----File: 157.png--------------------------------------------- +%-----Folio: 142------------------------------------------------ +days, and six of $31$ in leap years, and in other years seven +and five. But, as things are, we have four kinds of month +to provide for. We must clearly have one wheel $\mathrm{M}$ with $31$ +teeth, carrying a hand pointing to a month dial; for that is +much easier to see than numbers peeping through a hole, and +it is enough to print every third number, except at last $28$--$30$--$1$. +Then we want some contrivance to push on two +teeth in April, June, September, and November, three in +February in leap year, and four in other years. + +Let there be a $24$~hour wheel \textsc{Day}, which, by the +pin at $\mathrm{D}$ moving on to $d$, will move the long lever $\mathrm{CEFD}$ so +much to the right as will carry the horizontal click $\mathrm{FG}$ over +the space of $4$ teeth or pins of the month wheel, \textit{i.e.}\ will +drive that wheel $4$~days forward. That provides for common +Februaries. Then if the lever $\mathrm{CD}$ is stopped from going +more than the space of one tooth of $\mathrm{M}$ back again at the end +of the long months, as of other days, they also are provided +for. It must fall back the space of two teeth at the common +short months, and three teeth at the end of leaping Februaries. +Several ways have been invented for doing this. The simplest +is to have a four-year wheel, or disc $\mathrm{Y}$, with $4$ deep February +notches in it at quadrants, into which a long tooth $\mathrm{E}$, on the +lever $\mathrm{CED}$, can drop, and short notches for the $30$-day +months, and none for the long months, but the outside of the +wheel $\mathrm{Y}$ is the space of one tooth off the tooth $\mathrm{E}$ generally. + +But we have to consider how the year wheel is to be +moved at the end of every month, as it must be, and so as +not to be held fast by the tooth $\mathrm{E}$ in any notch. I think the +best way is to do it by another lever $\mathrm{LNM}$ on a stud in the +clock frame at $\mathrm{L}$, and a gathering click $\mathrm{NK}$, which takes +hold of one of the $48$ pins in $\mathrm{Y}$ when that lever is lifted, and +carries $\mathrm{Y}$ one step or month-space forward when the lever is +dropped by the snail $\mathrm{M}$ just before the last move of the month +is finished, or as the hand comes up to $1$. This divides the +work of moving the two wheels and levers more uniformly +than any other plan, besides making sure of the tooth $\mathrm{E}$ +%-----File: 158.png-------------------------------------------- +%-----Folio: 143----------------------------------------------- +being out of a notch before the year wheel wants to move: +not that it would signify on this plan if it were not, for then +the lever $\mathrm{LNM}$ would only wait to drop. Each of the wheels +wants a safety click or juniper, $\mathrm{A}$, $\mathrm{B}$, of the usual kind for +such motions. I only put pins instead of ratchet teeth to $\mathrm{M}$, +because the click $\mathrm{FG}$ will be safer not to slip out. + +The work might be simplified a little and the lifts made +less, and the year wheel need only be a quarter of the size, +if you will be content to move the month hand at the end of +February by hand. A week dial is quite superfluous, and so +I have not crowded the picture with one. It only wants a +seven-star wheel by the side of the day wheel, one ray of +the star being moved by the pin $\mathrm{D}$ after it has come to $d$ and +done its monthly work. It is desirable to distribute the +work as much as possible. The month dial ought to be at +least twice as large as in \hyperlink{fig26}{this drawing}, to be seen easily. + +In any clock which has all this extra work to do, special +care must be taken that the `motion' wheels (or dial work) +are held on the centre arbor by a squared spring, and a pretty +strong one (see p.~\pageref{strong_spring}), or it is sure to slip and gradually +drag, though the clock may be going right. + +Several\markboth{DIALS WITHOUT HANDS.}{DIALS WITHOUT HANDS.} persons have taken patents for clocks and watches +showing the time by figures appearing through a hole in the +dial instead of by hands.\index{Chronoscopic dials} Not that there is anything new in +that, except as to the machinery for doing of it. Days of +the month were generally so done 100 years ago at least; +and my old regulator by Holmes\index{Holmes, an old clockmaker}, already mentioned at p.~\pageref{holmes}, +shows the hours in that way. I do not profess to judge of +public taste, but it seems to me that all such inventions proceed +on the fundamental mistake of supposing that we \textit{read} +the figures of a dial. We do nothing of the kind, but judge +at once from the mere position of the hands and the well-known +marks for the hours and minutes. In fact dials are +better and clearer with no numbers at all, but merely $12$ +large spots for the hours and five-minutes, and $48$ small +ones for the other minutes, as I have often convinced people +%-----File: 159.png-------------------------------------------- +%-----Folio: 144----------------------------------------------- +by asking them if they want such a dial as they see in +several of my clocks. They always answer `Yes;' and +then are much surprised to find no figures, but only +the $12$ strong marks and $48$ small ones. And the +hands upon a dial, whether large or small, are more +conspicuous than any figures which can be conveniently +made to appear through a hole, especially if the hands are +of the proper colour\index{Hands of clocks and watches!the best colours for}---\textit{i.e.}\ black on a white or gilt dial or +gilt on a black one. + +Moreover, there is another objection to those `chronoscopic'\index{Chronoscopic dials}\index{Dials!chronoscopic}\label{chronoscopic} +dials: the figure-discs must be driven discontinuously, +or by jerks at the end-of certain periods; and if that is done +directly by the watch, as in Barlow's patent of 1866, the +strain on the wheels is so much greater at the short time of +action, and especially when the units and tens of minutes and +the hour all have to be changed at once, that it is impossible +for such a watch to go well. Besides the mere work of +moving the $3$ discs, all from the $5$-minute wheel of the train +with different intermediate wheels, there are jumper springs +to be moved too. Whether such watches have been ever been +made I do not know; I have only read the specification. + +It was patented in 1869 for clocks in a more practicable +form by \index{Siddons and Meese's clocks}Siddons and Meese, who brought me one to examine. +They have $3$ cylinders, $\mathrm{A~B~C}$, near together; $\mathrm{A}$ +with the ten digits 0~1\dots\dots~9 on its face for units of +minutes, $\mathrm{B}$ with blank~1~2~3~4~5 (blank being better than $0$ +there) twice over for the tens of minutes (making $12$ spaces), +and $\mathrm{C}$ with 1 up to 12 for the hours. An $8$-minute wheel +in the clock has $8$ pins in it, which are always lifting a +weighted lever, except at the moment when it drops from +one pin to another. The lever has a pall\footnote{If this word has any etymology it clearly should be spelt \textit{pall}, +not from the \textit{pallium} of an archbishop or a corpse, but from $\pi\alpha\lambda\lambda\omega$, to +strike, the origin of pallet. `Paul' or `pawl' are mere nonsense, of +the same order as the vulgar conversion of the expressive Yankee word \textit{bunkum}, for bluster, +into \textit{buncombe}, for no other reason than because +newspaper writers know there is a noble family of Duncombe, or the +auctioneers' conversion of the site of a house into scite, which only +shows themselves to be insciti.} or click which +%-----File: 160.png-------------------------------------------- +%-----Folio: 145----------------------------------------------- +\label{folio_145}first slips over and then brings down in falling one of $10$ +ratchet teeth on the side of $\mathrm{A}$, and so changes it from one +figure to another. Whenever $\mathrm{A}$ changes from 9 to 0 it also +moves on $\mathrm{B}$ one figure by the usual contrivance of numbering +machines for railway tickets, bank-notes, and pages of +ledgers; and when $\mathrm{BA}$ changes from 5~9 to blank~0, $\mathrm{B}$ in +like manner changes $\mathrm{C}$ one figure, $\mathrm{B}$ having $2$ levers on its +side corresponding to the two blanks. There are other +details of minor importance in Siddons and Meese's clocks, +for which the patent has been transferred to Gillett and +Bland, of the Steam Clock Factory at Croydon. + +As descriptions of the numbering machine are not +easy to find, I had better give one, at least sufficient to +illustrate its principle. Take first the simple case of +only two wheels or cylinders set near together on the +same axis, but loose, with the $10$ digits engraved on their +faces, one $\mathrm{A}$ for units and the other $\mathrm{B}$ for tens. A +carries on its side a small bent lever which generally +hangs loose, but at one place in the revolution, where $\mathrm{A}$ is +changing from 9 to 0, the lever has its tail caught by a fixed +obstacle, and for that moment the other end of the lever +cannot yield, but travels with its wheel. $\mathrm{B}$ has $10$ pins on +its side, and whenever the lever of $\mathrm{A}$ is in that condition it +catches one of those pins and so drives on $\mathrm{B}$ one step, or +changes it one figure. Then for the hundreds, $\mathrm{B}$ has a +similar lever on its other side which changes a wheel $\mathrm{C}$ in +like manner, and so on for as many figures as are wanted. +In clocks the change of the $10$-minute wheel has to be made +after 5 so as to show 0 or a blank next, instead of after 9 as +in numbering machines. + +\subsection[Equation of time clocks.]{Equation of time clocks.}\markboth{EQUATION OF TIME CLOCKS.}{EQUATION OF TIME CLOCKS.}\label{subsec:Equation_of_time_clocks.}\index{Clocks!equation of time}\index{Equation of time clocks}---A still more obsolete contrivance, +%-----File: 161.png-------------------------------------------- +%-----Folio: 146----------------------------------------------- +but worth recording for the principle of its +machinery, was that for making the hands of a clock show +solar instead of mean time, at least in a rude and approximate +way, which I suppose was used in the French public +clocks which did so up +to the year 1826. $\mathrm{A}a$ in +\hyperlink{fig27}{this figure} is a bevelled\label{bev} +wheel on the centre wheel +arbor, which in this case +is made to turn the +wrong way round, and +another equal bevelled +wheel $\mathrm{B}b$ rides upon it, +with a hollow spindle $bc$ +to which the minute-hand +is fixed. Between these +two is another small +bevelled wheel $\mathrm{D}$ of any +size, which would merely +reverse the motion, if it +was set on a fixed spindle +or arbor. But it is not, +for it rides on the end of +a bar or lever $\mathrm{DE}$, which +itself turns upon the centre +arbor and has its end $\mathrm{D}$ +beyond the wheel resting +on a plate of the odd +shape shown at $\mathrm{Q}q$, which +is fixed to the face of a +wheel which turns in a +year. Now if the lever $\mathrm{DE}$, or the centre of the small wheel, +is moved at any time in the same direction as the hand is +going, it will evidently push it forward just twice as much as +the lever itself is moved, and \textit{vice vers\^a.} If then the equation +\begin{figure}[htbp] +\centering +\hypertarget{fig27}{\caption{\sc Equation of Time Clock}} +\includegraphics[height=0.7\textheight]{images/fig27.png} +\label{fig27} +\end{figure} +%-----File: 162.png-------------------------------------------- +%-----Folio: 147----------------------------------------------- +plate $\mathrm{Q}q$ is on the right side of the clock-frame, the hand will +go ahead of its mean motion whenever $\mathrm{D}$ drops below the +mean radius of the plate from $\mathrm{O}$ the centre of the year wheel +and will fall behind mean time when the protuberant parts +of the plate are uppermost. The plate then may be so +shaped as to make the advance and retardation of the hand +agree with the `sun before clock' and `sun after clock' of +the equation of time. + +There are two other ways of giving a secondary motion +of this kind; one, by substituting a common small wheel or +pinion for the middle bevelled wheel, and putting it between +$\mathrm{A}a$ made as a common wheel, and $\mathrm{B}b$ made as an \textit{internal} +wheel, \textit{i.e.}\ with teeth inside its rim; but in that case you +must remember that $\mathrm{A}$ and $\mathrm{B}$ will have different velocities, +and therefore $\mathrm{A}$ must turn in less than the hour. The other +method requires neither bevelled nor internal wheels, and is +on the same principle as the one I shall describe more fully +under \textit{train remontoires.} + +Clocks for showing other celestial motions are mere +curiosities, and are always getting out of order from their +complication; so I shall not waste time in describing them, +but go on to something more practical. + +\section{MAINTAINING POWERS OR GOING BARRELS.}\markboth{MAINTAINING POWERS.}{MAINTAINING POWERS.}\label{sec:MAINTAINING_POWERS_OR_GOING_BARRELS.}\index{Barrels, going}\index{Maintaining powers of clocks or going barrels} + +Winding up a clock evidently takes the action of the +weight off the great wheel, and so the clock movement stops +for the time, though the pendulum goes on swinging. This +of course will not do in a clock of any accuracy, whether a +large or a small one, and as the same methods of keeping +the clock going (or some of them) are applied to both, I +shall describe them all together here, except one. + +The oldest of them all is \index{Huyghens!endless chain}\textit{Huyghens's endless chain.}\index{Maintaining powers of clocks or going barrels!endless chain}\label{endless} In +fig.~\ref{fig28} $\mathrm{P}$ in the `going wheel' is a pulley fixed to the +great wheel of the going part, and having short spikes set in +%-----File: 163.png----------------------------------------------- +%-----Folio: 148----------------------------------------------------- +it, or roughened in some other way so as to prevent a rope +or a chain hung over it from slipping. A similar pulley +rides on another arbor $p$, which may be the arbor of the +great wheel of the striking part, if the clock has one, and +attached by a ratchet and click to that wheel, or to the +clock-frame if there is no striking part. The weights are +hung as you see, the +little weight being +only big enough to +keep the string in +the pulleys\index{Pulleys}; but the +string or chain is +much longer, or one +at least of the weights +is always lower down +than I have been +obliged to draw it +\hyperlink{fig28}{here}. If you pull $b$, +the left hand of all +the strings, down, +the ratchet pulley +moves under the +click, and the great +weight is pulled up +by $c$, without taking +its pressure off the +going wheel at all. +This plan was generally +used in the old $30$~hour clocks, but went out with them, +as the action of a chain or even a rope hung in that way is +rough and uneven; and moreover the pulleys must be of +only half the usual diameter for the same time of going. + +\begin{figure}[ht!bp] +\centering +\hypertarget{fig28}{\caption{\sc Endless Chain}} +\includegraphics[width=288pt]{images/fig28.png} +\label{fig28} +\end{figure} + +\subsection[Harrison's going barrel]{Harrison's going barrel}\markboth{SPRING GOING BARREL.}{SPRING GOING BARREL.}\label{subsec:Harrison's_going_barrel}\index{Harrison!going barrel}\index{Maintaining powers of clocks or going barrels!Harrison's} is the maintaining power used +in all regulators now. The larger \label{2ratchets}ratchet wheel\index{Ratchet wheels} $r$ is the +one designated by the same letter in fig.~\ref{fig25} (p.~\pageref{fig25}); and +%-----File: 164.png---------------------------------------- +%-----Folio: 149------------------------------------------- +the click $\mathrm{R}$ is fixed to that wheel, which is connected with +the great wheel by a spring $\mathrm{SS}'$. While the clock is going the +weight acts on the great wheel $\mathrm{G}$ through the spring; but as +soon as you take off the weight by winding, the click $\mathrm{T}r$, +whose pivots are set in the frame, prevents the great ratchet +from falling back, and so the spring still drives the great +wheel during the time the clock takes to wind, especially as +it need only just keep the escapement going, for the pendulum +will take care of itself for that short time. The drop of +the great click over the teeth of its ratchet may be heard +\begin{figure}[ht!bp] +\centering +\hypertarget{fig29}{\caption{\sc Spring-going Barrel}} +\includegraphics[width=288pt]{images/fig29.png} +\label{fig29} +\end{figure} +%-----File: 165.png----------------------------------------------- +%-----Folio: 150-------------------------------------------------- +every $10$~minutes or so while the clock is going. Watches +have the same apparatus, with a spring click. + +\subsection[Bolt and shutter.]{Bolt and shutter.}\markboth{OTHER MAINTAINING POWERS.}{OTHER MAINTAINING POWERS.}\label{subsec:Bolt_and_shutter.}\index{Bolt and shutter}\index{Maintaining powers of clocks or going barrels!bolt and shutter}---Another contrivance, which is now +used only in large clocks, is an arbor with a weighted lever +at one end of it, with a click in the form of a spring bolt on +another lever; when the weighted arm is lifted up the click +`takes into' the teeth of some one of the train wheels, and the +weight then keeps the clock going till it works itself out of +gear in a few minutes and drops. The weighted lever is +outside the clock and is made with a cap or shutter which +shuts over the key-hole when it is down, to make sure of +your lifting it before you begin winding. With the usual +ingenuity for doing things wrong, this click is very often +made not as a sliding bolt, but with a hinge, so that there is +one position of the lever in which it jams against the teeth +and stops the clock for good, unless the winding man finds +it out and releases it, which he probably will not. Sometimes +too the click sticks and sometimes it slips, even if made +rightly. There is another defect besides in the common +bolt and shutter, viz.\ that it may work itself down and rest +upon the winder or key before the winding is done if the +man is slow about it, and then it does no good and the clock +stops for the time. + +\subsection[Improved bolt and shutter.]{Improved bolt and shutter.}\markboth{SIR E. BECKETT'S BOLT AND SHUTTER.}{SIR E. BECKETT'S BOLT AND SHUTTER.}\label{subsec:Improved_bolt_and_shutter.}\index{Bolt and shutter!Sir E.~Beckett's improved}\index{Maintaining powers of clocks or going barrels!bold and shutter!Beckett's improved}---To prevent these evils, +and to simplify the construction, I\index{Beckett, Sir E.!bolt and shutter} introduced the plan of +substituting for the `bolt' a segment $\mathrm{D}$, in fig.~\ref{fig37}, p.~\pageref{fig37}, +of a small wheel suited to the teeth of the great wheel, and +making the arbor $\mathrm{C}$, which carries that and the shutter $\mathrm{M}$, +to pump in and out of gear, and the shutter not covering the +key-hole, but made as a circular arc to the centre $\mathrm{C}$, which +all but touches the winder when it is on. The winder has a +ring, shown by the circle at $\mathrm{M}$, fixed round its end, which +prevents it from being put on until you have lifted the +shutter, and put it into gear with the great wheel, to hold +it up. As you go on winding, the clock goes on and the +%-----File: 166.png----------------------------------------------- +%-----Folio: 151-------------------------------------------------- +shutter descends, now behind the ring, which secures your +pulling it out of gear again when you take off the winder, +and yet it will keep in action full $10$~minutes if left to work +itself out. This plan is now generally used in superior +large clocks. The weighted arm should be long, so as not +to require a heavy weight to be lifted. + +I shall describe hereafter another totally different plan +for keeping a very large clock going when the winding takes +a long time; but as the spring \label{smallmaintain}going barrel does very well +for small clocks, and the improved bolt and shutter for any +but a clock of quite unusual size, I shall postpone that +description till we come to the Westminster clock. For the +same reason I need not repeat the description of Sir G.~Airy's\index{Airy, Sir G.~B.!maintaining power} +going barrel, which was applied to the Exchange clock, but +is so expensive that it is certain never to be used again. A +full description of it was given by him in vol.~7 of the Cambridge +Phil.~Trans. The object of it was not only to keep +the power always on the clock, but exactly the same power; +for the power of the spring falls below that of the weight, +and that of the bolt and shutter doubles it just at the times +of putting it on and taking it off; but that is of no consequence, +except in a revolving pendulum clock, for which his +apparatus was invented; he afterwards simplified the construction, +but it is still an expensive one, and the thing can +be done at a tenth of the cost by the Westminster method +without either loss or duplication of force. + +There is another maintaining power\index{Sun and@`Sun and planet' maintaining power}\markboth{`SUN AND PLANET' MAINTAINING POWER.}{`SUN AND PLANET' MAINTAINING POWER.} which has a tempting +and scientific look, but is not so good as it looks. A rim +at the back of the great wheel, $\mathrm{M}$ (fig.~\ref{fig29}), has internal +teeth at A---troublesome things to make---and in them works +a wheel $\mathrm{ABP}$ on a stud $\mathrm{B}$ in the end of the barrel, and also +in a pinion $\mathrm{C}$ fixed on the arbor which runs loose through +the barrel ends. When you wind up you apply some force $\mathrm{P}$ +to the intermediate wheel, and the same pressure $\mathrm{P}$ is communicated +to the great wheel because $\mathrm{BP = BA}$, $\mathrm{P}$ being +%-----File: 167.png----------------------------------------------- +%-----Folio: 152-------------------------------------------------- +\begin{figure}[htbp] +\centering\index{Maintaining powers of clocks or going barrels!sun and planet@`sun and planet' power}\index{Sun and@`Sun and planet' maintaining power} +\setlength{\unitlength}{0.028\textwidth}%needs to be this large for lines in diamond to be long enough for LaTeX. Smaller \path available if epic, eepicemu packages loaded. +\caption{\sc Sun-and-planet Power} +\begin{picture}(30,28)(-13,-15) +%diamond in centre +\put(0,1){\line(-1,-1){1}} +\put(-1,0){\line(1,-1){1}} +\put(0,-1){\line(1,1){1}} +\put(1,0){\line(-1,1){1}} +%Circle centre (0,0) radius 3 +\qbezier(3,0)(3,1.242641)(2.121320,2.121320) +\qbezier(-3,0)(-3,1.242641)(-2.121320,2.121320) +\qbezier(3,0)(3,-1.242641)(2.121320,-2.121320) +\qbezier(-3,0)(-3,-1.242641)(-2.121320,-2.121320) +\qbezier(2.121320,2.121320)(1.242641,3)(0,3) +\qbezier(-2.121320,2.121320)(-1.242641,3)(0,3) +\qbezier(2.121320,-2.121320)(1.242641,-3)(0,-3) +\qbezier(-2.121320,-2.121320)(-1.242641,-3)(0,-3) +%Circle centre (0,0) radius 12 +\qbezier(12,0)(12,4.970564)(8.485280,8.485280) +\qbezier(-12,0)(-12,4.970564)(-8.485280,8.485280) +\qbezier(12,0)(12,-4.970564)(8.485280,-8.485280) +\qbezier(-12,0)(-12,-4.970564)(-8.485280,-8.485280) +\qbezier(8.485280,8.485280)(4.970564,12)(0,12) +\qbezier(-8.485280,8.485280)(-4.970564,12)(0,12) +\qbezier(8.485280,-8.485280)(4.970564,-12)(0,-12) +\qbezier(-8.485280,-8.485280)(-4.970564,-12)(0,-12) +%Circle centre (0,0) radius 12.5 +\qbezier(12.5,0)(12.5,5.177670)(8.838835,8.838835) +\qbezier(-12.5,0)(-12.5,5.177670)(-8.838835,8.838835) +\qbezier(12.5,0)(12.5,-5.177670)(8.838835,-8.838835) +\qbezier(-12.5,0)(-12.5,-5.177670)(-8.838835,-8.838835) +\qbezier(8.838835,8.838835)(5.177670,12.5)(0,12.5) +\qbezier(-8.838835,8.838835)(-5.177670,12.5)(0,12.5) +\qbezier(8.838835,-8.838835)(5.177670,-12.5)(0,-12.5) +\qbezier(-8.838835,-8.838835)(-5.177670,-12.5)(0,-12.5) +%Circles centre (-7.5,0) radii 0.5 and 4.5 +\put(-7.5,0){\circle{1}} +\qbezier(-3,0)(-3,1.863961)(-4.318020,3.181981) +\qbezier(-12,0)(-12,1.863961)(-10.681981,3.181981) +\qbezier(-3,0)(-3,-1.863961)(-4.318020,-3.181981) +\qbezier(-12,0)(-12,-1.863961)(-10.681981,-3.181981) +\qbezier(-4.318020,3.181981)(-5.636039,4.5)(-7.5,4.5) +\qbezier(-10.681981,3.181981)(-9.363961,4.5)(-7.5,4.5) +\qbezier(-4.318020,-3.181981)(-5.636039,-4.5)(-7.5,-4.5) +\qbezier(-10.681981,-3.181981)(-9.363961,-4.5)(-7.5,-4.5) +%Circles centre (15.5,0) radii 1 and 3 +\put(15.5,0){\circle{2}} +\qbezier(18.5,0)(18.5,1.242641)(17.621320,2.121320) +\qbezier(12.5,0)(12.5,1.242641)(13.37868,2.121320) +\qbezier(18.5,0)(18.5,-1.242641)(17.621320,-2.121320) +\qbezier(12.5,0)(12.5,-1.242641)(13.37868,-2.121320) +\qbezier(17.621320,2.121320)(16.742641,3)(15.5,3) +\qbezier(13.37868,2.121320)(14.257359,3)(15.5,3) +\qbezier(17.621320,-2.121320)(16.742641,-3)(15.5,-3) +\qbezier(13.37868,-2.121320)(14.257359,-3)(15.5,-3) +%Horizontal lines +\put(1,0){\line(1,0){2}} +\put(-12,0){\line(1,0){4}} +\put(-7,0){\line(1,0){6}} +\put(12,0){\line(1,0){2.5}} +\multiput(3,0)(1,0){9}{\line(1,0){0.5}}%dotted line +%Vertical lines and arrows +\put(-12,0){\vector(0,-1){15}} +\put(-3,0){\vector(0,1){6}} +\put(0,1){\line(0,1){2.5}} +%Labels +\put(0,3.7){\makebox(0,0)[b]{C}} +\put(15.5,3.5){\makebox(0,0)[b]{H}} +\put(-3,6.2){\makebox(0,0)[b]{P}} +\put(-7.5,0.7){\makebox(0,0)[b]{B}} +\put(-11.8,0.2){\makebox(0,0)[bl]{A}} +\put(-9,9){\makebox(0,0)[br]{M}} +\put(-11.8,-15){\makebox(0,0)[bl]{W}} +\end{picture} +\label{fig30} +\end{figure} +whatever is necessary to lift the weight. Let $\mathrm{W}$ be the +effective weight at $\mathrm{A}$ when the clock is going: at $\mathrm{B}$ it is +$\mathrm{W}\frac{\mathrm{CA}}{\mathrm{CB}}=\mathrm{W}'$; and $\mathrm{P} = \frac{\mathrm{W}'}{2}$, since +$\mathrm{AP=2AB} \therefore \mathrm{P} = \frac{\mathrm{W}}{2}\frac{\mathrm{CA}}{\mathrm{CB}}$; which +cannot possibly $=\mathrm{W}$, however +small the winding pinion is, and if +it is very small it takes a long time +to wind. So this maintaining power +must be deficient, though it may do +for clocks with the common escapements, +which will go for a few +minutes with very little power on. Besides that, the winding +arbor has to work under double friction of the pressure +of twice $\mathrm{W}$, both above and below it. For all these reasons +I have never adopted it, either for large or small clocks. + +\subsection[Spring clocks.]{Spring clocks.}\markboth{SPRING CLOCKS.}{SPRING CLOCKS.}\label{subsec:Spring_clocks.}\index{Clocks!spring}\index{Spring!clocks}---Hitherto we have supposed all clocks +to be kept going by a weight. But many clocks have no +weight, but have a spring made of a long ribbon of steel +coiled up in a barrel for their moving force. This construction +however belongs so peculiarly to watches that I shall +defer the description of it till we come to them. I will only +mention here that the French clocks,\index{French clocks} like French and \index{Swiss watches}Swiss +watches, generally have the great wheel fixed to the barrel, +which of course makes the force on the train unequal. In +that case the barrel arbor goes loose through the barrel ends +and is fixed to the inner end of the spring, and has also a +strong ratchet squared on to it, with a click on the clock +frame, which holds it when you are not winding up. And a +barrel of this kind is of itself a `going-barrel,' for it keeps +the power on as much while you are winding as at other +times---in fact rather more. English spring clocks always +have a fusee with a chain, made as in the figure of a chronometer +movement, which will be given in the chapter on +%-----File: 168.png-------------------------------------------- +%-----Folio: 153----------------------------------------------- +watches, to equalise the force on the train. I understand that +this class of clocks is now sold more than any other English +ones, with half-second pendulums, either in cases made to +stand on a bracket or to hang up against a wall. + +\subsection[American clocks.]{American clocks.}\markboth{AMERICAN CLOCKS.}{AMERICAN CLOCKS.}\label{subsec:American_clocks.}\index{American clocks}\index{Clocks!American}---There have been great fluctuations +in the quality of these clocks since they first came here above +40 years ago, and there is now a great variety of them, and +they are certainly cheaper than most if not all others of the +same general quality. Their principal defect is in the lightness +of the pendulums. I have improved several of them +by increasing its weight. The wheels and plates of the +frame of these clocks are stamped out of sheet brass, and +they contain several ingenious contrivances. They have +advanced considerably in appearance at any rate since the +original Sam\index{Sam Slick was Eli Terry} Slick form; and, by the way, it seems +that the original Samuel Slick was one Eli Terry, whose +name ought to be preserved in a book on clock making. +But even these new ones are equally defective in the +weight of the pendulum, though they are longer; and +yet I can hardly suppose that the makers of such clocks are +as ignorant as a shopman here, who confidently assured me +that the weight of pendulums is of no consequence! It +would not cost a penny more to make them heavier. Some +superior ornamental clocks and regulators appear to be made +at the Howard watch and clock factory at Boston, U.S\@. I +read lately in the \textit{English Mechanic} that they make regulators +as well as turret clocks with my gravity escapements, +and that their own principal regulator has the four-legged +escapement. + +The old-fashioned `Dutch,'\index{Dutch clocks}\markboth{DUTCH AND FRENCH CLOCKS.}{DUTCH AND FRENCH CLOCKS.} \textit{i.e.}\ German\index{Clocks!German}\index{German clocks}, clocks, with +wheels of boxwood driving lantern pinions of wire stuck in +wood, have been in a great degree driven out by the Americans +with their superior appearance. But a more ornamental +kind of German clocks is now made, and I see in the +\textit{Horological Journal} of October, 1873, that there are now +%-----File: 169.png-------------------------------------------- +%-----Folio: 154----------------------------------------------- +nearly 2,000,000 clocks a year made in the Black Forest +`from the modest wooden clock up to the costly regulator,' +and that there are 1429 clock manufacturers there, employing, +one way or another, 13,500 people. Many of these +are called trumpet and cuckoo\index{Clocks!cuckoo}\index{Cuckoo clocks}\index{Trumpet and cuckoo clocks} clocks, in which the sound is +made by a small pair of bellows, worked at every blow of +what would ordinarily be the striking. The cuckoo is heard +much farther over a house than striking. I need hardly say +that the bird who appears at an open window is only a pretender, +and does not contain the bellows in his inside. + +\subsection[Improved French clocks.]{Improved French clocks.}\label{subsec:Improved_French_clocks.}\index{Clocks!French}\index{French clocks!improved kind of}---The old-fashioned French +chimney-piece clock, of which the form is well known, was +generally inferior to the commonest Dutch clock as a timekeeper. +But a very superior kind has been introduced of +late, far better than anything made in this country for two +or three times the price. They have the pin pallets made +of jewels, described at p.~\pageref{ruby}, and good pendulums of fair weight +for their size. They have also a peculiar means of +putting themselves in beat\index{Beat!self acting in French clocks} if they require it; for the pallets +are set what is called `spring tight' on their arbor, \textit{i.e.} +embrace it with a spring collar which will yield under +sufficient pressure, though tight enough to give the impulse +to the pendulum. If one pallet happens to work too deep, +from the clock being out of level, it reaches the bottom of +the teeth, or perhaps even the slight recoil of the pin pallets +against straight teeth is enough to push it back a little +into equal beat with the other pallet. These clocks have +also adopted the English, or `repeating,' striking part, which +will be described afterwards. Every one knows that the +old-fashioned French and German clocks oftener strike +wrong than right, and are apt even to be set wrong in +winding up the striking, which never happens with English +or with the improved French ones. The ornamental English +clock trade has ceased to exist, having been entirely driven +out by these, and also by the + +\subsection[Austrian clocks,]{Austrian clocks,}\markboth{AUSTRIAN CLOCKS.}{AUSTRIAN CLOCKS.}\label{subsec:Austrian_clocks,}\index{Austrian clocks}\index{Clocks!Austrian} with cases about $2\frac12$~feet high, which +%-----File: 170.png-------------------------------------------- +%-----Folio: 155----------------------------------------------- +first appeared in our 1862 Exhibition. Their chief defect is +the shortness of the arc of vibration, which makes them very +sensitive to the least disturbance, not merely as to rate +(as I showed at p.~\pageref{arc}), but even as to going at all. They +generally strike the quarters in a peculiar, and, I think, very +puzzling way, \textit{i.e.}\ $1$, $2$, $3$, $4$, on a single bell, and repeating +the hour at every quarter; so that from $12$ to $5$ you +have no idea what the clock means to say. + +\subsection[Self-winding Clocks]{Self-winding Clocks}\markboth{SELF-WINDING CLOCKS.}{SELF-WINDING CLOCKS.}\label{subsec:Self-winding_Clocks}\index{Clocks!self-winding}\index{Self-winding!clocks}\ have been made as long ago as the +1851 Exhibition. I have seen one by Mr.~Horstmann, at +Bath, with an endless chain made of a perforated wide watch-spring +running over pins in the main wheel, and worked +on the usual endless chain plan, but by a piston in a tube +filled with naphtha, which expands and contracts with the +temperature. I cannot say how far it is successful; and such +clocks are evidently of no real use. Sometimes one sees an +independent pendulum swinging in the hand of a bronze +lady, apparently motionless, on the top of a small clock; +but she really has a small twist at every beat in connection +with the clock below, and that pendulum does nothing. +Another curiosity sometimes exhibited is a balanced hand +turning all alone on a glass dial. This is managed by a +watch movement in the counterpoise, which tends to turn a +weight inside it all round the watch in twelve hours. It is +so poised that when the weight hangs at right angles to the +hand it will lie horizontal, pointing to either III.\ or IX\@. +When the weight is farthest from the centre, and therefore +most effective, the hand must point upwards; and when the +weight is nearest the centre the hand preponderates and +points downwards, and similarly at intermediate positions. +The weight in fact always hangs downwards absolutely in +the watch, and the hand relatively revolves round it. + +\subsection[Water clocks.]{Water clocks.}\markboth{WATER CLOCKS.}{WATER CLOCKS.}\label{subsec:Water_clocks.}\index{Time, measures of!water clocks}\index{Water clocks}---It is evident that a flow of water may +be made to drive a clock in various ways. A few years ago +I was asked to see some water clocks in which the +water came into a hollow spindle, and thence into four arms +%-----File: 171.png-------------------------------------------- +%-----Folio: 156----------------------------------------------- +radiating from it. As each arm passed its lowest position it +opened a cock in itself which discharged the water, and no +more was allowed to enter from the hollow spindle until +that arm came again to the top; so that the descending +arms were always weighted with water, and the ascending +ones empty and light. In some cases the weight was +increased by a bulb or closed bucket at the end of the arm; +and some of these were striking turret clocks, and they +required very few wheels. Whether they ever came into +use I do not know. I should think it would be difficult to +keep the water from spoiling the rest of the machinery, and +if such clocks require any attendance there would be no +material saving over a common clock which requires +winding. + +\subsection[Electrical clocks]{Electrical clocks\index{Clocks!electrical},}\markboth{BAIN'S AND SHEPHERD'S ELECTRICAL CLOCKS.}{BAIN'S AND SHEPHERD'S ELECTRICAL CLOCKS.}\label{subsec:Electrical_clocks}\index{Electrical clocks}\ properly speaking, are clocks going +by electricity, instead of by a weight wound up periodically; +but no such clocks have yet been invented capable of keeping +as good time as the commonest weight clock. They may be +divided into two classes. The first are those invented by +Mr.~Bain\index{Bain's electrical clocks}\index{Electrical clocks!Bain's} in 1840, modified more or less by other people, of +which the principle was this: the pendulum bob is apparently +a hollow brass cylinder, with the axis horizontal, and passing +over two permanent magnets, without touching them, which +are fixed to the clock case at one end, and nearly touch each +other with opposite poles, which are marked $\mathrm{N}$ and $\mathrm{S}$ on +the several magnets shown in fig.~\ref{fig32} (p.~\pageref{fig32}), omitting the +upper set for the present. The cylinder really contains a +long coil of insulated wire, of which the two ends run up to +a pair of suspension springs, which make a complete galvanic +circuit with wires somewhere connected with the poles of a +battery, and capable of being `broken.' The pendulum +pushed a light sliding rod backwards and forwards, which +made and broke contact. Whenever the circuit was complete +there was attraction one way or the other between the +magnets and the coil, and that attraction was enough to +%-----File: 172.png-------------------------------------------- +%-----Folio: 157----------------------------------------------- +maintain the swing of the pendulum against friction, and the +work of driving the train which it also had to do. For the +escapement was rather a `propelment,' like the action of +the pendulum on a common recoil escapement if you take +off the weight, for then the pendulum will drive the train +the wrong way, which may of course be reversed. But +these clocks never answered in any practical sense; nor +would anything but the strongest evidence, independent of +the inventor, convince me that any independent pendulum +directly maintained by electricity can succeed in keeping +good time for any considerable period. + +Shepherd's\index{Electrical clocks!Shepherd's}\index{Shepherd's electrical clocks}\label{shep} clocks, by which it was announced that all the +time of the 1851 Exhibition was to be kept, seemed more +promising, but they soon failed totally there, and the time +was kept by Dent's large clock, made from my design, now +at King's Cross. In them the electricity was employed to +lift a small gravity arm at every alternate beat, which gave +the impulse to the pendulum by falling on a pallet like the +down-pallet of a dead escapement, which had the advantage +of giving a constant impulse when it gave any. But +unfortunately it did not always lift. And any one who sets +to work to invent electrical clocks must start with this +axiom, that every now and then the electricity will fail to +lift anything, however small: and if his clock does not +provide for that, it will fail too. It is therefore unnecessary +to describe Shepherd's plan further now, as I did in +former editions. + +The other class of so-called electrical clocks are those where +a `normal' or governing weight-clock drives or controls other +subordinate ones; and these again may be either (1) a mere +dial, or `motion-work,' driven by electricity attracting a lever +which works an escapement; this was Wheatstone's\index{Wheatstone's electrical clocks} invention, +about the same time as Bain's: or (2) when the normal +clock keeps up the motion of a pendulum which drives an +escapement---Ritchie's plan; or (3) Jones's, where the +%-----File: 173.png-------------------------------------------- +%-----Folio: 158----------------------------------------------- +normal clock controls the pendulum of a common and inferior +kind of clock wound up as usual, the pendulum being +of the same length as the normal one. I have placed them +in mechanical, not historical, order. + +The first has never completely succeeded, and probably +never will, from the cause already stated. Old Mr.~Dent +also tried at it for some time, but in vain. Mr.~R.~L.~Jones\index{Electrical clocks!Jones's}\index{Jones's electrical clocks}\markboth{JONES'S ELECTRICAL CLOCKS.}{JONES'S ELECTRICAL CLOCKS.}\label{jones}, +when manager of the Chester station about 30 years ago, +hit upon the ingenious plan of controlling rather than attempting +to drive a subordinate clock, by sending a current +over its pendulum (in the same way as Bain's) at every beat +of the normal or governing clock. It does not matter if the +current sometimes fails for a few seconds, or even minutes +unless the subordinate pendulum has time to get more than +a whole beat wrong, in which case the error would be soon +augmented into two when the connection was resumed, which +is rather a serious evil; and I understand this plan has been +abandoned in some places which adopted it. + +Mr.~Ritchie\index{Electrical clocks!Ritchie's}\index{Ritchie's electrical clocks}\markboth{RITCHIE'S ELECTRICAL CLOCKS.}{RITCHIE'S ELECTRICAL CLOCKS.}, of 25 Leith Street, Edinburgh, has gone a +step farther, and is able to dispense with the winding of +the subordinate clocks by making the normal clock drive +subordinate pendulums, which drive the escapements, and +will maintain themselves for a few beats if the electricity fails +for that short time. This will evidently bear less of such +failure than Jones's plan; but still it appears from sufficient +experience and the testimony of the Astronomer Royal +of Scotland and others, that it answers very well. The construction +of the escapement is a matter of some consequence. +It is perfectly easy to drive a wheel and train by common +recoil pallets, provided the wheel is good-natured enough +always to stand still while the pallets are not moving it; +but not if the hands are subject to disturbance by wind; +and the very smallest motion of the hands would make a +large one of the scapewheel. Mr.~Ritchie accordingly uses +several forms of pallets designed to hold the wheel as well +%-----File: 174.png-------------------------------------------- +%-----Folio: 159----------------------------------------------- +as to drive it. The principle of them all is that of dividing +them into two like the pallets of a gravity escapement, +rising and falling with the pendulum. +\begin{figure}[htbp] +\centering +\caption{\sc Ritchie's Electrical Clock} +\includegraphics[height=0.7\textheight]{images/fig31.png}\index{Ritchie's electrical clocks} +\label{fig31} +\end{figure} + +In this figure~(\ref{fig31}) the pendulum is returning from the +extreme right, and has just deposited the right pallet, $\mathrm{BF}b$ +with its end pressing on the +tooth at $b$, and so trying to +turn the wheel that way. +But it cannot turn until the +pendulum has gone farther +and lifted the left pallet +which is now locking the +wheel at $\mathrm{G}$\@. As soon as it +does that, the weight of $\mathrm{B}$ +moves the wheel, and itself +falls a little more until +another tooth locks at $\mathrm{F}$\@. +Then the left pallet falls +and presses on a tooth at +$a$, but cannot move the +wheel until $\mathrm{F}$ is unlocked, +and so on. In large clocks +exposed to wind, a click is +added to prevent the wheel +from being blown backward +by a force of wind greater +than the weight of each +pallet for the moment; it +cannot be blown forward +by reason of the stops $\mathrm{FG}$\@. + +As the secondary clocks +are kept in order by the +normal one, they will bear +\markboth{SHORT AND SLOW PENDULUMS.}{SHORT AND SLOW PENDULUMS.}a short or slow pendulum on +the principle described at p.~\pageref{subsec:Short_and_slow_pendulums.}; and so a clock with a one or +%-----File: 175.png-------------------------------------------- +%-----Folio: 160----------------------------------------------- +even a two seconds pendulum can be comprised in the length +of an ordinary half-seconds `dial,' as they call those very short +\begin{figure}[htbp] +\centering +\hypertarget{fig32}{\caption{\sc Ritchie's Pendulums}} +\includegraphics[width=\textwidth]{images/fig32.png}\index{Ritchie's electrical clocks!their pendulums} +\label{fig32} +\end{figure} +clocks, which look no bigger than their dials. Accordingly +Mr.~Ritchie makes these pendulums, as in this figure~(\ref{fig32}). +%-----File: 176.png-------------------------------------------- +%-----Folio: 161----------------------------------------------- +The lower half of the pendulum is rather longer than the +upper, but both have bobs of wire coils in a cylinder, passing +over a set of magnets as before described. The suspension is +by two springs at $\mathrm{S}$, as shown in the right hand part of \hyperlink{fig32}{this +figure}, which is the section across the plane of vibration; +and one is connected with one battery wire, and the other +with the other, the pendulum itself being made with two +rods; and so the current goes down one and up the other, +being reversed at each beat as before. In this way also a +double attraction is got, as both bobs act in the same way. +The small ball above the lower bob is for regulating the +pendulum. The left hand figure is the front view. + +This is taken in substance from a paper by Mr.~Ritchie +read to the Royal Scottish Society of Arts in April 1873, +and published separately. His clocks are in use in connection +with the Liverpool Observatory, besides Edinburgh +itself, and a variety of other places. The great objection to +having all the clocks of any large establishment worked by +only one is the possibility of all time coming to an end by +any temporary failure of the one which `makes' the time +of all. It would be prudent to have two normal clocks +always ready to be connected with all the subordinate ones +in case one has to be stopped; and the normal clocks should +be good ones capable of going without any control. + +When the last edition of this book was published, the +Royal Institution, which is a sort of head-quarters of +electrical science, had just been converting all its clocks into +electrical ones, not on any of the controlling plans, but on a +driving one, by currents from a sort of small turret clock +with a hollow electrical coil for a bob, swinging a very large +arc over two permanent magnets. As I expected, and intimated +then, it turned out a failure, and was given up after +a few years. + +Another controlling plan is Lund and Blockley's\label{lund}, in which a +$\bigwedge$-shaped fork is brought down over the minute hand exactly +%-----File: 177.png-------------------------------------------- +%-----Folio: 162----------------------------------------------- +at the hour by electrical connection with a standard clock, so +as to bring it to the time if it is a little out either way. That +requires a complete clock wound up and going as usual, only +it need not go very well independently. There are also clocks +driven by pneumatic connexion with a standard one; but I +have no authentic information about their success. + +\subsection[Time balls and guns]{Time balls and guns}\markboth{ELECTRICAL TIME BALLS.}{ELECTRICAL TIME BALLS.}\label{subsec:Time_balls_and_guns}\index{Time balls and guns}\ are let off by electrical connection +with a normal clock which attracts an armature on a trigger +which lets off the ball or fires the gun when the connection is +completed by contact springs in the $12$ or $24$~hour wheel and +the minute wheel simultaneously. In like manner the Westminster +clock reports itself to Greenwich daily. A time ball +is usually a large wicker globe covered with painted canvas, +fixed to a piston which falls down into a bell-mouthed tube +just air-tight enough for the air to act as an elastic cushion. +It is hauled up by hand a few minutes before the time for +falling. But these also sometimes fail like electrical clocks, +and a better plan is to let a common strong clock electrically +controlled discharge the ball or gun mechanically, just as it +lets off a striking part. + +\section{STRIKING CLOCKS.}\label{sec:STRIKING_CLOCKS.}\markboth{CLOCKS STRIKING ONE.}{CLOCKS STRIKING ONE.}\index{Clocks!striking} +\index{Striking clocks}\index{Striking part!of house clocks} +The simplest form of a striking clock is represented in +fig.~\ref{fig33}. It only strikes one at every hour, which is sometimes +more agreeable than striking the full hour, especially +where you can easily see at once what the hour is. It is +very seldom that anybody has to count the striking of a +clock except in the night. Striking one requires no striking +part, or separate machinery to be wound up, the hammer +being lifted by a snail (or sometimes, but worse, by a pin) +on any wheel which turns in an hour, and dropped as the +minute hand reaches the hour. It cannot be done however +without affecting the friction of the clock, and therefore its +rate, except with a gravity escapement or some equivalent +%-----File: 178.png-------------------------------------------- +%-----Folio: 163----------------------------------------------- +contrivance to prevent the inequality of force from reaching +the pendulum; and the remark I made at page~\pageref{squaring} about +the importance of fitting the dial spring on to the centre +arbor with a square instead of a round hole, applies still +more strongly here, as the friction of that spring has to overcome +\begin{figure}[ht!bp] +\centering +\caption{\sc Clock striking one at the hour} +\includegraphics[width=0.7\textwidth]{images/fig33.png}\index{Striking part!of house clocks} +\label{fig33}\index{Clocks!striking!striking one at the hour} +\end{figure} +the resistance of the hammer spring. The short spring +against which the hammer shank falls is to prevent it from +jarring on the bell, and this is necessary in every case both +in large and small clocks, unless some other contrivance is +%-----File: 179.png----------------------------------------------- +%-----Folio: 164-------------------------------------------------- +resorted to for the same purpose, such as I shall speak of +under turret clocks. In common clocks this check is given +\begin{figure}[htbp] +\centering +\hypertarget{fig34}{\caption{\sc Common Striking Clock}} +\includegraphics[width=\textwidth]{images/fig34.png} +\label{fig34} +\end{figure} +%-----File: 180.png----------------------------------------------- +%-----Folio: 165-------------------------------------------------- +in a simpler way, as shown in fig.~\ref{fig34}, where the square top +of the stiff spring $\mathrm{S}$ butts against the square piece on the +hammer shank, whose own elasticity lets the hammer strike +the bell and then pulls it back again just out of contact. A +piece of vulcanised India rubber tied round the pillar also +answers very well. + +\hyperlink{fig34}{This figure} is a front view of the common construction of +an English\index{Clocks!striking!English or repeating striking work}\markboth{ENGLISH OR REPEATING METHOD.}{ENGLISH OR REPEATING METHOD.}\label{repeat}\index{Repeating striking work} striking clock: the foreign ones are different, as +I will explain presently. The wheels shown only by circles +(with a few of the scapewheel teeth) are within the frame; +only those with teeth are outside, and they are indicated by +the same letters as in p.~\pageref{fig25}. The hammer tail is raised by +$8$ pins in the second wheel of the striking train, which corresponds +to the centre wheel of the going train. The pinion +of that wheel generally has $8$ leaves, and is driven by the +great wheel of $78$, which therefore turns in $12$~hours; not +that that is at all material, and of course higher numbers +would be better. The striking wheel drives the wheel +above it once round for each blow, and that wheel drives a +fourth (in which you see a pin $\mathrm{P}$) six or any integral number +of turns for one of the third wheel, and the fourth wheel +drives a fly to moderate the velocity of the train and the +time of striking. + +The number of blows to be struck is regulated thus: the +dial-wheel $\mathrm{N}$ has a pin on its face which raises the \textit{lifting +piece} $\mathrm{LONF}$ a little before the hour, just far enough for it to +lift the long click $\mathrm{C}$ out of the teeth of the \textit{rack} $\mathrm{BKRV}$, +which then falls back (helped by a spring at its tail) as far +as the tail $\mathrm{V}$ can go by reason of the position of the snail $\mathrm{Y}$ +on the hour-hand wheel $\mathrm{H}$; which has steps in it, one for each +hour, so as to let the rack fall the distance of one of its own +teeth for every hour the clock ought to strike. This fall of +the rack makes the noise called \textit{warning} a few minutes +before the clock strikes. The reason why it cannot begin to +strike yet is that the pin $\mathrm{P}$ cannot pass a stop which is +%-----File: 181.png----------------------------------------------- +%-----Folio: 166-------------------------------------------------- +turned inwards from the lifting piece, through a large hole +in the frame, until that piece drops again, which it does +exactly at the hour by the advance of the pin in wheel $\mathrm{N}$\@. +Then the striking train is free, and that little piece $\mathrm{KG}$, +called the \textit{gathering pallet}, which is squared on to the prolonged +arbor of the third wheel, gathers up the teeth of the +rack, one for each blow of the hammer: the click is lifted as +each tooth passes, and prevents the rack from falling again, +and at last all the teeth are gathered up and the tail of the +pallet is stopped by the large pin $\mathrm{K}$ in the top of the rack, +and the train can go no further. + +The great feature of this English striking work is that you +may `strike'\markboth{REPEATING STRIKING WORK.}{REPEATING STRIKING WORK.} the clock as often as you like within the hour, +or stop it any number of hours, and yet it will always strike +right, because the striking depends on the position of the +snail attached to the going part, and not at all on the number +last struck. These clocks are therefore sometimes furnished +with a string to the outside, from the click, so that you can +pull it in the night and hear the hour. But this is just the +wrong way of doing it: for if you hold the string too long +the click will miss some of the teeth and the clock strike too +many, and if you drop it too suddenly the rack will not +have fallen its full distance and it will strike too few. The +right place therefore to put the string is to the lifting piece, +as at $\mathrm{F}$\@. (The piece $\mathrm{Q}q$ belongs to something else which I +shall speak of presently.) + +The improved French\label{newfrench}\markboth{NEW FRENCH STRIKING WORK.}{NEW FRENCH STRIKING WORK.} clocks, whose escapement I noticed +at p.~\pageref{subsec:Improved_French_clocks.}, have a better mode of stopping the striking than +the usual one in English house clocks: the better one is used +in our turret clocks when they have the rack movement. +Instead of the gathering pallet $\mathrm{G}$ (fig.~\ref{fig32}) on the third wheel +of the train being stopped by a pin in the tail of the rack +with a heavy blow, the striking is stopped by the pin $\mathrm{P}$ in +the fourth wheel coming against a stop in the long click $\mathrm{C}$, +which drops into a deeper notch in the rack than the others +%-----File: 182.png----------------------------------------------- +%-----Folio: 167-------------------------------------------------- +at the last blow of the hour, and so falls low enough to catch +that pin. + +\subsection[Strike and silent.]{Strike and silent.}\markboth{STRIKE AND SILENT.}{STRIKE AND SILENT.}\label{subsec:Strike_and_silent.}\index{Clocks!striking!strike and silent}\index{Strike and silent}---There are several ways of throwing +the striking work out of gear, so as to keep the clock silent. +I think the best, though not the usual one, is that shown in +fig.~\ref{fig32}, a small lever whose end $x$ falls before and stops a +pin in the rack when the other end of the lever is put up to +$si$ by an index or handle coming through the edge of the +dial. I have seen methods used which are very likely to +stop the going as well as the striking of the clock by leaving +the rack to fall. Another way is to make the piece $\mathrm{LONF}$ +push forward so as to escape the pin at $\mathrm{N}$, and be never +lifted; and this is unobjectionable. + +It may save people a little time if I tell them what hardly +anybody seems to know, that you may move the hands of an +\textit{English} clock forward through all the hours without waiting +for any of them to strike, except $12$, where the rack-tail has +to get over the great step in the snail; and even that is +often provided for by sloping the front of that step and the +face of the pin $\mathrm{V}$, to let the snail push it aside, the tail being +elastic enough to give way a little. In the same way the +tail of the lifting piece at $\mathrm{N}$ is always twisted a little to let +the lifting pin pass it backwards without lifting, so that you +may turn the hands back and the clock will not strike at all, +unless it has already given warning. The snail is sometimes +set on a separate wheel below the hour-wheel and moved by +jumps by a pin in the minute-wheel $\mathrm{M}$; this is called the +\textit{star wheel} and \textit{jumper;} but I can see no use in it, and therefore +shall describe it no further. + +\subsection[Locking-plate striking work.]{Locking-plate striking work.}\markboth{LOCKING-PLATE STRIKING WORK.}{LOCKING-PLATE STRIKING WORK.}\label{subsec:Locking-plate_striking_work.}\index{Clocks!striking!foreign or locking-plate method}\index{Locking-plate movement}---The principle of the +striking work still used in most foreign clocks, French, German, +and American, is shown in fig.~\ref{fig35} (p.~\pageref{fig35}), though the +actual arrangement of the pieces may be different. It is +generally used also in English turret clocks. You see the +rack and its click are gone, and instead there is a wheel $\mathrm{Y}$ +%-----File: 183.png----------------------------------------------- +%-----Folio: 168-------------------------------------------------- +called the locking plate or count wheel, which turns in the +$12$~hours, and may therefore be put on the arbor of the +great striking wheel, or driven by the pinion of the striking +\begin{figure}[htbp] +\centering +\caption{\sc Locking Plate Striking} +\includegraphics[width=\textwidth]{images/fig35.png} +\label{fig35} +\end{figure} +%-----File: 184.png----------------------------------------------- +%-----Folio: 169-------------------------------------------------- +wheel. It may be considered as marked out into $78$ divisions, +and notches made in it at the distances $1$, $2$, $3$, \&c., +into which a lever $\mathrm{OQ}$ can drop, which is connected with +the lifting piece. That is generally made with two stops +upon it, one a little behind and below the other; or else +there are two levers, one lifted by the other, with the stops +upon them respectively; and the pin $\mathrm{P}$ in the pin-wheel, or +in large clocks, on the fly arbor, stops against the first when +the clock has done striking, and against the other when the +lifting piece is lifted by the wheel $\mathrm{N}$ in the dial work. But I +introduced an \markboth{IMPROVED CONSTRUCTION.}{IMPROVED CONSTRUCTION.}alteration in this respect in turret clocks, +because one of the stops on the lever must be out of the +right position for direct action of the pin. Instead of two +stops on the lever, there are two pins on the wheel, $\mathrm{P}$ and $p$, +one a little behind and nearer the centre of the wheel than +the other, and $p$ is caught by the stop when it has been lifted +high enough to let $\mathrm{P}$ escape and `give warning.' + +There is, or ought to be, a disc $\mathrm{C}$ with a notch or cam +in it on the arbor of the third wheel, which turns once for +each blow, and so moves faster than the locking plate, and +therefore is more certain to lift the lifting piece quite out of +the way of both pins before the pin-wheel gets once round; +otherwise the clock might be, and clocks without this cam +sometimes are, prevented from striking at all, especially if +the parts are not adjusted with great precision. The lifting +piece evidently cannot fall again until another notch in the +locking plate comes under the tooth $\mathrm{Q}$\@. Sometimes the +lifting piece $\mathrm{LON}$ is made in two pieces, one lifting the +other, but I see no advantage in it, except where the pivot +$\mathrm{C}$ happens to be at an inconvenient distance from the locking +plate. In turret clocks with three-wheeled trains it is +generally more convenient to make the wheel $\mathrm{C}$ turn only +half round for each blow, and then there must be two cams +or two drops in the disc, as shown in the view of a large +quarter clock at p.~\pageref{fig40}. +%-----File: 185.png----------------------------------------------- +%-----Folio: 170-------------------------------------------------- + +\subsection[Half-hour striking.]{Half-hour striking.}\markboth{HALF-HOUR STRIKING.}{HALF-HOUR STRIKING.}\label{subsec:Half-hour_striking.}\index{Beckett, Sir E.!half-hour striking}\index{Clocks!striking!half-hour striking}\index{Half-hour striking}\index{Striking clocks!half-hours}---For striking \textit{one} no lift by the +locking plate is required, but only a long notch reaching +from $12$ to $2$; and for the same reason the clock can be +made to strike one at the half hours by dividing the locking +plate into $90 (=78+12)$ and leaving a wide notch between +every two hours, and putting a half-hour pin into the wheel +$\mathrm{N}$ (fig.~\ref{fig32}) besides the hour one. Most of the French clocks +are so made; but they have the inconvenience of striking +one three times between $12$ and $2$; so that between those +hours the striking tells you nothing. I once saw a turret +clock made to strike one feebly on a smaller bell, from the +going part, as shown at page~\pageref{fig33}, which gravity escapement +clocks will bear, though not others. It was not satisfactory, +and led me to devise the following plan. + +To make $12\frac12$ and $1\frac12$ silent, with the locking plate +movement, we evidently want something which will stop +the lifting piece, $\mathrm{LON}$ in fig.~\ref{fig37} (p.~\pageref{fig37}) of a clock of this +kind, from falling after it has been lifted to give warning, +until the next hour. And the way to do that is to have a +$12$-hour wheel (the one with $24$ ratchet teeth in fig.~\ref{fig37}) +with two steps in it, as you see, which come under the +tongue of the lifting piece just over that wheel at those two +half hours. The best way to drive it is by a gathering pin +or single tooth, which is shown in the hour wheel marked +$40$, and which moves the ratchet wheel one tooth just after +warning. There is also a spring click or jumper to keep it +in its place, which wheels driven in that way always require, +to make sure of the gathering tooth taking them up again. +But another thing has to be attended to. The locking plate, +instead of having $78$ teeth or spaces, as when there are no +half hours, or $90$, as when all the half hours strike, must +have $88$, and each notch must again be wide enough for +striking one, only it must be divided as if there were no half-past +twelve or one, for one o'clock is the same as one half +hour between twelve and two. +%-----File: 186.png-------------------------------------------- +%-----Folio: 171----------------------------------------------- + +\subsection[Half-hours with Rack Movement.]{Half-hours with Rack Movement.}\markboth{DIFFERENT METHODS OF DOING HALF-HOURS.}{DIFFERENT METHODS OF DOING HALF-HOURS.}\label{subsec:Half-hours_with_Rack_Movement.}\index{Half-hours with rack movement}---I have never +seen this in any English clock. Indeed the English house +clock-makers seem determined to lose every bit of the trade +rather than allow any single improvement to be made here, +and so they are losing more and more yearly. The modern +French\index{French clocks!improved kind of} arrangement of the rack movement has the rack +above the `motion' or dial wheels, acting by gravity without +a spring, and the striking is stopped by the long click dropping +lower at the end of the rack than it does in the teeth, +and low enough to catch a pin in the third wheel, instead of +the gathering pallet being stopped by a pin in the rack and +always tending to force it back. Half hours are struck by a +separate lever being brought under a pin anywhere on the +rack allowing it to fall one tooth only, the lifting piece being +of course lifted by a second pin in the hour wheel at the half +hours. In order to stop the striking at $12\frac12$ and $1\frac12$ there +would have to be a $12$-hour wheel with $2$ steps or long teeth, +as before described, to prevent either the rack or the lifting +piece from falling, whichever might be most convenient. +But this is not of so much use in small clocks standing in a +room, when you can look up and see whether it means one +o'clock or not, as in large ones, where it is a great convenience, +and saves the much greater cost of quarters with +the two more bells. It would never do to have a turret +clock striking the hours on one of the quarter bells, as it +would produce frequent confusion when they are heard at +such a distance that people would not be sure whether they +heard the smaller bell or not. It was done for some months +at Westminster by the genii who managed and advised things +there, as will be noticed afterwards. When Mears's Big +Ben II.\ cracked enough to spoil the sound, but no more, +they stopped the striking of the hours on him, and had them +struck on the fourth quarter bell, until I got the confusion +that it caused noticed in the newspapers, and then they +resumed striking on the great bell with a much lighter +%-----File: 187.png-------------------------------------------- +%-----Folio: 172----------------------------------------------- +hammer, which is there still. And for fear that should knock +a piece out of it, like the one in the famous broken bell of +Moscow, they put a huge wooden tea-tray under it to catch +the piece, and there it is to this day, with a hole in the +middle for the clapper `tail to come through,' which reminds +one of a celebrated poem of either Southey or Porson, for it +is attributed to both. + +The locking\index{Locking-plate movement} plate striking is specially objectionable for +moveable clocks, and for any that are liable to run down +for want of winding, like the American ones; because if +the striking once gets wrong, or stopped from not winding +up, or let off by accident, or the clock stopped by housemaids, +it strikes wrong afterwards, until it is struck round +to the right hour again. The American clocks have a wire +specially provided for this purpose, but the French have not, +and you have to put your finger in behind the left side of +the clock and lift the lever you will feel there, to make it +strike as often as is necessary to bring it right; which is a +great nuisance, and in some cases almost or quite an +impossibility. Striking on springs is a bad imitation of a +large bell, and is very inferior to a common bell, except +when heard very near. + +\subsection[Quarters.]{Quarters.}\markboth{QUARTER CHIMES.}{QUARTER CHIMES.}\index{Clocks!striking!striking quarters}\label{quart}---If the clock is to strike the quarters, a third +`part' or train of wheels is added on the right side of the +going part, with as many bells and hammers as may be +required. There is indeed a method of making the same +striking part do both for the hours and quarters, by sliding +the hour hammer tail out of gear with the pins, and the +quarter hammer tails into gear, and \textit{vice vers\^a;} but it +saves very little in cost, and is very seldom used; and +it requires a much heavier weight or stronger spring, and +stronger wheels, if it is to be done effectively. In that case +there can be no quarters at the hour; but that is of no consequence, +and perhaps rather an advantage with \textit{ding dong} +quarters. The construction of a quarter part is substantially +%-----File: 188.png-------------------------------------------- +%-----Folio: 173----------------------------------------------- +the same as of the hour striking part. If there are only $2$ +bells, the $2$ hammers are lifted by pins on each side of the +striking wheel, or they may be the same pins if the arbor of +one hammer is put above that of the other. They should +be so placed that the interval between each pair of blows, or +each chime, is twice that between the blows of each chime, +whether there are $2$ or $4$ bells. When there are more, the +interval between each chime requires to be as much as $3$ +spaces instead of $2$. When there are more than $2$ bells the +hammers are worked by a chime barrel, because the chimes +are not generally the same thing repeated, as they are +with \textit{ding dong} quarters. But this belongs more to turret +clocks, under which I shall go more fully into it. The +chime barrel is generally put on the third wheel, but it would +require less force to turn it on the second, for the reason +I gave before, that the more wheels there are between a slow +power and a quick work, the more is lost in friction, in a proportion +beyond what anybody would expect. As the barrel +naturally turns in an hour, the proportion of the pinion and +great wheel would be just the same as in the going part. + +The quarters may be let off either by the English +repeating method, or by the French locking plate. If they +are merely the same chime repeated $2$, $3$, and $4$ times, the +repeating movement should be used, as it has the same +advantage as in the hour striking part. But if each quarter +is a different tune, it should not be used, because repeating +the striking of the quarters in that case will throw the whole +tune into confusion; though this plain distinction is often +overlooked. The connection between the two striking parts, +when the quarters have the locking plate, is made by that +wheel performing the function of the wheel $\mathrm{N}$ in figs.~\ref{fig34}, \ref{fig35}, +in discharging the hour, as the 4th quarter finishes. + +The repeating\index{Quarter chimes!rack and repeating movements in small clocks} quarter movement is not so simple: the +principle of it is this:---The quarters have a rack, snail, \&c., +just like the hours, the snail being fixed on the wheel $\mathrm{N}$ so +%-----File: 189.png-------------------------------------------- +%-----Folio: 174----------------------------------------------- +as to turn in the hour, and with $4$ steps instead of $12$ (see +p.~\pageref{fig34}). The rack is so placed that when it falls for the 4th +quarter (its greatest drop) it falls against the hour lifting +piece somewhere between $\mathrm{O}$ and $\mathrm{N}$, so as to raise it and +the click $\mathrm{C}$\@. It is then held up by the lever marked $\mathrm{Q}{q}$ +catching hold of the pin close by it, and as the last tooth +of the quarter rack is gathered up it pushes $\mathrm{Q}q$ aside again, +which lets the lifting piece drop and the hour begin to strike. + +There is a very simple construction of a \markboth{QUARTER CLOCKS.}{QUARTER CLOCKS.}clock for striking +repetition quarters only, when it is wanted in the night, by +pulling a string which goes round a spring barrel, and so\label{wind} +winds it up as far as it is allowed to go by the position of +the quarter snail on the going part, which stops some pin or +lever connected with the barrel. This may be easily made +to indicate half quarters; for if there are $8$ steps in the snail, +then at about $50$~min.\ past the hour the lever could go +$7$ depths and the clock would strike $3$ \textit{ding dongs} and one +bell more; and it may either begin or end by letting off the +hour. This construction is in substance that of \textit{repeater} +watches, of which the striking part is both wound up and +let off by pushing in the handle. + +\subsection[Quarters--Tunes.]{Quarters--Tunes.}\markboth{QUARTER CHIMING CLOCK.}{QUARTER CHIMING CLOCK.}\label{subsec:Quarters--Tunes.}\index{Tunes, chime}---By this I mean chimes\index{Chime-tunes} not merely +repeated. And as these clocks for halls and rooms have +come much more into fashion since the Westminster chimes +were heard, I will give a picture of the construction I +arranged for them in a clock of my own before I designed +that clock, and which was followed in several others made +by old Mr.~Dent and afterwards by other makers. The chime +tunes themselves I shall leave till we come to turret clocks. +$\mathrm{Y}$, the locking plate, is fixed on the arbor of the second wheel, +which turns once in an hour, driving the chime barrel marked +$50$ for Westminster chimes, as will be explained afterwards. +For the present it is enough to say that it turns twice in the +hour, making $10$ chimes, but the fourth and first quarters +together are the same as the second and third together, and +%-----File: 190.png-------------------------------------------- +%-----Folio: 175----------------------------------------------- +\begin{figure}[htbp] +\centering +\hypertarget{fig36}{\caption{\sc Quarter Chimes, Striking Part}} +\includegraphics[height=525pt]{images/fig36.png} +\label{fig36} +\end{figure} +%-----File: 191.png-------------------------------------------- +%-----Folio: 176----------------------------------------------- +therefore it is not necessary to have a barrel with $10$ different +sets of pins on it, but only $5$. The wheel on its end therefore +has $50$ teeth, and is driven by the second wheel of the +train, of $100$, which also drives a pinion of $10$ on the third +wheel, which consequently turns once for each chime of +$4$ bells. That wheel also has two pins in it, $\mathrm{P}$ and $\mathrm{P}'$, +$\mathrm{P}$ being rather nearer the centre, and they are alternately +stopped by the piece at $\mathrm{L}$ projecting sideways from the +lifting detent $\mathrm{LON}$, of which the arbor is carried in cocks +from the frame, as you see, its arm $\mathrm{OQC}$ being in front of +the front plate of the clock and $\mathrm{OL}$ inside, near the back +plate where the third wheel is. The chime barrel is also +really set in cocks, not in the solid frame, in order that +it may be adjusted as to its teeth after the clock is put +together, which often saves a great deal of trouble, but it +would confuse the figure to show them \hyperlink{fig36}{here}. The fly should +be longer than will go inside the frame, to clear the arbor +below it, and that also is set in a long cock behind. + +The action is extremely simple. The $4$ pins in the hour +wheel $\mathrm{N}$ lift the long detent a little before each quarter, and +then the pin $\mathrm{P}'$ slips under the stop $\mathrm{L}$, which then catches +$\mathrm{P}$, the wheel moving on a very little. At the quarter the +detent drops off $\mathrm{N}$, and before the third wheel or its pins +come round again the locking plate has lifted the detent by +the inclined edges of its notches, such as $\mathrm{Q}$, so high that both +pins clear the stop $\mathrm{L}$; the motion of the locking plate \hyperlink{fig36}{here} +being much greater than in an hour striking plate like fig.~\ref{fig35} and figs.~\ref{fig37}, \ref{fig40} afterwards, where consequently a cam +wheel turning faster is required to make the lifting safe. +The locking plate keeps up the detent for $1$, $2$, $3$, or $4$ chimes +as required, and you see that by this method they can never +get mixed, as they can with the repetition or rack movement. +If they have got to strike wrong they only want `striking +round' till they are right again, and that is easily done +thus. You see the right-angled lever $\mathrm{BAD}$, with $Si$ and $St$, +%-----File: 192.png----------------------------------------------- +%-----Folio: 177-------------------------------------------------- +for \textit{silent}\index{Strike and silent}\markboth{STRIKE AND SILENT.}{STRIKE AND SILENT.} and \textit{strike}\index{Clocks!striking!various mechanisms for striking work}, against two pins in the frame. When +you lift the tail $\mathrm{D}$ to $Si$ the bevelled end $\mathrm{B}$ lifts the detent by +a pin in it, just enough to `give warning,' and it cannot fall +again. But when you bring it down again to $St$ the detent +does fall and the quarters strike whatever the locking plate +is ready for, which lets you know whether they require +more `striking on' to set them right. + +But we have still to let off the hour\label{hourstrike} striking. In large +clocks that is best done independently, as we shall see; but +in small ones it is done by the end of the detent being +raised by the snail kind of rise at $\mathrm{Y}$ in the locking plate +as the fourth quarter finishes, which lifts $\mathrm{C}$, the rack +click of the striking part (see fig.~\ref{fig34}). That is one way of +doing it. Another, which I designed for a later clock of my +own, allows the hours to strike even if the quarters are +silenced, by retaining the usual lifting piece of the hours +(which in the former plan is gone) and making the quarter +detent stop it from falling again till the quarters are done---if +they are in action; if not it simply does nothing. The +quarters are silenced by pressing a spring against the side of +the fourth wheel, by a slider at the edge of the dial. + +\subsection[Alarums.]{Alarums.}\markboth{ALARUMS.}{ALARUMS.}\label{subsec:Alarums.}\index{Alarums}---If you suppose a short hammer instead of a +pendulum fixed to the pallet arbor or the crutch of either +kind of recoil escapement, it would swing backwards and +forwards very quickly, and strike both sides of a bell of +proper size placed so as to inclose the hammer. This is the +way an alarum strikes, and not by the lifting of a hammer at +distinct intervals. The hammer is driven by a wheel like a +strong recoil crown escapement wheel (p.~\pageref{crown}) with a spiked +pulley or barrel attached to it by a ratchet and click, over +which a rope goes, with a small weight at one end, and a +smaller one at the other to keep the rope stretched and to wind +it up by. The alarum can only go when a stop lever is lifted +by a pin on a collar which is fixed on the hour hand wheel +by a friction spring, so that it can be set to go off at any hour +%-----File: 193.png----------------------------------------------- +%-----Folio: 178-------------------------------------------------- +you like. You must not wind it up till within $12$~hours of +the time it is intended to go off, or it will go $12$~hours too +soon. + +\subsection[Tell-tale clock]{Tell-tale\index{Clocks!tell-tale} clock.}\markboth{TELL-TALE CLOCK.}{TELL-TALE CLOCK.}\label{subsec:Tell-tale_clock}\index{Tell-tale clocks}---This is said in one of the Parliamentary +papers about the Westminster clock to be an invention of +Mr.~Whitehurst of Derby, for watching watchmen and telling +whether they are on the watch and in the proper place all +the night. That unpleasant little clock which one hears +striking the quarters $3$ or even $4$ times in some Westminster +Abbey sermons, is of this kind, and there are some in +the lobbies of the Houses of Parliament. There are a set of +spikes sliding in holes in a $24$~hour dial, one for every +quarter of an hour, which can be pushed in by pulling a +handle in the clock case during a few minutes of that quarter +only. So if any pin is found sticking out in the morning it +indicates that the watchman was either asleep or away at +the time belonging to that pin. The plate carries the inner +ends of the pins over an inclined plate or roller at some other +period of the $24$~hours, which pushes them all out again +ready for work the next night. + +\subsection[Musical clocks.]{Musical clocks.}\markboth{MUSICAL CLOCKS.}{MUSICAL CLOCKS.}\label{subsec:Musical_clocks.}\index{Clocks!musical}\index{Musical!clocks}---Clocks that play tunes---not short +quarter chimes, but tunes of several minutes, either on bells +or organ pipes, are not clocks in respect of their music, but +simply musical boxes or barrel organs turned by an independent +spring or weight and let off at the required time by +a lever from the clock. I shall speak of chimes on church +bells farther on. And nothing else occurs to me as +belonging to small or house clocks of sufficient use or +importance to require notice. So I pass on to the larger +branch of the art, which has been the subject of greater +improvements within the last 30 years than in the previous +century, and has reached a degree of accuracy equal to that +of the best astronomical clocks, and superior to that of +chronometers, and that not only without an increase, but +with a great reduction in the price. +%-----File: 194.png-------------------------------------------- +%-----Folio: 179----------------------------------------------- +\section{CHURCH OR TURRET CLOCKS.}\label{sec:CHURCH_OR_TURRET_CLOCKS.} +\index{Turret clocks}\markboth{TURRET CLOCKS.}{TURRET CLOCKS.} +It may be supposed that as the work of these clocks only +differs from that of house clocks in the size of the hands +and the weight of the hammers they have to move, you +have only to enlarge the machinery and the business is done. +But there is a very important fact in the way of that +conclusion: viz., that as you increase the strength of +machinery you increase its weight in a ratio as much higher +as the cube is higher than the square of any of its +dimensions; and when you increase weight you increase +friction,\index{Friction!in turret clocks} and friction is a word which ought never to be long +out of the mind of a clockmaker, or at least of a clock-designer, +inasmuch as the timekeeping part of a clock is the +only machine whose sole business is to overcome its own +friction, resistance of the air, and variations of heat, and to +do that in a constant and uniform manner. And there is +this further difference\index{Large and small clocks, difference between} between large and small clocks: in +small ones the force or weight required to work a hammer +of an ounce or two is generally about the same as is required +to keep the pendulum going, and so the two `parts' or +trains are about equal in strength; whereas in large clocks +the lifting of the hammer generally requires a great deal +more power than driving the hands and pendulum, and therefore +ought to have much heavier and stronger machinery. +Nevertheless the object of some clockmakers seems to be to +make the going train of large clocks as heavy and the +striking train as light as they can. + +\subsection[Pendulum.]{Pendulum.}\markboth{CHURCH CLOCKS.}{CHURCH CLOCKS.}\label{subsec:Pendulum.}\index{Pendulums!for church clocks|(}---I have already treated of pendulums for +large as well as small clocks at considerable length, and +there is little to add with reference to large clocks only. I +will only repeat that the construction and suspension of the +pendulum are of primary importance. + +The great majority of clockmakers, till lately, set their +faces against compensated pendulums\index{Compensation of pendulums}, and used nothing but +%-----File: 195.png-------------------------------------------- +%-----Folio: 180----------------------------------------------- +wooden ones. And so long as the clocks themselves are no +better than they are, it would undoubtedly be a waste of +money to compensate the pendulums, as the escapement +errors will far exceed the temperature one. But when you +have got a first-rate clock in other respects, it is absurd to +prevent it from going accurately by not giving it a pendulum +without which it cannot keep the same rate in hot +and cold weather. It is true that a $2$~seconds, or even a +$1\frac12$~second compensated heavy pendulum, is a rather expensive +affair if well made; and with a common dead escapement +probably the advantage is on the whole in favour of a +$13$~ft.\ wood pendulum of $3$~cwt.\ over a $5$~ft.\ compensated +one of half the weight, which will enable a clock with such +an escapement as I shall describe to keep within a second a +week of Greenwich time. The fashion of extravagantly +long pendulums has very properly gone out, as their +inconvenience and liability to be affected by the wind overbalances +any advantage from them in a moderately good +clock. There were several in Yorkshire until lately as long +as $56$~feet, or $4$~seconds: $20$~feet = $2\frac12$~seconds, which old +Doncaster church had, is the utmost length I should allow; +and I gave the calculations for a cheap form of compensated +pendulum of that length at p.~\pageref{pndcalc}.\index{Pendulums!for church clocks|)} + +\subsection[Position of clock.]{Position of clock.}\markboth{POSITION OF CLOCK.}{POSITION OF CLOCK.}\label{subsec:Position_of_clock.}\index{Turret clocks!best position for}---The worst of all positions for a large +clock is the usual one, on a stool on the upper floor of a +tower, for the reason I have already given at p.~\pageref{stool}. The +best is on stone corbels built deep into the wall. The +Westminster clock lies on independent walls, which of course +are stronger still. Where this cannot be done, cast iron +brackets bolted through the wall will do, or iron beams +across the room if it is not very wide. Wooden beams are +not to be trusted. When the clock is fixed as firmly as +this, the pendulum may be hung from the clock frame, if +that is itself strong enough, and the pendulum cock properly +fixed to it, or cast with it, though the wall is generally to be +%-----File: 196.png-------------------------------------------- +%-----Folio: 181----------------------------------------------- +preferred for a long and heavy pendulum, if the clock stands +near enough to it. But again it is inconvenient to have a +very large clock so close to the wall that a man cannot get +some access to it from behind. Therefore no general rule +can be laid down for the fixing of turret clocks, except that +firmness is the first consideration, to which everything else +must give way according to the circumstances of the tower. +I have already mentioned at p.~\pageref{arc} the increase of arc caused +by hanging a heavy pendulum from the wall instead of a +strong wooden frame from the ground; and as the escapement +errors vary inversely as the cube of the arc, the clock +should go more than twice as well with the firmer suspension; +and in fact it does. + +\subsection[Frame.]{Frame.}\markboth{FRAME.}{FRAME.}\label{subsec:Frame.}\index{Frames!for turret clocks}\index{Turret clocks!frame for}---The old established form of clock frame was a +sort of cage of vertical and horizontal bars, some of which +contain the bushes for the pivots of the wheels, and have to +be unscrewed from the principal bars in order to get any of +the wheels out. It was a great improvement on this to fix +the bushes themselves with screws instead of riveting them +into the bars, as it enabled the wheels to be taken out +separately, instead of all dropping loose at once and perhaps +bending their back pivots as soon as the front bar was +taken off. Mr.~Vulliamy\index{Vulliamy, Mr.} introduced this plan, and old Mr. +Dent used it in the Exchange\index{Exchange, Royal!clock} clock, of which a perspective +view is given in Tomlinson's Cyclop\ae dia under \textit{Horology}. +But he soon afterwards adopted a still better arrangement, +borrowed in principle from the French, who were strangely +ahead of us in this branch of clockmaking, until shortly before +the 1851 Exhibition. + +The French\index{French clocks!improved kind of} clockmakers are entitled to the credit of +having introduced the horizontal frame cast in one piece, +with the great wheel set in bushes or cocks below it, and the +smaller wheels above in separate frames of the A~shape +bolted to the great one. But much more has been done +since that. Dent's\index{Dent, E.~J.!Exhibition clock} clock, with a spring remontoire, which I +%-----File: 197.png-------------------------------------------- +%-----Folio: 182----------------------------------------------- +\label{folio_182}designed for him for the 1851 Exhibition, where it kept better +time\index{Gravity escapements!rate of some}\index{Rate!of some other gravity escapement clocks} than had ever been attained before, for nearly $6$~months, +will be described afterwards, though even that has been +superseded by the simpler and stronger construction of the +gravity escapement clocks. I will \markboth{SOME LARGE CLOCKS.}{SOME LARGE CLOCKS.}now describe a moderate-sized +turret clock of that kind, for a bell up to $5$ or $6$~cwt., +and therefore only needing the striking part winding once a +week, which will not do for large ones, and striking one at +the ten proper half-hours as before described. This was +made for a clock-tower of my house by Mr.~Joyce\index{Joyce's turret clocks}\index{Turret and church clock makers}, of Whitchurch, +Salop, the maker of the great Worcester\index{Worcester cathedral!clock} Cathedral +clock, striking on a $4\frac12$-ton bell, and a vast number of +smaller clocks. I ought to mention at the same time that +Messrs.~Potts\index{Potts, maker of Lincoln Minster clock and others}, of Leeds, in 1881, put up a still larger one in +the finest clock-room in the world, about $40$~ft.\ square, in the +tower of Lincoln\index{Lincoln Minster clock} Minster, striking on Great Tom and four +new quarter bells; and Gillett and Bland\index{Gillett and Bland's!clocks and bells}, of Croydon, who +made the clock for some still larger bells in the Manchester\index{Manchester Town Hall clock and bells} +Town Hall. But all these, and a multitude of others not +quite so large, by these makers, and by Smith of Derby, +belong to the class which will be described afterwards, +winding every one or two days in the striking parts. Dead +escapements have now become quite obsolete for all large +clocks that are intended to keep time within the maximum +that ought to be allowed, viz.\ $5$~seconds a week; for I hear +that some of these large clocks do not vary $5$~seconds a +month, except from some temporary cause. Therefore, +although I retain the description and picture of one pattern +of a dead escapement clock farther on, the time is come to treat +the gravity escapement as the standard one for this purpose. +It is very easy too to make this next picture serve for a dead +escapement by putting the necessary A-shaped small frame +on to carry the pallets, making the third wheel which drives +the gravity three-legs into a dead pin wheel, as described at +p.~\pageref{fig15}. +%-----File: 198.png-------------------------------------------- +%-----Folio: 183----------------------------------------------- + +\begin{sidewaysfigure}[p] +\centering\index{Beckett, Sir E.!general plans for turret clocks} +\caption{\sc Small Turret Clock with Gravity Escapement}\index{Turret clocks!Batch-wood clock} +\label{fig37} +\includegraphics[width=\textwidth]{images/fig37.png} +\end{sidewaysfigure} +%-----File: 199.png-------------------------------------------- +%-----Folio: 184----------------------------------------------- + +Very few architects\index{Architects!ignore bells and clocks}\markboth{ARCHITECTS AND CLOCK-TOWERS.}{ARCHITECTS AND CLOCK TOWERS.}\label{architects} have the least idea, or will condescend +to learn, how large a clock-tower must be to hold a clock of +moderate size properly, or bells either. Their notion seems +to be that it is the duty of what they call their `clients'---they +being the `patrons,' I suppose---to let them build +what they think pretty, and then get other people to make it +useful if they can. I must inform their `unfortunate clients' +then, that they cannot have a clock of the best construction +suitable for a bell of only $4$ or $5$~cwt., and one or more dials +of $4$~ft.\ diameter, unless they provide a clock-room at least +$6$~ft.\ square, and $7$ is better, and at least $30$~ft.\ fall for the +weights. The frame\index{Turret clocks!frame for!its construction} in such a tower as that is best built +into the wall about half a brick deep at each end, as mine is, +and of course made quite level and firm. It will then be firm +enough to carry the pendulum, without resorting to an independent +cock built into the wall. Mine is about $3$~cwt., and just +$99$~in.\ long to the bottom, being $1\frac12$~seconds, which happened +to be more convenient than a $1\frac14$~seconds one, besides being +rather better. As it is generally necessary to carry the +ropes up to some place above the clock-room to get all the +available fall, you have to provide space for them also, and +evidently more than if they go straight down from the +barrels, which is better if you have fall enough, as it saves a +good deal of friction\index{Friction!in turret clocks} in several ways. This depends on the +height of the clock-room from the ground, and the use you +want to make of the lower part of the tower, which should +all be considered beforehand, but never is, except by people +who look after their own work, who alone get it done well. + +Any \markboth{SMALL GRAVITY TURRET CLOCKS.}{SMALL GRAVITY TURRET CLOCKS.}one who is generally acquainted with clock-making +will understand from this picture more than could be shown +in it without confusion. The barrels\index{Turret clocks!iron barrels}, or great wheels of +both parts, are set under the frame in bushes of the construction +$a$ and $d$ together in p.~\pageref{fig38}, so that they can drive second +wheels in bushes of the form $b$ on the top of the frame,\index{Frames!for turret clocks} +which top is about $1\frac12$ wide, and is now always planed in a +%-----File: 200.png-------------------------------------------- +%-----Folio: 185----------------------------------------------- +machine, to carry all the cocks and bushes quite firm and +level. There are three cross bars cast in it at convenient +places, which are utilized also for carrying cocks for `leading +off,' for hammer-tails, winding-pinions, and anything else of +that kind. The great going wheel\index{Turret clocks!three-wheeled trains} generally has \index{Wheels, numbers of teeth}$120$ teeth, +and is $12$ or $13$~inches in diameter, and drives (first) the hour +wheel with $40$ teeth, on the arbor of which is the bevelled +wheel driving other bevelled wheels up to the dials, both +outside the tower, as usual, and in mine inside also to a dial +at the end of a long passage in the house. That leading off +goes downwards obliquely, and is omitted in the picture. +The half-hour snails, with the main bevelled wheel, are +clamped to the hour wheel by thumb-screws, to enable you +to set the hands when necessary; and it drives no more +wheels in the train, because it makes a better distribution of +the teeth to leave it independent. The great wheel therefore +drives the one marked $100$ with a pinion of $10$, which will +turn in $15$~minutes as the $40$ wheel takes an hour, whatever +may be the time of the great wheel, which is generally made +$3$~hours in these clocks. The $15$~min.\ wheel of $100$ drives +another pinion of $10$, $\therefore$ in $1.5$~min., and that having a wheel +of $90$ drives the scape-wheel pinion of $9$, which, with the double +three-legs and a $1\frac12$-sec.\ pendulum, turns in $9$~seconds. But +if the pendulum is $1\frac14$ sec, the scape-wheel will turn in +$6 \times 1\frac14$ or $7\frac12$~sec., and its pinion must either be $8$ driven +by $96$ or $9$ driven by $108$. + +In all clocks of this kind the pallet-arbors are set in small +cocks, on the large one which carries the pendulum, and the +scape-wheel itself has only a short arbor in $2$ cocks behind +the other wheels. The pendulum swings in a long slot in +the flange at the top of the frame, reaching from one cross +bar to the other; and the escapement fly also in another +space, with the two three-legged wheels between the back +bar and another which carries all the wheels. There is room +enough for all this, and a sufficient length of barrel, in the +%-----File: 201.png-------------------------------------------- +%-----Folio: 186----------------------------------------------- +width of frame that the striking part requires, which is +always a good deal more than the going part, on account of +the greater thickness of the rope, and the cams and levers +and the winding wheel. The frame is generally $4\frac12$~in.\ deep, +with a wide flange turned inwards all along the top, to set the +various cocks on. + +There is a little inconvenience in the third wheel turning +in $1\frac12$~min.\ instead of either $1$ or $2$, as you want an index of +some kind to mark seconds for regulating, unless you go +entirely by the striking. But this train distributes the teeth +so much the best that I adhere to it, and get over the other +difficulty either by a pair of small wheels in the proportion of +$3$ to $2$, the smaller carrying a seconds hand, or else depend +on an index placed over the rim of the $90$~seconds wheel, +which is graduated up to $30$, so as to give the seconds in +every half-minute, leaving you to see by the other dial, on +the hour arbor, which half-minute it is. With a $2$-sec.\ pendulum +there is no such difficulty; for the scape-wheel +then turns in $12$ sec, and its pinion of $10$ driven by a wheel +of $100$ lets that wheel turn in $2$~minutes; and that may have +a pinion of $10$ driven by $100$, which will turn in $20$~min.\ instead +of $15$, and consequently wants a pinion of $12$ to an +hour wheel of $36$. Several other numbers also would do; +but we shall see afterwards how the second wheel may +be used to obtain greater \index{Striking clocks!accuracy of discharge}precision in the time of beginning +to strike than you can get from an hour snail, a good way off +the escapement too, if the second wheel turns in $15$ or $20$ +minutes. And if you want to apply it to the half-hour +striking also, which only requires two pins ($\mathrm{T}$ in fig.~\ref{fig40}., +p.~\pageref{fig40}) instead of one, it must turn in $15$~min. The great +wheel need not turn in any particular time. Sometimes I +have had them for $4$~hours. In the Westminster clock it was +convenient to have it turning in $3$~h. $45$~m. A minute-hand +is, or should be, always set on the hour-wheel arbor, with a +dial to set the clock by, which is best done by letting the +%-----File: 202.png-------------------------------------------- +%-----Folio: 187----------------------------------------------- +gravity escapement run or stopping it for the necessary time, +which is another advantage of these clocks. + +\subsection[Wire ropes.]{Wire ropes.}\markright{WIRE ROPES BEST.}\label{subsec:Wire_ropes.}\index{Ropes, wire!best for turret clocks}\index{Turret clocks!wire ropes for}\index{Wire ropes best for large clocks}---The introduction of wire ropes, instead of +the old hemp ones of $5$ or $6$ times the thickness, did a great +deal towards enabling the barrels and clock frames to be +made smaller than the clumsy things of old times, which it +is no longer necessary to describe, as wire ropes and iron +barrels have become universal. But I find it is still necessary +to warn people against using zinced wire ropes. I +found long ago that for some reason or other zincing iron +wire or sheet iron tends to make it brittle, and sometimes +the zinc splits off, while tinning it has the contrary effect; +only it does very little towards preventing rust, for galvanic +reasons. But the best way of preventing rust on wire ropes +is to keep them well greased with a mixture of tar and +grease. Paint splits off with the bending of the ropes. + +\subsection[Striking from the great wheel]{Striking from the great wheel}\markright{STRIKING FROM THE GREAT WHEEL.}\ \label{subsec:Striking_from_the_great_wheel}\index{Striking part!of turret clocks}\index{Great wheel, striking from}was another important +improvement which followed from the use of wire ropes with +many more turns of the barrel for one winding up, and especially +those of steel wire, which may be thinner still. The +saving in friction, and consequently in weight, and the +strength required, is more than any one would suppose; and +that also has become universal in all clocks, except those +of makers who have steadfastly set their faces against all improvements, +and consequently never dare to accept contracts +guaranteeing the rate of time-keeping prescribed above, or +the raising of hammers that will bring the full sound out of +bells, which the old clocks never did. I will explain afterwards +the construction of the cams\index{Cams!for large clocks} which are now generally +cast on the great wheels, but in very large clocks are also +faced with steel. For an eight-day striking part I have come +to the conclusion that the best arrangement is to have about +$18$ cams working \markright{TWO STRIKING HAMMERS.}two hammers, so that each hammer-tail +and cam has the same action as if there were only half +the number of cams. In some of Dent's earlier clocks the +%-----File: 203.png-------------------------------------------- +%-----Folio: 188----------------------------------------------- +\index{Turret clocks!hammers of}hammer-tails were on opposite sides of the wheel, with two +sets of cams, each having half the number. But this is unnecessary +if they are placed as in fig.~\ref{fig37}, keeping quite clear +of each other, which is easily managed, taking care to place +them so as to make the intervals between the blows exactly +alike; \textit{i.e.}\ their centres must be on prolonged radii of the +wheel, $1\frac12$ cams apart. The reason for having\label{2hammer} $2$ hammer-tails +instead of one shorter and working over half the space, is that +the pressure of such a short lever sometimes cuts off the ends +of the cams if the lever end was not blunted enough, though +there are plenty of such clocks going without any such +result. On the whole it is better to avoid the risk, except +with small bells not above $2$~cwt., which only want hammers +of $4$ or $5$~lbs. If there are $22$ or $24$ cams, of course the +teeth of the great wheel, and of the small one on it, which +drives the locking-plate, must be increased; and remember +that when there are two hammers that $36$-wheel must still +be twice the number of the cams, as each cam strikes two +blows. I assume the locking-plate wheel to have one tooth +for every blow struck, though you may vary the number if +you keep the right proportion; \textit{e.g.}\ you might have $30$ and +$66$, instead of $40$ and $88$. Both these wheels are in front +of the frame. The great wheel of $108$, or $3 \times 36$, drives +a pinion of $9$, which therefore goes one third round for each +blow, and accordingly has $3$ cams to lift the detent. The +winding pinion should pump into and out of gear, as there +is no use in giving the clock the friction of turning it. Its +back pivot is accordingly set in a cock bolted to the cross +bar in the middle of the frame, with a key that drops into +a nick round the arbor to keep it in its place. In the drawing +it looks as if the second hammer lever pivot was in the +winding-pinion one; it is only optically so, as they say of +stars, which may either be really inside a nebula or billions +of miles behind it. + +The half-hour striking arrangement has been already +%-----File: 204.png----------------------------------------------- +%-----Folio: 189-------------------------------------------------- +described with reference to this (see p.~\pageref{subsec:Half-hour_striking.}). The jumper +spring is on the right side of the $24$ ratchet wheel with the +$12\frac12$ and $1\frac12$ o'clock steps on it. + +Returning to the going part, the maintaining power which +I always prescribe, except for very large clocks, has been +already described (p.~\pageref{smallmaintain}). Some clockmakers found, after +much trouble (of which they were warned before), that the +spring-going ratchet will not do for gravity escapement +turret clocks, except very small ones. Where the dials are +so large as to require more weight than can be wound up +without an auxiliary pinion like the striking part, I think the +Westminster maintaining power is the best (see also fig.~\ref{fig40}); +though this one in fig.~\ref{fig37} does perfectly well, and is generally +used for larger clocks. + +\subsection[Stops for weights.]{Stops for weights.}\markboth{STOPS FOR WEIGHTS.}{STOPS FOR WEIGHTS.}\label{subsec:Stops_for_weights.}\index{Stops for weights}\index{Weights, stops!for falling}---Where the weights do not go down +to solid ground there ought to be a large box full of broken +stones, not gravel, for them to fall on if a rope breaks. The +reason why stones are the best is that they give the weight +something to do in breaking them a little more, which uses up +a good deal of its force. Sawdust or chips are too elastic, and +sometimes throw the weight off on to the floor, and therefore +through it, as happened at St.~Albans lately, from over-winding. +Gravel is too hard to break, but still gravel or +even sand will take off a great deal of the force of a blow in +displacing it; but I am convinced that stones are the best. +They may be covered with a thin board, to look tidy. Their +depth should never be less than $2$~ft., and more according to +the bigness of the weight and the possible drop. But another +kind of stop\index{Turret clocks!stops against overwinding}\index{Weights, stops!for winding}\index{Winding stops!for clocks} also is requisite where the weights go out of +sight, to prevent over-winding, \textit{i.e.}, winding right up to the +fixed pulley. A mere straight stop to catch the top of the +weight will generally do, because it gives check enough to +make any man who is winding feel it, though of course +there is a little risk of the jerk and strain, for which extra +strength of rope must be provided; but this will not do +%-----File: 205.png----------------------------------------------- +%-----Folio: 190-------------------------------------------------- +when a great multiplying power has to be used. Nor is it +at all safe to rely on human stupidity attending to any mark +on the rope, which there was at St.~Albans, even if there is +always light enough to see it and the real winding man is +told about it, who is probably a mere blundering deputy of +the one who ought to do it. At Westminster, you will see +farther on, that I provided an absolute stop to the turning +of the handles beyond the proper times, both when the clock +is going to strike and when it is fully wound. But ropes +on long ungrooved barrels do not travel uniformly enough +for that method to be adopted with them; and besides that, +the ropes often overlap, though they had better not. It +would be easy enough to make each weight raise a lever with +a sort of click to it, which would ring a bell when the weight +has got to the top, in several ways. And now that electricity +is coming into use for everything, the weights might make a +contact to complete an electrical circuit when they reach the +top, and so might make any kind of noise which the winder +could not fail to hear, or drop a lever to stop him. + +\index{Lines and pulleys for winding up large clocks}\label{lines}\index{Pulleys}When the weights do not hang from the barrels, but the +ropes have to be led off to a fixed pulley somewhere, it is +necessary that it should be so far off and in such a position +that each rope may feed straight off and on the barrel, +without either separating or grinding against itself. It is +so much better to let them hang down, that I would rather +have them hang so by $3$ lines, which requires no more pulleys, +and only two-thirds of the height of $2$ lines, than lead off for +anything less than $15$ or $20$ times the length of the barrel. +But more than $3$ lines increase the friction enormously, and +should never be used; nor should $3$ together with a fixed +leading-off pulley, which makes $4$ lines or $3$ pulleys. The +weights in this clock go down within the frame, close to the +walls, and are boxed all the way down. Even if they did +not, the tower must not have been much smaller, on account +of the fly, in which length is of great value always for steadiness +%-----File: 206.png----------------------------------------------- +%-----Folio: 191-------------------------------------------------- +of striking, and you must have a reasonable space for +the handle to turn in winding, even if it goes the right way, +as it does here, not requiring the man to stand beyond it. + +\subsection[Four-wheeled trains.]{Four-wheeled trains.}\markboth{FOUR-WHEELED TRAINS.}{FOUR-WHEELED TRAINS.}\label{subsec:Four-wheeled_trains.}\index{Four-wheeled trains}---These horizontal frames evidently +require rather more length than a well-arranged cage +frame, in which the wheels stand over each other, and they +would require still more to contain a four-wheeled train. +Turrets are sometimes made so small that a horizontal frame +clock even of $3$ wheels cannot be got in. The clock can be +got into less length by making the frame something like a +pointed arch, which is also a strong form. Many years ago +I\index{Beckett, Sir E.!drop bushes for turret clocks@`drop bushes' for turret clocks} designed some small quarter clocks for a confined space, +to be sent to Mexico, and the arrangement on page~\pageref{fig39} +brings the work within the smallest possible limits. I believe +they were the strongest clocks of the size that had +ever been made. There are no loose bars whatever to the +frame, and instead of cylindrical bushes\index{Bushes, various kinds of} (fig.~\ref{fig38}~$a$) which +can only be let in near the middle of the bar, the bushes are +mostly of the form $c$, which admits of greater variety of +position, and also enables the wheels and other pieces to be +taken out singly with greater facility than the let in bushes. +Another bush, which is used in clocks with horizontal and +arched frames, is that at $b$, which is the best of all for convenience +of fixing, and adjusting the place of the wheels, +and taking them out separately. + +There is yet another kind of bush which I used first at +Westminster, and it is the best for the barrel arbors of +clocks with a horizontal frame. A hole of the shape $d$, is +cut out of the piece, which is then cast as a projection downwards +from the frame, large enough to hold a bush of the +form $a$, and with a slot below just wide enough to let the +arbor drop when the bushes are pulled out. Otherwise it is +necessary to bolt large pieces, or cocks, on to the frame, and +the back piece is sometimes difficult to get off. I shall call +these `drop-bushes'\index{Drop bushes@`Drop bushes' for large clocks} accordingly. At Westminster they are +%-----File: 207.png----------------------------------------------- +%-----Folio: 192-------------------------------------------------- +not used for the barrels, but for the third wheel arbors which +drive the flies. + +In connection with bushes\index{Bushes, various kinds of} it is necessary to warn people +against making oil holes in them, which is sometimes done +from overlooking the difference between the slow-going +pivots of clocks which do not need oiling once a year, and +the quick ones in other machines which require constant +feeding with oil or they will heat. Such holes in clock +bushes are very soon drained of oil and become receptacles +and feeders of dirt and grit. What little oil is needed easily +works in from the ends of the pivots, the old oil being first +wiped off. I shall say a little more about oil at the end of +this part of the book. + +\begin{figure}[htbp] +\centering +\caption{\sc Different Kinds of Bushes} +\includegraphics[width=\textwidth]{images/fig38.png} +\label{fig38} +\end{figure} + +Fig.~\ref{fig39} is a front elevation of those Mexico clocks, showing +as much as can be shown at one view without confusion, +and representing the wheels only as circles for the same +reason. They have $1$~sec.\ compensated pendulums with +bobs of nearly $1\frac14$~cwt.; where there is room, of course it +would be better to use $1\frac12$ or $1\frac34$~sec.\ pendulums. They +are calculated to strike the hour on a bell of $4$ or $5$~cwt.\ with +quarters in proportion, and will drive four $6$~ft.\ dials very +well. The whole length of a quarter clock on this pattern +is only $30$~inches, and for one without the quarters $21$~inches. +The flies may require rather more, according to the size of +the hammers. One fly\index{Turret clocks!position of fly} may go behind the other if necessary. +Those who build clock-towers should remember that +%-----File: 208.png----------------------------------------------- +%-----Folio: 193-------------------------------------------------- +\index{Turret clocks!larger ones}\index{Turret clocks!smaller ones}%couldn't find ref +there must be room for a man to stand and wind up the +clock besides. The hole in the upright bar where the pallets +are shown, is only in the back bar, which is widened out for +\begin{sidewaysfigure}[p] +\centering\index{Beckett, Sir E.!general plans for turret clocks} +\caption{\sc Four-wheeled Train Clock} +\label{fig39} +\includegraphics[width=\textwidth]{images/fig39.png} +\end{sidewaysfigure} +%-----File: 209.png----------------------------------------------- +%-----Folio: 194-------------------------------------------------- +it, and the two lumps which form the pendulum cock are +cast on the back. The cross bar which carries the locking +plate $78$ is only wanted on the front frame, and is omitted +on the back one, as it would interfere with taking out the +barrel. All the levers are so placed as to clear the ropes +when they have to be taken upwards. The small cam wheel +for lifting the locking lever of the striking part answers very +well: that of the quarters is in fact the locking plate itself. +If there are no quarters at the hour, the pinion of $20$ should +be $30$, and drive a separate locking wheel of $36$, which +will turn in $2$~hours, as $12$ cams are used in that time. + +\subsection[Size of fly.]{Size of fly.}\markboth{LARGE FLIES BEST.}{LARGE FLIES BEST.}\label{subsec:Size_of_fly.}\index{Fly, striking!for turret clocks}---There is no more frequent mistake in turret +clocks than that of making the fly too small to preserve uniformity +of time in striking, and the defect is generally incurable +for want of room. When the fly of the hour striking part is +too small the velocity increases after the first few blows; and +with quarters on four bells especially, some blows come +quick and others slow, according as the heavy or the light +hammers are being raised. You must have a considerable +superfluity of force beyond what will just raise the hammers, +and the regulation of time must be done by the fly. I do +not however see my way to prescribing any rule for the size +in proportion to the weight of hammers or bells beyond this, +that each arm of the fly of any large church clock ought to +be fully $2$~ft.\ long; and for the very large bells which have +lately come into fashion again, the flies must be still longer. +Length is much more effective than width. There may be +from $4$ to $8$ turns for each blow or each quarter, according +to the size of the clock. At Westminster we could get no +uniformity of striking quarters with a fly going faster than +$4$ times to each chime; $6$ or $7$ is generally the best number. + +When it is impossible to get room for flies of proper +length and size to equalise the time, something may be done +by using a three-armed fly, but that is by no means equal to +one with two arms of sufficient length. +%-----File: 210.png----------------------------------------------- +%-----Folio: 195-------------------------------------------------- + +I find it necessary to add, that the flies should on no +account be in front of the clock, for that involves the use of +a winder with a very long pipe to clear them, which is +harder to wind and strains the arbors. Fig.~\ref{fig47} will show how +to get plenty of room for them behind in clocks of almost +any size. In very large ones, such as Westminster, a +vertical rod may be carried up and the flies put quite away +at the top of the room. I have seen it done also in much +smaller clocks where there was no room otherwise for the flies. + +\section{LARGE CLOCKS WITH QUARTERS.}\label{sec:LARGE_CLOCKS_WITH_QUARTERS.}\markboth{LARGE QUARTER CLOCKS.}{LARGE QUARTER CLOCKS.} + +Fig.~\ref{fig40} (\textit{t.~o.}) is a front view of a larger clock than those +previously described, substantially according to the plan +which I settled for old Mr.~Dent's factory many years ago, +whereby we reduced the cost of large quarter clocks to little +more than a quarter of what it used to be, and at the same +time greatly increased both their accuracy and strength. +This only shows two quarter hammers for simplicity. Indeed +four could not be shown in an elevation, as the levers must +then all be on one axis or pin, and the cams come irregularly, +as will be explained under quarter chimes. As Fig.~\ref{fig37} was +of an eight-day clock, to which a quarter part might be +added much like the hour part, this is of larger clocks, with +heavy bells, and winding up the striking parts every day or +two days, according to the available fall. It is impossible to +strike heavy bells properly with an eight-day clock unless it +has a very unusual fall, and even then it would want very +inconveniently long barrels, and the old-fashioned clocks never +did strike properly. + +The hour great wheel \hyperlink{fig40}{here} has only $10$ cams, which I +consider the best number for the arcs that have to be described +by the cams and the hammer-tails or levers, when we are free +to use any number, which we cannot in eight-day clocks. +Therefore this requires only $16$ turns of the barrel for $24$ +%-----File: 211.png--------------------------------------------- +%-----Folio: 196------------------------------------------------ +\begin{sidewaysfigure}[p] +\centering\index{Beckett, Sir E.!general plans for turret clocks} +\hypertarget{fig40}{\caption{\sc Large Quarter Clock}}\label{fig40} +\includegraphics[width=\textwidth]{images/fig40.png} +\end{sidewaysfigure} +%-----File: 212.png--------------------------------------------- +%-----Folio: 197------------------------------------------------ +hours, or $156$ blows, and $2$ or $3$ more for a few extra hours; +or say $35$ or $36$ turns for winding every two days; and +therefore quite short barrels will do, with wire ropes as much +as $\frac 14$~in.\ thick, which are enough for all but very large +clocks beyond the ordinary patterns. + +The going part is always made to go a week, or rather $8$ +days and a fraction, to provide for the forgetting of a day. + +\index{Large turret clocks}\markboth{LARGE TURRET CLOCK.}{LARGE TURRET CLOCK.}It is impossible to give any rule for the size of the great +wheels, as it clearly ought to depend on the work they have +to do. For bells from about $30$~cwt.\ to $53$, a common range +for the tenors of large peals, an $18$-in.\ great striking wheel is +the best pattern to keep, as it is inconvenient to use many. +A $24$-in.\ wheel with only $10$ cams of proper size and strength +will do very well for bells up to $5$ or $6$~tons, or even $10$~tons, +if the teeth and cams are wide enough. The great going +wheel may be from $13$ up to $16$~inches for any four dials +from $7$ up to $12$~feet, and there are very few larger. The +other wheels may be in proportion. The scape-wheel legs +should be from $5$ to $6$~inches long, and you must allow +plenty of room for a long fly, not less than $9$ or $10$~inches, +especially for large dials, which should have a considerable +superfluity of force, to drive the hands in all weathers. For +that reason the scape-wheel arbor is put on a higher cock +than before. The pendulum is carried in the same way by +the frame. If it is a very large one it is well to put one or +two brackets or strutts from the wall to the back part of the +frame near the pendulum, but that is not necessary generally, +as this kind of frame for $18$-in.\ great wheels is only $5$~ft.\ $6$~in.\ long, +and forms a kind of arch when its feet are firmly bolted +to the corbels, which I need not say should be a great deal +deeper than there was room to show in \hyperlink{fig40}{this drawing}. If they +are iron brackets they should be built into the wall and wide +at the top also, to prevent any risk of sideway motion under +the swing of the pendulum. + +For\label{nocams} $10$ cams the great wheel had better have \index{Wheels, numbers of teeth}$100$ teeth, +%-----File: 213.png--------------------------------------------- +%-----Folio: 198------------------------------------------------ +and the pinion $10$; or $120$ and $12$ of course run rather easier, +which pinion will evidently go once round for each blow. +But if you want the clock to go $4$~days without winding and +to have only one hammer, $16$ cams will be better, and $192$ +teeth in the great wheel, driving a pinion of $12$ \label{twothirds}two-thirds +round for each blow. And then you may make the cam wheel +on that pinion with $2$ hollows in it one-third and two-thirds +of the circumference apart, and they will always come +right, because the number of the hours is odd and even +alternately, if it is put in the right position; which you +will find more easily by trial than by explanation here. But +this would not do when half-hours are struck by the hour +part, for two odds then often come together, such as $3$ and $1$, +$5$ and $1$, \&c. The general calculation for all numbers is +this. Let $p$ be the leaves of the pinion, which must be a +multiple of $3$ if you are to use that method; $n$ the teeth of +the great wheel, and $m$ the cams. Then $\frac23 p$ must $= \frac{n}{m}$ or +$n = \frac23mp$: $p$ must be taken as $12$ for this purpose, and +$\therefore n = 8m$. If $p$ has $10$ leaves and is only to go once +round, $n$ must evidently $= 10 m$. It is not convenient to have +two large hammers with a ringing peal, as it is difficult to +get room for them in the frame, though it is easy enough for +stationary clock bells. But it is unnecessary to consider all +that if the clock winds up every day or two, which is always +best for large ones. A few cocks and bushes are omitted in +the drawing to avoid confusion. + +In other respects this striking\index{Turret clocks!striking part} part is the same as in fig.~\ref{fig37}. +But I now show the plan for letting off the \markboth{LARGE QUARTER CLOCK.}{DISCHARGE OF STRIKING PARTS.}striking of +the hours more exactly than can be done by the slow motion +of the hour wheel and its snail, especially as it is a sort of +outrider to the train. This was first done in the Westminster +clock, but the plan now described for the first time was not +expedient there on account of the great size and weight of +%-----File: 214.png--------------------------------------------- +%-----Folio: 199------------------------------------------------ +the discharging\label{disch} levers. \hyperlink{fig40}{Here} you see that the long lever or +detent $\mathrm{DS}$ is carried over to the second wheel of the going +train, which has a square pin $\mathrm{T}$ on one of its spokes; and +there is another square pin $\mathrm{S}$ on the detent, now shown +below the other, the clock having just struck. But at some +minutes before striking $\mathrm{S}$ gets raised above the circle in which +$\mathrm{T}$ moves, which can be done, because at that time $\mathrm{T}$ is out of +the way. Just before the detent is going to drop off the snail +$\mathrm{T}$ has come under $\mathrm{J}$, and $\mathrm{J}$ cannot fall again till $\mathrm{T}$ slips from +under it, which will take place with perfect \index{Striking clocks!accuracy of discharge}accuracy at the +last beat of the pendulum for the hour, as the motion is large +enough to be visible, and a very little way off the scape-wheel. +This is inconsistent with altering the hands less than $15$ or $20$ +minutes, except by running the clock, as you easily can with +a gravity escapement. In the Lincoln\index{Lincoln Minster clock} Minster clock Mr.~Potts\index{Potts, maker of Lincoln Minster clock and others} +provided in this way for the quarters also, as did +Messrs.~Smith at St.~Paul's and Beverley\index{Beverley!clock}, which however +are not of so much consequence as the first blow of the +hour. The second wheel must in that case turn in $15$ +minutes; but without the quarters it may be either $20$ or $15$. +The pins $\mathrm{S}$ and $\mathrm{T}$ should be so placed and shaped that the +pressure may not tend to stop the wheel. (See also p.~\pageref{addenda_start}\label{199add}.) + +As I have already shown the maintaining\index{Maintaining powers of clocks or going barrels!Westminster clock plan} power which is +best for clocks not requiring an auxiliary winding wheel, I +show here the one which is best for those that do; though +the other, of which a piece is shown at $\mathrm{B}$, may be used for +them. This is the one that I designed for the Westminster +clock, and the principle of it will be described there. The +winding pinion and the bars which carry it, the front one +fixed and the back one hanging from the arbor, are out of the +vertical, because the action of gravity is wanted to make the +pinion and back bar which carries it fall on to a fixed stop, +when the winding is done, or suspended for a short time. +The back bar also carries the click which takes into ratchet +teeth cast on the back of the great wheel. It might go into +%-----File: 215.png--------------------------------------------- +%-----Folio: 200------------------------------------------------ +the other teeth, but for the risk of catching only on their tops +and slipping, so that ratchet teeth are safer, and practically +cost nothing when once the patterns are made to cast from. + +The arrangement of the quarter part for $4$ bells is practically +the same as for $2$, except that all the levers must be on one +steel pin, which should be screwed tight at its ends to help +to keep it stiff. Either for $2$ hammers or for $4$, the best way +is to cast one set of cams on one side of the great wheel and +another on the other, at the proper distances to make the +interval between successive chimes at least twice as great as +between the blows in each chime. For $4$ bells two other +sets of cam rings may be cast in one, and all bolted together. +Some clockmakers prefer an independent cam barrel driven +by the great wheel, to which there is no objection except the +extra friction, which I once found to make the difference of +requiring an auxiliary winding-wheel. When steel cams are +used they are all bolted to a wide ring or barrel cast with +or bolted to the great wheel, the nuts being inside it. I shall +have more to say about cams afterwards. Four quarter +hammer-tails cannot well be turned inwards as the hour one +can, in the form which makes the pressure on the arbor only +the difference instead of the sum of the two forces on the +lever. But they can have their wires in the middle, instead +of their fulcrum or arbor being there, as you see in the +Westminster clock, and in that way the friction on their arbor +is reduced to a minimum, the wires being put as near the +cams as possible. (See also p.~\pageref{add200}\label{200add}) + +Two \markboth{WAY OF FIXING TWO QUARTER LEVERS.}{WAY OF FIXING TWO QUARTER LEVERS.}quarter hammers---or two alternate hour hammers---can +also be placed as in this fig.~\ref{fig41}, which I designed long +ago with the same object of keeping the power and the work +on the same side of the arbor, and many large clocks were so +made at Dent's factory. It involves cams on both sides of +the great wheel, which are as easily cast as on one side. The +rope also should always pull on the same side of the barrel as +the cams, in order that the pressure on the great arbor may +%-----File: 216.png--------------------------------------------- +%-----Folio: 201------------------------------------------------ +\index{Quarter chimes!on two bells}be the difference instead of the sum of the weight and its +work, and consequently the friction much less. You may +fancy that these frictions of pivots, and of teeth when the +cams are not on the great wheel, cannot come to much compared +with a great striking weight, or a hammer of many +pounds weight raised $9$~in., or about $6$ vertically, $156$ times a +day; but you will find very few clocks in which the weight +$\times$ its daily fall is not more than twice or even three times +its theoretical `duty,' or the hammer $\times~78$~ft., which excess +is all due to these various frictions. + +\begin{figure}[htbp] +\centering +\caption{\sc Two-quarter Hammer} +\includegraphics[width=\textwidth]{images/fig41.png} +\label{fig41} +\end{figure} + +If no quarters are struck at the hour it is better to have $12$ +cams, the locking-plate being on the great wheel arbor, so +that they will turn in $2$~hours. In that case the pinion may +as well be of $12$, driven by the great wheel of $96$, and +therefore turning $\frac23$ round for each quarter chime as before +described for hours in some cases. + +Lifting the hammer by pins on the striking wheel, as in +house clocks, is totally wrong in large ones, and it is nearly +discontinued. The pins necessarily begin to act a good way +from the end of the lever, and therefore at the greatest disadvantage +%-----File: 217.png--------------------------------------------- +%-----Folio: 202------------------------------------------------ +as to leverage, and that at the very time when +the hammer is rising most vertically (in the usual way of +hanging) and requires the most force to lift it. The lifting +should be done by cams, which begin to act on the end of +the lever, and are properly shaped to act with the least +possible friction throughout, as I shall explain under the +\textit{Teeth of Wheels}. Pins with rollers on them are of very little +use, and do not obviate these objections, and are weaker than +fixed pins: they are nearly if not quite abandoned. + +\subsection[Cambridge and Westminster chimes.]{Cambridge and Westminster chimes.}\markboth{QUARTER CHIMES ON FOUR BELLS.}{CAMBRIDGE AND WESTMINSTER CHIMES.}\label{subsec:Cambridge_and_Westminster_chimes.}\index{Cambridge and Westminster chimes}\index{Chimes (quarter)!Cambridge and Westminster}---Considering +the thousands of men who had listened for 3 or 4 years +together to the famous St.~Mary's chimes at Cambridge, +during three quarters of a century, it is odd that no one +ever thought of copying them in any other public clock. +The last but one Lord Lansdowne tried it, but his clockmaker +Mr.~Vulliamy\index{Vulliamy, Mr.} made the mistake of ordering and hanging +the bells of four successive notes before writing to ask me +about them; whereas they ought to be such notes as E, D, +C, G; or the fourth bell must be a musical `fourth' below +the third: bells are always counted from the highest note +or smallest bell. At the Royal Exchange\index{Chimes (quarter)!Royal Exchange}\index{Exchange, Royal!chimes}, in 1845, they did +get so far as to adopt the Cambridge notes; but the Gresham +professor of music thought he could improve upon the tunes, +and spoilt them. I have been told by a Cambridge man of +the last century, that they were invented by the well-known +Dr.~Crotch in 1780, from an air of Handel's, who has +generally had the credit of inventing them, and perhaps +deserves it. + +\subsection[Doncaster quarters.]{Doncaster quarters.}\markboth{QUARTER CHIMES ON FOUR BELLS.}{DONCASTER QUARTERS.}\label{subsec:Doncaster_quarters.}\index{Doncaster!quarter chimes|(}\index{Chimes (quarter)!Doncaster and Scarborough}---For some time after I thought of +introducing them at Westminster, it was assumed that the +hour bell must be an octave below the third quarter, and +that they were therefore impossible with a peal of only $8$ +bells, if the quarters were to be struck at the hour. Moreover +playing $10$ chimes in every hour, requires nearly twice +as much power in the clock as playing $6$, which is sometimes +%-----File: 218.png--------------------------------------------- +%-----Folio: 203------------------------------------------------ +a consideration when there is not much fall for the weights, +and it makes a little difference in the cost. Again, if you +look at the Cambridge chimes (p.~\pageref{camchimes}) you see that the blow +on the lowest quarter bell (called 6), is repeated too quickly +in one place for a heavy hammer to be relifted immediately; +and accordingly in all very large clocks it is necessary, and +it is always desirable, to have two of those hammers, lifted +alternately. Avoiding it by a separate barrel, driven by the +great wheel, is a much worse plan. For all these reasons, in +a few church clocks, made before 1860, I adopted the plan +of omitting the quarters at the hour; but I should not do +so again with these quarters, because the hour chime is the +best of them all, though \textit{ding dong}, or any other mere +repetition quarters, are neither useful nor pleasing at the +hour. I also made a slight alteration in the third quarter in +those clocks, to avoid the quick relifting of the largest +hammer, and it sounds very nearly as well as the Cambridge +one. The quarter bells are therefore, $2$, $3$, $4$, $7$, of a peal +of $8$ at Doncaster and Scarborough parish churches, and the +cathedral at Fredericton, where the three-legged gravity +escapement was also first used.\index{Doncaster!quarter chimes|)} + +\subsection[Worcester and Chester Cathedral quarters.]{Worcester and Chester Cathedral\index{Chester cathedral chimes}\index{Chimes (quarter)!Chester and Worcester cathedrals}.}\markboth{QUARTER CHIMES.}{QUARTERS ON FOUR BELLS.}\label{subsec:Worcester_and_Chester_Cathedral_quarters.}---But +after a time I came to the conclusion, and other people have +gradually adopted it, that it is not at all necessary to have +the third quarter bell an octave above the hour bell, and +that the ear is quite satisfied if the fourth bell is two notes, +or even one, above the hour, because the interval of time +between the quarters and the hour ought to be from $6$ to $10$~seconds +with large bells. Accordingly in the great peal at +Worcester\index{Worcester cathedral!chimes, peculiar}, the Rev.~E.~Cattley\index{Cattley, Rev.~R.!Worcester chimes}, the author of it, and I, +as the designer of the clock and bells, agreed to take advantage +of the tenor of the peal for the fourth quarter bell, +though it is only $1 \frac12$ notes above the great single hour +bell of $4 \frac12$~tons; and thereby we got far more powerful +quarters than if we had kept them $2$ notes higher. At +%-----File: 219.png------------------------------------------------ +%-----Folio: 204--------------------------------------------------- +Chester Cathedral, and St.~Chad's, Headingley\index{Chimes (quarter)!Headingley}\index{Headingley, St.~Chad's chimes and peal}, near Leeds +and some other places, the 4th quarter bell is only one note +below the tenor, as at Doncaster, though they are the full +Cambridge quarters; and that is the plan which I now +always recommend when there are $8$ bells, or even $6$, with +an extra one added above for the first quarter. At Ossington +Church, having only a small peal of $6$, I recommended +to my namesake the late Speaker, a lower bell (out of the +peal) for the hours; and the same at S.~Shields lately. + +The \hyperlink{camchimes}{following} are these several arrangements, which are +suitable for any key, and therefore I have indicated them by +the bells in a peal of $6$, which these quarters require, leaving +the hour to be any note below the lowest quarter bell. + +\begin{table}[!hbtp] +\centering\index{Cambridge and Westminster chimes}\index{Cambridge and Westminster chimes}\index{Chimes (quarter)!Cambridge and Westminster}\index{Chimes (quarter)!Doncaster and Scarborough}\index{Chimes (quarter)!Royal Exchange}\index{Exchange, Royal!chimes}\label{camchimes}\hypertarget{camchimes}{}\index{Table!various quarter-chimes} +\begin{tabular}{r@{\,}c@{\,}r|l@{\,}l|l@{\,}c@{\,}l@{\,}l} +\multicolumn{3}{c|}{Cambridge and} & +\multicolumn{2}{c|}{Doncaster and} & +\multicolumn{4}{c}{Royal Exchange.} \\[-0.5ex] +\multicolumn{3}{c|}{Westminster.} & +\multicolumn{2}{c|}{Scarborough.} \\[1ex] +\multirow{2}{*}{2nd $\Big\{$} &3126 &\multirow{4}{*}{$\left.\rule{0pt}{5.5ex}\right\}$ 4th} & +1st &1236 &1st & 3126 &\multirow{2}{*}{$\Big\}$ 2nd} &\multirow{4}{*}{$\left.\rule{0pt}{5.5ex}\right\}$ 4th}\\ + &3213 & &\multirow{2}{*}{2nd $\Big\{$} & 3126 &\multirow{3}{*}{3rd $\Bigg\{$} &6213 & &\\ +\multirow{3}{*}{3rd $\Bigg\{$} &1326 & & &3213 & &1326 & &\\ + &6213 & &\multirow{3}{*}{3rd $\Bigg\{$} &2613 & &3213 & &\\ + &1236 &1st & &6213 & & & &\\ +\end{tabular} +\end{table} + +I call the bells $1$, $2$, $3$, $6$, in all cases for more easy +comparison, though they would be of various numbers +according to the peal they belong to, on account of the +numbers being always reckoned from the smallest, in the +order in which they ring. Indeed a peal of $6$ could not have +these chimes at all without an odd bell, either above as at +Headingley, or below as at Ossington. + +You see from the table that the Cambridge chimes are +repeated twice in the hour, and therefore the cams may be +fixed on a barrel\label{barrel} which turns in any multiple of the $5$ chimes +in that table. In some clocks the $5$ sets of cams alone are +put on a barrel driven by the great wheel, but with much +more friction than in other clocks that I know with bells +%-----File: 220.png----------------------------------------------- +%-----Folio: 205-------------------------------------------------- +of about the same weight; one, with this second barrel, +required a double multiplying power to wind it up, while +another, with the cams for an hour on the great wheel itself, +winds quite easily with a single pinion. At Westminster, as +you may see in the frontispiece, there are $3$ sets of cams, or +what may be called an hour and a half's chimes, on the +great wheel, \textit{i.e.}\ on a wide barrel attached to it, because it +happened to be convenient with the great fall we have there. +The cams may be cast in separate rings of cast steel, but it +is better to have smooth-faced steel cams screwed firmly to +a plain barrel, as they are at Westminster, and in all the best +very large clocks now. + +The interval\label{interval}\index{Chimes (quarter)!interval between each quarter} between each chime (\textit{i.e.}\ between the chimes +of each quarter) requires some attention. At Cambridge it +is $3$ times the interval between the blows of each chime. That +appears to me decidedly too slow, and at Westminster, Doncaster, +\&c., I made the interval only two spaces instead of +three. That again is perhaps rather too quick, and at +Worcester, and all the subsequent large clocks for which I +have given designs or specifications, there are $2\frac12$ spaces, +which sound the best of all. The barrel, or each portion of +it which contains the $5$ chimes, must then be divided into $55$ +spaces, of which each blow occupies $2$, and the intervals +between the chimes $5$ spaces. + +When there are two hammers for the 4th bell, as there +always should be, those cams may, and should be, made +longer than the others, as there is then ample room for it; +which diminishes the pressure on them, and makes it more +continuous, and so tends to equalise the time. This is +important, because the 4th quarter bell is much the heaviest, +and there is the least interval between its blows. + +In\markboth{LIFTING OFF HAMMERS.}{LIFTING OFF HAMMERS.} all quarter clocks, striking on a peal of ringing bells, provision +should be made for lifting off\index{Hammers, clock!lifting off}\label{lift} the hammers, or they are +almost certain to be broken when the bells are rung, and +perhaps the bells cracked besides. This is easily done by a +%-----File: 221.png----------------------------------------------- +%-----Folio: 206-------------------------------------------------- +lever; or, when the hammers are very heavy, it is better +done, as Mr.~Cattley\index{Cattley, Rev.~R.!lifting off hammers}\index{Turret clocks!lifting off hammers for ringing} arranged at Worcester\index{Worcester cathedral!clock}, by an eccentric +brought down over all the levers just where they come out +of the clock. The hammers must not only be lifted off the +bells, but so high that the cams do not lift them at all, or all +the wires will soon be broken by the jerks. And as the +clock is thus relieved of its work, it is better also to make +the turning of the eccentric, or pulling down the lever, let +down a wooden brake on the fly arbor, to help the fly to +stop the velocity and diminish the blow on the stops. + +\subsection[Quarters on two bells.]{Quarters on two bells.}\markboth{QUARTERS ON TWO BELLS.}{QUARTERS ON TWO BELLS.}\label{subsec:Quarters_on_two_bells.}\index{Quarter chimes!on two bells}\index{Time of striking (quarters)}---I have little more to say about +turret clocks with these than I said about house clocks at +p.~\pageref{quart}. The bells must be at the musical interval called a +fourth, and the higher of the two should be an octave higher +than the hour bell if there are quarters at the hour; though +that is not so material, and they may be the 1st and 4th of +a peal of $6$, or even $5$, or the 4th and 7th of a peal of $8$, +because there should be a longish interval of time between +the quarters and the hour, which saves the ear from being +offended with the want of the proper musical interval. The +old York Minster\index{Chimes (quarter)!peculiar, on two bells at York Minster}\index{York Minster!quarter chimes, peculiar} quarters, and a few others, were at the +interval of a fifth (which in music, though not in arithmetic, +is larger than a fourth), but they do not sound so well. + +\subsection[Time of striking.]{Time of striking.}\markboth{PRECISION OF STRIKING HOUR.}{PRECISION OF STRIKING HOUR.}\label{subsec:Time_of_striking.}\index{Striking clocks!accuracy of discharge}---The quarters are generally made to +let off the hour, as described at p.~\pageref{hourstrike}. But where accuracy +of time of striking is required, this plan is insufficient; for +it makes the first blow of the hour depend on the time both +of letting off, and of striking the quarters, both of which +may easily vary several seconds. It is therefore essential +to accuracy that the hour-striking should be let off by an +independent\index{Quarter chimes!should be independent of hour in large clocks} snail of its own, exactly at the hour, with the +quarters let off the requisite number of seconds before the +hour; though the other three quarters may be allowed to +strike at their proper times. Even this is not sufficient where +extreme accuracy is required, as I have already explained. +%-----File: 222.png----------------------------------------------- +%-----Folio: 207-------------------------------------------------- +The hammer should also be left `on the lift,' or nearly ready +to fall; which is in other respects also a good thing in a very +large clock, because it relieves the wheels and the stopping +pieces from a heavy pressure, and throws it all on the cams +and hammer work, which must in any case be strong enough +to bear it. In this case it is necessary to put a small click +somewhere, to act on a pin in the fly arbor to prevent the +train from running back when you wind up the clock: +indeed it is as well to put one always, as the winding always +tends to drive the train back. Where there is no special +provision for accurate striking, as above, care must be taken +to make the discharging snail large, and its corners +sharp and hardened, and those of the discharging lever or +lifting piece also. See also p.~\pageref{disch}. + +\subsection[Chime tunes.]{Chime tunes.}\markboth{CHIME TUNES.}{CHIME TUNES.}\label{subsec:Chime_tunes.}\index{Chime-tunes}\index{Tunes, chime}---There has been a considerable revival of +the old fashion of having tunes played on bells by machinery +for a few minutes at certain hours of the day. The old +machinery for this purpose was extremely simple, consisting +of a large barrel $2$ or $3$~feet in diameter, generally made of +wood, with strong iron pins screwed into it like a huge musical +box barrel, and pulling down levers which lifted hammers +on the bells like a common striking part. If there were +several tunes on the barrel, either that or the bed of levers +had an endway motion, shifting at the end of each tune, or +shifted once a day by the clock. The Royal Exchange\index{Exchange, Royal!chimes} +chimes are of this kind, only the barrel is of cast iron, with +a vast number of holes in it, in which pins or short cams +are screwed to play any tunes that the bells admit of. + +Some new ones of the old kind have lately been put up in +St.~Albans\index{Chimes (quarter)!St.~Alban's cathedral}\index{St.~Alban's cathedral chimes} Cathedral by Mr.~Godman, a clockmaker there +whom I have mentioned before, entirely from his own design. +The barrel is $7$~ft.\ long, of wood on iron rings, and the levers +are worked by cams of `phosphor bronze' screwed on, for $8$ +tunes on $8$ bells, which I think are quite tunes enough, and +more than were generally used in old times. The tunes shift +%-----File: 223.png----------------------------------------------- +%-----Folio: 208-------------------------------------------------- +themselves. The Westminster quarters are also put there on +the same plan and in connection with the chimes in a room +above the clock. Notwithstanding the superiority of those I +am going to describe next when constantly looked after by +a competent person, which they require, and which of course +costs money, I have returned to the opinion that for ordinary +churches, where there are seldom any funds to spare, +the old-fashioned chimes are the best. + +The chimes in some foreign churches\index{Foreign!churches, chimes in some}\index{Tunes, chime!on church bells} are played by hand, +I understand, without anything that can be called machinery. +The hammers, being light, are easily lifted a little by a man +playing on keys like a piano, only with his fist instead of his +fingers. I have seen tunes played on church bells here with +even less machinery than that. They just tie the bell-ropes +to the clappers, and the lower ends to rings on a board +screwed down to the belfry floor, bringing the clappers so +near to the bells that a slight pull will make them strike. +The man `operates' them (in American grammar) by pulling +some of the ropes with his hands and pushing others with +his arms, and so manages to play a feeble sort of tune. + +\section{NEW CHIME MACHINERY.}\label{sec:NEW_CHIME_MACHINERY.} + +The new kind just now referred to were introduced by +Gillett and Bland\index{Chime-tunes!improvements!by Gillett and Bland}\index{Gillett and Bland's!chime machinery|(} of Croydon, and by Lund and Blockley of +Pall Mall, both of whom bought some patent rights of an +inventor named Imhoff, and have both made improvements +of their own. The principle of the invention consists in +this, that the hammers are raised by a long barrel full of +cams which have nothing to do with dropping them, but +are continually at work raising any levers that happen to be +down. The levers are then caught and held by triggers, +which are let off by quite small pins on a wooden barrel just +like that of a common grind-organ. The barrel can also be +taken out and changed, besides each barrel holding several +tunes which change themselves by an endway motion. This +%-----File: 224.png----------------------------------------------- +%-----Folio: 209-------------------------------------------------- +\label{folio_209}figure shows Gillett and Bland's mode of lifting. Each lever +has a jointed beak which is lifted by one of the $7$ cams on +the barrel belonging to that lever; and when it has been +caught by the trigger +at the other end the +cam slips away, and the +beak drops, so as to +clear the cam next below, +and gets caught +again by the next to +that, because it falls +on to a block which +stretches out the beak. +This gives a greater lift +for a given number of +cams, and so allows +more cams to be put in +the barrel and more +lifting to be done with +a given velocity. + +\begin{figure}[htbp] +\centering +\caption{\sc New Construction for Chime Tunes} +\includegraphics[height=0.7\textheight]{images/fig42.png} +\label{fig42} +\end{figure} + +Lund and Blockley's\index{Chime-tunes!improvements!by Lund and Blockley}\index{Lund \& Blockley's!chime machinery} +lifting barrel has only +$4$ cams, and they lift +from $90^\circ$ before the +vertical up to their +highest position, by +means of a hinged +piece dropped from +each lever. They also +strike the Westminster +quarters by means of +the same set of pins as +the tunes: which I +must say I disapprove of altogether compared with a proper +quarter-striking part. I have seen an otherwise very satisfactory +%-----File: 225.png------------------------------------------------ +%-----Folio: 210--------------------------------------------------- +large clock of theirs, with chimes on a peal of $16$ +large bells for the Bombay University; and some smaller +ones. Gillett and Bland's\index{Gillett and Bland's!chime machinery|)} principal chimes are at Worcester +Cathedral, Boston and Croydon Churches, Bradford and +Rochdale town-halls, and at Eaton Hall\index{Bells in peals!Boston and Eaton Hall}\index{Chime-tunes!Boston and Eaton Hall}\index{Eaton Hall bells}. The performance +of both kinds is more accurate and satisfactory than in the +old-fashioned machines; but, like most superior machines, +they require a great deal more care and consequent expense +than the old rough ones. No chiming machinery can bring +the full tone out of bells, especially the large ones: but this +is stronger in lifting as well as more exact in letting off than +the old kind. Every bell requires two hammers, and at +Worcester some of them have three, because of the quick +repetition in some of the tunes. + +It is necessary to give one caution most strongly to +ambitious chime-cultivators. Avoid `chords,'\index{Chords in chime-tunes bad@`Chords' in chime-tunes bad} or two notes +sounded (professedly) at once. At Croydon they thought +they knew better, and a more horrible performance I never +heard from the rudest old-fashioned chime barrel of 200 +years ago. I believe the chords have since been abolished. + +Another caution is, not to attempt chimes on large and +small bells together\label{lsbad}\index{Bells in peals!large and small together, bad}. For some reason, which neither I nor +the bell-founders know, it is a fact well known that bells +below $4$ or $5$~cwt.\ cannot be made to sound homogeneous with +large ones. I shall have more to say of that in the chapter on +bells. They attempted it at Boston, and have got $42$ bells (including +the $8$ of the peal), some of only a few pounds weight +cast in Belgium, and chimes to play on them all together. I +and other people who went specially to hear them considered +them a failure. Even quarter chimes are never satisfactory +when large and small bells are mixed. The same result is +unpleasantly conspicuous at Eaton, though the bells there are +not so numerous, and were all cast in Belgium together. + +\subsection[Clock hammers.]{Clock hammers.}\markboth{CLOCK HAMMERS.}{CLOCK HAMMERS.}\label{subsec:Clock_hammers.}\index{Hammers, clock}---Turret clocks generally strike on bells +of a different shape from the hemispherical house clock bells, +which do not answer beyond a very small size, as I shall +%-----File: 226.png-------------------------------------------- +%-----Folio: 211----------------------------------------------- +explain more fully hereafter. Most people (except artists, +who always draw them wrong) are aware that the general +shape of church bells is that shown in figs.~\ref{fig43}, \ref{fig44}. The +clock hammer $\mathrm{CS}$ is always fixed\index{Hammers, clock!fixing}\markboth{FIXING OF HAMMER.}{FIXING OF HAMMER.} at right angles to the +swing of the bell, for two very obvious reasons: first, if the +bell was free to swing\index{Bell-hanging!for clocks} under the blow of the hammer, the +first blow of every hour would set it swinging a little, and +at every blow after that the bell would either be out of the +reach of the hammer altogether, or else jarring against it; +and another reason (if it is worth while to talk of other +reasons after this) is, that if the hammer was put in front of +the bell, all its machinery would have to be moved out of +the way before the bell could be rung at all. +\begin{figure}[htbp] +\centering\index{Hammers, clock!shape} +\caption{\sc Clock Hammer} +\includegraphics[width=\textwidth]{images/fig43.png} +\label{fig43} +\end{figure} + +The hammers of large clocks also differ from small ones in +acting by gravity, as you see. But they equally require a +check spring, or some other contrivance to keep them from +jarring the bell. When a church bell is rung \textit{up, i.e.}, swinging +once round for each blow, and \textit{set} mouth upwards, the +clapper lies on the bell, but not so heavily as a clock +%-----File: 227.png-------------------------------------------- +%-----Folio: 212----------------------------------------------- +hammer would, because it stands at a higher angle. The +usual kind of hammer spring is shown in fig.~\ref{fig43}; and $sc$ +in fig.~\ref{fig44} shows as much of the spring as there was room for. +\begin{figure}[htbp]\index{Bell-hanging!for clocks} +\centering +\caption{\sc Hammer Over Bell} +\includegraphics[width=\textwidth]{images/fig44.png} +\label{fig44} +\end{figure} +%-----File: 228.png-------------------------------------------- +%-----Folio: 213----------------------------------------------- +The spring is sometimes made adjustable, by having long +holes for the screws to go through, so that you can bring it +farther from or nearer to the bell as may be required in +course of time. India-rubber buffers\index{Buffers for large hammers} under the hammer +shank are better in some positions, and have the advantage +of never breaking, and being easily replaced or altered in +thickness. I used them at Westminster. + +I \markright{MODES OF HAMMER FIXING.}believe it is the fashion on the continent to fix the clock +hammers with their pivots above the bell, when it has not +to swing; and it has the advantage of securing a long +hammer shank, and therefore less angular motion for a given +lift, and moreover the effective weight of the hammer is not +so much lost in the lift as it is in the common position. But +on the other hand, with bells as tall as the foreign ones are, +the hammer shank stands much more vertically than in the +other way, and the rebound from the buffers or check spring +is greater, and a greater lift (obliquely) from the bell is +required to get the same momentum of the hammer; not +that that imposes more work upon the clock. At Westminster +we were obliged to adopt that plan, on account of +the construction of the tower and bell-frame, and there it +had this incidental advantage with regard to the great bell, +that we were enabled to get the hammer tail $\mathrm{T}$ directly over +the end of the lever in the clock, by setting the hammer +frame, or the pivots which carry it, a little out of the +cardinal position relatively to the tower, and so all cranking +was avoided and a vast quantity of friction saved. + +\subsection[Cranks.]{Cranks.}\markboth{CRANKS.}{CRANKS.}\label{subsec:Cranks.}\index{Cranks, different forms of}---Nobody who has not tried it can have any +idea how much of the force of a clock is wasted by having to +lift the hammer through cranks. Where the hammers are +not very heavy, you may sometimes use what I shall call +\textit{couple-levers} (for a reason which any mathematician will +know), of the form in fig.~\ref{fig45}~$a$, instead of a pair of cranks; +but when the hammers are heavy, and the arbor of the lever +has to be long, I find it is impossible to avoid some elastic +%-----File: 229.png-------------------------------------------- +%-----Folio: 214----------------------------------------------- +torsion in it, which wastes quite as much force as the +friction of a pair of cranks, and makes the hammers rise +with a tremble, which checks the force of the clock and +strains everything severely. For the same reason large +cranks should be made with a light connecting bar as in fig.~\ref{fig45}~$b$, +which increases the strength enormously and helps to +keep everything steady. The cranks and lever arms and +hammer shanks and tails should all be long. I know that +in modern towers, which are nearly always built too small +for properly hanging the bells, there is often great difficulty +in getting room for clock hammers and cranks at all; but +wherever there is room, the action will be easier and more +effective if all these arms are made long instead of short. + +\begin{figure}[htbp] +\centering +\caption{\sc Forms of Cranks} +\includegraphics[width=324pt]{images/fig45.png} +\label{fig45} +\end{figure} + +When the clock is above the bells, as in the Leeds town-hall, +and the Royal Exchange, it is a very common mistake +to put a tail to the hammer to pull down first, which of +%-----File: 230.png-------------------------------------------- +%-----Folio: 215----------------------------------------------- +course involves the necessity for another to pull up again. +It ought to be done as I designed it at Leeds (if there is +room) by pulling up at once from a lever set inwards or on +the same side of the arbor as the hammer itself, unless it +happens from some local peculiarities that this would involve +as many cranks as the other way. + +In several of the former editions I gave a design for +catching the hammer at its rebound without any buffer-spring; +but I have never heard of it being tried, and therefore +I do not repeat it, and have modified fig.~\ref{fig44} accordingly +to show a common buffer-spring. + +\subsection[The weight of hammer]{The weight of hammer}\markboth{WEIGHT OF HAMMER.}{WEIGHT OF HAMMER.}\label{subsec:The_weight_of_hammer}\index{Hammers, clock!weight}\ and its lift can only be +determined by experiments. Different thicknesses and qualities +of bells require different hammers. I have generally +found that large bells whose diameter $=12 \times$ the thickness +of the \textit{sound-bow} or thickest part (which is the best +proportion) require hammers of about a $50$th of their weight +to bring out the full tone, and small bells require heavier +ones. The lift has to be less for small bells than for large: +the least that is effective in bells above $3$ or $4$~cwt.\ is $6$~in.\ (measured +obliquely in the direction of the motion), and +beyond $13$~in.\ we did not find any improvement in the sound +of either of the great Westminster bells. Generally they are +a great deal less either in weight or lift, and often in both, +and therefore you hardly ever hear a church bell sound so +loud under the clock striking as in ringing with the clapper. +Thinner bells, as the larger ones of peals usually are, do +not require such heavy hammers as thick ones; but it must +be remembered that no hammer arrangement will get as +good a sound out of a thin bell as a thick one, because it is +radically inferior both in quantity and quality of sound. +But I shall have more to say of that in the chapter on bells +hereafter. I only add a word of warning against a piece of +ignorance by which I remember a very fine old bell being +cracked in a few months---viz.\ making the clock hammer to +%-----File: 231.png-------------------------------------------- +%-----Folio: 216----------------------------------------------- +strike it with a sharp edge instead of a flat or slightly rounded +face, as it ought to be. + + + + +\section{DIALS.}\label{sec:DIALS.} +\index{Construction of dials}\index{Dial work!of large clocks}\index{Dials!of public clocks}\index{Turret clocks!dials}\markboth{DIALS OF PUBLIC CLOCKS.}{DIALS OF PUBLIC CLOCKS.} + +The striking of church clocks, and perhaps of public +clocks in general, is of more value than their dials, except in +places where the public congregate. Indeed dials a good +way above the eye are of no use for indicating the time +very accurately, on account of the parallax which affects the +minute hand, except when it is nearly vertical. Moreover +many church towers would be utterly defaced by dials; +And it is to be hoped that the splendid church of St.~Mary's, +Beverley, now that its fabric has been restored to a condition +worthy of its architecture, will not long retain those +abominable dials in the tower windows, which belong to the +age when the inside of the church was divided into private +boxes, in which people might eat their dinner or play at +cards without their neighbours or the clergyman knowing +anything about it. + +But as dials must frequently be used, architects\index{Architects!their ignorance of requirements} might as +well condescend to learn something of their proper size, as +they profess to provide places for them, as they do for bells, +frequently in utter ignorance of what the provision ought to +be. Luckily there is such a simple rule for determining it +generally, which has now been long published, that they +have no excuse for doing it wrong. That rule is that the +diameter of the dial should not be less than a tenth of the +height of its centre from the ground. If you want to verify +this you have only to look at the dials of the Leeds Town +Hall, planned by an architect with the usual knowledge of +such things, $150$~feet high and only $11$ wide; and those of +the Bradford Town Hall\index{Bradford Town Hall tower and bells} are no better, but I do not know +the exact height; or that of St.~Pancras Church, $6\frac12$~feet +wide and about $100$~feet above the ground. The neighbouring +%-----File: 232.png-------------------------------------------- +%-----Folio: 217----------------------------------------------- +railway station however has inside it a large dial +$15$~feet wide, at the height of $55$, looking down the +largest space under one roof without pillars in the world, +viz.\ $700$~feet long and $240$ wide (the length of the +transept of St.~Paul's Cathedral, and more than the length +of the nave of any cathedral except Norwich, Winchester, +and St.~Alban's, the longest of them all). The external +dial of that station is rather too small; but that, and some +others which comply with the above rule are given in this +list, which I have compiled from various sources. + +\begin{table}[!hbtp] +\centering\label{largedial}\index{Table!sizes of public dials} +\begin{tabular}{lcrlr} + &\sc Dials. &\multicolumn{2}{c}{\sc Diameter.}&\sc Height.\\ + & &\ \ ft. &in.\ &ft.\\ +Mechlin &1 &40 & &about 300\\ +Westminster &4 &22 &6 &180\\ +St.~Paul's Cathedral &2 &17 & &126\\ +Shandon Church, Cork &4 &16 & &\\ +Pancras Station &4 &12 &9 &150\\ +Scarborough old Church &1 &12 & &on a hill\\ +St.~James's, Piccadilly &4 &10 & &\\ +King's Cross Station &4 &9 & &90\\ +Bow Church &2 &9 & &70\\ +Manchester Infirmary &4 &9 & &80\\ +Royal Exchange &4 &9 & &90\\ +St.~George's Church, Leeds &3 &8 &4 &57\\ +St.~Martin's in the Fields &4 &8 & &\\ +Horse Guards &2 &7 &5 &\\ +Marylebone Church &3 &7 & &about 60\\ +St.~Luke's, Chelsea &4 &6 &10 &72\\ +The Queen's Stables &6 &10 & &about 50 +\end{tabular} +\end{table} + +But if dials are sometimes too small, the opposite mistake +is often made, of figures\index{Dials!figures of}\index{Figures on dials useless, and proper size of}\markboth{SIZE OF FIGURES.}{SIZE OF FIGURES.} much too large, which is not a +compensation but an aggravation of the evil, for they practically +contract the size of the dial, in two ways; first by +%-----File: 233.png-------------------------------------------- +%-----Folio: 218----------------------------------------------- +contracting the plain surface in the middle, over which the +hands are most distinctly seen; and secondly, the larger +the figures are, the more they run into each other and fill +up the space of the figure ring itself, and make it still more +difficult to distinguish the place of the minute hand. Ignorant +people fancy that you see what o'clock it is by reading +the figures; as if any single figure which you see in a clock +dial indicated the figure which you read off; except for the +hour hand, and the hour also is at once recognized by the +position of the hand. You see the long hand pointing to +VIII, and you say, `$20$~minutes to something.' Both for +the hours and the minutes everybody really judges from +the position of the hands, and $12$ large spots would do +as well or better than figures. I have several clocks without +any figures at all round the principal dial, only $12$ strong +marks; and I never found anybody who even observed the +fact that the figures were absent until it was pointed out +to him, or complained of the want of them then. I came to +the conclusion after various trials, that the figures and +minutes together ought not to occupy above one third of +the radius of the dial; the figures may be two thirds of that +one third; and the minutes from half to two thirds of the +remaining one ninth of the radius, with every fifth minute +strongly marked by a larger spot than the others. The +Westminster\index{Dials!of the Westminster clock} dials might have been clearer, considering their +great size. They are not of my design, except that I gave +the architect some suggestions for them, which are partly +followed and partly not followed. They are unnecessarily +confused with iron frame-work, and the clear space is unduly +contracted by some broad rings supposed to be ornamental. +The Midland Station dials are much better. + +The only colours\index{Dials!colour and materials for|(} that seem to answer for dials and hands +are black or dark blue with gilt figures and hands, or some +very light coloured ground, such as white glass, with black +hands and figures. Good gilding will last fifteen or sixteen +%-----File: 234.png-------------------------------------------- +%-----Folio: 219----------------------------------------------- +years, as at the Royal Exchange, in the worst London +atmosphere: bad gilding of course wants renewing much +oftener, and is probably the dearest. Gilt hands on a +light ground are a complete failure. The external counterpoises, +if there are any, should be painted the same colour +as the ground of the dial, except where they are very short +in proportion to the hands, as at Westminster, in which +case they cannot be mistaken at any distance for the hands +themselves, and practically increase their visible length. + +Dials\index{Construction of dials}\label{dialmat}\markboth{CONSTRUCTION OF DIALS.}{CONSTRUCTION OF DIALS.} may be made of almost anything---stone, slate, +plaster, brick, iron, copper, and many old ones are of wood, +which however is the worst of all, as it always shows the +joints. In many cases the stone of the tower makes the +best dial. Generally it requires painting; but if it is such a +stone and in such a position that it will keep nearly white, it +will do very well with only the black figures and minutes +painted on it, and black hands, but by no means gilt ones. +Dials on brick work must of course be painted. It is quite +a mistake to suppose that a dial requires a very smooth +surface. Some of the most distinct I have ever seen are +painted on rather rough stone work; and brick will do as +well, either all flat, or with the figure circle a raised ring of +iron, or of any plaster that will stand. There are many +dials of cast iron; but I should never make more than the +figure ring of iron, unless there is a large hole in the wall +which wants covering; and even then it is generally better +to fill it with glass, which has all the effect of a dark ground +outside and is often convenient within. Slate makes a good +dial, but if it is not painted it becomes a pale grey colour. +I believe $6$~feet diameter is the largest size that can be got +in one piece, but the joints are almost invisible if well done. + +Copper\index{Dials!colour and materials for|)} dials are the commonest of all, and up to a +moderate size, probably the cheapest, except of course +when the dial is simply painted on the wall. But they are +generally made in the very worst form that could be +%-----File: 235.png-------------------------------------------- +%-----Folio: 220----------------------------------------------- +invented, viz., convex:\index{Dials!convex and concave} the effect of which is that the point +of the minute hand is thrown a long way off the dial, and +the parallax is so great that you cannot tell what it is +pointing at, except when it is nearly vertical, when seen +from below, as a public dial always is. One way to avoid +this is to countersink the middle, in which the short hand +travels, leaving the long hand to lie close to the raised figure +ring. I have lately seen some dials made of mosaic work, +like pavements, by Messrs.~Rust, of 16, Albert Embankment, +which look very well, and the price was not more than of +copper dials; and they can easily be made concave. + +\subsection[Concave dials.]{Concave dials.}\markboth{CONVEX AND CONCAVE DIALS.}{CONVEX AND CONCAVE DIALS.}\label{subsec:Concave_dials.}\index{Beckett, Sir E.!concave dials}\index{Concave dials for large clocks}---It occurred to me some years ago that +all the convenience of the light copper dials might be got, +with even more closeness of pointing than in a flat one, and +with as much stiffness as the convexity gives, and with less +distortion of appearance, simply by making them concave +instead of convex. If you draw a vertical section of a +convex and a concave dial, and three lines of sight, from the +top, the bottom, and the middle of each, to a spectator in +the street, you will see at once that the convexity makes the +upper half appear much smaller than the lower, whereas in +the concave one the two halves appear even more alike in +size than in a flat dial; and the closeness of the hand pointing +is evident. There are now a good many of such dials, and +no one who has seen them can fail to perceive their superiority +to convex ones. + +\subsection[Hands.]{Hands.}\markboth{CONSTRUCTION OF HANDS.}{CONSTRUCTION OF HANDS.}\label{subsec:Hands.}\index{Dials!hands of}\index{Hands of clocks and watches!for large clocks}---Large clock hands are so universally made of +copper that it is hardly worth while to notice any other +construction.\index{Hands of clocks and watches!proper construction and fixing}\index{Turret clocks!regulating and setting the hands} There is indeed---or was, a notable exception, +in Sir C.~Barry's famous gun-metal hands at Westminster\index{Barry, Sir C.!his Westminster clock hands}, +which is not likely to be repeated. The hands of the clock +at old Doncaster church, which perished in the fire of 1853, +were of mahogany, and stood very well; but I should think +copper ones are lighter, even including the stalk or centre +piece. Where they are very large, say $5$ or $6$~feet long, the +%-----File: 236.png-------------------------------------------- +%-----Folio: 221----------------------------------------------- +best form for them is that of the minute hands at Westminster, +viz.\ a tube of thin copper, whose section is two +segments of a circle, with a few diaphragms at intervals of +about $2$~feet to keep them stiff. The strength of this +construction is enormous, and it is also good for throwing off +snow, which sometimes accumulates on hands with broad +edges heavily enough to stop the clock. Smaller hands +may be made quite strong enough with a convex front and a +flat back, the section being an arc and its chord, or even as +a single flat piece of copper with the edges turned over +square. A mere rib or hollow bead raised along the middle +of a hand makes it strong enough for all ordinary sizes, but +it does not look well. `Galvanised' sheet-iron hands +have been tried, but the zinc peels off, and they must +be pronounced a failure. The minute hand should always +be straight, and plain, with a bluntish point. At the +broadest part, or near the dial centre, it should be about +a $13$th of its length, tapering to about half as much near +the point. The hour hand should be the same breadth, +ending just short of the figures in a broad piece called a +heart, of any shape you like. + +There should always be some external counterpoises\index{Counterpoises for clock hands}\index{Hands of clocks and watches!counterpoises}\index{Turret clocks!counterpoises for the hands} to +large hands, both for wind and weight. They should not be +above $\frac13$ the length of the long hand, and should be broad, +but of a shape not to be confounded with the heart of the +hour hand. The advantage of counterpoising the hands to +some extent for the action of the wind is evident; and the +other use of an external counterpoise is to diminish the tendency +of the hand either to twist the arbor, or what is more +likely, to work itself loose and shake over from one side to +the other every time it passes the vertical, as Reid says the old +hand of St.~Paul's cathedral used to do, and as Sir C.~Barry's +heavy hands\index{Barry, Sir C.!his Westminster clock hands} did at Westminster to such an extent as to stop +the clock. The only way to prevent this shake is to fit the +hands on a tapered square or hexagon at the end of the +%-----File: 237.png-------------------------------------------- +%-----Folio: 222----------------------------------------------- +arbor, and not a prismatic one. The latter may be called +engineers' fitting, and is perfectly right for many purposes +but perfectly wrong for this, for which the old clockmaker's +taper fitting alone will answer. It is found better not to +put the whole counterpoise for very long hands outside: +from one third to one half is quite enough, leaving the +remainder to be done by adjustable counterpoises inside, +which should be long rather than short, as they then do +the same work with less weight and friction on the arbor. + +\subsection[Illuminated dials.]{Illuminated dials.}\markboth{ILLUMINATED DIALS.}{ILLUMINATED DIALS.}\label{subsec:Illuminated_dials.}\index{Dials!illuminated}\index{Illuminated dials}\index{Turret clocks!dials!illumination of}---Occasionally it is possible, as at +the Horse-Guards east dial, to illuminate a common white +dial by reflection from a lamp on a roof projecting below it. +This answers well enough for dials to be seen a short +distance only, in the few cases where it can be done. Where +it cannot, the common way is to make the dial of glass, or +all of it except the figures and the rings to connect them +which form a solid framework of cast iron. The glass is +ground behind, or painted, or covered with muslin stuck to +it, and gas lamps are put behind it. But all these things +have such a bad appearance by day that the advantage of +illumination is dearly purchased at that cost. Now however +a white glass is made by Messrs.~Chance\index{Chance's glass for dials} of Birmingham, +and perhaps by other makers, which forms a very good +and always clean white dial by day (if left open for the rain +to wash its face) and a bright one by night: the hands and +figures must be black as with other white dials. It should +be $3$-$16$ths of an inch thick, or $22$~oz.\ to the square foot; +the middle of large dials has to be in two or three pieces, +which must be divided by bars not radial, or they will +look like hands at night; and all but the figures and minutes +should be gilt. + +The gas \label{gas}lamps of illuminated dials are generally kept +alight all day, turned down as low as they can be without +going out. They are usually tamed down in the morning +and up at night by a $24$~hour wheel in the clock, which has +%-----File: 238.png-------------------------------------------- +%-----Folio: 223----------------------------------------------- +pins screwed into its rim and taken out again from time to +time by the man who takes care of the clock. So long as +any of the pins are in the position to hold up a weighted +lever connected with the gas cock, it is turned down, and +when the lever drops off it is turned up. In the Westminster +clock three fan-shaped pieces were prepared on a $24$~hour +arbor, which can be opened out to $18$~hours or contracted to +$6$, according to the length of illumination required; but it +was afterwards determined by the authorities to turn the gas +completely off and on by hand. There was a clock in the +Exhibition of 1851 with completely automatic or self-adjusting +machinery for turning gas off and on at the proper time +throughout the year; and Gillett and Bland did the same +in the Bradford Town Hall clock; but the tower is so small +and crowded with bell beams, that they were actually hot +by day, and I advised putting out the gas by day at least. +The machinery puts it quite out now. It cannot be done at +all accurately by any uniform automatic motion, because the +clock times of sunrise and sunset vary irregularly from the +equation of time (p.~\pageref{timetable}), and very slowly near the solstices, +but at other times from $12$ to $15$~minutes a week. + +It is desirable to have a wall, if possible, behind illuminated +dials, instead of having them practically in the clock room; +partly because the wall may be made useful as a reflector, +and so save gas, and also because it protects the clock itself +both from the variations of heat and from the watery +vapour caused by burning the gas. Reflectors are a great +saving of light and of cost. It must be remembered also +that the counterpoises of the hands on glass dials must +neither be long ones outside, nor immediately behind the +glass inside, or they will cast a shadow and be confounded +with the hands at night. There should always be ventilation +over illuminated dials. + +\subsection[Dial wheels.]{Dial wheels.}\markboth{DIAL WHEELS.}{DIAL WHEELS.}\label{subsec:Dial_wheels.}\index{Dial wheels}\index{Wheels, numbers of teeth!for dials}---The construction of the dial-work of large +clocks differs very little from that of small ones. The principal +%-----File: 239.png-------------------------------------------- +%-----Folio: 224----------------------------------------------- +difference is that the numbers of the wheel teeth are differently +distributed. Instead of two equal $60$~min.\ wheels, there is a +pinion on the minute-hand arbor which drives a wheel corresponding +to the wheel $\mathrm{N}$ in pp.~\pageref{fig25}, \pageref{fig34}, \pageref{fig35}, only moving +slower; and that wheel has a pinion on its arbor which drives +the hour-hand wheel as in house clocks. If $t t_1$ are the numbers +of the wheels and $p p_1$ of the pinions, they have only to +satisfy this condition, $\frac{t t_1}{p p_1}=12$, bearing in mind also that, +from their position, the radius of one wheel must be as much +less than of the other as that of its pinion is greater. The +larger wheel is generally put on the hour-hand arbor. The +most convenient numbers are $90$ and $100$ for the wheels, +and $25$, $30$, for the pinions, or in smaller clocks $72$, $80$, +and $20$, $24$. + +The bevelled wheels leading from the clock to the dials +ought to be of a good size, not less than $5$~inches wide in +small clocks, and $7$ to $9$~inches in large ones. They need +not be very strong, as they have only to move the hands; +but the advantage of their being large is that any given +amount of shake in the teeth allows less angular motion of +the hands. In the old way of fixing clocks on a stool in the +middle of the room, which I have already shown to be the +worst, there was generally a vertical rod from the clock +running up the middle of the room, with $2$ horizontal +bevelled wheels, one on the bottom worked by the clock, +and the other at the top working $4$ others leading to each +dial; and in that case it is necessary that the bevelled +wheels on the vertical rod should be larger than all the +others, both the first one in the clock, and the others leading +off to the dials; otherwise the $4$ leading-off wheels will take +into each other as well as into the horizontal wheel. Where +the vertical rod does not lead into the middle of the room +this does not occur, but there must then be two nests of +$3$ wheels each, if there are $4$ dials, besides the two wheels in +%-----File: 240.png------------------------------------------ +%-----Folio: 225--------------------------------------------- +the clock. I have seen several more wheels added, through +a singular piece of ignorance that it is not the least necessary +that the rod which leads upwards should be vertical. I was +rather glad that it was necessary to put it very \markboth{OBLIQUE LEADING OFF.}{OBLIQUE LEADING OFF.}oblique in +the Westminster clock as an example of such treatment (see +frontispiece). With bevelled wheels of the common shape, +intended to lie at right angles to each other, the rod must +be in a vertical plane parallel to the clock wheels, but there +can seldom be any difficulty in that: if there should be, +the bevelled wheels have only to be made for the proper +angle. + +Even in such a clock as that of the Royal Exchange\index{Exchange, Royal!clock}, +undoubtedly the best that had been made up to that time, +the odd mistake was committed of supposing that nests of +bevelled wheels could not be connected obliquely. When I +remodelled the clock in 1854, I removed all the intermediate +bevelled wheels, and connected the central nest of them with +the one in the clock by an oblique rod, like that of Westminster. +When there is only a small parallel displacement +it is managed by a loose cross riding with sufficient play +endways in the sockets of two half universal\index{Universal joints} joints on the +rods. Where the rods are too much out of the straight line +for that, a short oblique rod is interposed with common +universal joints at each junction, and these will do well +enough where the obliquity is not very great, provided +always the oblique rod lies between two parallel ones; otherwise +the velocity is not uniform. But where the obliquity +is great, rigid rods with the bevelled wheels on them are +better, for the wheels may be at any angle. Nevertheless +universal, or half universal joints, are properly used +wherever a rod is either too long to do without several +supports, or where there is any risk of there being an +unequal strain upon it in one direction, or where bevelled +wheels can be saved by a jointed rod with very slight +deviation from straightness. Turret clocks are generally made +%-----File: 241.png-------------------------------------------- +%-----Folio: 226----------------------------------------------- +with the minute-hand on the internal dial turning the wrong +way round, to provide for the case of the external dial arbor +being able to go straight through the wall from the back of +the clock, as it does when the clock can be placed immediately +behind a single external dial. + +I have lately seen a new kind of \markboth{UNIVERSAL JOINTS.}{UNIVERSAL JOINTS.}universal joint, almost +ridiculously simple, in an universal or any-way-pointing drill, +called Morrison's\index{Morrison's universal joint}\index{Universal joints!new American}, from America. If you take a common spiral +wire bell-spring and twirl one end of it while you hold it bent at +any angle, the other end will twirl uniformly; which is not +the case with very oblique universal joints. This kind of +connection might often be used with advantage in leading off, +and with less loss of force than from the friction of bevelled +wheels, though of course there is some slight loss of force in +continually bending the spring. The spring must be strong +enough not to let the wind move the hands. + +\begin{figure}[htbp] +\centering +\caption{\sc Universal Joints} +\includegraphics[width=0.5\textwidth]{images/fig46.png} +\label{fig46} +\end{figure} + +Sometimes the clock has to be placed a long way below +the dials, $30$ or $40$~feet or more, and then it is necessary to +provide both for the weight and +the want of stiffness of such a +long leading-off rod; and this +is best done by a pair of friction +plates and rollers at the +top. The lower plate is set +on the beams which carry the +nests of bevelled wheels or +\textit{motion work:} on that lie three +small flat cheese-shaped rollers +on a horizontal tripod, with a +hole in it for the long rod to +go through quite loosely; and the other plate is fixed to the +top of the rod, which is in fact hung by it, the rollers carrying +the weight, and with no sensible friction on their own +centres, for the three-legged pivots have no weight upon +them. This kind of suspension is also used for heavy +%-----File: 242.png------------------------------------------ +%-----Folio: 227--------------------------------------------- +weathercocks which work a wind-dial inside the house, and +the ease with which a very heavy weight can be turned in +that way is surprising. + +\subsection[Weathercocks.]{Weathercocks.}\markboth{WEATHERCOCKS.}{WEATHERCOCKS.}\label{subsec:Weathercocks.}\index{Weathercocks}---As these are generally fixed by clockmakers +in such cases as those last mentioned, I may as well +mention that a weathercock which is intended to answer +steadily to the wind, ought not only to be long in the vane +and thin in the tail, but equipoised; and so far from the vane +being perforated for ornament, it should be double, with the +two flat sides or vanes spreading out at a small angle from +the axis. When the cock works a dial it must be fixed to a +rod working loosely in a tube, and the top of the tube covered +with an inverted funnel on the rod; as also the rods or wires +which work the clock-hammers should be funnelled, over a +short pipe soldered to the leads, wherever they are exposed +to rain: otherwise the wires lead down the wet into the +clock. And the weights and ropes should be enclosed in a +case to keep them from the rain and wind, if they are in an +exposed place. (See also p.~\pageref{weathercocks}.) + +\subsection[Ventilation of clock-room.]{Ventilation of clock-room.}\markboth{VENTILATION OF CLOCK-ROOM.}{VENTILATION OF CLOCK-ROOM.}\label{subsec:Ventilation_of_clock-room.}\index{Clock-room, ventilation of}\index{Ventilation of clock-rooms}---The clock-room at the +Exchange was at first made with the object of keeping out +the dust and damp in every possible way: even the slits in +the floor for the ropes had sliders to them; the clock was +enclosed in a glass case, the plate-glass cover originally +placed over the escapement being found not enough to keep +it from the damp. When the clock was repaired, and some +of the brass-work replaced with iron in 1854 (for a reason +which I shall mention hereafter), I suggested the removal of +all this glass, and encouraging instead of preventing a draught +through the room. This was done; and although the wet +used to stand in drops upon the clock before in damp weather, +it has been perfectly dry ever since. The same thing has +been found in small clock-cases: they may easily be too air-tight. +I do not mean that there is any objection to enclosing +a clock in a case, and of course it is absolutely necessary +%-----File: 243.png------------------------------------------ +%-----Folio: 228--------------------------------------------- +where the clock-room cannot be kept locked against everybody +but the man who has the care of it; only there should +be a draught through the room, and the case itself not too +close to let air through it. If the room can be kept warm +enough to prevent the damp from condensing on the clock it +is better still. +\section{TRAIN REMONTOIRES.}\label{sec:TRAIN_REMONTOIRES.}\index{Remontoire!train}\index{Train remontoires}\markboth{TRAIN REMONTOIRES.}{TRAIN REMONTOIRES.} + +I have postponed this branch of the subject till I had gone +through all the more ordinary work of turret clocks. A train +remontoire differs in principle from a remontoire escapement +(of which I have already treated) only to this extent: the +small weight or spring which gives the impulse to the pendulum +is not wound up at every beat, but at some longer +intervals, seldom more than half a minute; or the remontoire +work, you may say, is put one step farther back, acting on +the scapewheel instead of on the pendulum. So that if a train +remontoire of constant force and friction is made to act on a +dead scapewheel, the only variation of force to which the +pendulum is subject will be that arising from the pallet +friction. In small clocks the variations of the pallet friction +are generally much greater than of the train friction, and +therefore a remontoire would be of little or no use; but in +large clocks with heavy wheels and large hands to drive, the +contrary is the case; and there accordingly, either a train remontoire +or a remontoire escapement is of great use, provided +they really do what they profess---which many of them do +not. + +The simplest form of train remontoire acting by a weight +is that described in \index{Reid on train remontoires|(}\index{Train remontoires!Reid's}Reid's book, on the endless chain principle, +which I have already described for a going barrel at p.~\pageref{endless}. +The scapewheel is not driven by the clock train, but it has a +spiked pulley on it which carries one loop of the endless +chain, and the other is carried by a similar pulley on an arbor +%-----File: 244.png-------------------------------------------- +%-----Folio: 229----------------------------------------------- +driven by the train and turning in the same time as the scapewheel. +This remontoire arbor has a few long spikes sticking +out from it, at different distances along the arbor, and they +are just long enough to reach the middle of the scapewheel +arbor, and can slip past it through a nick cut for the purpose, +whenever that nick comes into the right position, which it +does once in every turn of the scapewheel; then the remontoire +arbor turns and winds up the endless chain a little +until the next spike falls against and is stopped by the scapewheel +arbor, till its nick also presents itself and lets that +spike slip through, as you see in this drawing. + +Nevertheless, that construction is far from satisfying all +the conditions of a remontoire. The action of a chain +cannot be made smooth and uniform, and a rope or string +passing only half round a pulley is sure to slip in time, and +so the remontoire would fail. Moreover, Reid says that +although the Edinburgh clock went very well for a time, yet +it became necessary to remove the remontoire in consequence +of the banging of the spikes against the scapewheel arbor.\index{Reid on train remontoires|)} +That however would be easily cured by a fly; which may +now be considered a necessary element of every remontoire: +for there are several other kinds. + +One is the bevelled wheel\index{Remontoire!bevelled wheel}\index{Train remontoires!bevelled wheel}\markboth{BEVELLED WHEEL REMONTOIRE.}{BEVELLED WHEEL REMONTOIRE.} remontoire, which was used in +many of the French turret clocks in the 1851 Exhibition. I +have already explained the principle of it, so far as the +bevelled wheels are concerned, at p.~\pageref{bev}; but something +more is now required. In fig.~\ref{fig47} (\textit{t.~o.}), consider the dark +disc $\mathrm{FG}$ and the pulleys omitted for the present (we shall +want them presently for something else). $\mathrm{X}$ is part of that +wheel of the clock which would naturally drive the scapewheel +$s$ if there were no remontoire, and if it were fixed to the arbor +of the pinion $t$ which $\mathrm{X}$ does drive. It also drives another +pinion $\mathrm{P}$ on an arbor $\mathrm{PQ}$ which I call the remontoire arbor, +because it carries two long spikes not quite in the same +straight line, or not at right angles to $\mathrm{PQ}$, which can pass +%-----File: 245.png-------------------------------------------- +%-----Folio: 230----------------------------------------------- +\begin{figure}[htbp] +\centering\index{Fly, remontoire} +\caption{\sc Bevelled-wheel Remontoire} +\includegraphics[height=535pt]{images/fig47.png} +\label{fig47} +\end{figure} +%-----File: 246.png-------------------------------------------- +%-----Folio: 231----------------------------------------------- +alternately through two nicks in the scapewheel arbor. When +the arbor is stopped the train and the wheel $\mathrm{T}$ do not move; +but the weight of the middle bevelled wheel $\mathrm{R}$, with any weight +($+$ or $-$) attached to it, always presses down the far side of +wheel $\mathrm{S}$, and of the scapewheel s fixed on the same arbor, +and that force is practically constant. When the scapewheel +arbor lets a remontoire spike pass, the pinion $\mathrm{P}$ turns half +round and lets the train move a little, and lift up the right +side of wheel $\mathrm{R}$, and therefore lift up its centre half as +much, and then the other spike is held by the scapewheel +arbor. The fly may be driven by the wheel $\mathrm{D}$ anywhere, +either on the remontoire arbor or any other. We shall see +another way of driving it presently. + +\subsection[Continuous motion remontoire.]{Continuous motion remontoire.}\markboth{CONTINUOUS MOTION REMONTOIRES.}{CONTINUOUS MOTION REMONTOIRES.}\label{subsec:Continuous_motion_remontoire.}\index{Remontoire!continuous motion}\index{Continuous motion clocks}\index{Train remontoires!continuous motion}\index{Wagner's continuous motion remontoire}---In connection with +this I will describe a remontoire exhibited in 1851, by +Messrs.~Wagner, the great turret clock makers of Paris, for +the purpose of getting a continuous motion for telescope-driving +clocks, or clocks to drive a barrel on which times of +observation may be recorded at less intervals than a second, +with all the advantage of a vibrating instead of a revolving +pendulum. The action for the vibrating pendulum which is +driven by the scapewheel $s$ is exactly what I just now +described, except that there is no spike wheel and no sudden +letting off. Instead of that there is a large pulley $p$ on the +arbor of the wheel $\mathrm{T}$ which lifts the remontoire arm $\mathrm{VRW}$\@. +This pulley drives a much smaller one on the arbor of a fly +$\mathrm{FF}$, which runs inside a tin drum without a bottom, which +is hung over it by two wires $\mathrm{WW}$ from the end of the remontoire +arm. The weight of the drum is counterpoised so +as not to let it preponderate too much. The fly is the thing +which regulates the velocity of the clock train, which is +always moving; the farther the drum falls over it and cuts +off the air within from the air outside, the faster the fly will +turn, and vice vers\^{a}; and things are so adjusted that the +continuous motion of the clock train driving the fly will just +%-----File: 247.png----------------------------------------------- +%-----Folio: 232-------------------------------------------------- +keep pace with the average motion of the scapewheel driving +the pendulum by beats as usual. If the clock falls behind +the proper speed the remontoire wheel and its drum falls a +little and lets the fly go quicker, and if too fast it rises and +the velocity of the fly is checked. The one in the Exhibition +seemed to go very steadily; and as there is nothing in all +this at all difficult to make, I am surprised that more complicated +contrivances should be used for such purposes as I +have mentioned. + +Mr.~De~la~Rue\index{De~la~Rue's telescope-driving clocks}\index{Telescope-driving clocks!Cooke's, Bond's, and De la Rue's}\markboth{FOR DRIVING TELESCOPES.}{FOR DRIVING TELESCOPES.} and Mr.~Cooke\index{Cooke!his telescope-driving clock}\label{telescope} appear to have hit simultaneously +on the following plan for a telescope-driving +clock, which retains the advantage of a vibrating pendulum, +and may have a gravity escapement also. In the figure at +p.~\pageref{fig47} suppose the two opposite bevelled wheels to be respectively +fixed on the `centre arbors' of two clock trains, +the left hand one ending in a vibrating pendulum, and the +right in a conical pendulum or a fly. And let the arbor of +the intermediate wheel (omitting all the wind apparatus +$FGF$) be held by a spring instead of the constant weight +$\mathrm{C}$\@. At every beat of the pendulum the left hand train will +stop for a moment, but the fly-wheel train, of which the +barrel is to drive the telescope, will go on by its own +momentum, and because the spring allows the intermediate +wheel, and therefore the right hand wheel and its train, to +move a little. If that train is inclined to go too fast, the +spring will diminish the force upon it; and if too slow, will +increase it. Of course the weight and fly are to be adjusted +so as to make that train go naturally as nearly as possible +with the other. + +A still simpler telescope-driver was invented by Mr.~R.~F.~Bond\index{Bond's telescope-driving clock}, +of Boston, U.S., brother of the well-known Professor +of Astronomy there. As I understand the description, one +arbor of the clock has two wheels on it, one fixed, and the +other connected with it by a spiral spring. The second of +these wheels is either the scapewheel or the one below it, +%-----File: 248.png----------------------------------------------- +%-----Folio: 233-------------------------------------------------- +and the other ultimately drives a fly, which allows the train +to so continuously, the spring equalising the force sufficiently +every beat. Mr.~Cooke said it did not answer, but +Mr.~Bond replied with a testimonial from the late Rev.~W.~R.~Dawes, +F.R.A.S., who had the reputation of being +the best observer of his time, that the `performance was +exquisite; that it kept the thread of the micrometer +dividing a star for nearly an hour together with a magnifying +power of $800$ or $1000$ on, and that no jerk or +interruption was perceptible.' Lord Lindsay, P.R.A.S., +invented another, too complicated to describe here, on the +ground that neither Cooke's nor Bond's clocks would drive a +large telescope fitted with spectroscopic apparatus steadily +enough for that purpose.\footnote{All these contrivances are described in the R.A.S. Notices, +vols.~27 and 33, and \textit{Horological Journal}, of February and +April 1868.} + +The Royal Exchange\index{Dent, E.~J.!Royal Exchange clock}\index{Exchange, Royal!clock} clock was originally made with a +gravity remontoire, though it was afterwards altered. +Instead of bevelled wheels, Mr.~Dent used an \textit{internal} \index{Remontoire!internal wheel}\index{Train remontoires!internal wheel}\markboth{INTERNAL WHEEL REMONTOIRE.}{INTERNAL WHEEL REMONTOIRE.}wheel, +\textit{i.e.}\ one with teeth on the inside of the rim, instead of the +outside. That wheel $\mathrm{D}$ (fig.~\ref{fig48}, \textit{t.~o.}) had the letting off spikes +on its outside; at least a wheel on the same arbor had, +which is the same thing. It was driven by the centre +wheel of the clock, and whenever it moved it lifted the +remontoire arm and weight by means of the small wheel $\mathrm{B}$ +lying between the internal teeth and the wheel $\mathrm{C}$ on the +arbor of the wheel $\mathrm{F}$ which drove the scapewheel: that +arbor being of course independent of, though in the same +line with the arbor of the wheel $\mathrm{D}$ and its pinion. The +remontoire was let off at every $20$~seconds; which however +is not so good an interval as $30$, because it is not easy to +distinguish whether the hands are pointing to $10$~seconds +before or $10$~seconds after the half minute; whereas it is +perfectly easy to see whether they are pointing to a minute +%-----File: 249.png----------------------------------------------- +%-----Folio: 234-------------------------------------------------- +or a half-minute, if the dial is properly made, as I have +already described. This facility for taking the exact time +from the dial by the jump of the hands is one of the advantages +of a train remontoire, where the momentum of the +hands is not too great. + +\begin{figure}[htbp] +\centering +\caption{\sc Royal Exchange Remontoire} +\includegraphics[width=\textwidth]{images/fig48.png} +\label{fig48} +\end{figure} + +There \markboth{SIMPLEST TRAIN REMONTOIRE.}{SIMPLEST TRAIN REMONTOIRE.}is yet another way of making a train remontoire +without either bevelled or internal wheels. In fig.~\ref{fig49} (next +page) $\mathrm{E}$ is the scapewheel, and $e$ its pinion driven by the +remontoire wheel $\mathrm{D}$ which rides with its pinion $d$ fixed to it +on a stud in the remontoire lever AP\@. The centre wheel $\mathrm{C}$ +drives that pinion and a smaller one $g$ on a wheel which +drives another pinion $f$ on the fly arbor, which has also the +remontoire spikes $\mathrm{AB}$ attached to it. The numbers of the +teeth are so arranged that the fly will turn once for each +turn of the scapewheel, and the scapewheel arbor has only +%-----File: 250.png----------------------------------------------- +%-----Folio: 235-------------------------------------------------- +two notches in it, so as to let off one remontoire spike every +seconds. It is evident that the scapewheel is always +\begin{sidewaysfigure}[p] +\centering +\caption{\sc Simplest Train Remontoire}\label{fig49} +\includegraphics[width=\textwidth]{images/fig49.png} +\end{sidewaysfigure} +%-----File: 251.png-------------------------------------------- +%-----Folio: 236----------------------------------------------- +driven by the remontoire wheels and weight, and not affected +by the clock train. There were several French clocks of +this construction in the Exhibition of 1851, but they all +had the fly driven by an endless screw, which is objectionable +because it involves an immense amount of friction +and the motion of the train was so slow that you could +hardly distinguish the jump of the hands. + +\subsection[Spring Remontoire.]{Spring Remontoire.}\markboth{SPRING REMONTOIRE.}{SPRING REMONTOIRE.}\label{subsec:Spring_Remontoire.}\index{Remontoire!spring}\index{Spring!remontoires}\index{Train remontoires!spring}---But it must be observed that all +these gravity remontoires are still subject to the friction of +the remontoire wheels themselves, which is not inconsiderable, +although it is much less, and less variable, than +that of the clock train and hands. To avoid this, it was +long ago attempted to contrive a spiral spring remontoire +which would drive the scapewheel without any sensible +friction. One of these is described in Reid's article in the +seventh edition of the \textit{Encyclop\ae dia Britannica}; and another +was invented by Sir G.~Airy\index{Airy, Sir G.~B.!spring remontoire},\footnote{See \textit{Horological Journal}, xvii.~22.} and two or three specimens +of it were made by old Mr.~Dent. They all went on the +plan of connecting two wheels, or a wheel and pinion, on the +same arbor by a spiral spring, one being fixed to the arbor +and the other riding upon it; and the consequence was that +the scapewheel was always subject to the friction of the +other wheel set upon its arbor and pressed tight upon it by +the action of the spring, which was probably worse than the +ordinary friction of the train; and they were all failures. + +This difficulty however may be got over by a very simple +contrivance which I\index{Beckett, Sir E.!spring remontoire} invented in 1849, and which was used +in several large clocks, and would have been in many more +but for its having been superseded by the cheaper and +simpler gravity escapement already described (p.~\pageref{subsec:Sir_E.Beckett's_Gravity_Escapements.} to +\pageref{gravend}). In fig.~\ref{fig50} (next page) $\mathrm{E}$ is the scapewheel and $e$ its +pinion, not fixed to the arbor of $\mathrm{E}$ nor riding upon it, but +upon an independent stud $k$ screwed to the clock frame. In +front of the pinion a small bush is pinned on to the same +%-----File: 252.png-------------------------------------------- +%-----Folio: 237----------------------------------------------- +stud which carries the pivot of the scapewheel arbor, on +which is set a large watch spring $s$, of which the outer end +is held by a pin $h$ screwed into a small plate fixed to the +\begin{figure}[hbtp] +\centering\index{Fly, remontoire} +\caption{\sc Sir E.~Beckett's Spring Remontoire} +\includegraphics[height=535pt]{images/fig50.png}\index{Remontoire!spring}\index{Spring!remontoires}\index{Train remontoires!spring} +\label{fig50} +\end{figure} +%-----File: 253.png-------------------------------------------- +%-----Folio: 238----------------------------------------------- +front of the pinion, so that the pinion acts on the scapewheel +by the intervention of this spring without any friction +except that of the coils of the spring upon each other, +if they touch at all. The wheel $\mathrm{D}$ which drives that pinion +also drives another on the fly arbor $f$. If the scapewheel +turns in a minute, there will be two nicks across its arbor, +as in fig.~\ref{fig47}, for the remontoire spikes or stopping springs +to act upon. But if it turns in two minutes, as the pin +scapewheels generally do, a different plan is adopted: the +scapewheel arbor is then brought through to the front of +the clock frame and has a small steel cylinder set upon +it, with two nicks across its face, not its side, one broad +and shallow and the other deep and narrow; the remontoire +springs set on the two arms of the fly have corresponding +shapes, so that one will pass through the broad +nick only and be stopped by the narrow one, and the other +will pass through the deep nick but be stopped by the +shallow one. The fly in this case makes half a turn for +every quarter turn of the scapewheel, and therefore its +pinion must be only half the size of the scapewheel pinion. +In very large clocks such as the Exchange, in which the +gravity remontoire was replaced\markboth{ALTERATION OF EXCHANGE CLOCK.}{ALTERATION OF EXCHANGE CLOCK.} by a spring one in 1854, +the fly is made separate from the remontoire arms, with +a ratchet and click as usual to let it run on a little by +its own momentum; but in smaller ones it does very well +to put the remontoire spring stops on the fly itself. + +The wheel shown at $\mathrm{F}$ with a kind of detent in it, is for +setting up or letting down the spring with reference to the +remontoire arms, and so increasing or diminishing the force +on the scapewheel. + +This was the construction of old Mr.~Dent's\index{Dent, E.~J.!Exhibition clock} large clock in +the 1851 Exhibition, now at King's Cross\index{King's Cross clock} station, which was +found only $3$~seconds \index{Rate!of 1851 Exhibition Clock}wrong at the closing of the Exhibition, +though it had never been altered during the $24$~weeks it was +there, after its preliminary regulation. I never knew any clock +%-----File: 254.png-------------------------------------------- +%-----Folio: 239----------------------------------------------- +with such a rate as that, and yet it has only a common +unjewelled pin-wheel escapement, and a $1\frac12$~sec.\ zinc and +iron pendulum, and most of the wheels are of cast iron. It +has sometimes gone since for several months together +without any noticeable variation. + +The Exchange\index{Exchange, Royal!clock!alterations of} clock was immensely improved by that +alteration, and made as good as that of the King's Cross +clock in general, but I have no exact record of its rate. +I must confess however, that this kind of remontoire is +not safe to put into clocks left in any common hands, as I +have found by experience that the first time the clock wants +cleaning or repairing---or even without that opportunity---a +stupid workman, or master, makes a point of destroying the +remontoire. I knew one case where it was done as soon as +an ordinary clockmaker got the care of it---and that at +Manchester, the city of machinery. This cannot happen +with a gravity escapement, which is also much cheaper. +The Exchange clock has been altered by Gillett and Bland +to the double three-legged gravity escapement, which is now +the standard one for all large\index{Gravity escapements!best for large clocks} clocks. Therefore it is no +longer necessary to explain further details of the spring +remontoire, as in former editions. + +\subsection[Cast-iron wheels.]{Cast-iron wheels.}\markboth{CAST-IRON WHEELS.}{CAST-IRON WHEELS.}\label{subsec:Cast-iron_wheels.}\index{Cast iron!for clock wheels}\index{Wheels for clocks!cast iron}---The success of the contrivances for +cutting off the variations of force from the pendulum led to +another alteration which helped to reduce the price of large +clocks considerably; and that was the making all the wheels +below the escapement, and all the dial wheels, of cast iron +instead of brass or gunmetal. Mr.~Vulliamy had before +recommended that as a good construction for cheap clocks, +but it had always been thought that they could not be also +good ones on account of the greater friction of the train. +I believe that apprehension was very much exaggerated, even +for clocks of the common construction, provided of course +the escapement is light and well made; but as soon as you +cut off the friction of the train from affecting the escapement +it is obvious that cast-iron wheels are just as good as brass +%-----File: 255.png-------------------------------------------- +%-----Folio: 240----------------------------------------------- +or gun-metal. The clockmakers in general violently denounced +it, probably for no better reason than that it +lowered their prices enormously, the price being now only +\pounds 200 for clocks of greater power and far greater accuracy +than those for which \pounds 500 used to be charged not many +years ago. + +The cast iron wheel controversy came to a head in some +of the Lancashire papers soon after the making of the clock, +from my design, for the Manchester Infirmary; and the +advocates of brass wheels had clearly no case whatever. +Their three points against cast iron were friction, rust, and +liability to break. The friction of the train is absolutely +immaterial with a remontoire, or a gravity escapement, and +no large clock can go with great accuracy without some +such contrivance. The next objection is obvious nonsense, +because all except the acting surfaces are painted, and they +are of course oiled as in all other iron wheel machinery. +The liability to break is a mere question of experience. +Those who condemn them for clocks must be very ignorant +of the extent to which cast iron wheels finer than are ever +used in church clocks are used in every factory in Yorkshire +and Lancashire. I made particular inquiries once as to the +sizes down to which the teeth are cast in iron wheels for +spinning machinery (for that is what I mean by cast iron +wheels), and I found that they are cast with quite sufficient +accuracy with teeth as small as $\frac{1}{10}$~inch thick; which is +smaller than any I have seen used in clocks, because there +is very little saving in cost in using iron wheels so small as +that. The great saving of course is in the large wheels of +the train, and the dial and bevelled wheels, of which a good +many of the same pattern and no very fine pitch are required. + +Before I leave the cast iron wheels I should observe that +they work better with cast iron pinions\index{Cast iron!for steel pinions} than with steel +ones: indeed cast iron and steel seem never to work well +together, at least in no clock-work that I am acquainted +%-----File: 256.png-------------------------------------------- +%-----Folio: 241----------------------------------------------- +with if there is much pressure between them. I have seen +cast iron fly ratchets used with steel clicks, by clockmakers +who would not listen to the proposal of iron wheels and +pinions for any but the commonest clocks, and they had to +be removed, and replaced either by wrought iron or brass +ones. I have seen and heard of brass teeth worn out in +an almost incredibly short time, long before iron teeth in +the same clock showed any signs of wearing. Moreover +few people have any idea how rapidly brass is corroded +and in fact destroyed\label{decay} by such an atmosphere\index{Brass-work destroyed by town atmosphere} as that of +London and other large towns. I have several times seen +the brass tubes which had been used in dial work, and thin +pieces of brass elsewhere, brought back to be replaced with +iron because they had become completely rotten. It was +so at the Royal Exchange in eight years. + +In this respect gun-metal\index{Gun metal!its composition}\markboth{CAST IRON AND GUN-METAL.}{CAST IRON AND GUN-METAL.} is better, which is copper and +tin instead of copper and zinc, but for large wheels\index{Gun metal!for clock wheels} it is no +way superior to iron; and it is generally made too soft. +It is equally absurd to polish iron work, except the acting +surfaces; that rusts even sooner than brass begins to corrode; +in fact very often in a week after the clock is put up. +Then somebody who has the care of it floods it all with oil, +and it is filthy ever after. The only proper rule to lay down +is that \textit{all non-acting surfaces should be painted}\index{Painting!all ironwork of large clocks}. In the +Westminster clock even the small brass wheels in the +escapement are painted like the iron ones. + +The truth is that all this `finishing'\index{Finishing@`Finishing' too much undesirable}\markboth{`FINISHING' AND JOBBING.}{`FINISHING' AND JOBBING.} of non-acting surfaces +is what old Dent used to call `working for fools.' It has +literally no other object (as plenty of clockmakers have +confessed to me) than to make an impression on the `fools' +(in and out of the trade) who go to see a new clock in the +first month after it is put up, and never see or want to see +it again. Such people as these think it a much finer thing to +have a clock look bright for a month and never keep time +within a minute a week---or a day, for what they know---than +%-----File: 257.png-------------------------------------------- +%-----Folio: 242----------------------------------------------- +`to look like a patent mangle,' but keep time within a +second a week. + +I must warn people however against some altogether +cast-iron clocks which got into vogue some years ago by +their extreme cheapness, if they could be called cheap at +any price. I heard constant complaints of them, and had +to subscribe once to help a friend to get rid of one and +substitute another of a proper kind. I shall give presently a +form of specification showing how much of a large clock +may be of cast-iron. + +A few years ago I learnt when it was too late that a +deputation from the corporation of a considerable town had +come to London to negotiate for a first-rate town-hall clock, +and after wandering about for some time they fell into the +hands of `an eminent firm' who boast of sending clocks all +over the world, and engaged to pay them more than would +have bought the best possible clock for one which was +warranted to keep time within $5$~\textit{minutes} (not seconds) +a week; whether it actually does perform that feat I do not +know, but I heard casually of some other of its successes, +which gave hopes of it breaking down altogether. + +Another common cause of bad church clock making is the +inveterate habit of \index{Jobbing in contracts for public clocks}\label{jobbing}jobbing for the benefit of a townsman by +giving the order to a watchmaker who never made a turret +clock in his life, and who immediately goes or writes to one +of the few real makers for the cheapest clock that will serve +his purpose, and probably charges for it as much as the +people could have got a first-rate one for, if they had had a +competition of the best real makers of large clocks, or even +gone to one of them alone. The local watchmaker, by way +of carrying out the fraud completely, generally insists on the +real maker putting, not his own, but the pretender's name +on the clock. If this were merely a question between the +makers who consent to do so, and those who will not, I +should leave them to find their own remedy; but as it +%-----File: 258.png-------------------------------------------- +%-----Folio: 243----------------------------------------------- +affects the general credit of our public clocks, I think it +right to give this warning, though it will probably not be +read by one in a hundred, or attended to by one in a +thousand, of those for whom it is intended. It would be far +better to do the `native talent' job in a straight-forward +way by letting the local watchmakers draw lots for a \textit{bonus} +of \pounds 20, and then advertise for tenders under proper conditions, +such as I suggest below. + +The practice of insisting on clockmakers tendering for +bells, except quite small and common ones, is almost equally +objectionable. Every now and then, one party or the other +has paid dearly for it themselves; for which also I do not +care; but the more material thing is, first that two profits +have to be got out of the transaction without any real +necessity for a middle man, and that there is practically much +less responsibility and control than when you deal directly +with the bell-founder. You might as well insist on the clockmaker +fitting up an observatory with telescopes,\footnote{There was indeed +one clockmaker quite competent to do both, the +late Mr.~Cooke\index{Cooke!clock and telescope maker}, of York; but then he made the telescopes himself, +and was one of the best makers of his time.} or trust a +builder to put in painted windows and the organ in a church. + + + + +\section{SPECIFICATIONS FOR PUBLIC CLOCKS.}\label{sec:SPECIFICATIONS_FOR_PUBLIC_CLOCKS.}\index{Specifications!for public clocks}\index{Turret clocks!specification for}\markboth{SPECIFICATIONS FOR PUBLIC CLOCKS.}{SPECIFICATIONS FOR PUBLIC CLOCKS.} + + +Every now and then I happen to see specifications for +large clocks, either prepared by somebody belonging to the +office which has to order it, or in the form of a tender sent +in by some advertising clockmaker, and I hardly know which +are generally the worst, except that the author of the tender +does know what he is about, and takes care to put in as +many adjectives and as few substantives as he can, and the +author of the specification never does know what he is about. +An elaborate specimen of this kind was shown to me some +years ago, from a Government office, which stipulated among +%-----File: 259.png-------------------------------------------- +%-----Folio: 244----------------------------------------------- +other remarkable things, that the pendulum was `to vibrate +$2$~seconds, but to be as long as the room admitted of.' It +was also to have \textit{convex} copper dials a \textit{quarter} of an inch +thick, and a \textit{dead} escapement; which were three specimens +of the author's practical knowledge of the present state +of science. The specification, though of many pages, did +not contain a single thing, except the probably impossible +pendulum, of the slightest value towards securing +what (I suppose) was wanted, either in the way of time-keeping +or striking. Sometimes the providing of a clock and +bells is entrusted to the architect, by people who are not +aware that modern architects rather boast than are ashamed +of being totally ignorant of every thing of the kind. I have +heard people who ought to know better say, that `the only +way is to throw all the responsibility of everything connected +with the building on the architect,' and utterly puzzled when +I asked them what those fine words meant, or what would +they do if everything turned out wrong, as it generally does +in that case. I will therefore give a specimen of the +specification suitable for a large church clock, though I cannot +adapt it to all possible circumstances; and a much stricter +one is requisite for a general competition than for one +limited to a few makers whose work I know to be of the best +kind. Indeed no specification can secure a good clock from +a bad clockmaker\index{Jobbing in contracts for public clocks}; and it ought not to be necessary to warn +people (but I find it is) that those who blow their own trumpet +loudest in advertisements are very often the least to be trusted, +especially in an article of which most purchasers are quite +incapable of judging, until it is too late. All that a stringent +specification can do is to frighten away bad makers from +tendering at all; and for that purpose the first clause of the +following form is useful in a general competition, provided +is certain to be enforced. +\begin{enumerate} +\item To make and fix a clock with $m$ dials of $n$ feet +diameter, and striking the hours and Westminster quarters, +%-----File: 260.png-------------------------------------------- +%-----Folio: 245----------------------------------------------- +on bells which are or would be the 2nd, 3rd, 4th, 7th, and +tenor of a peal of $8$, the tenor weighing ------. + +\item The dials to be concave and made of copper, or painted +on the wall, if smooth enough, or with the figures and +minutes of cast iron, in rings. If the dials are to be illuminated +they \textit{must} be of cast iron, and should have opal glass +$22$~oz.\ to the foot, except behind the minutes, which may +be $16$~oz.\ to the foot. There must be no straight radiating +pieces of iron in the middle. [Architects should be made to +understand (if possible) that dials intended to be illuminated +must have a clear opening in the wall of the full diameter of +the dial.] + +\item The long hands to have a short external counterpoise, +painted the same colour as the dial, if not illuminated, and +the hands, figures, and minutes to be gilt. If illuminated, +the hands, figures, and minutes to be black, and all the rest +gilt. The long hands to be straight and plain. + +\item The escapement to be the double three-legged gravity, +and care must be taken to leave room for the fly of sufficient +length, and to make the angles such as to run no risk of +tripping, and generally according to this book. + +\item The pendulum to have zinc compensation with iron +rod and tube, and bob not less than $2$~cwt. To beat $1\frac12$ +seconds for a clock with several large dials, but may be $1\frac14$ +for a smaller clock, or if there is no room for a $1\frac12$~second +pendulum. It is to swing $2\frac12^\circ$ from zero, and to have a +block under it in case the spring breaks, and a degree plate. + +\item The clock must lie on stone corbels or iron beams, or +brackets bolted through the wall, and the pendulum cock +either bolted to the wall, or rising from the clock-frame, +which is to be generally on the plan at p.~\pageref{fig40} of this book; +but the great wheel arbors are to be in drop bushes of the +form $d$, at p.~\pageref{fig38}. + +\item There is to be a minute dial, and either one for seconds +or a wheel marked for that purpose, with a fixed index. +%-----File: 261.png-------------------------------------------- +%-----Folio: 246----------------------------------------------- + +\item To have the improved bolt and shutter maintaining +power (p.~\pageref{smallmaintain}) or the Westminster one for a very large clock +The going part to go a little over eight days. + +\item The striking parts\index{Striking part!of turret clocks} to be wound up every one or two days, +except in small clocks [or they will never strike efficiently]. +All the striking to be done by steel-faced cams on the great +wheels. The 4th quarter bell to have two hammers (see +p.~\pageref{2hammer}). In smaller clocks cast-iron cams will do. + +\item The hour striking to be let off independently of the +quarters, and the first blow to be struck exactly at the hour, +the hammer being left on the lift: the other quarters to +begin exactly at $15$, $30$, and $45$~minutes. + +\item \index{Hammers, clock!weight}The hour hammer to be not less than a $60$th of the +weight of the bell, and to be raised not less than $9$~inches; +the quarter hammers to increase in weight upwards from a +$60$th to a $40$th of the weight of their bells, and all the +hammers to be raised enough to bring the full tone out of +the bells: small ones at least $6$~in., and the hour one at least $9$. + +\item There must be either levers or eccentrics to lift the +hammer levers completely off the cams, when the bells are +ringing, if there is a peal. + +\item The small wheels of the going part to be of brass or +hard gun-metal, driving lantern pinions. All the larger wheels +and the pinions driven by them may be of cast iron, and their +being of brass or gun-metal will be considered no reason for +a higher price. All bushes to be brass or gun-metal. The +large pivots to be case-hardened, the smaller ones and their +arbors to be of steel. The pulleys to be large and pivotted +in brass bushes. + +\item The barrels of sheet iron brazed, with iron or steel +wire ropes \textit{not} coated with zinc [which makes them crack], +and the pulleys to be so placed that the ropes do not grind, +or go twice over the barrel. + +\item The flies not to be in front of the clock, and to be long +enough to make the time of striking quite uniform, and slow +%-----File: 262.png-------------------------------------------- +%-----Folio: 247----------------------------------------------- +enough. The fly ratchets to be either squared or keyed on, +and not merely pinned. The ratchets \textit{not} to be of cast iron, +and each to have two clicks. [Many smashes have occurred +for want of attention to these two conditions.] + +\item All the iron-work except acting surfaces to be painted +blue [black is more difficult to see if anything is wrong, and +if not painted iron only gets rusty]. + +\item If the weights go out of sight there must be something +to stop or warn against winding them too far. And +also a large box with $3$~feet deep of small stones, to catch +the weights if they fall; unless they go down to the ground +of the tower, when they can only break flags. + +\item All wheels to take out separately by unscrewing the +bushes; and pulleys to be placed where they can be oiled. + +\item On all points not specified, the clock is to be made +according to the directions of this book, applicable to clocks +of the kind now required. + +\item The clockmaker to provide (or design and superintend) +a strong wooden case for the clock, with glass showing the +minute dial if it is in the belfry, and so arranged that the +striking parts can be wound without opening the case; +unless the clock is in a room always locked up, and protected +from weather. In many places it is necessary to +have a case for the weights, and pulleys at the top, if +exposed in a bell-chamber. + +\item The estimate to state the cost of the clock and dials, +and of the fixing, case, \&c., separately. + +\item \label{degerr}Half the price to be paid on the clock being completed, +to the satisfaction of such person, not objected to for +good reasons assigned by the clockmaker, as the committee +may appoint, and \textit{the other half when it has gone for three +calendar months continuously, without varying more than five +seconds in any week}---tested by the striking of the first blow +of any hour. [This is an ample margin to allow now that we +know from the Westminster and other clocks that they may +%-----File: 263.png-------------------------------------------- +%-----Folio: 248----------------------------------------------- +be made to go without much more than a second a week +variation. Every town now has the means of testing its +clocks by electric telegraph time at the post office, but not +so exactly as it ought to be. And if there is any neighbouring +observatory, or meridian instrument, properly attended +to, that is much better.] +\end{enumerate} + + + + +\section{CONSTRUCTION OF THE WESTMINSTER CLOCK.}\label{sec:CONSTRUCTION_OF_THE_WESTMINSTER_CLOCK.}\index{Westminster clock!construction}\markboth{THE WESTMINSTER CLOCK.}{THE WESTMINSTER CLOCK.} + + +The frontispiece of this book is a front elevation of this +great clock, or so much of it as can be shown in one view +without confusion, for which purpose I have drawn the +wheels and pinions only as circles. As I have inserted the +numbers of the teeth, and the size of all the parts may be +taken from the scale, I shall say no more than that the +frame is $15\frac12$~feet long and $4$~feet $7$~inches wide. The +going part does not occupy above $2$~feet of this width, the +front bushes of the wheels being carried on a separate bar +lying on the two cross pieces of which the ends are shown +in the drawing bolted to the great back and front girders. + +\subsection[Double-barrelled Crab.]{Double-barrelled Crab.}\markboth{DOUBLE-BARRELLED CRAB.}{DOUBLE-BARRELLED CRAB.}\label{subsec:Double-barrelled_Crab.}\index{Crab, double-barrelled}\index{Double-barrelled crab}---The space between the front +of the going part and of the great frame happens to be convenient +for the fall of the ropes from a double-barrelled +crab (fig.~\ref{fig51} next page), which is fixed upon the iron beams +$\mathrm{BB}$ which go across the room from east to west to carry +the `motion work' or nests of bevelled wheels above the +clock, of which the first pair are shown in the drawing. +This crab is the only means of getting anything into the +clock room which is too heavy to be carried by a man +up the stairs. It consists of two small equal barrels, with +four pulley grooves in each, each having an equal wheel +at the end turned by equal pinions on the winding arbor. +The rope passes over the outer halves of the two barrels +$4$ times, one end falling down the clock shaft or well for +the weights while the other rises; and it can either be used +%-----File: 264.png-------------------------------------------- +%-----Folio: 249----------------------------------------------- +\begin{figure}[htbp] +\centering +\caption{\sc Double-barrelled Crab} +\includegraphics[height=535pt]{images/fig51.png} +\label{fig51} +\end{figure} +%-----File: 265.png-------------------------------------------- +%-----Folio: 250----------------------------------------------- +with a single rope, or with pulleys. The \textit{pall} $\mathrm{P}$ is in effect a +silent click to hold the rope when the handle $\mathrm{H}$ is let go; +and it will turn over on the horizontal pillar at the top of the +crab, to act the opposite way when the barrels are worked +the other way. + +The great advantage of it is that it avoids the crowding +and overlaying of a long rope on the barrel, which makes the +work harder at every fresh `overlay,' as it practically increases +the diameter of the barrel; and that becomes so intolerable that +the plan of pulling off the rope by hand after three or four coils +on the barrel has to be resorted to in long lifts; and that +again involves the difficulty of having to slide the coils back +to the beginning of the barrel, holding the rope by the hands +of several men, or by some supplementary machinery, for +very great weights, as was done with Big Ben in 1859. `Great +Paul' was raised on 3~May, 1882, by a double-barrelled crab, +or rather two of them, and pulley blocks besides; with only +this difference, that the ropes were crossed between the +barrels to give greater frictional hold; but that also causes +a considerable friction of the ropes against each other, and is +really unnecessary. A crab like this, not with the ropes +crossed, driven by steam, was used for taking up the ribs of +the great domes of the 1862 Exhibition. I had recommended +it in the 1860 edition for taking up heavy bells,\footnote{The differential pulley with an endless chain in notched grooves is +now largely used for moderately heavy weights, the chain being pulled +by hand as in the old-fashioned $30$-hour clocks; but it will not do for +great weights.} and in the +later editions I suggested a further improvement, shown in +fig.~\ref{fig52} (next page), by putting the pinions right in the middle +between the wheels, and making them all roll on blank `pitch +circles' (see chapter on teeth of wheels), besides having small +teeth cast by the side of the circles. This will take a great +deal of pressure off the barrel pivots, and also off the driving +pivots where it does mischief, and transfer it to the rolling +circles, where it is useful in driving and relieves the teeth, +%-----File: 266.png-------------------------------------------- +%-----Folio: 251----------------------------------------------- +and would almost drive without any. They may consequently +be made much smaller, and the wheels also, and yet +with the same power as a much larger crab of the common +kind; especially if $4$ wheels are used: which also has the +advantage of relieving all the pivots equally. $18$~inch wheels +with $1\frac12$~inch pinions would be strong enough for all ordinary +work of single multiplying crabs. And it is easy to add +another wheel and pinion for larger ones. +\begin{figure}[htbp] +\centering +\caption{\sc Another form of Double-barrelled Crab} +\includegraphics[height=0.7\textheight]{images/fig52.png} +\label{fig52} +\end{figure} +%-----File: 267.png-------------------------------------------- +%-----Folio: 252----------------------------------------------- + +The teeth of the pinions and wheels respectively should be +made as will be explained under `Teeth of Wheels,' the +pinion teeth alone projecting beyond the pitch circle. The +rolling circles must be hard, or they will bruise each other. +The arrangement of the frame also will depend on the work +for which the crab is intended; I only show what affects +its principle. The horrible noise of the common \textit{pall} may +be avoided by putting a wedge-shaped one between any two +of the rolling circles, with a slight spring acting on it, +according to the direction of driving for the time. This will +act as a silent pall as soon as you let go the handle. + +Returning to the clock, the back of the frame is $2$~feet +$5$~inches from the west wall of the room, which is the east +wall of the ventilating chimney or air-shaft of the Houses of +Parliament running all the way up the tower. The room is +$28$~feet by $18$, and the clock lies, as shown in the drawing, +on the north and south walls of the shaft or well for the +weights, which is $174$~feet high, and the floor of the room is +$2\frac12$~feet below the top of two iron plates which cover the +walls and are spread out behind and built in quite through +the wall of the airshaft, so as to prevent any possibility of +endway motion of the clock frame, which is bolted to the +plates. The pendulum cock is a large frame +work cast in one piece and also built in through the wall, +quite independent of the clock frame. The pendulum +chamber is made of sheet iron within the weight shaft, in +order to protect the pendulum from the wind: you can +descend into it by a ladder and a trap-door; which can +seldom be wanted, as there is a degree plate set on the floor +under the clock, which is a little lower than the general floor +of the room, and is covered with a grating lying on the +beams which carry the returned end of the ropes. + +\subsection[Regulation.]{Regulation.}\markboth{REGULATION OF THE CLOCK.}{REGULATION OF THE CLOCK.}\label{subsec:Regulation.}\index{Westminster clock!regulation of the pendulum}---The mode of regulating the pendulum +by small weights has been sufficiently described at p.~\pageref{accelerate}. +Whenever a larger alteration is required, in consequence of +%-----File: 268.png-------------------------------------------- +%-----Folio: 253----------------------------------------------- +thunder-storms or an accidental disturbance of the pendulum, +either stopping the scapewheel or letting it trip one beat by +lifting a pallet alters it $4$~seconds, whereas you cannot put a +dead escapement forward at all, nor stop it without considerable +risk of spoiling a tooth. + +The pendulum weighs altogether very nearly $700$~lbs., of +which the bob is about $4$~cwt. In other respects it has been +already described at p.~\pageref{subsec:Suspension_of_pendulums.}. The spring is a $60$th of an +inch thick and $3$~inches wide, and the free part of it $5$~inches +long. The great pin through the upper chops has nuts on +its ends to adjust it to the exact centre between the pallet +arbors. Those are not shown at page~\pageref{fig09}, because they are +not generally used. The pendulum\index{Pendulum2@Pendulum!of the Westminster clock} cock, and the position +of the floor behind the clock, are so arranged that a tall man +can stand with his head inside the cheeks of the cock so as +to look square at the escapement\index{Gravity escapements!in the Westminster clock}; which is + +\subsection[The double three-legged gravity escapement,]{The double three-legged gravity escapement,}\markboth{THE DOUBLE THREE-LEGGED GRAVITY ESCAPEMENT.}{THE DOUBLE THREE-LEGGED GRAVITY ESCAPEMENT.}\label{subsec:The_double_three-legged_gravity_escapement}\index{Westminster clock!gravity escapement}\ as +shown at p.~\pageref{fig24}. The scapewheel teeth are equidistant +and $6$~inches long; and though the clock has to drive about +a ton and a half of hands and dial-work through all weathers, +the pressure and friction on the stops are so little that I +could find no difference in the weight required to lift the +pallets (by a thread over a small pulley) whether the teeth +were bearing on them or not,---\textit{i.e.}, it was less than the +friction of the pivots and the pulley. The weight required +to lift each pallet through the angle of impulse was an ounce +falling $.9$ of an inch, which is therefore the amount of +impulse received by the pendulum at each beat. In other +words, the daily momentum of clockweight required to drive +the pendulum, or $\mathrm{W}h$ in all the calculations about escapements, +is only about $200$~pound-feet, while $\mathrm{M}l$ is $9100$, a +much smaller proportion than in the finest astronomical +clocks, but yet larger than it was in the three-legged dead +escapement which we had at first (p.~\pageref{subsec:Three-legged_dead_escapement.}), on account of the +loss of force by the impact of the pendulum on the pallets. +%-----File: 269.png-------------------------------------------- +%-----Folio: 254----------------------------------------------- +The fly is $11$~inches long in each vane and nearly $2$~inches +wide: it is set on the arbor by what may be called a silent +ratchet, or a steel-faced roller with stiff springs bearing +endways against it, but obliquely, so that the fly can run +forwards, but not backwards. It is almost impossible to +make the escapement trip by any force you can apply to it +by hand; and it once went for several days without tripping +though the fly had been accidentally left loose. + +\subsection[Maintaining power.]{Maintaining power.}\markboth{MAINTAINING POWER IN WESTMINSTER CLOCK.}{MAINTAINING POWER IN WESTMINSTER CLOCK.}\label{subsec:Maintaining_power.}\index{Maintaining powers of clocks or going barrels!Westminster clock plan}\index{Westminster clock!maintaining power}---The going part of this clock takes +about $20$~minutes to wind up, and therefore none of the +common maintaining powers would do. A bolt and shutter +(see p.~\pageref{subsec:Improved_bolt_and_shutter.}) might indeed have been made to lift higher than +usual and so keep in action longer; but it would have had +to be very heavy, and moreover there was the risk of the +man being interrupted while winding, or stopping to rest, +and so letting it run out of gear or stick fast. Sir G.~Airy +had proposed a modification of his Northumberland telescope +apparatus, which I have already mentioned as having been +used in the Exchange clock; but that is also liable to run +out of gear, and is open to other objections; and so the +following much simpler plan was adopted. The barrel in +any case would require an auxiliary pinion to wind it, taking +into a wheel on the end of the barrel itself, close to the great +wheel; and the only addition is, that the back end of the +winding arbor runs in a loose bar, which hangs obliquely +from the back pivot of the barrel (as shown in the drawing), +and has a click on it which acts upwards in a set of ratchet +teeth cast on the back of the great wheel. When the clock +is going and not winding, these ratchet teeth pass under the +click, just as in Harrison's going ratchet (see p.~\pageref{subsec:Harrison's_going_barrel}); but as +soon as you begin to wind they stop the click and the bar +from rising as it tries to do, and the great wheel itself thus +becomes the fulcrum for the winding up of the barrel, and +so the clock weight is for the time transferred to the great +wheel directly, instead of through the barrel. +%-----File: 270.png-------------------------------------------- +%-----Folio: 255----------------------------------------------- + +The winding arbor fits loosely in both the bushes, because +the back pivot and its bush in the bar gradually move a little +upwards as the great wheel turns, while the front one of +course remains fixed in the clock-frame. When it has +moved as far as it was thought prudent to let it go, a long +tooth on the winding arbor catches against a stop in the +back frame, and the man cannot wind any farther without +turning the handle back a little to allow the bar to drop and +the click to take up another mouthful of the ratchet teeth. +The unusual length of the winding arbor, $4$~feet $2$~inches, +makes this sideway motion insignificant for $10$~minutes +motion of the great wheel: if the frame were narrower it +could still be used, taking care to put the stop so as to +prevent too much oblique action. Very few clocks take as +much as $5$~minutes to wind up the going part. If you take +the trouble to calculate the pressure, you will find that there +is rather more force on the clock in winding than usual; +which however is of no consequence. If the winding pinion +were larger in proportion to the wheel the difference would +be greater; but it might always be equalised by hanging a +weight on the loose bar, just enough to counterpoise the +difference. The winding pinion pulls out of gear with the +wheel in the usual way. + +\subsection[The dials]{The dials}\markboth{DIALS AND HANDS.}{DIALS AND HANDS.}\label{subsec:The_dials}\index{Westminster clock!dials}\ are $22\frac12$~feet in diameter, or very nearly $400$~feet +in area, and are made of cast iron frame work filled with +a very expensive kind of opal glass, which appears to me +no better than some much cheaper glass of the same colour +by Chance of Birmingham, which is used in other clocks. +The dials and the hands together cost no less than \pounds5334, +which is more than the whole cost of the clock and all the +striking work up in the bell chamber. I shall have more to +say of this in the history of the clock. The minute spaces +are a foot square, and the figures $2$~feet long. The dials +would have been clearer, and the hands more visible upon +them, if the framework rings, beyond the minutes and the +%-----File: 271.png-------------------------------------------- +%-----Folio: 256----------------------------------------------- +figures, had been omitted, as they diminish the clear space in +the middle of the dial by about one third of its area. The +dials stand $5$~feet from a whited wall which is the main wall +of the clock room and clock-tower, and in front of which are +the gas lights for illumination. I had provided by request +that the clock should be able to light up and turn down the +gas if required, in the way described at p.~\pageref{gas}, but it was +finally thought better to light them by hand, and I think so +too. There is nothing peculiar in the dial-work except its +size, which may be judged of from the drawing of the clock +and fig.~\ref{fig51} (p.~\pageref{fig51}), and the fact that the minute wheel arbor +is $8$~feet long and $3\frac12$~inches thick; it is of course tubular, +except at the ends. The dial centres are exactly $6$~feet +above the top of the walls, or $180$~feet from the ground. + +\subsection[Hands.]{Hands.}\index{Hands of clocks and watches!of the Westminster clock}\label{whands}\index{Westminster clock!hands}---The minute hands, as made from my design, +after the architect's two successive sets had failed, are thin +copper tubes of a section formed by two segments of circles, +with a few diaphragms soldered in, set on a gun-metal +stalk or central piece, which also forms a partial counterpoise +both for wind and weight outside, there being another +of cast iron inside the clock room, to divide the pressure +between the two ends of the arbor. This copper tube of +each minute hand only weighs about $28$~lbs., though they +are $9\frac12$~in.\ wide near the centre, running off to $5\frac12$ at +the end; the gun-metal stalk of each hand weighs very +nearly $1$~cwt.; but the whole of that weight is near the +centre, and so its moment of inertia at each beat of the +pendulum affects the clock very much less than if the +same weight were distributed all along the hand. It is +remarkable that from the momentum of the hands, and the +general elasticity of the leading off rods, they move continuously, +and with no visible jump as usual. The length of +each hand and its external counterpoise is $14$~feet; and the +total weight of each hand with its external and internal +counterpoises is now within $2$~cwt., whereas Sir C.~Barry's\index{Barry, Sir C.!his Westminster clock hands} +%-----File: 272.png-------------------------------------------- +%-----Folio: 257----------------------------------------------- +$4$~minute hands and counterpoises (of which I shall have to +speak in the history of the clock) weighed a ton and a +quarter. His hour hands are still there; for though very +bad in construction and three times as heavy as they need +be, their motion is so slow that they do not sensibly affect +the clock as the minute hands did, and so they may as well +stay until they become unsafe. One of them cracked and +had to be taken off. The hour hand arbor is a tube $5\frac12$ +inches wide, and lies on large friction rollers both behind +the dial and within the clock room. It was easy enough to +put the clock room end of the minute hand arbor on friction +rollers too, as it of course projects beyond the other; but at +the other end it is managed by setting the pivots of $4$ smaller +rollers in a pair of rings screwed outside the hour hand tube, +and cutting holes in that for the rollers to go through and +reach the minute arbor, so that those rollers move in a $12$ +hour orbit of their own, besides the pair in action for the +time turning on their own pivots. + +\subsection[Quarters.]{Quarters.}\markboth{WESTMINSTER CLOCK.}{QUARTERS.}\label{subsec:Quarters.}\index{Quarter chimes!of Westminster clock}\index{Westminster clock!striking parts}---There is nothing very peculiar in the striking +of the quarters. The position of the levers and cams is +evident from the picture. The wires go up alternately on +opposite sides of the winding-wheel arbor to prevent their +fouling each other; each bell has two hammers because in +that way we get longer cams with less pressure on them, +and on the levers. The hammers are all nearly a $40$th of +the weight of their bells, which I am satisfied is the proper +proportion for bells on this scale of thickness, which is that +of the smaller and thicker bells of church peals, as I shall +explain more fully afterwards. The levers are all $19\frac18$~in.\ long, +and their centre is nearly $36$~in.\ from that of the wheel. +The cams\index{Cams!in the Westminster clock} are of wrought iron with hard steel faces, screwed +onto a cast iron barrel which is bolted to the great wheel, +and they are constructed on the circular section which I +shall describe for cams under the \textit{Teeth of wheels}. Between +the clock and the bell chamber there is another low room in +%-----File: 273.png-------------------------------------------- +%-----Folio: 258----------------------------------------------- +which the cranks are, for leading off from the vertical wires +to the $4$ quarter bells. These wires are in fact wire ropes\index{Ropes, wire!in the Westminster one}: +I had them substituted for the iron rods which were at first +used both in the quarters and the hour striking parts, and +thereby got rid of an amount of concussion and noise in +striking, which sounded as if the clock was shaking to +pieces. Now the action in the clock room is so silent that +you hear nothing except the bells and the passing of the +click which stops the train from running back in winding. + +\subsection[Hour-striking part.]{Hour-striking part.}\markright{HOUR-STRIKING PART.}\label{subsec:Hour-striking_part.}\index{Striking part!of Westminster clock}\index{Westminster clock!striking parts}---The great striking-wheel has $10$ +cams $2\frac12$~in.\ wide cast upon it, and these have steel faces +screwed onto them. The lever has a thick part in the +plane of the cams and a longer and thinner piece lying +behind the wheel and having the hammer rope attached to +it, or rather a short rod with a swivel and nut to take up +the rope. The rope is half an inch thick, the same as is +used for the striking weights, and is about $25$~feet long and +reaches up to the horizontal arm of the great hammer lever, +which projects $5$~ft.\ $4$~in.\ from the pivots, which are forged +as part of the collar in which the great bell hangs (see page~\pageref{fig44}). +The hammer shank is also double, going through $8$ +holes in the cast iron head, which weighs $4$~cwt.\footnote{It did weigh $7$~cwt., but was reduced when the bell became +partially cracked, as related afterwards.} and is +lifted $13$~in.\ from the bell, or about $9$~in.\ vertically. Then +is an iron plate screwed to the hammer shank, which falls +on india-rubber buffers $5$~in.\ thick, carried by a kind of long +stirrup hung from the bell frame. The other hammers are +prevented in the same way from jarring on the bells. The +construction of the bell frame, which is entirely different +from the usual form of frame for swinging bells, made it +impossible to fix the hammers or the buffers in any other +way: not that there is any objection to this, except that it +is more expensive, and the hammer shank is farther from +being horizontal. +%-----File: 274.png-------------------------------------------- +%-----Folio: 259----------------------------------------------- + +The second wheel turns $\frac23$ round for each blow, as I +explained that it might at page~\pageref{twothirds}, and the third wheel and +$4$ turns for each blow. The fly arbors are placed +vertically in order to get room for the flies, which have to +be put near the top of the room. The vanes of the hour fly +are each $2$~ft.\ $4$~in.\ square and extend $3$~ft.\ from the arbor: +the quarter ones are rather larger. To prevent all risk of +accident, the ratchets are not pinned but `squared' on the +arbors under the flies themselves with an octagonal fitting, +and each fly has two clicks. The stops are set on springs +to diminish the blow at stopping, and the striking work is +stopped on the lift, both for accuracy of discharging and for +diminishing the constant strain on the wheels and arbors. +Each striking weight is, or was before the hour hammer was +reduced, nearly a ton and a half; and you may observe +that each of the three parts is so arranged that the weight +hangs between the arbor of the great wheel and the +teeth or cams which have the heavy work to do, so as to +reduce the pressure and friction on the arbors as much as +possible. If this striking part had been made as they often +are, and lifting by pins instead of cams, the weight would +very likely have had to be $3$~tons, or more than a man could +wind up in a day. + +The mode of letting off the hour-striking is peculiar. It +was one of the original conditions, that the first blow of the +hour should always be struck within a second of the real +time; and in order to do this it was not sufficient that the +clock should go far more accurately than usual, but there +must also be the means of making the hammer fall exactly +when the clock reaches the 60th second of the last minute +of the hour. First then it was necessary to leave it on the +lift and nearly ready to fall as soon as the striking part is +discharged; and secondly, to have some more sudden and +precise means of discharging it than the slow motion of a +snail turning in an hour. It was at first intended to do it +%-----File: 275.png-------------------------------------------- +%-----Folio: 260----------------------------------------------- +by the train remontoire described at p.~\pageref{sec:TRAIN_REMONTOIRES.}; but when it +became expedient to abandon this and rely on the improved +gravity escapement which I invented after the clock was +partly made, it became necessary to contrive some other +plan for discharging the striking part with equal \index{Striking clocks!accuracy of discharge}accuracy: +and this is it. $\mathrm{PQ}$ is the ordinary discharging lever lifted +by the snail on the hour arbor, $\mathrm{P}$ being the first stop against +which the arm $\mathrm{EF}$ on the third wheel of the striking train +is stopped when it has done striking.\footnote{This lever, and several others, are omitted in the elevation of the +clock (frontispiece), as they could not be shown without confusion; +and as the snails are all shown, any intelligent reader will understand +where the discharging levers must be: there is an intermediate one +from the quarter snails to the quarter locking lever.} The second or +warning stop $\mathrm{D}$ is not on $\mathrm{PQ}$, but on a short independent +lever $\mathrm{CD}$\@. $\mathrm{BAS}$ is another lever set on pivots $\mathrm{A}$ on the +cross bar of the great frame, and its heavy end $\mathrm{S}$ is lifted +and dropped by a snail on the $15$-minute wheel of the +escapement; when it drops it tips up the second stop lever +$\mathrm{CD}$, not merely by dead weight, but with a blow, which is +\begin{figure}[htbp] +\centering +\caption{\sc Mode of Discharging Exactly} +\includegraphics[width=\textwidth]{images/fig53.png} +\label{fig53} +\end{figure} +%-----File: 276.png-------------------------------------------- +%-----Folio: 261----------------------------------------------- +certain to overcome any friction there can be between the +two stopping pieces. The lever $\mathrm{BAS}$ drops every quarter +of an hour; but it does nothing except when the stopping +piece is resting against the second stop, \textit{i.e.}, when the +clock has given warning for the hour. It is let off at +the 58th second, or the last beat but one of the pendulum +in the hour, and the train just gets far enough into motion +to let the hammer fall as the seconds hand makes its last +jump for the hour, and it acts with the greatest precision. + +This precision in letting off the hour-striking made the +want of it disagreeably apparent in the quarters, which were +at first discharged in the usual way by a snail on the hour +arbor which leads off to the dial work; and we had to put a +larger snail for them on a separate arbor under the escapement +wheels, free from the shake of the hands and dial +work; this answers very well and there is never more than +$2$~seconds difference now in the time of discharging the +quarters. The 1st, 2nd, and 3rd quarters all begin to strike +at those times respectively; but the 4th quarter is let off +about $20$~seconds before the hour so that it may have done +striking before the hour begins at the real time. + +That, by the bye, is an objection to a train remontoire let +off at the usual half-minute intervals, viz., that it makes the +interval between the quarters and the hour disagreeably long, +if the hour is to begin striking exactly at the hour as it should +do. Even $20$~seconds is too long an interval for any but very +large bells. However since the invention of these gravity +escapements train remontoires may be considered extinct, +as they cost much more, and are no better, and are almost +certain to be destroyed, or at least put out of action. + +\subsection[Winding of striking parts.]{Winding of striking parts.}\markright{WINDING OF STRIKING PARTS.}\label{subsec:Winding_of_striking_parts.}\index{Westminster clock!striking parts!winding of}---Each of these takes about +$5$~hours to wind, and requires double multiplying wheels, +which are as to size repetitions of the large wheels and +pinions of the train, with a modification of the shape of +teeth, which will be explained afterwards, because different +%-----File: 277.png----------------------------------------------- +%-----Folio: 262-------------------------------------------------- +shapes are proper for driving and for driven teeth, though +that is very seldom attended to. The striking parts wind +twice a week; for although they might have been made to +go a week, the weight would have had to be twice as +much---and more, on account of the increased friction; and a +man could not have wound up each of them in an ordinary +working day. Moreover the whole work must have been +heavier and larger and had a greater strain upon it. Even +in much smaller clocks than this I always design the striking +parts to go less than a week. I do not believe that there +is a clock in the world that strikes a large bell, say above a +ton weight, \textit{properly}, with winding once a week; unless it +happens to have an unusually large fall for the weights. + +There were various \index{Westminster clock!striking parts!curious suggestions for winding}suggestions made both publicly and +privately for winding the clock by water, by a steam engine, +and even by a kind of weighbridge or sinking platform to be +worked involuntarily by people walking over Westminster +bridge, which would have to rise between every two walkers +to do any good: a turnstile would have been a much more +practicable thing. I forget whether anybody proposed to +turn the tide to account for the purpose, but I daresay they +did. It never occurred to these inventors that the interest +on the cost of construction and the expense of looking after +any such machine would far exceed the wages of two +winding men for five or six hours twice a week. + +In most large clocks the winding pinion simply `pumps' +out of gear with the winding wheel on the front end of the +barrel, and it does not much signify if it is left in, as the +friction caused by it is not much. But this would not +do for a pair of large wheels, and there was not room to +make the great winding pinion pump out of gear. Moreover +it was absolutely necessary to have some contrivance for +automatically stopping\index{Winding stops!for clocks} the winder a little before every +striking of the part he is winding; which occurs in no other +clock, as none takes anything like a quarter of an hour to +%-----File: 278.png--------------------------------------------- +%-----Folio: 263------------------------------------------------ +wind either part, and if it did you need only slip off the +handle. That is managed thus. In each striking part a +long lever (omitted in the frontispiece to avoid confusion) +stands in the way of a tooth or arm on the winding arbor: +when the man begins to wind he must lift this lever up on +to a certain hook which will hold it up so long as the weight +of the lever rests upon it; but when the weight is relieved +the hook falls back: this is done by the snail a few minutes +before the clock is going to strike, and just a minute before +it strikes the snail lets the lever drop again, and the hook +being then out of the way, it drops completely and \index{Stops for weights}\index{Turret clocks!stops against overwinding}\index{Weights, stops!for winding}stops the +winder; and he then throws the winding-wheels out of gear, +and in again when the striking is done. + +This throwing out of gear is also done by a new method: +the first pivot of the second (150) winding-wheel arbor is set +in an eccentric bush, which can be turned in its own holes +by a lever with a handle to it, as you see in the drawing, +and the eccentricity is just enough to take the teeth of that +pinion out of gear with the great winding wheel, leaving the +2nd wheel in gear with the winding-pinion (14). Besides +this the ropes themselves stop the winder when the weights +are wound up to the top, by throwing another lever off a +hook on which it has to be set before the man can begin +winding. In all these winding and maintaining power +contrivances there are some further provisions for enabling +the man to turn the winding handle back a little, to let the +barrel ratchets down softly on to their clicks, but it is +hardly worth while to describe them. + +\subsection[Rate.]{Rate.}\markright{RATE.}\label{subsec:Rate.}\index{Gravity escapements!rate of some}\index{Rate!of the Westminster clock}\index{Westminster clock!rate}---Provision is made in the clock for reporting its +own rate of going to the Greenwich observatory at any convenient +hour or hours every day, by electric telegraph, as I +have already described under `electrical clocks' at p.~\pageref{subsec:Electrical_clocks}; +and it has been arranged by the Astronomer Royal that it +should give two signals a day, at an hour before and after +noon, for greater accuracy. The average performance of the +%-----File: 279.png--------------------------------------------- +%-----Folio: 264------------------------------------------------ +clock is reported by him annually to the Board of Visitors +of the Observatory, and for years the report has been practically +the same. Last year, 1881, its error was under $2$~sec.\ on +$84$~per~cent.\ of the days of observation; between $2$ and +$3$~sec.\ on $14$; between $3$ and $4$ on $2$. They were almost +exactly the same in 1872. + +Sir G.~Airy sent me, for the purpose of the inquiry into +the barometrical error (see p.~\pageref{barerr}), the complete rating of +the clock for 1872, except Sundays and a few odd days. +Rejecting three abnormal disturbances, one of which reached +$8$~sec.\ in a week of thunderstorms, and two others of $5$~sec., +which came suddenly, and evidently from something done in +the clock-room, because the daily variations never reached +$2$~sec.\ at any other time, the average daily variation was only +$0.2$~sec.\ on each side of zero, or $0.4$~sec.\ altogether; and taking +it on all the Saturdays in the year, the average weekly variation +was just $1$~sec, or exactly half that of one of old Mr.~Dent's +best regulators which I happen to have had for +nearly two years while we were trying the Exchange clock. +Therefore the first blow of the hour may be presumed to +differ considerably less than a second from GMT, and is +practically always right within $2$~seconds. In hearing it at +a distance you must allow nearly $5$~seconds a mile for the +velocity of sound. + +Some enemy set afloat the statement that the clock is +`controlled' by electrical connection with Greenwich, in +some such way as is described at p.~\pageref{jones}, instead of merely +reporting its own performance; and the story has been repeated +by people who ought to have known better, or might +easily have learnt, by writing either to the Astronomer Royal +or me, or from any edition of this book after the first. +A signal is sent back from Greenwich at some hour daily, for +the information of the winding men, but they never touch +the pendulum unless the error is $2$~seconds, which happens +very seldom. +%-----File: 280.png--------------------------------------------- +%-----Folio: 265------------------------------------------------ + +\subsection[History of the clock.]{History of the clock.}\markboth{HISTORY OF THE CLOCK.}{HISTORY OF THE CLOCK.}\label{subsec:History_of_the_clock.}\index{Westminster clock!history}---It is no longer necessary to +relate as fully as in 1860 the history of the 16 years of +disputes relating to this clock; for it was the subject of +violent disputes before I\index{Beckett, Sir E.!plan for the Westminster clock|(} had anything to do with it. I shall +only say as much as may possibly be useful with reference +to any similar transaction hereafter. Not that I expect +such warnings to be attended to, except perhaps in exactly +the wrong way; for I know very well that the tendency of +the official mind to get things done with as little trouble as +possible is infinitely stronger than to get them done as well +possible. I was only brought into this business originally +with the view of saving somebody else trouble; and as soon +as it was found that by the legal effect of the contract I had +real power to direct the work, every possible effort was made +to get rid both of it and me. No official who joined in +those attempts cared three half-pence how the clock was +made. Luckily I did care, and knew what would become +of it if I gave it up. And as the biographers of Sir Charles +Barry have told their story on his behalf, I shall also, without +the least resentment against them, repeat mine, of which +not a word has been ever contradicted. + +No \markright{EARLY DISPUTES ABOUT THE WESTMINSTER CLOCK.}one who has read in the Parliamentary papers the +early correspondence, beginning in 1844, can have the +smallest doubt that the architect had made up his mind +that the late Mr.~Vulliamy\index{Vulliamy, Mr.!and the Westminster clock} should make the clock, and no +one else. Mr.~Vulliamy himself was so confident about it, +that even after the Astronomer Royal had utterly condemned +his plan for it, as `only suitable for a large village clock,' +and recommended old Mr.~Dent\index{Dent, E.~J.!Westminster clock|(}, he said to me, `Dent will +never make that clock.' After that, the matter went to sleep +till November 1851, when the Duke of Somerset, then Lord +Seymour and First Commissioner of Works, asked me to +act as referee with the Astronomer Royal, on his recommendation. +I examined the plans at the Office of Works, which +had been sent in in 1846, and found that Vulliamy's was +%-----File: 281.png-------------------------------------------- +%-----Folio: 266----------------------------------------------- +quite as deficient in strength (for which Sir G.~Airy had +commended it) as it was in all provisions for accuracy: +indeed more so, because accuracy is a question of degree; +but such a clock as that, striking on a bell of half the weight +that had been fixed upon, would have destroyed itself in +week. By some strange omission, Dent had never been +told that the bell was to weigh $14$~tons, and he had assumed +it to be much less, and consequently his plan was defective +too, though not so defective, and that only in size, not +in principle. The plans of Whitehurst, of Derby, which +Sir G.~Airy\index{Airy, Sir G.~B.!conditions for Westminster clock} had reported on more favourably than Vulliamy's +could not be found in the office; and it was evident that +Dent's had been somewhere else, where they had been very +roughly handled, dirtied, torn, and mended, which was +certainly not done at Greenwich. + +Whitehurst was dead, and Vulliamy had refused to accept +the Astronomer Royal's conditions as to the performance of +the clock, which the Clockmakers' Company also pronounced +impossible, though they have been far exceeded in accuracy +now. So we agreed that it was useless to apply to any one +but Dent, and that the only practicable way was to ask him +if he would make for any definite sum such a clock as we +should require, from his own knowledge and our information +as to what was intended, and such general plan as we could +give him, in the unfinished state of the tower. He agreed to +do so, for a sum which was soon found to be inadequate, and the +arrangement was altered into his keeping a separate account +of all outlay on the clock, and receiving $10$~per~cent.\ profit on +it, which ultimately came to \pounds 4080, only an eighth more than +Vulliamy's\index{Vulliamy, Mr.!and the Westminster clock} estimate for a clock totally unfit for the work. + +The Duke of Somerset went out of office soon after giving +Dent the order in 1852; and then began, and lasted through +the reigns of his successors, Lord John Manners and Sir W.~Molesworth, +a series of intrigues and attempts to get rid of +or alter old Mr.~Dent's contract, and then to repudiate his +%-----File: 282.png-------------------------------------------- +%-----Folio: 267----------------------------------------------- +successor F.~Dent, and then---or rather, all along---to get +rid of me; for they all knew very well that for various +reasons the Dents alone could not contend against them, nor +go on with the work at all. Sir C.~Barry demanded working +drawings of the clock from Dent, who told him very truly that +there were none, and would be none, except such sketches as +I might give his men from time to time. Then he applied to +the Astronomer Royal for them, who desired me to make and +send them. I answered that I should do nothing of the +kind: the Office of Works might show him the signed plans +if they liked (as in fact they did), which were all that could +possibly concern him; at any rate I should make no others. +Thereupon Sir G.~Airy resigned; and as his knowledge of +large clocks was purely theoretical, and not one of the +suggestions he had made could be adopted, his resignation +saved a good deal more of unprofitable correspondence. The +Office of Works made that another excuse for trying to get +rid of me, and went so far as to consult the Attorney and +Solicitor General about it. + +Then they tried the obstructive policy of refusing any +information about the tower, in spite of my warning that +the only consequence would be that they would probably +have to pay for altering the clock when it got there; for +which they cared nothing, as the nation and not they would +have to pay for it. Still the work went on, and as the +inscription on it records, the clock was made in 1854, and +after going in the factory for 5 years was fixed in the tower +in 1859, and was set going permanently in 1860. + +Sir C.~Barry\label{barryhands} was particularly anxious to design the hands, +and I rather unwillingly and with some misgiving consented, +having already reason to put very little faith in his +mechanics. He first produced some cast iron ones, of +such frightful weight that I would not even let them be put +on. He then tried some of gun-metal, which were lighter, +but still far too heavy for the clock, besides being so fixed +%-----File: 283.png-------------------------------------------- +%-----Folio: 268----------------------------------------------- +on by his engineer that they fell over a minute or two every +time they passed the vertical. And so we removed them, +at least the minute hands, and made new ones, as described +at p.~\pageref{whands}, which have always gone quite easily, except once +when loaded with snow which froze upon a partial thaw, +and broke down hundreds of miles of telegraph wires at the +same time that it stopped the clock. Before Dent's final +bill was paid, the Astronomer Royal inspected the work, +though his legal control over it was gone, both from his +resignation, and from other causes, and he candidly expressed +his entire approval of it, and especially of the escapement, +on which its performance chiefly depends. It is due to Lord +Llanover, though he is dead, to say that in his time I had +no trouble with the Office of Works. + +As soon as it was finished, Mr.~W.~Cowper Temple\label{ctemple}, who +had then been made First Commissioner of Works by Lord +Palmerston his step-father, told the House of Commons, with +evident satisfaction, and the gratitude natural to some people, +that my connection with the clock had ceased, and that it +was handed over to the Astronomer Royal. The next I heard +of it was that he had replaced the great check spring of the +hour-striking part by a contrivance of his own, which soon +produced a smash, and then the old spring was quietly +restored, and is there now, and there have been no more +such experiments. I must however do him the justice to +say that he had previously written to me `that the clock +would be far better in my hands than in any other person's;' +not that there was really any more for me to do, beyond +nominal superintendence of the clockmakers who have the +care and winding of it by an independent contract, viz., the +successors of the Dents\index{Dent, E.~J.!Westminster clock|)} in the Strand. By an odd coincidence, +I had the pleasure of giving a sort of clinical lecture +on the clock to as many members of the Horological Institute +as the room would hold, on the 21st anniversary +of our signing the plans for it, 29 January 1873.\index{Beckett, Sir E.!plan for the Westminster clock|)} +%-----File: 284.png-------------------------------------------- +%-----Folio: 269----------------------------------------------- + + + + +\section{THE WESTMINSTER BELLS.}\label{sec:THE_WESTMINSTER_BELLS.}\markboth{THE WESTMINSTER BELLS.}{HISTORY OF THE WESTMINSTER BELLS.} + +\index{Westminster bells, the!their history} +I had better give the history of them also here. In 1852 +Astronomer Royal declined to have anything to do +with the bells, as he did not profess to understand them; +and nothing was done towards getting them, beyond +some abortive correspondence with me by Sir W.~Molesworth, +and his giving a commission to Sir C.~Barry and Professor +Wheatstone to learn what they could about bells at the Paris +Exhibition of 1855, which proved to be nothing. In 1856, +Sir B.~Hall (Lord Llanover) asked me to take them in hand, +and it was then arranged that I, with Sir C.~Wheatstone, and +the late Rev.~W.~Taylor\index{Taylor, Rev.~W.!and the Westminster bell}, who had paid some attention to the +subject in a theoretical way (and must be distinguished from +his namesake the bell-founder), should be the referees. +Sir C.~Wheatstone never acted, beyond telling us the +result---or rather, no result---of his inquiries at Paris, and Mr.~Taylor +would take no responsibility beyond giving the final +certificates. I therefore prepared a specification, which was +sent to the three English bell-founders. + +Mr.~Mears\index{Mears, bell-founders} refused to accept the referees because they had +among them spoken ill of his two condemned Royal Exchange\index{Mears, bell-founders!Royal Exchange and York} +peals, of his great York Minster bell, and a rather larger +one which he had sent to Montreal. He also declared that +nobody else could make the bells; and his tender was not +the lowest. Mr.~Taylor's (of Loughborough) was; but he +wanted some terms which could not be acceded to. Messrs.~Warner\index{Warners, bell-founders} +required the referees to take the responsibility of +giving the patterns for the bells; \textit{i.e.}, they confessed that +they did not know how to make such large bells of the +proper notes: they had previously copied all their bells from +existing ones. However I was able to do that for them, and +so their tender was accepted, though they demanded ten +guineas a cwt., while the usual price was seven, and they +were to recast any of them (unless condemned for bad +%-----File: 285.png-------------------------------------------- +%-----Folio: 270----------------------------------------------- +casting, in which case they were to recast for nothing) for +\pounds 2 a cwt., and also to cast any small experimental bell +the same price. + +They made the great bell first; and from some mismanagement +it came out thicker than the pattern, and two tons +heavier than was intended, and required a clapper twice +heavy as we had reckoned on by analogy to other bells. +Undoubtedly we had a right to reject it; but it appeared a +sound casting, except some holes at the top, and was generally +praised by the public who heard it, though there was always +something unsatisfactory in its tone. And no wonder; for +after being rung occasionally for some weeks, it one day +cracked, no doubt from the weight of the clapper which it +required to bring out its tone, and when it was broken up +there was found a great flaw in it, where the two streams of +metal meeting round it had never joined. So we were in +every way well rid of Big Ben\index{Big Ben of Westminster!the first and second} the first. + +The founders however had cast then the fourth quarter +bell of four tons successfully, and there was no intention of +taking the job out of their hands. But they demanded a +price for recasting enormously beyond the \pounds $2$~per~cwt., +which they had agreed to before, evidently presuming that +neither of the other founders would be employed. Mr.~Mears +had learnt something by experience, and no longer objected +to the referees, and offered to recast the bell at a more +reasonable price, and so this time his tender was accepted. +He however was still more unlucky; for he produced a +bell which partially cracked also, after a few months striking; +and Dr.~Percy\index{Percy, Dr., his report on the Westminster bell} pronounced it, on cutting a hole down to the +bottom of the crack, and analysing the metal, `a defective +casting, porous, unhomogeneous,' and at the place where it +is cracked, not of the composition I had prescribed, and +therefore much more brittle. + +Mr.~Mears also determined to conceal this porosity from +the referees by filling up the holes with cement, before he +%-----File: 286.png-------------------------------------------- +%-----Folio: 271----------------------------------------------- +let us know that the bell was ready to be seen. And when +I publicly charged him with having done so, he put a bold +face on the matter, and brought an action for libel, and had, +no doubt, found half-a-dozen engineers and brass-founders +ready to swear that porous castings are as good as sound +ones. But he also found that I had got a piece\label{taster} of the bell +analyzed, and knew that the composition was wrong, besides +the porosity and its concealment. So his counsel accepted +his costs without a verdict, after making a speech in which +he confessed and declared that the composition had miscarried, +and become unhomogeneous; that he had filled up +the holes, \textit{because he thought them immaterial}---as if he was to be +the judge of that; and that it was impossible---\textit{i.e.}\ that he +did not know how---to cast large bells without holes in them! + +His successor, who had bought Mears's declining business, +twenty years afterwards thought he would try again, evidently +with the object of advertising himself, on my once more +publishing the fact that Big Ben II\index{Big Ben of Westminster!the first and second}.\ was a disgrace to its +founders. His workmen who had been with Mears had to +confess the concealment of the holes, and again they and all +his party asserted that it is impossible to cast large bells +without holes, and that it was their regular practice to fill +them up with cement coloured with bell dust: which both +Taylor and Warner's people utterly contradicted, and I have +every reason to believe, quite truly. + +Though Dr.~Percy had been asked to examine the bell as soon +as the cracks were discovered, he was not allowed by Mr.~Cowper +Temple, then First Commissioner of Works, to cut into +it for nine months after. If that had been done at once, as I +desired, Mears's action would never have been heard of. + +He had also got a report from Sir G.~Airy\index{Airy, Sir G.~B.!his report on the Westminster bells}\label{gairyreport}, who, although +he declined meddling with the bells before because he did +not understand them, felt no difficulty in giving judgment on +them afterwards, with the help of two musical assistants and +fiddle `tuned to the pitch of the Italian opera'---as if the +%-----File: 287.png-------------------------------------------- +%-----Folio: 272----------------------------------------------- +pitch of the Italian opera had anything to do with the +question whether five bells are good or bad, or in tune with +each other. Mr.~Turle, the organist of Westminster Abbey, +had given his opinion before we certified them, that the four +quarter bells were `all that can be desired, both in tune and +tone,' which are very different things (for a set of iron pots +may be in tune), except that `the fourth is a shade too flat' +But Sir G.~Airy came to a very different conclusion, viz., +that the fourth bell was \textit{a note and a half too sharp}, and the +first about the same, the third `rather sharp,' and the second +alone right. On the whole, he was `much dissatisfied with +those bells,' and thought two at any rate must be recast\index{Airy, Sir G.~B.!failure of his alteration of the striking work}. +Afterwards he began to have a little misgiving about it, and +thought it might be advisable to try again before recasting +them; but he never did try again. I suppose it had then +occurred to him, as a mathematical fact of which he certainly +was not ignorant, that the two bells could not be a note +and a half too sharp without being a sixth less in diameter +than they are, or else a great deal thicker. He also +pronounced the great bell, which Dr.~Percy had not then +ascertained to be cracked three inches deep, and to have +almost every possible unsoundness, `perfectly sound for all +practical purposes, and the cracks probably superficial,' and +that it only wanted a lighter hammer \textit{faced with tin!} + +This seems to have been too much even for Mr.~Cowper\label{ctemple2} +Temple to swallow; for although he sent me one of the +polite and intelligent epistles which I used to receive from +him and Mr.~Alfred Austin, then the secretary of that office +saying that he `disagreed with every word of the stricture +I had sent him on Sir G.~Airy's report' (as if his adoption +of it made it less ridiculous), he afterwards consulted +Mr.~Turle again, and no quarter bells were recast, nor was +the great hammer faced with tin; and after getting Dr.~Percy's +report he told the House of Commons that the bell +was, not `perfectly sound,' but `irretrievably cracked,' as it +%-----File: 288.png-------------------------------------------- +%-----Folio: 273----------------------------------------------- +is, though the defect is much less perceptible than one would +expect. The hours were struck on the fourth quarter bell +for three years, which made them difficult to distinguish at +a distance, and after a paragraph in the \textit{Globe} to that effect, +the striking was resumed on the great bell with a lighter +hammer striking in a different place, which was easily done +by my arrangement for turning the bell any degree round by +giving it a mushroom or button-shaped top (see p.~\pageref{fig44}). +When the new great bell of St.~Paul's has taught people the +difference between a cracked bell and a sound one, perhaps +`this great country' and `the model legislature of the world,' +as it is the fashion to call them, may screw up their courage +to the vast undertaking of recasting their own great clock bell +at the cost of six or seven hundred pounds. + +The cost\label{cost}\index{Westminster bells, the!their cost}\index{Westminster clock!cost} of the bells, including \pounds 750 for recasting `Big +Ben' was under \pounds 6000, while the cost of the iron frame +provided by the architect was about \pounds 6600 partly in consequence +of its being made too weak at first, so that it shook +under every blow of the hammers, as I had told him that it +would. And as the clock, with my hands, cost only \pounds 4080, +while his hands and dials alone cost \pounds5334, you see that +the actual clock and bells cost much less than the architect's +appendages to them. + + + + +\section{TEETH OF WHEELS.}\label{sec:TEETH_OF_WHEELS}\index{Teeth of wheels} +\markboth{TEETH OF WHEELS.}{TEETH OF WHEELS.} + +There are various treaties on this subject, and I only +intend to say as much on it as it is necessary that a clockmaker +should understand, if he means his wheels and +pinions to run together smoothly instead of wearing themselves +out by jerking and scraping, which I have known to +happen in a very few years. The most comprehensive view +of the whole theory of tooth-drawing (at least of this branch +of the art) is in a paper by Sir G.~Airy\index{Airy, Sir G.~B.!on wheel teeth} in the 2nd vol.\ of +the \textit{Cambridge Transactions}, and it was further expanded by +Professor Willis in his \textit{Principles of Mechanism}. +%-----File: 289.png----------------------------------------------- +%-----Folio: 274-------------------------------------------------- + +Some persons have a mistaken impression that the object +to aim at in constructing wheel-teeth is to make them roll +on one another without any rubbing friction. This can +indeed be done by what are called \textit{involute} teeth, of the +shape described by a point in a string unwound off the +circumference of a wheel: but they are really useless +because they are so oblique that they produce a squeezing +pressure between the two wheels which is more than +equivalent to any saving in friction. The great thing to +aim at in describing teeth is to make the relative velocity of +the wheels uniform from the beginning to the end of the +contact of each pair of teeth, which of course involves also +the absence of all concussion or drop of the teeth. Another +point is to have the action entirely or chiefly between the +teeth which are separating from each other, and not between +those which are approaching, which is commonly expressed +by saying that the action should be after the line of centres +of the wheels and not before it. The reason of this will be +evident at once if you draw some teeth with a very rough +outline, so as to give an exaggerated view of the effect of +friction, for you will see that there is a degree of roughness +which will make the teeth jam against each other and not +let them slide at all as they approach the line of centres, +but that no degree of roughness will do this when they are +leaving contact or are past the line of centres. The most +perfect thing is when the contact takes place for a very +short distance only close to the line of centres; and this +can only be with very small teeth, and therefore very high +numbers (except with involute teeth, which I have already said +will not do for another reason). There is indeed a contrivance, +which I have somewhere seen called White's\index{White's gearing} gearing, for +getting this kind of action with large teeth in heavy machinery, +by putting several large-toothed wheels close together, +with the teeth of each a little behind the other, as in figure~\ref{fig54}~$a$ +(next page): but this is never used in clockwork. +%-----File: 290.png-------------------------------------------- +%-----Folio: 275----------------------------------------------- + +\subsection[Helix-teeth.]{Helix-teeth.}\markboth{HELIX-TEETH.}{HELIX-TEETH.}\label{subsec:Helix-teeth.}\index{Helix teeth}\index{Teeth of wheels!helix teeth}---A modification of this plan, though very +unlike it in appearance, has been occasionally used in +clocks under the erroneous name of the \textit{helix lever}. The +teeth certainly do at first sight suggest the idea of an endless +screw, but are essentially different, the arbors +being parallel, and not at right angles as in an endless +screw. If you suppose a good many very thin toothed +wheels put together side by side, each with its teeth a little +behind its neighbour, they will present a surface like a +rough tooth with a sloped face, as in the upper part of \hyperlink{fig54}{this +figure}~$a$. Then go a step +farther and suppose the +rough edge to be smoothed +off, and the result will be +a smooth-faced oblique +tooth, like the lower one +in the figure, which will +drive teeth of corresponding +obliquity on another +wheel, and the contact will +be solely at the line of +centres, where there is no +friction. But when the +teeth thus become smooth, +there will evidently be a +great endway pressure on +each arbor, which there is +not while the teeth are square, or belonging to separate +wheels put together. This endway pressure may however +be neutralised by again putting two such wheels together +with the teeth sloped opposite ways as at $b$. There was a +German turret clock on this plan in the 1851 Exhibition, +which certainly went with a very small weight; and small +clocks with the single helix tooth had been made in England +many years before by Macdowall (see p.~\pageref{macd}) which also +\begin{figure}[hbtp] +\centering +\hypertarget{fig54}{\caption{\sc Helix Teeth}} +\includegraphics[width=0.6\textwidth]{images/fig54.png} +\label{fig54} +\end{figure} +%-----File: 291.png-------------------------------------------- +%-----Folio: 276----------------------------------------------- +required less force than usual, from the smallness of the +friction in the teeth. I do not know that the advantage is +worth the expense; but as this construction is very little +known, I explain it in case it may be turned to any use +hereafter. + +\subsection[Epicycloidal teeth.]{Epicycloidal teeth.}\markboth{EPICYCLOIDAL TEETH.}{EPICYCLOIDAL TEETH.}\label{subsec:Epicycloidal_teeth.}\index{Epicycloidal teeth}\index{Teeth of wheels!epicycloidal teeth}---It may be said without exaggeration, +I believe, +that all the teeth +now used in machinery +are constructed +either +as \index{Hypocycloid and epicycloid}epicycloids or +hypocycloids, +and the meaning +of those words is +this:---If you roll +a circle $\mathrm{AGP}$ +\textit{on} another circle +$\mathrm{ARY}$, the curve +$\mathrm{RP}$ traced by +any point $\mathrm{P}$ in +the rolling circle +is called an epicycloid +to the circle +$\mathrm{ARY}$; and +if you roll the small circle $\mathrm{AGP}$ \textit{within} a larger than +itself, such as $\mathrm{AQX}$, the curve $\mathrm{PQ}$ traced by $\mathrm{P}$ is a +hypocycloid to that circle. And it is remarkable that +if the tracing circle is exactly half the size of the one in +which it rolls, the hypocycloid $\mathrm{PQ}$ is a straight line, and +part of the diameter of the large circle, and therefore teeth +so described are called radial teeth. +\begin{figure}[hbtp] +\centering +\setlength{\unitlength}{0.05\textwidth} +\caption{\sc Epicycloidal Teeth}\index{Teeth of wheels!epicycloidal teeth} +\begin{picture}(16,16)(-8,-2) +\put(0,0){\line(0,1){7}} +%Circle centre (0,3) radius 3 +\qbezier(0,0)(1.242641,0)(2.121320,0.878680) +\qbezier(0,0)(-1.242641,0)(-2.121320,0.878680) +\qbezier(2.121320,0.878680)(3,1.757360)(3,3) +\qbezier(-2.121320,0.878680)(-3,1.757360)(-3,3) +\qbezier(0,6)(1.242641,6)(2.121320,5.12132) +\qbezier(0,6)(-1.242641,6)(-2.121320,5.12132) +\qbezier(2.121320,5.12132)(3,4.24264)(3,3) +\qbezier(-2.121320,5.12132)(-3,4.24264)(-3,3) +%Circle centre (0,7) radius 7 +\qbezier(0,0)(2.899496,0)(4.949747,2.050253) +\qbezier(0,0)(-2.899496,0)(-4.949747,2.050253) +\qbezier(4.949747,2.050253)(7,4.100507)(7,7) +\qbezier(-4.949747,2.050253)(-7,4.100507)(-7,7) +\qbezier(0,14)(2.899496,14)(4.949747,11.949747) +\qbezier(0,14)(-2.899496,14)(-4.949747,11.949747) +\qbezier(4.949747,11.949747)(7,9.899493)(7,7) +\qbezier(-4.949747,11.949747)(-7,9.899493)(-7,7) +%Two radii +\put(0,3){\line(3,-1){2.846050}} +\put(0,7){\line(2,-3){3.882901}} +%Arc (2pi/7) of circle centre(0,-17) radius 17 +\qbezier(0,0)(3.880139,0)(7.376024,-1.683529) +\qbezier(0,0)(-3.880139,0)(-7.376024,-1.683529) +%Curve PR, $\mathrm{R}$ chosen approximately, $\mathrm{Q}$ used as angle point +\qbezier(2.846050,2.051317)(3.882901,1.175649)(3.9,-0.453399) +%Curve PQ, with angle point chosen approximately, on the line OQ +\qbezier(2.846050,2.051317)(3.482901,1.775649)(3.882901,1.175649) +%Labels +\put(0,-0.2){\makebox(0,0)[t]{A}} +\put(0,7.2){\makebox(0,0)[b]{O}} +\put(-2.8,3){\makebox(0,0)[tl]{G}} +\put(6.8,7){\makebox(0,0)[tr]{X}} +\put(2.646050,2.051317){\makebox(0,0)[tr]{P}} +\put(3.882901,1.1){\makebox(0,0)[tl]{Q}} +\put(3.9,-0.6){\makebox(0,0)[t]{R}} +\put(7,-1.8){\makebox(0,0)[t]{Y}} +\put(0,13){\makebox(0,0)[t]{\it Runner}} +\put(0,-2){\makebox(0,0)[l]{\it Driver}} +\put(2,-2){\vector(1,0){2}} +\end{picture} +\label{fig55} +\end{figure} +Now suppose $\mathrm{ARY}$ is the circumference of what is called +the \textit{geometrical} or \textit{pitch} circle of a wheel which is intended +to drive another, and $\mathrm{AQX}$ the pitch circle of the wheel to +%-----File: 292.png-------------------------------------------- +%-----Folio: 277----------------------------------------------- +be driven, which is generally called the `follower,' but +which I think it better to call the \markboth{TEETH OF WHEELS.}{TEETH OF DRIVER AND RUNNER.}\textit{runner}, as followers do +not usually run before their driver; then it is easy to see +that the arc $\mathrm{AP}$ of the tracing circle is equal both to $\mathrm{AR}$ +and to $\mathrm{AQ}$, and also that the epicycloid is always more +convex than the hypocycloid, and therefore that the point +$\mathrm{P}$ in the tracing circle is always the point of contact +between two teeth so traced, and the velocity of the two +wheels is always the same as if their pitch circles rolled +upon each other without any teeth at all; and therefore +it is constant in all positions of the teeth. It is hardly +necessary to observe that the teeth of the driver, to act +after the line of centres, must be wholly outside its pitch +circle, and those of the runner wholly within. The part +of a tooth within the pitch circle is generally called its +\textit{flank} or \textit{root}, and the part outside is called the \textit{point}, or +the \textit{addendum}, and sometimes the \textit{curve}, because the flank +is generally made radial, \textit{i.e.}\ a hypocycloid described by a +circle of half the diameter of the pitch circle. For it is +further to be observed, that although the points of the +driver and the flanks of the runner must be traced with +the same circle, it is not the least necessary that the +points and the flanks of the same teeth should be traced +with the same circle. + +In clockwork the wheels always drive and the pinions +run, except the $12$~hour wheel in the dial-work, and the +winding wheels and pinions if there are any. It can be +proved, as you may see in Professor Willis's\index{Willis, Prof., his table of wheelwork} \textit{Principles of +Mechanism}, but the proof is too long to give here, that no +pinion of less than $11$ leaves (except of a kind which I +shall describe presently) can be driven entirely after the +line of centres. A pinion of $10$ can very nearly; and there +is so much difference between the force required to drive +pinions of $8$ and those of higher numbers, that some +spring clocks with Macdowall's escapement which answered +%-----File: 293.png-------------------------------------------- +%-----Folio: 278----------------------------------------------- +perfectly with pinions of $10$ or $12$, failed with the common +pinions of $8$, for want of force to drive the two extra wheels +in the train. Professor Willis gave the \hyperlink{willis}{following} table of +the lowest numbers which will work together with all the +action after the line of centres:--- + +\begin{table}[!hbtp] +\centering\hypertarget{willis}{} +\setlength{\tabcolsep}{4pt} +\begin{tabular}{lrrrrrrrrrrrrrrr} +Driver &54 &30 &24 &20 &17 &15 &14 &13 &12 &11 &10 &9 &8 &7 &6 \\ +Runner &11 &12 &13 &14 &15 &16 &17 &18 &19 &21 &23 &27 &35 &32 &176 +\end{tabular} +\end{table} +\begin{figure}[hbtp] +\centering +\caption{\sc Drivers and Runners} +\includegraphics[width=324pt]{images/fig56.png} +\label{fig56} +\end{figure} + +The practical inference from this is, that if you use these +numbers, or any higher ones, together, the driving teeth\index{Driving and running teeth} +require no flanks and the running ones no points: indeed +if you mean to prevent any action before the line of centres, +the runners obviously must have no points, because if they +have they will be geometrically identical with the teeth of +a pinion intended to drive the wheel after the line of centres +when reversed. Suppose for instance, what is nearly the +case in the Westminster clock, that the great striking wheel +at one end of the barrel and the great winding wheel at the +other are both of the same size and number of teeth, and +%-----File: 294.png-------------------------------------------- +%-----Folio: 279----------------------------------------------- +that their pinions are also the same; then as the striking +wheel always drives, but the winding wheel is always driven +by its pinion, the striking pinion and the winding wheel +ought to have no points to their teeth, and the sections +of the two wheels and pinions would be as in fig.~\ref{fig56}, the +right hand representing the striking part and the left the +winding, and the action being in both cases, you observe, +after the line of centres $\mathrm{AC}$, as the arrows indicate. + +It is evident that the same wheel cannot properly drive +two unequal pinions with radial teeth. Whenever the +same wheel has to drive two such pinions, the flanks of +the pinion teeth and the points of the wheel teeth must be +traced with the same circle, and that circle must not be +larger than half the size of the smaller pinion, or else it +will make the teeth of that pinion weaker at the roots +than even radial teeth are, which are of course narrower at +the bottom than the top, and therefore are a weak form, +especially in small pinions. A case of this kind occurs in +every clock on the patterns I have described at pp.~\pageref{fig37} and +\pageref{fig40}, and in the Westminster clock, and in short wherever +the second wheel in the going train does not turn in an +hour, and the dial work is driven independently. In this +case, the $40$ teeth of the hour wheel (or whatever the number +may be) require no points, and should be hypocycloids +described by a tracing circle of half the diameter of the other +pinion of $10$ or $12$ which is driven by the great wheel, if the +teeth of that pinion are radial. + +\subsection[Lantern pinions.]{Lantern pinions.}\markboth{LANTERN PINIONS.}{PROPER USE AND CONSTRUCTION OF LANTERN PINIONS.}\label{subsec:Lantern_pinions.}\index{Lantern pinions for clocks|(}\index{Pinions of clocks!lantern}\index{Teeth of wheels!lantern pinions}---But there is another, perfectly +different kind of pinion, which is much better for small +numbers than radial teeth or leaves, viz.\ what is called +a lantern pinion, and in old books, a `trundle.' These two +figures~(\hyperlink{fig57}{\textit{t.~o.}}) will show its construction better than any explanation. +I believe it is the oldest form of pinion in the +world, but it had almost (if not quite) fallen into disuse in +England, when it was restored in Dent's turret clocks about $30$ +%-----File: 295.png-------------------------------------------- +%-----Folio: 280----------------------------------------------- +years ago. They work with much less friction than common +leaved pinions of low numbers, when driven, the run upon +them being less and the action wholly after the line of +centres, and the shape of the wheel teeth requiring less +accuracy to drive them smoothly. They are not however +proper for driving, because then you see the action comes +all before the line of centres. In some French turret clocks +the winding pinions are nevertheless wrongly made as +lanterns, and the pins themselves pivotted instead of +\begin{figure}[htbp] +\centering +\hypertarget{fig57}{\caption{\sc Lantern Pinions}} +\includegraphics[height=357pt]{images/fig57.png} +\label{fig57} +\end{figure} +%-----File: 296.png-------------------------------------------- +%-----Folio: 281----------------------------------------------- +rivetted in their sockets so as to turn while they are working, +which makes the working loose and shaky and the +pinion itself very much weaker than when the pins are fast, +and saves very little in friction besides. + +For the purpose of geometrical construction, we may first +consider the pins as being of infinitely small thickness, and +then the teeth which drive them would be of the dotted form +$\mathrm{PR}$ fig.~\ref{fig57}, being epicycloids traced on the wheel with a +circle the full size of the pitch circle of the pinion. Then in +order to get the shape of the teeth for pins of the actual size, +you must gage off half the breadth of the pin from each side +of the tooth, which reduces it to $pr$ and you may leave on +just as much point as will keep hold of the departing pin $\mathrm{P}$ +until another tooth has got well hold of the next pin just as +it crosses the line of centres. This operation of reducing the +theoretical to the actual tooth is practically equivalent to +tracing the tooth with a smaller circle: how much smaller, +will depend on the number, \textit{i.e.}\ on the thickness, of the pins, +in proportion to the size of the pinion. I find that a lantern +of $8$ or $10$ requires a tooth which fits a leaved pinion of the +same number so nearly that I can see no difference in the +curves on a pattern as large as $9$~inches diameter; and even +with $12$ the difference is very small; although a theoretical +lantern pinion with pins of no thickness requires the same +shape of teeth as a radial pinion of twice its size. I have no +doubt that a lantern of $8$ runs as easily as a leaved pinion of +$12$, and of course it requires only $\frac23$ the number of teeth in +the wheel, and is also itself stronger, and much less liable to +break, both in hardening and in working afterwards. + +I may however repeat the caution that cast iron wheels do +not work so well with steel pinions, which lanterns necessarily +are (or rather, they, soon wear them out), as with +cast iron; and therefore if the great wheel only is of iron and +the smaller ones of brass or gun metal, the pinions should be +made of cast iron\index{Cast iron!for steel pinions} or steel accordingly. Also it should be +%-----File: 297.png-------------------------------------------- +%-----Folio: 282----------------------------------------------- +borne in mind that you cannot draw out an arbor with a +lantern pinion endways, by unscrewing the front bush only +and therefore they should not be used where you cannot conveniently +get at the back bush to take it off. These pinions +are used in all the American clocks and also in the cheap +German or `Dutch' clocks, both of which, it is well known, +will go with an amount of dust in their insides which would +stop a clock with leaved pinions completely. But the English +clockmakers will not use them in small clocks; and as +English small clocks are not yet made in factories as large +ones are, and as they are everywhere else in the world, the +men who make them up have the power of obstructing every +such improvement, and exercise it by immediately charging a +higher price for every deviation from the common form, or +for everything which they fancy is going to be applied to some +new use. + +The leaved\index{Leaved pinions}\index{Pinions of clocks!leaved}\index{Teeth of wheels!leaved pinions}\markboth{LEAVED PINIONS.}{LEAVED PINIONS.} pinions of English house clocks are made out +of `pinion wire,' which is in fact a very long pinion drawn +through a hole like wire, and the leaves are turned off to form +the arbor and pivots (see p.~\pageref{pivots}). The American and Dutch +clocks prove clearly enough that lantern pinions\index{Lantern pinions for clocks|)} can be made +at least as cheap as others; and if any man of skill, capital, +and determination would follow the example of Mr.~Hobbs in +locks, and set to work to manufacture clocks in a factory of +his own, we should soon see this and other improvements +made, and the clock trade recovered out of the hands of +foreigners, to whom it has been in a great measure sent away +by this combination of workmen, who will ruin this and every +trade in the kingdom if they are allowed to have their own +short-sighted way. + +Inasmuch as English clocks are thus made by hand, and +therefore probably no two are exactly alike, it is necessary +to have a tool for marking the places where the holes for the +pivots of the wheels are to be drilled, to bring them to the +proper depth for working. This \textit{depthing tool}\label{depthing}\index{Depthing tool@`Depthing' tool described}\markboth{DEPTHING TOOL.}{DEPTHING TOOL.} is something +%-----File: 298.png-------------------------------------------- +%-----Folio: 283----------------------------------------------- +like two vices framed together parallel to each other, each +carrying a thick sliding pin sideways through each of its +jaws. These $4$ pins have a small hole or `centre' at the +inner end and a point at the outer. The pivots of the pair +of wheels to be fitted are put in the $4$ centred ends of the +pins, and the machine is adjusted by trial till the wheels are +felt to work together comfortably. Then the points at the +outer ends of each pair of pins indicate the distance of the +centres of the wheels, and may be used to mark that distance +on the frame-plate. If you cannot get two wheels to work +together without shake (so long as they are driven the same +way) by any adjustment of their depth, the teeth are wrongly +cut in one of them at least, and they have no business to be +used. + +\subsection[Internal wheels]{Internal wheels}\markboth{INTERNAL WHEELS.}{INTERNAL WHEELS.}\label{subsec:Internal_wheels}\index{Teeth of wheels!internal wheels}\ are wheels with the teeth turned inwards +in which case the rim must evidently be raised in a +different plane from the spokes. They are never used in +clock-work, except for some special purpose, such as Sir G.~Airy's +maintaining power in the Exchange clock (p.~\pageref{smallmaintain}) or +in a sun and planet wheel for the same purpose, neither of +which are desirable, and in some train remontoires (p.~\pageref{fig48}). +Whenever they have to be used they are best made with pins +driven into the flat rim, especially if they have to be driven +and not to drive. Otherwise the same rules apply to the +construction of internal teeth as to external ones. They +almost necessarily involve the fixing of the wheel or pinion +which works into them on a stud instead of on an arbor +with pivots, which is generally objectionable and ought +never to be allowed if it can be helped, either for wheels or +pulleys. + +\subsection[Bevelled wheels.]{Bevelled wheels.}\markboth{BEVELLED WHEELS.}{BEVELLED WHEELS.}\label{subsec:Bevelled_wheels.}\index{Bevelled wheels}\index{Teeth of wheels!bevelled wheels}\index{Wheels for clocks!bevelled}---When the direction of motion has to +be changed, as it often has in leading off to dial-work in +turret clocks, bevelled wheels are used (as shown in p.~\pageref{fig47}). +They may be made to act through any other angle just as +well as $90^\circ$. The only condition to be satisfied is that the +%-----File: 299.png-------------------------------------------- +%-----Folio: 284----------------------------------------------- +teeth should in every respect converge to the point where +the two arbors would meet if prolonged, as if they were on +the faces of two cones. Nevertheless in a great many bevelled +wheels, the sides of the teeth do not converge properly, +the spaces being made of the same width all along, and so +the teeth converge too much, and have no contact at all +except just at their outer edges. The reason of this is that +if the sides of two adjacent teeth are cut in the common way +with the same cutter, the breadth of the cut is the same +throughout, and not narrower at the inside than the outside, +and therefore the teeth evidently taper too much. Fortunately +there is seldom much pressure on the bevelled +wheels in clocks, and therefore the defect is not very +material: but still it is one, and its frequent occurrence is +another reason why the bevelled wheels should be large in +diameter rather than in thickness; for the larger they are +the less pressure there is on the teeth, and the less any +inaccuracy of cutting is felt (as it is in wheels of all shapes), +and also the less shake of the hands and wheels there will +be for any given amount of shake in the teeth. + +\subsection[Skew-bevelled wheels.]{Skew-bevelled wheels.}\markboth{SKEW-BEVELLED WHEELS.}{SKEW-BEVELLED WHEELS.}\label{subsec:Skew-bevelled_wheels.}\index{Skew-bevelled wheels}\index{Wheels for clocks!skew-bevelled}---It may be worth while to know +that bevelled wheels can be made with oblique teeth, to work +with their arbors not in the same plane, provided they have +only to work one way; but the friction is very great if they +work what may be called the wrong way, and even in the +right way the friction is more than in the usual conical +wheels. I have never myself seen any clock where it was +necessary to resort to this construction, which may be found +in books on machinery, and therefore I only mention it in +case anybody may have occasion to resort to it. + +\subsection[Cams]{Cams}\markboth{CAMS TO RAISE LEVERS.}{PROPER FORM OF CAMS.}\label{subsec:Cams}\index{Cams}\index{Teeth of wheels!cams}\ may be defined as teeth which have to raise a lever, +or a sliding rod, and not a succession of teeth, and therefore +each cam must work up to its end, and drop the lever there, +whereas in wheels a second pair of teeth may and always +should come into action before the preceding pair have quite +%-----File: 300.png----------------------------------------------- +%-----Folio: 285-------------------------------------------------- +separated. The simplest form of cams to raise a lever is +that shown in any of the pictures of striking work of house +clocks, figs.~\ref{fig33} to \ref{fig36}, viz.\ a set of pins stuck into the side of +a wheel which catch the lever at some distance from its end +and work up to the end and then let it drop off. This does +well enough for very light hammers requiring only a small +clock weight, but is the worst plan that could be invented +for large ones. If you take the trouble to draw a wheel with +$8$ pins in it, each pin acting on the lever through about $36^\circ$ +(leaving the difference between that and $45^\circ$ for the clearance) +you will see that the angular lift of the lever towards the end +of its motion is only one third of what it is at the beginning, +and therefore $\frac23$ of the clock weight is wasted during part of +the lift. And that is by no means all; for if you look at +p.~\pageref{fig43} you will see that, as turret clock hammers are usually +fixed, the weight of the hammer acts more vertically or +requires more force to lift it at the beginning of its motion, +where the pin has least leverage or power, than at the +end, where it has most; and besides all this, the loss of +power by friction in driving through short levers is much +greater than through long ones with less angular motion. +Under all these circumstances it is no wonder that the weight +required to make a large clock strike is often three or four +times the theoretical `duty' of the clock, or the equivalent +of the hammer $\times$ its lift $\times$ as many blows as it strikes for +once winding; \textit{i.e.}\ that $\frac23$ or $\frac34$ of the force is wasted in +bad leverage and friction: whereas in the Westminster striking +part little more than $\frac14$ of the theoretical duty of the +clock weight is lost in friction, leverage, and the necessary +clearance or drop for the lever. + +The first condition therefore which the striking cams +ought to satisfy is they should begin to act at the end of the +lever. It is not necessary that the action should be quite at +the end all the way through, provided it is so at the beginning, +where the lift is hardest for the clock, and at the end +%-----File: 301.png-------------------------------------------- +%-----Folio: 286----------------------------------------------- +of the action so as to let the lever drop suddenly; for which +reason also rollers are worse than half round pins, besides +the reasons just now given against using pins at all. The +curve which does keep the cam\index{Cams!proper form of}\index{Teeth of wheels!cams!construction of} acting on the end of the +lever throughout, and as a tangent to itself, without any +scraping, is called in mathematics the \textit{tractrix}. If you wish +to describe it, the way is this. Set a smooth round board of +the size of the cam wheel with stiffish paper pasted over it +(to efface the grain of the wood) on a pin through the centre +on a horizontal table; and set also on the table, on another +pin, a model of the intended lever, with a vertical pencil at +its intended point, so as to press upon the paper, the lever +being weighted a little. Set the lever on the line of centres +and turn the wheel; it will drag the pencil over its surface +in a curve which is the \textit{tractrix}\index{Tractrix curve, to describe for cams}, unless it has been disturbed +by some inequality of friction between the paper and the +pencil, or at the axis of the lever; which is so likely to +happen that you cannot safely rely on this construction, +unless you find that a good many of the curves so traced +agree with each other. + +It\label{camcalc} fortunately happens however, that there is an epicycloid +which agrees with this so nearly that it may be +used without sensible error. Suppose $r$ is the radius of +the circle which forms the bottom of the cams (\textit{i.e.}\ their +theoretical pitch circle, allowing nothing for clearing the end +of the lever) and $l$ the length of the lever. The lever will +work as a tangent on its end throughout (without any appreciable +error for such length of cam as is ever wanted) on +epicycloidal cams traced with a circle whose $\normalfont{diameter} +=\sqrt{r^2+rl}-r$. Thus if $r=8$~in.\ and $l=4$~in.\ the radius of the +tracing circle will $=.95$~in. Another advantage of these +cams is that you may cut them off at any length, provided +only you keep the lever of the proper length; if you alter +that you will get scraping friction, and soon wear out either +the cams or the lever. +%-----File: 302.png-------------------------------------------- +%-----Folio: 287----------------------------------------------- + +\markright{MODES OF TRACING CAMS.}If you prefer having circles to deal with instead of epicycloids, +there is another form of cam, which was suggested to +me by Mr.~Effingham Lawrence (another horological lawyer, +like Mr.~Bloxam, and all the members but one of that jury +in the 1851 Exhibition, both English and foreign), and which +acts quite as well as the epicycloid or tractrix, provided you +take care not to alter the length of the cam: \textit{i.e.}\ you must +not put more or fewer cams on the wheel than they are +designed for, and you must take care that the proper distance +of centres of the wheel and lever is preserved. In +fig.~\ref{fig58}, $\mathrm{CAL}$ is the line of centres, and $\mathrm{AB}$ the space for +one cam on their pitch circle; by which I mean the space +occupied in lifting, for you see a little space is left below the +line of centres before the next cam begins, to prevent the +lever dropping onto the cam itself, which shakes the clock +most injuriously. $\mathrm{AP}$ is the arc of the lever. Draw $\mathrm{AT}$, +which is a tangent to the two circles at $\mathrm{A}$, and $\mathrm{BT}$ a tangent +\begin{figure}[htbp] +\centering +\caption{\sc Modes of Tracing Cams} +\includegraphics[width=\textwidth]{images/fig58.png} +\label{fig58} +\end{figure} +to the cam circle at $\mathrm{B}$\@. That point $\mathrm{T}$ will also evidently +be the place where a tangent to the circle $\mathrm{AP}$ at $\mathrm{P}$ would +meet the others; or in other words, $\mathrm{T}$ is the centre of a +circle $\mathrm{BP}$, to which the lever itself will be a tangent both at +the beginning and the end of the lift, although the contact +%-----File: 303.png-------------------------------------------- +%-----Folio: 288----------------------------------------------- +will be a little way from the end during some intermediate +part of the action. The backs of the cams must be cut out +a little deeper than down to the pitch circle, to let the lever +drop freely; and it is important to remember that the end of +the lever itself should not be left sharp, or it will cut off the +ends of the cams if they are not very hard, and perhaps break +them if they are. I know that by experience. + +It does not occur to me that cams can ever be required in +clock-work for lifting a vertical rod sliding like a stamper. +If any such case should occur, involutes of the wheel circle +would be the right shape for the cams.\footnote{This is no exception to the epicycloidal rule, for an involute is +in fact an epicycloid traced by a circle of infinite size, \textit{i.e.}\ by +a straight line.} There may also be +cases where it would be worth while to pull down a long +striking rod by pins in the wheel catching a square hook at +the end of the rod, and dragging it on with a little sideway +motion until it is struck off the pins by a horizontal stop: +this would avoid all the lever work and all friction except at +the striking off of the hook. + +\subsection[Oil for clocks.]{Oil for clocks.}\markboth{OIL FOR CLOCKS.}{OIL FOR CLOCKS.}\label{subsec:Oil_for_clocks.}\index{Oil for clocks}---I believe it is now generally understood +that sweet oil is the worst that can be used for machinery, +large or small, except when it is purified in certain ways not +known to the public; and then it is too expensive for use in +large or common clocks. For them purified sperm oil, such +as is now made wholesale for other machinery, is quite good +enough. Common neat's-foot oil may also be purified into +a very good oil, which will hardly freeze here. It can only +be done in cold weather; it should be shaken in a bottle +with water until it becomes a thick white soup, and then +left to stand, and the fine oil that gradually comes to the top +skimmed off, taking care to get none of the thick. If it is +done in a warm temperature, oil appears at the top as fine, +which has no business there, and will not remain fine in +cold weather. +%-----File: 304.png-------------------------------------------- +%-----Folio: 289----------------------------------------------- + +I have found two advantages in using the animal and +sperm over vegetable oil, which some persons may be +glad to learn. Working in iron with the common olive oil +dirties your hands so that it is very difficult to clean them, +whereas animal or sperm oil helps to clean them. It also +preserves iron from rust far better and longer, and does not +turn green on brass, \textit{i.e.}\ does not produce verdigris. I +understand that petroleum is better still for preventing rust. +It is difficult to make amateur clock-cleaners understand or +remember that putting oil to pinions driven by brass or gun-metal +wheels wears them out; but this does not apply to +cast iron; and all pivots should be oiled, and acting surfaces +generally. Oil must never be put to the beat pins of a +gravity escapement, or it will make them stick to the +pendulum quite enough to affect its rate; but it should be to +the pallet pivots. I have known the want of it, both there +and in the common pallet pivots, affect the arc sensibly. + +It must be remembered that oil has always a tendency to +run away from small points of teeth, the ends of pins, \&c., +to the thicker parts of the wheel. In some French clocks +the teeth of the dead scapewheel are accordingly made with +a kind of lump at the end; but this wastes more space in +the clearance or drop, and it is never done in English clocks, +so far as I have seen; nor do I know anything that will +answer---except putting on fresh oil when it is wanted. Dirty +oil should always be cleaned off before putting fresh oil on. +When it has got very thick it sometimes requires soda in +warm water to remove it. +%-----File: 305.png-------------------------------------------- +%-----Folio: 290----------------------------------------------- + + + + +\chapter{WATCHES AND CHRONOMETERS.}\label{chap:WATCHES_AND_CHRONOMETERS.} +\phantomsection +\addcontentsline{toc}{section}{Watches and Chronometers.} + +The early history of watches\label{History_of_early_watches}\index{Watches!their early history} is no less obscure than that +of clocks, though many centuries later. Tradition assigns +the invention to the town of Nuremberg, in the fifteenth +century. According to a once famous book, Derham's +`Artificial Clockmaker,' of 1714, and Beckmann's `History +of Inventions,' they appear to have existed in the time +of our Henry VIII., and of Louis XI., of France, and +especially of the Emperor Charles V., who used to keep +many watches going, as near together as he could. Erasmus +had a watch given him by a Polish nobleman, early in the +sixteenth century. And by Queen Elizabeth's time they +had become pretty common, and are alluded to by Shakspeare +in \textit{Twelfth Night}---`I frown the while, and perchance wind +up my watch.' The London Company of Clockmakers was +incorporated in 1631; and not long after that, the invention +of the spring balance, the distinctive element of watches, +was contended for between Huyghens\index{Huyghens!theory of balance-spring for watches} and Dr.~Hooke\index{Hooke, inventor of the balance-spring of watches}, who +both claimed the invention of the pendulum for clocks +(see p.~\pageref{huyghens}). It seems clear that Hooke first enunciated +the discovery of the isochronism of springs in the short +sentence, \textit{Ut tensio sic vis;} or the force varies as the degree +of tension: which rule however we shall see presently has +two rather curious exceptions. + +\subsection[The main-spring]{The main-spring}\markboth{MAIN-SPRINGS.}{MAIN-SPRINGS.}\label{subsec:The_main-spring}\index{Mainspring of watches}\index{Watches!mainspring}\ of a watch is a thin ribbon of steel +coiled up in a barrel round a strong spindle, to which one +end of the spring is fixed, the other end being fixed to the +barrel. When it is wound up the coils lie close together +upon the spindle or arbor, and as the spring runs down, the +coils separate from the arbor, and lie close to the barrel. +The simplest construction, still used in most of the foreign +%-----File: 306.png--------------------------------------------- +%-----Folio: 291------------------------------------------------ +watches, is for the barrel arbor to be the winding arbor, +having a ratchet wheel squared onto it, held by a click on +the frame or plate of the watch, and the great wheel is on +the barrel itself; and in this case, as I explained at p.~\pageref{folio_145}, +with reference to spring clocks, no temporary maintaining +power `going\index{Maintaining powers of clocks or going barrels!going-barrel in watches} barrel' is required to keep the watch going +while you are winding it up. But it is obvious that as the +force of the spring is greater when it is tightly wound up +than when it is loose, the force of the train will be very +far from constant throughout the day, although that may not +affect the going of the watch from one day to another. On +the other hand, there is found to be a very singular exception +to that rule of Dr.~Hooke's, stated just now, inasmuch as +there is a position of the spring coiled in a barrel in this +way, in which there is no material variation of its force for +a few turns. And certainly some of the foreign watches +made in this way go very well. + +Even if a watch does go rather faster at one time of the +day than another (which it is not certain that such watches +do), it is of no consequence, provided they go uniformly +from day to day; and there has been strong testimony +published in the \textit{Horological Journal}, that they do, when +well made, of course. I have seen watches with tapered +main-springs (though the foreign ones are not tapered), in +which you could not perceive any difference in the force, by +the usual testing apparatus of a weighted lever, whether +the spring was wholly wound up or not. And if this is +so, the addition of any more machinery, being superfluous, +is mischievous, and only increases the expense and size of +\begin{figure}[!htbp] +\centering +\caption{\sc American Main-spring Barrel} +\includegraphics[width=0.6\textwidth]{images/fig59.png} +\label{fig59} +\end{figure} +the watch, and risk of the chain breaking, perhaps the most +common of all accidents. There is evidently a tendency +in watch-making now to dispense with such machinery, except +for marine chronometers, which are required to go uniformly +at all times of day, and not merely from day to day. +Accordingly, both in Switzerland and America, which are +%-----File: 307.png--------------------------------------------- +%-----Folio: 292------------------------------------------------ +gradually stealing away our common watch trade, as well as +that in many kinds of clocks, the fusee and chain (which I +will describe presently) are almost universally omitted.\index{Fusee of watches!often dispensed with} + +\begin{wrapfigure}{o}{155pt} +\centering +\caption{\sc American Watch} +\includegraphics[height=500pt]{images/fig60.png} +\label{fig60} +\end{wrapfigure} + +But in that case there is another risk of breaking, for +when the spring breaks, the barrel recoils violently from +the sudden removal of the pressure, and often breaks some +teeth of the great wheel fixed upon it. Partly to avoid +this, and also for general improvement in strength and +arrangement of the train, the American\label{uswatch}\markboth{AMERICAN MAIN-SPRING BARREL.}{AMERICAN MAIN-SPRING BARREL.} watches\index{American clocks!watches}, as made +by the \index{Howard@`Howard Clock Company,' of America}`Howard Company,' under a patent by a Mr.~Reed +of 1857, have the spring contained in an immovable barrel\index{American clocks!mainspring barrel}, +which is a solid part of the upper plate of the frame +(calling the dial side the +lower). The outer end of the +spring hooks to the barrel as +usual, and the inner end to +the winding arbor, on which +the great wheel rides, with a +spring maintaining power, just +like those of a clock described +at p.~\pageref{subsec:Harrison's_going_barrel}. For safety +also, the main-spring is held +by two clicks, much stronger +than the single one generally +put into fusee watches, and the maintaining spring is also +very strong. Fig.~\ref{fig59} is a plan of this, and fig.~\ref{fig60} a +section of the whole watch. It may be observed also that +a watch of this kind turns the same way in winding as +one with a fusee, whereas the common foreign watches turn +the opposite way: not that there is any real importance in +this, except that the absence of uniformity sometimes causes +people to wind a new watch forcibly the wrong way. + +To prevent that, Breguet invented what is called the tipsy +key\index{Breguet's tipsy key}\label{tipsy}\index{Tipsy winding-key}\markboth{TIPSY WINDING KEYS.}{TIPSY WINGING KEYS.}, not that that adjective belongs to the `winder,' in the +clockmaker's sense of a key, but in the more human sense. +%-----File: 308.png--------------------------------------------- +%-----Folio: 293------------------------------------------------ +The handle is connected with the pipe by a pair of ratchets, +which would be called \textit{clutches} in large machinery, which +which can pass each other one way, but not the other; and they +are kept together, and then hardly visible, by a spiral +spring, which gives way, and lets one pass over the other +if the handle is turned the wrong way. +The best shape for a winding key\index{Key!best watch}\index{Watch keys, best kind of}\index{Winding keys!for watches} is +like a pencil with a rough handle, to +enable you to twirl it more easily +between your fingers. You thereby +apply less force, and are less likely to +do mischief by wrong, or over winding; +and moreover you keep the watch +steady, instead of turning it in your +left hand, and agitating the balance at +every turn. + +If you compare figure~\ref{fig60} with \ref{fig61}, +you will see that in the latter, which +is the common English fusee and chain +watch, the third wheel of the train +has to be sunk in the plate below the +centre wheel, whereas in the American +watch (fig.~\ref{fig60}) it stands free and +clear. There are a few other things in +this arrangement which had better be +postponed till other parts of the watch +have been described, and we will +proceed with the description of the +common English watch construction, +and therein first of the + +\subsection[Fusee.]{Fusee.}\markboth{FUSEE.}{ENGLISH WATCH MOVEMENT.}\label{subsec:Fusee.}\index{Watches!fusee}\index{Fusee of watches}---That piece is a hollow-sided cone, which you +see in this picture of a chronometer or English watch movement, +with a chain round it and the barrel, and the +great wheel is no longer on the barrel, but on this conical +piece called the fusee. When the spring is wound up +%-----File: 309.png--------------------------------------------- +%-----Folio: 294------------------------------------------------ +and its force is greatest, the chain acts on the small end +of the fusee, and therefore with the smallest leverage; and +as the spring unwinds, the chain acts on a thicker part of +the fusee, and it can be, and in good watches is, so adjusted +that the force on the train and escapement is constant. It +was suggested by Mudge\index{Mudge!invented the lever escapement for watches}, the inventor of the lever escapement +in the form now used in 99 out of 100 English\index{English fusee watch} +watches, that the usual position of the chain is wrong: and +so it is; for you see in fig.~\ref{fig61} that it acts on the opposite +side of the fusee to the centre pinion, and consequently the +pressure and friction on the fusee pivots (which are necessarily +large ones) is the \textit{sum} of the force of the spring on the +fusee and of the great wheel on the pinion; whereas if the +\begin{figure}[htbp] +\centering +\caption{\sc English Fusee Watch} +\includegraphics[width=\textwidth]{images/fig61.png}\index{Watches!general construction} +\label{fig61} +\end{figure} +%-----File: 310.png--------------------------------------------- +%-----Folio: 295------------------------------------------------ +spring acted on the same side as the pinion, it would only +be the \textit{difference}. I confess I know no reason why the +common arrangement should be adhered to, except that it is +the common one, which is generally considered reason enough +for anything bad. + +The train of wheels\index{Train of wheels!in watches}\index{Wheels, numbers of teeth!in watches} in a watch is much the same as in a +clock except that the scapewheel is not the wheel which +turns in a minute and carries the second hand, but is another +faster wheel. In a pocket lever watch the balance generally +beats in $2$-$9$ths of a second, and in a chronometer\index{Chronometers} either in that +time or in $\frac14$~sec. The scapewheel generally has $15$ teeth, +and therefore turns in $6$~seconds, or something near it. In +a good lever watch the pinions are generally $7$, $8$, $8$, $10$, and +the wheels $63$, $60$, $64$, $75$; in a pocket chronometer the +pinions are $8$, $10$, $10$, $12$, and the wheels $80$, $75$, $80$, $72$; in +box\index{Box chronometer} or marine chronometers the numbers are still higher, the +pinions being $10$, $10$, $12$, $14$, and the wheels $80$, $80$, $90$, $90$. +Box chronometers are generally made to go rather more than +$2$~days, though they are wound up every day, and they have +a small hand on what is called the `up and down' circle in +the dial, indicating how far the barrel has run down. In +these watch trains it must be observed that where a slow +wheel has fewer teeth than a quick one, the teeth must be +larger, or the wheels could not be put into the frame. I +think no pinion so low as $7$ should be admitted, and I cannot +understand why $9$ should be a prohibited number in clocks +and watches, as it seems to be, or at any rate was until I +introduced it frequently in turret clocks. + +Common watches have the balance above the upper plate.\index{Watches!general construction} +What are called \textbf{three-quarter plate}\index{Three-quarter plate watches} watches have a large +piece of that plate cut away, and the balance lies about level +with the rest of the plate, and most of the wheels have their +upper pivots in cocks screwed to the lower plate. This +saves thickness in the watch. + +\subsection[Winding stops.]{Winding stops.}\markboth{WINDING STOPS.}{WINDING STOPS.}\label{subsec:Winding_stops.}\index{Stop, winding, of watches}\index{Watches!winding-stops}\index{Winding stops!for watches}---A watch, or a spring clock, with a +%-----File: 311.png--------------------------------------------- +%-----Folio: 296------------------------------------------------ +fusee, is stopped from being overwound by a long tooth which +you see in fig.~\ref{fig61}, sticking out from the thin end of the +fusee. There is a spring lever with a hook fixed to the +frame with a little play on its pivot, so that when the chain +comes to that end, or the fusee is full, it pushes the lever +just far enough for its hook to catch the tooth, and so stops +the winding. In foreign watches without a fusee, a thing +called the \textit{Geneva stop}\index{Geneva stop}\index{Stop, Geneva} is used: it consists of a small wheel +on the barrel-arbor, with only one tooth in it, and the rest +of the circumference filled up blank; this tooth works into +the teeth of another loose wheel, with the hand on it in +fig.~\ref{fig62}, which has only as many teeth as the turns that the +barrel has to make in winding, and has also a blank space in +its circumference. The one-toothed wheel turns the loose +wheel through the space of one tooth for every turn of +the barrel, and when those teeth are all past, the one-tooth +jams against the blank in the loose wheel and lets the barrel +turn no more, and so stops the winding. These two wheels +are above the upper plate. The same thing might be put +on a fusee arbor, but the spring stop is preferred. + +\begin{figure}[htbp] +\centering +\caption{\sc Up and Down Dial} +\includegraphics[width=0.7\textwidth]{images/fig62.png} +\label{fig62} +\end{figure} + +\subsection[The `up and down dial,']{The `up and down dial,'}\markboth{THE `UP AND DOWN DIAL,'}{THE `UP AND DOWN DIAL,'}\label{subsec:The_`up_and_down_dial,'}\index{Up@`Up and down' dial}\ just now described, on the usual +construction, involves +an additional pair of +wheels. But Mr.~A.~L.~Dennison\index{Dennison, A.~L., of America!his improved Geneva stop} of +America, now settled +here, who is said to +have been the originator +of watch-making +by machinery (which +at last is taking root +here, at Messrs.~Rotherham's well-known +watch factory +at Coventry), patented a modification of the Geneva +%-----File: 312.png--------------------------------------------- +%-----Folio: 297------------------------------------------------ +stop which enables this kind of indicator to be added without +any more wheels. It consists merely of adding a short +arbor and hand to the loose or second or star wheel of the +Geneva stop which is applied to watches on the American +plan described at p.~\pageref{uswatch}. These pieces are shown in this +figure~\ref{fig62} of which the right hand part is the plan and the +other the section. This is not of so much value in a +common watch as in a chronometer, but is convenient +to be able to see at a glance whether you have wound +your watch up fully, without the risk of straining it in +trying. + +\subsection[The dial wheels]{The dial wheels}\markboth{WATCH DIAL WORK.}{WATCH DIAL WORK.}\label{subsec:The_dial_wheels}\index{Dial wheels!of watches}\index{Watches!dial wheels}\index{Wheels, numbers of teeth!for dials}\ of a watch are more like those of a +turret clock than of a house clock in the division of the +numbers of the teeth, as there is no occasion for the intermediate +wheel called $\mathrm{N}$ in pages~\pageref{fig25}, \pageref{fig34}, to turn in an +hour, as it does in house clocks to discharge the striking, +and even in silent clocks for uniformity. The hand sockets +are also only held on by friction without any spring. In +other respects the train of a watch is substantially the same +as that of a small clock until we reach the escapement, except +that there is one more wheel in the train, for the reason +given just now. The dial pinions in a good watch are $12$ +and $14$, and the wheels $42$ and $48$; in a box chronometer +they are $14$ and $18$, and $54$ and $56$. + +\subsection[Balance spring.]{Balance spring.}\markboth{BALANCE SPRING.}{BALANCE SPRING.}\label{subsec:Balance_spring.}\index{Balance spring}\index{Watches!balance-spring}---The rest of the machinery of a watch\index{Balance springs of watches} +only differs in size from that of a clock, until we come to the +escapement and the balance. We shall consider the various +escapements presently, but the object of them all is the same +as in clocks, to produce an escape of teeth by the vibration +of a balance, the time of which depends on its own moment +of inertia and a coil of very thin steel wire called the balance +spring, and sometimes popularly the hair-spring from its thinness, +and sometimes (very absurdly) the pendulum-spring, +though it is of the very essence of a pendulum to act solely +by gravity and the essence of a balance to be free from the +%-----File: 313.png--------------------------------------------- +%-----Folio: 298------------------------------------------------ +action of gravity, or else the `balance' is not balanced and +the watch will go differently in different positions. The +spring by which a pendulum is hung produces no sensible +effect on its time, and is only used to avoid the friction +any other mode of suspension. + +The balance-spring is fixed at its outer end to a stud in +the watch, and at its inner to the balance arbor or staff +at the neutral position of the spring the balance is at the +middle of the escape. In some kinds of escapements therefore +the balance cannot stand still if the watch is wound up; +and in all of them the spring tends to bring the balance back +again after it has gone a certain distance, depending on the +force of the escapement and the cleanness of the pivots and +teeth on one hand, and the strength of the spring on the +other, and then the balance swings an equal distance beyond +zero the other way. Whereas in the original clocks with a +balance but no spring (p.~\pageref{sec:BALANCE-WHEEL_ESCAPEMENTS.}) it was only the recoil of the +escapement that brought the balance back again, and such a +balance could not have been used with any kind of dead +escapement, because it would never have returned. Moreover, +considering that a pendulum moves by gravity, through +an arc of only $4^\circ$ or $5^\circ$ with a variation never amounting +to $30'$ in a good clock, while the balance swings independently +of gravity\label{free} through an arc of sometimes $400^\circ$ and +sometimes no more than $100^\circ$, it is evident that a watch +escapement must be a very different thing from that of a +clock. + +When I say that a balance is independent of gravity, you +must remember the distinction between mere mass, which +we denoted by the letter $\mathrm{M}$ in treating of pendulums, and +mass acting as a force by means of its weight, \textit{i.e.}\ by the +earth's attraction, which we called $\mathrm{M}g$. The mass and the +moment of inertia of a balance have quite as much to do +with its motion as they have in a pendulum, but the force +which makes it vibrate or return from the impulse given in +%-----File: 314.png--------------------------------------------- +%-----Folio: 299------------------------------------------------ +the escapement is not gravity, which must be entirely excluded, +for the reason just now given. It was to this +balance spring that Hooke's law of the force varying as the +tension or space moved through (which always implies +\markright{NOT ALWAYS ISOCHRONOUS.}isochronism) was meant to apply, and does apply pretty +generally; but not invariably, because it is found that not +every length of a given spiral spring is quite isochronous, but +only certain lengths, which have to be determined by experiment. + +The time of vibration therefore depends on the moment of +inertia of the balance directly and the force of the balance +spring inversely; and in a given spring the force varies +inversely as the length. Consequently you can quicken the +vibration either by reducing the moment of inertia or the +size of the balance, or by shortening the effective length of +the spring. The latter method is used in all common watches, +and the former in chronometers and watches in which extreme +accuracy is aimed at. + +\subsection[Regulation]{Regulation}\markboth{REGULATION OF WATCHES.}{REGULATION OF WATCHES.}\label{subsec:Regulation}\index{Regulation!of watches}\index{Watches!regulation}\ of a common watch, to make it go faster or +slower, is done by a lever or index $\mathrm{SPT}$ (fig.~\ref{fig63}), which +turns on a ring set on the watch plate (through which the +\textit{staff} or arbor of the balance has to pass from the inside to +the outside of the watch frame), and it has two small pins at +$\mathrm{P}$ which embrace the spring, one end of the spring being +fixed to the frame at $\mathrm{R}$ and the other end to the balance at +$\mathrm{S}$\@. It is evident that as you turn the regulator to the right +you shorten the length of the acting part of the spring and +so make the vibrations faster, and if you move it to the left, +slower. If the regulator has been moved as far toward \textit{fast} +as it can go and the watch still looses, the spring must +be taken up altogether at $\mathrm{R}$; and then in order that the +balance may still be in the middle position of the escapement +when the spring is neutral, the piece $\mathrm{S}$ by which +it is attached to the balance is itself a ring which fits +tightly round the staff and can be moved when the balance +%-----File: 315.png--------------------------------------------- +%-----Folio: 300------------------------------------------------ +is taken out, to alter the position and length of the +spring. + +\begin{figure}[ht!bp] +\centering +\caption{\sc Regulation of Watches} +\includegraphics[height=300pt]{images/fig63.png} +\label{fig63} +\end{figure} + +It must have occurred to everybody who has had to regulate +a good watch for very small errors that there is a want +of some better method than the common one both for moving +the regulator and for seeing how much you move it. Occasionally, +but very +rarely, the index is +made to move by a +tangent screw\index{Timing screws}, turnable +by the watch +key, and I am surprised +that good +watches are not always +made in this +way. But I have +lately seen another, +in the American +watches referred to +at p.~\pageref{subsec:The_`up_and_down_dial,'}, which is +still more delicate, +and also easier to +make. The index +is resisted one way +by a slight spring +fixed to the plate, +and a common screw, in the same direction as a tangent +screw, acts upon it the other way. This avoids the shake +of a tangent screw, and you know that however little you +turn the screw you move the index some distance. In +these cases you must learn by trial how much half a turn +of the screw accelerates or retards the watch per day, and +after that you can regulate it to the utmost nicety---so far +as its errors are amenable to regulation. + +Another method suggested by the late Mr.~Dent\index{Dent, E.~J.!regulation of watches} is shown +%-----File: 316.png-------------------------------------------- +%-----Folio: 301----------------------------------------------- +in fig.~\ref{fig63}. Instead of being made with a point, the index +has fine bevelled edges lying quite over the index plate, +which is to be made with oblique divisions and two or three +cross lines, like the scale generally engraved on a dividing +rule: this enables the eye to measure much smaller divisions +than could be either seen or cut upon a degree plate of the +common form. But this does not remove the difficulty of +moving it a very little, and the screw is manifestly better. +The old plan\index{Regulation!of watches!the old plan} of a segment of a wheel turned by a pinion +with the index fixed to it +(fig.~\ref{fig64}) is better than +the common one, and I +do not know why it is +disused. +\begin{figure}[htbp] +\centering +\caption{\sc Old Plan} +\includegraphics[width=0.7\textwidth]{images/fig64.png}\index{Regulation!of watches!the old plan} +\label{fig64} +\end{figure} + +This mode of regulating +by shortening the +effective length of the +spring is not accurate +enough for chronometers +for another reason, viz.\ that +all lengths of the +spring are not quite isochronous for different arcs of vibration, +and therefore if you have got the spring adjusted +for an isochronous length, it will become unisochronous +if you shorten it a little; and moreover a spring moving +in that way, partly held fast at the ends and passing +loosely through curb pins at $\mathrm{P}$, is not so steady as +one held fast only at the ends. Chronometer balances +are therefore regulated by \textit{timing-screws}, which are screws +with heavy heads set in the rim of the balance: screwing +them in of course diminishes the moment of inertia +and quickens the balance, and vice vers\^a. In chronometers +also the spring is generally made as a cylindrical spiral and +not a flat one. Some chronometer makers have doubted +whether there is any advantage in the cylindrical form, but +%-----File: 317.png-------------------------------------------- +%-----Folio: 302----------------------------------------------- +it is now almost universally adopted, and therefore I +suppose the balance of experience is in favour of it. It is +now said that the best form is one that combines both +or a cylinder returned into a flat spiral both at top and +bottom. + +\markright{FORMS OF BALANCE SPRINGS.}But the quality of the spring is probably of more importance +than its form. A medal of the highest class was +awarded in the 1851 Exhibition to M.~Lutz\index{Lutz of Geneva, his balance springs} of Geneva for +some balance springs, made by a secret method, which bore +being pulled out nearly straight, and laid on a hot plate +without suffering any change of form, which was not the +case with any others which were then submitted to us. +I see that aluminium bronze has been successfully used in +Saxony for balance springs\index{Aluminium bronze!balance springs}; but I know nothing more of +them. + +\subsection[Glass balance springs]{Glass balance springs}\markboth{GLASS BALANCE SPRINGS.}{GLASS BALANCE SPRINGS.}\label{subsec:Glass_balance_springs}\index{Balance spring!glass}\index{Glass balance springs}\index{Watches!glass balance springs for}.---These were suggested by +Berthoud but have been very little used. The rate of a +chronometer with a glass spring, which Dent sent to Greenwich +many years ago, was very good; and they have the +advantage of varying so much less than steel or any other +metal in elasticity that they require very little compensation +of the balance. I do not know why they have not been more +used, unless it be from the fear of breaking them when anything +is done to the watch\index{Balance springs of watches}. It appears that with them, as +with steel springs, the watch always gains after a new spring +has gone a few months, as if it acquired more elasticity by +working; and this is analogous to what takes place in bells, +which become more sonorous, \textit{i.e.}\ more elastic, after a few +months ringing. + +\subsection[Timing for position.]{Timing for position.}\markboth{TIMING FOR POSITION.}{TIMING FOR POSITION.}\label{subsec:Timing_for_position.}\index{Timing screws!timing for position}\index{Watches!timing for position}---As a watch sometimes lies flat on +a table, and sometimes vertical, and not always in the same +position in your pocket, it is necessary that the balance +should keep the same time in all positions, both horizontal, +and with either iii, vi, ix, or xii, upwards. With a heavy +balance it is impossible to get the same arc of vibration when +%-----File: 318.png-------------------------------------------- +%-----Folio: 303----------------------------------------------- +\begin{figure}[htbp] +\centering +\hypertarget{fig65}{\caption{\sc Box Chronometer in Gimbals}} +\includegraphics[width=0.6\textwidth]{images/fig65.png} +\label{fig65} +\end{figure} +the watch is vertical and horizontal, because the friction of +the pivots is much greater when they are acting on their +sides than on the point of one of them. If you take a small +chimney-piece clock with a balance and hold it sideways so +that the balance becomes vertical and its staff horizontal, +you will see the vibration diminish very much, and then the +least want of isochronism +in the spring will set the +rate wrong. \markboth{BOX CHRONOMETER IN GIMBALS.}{BOX CHRONOMETER IN GIMBALS.}Marine chronometers\index{Chronometers}\index{Marine chronometer}, +which are only +very large watches, are +therefore always set horizontally +in a box, in \textit{gimbals}\index{Gimbals, chronometer}, +as in \hyperlink{fig65}{this drawing}, +which keep the watch horizontal, +even when the box +is tilted by the ship: if the +box is tilted at $\mathrm{E}$ or $\mathrm{W}$, it +turns on the outer pivots $\mathrm{NS}$ of the gimbal ring, and +if the $\mathrm{N}$ or $\mathrm{S}$ side is tilted, then the box and ring together +turn on the inner pivots at $\mathrm{W}$ and $\mathrm{E}$ leaving the watch +steady. The level of the pivots should be only just +enough above the centre of gravity of the watch to +make it keep its level, for if the c.g.\ is much below the +points of support the watch will swing when they are +moved. + +\subsection[Ship time-pieces.]{Ship time-pieces.}\markboth{SHIP TIME-PIECES.}{SHIP TIME-PIECES.}\label{subsec:Ship_time-pieces.}\index{Ship time-pieces}\index{Timepieces, ship}---There is another kind of ship-clocks +made to hang against a wall, not pretending to the accuracy +of chronometers, but a very neat and convenient and cheap +form of time-piece for other places as well as ships. They +are a large $8$-day lever watch with the balance staff and the +scapewheel arbor vertical, and therefore the third wheel in +the train a \textit{contrate} or crown-wheel as at p.~\pageref{crown}. Like other +things, they are of very different qualities with the same +%-----File: 319.png-------------------------------------------- +%-----Folio: 304----------------------------------------------- +external aspect. They do not work well without a fusee, +though many of them are made so for cheapness and the +contrate wheel arbor ought to have an end-stop to the pivot +which tends to push away from the scapewheel pinion and +work upon its shoulders, and the two vertical arbors +ought still more to have their lower pivots resting on stops, +either of hard steel or jewels, to take the weight and friction +off their shoulders. End stops are sometimes put to +the horizontal arbors of highly finished clocks; but as there +is no end pressure on them, I think it is hardly worth while +there, though it is in the two cases I have just mentioned. +\markboth{CHIMNEY-PIECE CLOCKS.}{CHIMNEY-PIECE CLOCKS.}Chimney-piece\index{Chimney-piece clocks} clocks with balances (the only ones which +housemaids will allow to go, unless they are too heavy to +move) ought always to have them compensated, for otherwise +the great changes of temperature to which they are +exposed will make it impossible for them to go right, as I +shall now explain. + +\section{COMPENSATION OF BALANCES.}\label{sec:COMPENSATION_OF_BALANCES.}\index{Balances, compensation of}\index{Compensation of balances!common} +\index{Watches!compensation of balances}\markboth{COMPENSATION OF BALANCE.}{COMPENSATION OF BALANCE.} +Watch balances, or rather the springs on which their time +depends, vary much more with heat and cold than pendulums, +and therefore compensation is still more essential if you +expect great accuracy of rate; and if it were not that +watches are kept at a pretty even temperature during the day +by near contact with men's bodies, their variations in hot and +cold weather would be enormous: women's watches being +generally worn loose, go worse than men's for that reason. +A small portable clock with a balance uncompensated goes +twenty times worse than the commonest pendulum clock. +The balance itself also expands a little with heat, as a pendulum +does, but the effect of that is small compared with the +variation of the force of the spring. It appears from some +experiments made by Berthoud in 1773, and others by +Dent communicated to the British Association in 1833, +%-----File: 320.png-------------------------------------------- +%-----Folio: 305----------------------------------------------- +which nearly agreed, that the loss of time due to expansion +of the balance for a rise of temperature from $32^\circ$ to $100^\circ$ is +not a $5$th of that due to the loss of elasticity and elongation +of the spring, and that the two together amount to no less +than $6\frac12$~minutes a day; and a variation of $33^\circ$ would produce +a variation of an hour in $3$~weeks; whereas we saw that +a common iron wire pendulum would only lose $10$~sec.\ a day +for such an increase of heat, and a wooden one not more +than $1\frac12$~seconds. + +The first watch compensation was made by Harrison\index{Harrison!inventor of watch compensation}\label{harrleroy}, who +has been mentioned several times already as the inventor of +various horological improvements; and he received the first +parliamentary reward for improvements in chronometers +with a view to finding longitude at sea. His method is quite +disused now, and indeed he was himself dissatisfied with it, +and suggested that the compensation ought to be done in the +balance and not by any contrivance for altering the effective +length of the spring, which was the principle of his own and +all the early compensations. For this purpose he put the +curb pins ($\mathrm{P}$ in fig.~\ref{fig63} p.~\pageref{fig63}) on a compound bar, of which +one side was made of brass and the other of steel. As +brass expands more than steel, the bar bends to the steel side +when the heat increases, and thus the curb pins were moved +along the spring, as they are by hand in the common regulator. +It is not necessary to dwell on any of the various modifications +of this plan, as they are all now abandoned for the +balance of compound bars, which appears to have been first +made, as well as a mercurial compensation balance, by Julien +le Roy, a celebrated French clockmaker, but afterwards +much improved by the first Arnold, Earnshaw, and various +other English makers. A great variety of these early contrivances +may be found in Rees's Cyclop\ae dia by those who +are curious about them. + +The plan\markright{COMMON METHOD.} which is now always used, with some modifications +in certain cases, as I shall explain afterwards, is +%-----File: 321.png-------------------------------------------- +%-----Folio: 306----------------------------------------------- +\begin{figure}[htbp] +\centering +\hypertarget{fig61}{\caption{\sc Common Method of Compensation}} +\includegraphics[width=0.5\textwidth]{images/fig66.png} +\label{fig66} +\end{figure} +exhibited in \hyperlink{fig61}{this drawing}: $tat^\prime$ is the main bar of the +balance, with the timing screws $tt^\prime$ for regulation at the ends; +and $t b, t^\prime b^\prime$ are two compound bars, of which the outside is +brass and the inside steel, carrying weights $b b^\prime$ which may +be screwed on at different places. As the heat increases, +those bars with their weights +bend inwards and diminish +the moment of inertia of the +balance. The only secure +way of making these balances +is to cut them out of a solid +steel disc round which melted +brass is run which \textit{brazes} itself +fast on. This plan of uniting +the metals was introduced by +Earnshaw, it appears, besides +various other improvements +in the construction of chronometers, +in which very little alteration has been made in +nearly 100 years. The principal expense of a really compensated +balance is in the time required for adjusting it, +which can only be done by trial. Many watches are sold +with balances only constructed for compensation but never +adjusted, and therefore under or over compensated, or with +no regularity in the action of the compensation; and some +still worse, with a mere sham compensation, resembling a +compensated balance only in appearance, sometimes not even +cut through. + +\subsection[The chronometrical thermometer]{The chronometrical thermometer}\markboth{THE CHRONOMETRICAL THERMOMETER.}{THE CHRONOMETRICAL THERMOMETER.}\label{subsec:The_chronometrical_thermometer}\index{Chronometrical thermometer}\index{Thermometer, chronometrical}\ is simply a watch +with a balance compensated the wrong way, \textit{i.e.}\ with the +brass inside and the steel outside, so as to increase the +retardation from heat and the acceleration from cold. The +use of it is to measure the quantity of heat or cold received +during any given period without recording the actual degree +of heat or cold at any particular time. It is therefore +%-----File: 322.png-------------------------------------------- +%-----Folio: 307----------------------------------------------- +used at the Greenwich Observatory for trying the rates of +compensated chronometers under great variations of temperature. + +\subsection[Secondary compensation.]{Secondary compensation.}\markboth{SECONDARY COMPENSATION.}{SECONDARY COMPENSATION.}\label{subsec:Secondary_compensation.}\index{Chronometer escapement!secondary compensation}\index{Compensation of balances!secondary}\index{Secondary compensation!theory of}\index{Watches!compensation of balances!secondary}---When chronometers had +brought to great perfection, so as to go with scarcely +any sensible variation of rate while they were kept within +moderate limits of temperature, it was observed that they +always lost if the temperature either rose or fell beyond +those limits; and on the other hand, if the compensation +adjusted for two extreme temperatures, then the watch +always gained at mean ones. I believe it has never +been disputed that old Mr.~Dent was the first person to +explain the cause of this error, in the \textit{Nautical Magazine} in +1833; and he gave the following illustration of it: The +diminution of the force of the spring proceeds uniformly in +proportion to the increase of heat, and may therefore be +represented by a straight line inclined at some angle to +another straight line which is divided into degrees of temperature. +But the inertia of a compound balance such as I have +described cannot be made to decrease quite as fast as the +heat increases; and therefore its rate of variation can only +be represented by a curve, and can only coincide with the +straight line representing the variation of force of the spring +in two points, either the two extremes, or two means, or one +mean and one extreme point: in other words, the compensation +can only be exact for some two temperatures for which +you may choose to adjust it. + +The same thing may be shown mathematically\label{2ndmath}\markboth{MATHEMATICAL THEORY OF THE SECONDARY COMPENSATIONS.}{MATHEMATICAL THEORY OF THE SECONDARY COMPENSATIONS.} as follows: +Let $r$ be the distance of the compensation weights from the +staff or axis of the balance, and we may call them both together +$\mathrm{M}$, and for this purpose we have nothing to do with the rest +of the balance. Let $dr$ be the increase of distance of the +weights for some given decrease of heat. Then the new +moment of inertia of the balance will be $\mathrm{M}(r^2 + 2r dr + dr^2)$, +and the ratio of the new inertia to the old will be +%-----File: 323.png-------------------------------------------- +%-----Folio: 308----------------------------------------------- +$1+\frac{2dr}{r}+(\frac{dr}{r})^2$; and now the term $(\frac{dr}{r})^2$ is too +large to be disregarded as it may be in the similar formula +for pendulums, because $dr$ must be much larger in proportion +to $r$ than it is in a pendulum, as we have seen already. Again, +the ratio of the moment of inertia for an equal increase of +heat to its amount of inertia in the middle state will be +$1-\frac{2r}{r}+(\frac{dr}{r})^2$, assuming that equal successive increments +of heat produce equal variations of $r$, which however +is not quite the case, as it is in pendulums. Consequently +the increase of moment of inertia, for a given rise of temperature +is less than its decrease for an equal fall by $2(\frac{dr}{r})^2$, or +the compensation fails to that extent in one of the three +states of cold, middle, or hot temperature. + +The correction of this error is called the secondary or +auxiliary compensation, and it is the point to which I think +every chronometer invention for the last thirty-five years +has been directed, chiefly because the chronometers are now +exposed to such extreme and unnatural variations of temperature +in the Greenwich trials\index{Greenwich!trials of chronometers at}---nearly as much as $100^\circ$, that +the attention of the makers seems to be withdrawn from +everything else; and every year's tables display an +increased number of contrivances for this purpose, but +no increased accuracy in the recorded rates of the best of +them. + +\subsection[Greenwich trials.]{Greenwich trials.}\markboth{GREENWICH TRIALS.}{GREENWICH TRIALS.}\label{subsec:Greenwich_trials.}\index{Chronometer escapement!secondary compensation!trials at Greenwich}---When the rates of some chronometers +were returned to Greenwich after one of the Arctic +expeditions, the Astronomer Royal reported that they had +been \textit{kept so warm} that they afforded no test of the relative +value of the different modes of compensation employed in +them. I think it might also have been inferred from that +fact that the trials at home in such unnatural variations of +temperature are only calculated to test a single and comparatively +%-----File: 324.png--------------------------------------------- +%-----Folio: 309------------------------------------------------ +immaterial quality of the chronometers, and to +frighten away from public trial every invention for the +general improvement of the instrument in other respects. +Any nautical man who wants chronometers for real use +would rather have one that would not vary a second a +week in such temperatures as it is likely to be exposed to +in any voyage in a ship's cabin, than one which may possibly +go better than it at some extreme and improbable variation +of temperature, but worse in all ordinary and probable +variations. + +Mr.~Hartnupp's report of the trials of above 1000 chronometers +at Liverpool\index{Chronometer escapement!secondary compensation!trials at Liverpool}, in 1872, says that the best of them, +with the ordinary compensation, generally gain $6$~sec.\ a day +more at $70^\circ$ than at $55^\circ$ or $85^\circ$, if the compensation is +adjusted for these two temperatures, and that those which +have the same rate at $55^\circ$ and $70^\circ$, or at $85^\circ$ and $70^\circ$, +lose $1.5$ sec, for a change of $15^\circ$ below or above the +temperatures for which they are compensated. He adds, +that the connection between rate and temperature remains +constant for a long time. + +\subsection[Eiffe's compensation balance]{Eiffe's compensation balance}\markboth{EIFFE'S COMPENSATION BALANCE}{EIFFE'S COMPENSATION BALANCE}\label{subsec:Eiffe's_compensation_balance}\index{Compensation of balances!Eiffe's}\index{Eiffe's compensation balance}\index{Secondary compensation!inventions for|(}\ was the first invention +for this purpose which was disclosed; and a reward of 300\textit{l}.\ was +therefore given him by the Admiralty on the recommendation +of the late Astronomer Royal. At the very time while +this invention was under trial at Greenwich, Mr.~Molineux +took out a patent for one precisely similar; which is only +one of the usual proofs that when the time is ripe for an invention, +it is almost sure to be made by several people at once, +of whom one gets rewarded---or suffers, by a patent. Mr.~Eiffe described several methods for effecting the secondary +compensation; the one which he chiefly relied on, and +which has been followed by some other makers, is a balance +in which the compensation bar, or a screw in it, is made to +reach another in the form of a spring with a small weight +upon it, when it has bent inwards to a certain extent, and it +%-----File: 325.png--------------------------------------------- +%-----Folio: 310------------------------------------------------ +carries that other with it, so as to diminish the moment of +inertia still more than the single compound bar. It seems +an obvious objection to this, that it is discontinuous, \textit{i.e.}, that +the secondary compensation comes into action suddenly at +one change of temperature only. Nevertheless it appears to +answer as well as or better than many others which are free +from that objection. + +\begin{figure}[htbp] +\centering +\caption{\sc Dent's Balance} +\includegraphics[width=0.7\textwidth]{images/fig67.png} +\label{fig67} +\end{figure} + +\subsection[Dent's balance.]{Dent's balance.}\markboth{DENT'S BALANCE.}{DENT'S BALANCE.}\label{subsec:Dent's_balance.}\index{Compensation of balances!Dent's}\index{Dent, E.~J.!compensation balance}---That objection was obviated in +Dent's balance, of which +also there were several +forms: this is the one which +he proposed as the best +in his pamphlet on the +subject. The flat cross-bar +$rr'$ is itself a compensation +bar with the brass +below and the steel above, +so that if the compensation +weights $bb'$ were set upon +upright stems from the bar +they would be bent in towards +the axis when the +heat increases. But they +are in fact set upon some other bent compensation bars $st$, +$st'$, of which the brass is inside the bend, and consequently +the weights approach the axis more than if they were set on +stems of fixed length; and as they can be set anywhere on +the stems the compensation is thus adjustable. The reason +why the bent bars stand outwards across the principal bar +is to leave room for the balance spring, which is attached +to the smaller cross-bar $d$ shown in fig.~\ref{fig67}, in which +spring is omitted to avoid confusion. This compensation +has the advantage of being continuous. + +Loseby's\index{Compensation of balances!Loseby's}\index{Loseby's!balance for watches} balance was an ingenious alteration of a previous +mercurial compensation of Le Roy into this form. +%-----File: 326.png--------------------------------------------- +%-----Folio: 311------------------------------------------------ +$\mathrm{DD}$ are the weights on the usual compound bars $\mathrm{BB}$, for +the primary or principal compensation. Besides, there are +two small bent thermometers with the bulbs at $\mathrm{F}$, and the +tubes at $\mathrm{E}$, into which the mercury runs as the heat increases, +and so more of the weight of the balance is carried inwards than +is due to the mere bending of the primary bars. The tubes +are sealed with a little air included. $\mathrm{CC}$ are the usual timing +screws independent of the compensation. The action +\hyperlink{fig68}{here} is equally continuous with Dent's, and Loseby's +chronometers generally got a very high place in the Greenwich +lists during the seven years in which he sent them +there; and he would have done wisely to be content with +that success. But he applied no less than four times for a +reward for his invention, and the Astronomer Royal four +times reported against his claim, on the ground that his +balance was neither the first to do what was wanted, nor +was proved to be the best. Mr.~Loseby then sent to the +Admiralty a long memorial, containing a comparison\markboth{LOSEBY'S V. DENT'S COMPENSATION.}{LOSEBY'S V. DENT'S COMPENSATION.} of the +\begin{figure}[htbp] +\centering +\hypertarget{fig68}{\caption{\sc Loseby's Balance}} +\includegraphics[width=0.7\textwidth]{images/fig68.png} +\label{fig68} +\end{figure} +%-----File: 327.png--------------------------------------------- +%-----Folio: 312------------------------------------------------ +rates of his chronometers with others in the Greenwich lists +for 5 years, to prove that his was the best; and the last +horological paper to which old Mr.~Dent put his hand before +his death was a counter statement, showing that a proper +analysis of those very trials exhibited Loseby's compensation +to be decidedly inferior to Dent's own, and not at +all superior to Eiffe's or several others of which the constructions +were not disclosed. + +After his death in 1853 the controversy was carried on in +the Society of Arts' Journal by Mr.~Loseby and me, as he +had assumed that I wrote Dent's paper for him, and so I +extended the analysis to the whole seven years during which +Loseby's chronometers were at Greenwich, and with the +same result. The nature of the analysis is simple enough, +viz.\ this: If you divide the $6$~months of published rates +in each year into $3$~periods, one containing all the coldest +weeks, another all the hottest, and another the mean temperature +weeks---and whether you make the division into equal +periods, or into two periods of $6$~weeks of extreme temperatures, +and $13$ or $14$ of mean, or make it just where the +register shows that the greatest breaks of temperature actually +occurred---the result was always the same, that Loseby's +compensation was the most successful in only one of the +seven years, three other makers' each once, and Dent's three +times. Sir G.~Airy, the Astronomer Royal, was therefore +clearly right in rejecting Mr.~Loseby's claim to a public +reward, whatever may have been his personal skill in +preparing a single chronometer for trial in a year, and so, on +the whole, getting a high place in the list. + +\subsection[Kullberg's]{Kullberg's}\markboth{KULLBERG'S COMPENSATION BALANCE.}{KULLBERG'S COMPENSATION BALANCE.}\label{subsec:Kullberg's}\index{Compensation of balances!Kullberg's}\index{Kullberg's!compensation balance}\ compensation balance has been so successful in +the Greenwich trials that I add a description of it to those +mentioned before. The drawing in the \hyperlink{fig69}{next page} shows its +shape, but not the peculiarity of its construction; for the +brass is attached to the top of the cross-bar $\mathrm{AC}$, but to the +bottom of the curved rims $\mathrm{CB}$, the effect of which is that the +%-----File: 328.png--------------------------------------------- +%-----Folio: 313------------------------------------------------ +ends of the cross-bar are carried downwards by heat, and the +weights $\mathrm{P}$ upwards, and more inwards than if the cross-bar +did not bend, as it does also in Dent's balance; $\mathrm{DD}$ +are the timing screws. The principle of it is better illustrated +by the second sketch, of half the balance seen edge-ways +and with its action enormously exaggerated. The thick +line is the steel and the thin one the brass. The principle of +its action is the same as Dent's, but it is simpler and stiffer +I doubt whether it is necessary to have a curved rim at all, +and whether sufficient compensation could not be got by +making the pieces $\mathrm{CB}$ straight, each lying close by the staff +$\mathrm{AE}$\@. Mr.~Kullberg has also made balances of the common +form but with much wider rims hollowed outwards, looking +like a pulley with a very flat groove. The expansion sideways +of the outer brass rim tends to flatten it, and so makes +it easier to bend inwards under the expansion of the brass +end ways; but he says he has not yet succeeded in getting +sufficient secondary compensation in this way; as was the +case also with +\begin{figure}[htbp] +\centering +\hypertarget{fig69}{\caption{\sc Kullberg's Compensation Balance}} +\includegraphics[width=\textwidth]{images/fig69.png} +\label{fig69} +\end{figure} + +\subsection[Dent's prismatic balance.]{Dent's prismatic balance.}\markboth{DENT'S PRISMATIC BALANCE.}{DENT'S PRISMATIC BALANCE.}\label{subsec:Dent's_prismatic_balance.}\index{Compensation of balances!Dent's prismatic}\index{Dent, E.~J.!prismatic balance}---This was also invented by +the first Mr.\ Dent and improved by the second, for the +purpose of effecting the primary and secondary compensation +together, or a sufficiently near approximation to it, by a +simpler construction than any of the others. The steel part +of the balance is the usual flat bar; but the brass is an obtuse-angled +%-----File: 329.png----------------------------------------------- +%-----Folio: 314-------------------------------------------------- +bent prism. This invention was founded on the +fact that a bar of that form bends more easily from the angle +than towards it, and therefore the compound bar bends +in more easily and farther than it does outwards, +for equal degrees of heat. It has the +advantage of making the balance stronger also. +It was not supposed that this would make the +secondary compensation complete for the extreme temperatures +of the annual Greenwich trials; but there seems no doubt +that it is better than the common flat bar compensation. + +\begin{wrapfigure}{O}{0.25\textwidth} +\centering +\caption{\sc Dent's Prismatic Balance} +\includegraphics[width=0.25\textwidth]{images/fig70.png} +\label{fig70} +\end{wrapfigure} + +There have been sundry other inventions for secondary +compensation\index{Balances, compensation of}. Indeed nearly every maker in the Greenwich +lists professes to have one of his own. The late Astronomer +Royal invented one in 1875 and went so far as to get an +Admiralty order that it should be used; but the trade pronounced +it a failure, and the order was first suspended and +then withdrawn. \markboth{CHRONOMETERS INFERIOR TO CLOCKS.}{CHRONOMETERS INFERIOR TO CLOCKS.}It is difficult to compare the general +performance of the best clocks with that of chronometers +under severe trials. The best recorded rates of chronometers\index{Chronometers!rate of}\index{Rate!of watches} +seem to be a daily variation of not more than half a second +during the time of trial; which, however, might come to a +good deal if continued. I am inclined to say that the rate of +a very good watch in ordinary use, and a lever quite as much +as a chronometer according to my experience, is sometimes +nearly equal to that of the best clocks for some months +together. For ordinary use no secondary compensation is +at all necessary.\index{Secondary compensation!inventions for|)} + +\section{WATCH ESCAPEMENTS.}\markboth{WATCH ESCAPEMENTS.}{WATCH ESCAPEMENTS.}\label{sec:WATCH_ESCAPEMENTS.} +\index{Escapements of watches}\index{Watch!escapements|(} +There is a greater variety of escapements which may all +be said to be in use in watches than there is in clocks, +omitting in both cases merely fancy ones of which only a +few specimens have been made rather for show than for +use, and which I do not think it worth while to describe, +either for clocks or watches. +%-----File: 330.png--------------------------------------------- +%-----Folio: 315------------------------------------------------ + +\subsection[Vertical escapement.]{Vertical escapement.}\markboth{VERTICAL ESCAPEMENT.}{VERTICAL ESCAPEMENT.}\label{subsec:Vertical_escapement.}\index{Escapements of watches!vertical}\index{Vertical watch escapement!Gray's}% +---The original watch escapement, +which has remained in use for about two centuries, but is +almost gone, exactly corresponds to the old crown-wheel +escapement in clocks described at p.~\pageref{crown}. This figure~(\ref{fig71}) +shows the mode of arranging it in a watch. There are in +fact two crown wheels in it, for the wheel with its arbor +vertical, the minute wheel of the train, is one, and the +scapewheel itself is another. The plain rimmed wheel is the +balance. It has all the properties of the recoil escapements +in clocks, and is very inferior in accuracy to any of the others, +and now has hardly the advantage even of cheapness over +the lever, which is the standard English watch escapement. + +\begin{figure}[htbp] +\centering +\caption{\sc Vertical Escapement} +\includegraphics[width=0.7\textwidth]{images/fig71.png} +\label{fig71} +\end{figure} + +A very simple vertical escapement, \textit{i.e.}\ one involving a +crown wheel, was invented (or perhaps re-invented) for cheap +watches by the late Mr.~John Gray\index{Escapements of watches!Gray's}\index{Gray's vertical watch escapement}, a well-known dentist. +The teeth lie dead on a thick verge or cylinder except at +the moment when they pass through notches cut across it; +and they give an impulse in passing. It involves no more +friction than the horizontal escapement, the commonest in +foreign watches. The crown wheel prevents the watch +from being thin, but one which Mr.~Gray lent me for trial +was not thicker than most silver watches, and went very well. + +\subsection[Lever escapement.]{Lever escapement.}\markboth{LEVER ESCAPEMENTS.}{LEVER ESCAPEMENTS.}\label{subsec:Lever_escapement.}\index{Lever escapement}---This in its original form was +invented by Berthoud\index{Berthoud on escapements} about 100 years ago, and according +to the picture of it in Rees's Cyclop\ae{}dia it is identical in +%-----File: 331.png--------------------------------------------- +%-----Folio: 316------------------------------------------------ +all but the position of some of the parts with the rack-lever +escapement, of which Litherland of Liverpool used to be the +great maker: the first watch I ever had was one of that +kind. If you suppose the crutch of the dead escapement of +a clock to end in a piece of a wheel, of radius equal to the +crutch, and working into a pinion set on the arbor of a +balance, just like the regulator in fig.~\ref{fig64} at p.~\pageref{fig64}, that +is the rack-lever escapement. The objections to it are the +friction of the rack, \textit{i.e.}\ of the wheel and pinion, and the +dead friction on the pallets. + +These were almost entirely got rid of by the modification +of it which was invented by Mudge about thirty years afterwards, +and which used to be called the \textit{detached lever}, but is +now generally called the lever escapement simply, since the +rack has gone out of use; and the term `detached' is now +applied to another class of escapements. It is a curious +fact in the history of watchmaking, that a parliamentary +committee in 1793 thought fit to award to this Mr.~Mudge +(or his son for him) 3000\textit{l}, the same sum as Arnold and +Earnshaw had had from the Board of Longitude, in opposition +to the opinion of that Board, for a chronometer escapement +which was not worth a farthing, and indeed turned out +worth a good deal less than nothing to his son, who spent a +considerable sum in making them. However he well +deserved his 3000\textit{l\. }for the invention of this lever escapement, +of which 100 times more are now made in England +than of all the other escapements together, and which is +quite equal to the best in accuracy of performance. The +following is the construction of it (see \hyperlink{fig72}{next page}). + +The scapewheel and pallets are precisely those of a clock +dead escapement; but the pallets $\mathrm{AB}$ are set on a lever +which turns on their arbor $\mathrm{C}$ and has a notch at the end, +into which a pin $\mathrm{P}$ in a small disc on the verge of the +balance works, being in fact a single tooth of the old rack-lever +pinion. The teeth only just lock on the dead part of +%-----File: 332.png--------------------------------------------- +%-----Folio: 317------------------------------------------------ +the pallets, and the pin and the notch are so arranged that +as soon as the escape has taken place the pin slips out of the +notch, and so the balance is detached from the lever during +the remainder of its swing. When it comes back again the +pin re-enters the notch, moves the lever just enough to send +the tooth onto the impulse face of the pallets, and then the +scape-wheel acts on the lever and balance until that tooth +\begin{figure}[ht!bp] +\centering +\hypertarget{fig72}{\caption{\sc Lever Escapement}} +\includegraphics[height=360pt]{images/fig72.png} +\label{fig72} +\end{figure} +%-----File: 333.png--------------------------------------------- +%-----Folio: 318------------------------------------------------ +has escaped and another tooth has dropped onto the dead +face of the other pallet, when the pin passes out of the +notch in the other direction and the balance is again free. +The dead faces have a little recoil the wrong way, to prevent +the risk of the teeth slipping off while the balance is free; +and besides that, there is a `guard-pin' $\mathrm{S}$ on the lever, which +moves through a notch in the `roller' at the same time +that $\mathrm{P}$ moves through the lever notch: $\mathrm{S}$ has no actual +contact, but it is there to prevent the lever from shaking +back and making a false escape while the balance is free. +The pallets are always jewelled\index{Jewelled pallets}, except in very cheap +watches, and the staff or verge of the balance ought always +to have jewelled pivot holes, and in good watches the staff +of the lever also has. + +It should be noticed that you cannot let a lever watch run +down, for repairs or any other purpose, by merely taking +out the balance, because the lever will stop it. This is sometimes +inconvenient; and another part of Mr.~A.~L.~Dennison's\index{Dennison, A.~L., of America!lever escapement bridge} +plan is to set the upper pivot of either scapewheel or +lever in a bridge or cock, which can be taken off so as to let +the train run down. The same remark applies to the chronometer +escapement, but not to the vertical, horizontal, or +duplex, in all of which the staff of the balance does the +escaping directly on the wheel. + +The balances of lever watches are generally made to +\markboth{ARC OF VIBRATION.}{ARC OF VIBRATION.}vibrate about three quarters of a circle\index{Arcs of vibration in clocks!watches}, or $270^\circ$ from zero, +when the watch is clean and lying flat, which always +diminishes when they are in the pocket, and also as the oil +thickens. Nevertheless, under a sudden jerk or twist, the +balance sometimes swings quite round, and then the pin +strikes the lever again, and occasionally (though very +seldom) hard enough to break itself. Several inventions +have been made to enable the lever to give way a little when +that happens, but I cannot find that any of them have been +successful, however promising they may have been in +%-----File: 334.png--------------------------------------------- +%-----Folio: 319------------------------------------------------ +appearance, and on merely trying an experiment. Several +of them are described in the \textit{Horological Journal}, ii. 53, xii. +80, and a very ingenious one in April 1882, by Mr.~Hillgreen, +dispensing with the lever altogether by putting the +pallets on the balance arbor, not rigidly, but connected by +the balance spring, so that the balance may swing as far as +it likes. But as no escapement can be pronounced successful +until it has been proved by long experience, I only thus refer +it. + +\begin{figure}[htbp] +\centering +\caption{\sc Horizontal Escapement} +\includegraphics[width=\textwidth]{images/fig73.png} +\label{fig73} +\end{figure} + +\subsection[Horizontal or cylinder escapement.]{Horizontal or cylinder escapement.}\markboth{HORIZONTAL OR CYLINDER ESCAPEMENT.}{HORIZONTAL OR CYLINDER ESCAPEMENT.}\label{subsec:Horizontal_or_cylinder_escapement.}\index{Escapements of watches!horizontal or cylinder}\index{Horizontal or cylinder escapement}---It seems strange +that Graham\index{Graham's!horizontal watch escapement}, the inventor of the dead escapement, should +not have been the author of its adaptation to watches, and +should have invented instead a very different one, in appearance +at least, which is now almost as universally used in +foreign watches as the lever, which you see originally came +from France, is in English ones. The verge of the balance +in fig.~\ref{fig73} is expanded into a comparatively large hollow +cylinder in the middle, large enough to hold both a tooth of +%-----File: 335.png------------------------------------------------ +%-----Folio: 320--------------------------------------------------- +\begin{figure}[htbp] +\centering +\caption{\sc Horizontal Escapement} +\includegraphics[width=\textwidth]{images/fig74.png} +\label{fig74} +\end{figure} +the scapewheel and a short stem on which each tooth stands; +and about $150^\circ$ also of the side of the cylinder is cut away, +leaving only the shaded portion $ab$ in fig.~\ref{fig73}, or $\mathrm{AE}$ in +fig.~\ref{fig74}; in which the tooth $\mathrm{B}b$ has just escaped, giving the +impulse to the balance by its oblique face acting on the edge +of the cylinder as it passes out. The point of the next tooth +$\mathrm{A}a$ then falls on the outside of the cylinder, just as a tooth +in a clock escapement falls on the dead face of the pallets, and +it rests there till the balance returns, and then the outside of +that tooth begins to give the impulse until it escapes into the +inside of the cylinder and is stopped there, as at $\mathrm{D}$, till the +balance returns again. The inferiority of this to the lever +escapement is evident, inasmuch as the balance is always +subject to the friction and pressure of the teeth; and moreover +if the staff of the balance gets broken by a fall it is expensive +to replace with a new one, which it is not in the lever. +In the best watches the cylinder is made of a ruby, and the +wheel is generally made of steel, instead of brass as in the +other escapements. +%-----File: 336.png--------------------------------------------- +%-----Folio: 321------------------------------------------------ +There is a French escapement rather like this, called the +\textit{virgule escapement}\index{Escapements of watches!virgule}\index{Virgule escapement}\markboth{VIRGULE ESCAPEMENT.}{VIRGULE ESCAPEMENT.}, in which the teeth are in the plane of +the wheel as usual, with small pins rising from them near +the points, which act on a hollow cylinder, smaller than in +the horizontal escapement. At one beat of the balance a +pin only passes from the outside to the inside of the cylinder +without giving any impulse. At the other beat the +emerging tooth acts upon a long impulse face or pallet added +to the cylinder and gives the impulse. They are very +little made. Most of the foreign watches have the horizontal +escapement. + +\subsection[Duplex escapement.]{Duplex escapement.}\markboth{DUPLEX ESCAPEMENT.}{DUPLEX ESCAPEMENT.}\label{subsec:Duplex_escapement.}\index{Duplex escapement}\index{Escapements of watches!duplex}---This is probably so called because +the scapewheel has two sets of teeth, one for the locking +and the other for the impulse. The inventor of it is not +known. Its action is peculiar and requires some attention +to understand it. It is even more distinctly than the virgule, +a single beat escapement\index{Beat!single-beat escapements}\index{Escapements of clocks!single beat}, for the scapewheel only moves +sensibly at every other beat, \textit{i.e.}\ at every vibration of the +balance in one direction only: not that this makes any +difference in the time of revolution of the scapewheel, +because in all double beat escapements only half a tooth-space +passes the pallets at each beat, whereas in the single +beat escapements a whole space passes, or one tooth runs +immediately into the place occupied by the previous one: +the effect of which is that in a duplex or a chronometer +escapement the scapewheel almost looks as if it did not +move at all. $\mathrm{V}v$ is the verge of the balance, which is made +of a ruby and has a nick in it through which the long teeth +of the scapewheel can pass: one of them is represented as +just escaping, and at the same moment one of the impulse +pins $\mathrm{S}$ is just ready to act upon the tooth or pallet $\mathrm{P}$ on the +verge, and so to give the impulse to the balance. By the +time $\mathrm{S}$ has got to $t$ the next locking tooth $\mathrm{B}$ has fallen upon +the verge and is stopped there as shown by the dotted line +$bv$. When the balance returns, the nick slips past the +%-----File: 337.png--------------------------------------------- +%-----Folio: 322------------------------------------------------ +tooth $bv$, and the balance goes on till the pallet has got into +the position $p$, with the nick quite beyond the tooth, and +then the balance comes back again in the impulse direction; +the tooth enters the nick and the escape begins, the impulse +pins moving from $s$ to $\mathrm{S}$ and from $t$ to $\mathrm{T}$ without giving any +impulse, except the small amount which the balance receives +from the long tooth acting on the nick in the verge until it +escapes in the position \hyperlink{fig75}{here shown}, as before. + +\begin{figure}[htbp] +\centering +\hypertarget{fig75}{\caption{\sc Duplex Escapement}} +\includegraphics[width=\textwidth]{images/fig75.png} +\label{fig75} +\end{figure} + +Therefore the balance here also is never free, but the +cylinder on which the friction takes place is smaller than in +the horizontal escapement, and what is of still more consequence, +the impulse is given directly across the line of +centres in the most favourable way, which constitutes the +great merit of the escapement, and makes it rank next to the +chronometer or completely detached escapement, which I +shall next describe. But it requires great accuracy of construction +%-----File: 338.png--------------------------------------------- +%-----Folio: 323------------------------------------------------ +and is liable to stop from any sudden twist of the +watch which prevents the balance from once swinging far +enough for the nick to clear the tooth; and on the whole it +seems to be going out of use, as being neither so cheap nor +so safe as the lever, and not so good as the chronometer +escapement, which is used in all watches requiring very +great accuracy. But that also is liable to stop in common +wearing, and some levers go quite as well, and I prefer them +on the whole. + +\subsection[Chronometer, or detached escapement.]{Chronometer, or detached escapement.}\markboth{CHRONOMETER, OR DETACHED ESCAPEMENT.}{CHRONOMETER, OR DETACHED ESCAPEMENT.}\label{subsec:Chronometer,_or_detached_escapement.}\index{Chronometer escapement}\index{Detached escapements!for watches}\index{Escapements of watches!chronometer or detached}\index{Lever escapement!chronometer escapement}---The principle +of this escapement, as of the lever, seems to have been +invented in France, by Julien le Roy; but also, like the +lever it acquired its now standard form in England, under +the improvements of the first Arnold, who died in 1799, and +Earnshaw, the latter of whom appears to have beaten with +his ordinary chronometers the picked ones both of Arnold +and his other rivals of that time, such as Brockbank, Emery, +and others. The second Arnold, who died in 1842, was as +different from the real chronometer man, as many sons are +from eminent fathers, and owed his reputation first to +his name, and afterwards to his partnership with old +Mr.~Dent, who told me that the business had fallen so low +as to be a losing one when he joined it for a few years. + +I do not, however, see any material difference in principle +between Arnold and Earnshaw's escapements, except that +Arnold's detent $\mathrm{DTV}$ (fig.~\ref{fig76}) turned upon a pivot at $\mathrm{D}$ with +a spiral spring round it, while Earnshaw's is set upon a +straight spring as in \hyperlink{fig75}{this drawing}, which diminishes the +friction. That is doubtless a great advantage, but I cannot +help thinking that Earnshaw's personal skill had a good +deal to do with the superiority of his chronometers. + +It should also be known that Earnshaw was the first +watchmaker who had sense enough to set at defiance the +vulgar and ignorant prejudice for `high finish'\index{Finishing@`Finishing' too much undesirable} of the non-acting +surfaces, and to leave them `in the gray,' as it is +%-----File: 339.png--------------------------------------------- +%-----Folio: 324------------------------------------------------ +called. But so long as smooth work which everybody can +see is easier than accurate work which few people can judge +of, watches, like other things, will be got up for show. +Old Mr.~Dent used +to say, `We must +work for the fools.' +Nevertheless, in large +clocks we have got +rid of this folly to a +great extent, and convinced +people that +painted iron can go +better and last longer +than polished brass, +when the work is +properly constructed. + +\begin{figure}[ht!bp] +\centering +\caption{\sc Chronometer Escapement} +\includegraphics[height=0.6\textheight]{images/fig76.png} +\label{fig76} +\end{figure} + +This drawing (fig.~\ref{fig76}) shows the form +in which the chronometer +escapement +has now been made +for many years. The +verge has a small +tooth $\mathrm{V}$ upon it +which pushes aside a +lever or \textit{detent} $\mathrm{VTD}$ +as it passes in one +direction, but can pass +the other way without +moving the detent, +by merely pushing +aside a very slight +spring $\mathrm{TV}$ set on the +end of the detent, which is therefore called the passing spring. +The detent is attached to the watch frame by a spring at $\mathrm{D}$, +%-----File: 340.png--------------------------------------------- +%-----Folio: 325------------------------------------------------ +like a stiff pendulum spring, so as to avoid the friction of any +pivots, as its motion is very small, and it has a stop $\mathrm{T}$ against +which the teeth of the scapewheel are stopped as soon as the +escape has taken place. It then rests itself against a pin $\mathrm{E}$\@. +The impulse is given exactly as in the duplex escapement, +by the scapewheel teeth $\mathrm{A}$ acting directly on the pallet $\mathrm{P}$ +projecting from the verge, although their form is rather +different. The impulse begins as soon as the tooth $\mathrm{V}$ has +unlocked the detent: it is shown exactly in that position +in the figure. The detent stop is a little undercut for safety, +as the pallets are in the lever escapement, and it is always +made of a jewel in good chronometers, and so is the impulse +pallet. The chronometer +escapement +has been +made on the duplex +plan, of long +teeth for the locking, +and short for +the impulse, but +that has never +been generally +adopted. + +\begin{figure}[htb] +\centering +\caption{\sc Lever Chronometer Escapement} +\includegraphics[height=300pt]{images/fig77.png} +\label{fig77} +\end{figure} + +\subsection[Lever chronometer +escapement]{Lever chronometer escapement}\ (fig.~\ref{fig77}).---This is a +combination of +the lever and the +detached escapement, +which has +been several +times re-invented, +although---or +because---it has never turned out as good as it looks. +%-----File: 341.png--------------------------------------------- +%-----Folio: 326------------------------------------------------ +Therefore it may be useful to preserve its epitaph as +a warning. Its action is this. The pallets $\mathrm{AB}$ (fig.~\ref{fig77}), +which look like the lever escapement, only just lock, and +have no impulse. The balance is here represented at the +moment of unlocking $\mathrm{A}$ and the impulse going to begin at +$\mathrm{C}$, exactly as in the common chronometer. By the time +the impulse is finished the tooth now between $\mathrm{A}$ and $\mathrm{B}$ will +arrive at pallet $\mathrm{B}$ and be stopped there. As the balance +returns it will unlock $\mathrm{B}$, which lets the wheel run a very +little, just enough to carry that tooth past the pallet into +the position shown in the figure, and transfers the locking +to $\mathrm{A}$ again; and this is what corresponds to the passing of +the passing spring in the chronometer. Things are then +again in the condition ready for the unlocking of $\mathrm{A}$ +and giving the impulse as before. This, like the French +virgule escapement, wastes a little of the motion of the +wheel in passing from one locking to the other without any +impulse. + +\subsection[Tourbillons.]{Tourbillons.}\markboth{TOURBILLONS.}{TOURBILLONS.}\label{subsec:Tourbillons.}\index{Tourbillon escapement}---I saw in the \textit{Horological Journal} that what +is called the tourbillon escapement was reported to have +done the best in 3 years' trials of chronometers at the +Neufch\^{a}tel Observatory. It is not however really an escapement +at all, but an additional piece of machinery which may +be used with one escapement as well as another, like a +train remontoire. The scapewheel and balance are set in +a frame which revolves every minute, or thereabouts; and +the object is to make the watch correct its own `errors +of position' by making the balance pass through all positions +frequently. Consequently it would not be of much use for +marine chronometers, which are always kept horizontal by +being set in gimbals. The tourbillon frame is driven by the +third wheel of the train: what would be the fourth wheel is +fixed by its rim to the watch plate a little above it, the tourbillon +arbor going right through them: the pinion of the +scapewheel rides round the fixed wheel as a `planet,' as the +%-----File: 342.png----------------------------------------------- +%-----Folio: 327-------------------------------------------------- +tourbillon revolves; which is the same thing as if the fixed +wheel revolved and the tourbillon frame stood still, except +that the scapewheel makes one more revolution for every turn +of the tourbillon, or as many as if the fourth wheel teeth were +increased by the number of the scapewheel pinion, that being +the effect of sun and planet wheels, just as there is one +more sidereal than solar days in a year (see p.~\pageref{1more}). + +\subsection[Remontoires.]{Remontoires.}\markboth{REMONTOIRES.}{REMONTOIRES.}\label{subsec:Remontoires.}\index{Remontoire escapements}---The escapement for which Mudge +received the parliamentary reward I have already spoken of, +was on the remontoire principle, and there have been others +on the same principle. But they have never come to any +good and I do not believe they ever will in watches, +although they are very useful in large clocks with any +except a gravity escapement of good construction. But +the conditions are essentially different in so many respects +that no inference can be drawn from one which can be +of any use for the other. It is sufficient to say that +the friction of the train and dial work is the great source +of variation in large clocks, and that the pendulum arc +varies very little; while the variation of the arc of the +balance in a watch is very large indeed in different states of +the oil and in different positions; and nothing is more requisite +to impress on horological inventors than this, that +nothing more complicated than what is now in use has the +smallest chance of being adopted. And for that reason I +do not think it is worth while to increase the size of this +book by describing any other of the numerous escapements +that have been invented at various times. + +\subsection[Repeaters]{Repeaters}\markboth{REPEATERS.}{REPEATERS.}\label{subsec:Repeaters}\index{Repeaters}\index{Watches!repeaters}---or striking-watches, have so much gone out +of use that no English workmen now even profess to make +them. All that are sold at all here come from Switzerland. +In watches as in clocks, time-keepers which profess +to perform many feats generally perform them all +ill, and frequently require mending to make them go at +all. I shall therefore merely indicate the general nature of +the machinery of repeaters: full descriptions of it may be +%-----File: 343.png--------------------------------------------- +%-----Folio: 328------------------------------------------------ +found in Reid's book and in Rees's Cyclop\ae dia. Watches +were never made (so far as I know) to strike spontaneously: +but pushing in the handle knob is made to wind up the +spring of a striking part to such an extent as the position of +the dial-work allows it to go, as I have already described +under the striking work of clocks at p.~\pageref{wind}. The watch +then strikes the hour either on a very flat bell or on a ring +surrounding the works, like those spiral springs on which +small clocks sometimes strike, and the quarters, and perhaps +a half-quarter afterwards, on two other rings, or on another +less sonorous part of the hour-bell.\index{Watch!escapements|)} + +\section{KEYLESS WATCHES, \&c.}\label{sec:KEYLESS_WATCHES.}\index{Keyless watches}\index{Watches!keyless}\markboth{KEYLESS WATCHES.}{KEYLESS WATCHES.} + +A watch may be made to wind without a key in several +ways. One plan is to put a kind of gathering click to the +handle knob, which pushes in and takes hold of a ratchet +set on the barrel, or the fusee if there is one, and winds it +up as you pull the handle out again. But this was very +liable to get out of order, and was also objectionable because +it pumped air into the watch, which produced condensation +of moisture; and the following plan (fig.~\ref{fig78}) was invented +by a foreigner and adopted by Dent and some other +makers: $d$ is a wheel set on a ratchet on the barrel arbor, +so that it will only turn the barrel the right way (there is +not room to introduce this machinery in fusee watches of +the common size); $c$ in the left hand figure is an intermediate +oblique bevelled wheel between $d$ and a pinion $b$ on +the handle. It is evident therefore that if you turn the +handle $a$ the right way you will wind up the watch, and if +you turn it the wrong way you will do no harm. + +But besides this you can set the hands by the handle; for +there is a small wheel $e$ on the hand arbor with another $f$ by +the side of it on a lever $fgh$, by which that intermediate +wheel can be thrown into gear with $d$ as well as $e$, the lever +%-----File: 344.png--------------------------------------------- +%-----Folio: 329------------------------------------------------ +coming through the side of the watch-case; and then it is +clear that by turning the handle either way you can turn +the hands. If you have to turn the same way as serves to +wind the watch you do also wind it a little (and therefore if +it is fully wound you cannot set the hands that way); but +if the other way, then you do not move the barrel, as the +wheel $d$ slips on the ratchet. + +\begin{figure}[htb] +\centering +\caption{\sc Keyless Watches} +\includegraphics[width=\textwidth]{images/fig78.png} +\label{fig78} +\end{figure} + +Another keyless watch, by Mr.~Kulberg\index{Keyless watches!Kullberg's}\index{Kullberg's!keyless watch}, described imperfectly +in the \textit{Horological Journal} of April 1869, appears to +be now more generally used than that just described. +I cannot afford space here for more than a statement +of its principle, and a fuller description would be of no +particular use to anybody. The wheel $d$ in the last +figure is driven by the pinion $b$ in the pendant, without +the oblique bevelled wheel, and that wheel $d$ (for setting) +drives another, and that other the centre or cannon +pinion of the minute hand, in much the same way as in +%-----File: 345.png--------------------------------------------- +%-----Folio: 330------------------------------------------------ +Dent's when pushed into gear. But the winding is done +differently. The wheel $d$ is set on what is called a platform, +having a sideway motion something like a remontoire frame +in a large clock; and the first thing turning the knob and wheel +does is to move the platform a little (when it is not pushed +into gear for setting) so as to move itself into gear with the +fusee, which it then proceeds to wind. The platform is kept +out of the way generally by a spring, so that neither the +fusee nor the centre pinion is touched by either of the wheels +on the platform. + +Mr.~A.~L.~Dennison\index{Dennison, A.~L., of America!keyless watch}\index{Keyless watches!Dennison's} patented another keyless watch, which +is fully described in his Specification, No.~356 of 1872. There +are also other methods (see \textit{Horological Journal}, April 1874). +The advantages of these modes of winding and hand-setting +are that the watch has never to be opened, which lets air +and dust in, and so the back requires no hinge, which never +works quite air-tight, but snaps on as a separate piece; and +also that the inner case or `dome' is saved. + +\subsection[Self-winding watch.]{Self-winding watch.}\markboth{SELF-WINDING WATCH.}{SELF-WINDING WATCH.}\label{subsec:Self-winding_watch.}\index{Self-winding!watch}\index{Watches!self-winding}---Napoleon~I.\ had a watch which +wound itself up as he walked, by means of a weighted lever +with a slight spring under it, which danced up and down at +every step, and had a click taking into a ratchet on the barrel. + +\subsection[Pedometer.]{Pedometer.}\markboth{PEDOMETER.}{PEDOMETER.}\label{subsec:Pedometer.}\index{Pedometer, the}---A similar lever may be made to drive a +train like a watch train, but without any escapement, and +then it in fact counts the number of your steps and indicates +them on a dial. You can adjust it for the number of steps +which you usually take in a mile, and then it measures the +distance you walk, in a rough and approximate way; but it +ought to be understood that it is really nothing but a step-counter, +and unless it is properly adjusted, and you are walking +at the rate for which it is set, it is worth nothing for +measuring distances accurately. + +\subsection[Stop watches.]{Stop watches.}\markboth{STOP WATCHES.}{STOP WATCHES.}\label{subsec:Stop_watches.}\index{Stop-watches}\index{Watches!stop}---It is sometimes convenient to have the +means of marking a short interval between two observations +with a watch, or to mark the exact time of an observation +%-----File: 346.png--------------------------------------------- +%-----Folio: 331------------------------------------------------ +without looking off the thing you are watching. Several +contrivances have been invented for this, most or all of them +involving some kind of duplication of the seconds hand. In +one there are two seconds hands on concentric arbors connected +by a very weak spiral spring, and when you push in +a pin one of them is stopped, while the other will go on for +some seconds without the connecting spring having force +enough to stop the watch. But this is clearly objectionable, +and a better plan is to have the two hands or their arbors +connected by a sort of eccentric or heart-shaped piece acted +on by a spring which brings them together again either +forward or backward, through whichever is less than half +a revolution. Several watches of different constructions, on +this \textit{split-seconds} plan were exhibited in 1851, and others have +been invented since, called `chronographs,' and other names. + +One of them is of this kind, so far as I can describe it here. +Pushing in a pin for a moment drives on a ratchet wheel +with a few square teeth half a tooth-space; and that raises +(as we may say) a spring lever, which carries a pinion with +a disc or `roller' on it (which is always going with the +train) into frictional contact with another disc on the arbor +of the extra seconds hand, which is thus set going with the +train. Pushing in the pin a second time drives the ratchet +wheel another half space, and so lets the lever fall again, +into a space between two teeth, and takes the discs out of +contact, and \textit{might} leave the hand standing at whatever point +it has reached: which might be useful for some purposes, +but is not in fact done; because it is of more consequence to +have the hand returned to $0$, and you can look where it has +reached before returning it. That is done thus:---the second +movement of the pin also brings a `jumper' spring to bear +on the heart-shaped piece which is fixed on the hand arbor +(as before described), and so sends it backward or forward +to $0$ according as it is left before or after $30$~sec., or half way +round the dial. +%-----File: 347.png--------------------------------------------- +%-----Folio: 332------------------------------------------------ + +In watches of this kind, at least in some shown to +me by Lund \& Blockley\index{Lund \& Blockley's!stop watches} of Pall Mall, the stop-seconds hand +is central, which gives it the benefit of the full size of the +dial, and enables the space of each ordinary minute to be +subdivided into fractions of a second corresponding to the +time of vibration of the balance. For this reason also a +single beat escapement, like the chronometer or lever-chronometer +or duplex, is not so good for these split-seconds +as a double beat one, such as the lever or horizontal +or the old vertical, in which the scapewheel moves +equally for every beat of the balance, and not only for +alternate ones. The falling of a small time-ball in a suitable +frame (see p.~\pageref{subsec:Time_balls_and_guns}) is easily made to push in the pin the first +time, and when you take up the watch afterwards you see +by the difference between the two seconds hands how much +it is before or after Greenwich time. + +\begin{figure}[htbp] +\centering +\caption{\sc Recording Watch} +\includegraphics[width=\textwidth]{images/fig79.png} +\label{fig79} +\end{figure} + +There is also another perfectly different plan, which enables +you to make a mark on the dial at the exact time when you +push in the pin at the time of observation. In fig.~\ref{fig79}, $\mathrm{DD}$ +is the dial of a large watch, with the seconds hand $\mathrm{EAB}$ in +the middle: the hand is double, and the lower piece of it +ends in a little spoon with some thick ink in it and a hole +in the bottom through which a point from the upper hand +%-----File: 348.png--------------------------------------------- +%-----Folio: 333------------------------------------------------ +$\mathrm{EAB}$ can pass and make a mark on the dial. That hand is +pulled down very suddenly by a lever $\mathrm{DPC}$ which slips over +a stop of a shape difficult to describe, being pushed in by +the knob $\mathrm{K}$, and is immediately thrown out of contact again +with the link $\mathrm{AC}$, by means of which it pulls down the hand. + +Dials of watches\index{Dials of watches}\label{dialcase}\index{Watch!dials} and of small clocks are either made of +gold or silver (which soon tarnishes) or of copper covered +with enamel, which is a kind of glass. Such dials with +black hands are more distinct than any other kind, and if +the black figures are burnt in with black enamel, the dials +would be everlasting and never want painting. I noticed +the absurdity of gold hands on gilt dials before, at p.~\pageref{reg}. +Some of the public clocks in Paris have enamelled dials, +which are far more expensive than white glass ones +would be. + +\subsection[Watch cases.]{Watch cases.}\markboth{WATCH CASES.}{WATCH CASES.}\label{subsec:Watch_cases.}\index{Watch!cases}---I am not aware that there is anything else +of a rudimentary character, or belonging to the principles +of watchmaking, which requires notice. Minute details of +watchmaking can be learnt by nothing but experience; +whereas clockmaking is easily learnt by any person of +mechanical ability. Case-making is not horology, and I +have nothing to say about it, except that the cases of what +are called hunting watches, which fly open with a spring +when you press the handle, cannot be so close against air +and dirt, as those which snap tight together. Persons who +are afraid of breaking their watch-glasses, may be tolerably +safe with `half hunting watches,'\index{Half-hunting watches@`Half-hunting' watches} which have only a small +and strong glass in the middle of the cap, which may then +fit tight, and need never be opened except when the hands +want altering. The closeness of the case makes a great +difference in the time a watch will go without cleaning.\index{Cleaning watches} They +generally want at least cleaning about every two years; +though very good ones, with all the escapement work +jewelled and well-made, will go 4 or 5~years with no +material variation of rate, which I think may be regarded as +%-----File: 349.png--------------------------------------------- +%-----Folio: 334------------------------------------------------ +one of the greatest triumphs of mechanical art. At the same +time it should be remembered that letting either watches or +clocks go too long without being cleaned and oiled is very +bad economy; for as soon as the oil is all gone wearing out +of the pivots begins. + +\subsection[American watch-factories.]{American watch-factories.}\markboth{WATCH-MAKING MACHINERY.}{WATCH-MAKING MACHINERY.}\label{subsec:American_watch-factories.}\index{American clocks!watch factories}\index{Watches!American factories}---In the \textit{Horological Journal} +for April 1869, and January 1873, there are accounts +of some of these factories, where watches are made by +machinery, so that every piece will fit every watch of the +same pattern; on the same principle as Hobbs's locks. +There can be no doubt in the mind of any one who understands +machinery that this is the best, as well as the cheapest +way of making machines which require precision and uniformity. +Adjustments will after all have to be made by +hand, and a machine which has always to be in motion is +not quite on a level with a lock. The degree to which +machine-making of machinery can be carried cannot be +defined \textit{\`{a} priori}. To a certain extent the same thing is +done at the celebrated watch-factory of Messrs.~Rotherham +at Coventry, and also at Prescott in Lancashire, where watch +`movements,' \textit{i.e.}\ the train set in the frame, are chiefly made. +I can give no description of the American machinery here, +but its elements are stamping plates and the holes in them +and the wheels, and then cutting the teeth of many wheels +together. Although labour is dearer in America than here, +this machinery enables them to undersell English watches +of the same quality, as the Swiss also do with cheaper labour +and more organization, though with less use of machinery; +and if our English makers do not bestir themselves they +will lose the trade in all but the best watches, as they have +already lost that of both cheap and ornamental clocks. +%-----File: 350.png--------------------------------------------- +%-----Folio: 335------------------------------------------------ + +\chapter{BELLS.}\label{chap:BELLS.} +\phantomsection +\addcontentsline{toc}{section}{Bells.}\markboth{HISTORY OF BELLS.}{HISTORY OF BELLS.} + +There is still less to say of the history\index{Bells!history of famous ones, and their makers} of bell-founding +than of clock-making. Indeed it is hardly a progressive +art; for as soon as the right shape and composition are +discovered, and the means of making a sound casting, there +is nothing more to do, except to see that that is done. +Small bells, probably not cast but hammered, and of gold, +are, we know from the Bible, as old as the time of Moses; +and some such old bells of sheet copper and even sheet iron +are said to have been found at Cologne and in Ireland. The +Romans also had them apparently. They can only be +very thin, and of a very inferior sound to our thicker cast +bells. The nearest modern approach to them is the Chinese +gong\index{Chinese!gongs}\index{Gongs}, which is made exactly of our bell-metal, but hammered, +which that metal oddly enough admits of when it is heated +and cooled suddenly in water. Gongs, like thin bells, sound +very ill except when you are near them, and have less power +than the same weight of metal cast into a bell of a much +higher note. The following is the short history of cast bells +given in some of the Encyclop\ae dias:--- + +`The large bells now used in churches are said to have +been invented by Paulinus, bishop of Nola in Campania, +about the year 400. They were probably introduced into +England very soon after. They are mentioned by Bede +about the close of the seventh century. Turketul, abbot of +Croyland, who died about 870, gave a very large bell to +that abbey; and his successor Egelric cast a ring of six +%-----File: 351.png--------------------------------------------- +%-----Folio: 336------------------------------------------------ +others. Pope John XIII.\ consecrated a very large new cast +bell in the Lateran Church in 968.' + +It is said in \textit{Otte's Glockenkunde}, the latest German book +on the subject, but one which does not contain much information +of a practical kind, that bell-founding flourished in +all the monasteries in the twelfth century, and that there were +travelling bell-founders who went about casting bells where +they were wanted. I suspect this practice went on very +much later; for it is impossible to believe that there were +regular bell foundries in anything like the number of places +from which the `legends' on still existing bells testify that +they have come. The great clock-bell on the south-west +tower at Canterbury was recast in the cathedral yard as +lately as 1762. Indeed the carrying of very large bells +along the roads of old times would have been a more serious +affair than casting them. A great deal of curious matter of +all kinds, historical, practical, and artistic, has been collected +by the Rev.~H.~T.~Ellacombe\index{Ellacombe, Rev.~H.~T.!on the bells of Devon} in a quarto volume on `The +Bells of Devon and Bells of the Church' generally, who +rings peals himself at above the age of eighty. I shall confine +myself to the practical. + +The founders\index{Bell-founders!some celebrated ones|(}\index{Old bell-founders|(}\label{founders}\markboth{OLD BELL FOUNDERS.}{OLD BELL FOUNDERS.} of church bells in England have for many +years been very few. The most famous bell-founding family +on record were the Rudhalls\index{Rudhalls, famous bell-founders formerly} of Gloucester, who are known +to have flourished there from the time of Henry~VIII., and +some people think still earlier, till about 60 years ago. They +cast the Westminster Abbey and Chester Cathedral bells, and +the Magdalen bells at Oxford\index{Bells!Oxford and York very bad} (of which the large ones are +too thin), and a great many others. Farther back the +Purdues of Salisbury seem to have been equally famous for a +long time. One of them cast the great single clock bell, +called Peter, of Exeter, and some of the bells of that the large +ringing peal in the kingdom, though now exceeded by those +of Manchester and Bradford, which are only chimed by +machinery\index{Chiming hammers!by machinery}---a very inferior mode of sounding bells. Miles +%-----File: 352.png--------------------------------------------- +%-----Folio: 337------------------------------------------------ +Gray was the great founder of the eastern counties in the seventeenth +century: the famous tenor bell of the noble church of +Lavenham is his, which is considered the best in England +for its weight, $24$~cwt. The firm of Watts, Eayres and Arnold +existed in Leicester and St.~Neots for two centuries, and is now +represented by Taylor\index{Taylor, bell-founder}, of Loughborough, whose foundry now +has more than the old celebrity of the Rudhalls and Purdues, +and the more modern Whitechapel foundry of Phelps\index{Phelps \& Co., old bell founders}, Lester, +Pack and Chapman, and several generations of Mearses\index{Mears, bell-founders}, +until the last destroyed its reputation by a multitude of very +bad bells, and finally their Big Ben exploit, before spoken of. +The only other founders of bells or peals worth notice now +are the Warners\index{Warners, bell-founders}, of Cripplegate, whose Big Ben I.\ was very +nearly as large and heavy as Taylor's `Great Paul,' but very +inferior to it in sound and casting. They made the quarter +bells at Westminster, of which the largest is about $4$~tons, +and several others for Leeds, and other town-hall clocks, of +about the same size, and the whole, or the greater part, of +several large peals at Doncaster and Kensington parish +churches, and St.~Nicholas, Aberdeen, Fredericton Cathedral, +and many smaller ones. Gillett and Bland\index{Gillett and Bland's!clocks and bells}, the clockmakers +at Croydon, who have been mentioned before, now +make their own clock bells, and, I believe, ringing peals also, +but I have not heard any of them. There is a nice new +peal of eight at St.~Andrew's, Wells Street, by Lewis, an +organ-builder also, at Shepherd's Lane, Brixton, but too thin, +the tenor being E~flat, and only $21$~cwt., which should be F\@. +The firm of Moore\index{Moore, Holmes, and Mackenzie, bell-founders}, Holmes, and Mackenzie, at Redenhall, +Norfolk, have a patent for making the clapper of a `raised' +bell fall out of contact as soon as it is struck; but I know +nothing more of them; nor of several others who advertise +as bell-founders, which may mean anything. Tom of Oxford\index{Great Tom of Oxford}\index{Tom of Oxford, a very bad bell}\markboth{TOM OF OXFORD AND PETER OF YORK.}{TOM OF OXFORD AND PETER OF YORK.}, +by Hodson\index{Bell-founders!some celebrated ones|)}\index{Old bell-founders|)} in 1680, is decidedly the worst of all our great +bells, though he also made good bells of moderate size close +by at Merton College. The tradition that Tom came from +%-----File: 353.png--------------------------------------------- +%-----Folio: 338------------------------------------------------ +Oseney Abbey is a fiction; and even if some predecessor +did, it is a melancholy fact there is no personal identity and +very often no resemblance between an old bell and its recast +successor. The Oseney bells were once called the best in +England, and were moved to Christchurch Cathedral, but +have been all recast long ago. + +Great Tom\index{Great Tom of Oxford} might be recast\index{Bells!price for casting and re-casting}\label{price} for nothing into a very much +more powerful and an infinitely better bell (for it hardly +could be worse) by reducing the weight about a third, +though, if the College does recast it, they are not likely +so to reduce it for the sake of a hundred pounds or so. I +wonder none of the Christchurch men have managed to get +it cracked before now, and so compelled the College to recast +it. Mears's great bad bell of York\index{Bells, Oxford and York very bad}\index{York Minster!great bell, a bad one} ought to be treated in +the same way; and if that were reduced a third in weight, +which is a little more than a note in sound, it would still keep +its rank as the third largest bell in England. It is all but +useless now. Every now and then there is a movement for +getting something done with it, and getting the clock made +to strike on it (which the present clock is not strong enough +to do), but it always dies away again. Whatever is the price +of copper, and therefore of bell-metal\index{Bell-metal!its composition}\index{Composition of bell-metal}, the founders invariably +charge two guineas a cwt.\ for re-casting, \textit{i.e.}\ they give you +back at that price as much metal as they receive; and as +the price of new bells generally fluctuates round seven +guineas, you may expect to get a new bell about five-sevenths +of the weight of the old for nothing. + +Bryant\index{Bryant, bell founder and clockmaker} of Hertford was a celebrated maker of both clocks +and bells early in this century. There are some nice peals +of his at Waltham Abbey, Saffron Walden, and St.~Alkmund's, +Shrewsbury, a town full of peals, both bad and +good. The best peal of $5$ bells I ever heard, at Castle +Camps in Cambridgeshire, was by Dobson, who lived at +Downham but failed and died in the Charter House. He is +said not to have been equally successful with larger bells. +%-----File: 354.png--------------------------------------------- +%-----Folio: 339------------------------------------------------ +All these have disappeared, besides many smaller ones; +among which I ought to mention Daniel Hedderley of +Bawtry, as the founder of the fine old peal at Doncaster +Church, which was inferior to none, but is closely imitated +both in weight and tone by the new one of 1858 by Messrs.~Warner, +which will be given presently. + +The art of bell-founding is evidently no better understood +abroad\markboth{FOREIGN BELL-FOUNDING.}{FOREIGN BELL-FOUNDING.}\index{Bell-founders!foreign}\index{Foreign!bell-founding}\label{foreign} than here. There were some beautifully cast +bells from various places on the continent in the 1851 and +1862 Exhibitions, but they were nothing remarkable in +sound, and the best in appearance are by no means always +the best in sound. Notwithstanding the laudation of a +Belgian foundry by a musical amateur of no experience in +bell-making, the Boston bells cast there (p.~\pageref{lsbad}), and the +heavier peal which the Duke of Westminster was advised by +another musician to get there for his chimes at Eaton\index{Eaton Hall bells}\index{Bells in peals!Boston and Eaton Hall}, are +by no means equal to many modern English bells of corresponding +size, and the small ones are a decided failure. +That however is from another cause which will be noticed +afterwards, but it proves that the Belgian founders have no +special secret. The art had reached its lowest point about +30 years ago, when three bad peals in succession were cast +for the Royal Exchange\index{Mears, bell-founders!Royal Exchange and York}. I doubt if there was a fairly good +peal of bells cast from about 1830, or perhaps earlier, till the +Doncaster\index{Doncaster!bells} one in 1858. Certainly the previous Doncaster +peal of 1835 by Mears\index{Mears, bell-founders}, which was burnt with the church in +1853, was very inferior to the older one of 1722, and to +many others of the last century and the earlier part of this. + +When we began the Westminster\index{Westminster bells, the} bell business in 1855, I\index{Beckett, Sir E.!experiments for the Westminster bells|(} +found there was as good as nothing of a practical kind to be +learnt from books, and what little there was was contradictory, +and some of it evidently wrong, and not always right +even on the simple arithmetical relation of the musical notes +to the different sizes of \textit{similar} bells (using that word in its +mathematical sense, of all the proportions varying alike). +Accordingly, when I had to undertake the designing of those +%-----File: 355.png--------------------------------------------- +%-----Folio: 340------------------------------------------------ +bells, for the reason which I had to state at p.~\pageref{sec:THE_WESTMINSTER_BELLS.} I stipulated +for the power to make experiments as to thickness, +shape and composition; and in every one of them I found +reason to alter the traditional practice of the founders more +or less. The result has been that nearly as good bells can +now be made as ever, and they would be quite as good if it +were possible to get copper\index{Bell-metal!its composition}\index{Composition of bell-metal}\index{Copper for bell-making}\label{Old_bell_metal} of the old quality; but we had +a convincing proof that it is not, in the fact that several pieces +of \markboth{ANALYSIS OF OLD BELL-METAL.}{ANALYSIS OF OLD BELL-METAL.}old bells that were analysed at the School of Mines contained +fully $.25$ of tin\index{Tin in bell-metal}, or tin in the proportion of $1$ to $3$ +copper, while our experiments showed that modern copper +will bear no such quantity of tin without being too brittle to +be safe for ringing\index{Beckett, Sir E.!experiments for the Westminster bells|)}. This is only one of a thousand proofs +that the effect of science upon `common things' is simply to +make them worse than they used to be. No doubt in this +case the reason is that more copper is got out of the ore. +So also they have found out a way of spoiling \index{Lead!decay of, on church roofs \&c.}lead by robbing +it of the little silver which nature has put into it as a protection +from being so easily convertible into sugar of lead, +which is poison, by the action of soft water with anything +that turns it acid, and especially if it is laid on oak, which +the lead of old church roofs always was. Lincoln's Inn +Hall had to be re-roofed with slate because the lead on oak +had decayed into holes in less than 20 years, while the old +lead on many church roofs of oak has lasted for 500 years. + +It is surprising how little even musicians bear in mind the +distinction between making bells in tune with each other, +which a set of cast iron pots might be, and making them +individually good in tone: and the best musician in the +world is no judge of that unless he knows by experience +what sort of tone is attainable by good bells of something +like the same size as those he has to judge of. Mears's\index{Mears, bell-founders} two +first peals at the Exchange were duly certified by musicians +of repute, and I dare say they were in perfect tune, but most +of them were thoroughly bad bells---so bad that after being +%-----File: 356.png--------------------------------------------- +%-----Folio: 341------------------------------------------------ +twice paid for they were condemned to be recast again in +spite of the musical certificates. The fault of the present +peal by the late (not the present) Mr.~Taylor is that they are +too thin as I warned him that they would be if he aimed at +getting those notes with that weight of metal. I suspect +also that the composition is too soft, or has too little tin, as +that was a very common fault of modern bells until the +Westminster experiments. + +Fortunately a peal of bells not quite in tune can be tuned\index{Bells!tuning}, +although the tone or quality of a bad bell cannot be mended. +They are made flatter by turning a little off the inside of the +sound-bow or thickest part; and they can be sharpened a +very little by cutting off the edge so as to reduce the diameter +of the mouth; but this blunting of the edge is very apt to +spoil the bell, and it is seldom done now. (See p.~\pageref{add341}\label{341add}.) + +\subsection[Notes of bells.]{Notes of bells.}\markboth{NOTES OF BELLS.}{NOTES OF BELLS.}\label{subsec:Notes_of_bells.}\index{Bells!notes}\index{Notes of bells}---The whole theory of the designing of +bells to produce the required musical notes is deduced from +this mathematical law---that the number of vibrations in a +second, in \textit{similar} bells varies as $\frac{(\mathrm{thickness})^2}{\mathrm{diameter}}$; or in other words, the depth of the notes or the time of vibration varies as $\frac{\mathrm{diameter}}{(\mathrm{thickness})^2}$. Consequently, if you want to make +(a very bad thing) a peal of bells all of the same absolute +thickness (not the same proportionate thickness), their other +dimensions must be as the square roots of a set of numbers +in the inverse ratio of the vibrations belonging to the proposed +notes. But if the thickness itself varies with the diameter, +then the sizes will be simply as those numbers; and +therefore all the dimensions of `a peal of $8$ tuneable bells,' +according to the old phrase, which means a peal sounding +the $8$ notes of the diatonic scale, will be in this proportion--- +\[ +\begin{array}{ccccccccc} +1, & \frac89, & \frac45, + &\frac34, & \frac23, + & \frac35, & \frac{8}{15}, + & \frac12; & \textrm{or} \\[1ex] +60, & 53 \frac13, + & 48, & 45, + & 40, & 36, + & 32, & 30; +\end{array} +\] +%-----File: 357.png--------------------------------------------- +%-----Folio: 342------------------------------------------------ +and so on for a larger number of bells, each being half the +size of the octave bell below it. These are the lowest +numbers which will represent the inverse ratio of the vibration +of the $8$ notes without more fractions; and they are +easy to remember as a standard, from which any others may +be deduced, these being the diameters in inches of a peal of +bells in the key of D~flat, of the best weight or thickness for +such a peal, supposing that the small bells were not made +thicker for their size, and therefore larger for their notes, +than the large ones, as they always are, to prevent them +from being overpowered when they are all rung together as +will be seen from the peals which I shall give presently. + +It may save some trouble to observe that in designing +peals of bells we have nothing to do with what is called +musical \textit{temperament}, which was long a vexed question in +organ tuning, inasmuch as a peal of bells is always played +or rung in the same key. That question would arise if +you took the 7th and 6th of a peal of $8$ bells (counting, +remember, from the smallest) to make them the 8th and 7th +of a smaller peal; for in that case you see the $53\frac13$ and +$48$~inches would not be in the right proportion, of $9$ to $8$, +but the $53\frac13$ ought to be $54$; though both would be called +E~flat, and the error is too slight to be perceived except by +very good ears. The same occurs in playing the Westminster +and Cambridge, or the Doncaster quarters on the 2nd, 3rd, +4th, and 7th of a peal of $8$, as described at p.~\pageref{subsec:Worcester_and_Chester_Cathedral_quarters.}; for the +sizes of those bells will be, as we saw just now, $32$, $36$, $40$, +$53\frac13$, whereas the $36$~in.\ ought to be only $35.55$ to make it +exactly in tune as the second of a peal of $6$ or of $10$ bells. +Without regard to temperament, bells (on any given scale of +thickness) two whole notes apart are always as $4$ to $5$ in diameter; +$1\frac12$ note apart, as $5$ to $6$: $3$, as $3$ to $4$; but an +interval of $3$ notes (\textit{i.e.}\ $4$ bells) of the diatonic scale always +includes one half tone, such as BC or EF\@. Three bells +must have no half-tone interval. +%-----File: 358.png--------------------------------------------- +%-----Folio: 343------------------------------------------------ + +\subsection[Weight of bells.]{Weight of bells.}\markboth{SCALE OF WEIGHTS.}{PROPER SCALE OF THICKNESS.}\label{subsec:Weight_of_bells.}\index{Bells!scale of weights}\index{Weights and sizes of bells}---The weights of \textit{similar} bells, \textit{i.e.}\ of +those in which the thickness and all the dimensions keep +the same proportion to each other, vary as the cubes of the +diameters, or any of the other dimensions; and therefore the +weights of a peal of $8$ such bells would be in this proportion +(making the tenor $100$ for facility of calculation)--- +\[ +\begin{array}{cccccccc}\index{Table!weights and sizes and notes of bells} +100, & 70.23, & 51.2, & 42.2, & 29.63, & 21.6, & 15.18, & 12.5.\\ +\end{array} +\] +The Westminster\index{Westminster bells, the} bells, which would be the treble, second, +third, sixth, and tenor of a peal of ten, are very nearly in +this proportion; for in them the thickness does vary as +the other dimensions, except that the smallest was made a +little thicker than the others for its size, in order that its +sound might be strong enough. Bells $1\frac12$ note apart are as +$58$ to $100$ in weight; and half a note nearly as $5$ to $6$. + +But we have still to ascertain what is the proper weight +for any given size or note. From the practice of some of +the modern bell-founders you might suppose that it may be +almost any weight you please, at least within very wide +limits, as one sees bells of about half the weight of old ones +and yet of the same note; and then people are surprised +that they sound worse. + +Postponing for the present the consideration of bells to +ring in peals, any one who takes the trouble to compare the +weights and the cubes of the diameters in the list of the +principal large bells of Europe at the end of this book, will +see that the bell-founders of all ages and countries have +agreed in fixing rather narrow limits for the variations of +weight in proportion to the diameter of their bells. And +this is by no means from any blind following of each other; +for there is a good deal of variety in the shape and the +distribution of thickness over the different parts of the bell, +although it all ends in this near agreement of the proportions +of weight and size; which would be nearer still, but +for the foreign bells being generally taller than ours. +%-----File: 359.png--------------------------------------------- +%-----Folio: 344------------------------------------------------ + +Taking $6$~ft.\ diameter as a convenient standard to reduce +them to, you will find that the \textit{least} weight for a bell of $72$ +inches would be $72$~cwt., which is easy to remember; or in +smaller figures, $9$~cwt.\ ( = $1008$~lbs.) for $3$~ft.\ diameter. And +such a bell will be nearer B~flat than any other note, according +to the proposed universal pitch, in which A has $880$ +vibrations in a second, or that number multiplied or divided +by some power of $2$. The diameter of bells on that scale +is about $13$ times the thickness\label{thickness} of the sound-bow or thickest +part; for if some of them are rather thinner there, they are +thicker above the sound-bow, and so the total weight is the +same. But nearly all the great European bells, as you may +see from comparing their sizes and weights, are very +considerably heavier than that scale, and the average +\textit{modulus} for them may be taken at $4$~tons for $6$~ft.\ diameter, +or $10$~cwt.\ for $3$~ft., and in that case they will be nearly a +note higher. The Westminster bells are very nearly on this +thicker scale, or their diameter is nearly $12$ times their +thickness; and so is the new Great Paul\index{Great Paul of London}\index{St.~Paul's!the great bell} bell: indeed +apparently on a still heavier scale, but it is somewhat taller +for its width than the other great English bells. Some of +the bells in the list (if their recorded weights are right) are +still heavier than this, which I shall generally call the $12$, and +the other the $13$ scale; which last gives the before-mentioned +size of $5$~ft.\ for a D~flat bell, weighing about +$42$~cwt., instead of $30$ or less, as D bells are often made +now, but never with my consent. + +This $13$ scale agrees more nearly in weight than any +other simple proportion with that used by the \markboth{OLD V. MODERN THICKNESS.}{OLD V. MODERN THICKNESS.}old bell-founders +in the large bells of peals, which were made rather +thinner than large single bells, and the small ones thicker, +to prevent them from being overpowered by the large ones. +The tenor\index{Tenor bell in a peal, proper proportions of} of the great peal at Exeter weighs only a $16$th less +than its weight on the $13$ scale of the Doncaster peal; and +`the great bell of Bow,' and the tenor of York Minster, and +%-----File: 360.png--------------------------------------------- +%-----Folio: 345------------------------------------------------ +the similar one at Sherborne (lately cracked and recast) are +still nearer to it; although anyone measuring their thickness +at the sound-bow only might fancy they were on a thinner +scale. The Exeter one, for instance, is only $\frac{d}{15}$ at the +sound-bow, but the waist is $2$~inches thick, or $\frac{d}{36}$, and +not $\frac{d}{45}$ as some modern founders would make it, and the +weight is that of a rather thick\index{Thickness of bells} bell. I am satisfied +however that no sound-bow\index{Bells!thickness of sound bow} ought to be so thin as that +proportion, and that even thickening the waist does not +compensate for it. There is a fulness and softness in the +sound of a thick bell which a thin one never has. The old +bell-founders evidently knew that it is a law of nature that +a given weight of bell-metal is only capable of sounding a +very narrow range of notes with good effect; and if you +infringe that law and make your bells thinner for the sake +of getting deeper notes out of them, you are as certain +as usual, in fighting with laws of nature, to pay for it +by a more than equivalent loss in the quality of the tone. + +And it happens that this loss is even greater now than it +would have been a century ago, on account of the difference +in the quality of the copper which I have already spoken of. +It is less tough in working, capable of holding less tin +without becoming too brittle, and apparently incapable of a +certain softness of sound which even thin old bells sometimes +have, but thin new ones never. Indeed it must be admitted +that some of the finest old tenors\index{Tenor bell in a peal, proper proportions of} are what we should now +call thin. They would probably have been better still if they +had been thicker. As a peal of bells is a luxury, meant +to give pleasure to those who listen to them, and not a +necessary of life, it is astonishing that people will go +on raising large subscriptions for them without taking the +least trouble to ascertain that they get what is really the +%-----File: 361.png--------------------------------------------- +%-----Folio: 346------------------------------------------------ +best thing for their money, and forgetting that you pay for +the same weight of metal whether the bells are thick or thin, +only in one case you get them of the right notes for their +weight, and in the other case wrong, and so make the bells +bad instead of good. + +The \hyperlink{diams}{following} is a table of diameters and weights\index{Bells!scale of weights} \markboth{SCALE OF WEIGHTS AND SIZES.}{SCALE OF WEIGHTS AND SIZES.}of an +octave of bells, including all the half-notes, on the $13$ scale +of thickness, and also on the $12$ scale; from which you may +easily interpolate a $12\frac12$ scale; and larger or smaller bells +than these may be at once deduced from those an octave +above or below them in the same scale. Single bells, and +especially small ones, should always be on the $12$ scale, or +very near it; but the tenors of peals\index{Bells in peals!sizes, \&c.} on the $13$ scale. The +smallest bells of large peals are generally still thicker, +sometimes as thick as a $10$th of their diameter, and often +an $11$th; and therefore they exceed any weights deduced +from \hyperlink{diams}{this table}, as you may see in the large peals which will +be given presently:--- + +\begin{table}[!hbtp] +\centering\index{Bells!scale of weights}\index{Table!weights and sizes and notes of bells}\index{Weights and sizes of bells}\hypertarget{diams}{} +\begin{tabular}{|ll|ll|ll|} +\hline +\multicolumn{2}{|c|}{\rule[-1ex]{0pt}{4ex}$13$ \sc Scale.} & \multicolumn{2}{c|}{\sc Diameter.} & \multicolumn{2}{|c|}{$12$ \sc Scale.} \\ +\hline +cwt. & &\ &inches. & & cwt.\\ +$72$ & B\,fl. & &$72$ & C &$80$ \\ +$60$ & B & &$67\frac12$ & D\,fl.&$66$ \\ +$51$ & C & &$64$ & D &$56$ \\ +$42$ & D\,fl. & &$60$ & E\,fl.&$46\frac12$ \\ +$38$ & D & &$57\frac12$ & E &$41$ \\ +$31$ & E\,fl. & &$54$ & F &$34$ \\ +$26$ & E & &$51$ & G\,fl.&$28\frac12$ \\ +$21$ & F & &$48$ & G &$24$ \\ +$18$ & G\,fl. & &$45$ & A\,fl.&$21$ \\ +$15$ & G & &$43$ & A &$17$ \\ +$12\frac12$ & A\,fl. & &$40.5$ & B\,fl.&$14$ \\ +$11$ & A & &$38.4$ & B &$12$ \\ +$9$ & B\,fl. & &$36$ & C &$10$ \\ +\hline +\end{tabular} +\end{table} +%-----File: 362.png--------------------------------------------- +%-----Folio: 347------------------------------------------------ + +Until about 14 years ago the largest ringing peals in England +and therefore in the world, was that of Exeter Cathedral\index{Bells in peals!Exeter}\index{Exeter Cathedral bells}\markboth{EXETER AND YORK PEALS.}{EXETER AND YORK PEALS.}, +which is the largest still, and those of York Minster\index{Bells in peals!York Minster}\index{York Minster!bells},\index{Bow Church bells and York} Bow +Church\index{Bells in peals!Bow Church}, and St.~Saviour's, Southwark\index{Bells in peals!Southwark}, otherwise called St.~Mary Overy, which were all practically of the same size. The +Bow peal is the best of the three, the new York one, which was +cast by Mears after the fire of 1840, caused by a clock-maker +leaving a candle burning, being very inferior to the old ones +from the same foundry and patterns. The Southwark peal is +half a note lower, being a little thinner, and for that reason worse. + +\begin{table}[!hbt] +\begin{minipage}{\textwidth} +\renewcommand{\footnoterule}{} +\centering +\label{EYB}\index{Table!weights and sizes and notes of bells} +\renewcommand{\arraystretch}{1.15} +\begin{tabular}{rrrrrl|r|lrr@{}lrrr} +\multicolumn{6}{c|}{} & \multicolumn{1}{c|}{} & +\multicolumn{7}{c}{\sc Bow Church, 1762, and} +\\* +\multicolumn{6}{c}{\sc Exeter Cathedral Bells\footnote{The tenor and 5th were recast by Taylor, 1902, and the whole +peal rehung in iron frames. The old tenor weighed $62$~cwt.\ $2$~qr.\ $11$~lb., +though reputed as weighing $67$~cwt.\ $1$~qr.\ $18$~lb.}}\index{Exeter Cathedral bells} & +\multicolumn{1}{|c|}{} & \multicolumn{7}{c}{\sc old York Minster, 1765.} +\\*[1ex] +cwt.&qr.&lb. &ft.&in. & & & &ft.&\multicolumn{2}{c}{in.}&cwt.&qr.&lb.\\* +$72$ &$2$ &$2 $ &$6$ &$0$ &B\,fl. &$10$ &C &$5$ &$4 $ &$\frac12$ &$53$ &$0$ &$25$ \\* +$40$ &$3$ &$19$ &$5$ &$3\frac18$ &C &$9 $ &D &$4$ &$9 $ &$\frac12$ &$34$ &$2$ &$6 $ \\* +$33$ &$2$ &$11$ &$4$ &$9\frac58$ &D &$8 $ &E &$4$ &$3 $ &$\frac13$ &$26$ &$0$ &$13$ \\* +$28$ &$0$ &$4 $ &$4$ &$6$ &E\,fl. &$7 $ &F &$4$ &$0 $ &$\frac13$ &$21$ &$0$ &$23$ \\* +$19$ &$0$ &$19$ &$3$ &$11\frac14$ &F &$6 $ &G &$3$ &$8 $ & &$16$ &$0$ &$4 $ \\* +$18$ &$0$ &$4 $ &$3$ &$8\frac12$ &G &$5 $ &A &$3$ &$5 $ & &$13$ &$2$ &$22$ \\* +$10$ &$1$ &$2 $ &$3$ &$3\frac14$ &A &$4 $ &B &$3$ &$2 $ &$\frac12$ &$12$ &$0$ &$7 $ \\* +$8 $ &$2$ &$0 $ &$3$ &$0$ &B\,fl. &$3 $ &C &$3$ &$0 $ & &$10$ &$0$ &$0 $ \\* +$8 $ &$3$ &$10$ &$2$ &$10\frac34$ &C &$2 $ &D &$2$ &$10$ & &$9 $ &$1$ &$5 $ \\* +$7 $ &$3$ &$22$ &$2$ &$8\frac38$ &D &$1 $ &E &$2$ &$8 $ &$\frac12$ &$8 $ &$3$ &$7 $ \\* +\cline{1-3} \cline{12-14} +$247$ &$3$ &$9$ &\multicolumn{7}{c}{} & &$205$ &$0$ &$0$ \\* + +\cline{1-3} \cline{12-14} +\end{tabular} +\end{minipage} +\end{table} + +The two largest \index{Peals of bells, some of the largest}\markboth{LARGEST MODERN PEALS.}{LARGEST MODERN RINGING PEALS.}modern ringing peals are those of St.~Paul's +and Worcester\index{Bells in peals!Worcester} Cathedrals, both by Taylor, of the patterns +and composition which I arrived at as the best after the experiments +made for the Westminster Bells, modified a little +by some later ones, as I shall explain farther on. The St.~Paul's +peal\index{Bells in peals!St.~Paul's} is on the whole better than Exeter, of which +some of the bells are bad; and the Worcester peal is quite +equal, if not superior to that of Bow. +%-----File: 363.png--------------------------------------------- +%-----Folio: 348------------------------------------------------ +\begin{table}[!hbtp] +\centering\label{SPW}\index{St.~Paul's!peal of bells}\index{Table!weights and sizes and notes of bells}\index{Worcester cathedral!bells} +\renewcommand{\arraystretch}{1.15} +\begin{tabular}{llrrr|r|llrrrl} +\multicolumn{5}{c|}{\sc St.~Paul's\index{Bells in peals!St.~Paul's}, 1878} & \multicolumn{1}{c|}{} & +\multicolumn{5}{c}{\sc Worcester\index{Bells in peals!Worcester}, 1869}\\ + & & & & & & & & & & & ins. \\[-1ex] + & in. &cwt. & qr. & lb. & & &in. & cwt. & qr. & lb. & thick. \\ +B\,fl. & $69$ &$62$ & $0$ & $0 $ & $12$ & D\,fl.& $63$ & $50$ & $0$ & $0 $ & $4.8$ \\ +C & $61\frac14$ &$44$ & $2$ & $0 $ & $11$ & E\,fl.& $56$ & $34$ & $2$ & $12$ & $4.07$ \\ +D & $55\frac14$ &$30$ & $2$ & $22$ & $10$ & F & $50.4$ & $26$ & $1$ & $8 $ & $3.7$ \\ +E\,fl. & $52\frac12$ &$28$ & $0$ & $7 $ & $9 $ & G\,fl.& $47\frac14$ & $21$ & $2$ & $11$ & $3.44$ \\ +E & $47\frac58$ &$22$ & $1$ & $18$ & $8 $ & A\,fl.& $42\frac12$ & $15$ & $2$ & $11$ & $3.1$ \\ +G & $43\frac12$ &$16$ & $2$ & $21$ & $7 $ & B\,fl.& $38\frac12$ & $12$ & $0$ & $0 $ & $3$ \\ +A & $39\frac58$ &$14$ & $0$ & $4 $ & $6 $ & C & $36$ & $11$ & $0$ & $24$ & $3$ \\ +B\,fl. & $38\frac58$ &$13$ & $2$ & $14$ & $5 $ & D\,fl.& $35$ & $10$ & $1$ & $21$ & $2.9$ \\ +C & $36\frac38$ &$11$ & $3$ & $21$ & $4 $ & E\,fl.& $32\frac12$ & $8 $ & $3$ & $0 $ & $2.8$ \\ +D\,fl. & $34$ &$10$ & $0$ & $3 $ & $3 $ & F & $30\frac12$ & $7 $ & $3$ & $10$ & $2.7$ \\ +E\,fl. & $32\frac12$ &$9 $ & $1$ & $15$ & $2 $ & G\,fl.& $29\frac12$ & $7 $ & $0$ & $22$ & $2.44$ \\ +E & $31$ &$8 $ & $1$ & $16$ & $1 $ & A\,fl.& $28$ & $6 $ & $3$ & $19$ & $0$ \\ +\cline{3-5} \cline{9-11} +& Total & $271$ &$3$ & $1$ & \multicolumn{2}{c}{} & Total & $212$& $2$ & $2$ \\ +\cline{3-5} \cline{9-11} +\end{tabular} +\end{table} + +All the $5$ largest bells at St.~Paul's\index{Bells in peals!St.~Paul's}\index{St.~Paul's!peal of bells} are only on the $14$ scale +of thickness, and they would have been better on the $13$ scale, +but the tenor inconveniently heavy to ring. On the other +hand the $9$ smallest are all practically $3$~in.\ thick, which also +I do not approve of nearly so much as the graduated thickness +of Worcester, except the treble there, which gave a great deal +of trouble from the highness of the note, and is not satisfactory. +But the two trebles there are simply a mistake, +and the peal of $10$ sounds a vast deal better than the peal of +$12$, as is always the case. It is not so bad at St.~Paul's, +because the notes are lower and the bells heavier and slower. +But even there the $12$ sound confused, and inferior to $10$. +At Worcester three extra bells have been added to make some +more half-notes, DAC, for the chimes, which I omit in the +list of the peal. In both cases I shall notice the great single +bells separately. The Rochdale Town Hall\index{Bells in peals!Rochdale}\index{Rochdale chimes and tower} has a peal for +chimes only, almost identical with Worcester. It should be +noticed that the addition of an odd 13th bell only half a note +below the treble, instead of the whole one, makes a useful small +%-----File: 364.png--------------------------------------------- +%-----Folio: 349------------------------------------------------ +peal of $8$, omitting the $4$ largest of the great peal, subject to +the difficulty of making a satisfactory treble of a higher note +than F or F~sh.\ at the highest. That bell at Worcester is a +fair one, though the G~sh.\ treble is not. The upper $6$ of a +peal of $10$ make a proper peal of $6$. + +The largest modern peals, all by Taylor, are those of Manchester\index{Bells in peals!Manchester} +and Bradford\index{Bells in peals!Bradford} Town Halls, and of St.~Paul's Cathedral; +but the Bradford peal cannot be rung, only chimed\markright{SOME CHIMING PEALS.} by +machinery. The St.~Paul's peal is really a more powerful +and better one than Exeter, though that is rather larger; +but some of the bells are too thin and otherwise inferior. +Sir Christopher Wren, very unlike most modern architects, +who will not condescend to learn anything of such matters, +but consider themselves qualified to give orders for anything +that is wanted, whether architectural or not, had prepared a +tower capable of bearing such a peal in full swing with perfect +safety. It does not even shake sensibly under the ringing, +which is the case nowhere else that I know of with a moderately +heavy peal. The next largest modern ringing peal is +that of Worcester Cathedral, especially without the two +trebles. The St.~Paul's peal, being heavier and slower, bears +them better; but even there---and everywhere---it is impossible +to hear the $12$ as distinctly or as pleasantly as $10$. +For playing tunes there is no objection to any additional +bells, as half-notes outside the diatonic scale, which alone +is fit for ringing. There are two other chiming peals still +larger, which I ought to give, at the Bradford and Manchester +Town Halls (see \hyperlink{Bradford_and_Manchester}{next page}). Both of those also are by +Taylor. This Manchester peal is the best proportioned of +them all, except that even here perhaps the small bells vary +too little. You see the large bells are on a thicker scale than +St.~Paul's, while the small ones are thinner and lighter for +the same notes, but quite heavy enough, as I proved by the +Doncaster peal (p.~\pageref{donc}). + +%-----File: 365.png--------------------------------------------- +%-----Folio: 350------------------------------------------------ +\begin{table}[!hbtp] +\centering\index{Manchester Town Hall clock and bells}\label{Bradford_and_Manchester}\hypertarget{Bradford_and_Manchester}{}\index{Table!weights and sizes and notes of bells} +\renewcommand{\arraystretch}{1.15} +\setlength{\tabcolsep}{4pt} +\begin{tabular}{llrrr|c|llrrrr} +\multicolumn{5}{c|}{\sc Bradford\index{Bradford Town Hall tower and bells}, 1873.} & \multicolumn{1}{c|}{} & +\multicolumn{6}{c}{\sc Manchester, 1876.}\\ + & & & & & & & &ringing & & & \\[-1ex] + &in. &cwt. &qr. &lb. & & &in. &number. &cwt. &qr. &lb. \\ +A &$77\frac14$ &$87$ &$0$ &$0 $ &12 &G &$91\frac12$ &\dots &$162$ &$3$ &$0 $ \\ +B &$67$ &$59$ &$2$ &$0 $ &11 &A &$80$ &\dots &$100$ &$2$ &$0 $ \\ +C\,sh. &$59\frac38$ &$41$ &$2$ &$9 $ &10 &B &$70$ &\dots &$71 $ &$0$ &$0 $ \\ +D &$56$ &$38$ &$0$ &$10$ &9 &C &$65\frac34$ &10th &$52 $ &$0$ &$0 $ \\ +E &$50$ &$24$ &$1$ &$14$ &8 &C\,sh. &$61\frac12$ &\dots &$43 $ &$2$ &$0 $ \\ +F\,sh. &$45\frac38$ &$18$ &$3$ &$14$ &7 &D &$58\frac34$ &9 &$39 $ &$0$ &$0 $ \\ +G &$43\frac12$ &$15$ &$3$ &$25$ &odd &D\,sh. &$55$ &\dots &$31 $ &$2$ &$0 $ \\ +G\,sh. &$41\frac12$ &$13$ &$3$ &$23$ &6 &E &$52\frac38$ &8 &$27 $ &$0$ &$4 $ \\ +A &$39\frac12$ &$12$ &$2$ &$22$ &5 &F &$50\frac34$ &7 &$23 $ &$0$ &$11$ \\ +B &$35\frac12$ &$9 $ &$0$ &$22$ &4 &F\,sh. &$47\frac34$ &\dots &$21 $ &$1$ &$7 $ \\ +C\,sh. &$33\frac34$ &$8 $ &$2$ &$17$ &3 &G &$45\frac14$ &6 &$17 $ &$1$ &$7 $ \\ +D &$33$ &$8 $ &$0$ &$11$ &2 &G\,sh. &$43\frac34$ &\dots &$16 $ &$0$ &$6 $ \\ +E &$30\frac34$ &$7 $ &$3$ &$2 $ &1 &A &$41\frac12$ &5 &$14 $ &$1$ &$3 $ \\ +\cline{3-5} +Total &tons &$17$ &$3$ &$10$ & &B &$37\frac38$ &4 &$10$ &$0$ &$14$ \\ +\cline{3-5} +\multicolumn{5}{l|}{\multirow{6}{0.4\textwidth}{% +\parbox{0.4\textwidth}{\rule{0pt}{4ex}In the Manchester peal the +10 numbered bells are hung +for ringing. The tenor has +been recast rather larger +than at first, after being +cracked by the clock hammer, +which weighed nearly a $30$th +of the bell, which is +decidedly too much.} +}} & & C & $36\frac38$ & 3 & 9 & 3 & 14 \\ +\multicolumn{5}{l|}{} & &C\,sh. &$34\frac58$ &\dots &$8$ &$3$ &$0 $ \\ +\multicolumn{5}{l|}{} & &D &$33\frac34$ &2 &$8$ &$2$ &$9 $ \\ +\multicolumn{5}{l|}{} & &D\,sh. &$32$ &\dots &$7$ &$3$ &$14$ \\ +\multicolumn{5}{l|}{} & &E &$31\frac12$ &1 &$7$ &$2$ &$7 $ \\ +\multicolumn{5}{l|}{} & &F &$33\frac12$ &\dots &$7$ &$1$ &$5 $ \\ +\multicolumn{5}{l|}{} & &F\,sh. &$29\frac12$ &\dots &$6$ &$3$ &$4 $ \\ +\cline{9-12} +\multicolumn{5}{l|}{} & & Total & &tons 34&5&2 &3 \\ +\cline{9-12} +\end{tabular} +\end{table} + +It is a pity that Town Councils will not make up their minds to have peals of bells before instead of after their +towers\label{Bad_modern_towers} are built, and that architects cannot learn that bells +sound worse for being crowded together, and better the +higher up they are: in other words, that bell chambers +ought to be as large and as high as possible, as they were in +old cathedrals and large churches. Now they seem to resort +to every possible device to make them small, and the towers +so weak that even if they are large they will not bear a peal +of large bells, as was the case with that of St.~John's Chapel +at Cambridge, which is as large inside as Worcester Cathedral +tower. The Bradford tower\index{Bradford Town Hall tower and bells} is no wider than that of a +moderate old village church tower, and so is that of Eaton. +Rochdale\index{Rochdale chimes and tower} is still smaller. + +I have given them all in flats or sharps as they were sent to +me, though there is no real difference between bells called D~flat +%-----File: 366.png----------------------------------------------- +%-----Folio: 351-------------------------------------------------- +and C~sharp, except that D~flat sometimes means that the bell +is nearer D than C\@. Of course the notes very seldom happen +to be exactly those of the received standard pitch, and there +is no advantage in their being so. + +I next give two modern peals of \markboth{PEALS OF EIGHT BELLS.}{PEALS OF EIGHT BELLS.}eight, of successive sizes. +They would differ by only half a note\index{Notes of bells} and not (nominally) by +a whole one, but that the `sweeps' were rather different, and +I don't believe they really differ by a note. But as I have +said throughout, notes are of no consequence provided +only the bells are in tune among themselves. The Doncaster +peal\index{Bells in peals!Doncaster}\label{donc} was cast by Messrs.~Warner\index{Warners, bell-founders} at the same time as the +quarter bells of Westminster. The Croydon one, by Taylor\index{Taylor, bell-founder} +in 1870, is substantially the same, but a little heavier, +especially in the smaller bells, which the bell-founders are +always struggling to increase, with no benefit that I can see. +The Burton\index{Bells in peals!Burton}\index{Burton and Ossett bells} peal is at St.~Paul's church there, which was +built by Mr.~Bass, substantially from my design, as well as +the bells. Ossett\index{Bells in peals!Ossett} is near Wakefield:--- +\begin{table}[!hbtp] +\centering\label{DB}\index{Table!weights and sizes and notes of bells} +\renewcommand{\arraystretch}{1.15} +\begin{tabular}{llrrr|r|llrrr} +\multicolumn{5}{c|}{\textsc{Doncaster, 1858, Warner.}} & & +\multicolumn{5}{c}{\textsc{Burton and Ossett, Taylor.}} \\ + &in. &cwt. &qr. &lb. & & &in. &cwt. &qr. &lb. \\ +E\,fl. &$54$ &$30$ &$1$ &$0 $ &8 &F &$51$ &$25$ &$3$ &$21$ \\ +F &$48$ &$21$ &$0$ &$24$ &7 &G &$45$ &$19$ &$0$ &$0 $ \\ +G &$43\frac14$ &$15$ &$1$ &$10$ &6 &A &$40\frac12$ &$13$ &$1$ &$9 $ \\ +A\,fl. &$41$ &$13$ &$0$ &$0 $ &5 &B\,fl. &$38\frac12$ &$11$ &$3$ &$14$ \\ +B\,fl. &$37$ &$9 $ &$0$ &$0 $ &4 &C &$35$ &$9 $ &$3$ &$9 $ \\ +C &$34$ &$8 $ &$0$ &$10$ &3 &D &$32\frac12$ &$7 $ &$1$ &$25$ \\ +D &$32\frac14$ &$7 $ &$0$ &$11$ &2 &E &$30\frac12$ &$7 $ &$1$ &$9 $ \\ +E\,fl. &$31$ &$6 $ &$2$ &$5 $ &1 &F &$27\frac12$ &$6 $ &$2$ &$4 $ \\ +\cline{3-5}\cline{9-11} + &Total &$110$ &$2$ &$12$ & & &Total &$101$ &$1$ &$10$ \\ +\cline{3-5}\cline{9-11} +\end{tabular} +\end{table} + +It is not worth while to insert any smaller peals of $8$: +indeed no peal of $8$ with a tenor less than about $4$~feet diameter, +and $21$~cwt., is worth having. A nice peal of that size, by +Warner, was hung at Hunslet Church, Leeds, a few years +ago, of the total weight of $85$~cwt. There are plenty of +%-----File: 367.png----------------------------------------------- +%-----Folio: 352-------------------------------------------------- +peals of $8$ with E tenors weighing $17$~cwt., and even less, +made for foolish people who insist on having bells of the +deepest possible note and for the smallest possible price, +and lazy ringers like them better than the good old-fashioned +heavy bells, but they are miserable things. + +I next give two new peals of $8$ and \markboth{PEALS OF SIX BELLS.}{PEALS OF SIX BELLS.}$6$, one unusually heavy +for its size for this reason. The three largest bells were +made at first without the intention of adding any others, +and I determined to have them heavy for their size to sound +well alone. They were accordingly made even thicker than +a $13$th. Afterwards the other three were added, and then +a separate bell to make the Cambridge and Westminster +quarters (see p.~\pageref{folio_209}), and then a treble to make a ringing +peal of $8$ was given. That church at Headingley\index{Bells in peals!Headingley}\index{Headingley, St.~Chad's chimes and peal} was also +designed and partly built by me. The Gainford peal\index{Bells in peals!Gainford}\index{Gainford peal of bells} is +a particularly good one, made by Taylor\index{Taylor, bell-founder} for a fine old church +which has been admirably restored. I consider that the +model size for an ordinary peal of $6$, and very nearly as small +as they will bear without running into objectionably high +notes. There is a very nice peal by Taylor at Coddington, +near Malvern, half a note higher than this, which is quite the +smallest that will do:--- +\begin{table}[!hbtp] +\centering\label{HG}\index{Table!weights and sizes and notes of bells} +\begin{tabular}{llrrr|r|llrrr} +\multicolumn{5}{c|}{\textsc{St.~Chad's, Headingley.}} & & +\multicolumn{5}{c}{\textsc{Gainford, 1865.}} \\ + &in. &cwt. &qr. &lb. & & &in. &cwt. &qr. &lb. \\ +G &$46$ &$19$ &$0$ &$15$ &6 &A\,fl. &$40\frac12$ &$12$ &$0$ &$11$ \\ +A &$41$ &$14$ &$0$ &$0 $ &5 &B\,fl. &$36$ &$8 $ &$3$ &$18$ \\ +B &$37\frac12$ &$10$ &$0$ &$11$ &4 &C &$32\frac12$ &$8 $ &$0$ &$18$ \\ +C &$36$ &$9$ &$3$ &$24$ &3 &D\,fl. &$31$ &$8$ &$0$ &$0 $ \\ +D &$34$ &$9$ &$0$ &$9 $ &2 &E\,fl. &$30$ &$6$ &$2$ &$17$ \\ +E &$32$ &$7$ &$2$ &$19$ &1 &F &$29$ &$6$ &$1$ &$14$ \\ +F\,sh. &$30$ &$7$ &$0$ &$21$ & & &$ $ &$ $ &$ $ &$ $ \\ +G &$29$ &$ $ &$ $ &$ $ & & &$ $ &$ $ &$ $ &$ $ \\ +\cline{3-5}\cline{9-11} + & Total &$77$ &$0$ &$15$ & & &Total &$50$ &$0$ &$22$ \\ +\cline{3-5}\cline{9-11} +\end{tabular} +\end{table} + +The tenor of the beautiful little peal of $5$ at Castle Camps, +cast by Dobson in 1828, is $40$~in.\ and $11$~cwt., and the treble +%-----File: 368.png----------------------------------------------- +%-----Folio: 353-------------------------------------------------- +$5$~cwt.~1 qr.; but nobody gets peals of $5$ now, for they cost +very little less than $6$, and sound much worse. + +Although some very good old bells are thinner\label{thicknessls}\markboth{BELLS MAY BE TOO THICK OR THIN.}{BELLS MAY BE TOO THICK OR THIN.} than that +$13$th of the diameter which I have prescribed as the least +thickness to be allowed, and no such bells can be made of +modern tin and copper, as I have already said, yet the +\textit{best} modern bells on the $13$ scale are better than any +old ones on the $15$ scale. A fashion arose in the last +century of making the trebles enormously thick, even with +the tenors thin, and some of the bell-founders of the +present time require constant repression to prevent them +doing so. I was assured that the trebles of the Doncaster\index{Doncaster!bells} +peal would never be heard with the large bells on +my scale of thickness; but they are remarkably distinct. +The treble is on the $d = 11t$ scale. In peals of $10$ they +may go up as high as a $10$th, but anything beyond that makes +the bell too thick to ring---I mean to sound, not to swing. +I know a peal of which the middle bells alone are good +for anything, because the tenor is too thin and the treble +too thick to sound over the middle ones. The rule that I +always adopt is to prescribe the $13$ scale for half the bells in +the peal, and let the others increase in proportionate thickness +gradually up to some maximum, which I usually +define by limiting the diameter of the treble. And I have +several times advised people not to pay the founders for any +weight due to excess above the prescribed diameters, which +is easy to calculate. There is not the least difficulty in +casting to any prescribed diameters. + +The $4$ largest bells at Doncaster were \index{Maiden bells}\markboth{MAIDEN BELLS.}{MAIDEN BELLS.}\label{maiden}`maidens,' \textit{i.e.}\ they +came out not only of the prescribed diameter, but thickness +too, so that they required no tuning: the smaller ones were +intentionally made just too thick, so that all the tuning +might fall on them, and they required very little. A good +many of the Worcester\index{Worcester cathedral!bells} bells are also maiden; and every now +and then, but very rarely, a whole peal, for instance that of +%-----File: 369.png---------------------------------------------- +%-----Folio: 354------------------------------------------------- +St.~Andrew's, Wells Street, is so; but I always regard them +with some suspicion that one or two bells have been left a +little out of tune for the sake of calling it a maiden peal. + +\subsection[Sizes of peals.]{Sizes of peals.}\markboth{SIZES OF PEALS.}{SIZES OF PEALS.}\label{subsec:Sizes_of_peals.}---I have given the minimum for peals of +$8$ and $6$. The smallest tenor suitable for $10$ bells is D~flat, +of $5$~feet diameter and $42$~cwt., or D at the very highest +for the same reason that F, $48$~in.\ of $21$~cwt., is the lightest +tenor for a good peal of $8$; viz.\ that if you go much higher +you run into a G~sharp treble, which, for some reason that +neither I nor the bell-founders have discovered, though the +fact is certain, never sounds well together with large bells. +At that point some change takes place in the character of the +sound, and bells above and below it do not sound homogeneous. +Peals of $12$ I have already said I disapprove of +altogether; and it is nothing but the vanity of having them +which induces ringers to cry out for them, and subscribers +to find money for them. It is almost impossible, with the +very best ringing, to distinguish the bells in them, and the +best ringing is very difficult to get. If you will have $12$ bells +the tenor should not be higher than C, for the same reason +as I gave just now, and even that makes the treble G, though +that is not quite so hopeless as G~sharp. A B-bell would +probably be the best for such a peal, and anything below that, +if of proper strength, roars over the others in a way which +does not produce a good effect. Perhaps even the Bradford +chimes would have been better without the A tenor, though +no bell is too big for a clock to strike on. The tenors of +Exeter and St.~Paul's, you see, are B~flat; but both would +be on a better scale of thickness if they had been B with the +same weight, or more like the B bell at Manchester, which is +not rung however. The Southwark B tenor is decidedly too +thin. + +I am speaking here only of ringing peals, in which the +time of each round is governed by the weight of the largest +bell. The only limit to the number of chiming bells, with +%-----File: 370.png---------------------------------------------- +%-----Folio: 355------------------------------------------------- +as many notes as you please beyond the diatonic scale, is +that difficulty of getting small bells above C to mix well with +the large ones\index{Bells in peals!large and small together, bad}, which is painfully apparent both at Boston +Church and Eaton Hall\index{Bells in peals!Boston and Eaton Hall}\index{Eaton Hall bells}, where alone it has been tried in +England; and as both these peals are entirely or chiefly +Belgian, the defect cannot be attributed to any inferiority of +the English founders. The largest bells in both peals are +good enough. (See p.~\pageref{add355}\label{355add}.) + +\subsection[Shape of bells.]{Shape of bells.}\markboth{SHAPE OF BELLS.}{SHAPE OF BELLS.}\label{subsec:Shape_of_bells.}\index{Bells!proper shape for}\index{Shape!of bells}---Hitherto I have assumed that the bells +are to be of the well known and universal shape of church +bells, as shown accurately enough for this purpose at page~\pageref{fig44}. +And I am convinced it is the right shape, notwithstanding +the multitude of public and private assurances which we had +that it is wrong, and that the hemispherical\index{Bells!hemispherical, bad}\index{Hemispherical bells} form, or something +like it, is right. The persons who kept making these +suggestions evidently did not know that large and small bells +require different shapes. Why it is so, I do not pretend +to explain. But the hemispherical form had been used for +ages in small clock and house bells up to the largest size at +which it can properly be used. I had tried myself for +several years, and with several founders, to get one made as +large as $9$~inches diameter that would sound well in a house +clock, and I was obliged to give it up and be content with +one of $7$~inches, which seems to be the limit of their musical +capacity. There was a very large one in the 1851 Exhibition, +but it was obliged to be struck with a muffled hammer: +otherwise the sound would have condemned it at once. + +I know that bells of $3$ or $4$~cwt.\ of that shape are made +for cemeteries\index{Cemetery bells}, for which their horribly doleful sound is +appropriate enough; and as they have the advantage of not +being heard nearly so far as bells of the common shape, it is +perhaps still more appropriate. But those are not the qualities +usually sought for in either ringing bells or clock bells. + +On the other hand, small bells of the usual church form, +such as musical hand bells,\index{Hand-bells}\index{Musical!hand-bells} require to be thinner and +straighter in the side, or more conical than larger ones, +%-----File: 371.png---------------------------------------------- +%-----Folio: 356------------------------------------------------- +which are bad if the sides are less hollow than at pp.~\pageref{fig43} +and \pageref{fig80}. I exhibited a $6$~in.\ bell-metal model of the Westminster +bells at the Royal Institution in 1857, and it +sounded worse than a common door bell, or a railway hand +bell. But above $2$~feet in diameter, all these peculiarities +vanish; and according to my observation and experience, +and the universal practice of the bell-founders of all ages the +long-established shape and proportion of church bells appears +to be equally right for a bell of $4$~cwt.\ and of $220$~tons, the +probable weight of the largest Russian bell. I may just mention +here that the form of a very prolate hemispheroid, which the +Chinese\index{Chinese!bells} and Indian\index{Bells, Chinese and Indian} bells have, is so manifestly bad\index{Indian bells!bad shape}, that no one +need hear them twice to know that that at any rate is wrong. + +But when you have to design bells for construction it is +necessary to go somewhat farther than this general conclusion; +inasmuch as what we may fairly enough call the +established form of bells, when speaking popularly, or +comparing it with a very different form, will be found to +have considerable variations of its own---considerable at +least to the eye of a person who knows what a great +difference in tone may be produced by an apparently small +difference in shape. This, and the thickness, and the composition +of the metal, were the three great points to be +settled in the experiments and observations, which, as I +have already said, were made before and during the two +years which were occupied in casting the Westminster bells. +It would be tedious and useless to describe the different +variations that were tried. They ended in our coming to +the conclusion that the best shape was something between +the most common English pattern and the usual foreign one. +It is indeed a good deal nearer to the English than to the +continental pattern, except the Russian, which I was surprised +to find from a section given in \textit{Lyall's Russia}, after +the first Westminster bell was made, agrees very nearly with +that pattern. +%-----File: 372.png----------------------------------------------- +%-----Folio: 357-------------------------------------------------- + +After trying and observing the effect of a great many +patterns, and without any \textit{\`a priori} theory in favour of any +particular curve, I saw that the one which we all thought +the best in effect was very like an \index{Sweep or section of bells}ellipse in section, though +not the same ellipse as had been previously, and is still used +by some of the English founders. And after further experiments +with slightly varying shapes, I\index{Beckett, Sir E.!rules for bell construction}\index{Bells!rule for construction of large bells}\index{Construction of bells!rule for}\markboth{RULE FOR CONSTRUCTION.}{RULE FOR CONSTRUCTION.} came to the conclusion +that the following is the best for large bells on +the $13$ scale of thickness. Thicker ones only require a +slight modification of the outside curve, and it is not worth +while to complicate the description by going into more +details for them. (See next page, fig.~\ref{fig80}.) + +Consider the diameter of the bell mouth divided into +$24$ equal parts. Then the inside sweep is simply the +quadrant of an ellipse, whose semiaxis major $\mathrm{AC}$ is $14$, +and minor $\mathrm{BC}$, $6$ `parts;' in which I shall now give all the +measures. You see at once the arrangement and lengths +of all the vertical and horizontal lines in the figure. To +draw this ellipse, mark $\mathrm{B}$ at $14$ above $\mathrm{D}$, and with radius +$14$ from centre $\mathrm{B}$ mark $\mathrm{S}$, and also $\mathrm{H}$ (beyond the size of +the page), in the line $\mathrm{AC}$ prolonged. $\mathrm{S}$ and $\mathrm{H}$ are the foci +of the ellipse; which is drawn in the well known way, by +sticking pins in a table at $\mathrm{S}$ and $\mathrm{H}$, through the ends of +a thread made just long enough to reach over $\mathrm{SBH}$, and +running a pencil along it, keeping it stretched. The pencil +will then trace out the elliptic quadrant $\mathrm{AP}8\mathrm{B}$, the $8$ +indicating $8$ parts from $\mathrm{A}$, for a purpose I shall mention +presently. + +The outside can obviously be made of no single curve, +but must be compounded of several curves in some empirical +way to produce what we find to be the best proportions of +thickness throughout. As the thickness of the waist of the +bell is to be a third of the sound-bow $\mathrm{PQ}$, which is a $13$th +of the diameter, $b$ must be a $39$th, or practically $2$ thirds of +a `part,' outside of $\mathrm{B}$\@. It is necessary to put the minor +%-----File: 373.png----------------------------------------------- +%-----Folio: 358-------------------------------------------------- +\begin{figure}[htbp] +\centering\index{Elliptical section of a bell} +\caption{\sc `Sweep' or Section of a Bell} +\includegraphics[height=536pt]{images/fig80.png}\index{Sweep or section of bells} +\label{fig80} +\end{figure} +%-----File: 374.png----------------------------------------------- +%-----Folio: 359-------------------------------------------------- +axis $cb$ of this ellipse $\frac12$~p.\ below $\mathrm{CB}$, to make it come +right below. From centre $b$ with radius $11$ mark $s$ and $h$ +for the foci of another ellipse, and then describe the quadrant +$a\mathrm{R}b$, in the same way as before. The lower part $a\mathrm{R}$ +is useless, and that part of the bell curve is made up thus:---draw +$s\mathrm{QP}4$ to the point $4$ in the base, and mark off +$\mathrm{PQ} =$ a $13$th of the diameter. Then, with a radius of +$3\frac12$ or $4$ (for there is hardly any difference), draw the +circular arc $\mathrm{AQ}$, letting the centre $\mathrm{K}$ come where it +happens. The remaining little bit $\mathrm{QR}$ is easily filled up by +hand. This makes the thickness $= 1$ at $8$ from $\mathrm{A}$. + +The lowest bells are somewhat taller than the elliptic +quadrant which forms the inside sweep, and the remainder +is simply added as a cylinder. The top is drawn as a +circular arc with a radius $= 16\frac12$ to $18$, from $\mathrm{E}$ the centre +of the base, small and thick bells being usually made taller +than large ones. This one is drawn with radius $17$ for +simplicity. I have drawn the crown without \textit{canons,} or +ears for hanging in the old fashion, for a reason which I +shall give afterwards; and have accordingly added two of +the $4$ or $6$ bolts $\mathrm{XX}$, for hanging the bell to the stock; and +$\mathrm{Y}$ the larger bolt to which the clapper\index{Clappers} is hung at $\mathrm{T}$, which +I have inserted to show its length, and to remind people +that the \textit{pit,} or frame to hold a swinging bell, must be a good +deal longer than twice the height of the bell, as I have +known it forgotten, and the frame spoilt in consequence; +and if the clapper catches the frame the bell is almost sure to +be cracked. The pit should be at least $5$-$3$rds of the diameter +of the bell; and for tall bells, or bells hung long, or with +the gudgeons above the crown, the pit must be longer still. +The clapper should strike at the thickest part of the +sound-bow. The tail $\mathrm{F}$, called the \textit{flight}, is almost always +requisite to make the clapper fly properly, and its axis, or +pivot at $\mathrm{T}$, must be sensibly below the bell gudgeons, or the +clapper will not fly at all. This only has to be considered +%-----File: 375.png----------------------------------------------- +%-----Folio: 360-------------------------------------------------- +when the bell is \textit{tucked up}\index{Bells!tucking up@`tucking up'} in the stock; for otherwise +clapper axis cannot help being below the gudgeons. + +Very thick bells require the sound-bow\index{Bells!thickness of sound bow}\index{Sound-bow of bells} to be rather +higher than in the above figure, and therefore the lip to +project a little more outwards, or it becomes too lumpy. In +that case, the bit of curve $\mathrm{AQ}$ requires drawing with +longer radius than $4$. But minor details of this kind must +be left to the judgment of the bell-founder. I have given +these fundamental rules, because the time may come +again, as it did when I undertook to design the Westminster +bells, that there may be no means of learning these things, +except by going through a course of experiments again, or +else accepting what the bell-founders call experience, which +means nothing but the way they happen to have been doing +things for some time. The then existing `experience' was +manifestly wrong. + +This construction makes the sound-bow, and also the +part above it, rather fuller outside than had been usual. +According to all the sections in books, and in most of the +bells that I have seen, you can lay a straight edge against +the lip and the top shoulder of the bell; but in the Westminster +pattern the straight edge would be thrown out a +little beyond the lip, by the protuberance of the sound-bow. +I do not profess to give any reason why this pattern should +be any better than the more hollow ellipse, of major axis $12$, +which was the more usual English pattern, instead of $14$, or +than the foreign pattern, which is not an ellipse at all, but +a very much \textit{less} hollow curve, and not ending horizontally +at the mouth: all I can say is, that having tried them all, +both I and other people who examined them came to the +conclusion that this is the best in effect. The greater +tallness of the foreign bells, beyond the height of $18$ `parts,' +at any rate, which has sometimes been copied in English +ones, appears to me to be a pure waste of metal in large bells, +besides being a serious incumbrance in the increased momentum +%-----File: 376.png----------------------------------------------- +%-----Folio: 361-------------------------------------------------- +and centrifugal force of the bell in ringing; and I believe +all the bell-founders are of that opinion now. Among other +experiments we tried making the `waist' thinner than a +third of the sound-bow, but it produced an unpleasant +whistling sound and was plainly wrong. + +\subsection[Composition of bell-metal.]{Composition of bell-metal.}\markboth{COMPOSITION OF BELL-METAL.}{COMPOSITION OF BELL-METAL.}\label{subsec:Composition_of_bell-metal.}\index{Bell-metal!its composition|(}\index{Composition of bell-metal}---I\index{Beckett, Sir E.!rules for composition of bell metal} exhibited in a lecture at +the Royal Institution, in 1857, a variety of small bells of +different shapes, metals, and alloys, and different proportions +of copper and tin, which had been suggested as possible +improvements on the usual composition of old bells. It was +clear that none of them were improvements, and that something +near the proportion of $3$~lbs.\ of copper to $1$ of tin had +been generally used by the old founders. The tin was +sometimes a little more than that, or tin and antimony +together, which both produce the same effect of making the +alloy brittle, and I understand are difficult to distinguish in +the analysis. But it was also clear from experiments that +$3$ to $1$ with modern copper is the turning point between safe +and unsafe brittleness, although the sound improves as you +increase the tin up to that proportion, and even higher; and +that antimony is an inferior substitute for tin. I found it was +the modern practice to use much less than this. Accordingly +we fixed on $22$ to $7$ for the Westminster\index{Westminster bells, the} bells, and others +made about the same time; none of which have cracked, +and we had great difficulty in breaking an experimental bell +of that composition. The specific gravity\index{Bell-metal!its specific gravity}\index{Specific gravity!of bells} of the sound part +of Mr.~Mears's\index{Mears, bell-founders} bell, as of the previous one, is $8.8$, but of the +unsound part only $8.32$: some thin pieces at the edge of +the first bell were as high as $8.94$, and very difficult to break. +There is no such test of good casting\index{Casting of bells, test for good} as a high specific +gravity; but unfortunately it cannot well be applied to large +bells, as it involves weighing them in water: for the specific +gravity is the weight in air divided by the difference between +the weights in air and in water. + +But I have since come to the conclusion, for chemical +%-----File: 377.png----------------------------------------------- +%-----Folio: 362-------------------------------------------------- +\markright{REASONS FOR PROPORTION OF 13 TO 4.}reasons, that the proper composition for bells is $13$ of copper +to $4$ of tin, though it is not mentioned in any book, nor +came out exactly on the analysis of any old bell-metal. But +in old times the doctrine of `chemical equivalents' or atomic\label{atomic} +weights was unknown; and the reason why $13$ to $4$ is the +proper proportion is, that it is the only one near $3$ to $1$ which +is in atomic proportions. For the `atomic weight' of copper +is $32$, and of tin $59$, and $\frac{13}{4} \times 59 = 6 \times 32$; or the +mixture of $13$ to $4$ by weight is a true chemical combination +of $6$ atoms of copper to $1$ of tin, and is written in chemical language +$\mathrm{Cu}_6 \mathrm{Sn}$ ($\mathrm{Sn}$ being short for stannum, tin). (See p.~\pageref{add362}\label{362add}.) + +I am aware that some persons who know more of +chemistry than I do dispute the application of that theory +to metallic alloys, on the ground that the metals do not +refuse to combine in other proportions, as gases do and some +other compositions. But the practical question is whether +those proportions do not combine more firmly and with less +risk of the alloy becoming unhomogeneous in cooling, or +otherwise defective. And I am convinced that they do. +Without going into other metals, telescope speculums only +differ from bell-metal in containing rather more tin, and no +alloy has to undergo such severe tests as they have. Lord +Rosse made all his speculums as $\mathrm{Cu}_4 \mathrm{Sn}$, or $128$ to $59$ by +weight, and a very little deviation from that proportion runs +great risk of spoiling the speculum. I have seen some +specimens intentionally varied a little, and certainly the +difference between the appearance of a fracture of the metal +of atomic proportions, and of one very slightly deviating +from it, is remarkable. I was very near prescribing the +above-mentioned atomic proportion for the Westminster +metal, and indeed I published it as a suggestion in 1856; +but it only differs about $.01$ from the $22$ to $7$, which Mears +told me agreed with his own practice, and it was therefore +inserted in his contract.\index{Bell-metal!its composition|)}\index{Composition of bell-metal} Although not one bell in 1000 +%-----File: 378.png----------------------------------------------- +%-----Folio: 363-------------------------------------------------- +may fail in casting to the extent that Mears's\index{Mears, bell-founders!their Westminster bell} bell did, +and small ones probably not at all, because they cool before +the metals have time to separate, it is clear that there is a +tendency to do it; and indeed I find it is well known at +Woolwich as a thing to be provided against in casting large +guns of gun-metal, which is about $1$ \index{Tin in bell-metal}tin to $9.5$ copper. + +It seems to me at any rate imprudent not to avail ourselves +of this undoubted law of nature, especially as there is +an atomic combination which happens to be a particularly +convenient proportion, being exactly a mean between the $3$ +to $1$ which is just too brittle to be safe, and the $3\frac12$ to $1$ +which the bell-founders like because it is easier to tune, but +which is certainly softer and less sonorous than it need be. I +always now therefore require large bells to be made of this +$13$~lbs.\ of copper to $4$ of tin, or $76.5$ and $23.5$ of the whole +alloy; and they should be rejected as unhomogeneous if any +part of the bell is proved to be beyond the limits of $77$~per~cent.\ of +copper or $23$ of tin. It must not be supposed however +that this would have prevented the porosity of Mr.~Mears's +bell, which is a quite independent defect, and would +have made the bell a bad one, even if it had not also miscarried +in composition. + +The only other atomic combination within the range of +bell metal is $\mathrm{Cu}_7 \mathrm{Sn}$, or \label{195}$19$ copper to $5$ tin by weight; but +that is too soft, except for small house bells, which are +thinner and have clappers much larger in proportion than +church bells. Old Tom\index{Old Tom of Lincoln} of Lincoln and the old York\index{York Minster!bells} Minster +bells of 1765, and probably the Bow bells, of nearly the +same date and made from the same patterns, contained $.03$ +of antimony, which has a hardening effect like tin. That is +much too large a quantity to have got in by accident; but +there was certainly no improvement in the sound from +introducing about $.03$ of antimony\index{Antimony in some bells} into a small bell. The +antimony diminishes the specific gravity of the alloy, which +tin does not, though so much lighter than copper by itself. +%-----File: 379.png----------------------------------------------- +%-----Folio: 364-------------------------------------------------- +So far as I have an opinion on the point, it is at present +against the antimony, and the bell-founders have the same +opinion. Very small quantities of iron\index{Iron in bell-metal wrong|(}, lead\index{Lead!adulteration in bells}, zinc\index{Zinc!in bell-metal}, arsenic\index{Arsenic in bell metal}, +and sulphur sometimes appear in the analysis of bells; but +they are mere impurities\index{Bell-metal!impurities of}\markboth{IMPURITIES OF BELL-METAL.}{IMPURITIES OF BELL-METAL.}. I have indeed seen lead and zinc +in considerable quantities innocently put down in books as +ingredients of bell-metal; but they are mere adulterations; +for both those metals are injurious and have no business there +at all, especially the lead: a little zinc is sometimes put into +small bells, I do not know for what reason. + +\subsection[Steel bells.]{Steel bells.}\markboth{STEEL BELLS.}{STEEL BELLS.}\label{subsec:Steel_bells.}\index{Steel!bells, bad}---I have frequently been asked my opinion +of these bells, which are made both in Germany and at +Sheffield. And I answer, as I did to the makers who asked +me for a testimonial, that if the object of bells is to make +the greatest noise for the least money, steel bells are very +good ones, but that the less they asked me to say about the +quality of the noise the better. It was remarked in the +1862 Exhibition that the sound of the very large ones was +rather less horrible than of the smaller ones; and that was +the best I heard anybody say of them. I have heard nothing +of them since 1862. Moreover they require hammers two or +three times as heavy as bell-metal bells: if so, there would +be little saved in using them for large clock bells, as the clocks +would cost much more. + +\subsection[Silver.]{Silver.}\markboth{SILVER IN BELLS USELESS.}{SILVER IN BELLS USELESS.}\label{subsec:Silver.}\index{Bell-metal!silver useless in}\index{Silver, none in bell-metal}---The most inveterate of all popular delusions +about bells is the notion that old bells had silver in them, +and that all bells would be improved by it. There is not +the slightest foundation for that belief. Nevertheless we +had some experiments made for the purpose of being quite +sure that silver was of no use, either with reference to sound +or strength of the metal; several different proportions were +tried, beginning with sixpence in a bell of nearly a pound +weight, and it was clear that the silver rather did harm than +good in both respects. I suppose the delusion has arisen +from the ring of shillings and half-crowns, which justifies no +%-----File: 380.png----------------------------------------------- +%-----Folio: 365-------------------------------------------------- +such inference, any more than in the case of aluminium, +which some people fancied would make very fine bells, until +I exhibited one at the Royal Institution, which M.~St.~Claire +Deville of Paris was good enough to cast for the purpose, +and the sound was worse than of cast iron\index{Composition of bell-metal}. A bell of copper +and aluminium was also bad\index{Aluminium bronze!bad for bell metal}, though the bronze of $9$ copper +to $1$ aluminium is in other respects a very superior metal to +either brass or any alloy of copper and \index{Tin in bell-metal}tin. No composition +for bells has yet been discovered equal to copper\index{Copper for bell-making} and tin in +the proportions I have given. There was a large bell of iron +and tin in the 1851 Exhibition; but that also was very +inferior indeed to bell-metal; and it required an enormous +blow to bring out the sound, though it was thin, and was +at last cracked thereby.\index{Iron in bell-metal wrong|)} + +\subsection[Moulding.]{Moulding.}\markboth{DIFFERENT WAYS OF BELL-MOULDING.}{MODES OF CASTING.}\label{subsec:Moulding.}\index{Bell-moulding!different methods of}\index{Moulding bells}---There are two different ways of making the +moulds for bells. As to the internal mould or \textit{core} they are +nearly identical, that being made by covering a cone either +of brickwork or of cast iron with moulding clay, which is +\textit{swept} over into the shape of the inside of the bell by a piece +of wood called a \textit{sweep}\index{Sweep or section of bells} or \textit{crook} fixed to an axis or spindle +set up in the middle of the core. The advantage of the iron +core is that it can be lifted up and put into a furnace to dry, +instead of lighting a fire inside it. At this point the difference +between the two methods begins. The old method is +to make a clay bell on the core by means of another crook, +and when that is dry to make the outside mould or \textit{cope} on +the top of that. The cope has hair and hay-bands, and in +large ones, iron bands worked into it, to make it hold +together and lift off when it is dry; then the clay bell or +\textit{thickness} is knocked to pieces, the cope dropped down again +and weighted with earth in the pit where the bells are cast, +and the metal poured in at the top through one hole, another +being left for the air to come out at. + +In the other way there is no \textit{thickness} made, but the cope +is an iron case lined with clay, and swept out by an internal +%-----File: 381.png----------------------------------------------- +%-----Folio: 366-------------------------------------------------- +sweep to the shape of the outside of the bell. The \textit{wires}, or +ornamental rings round the bell, are made in both cases by +the second sweep, and the letters, and any other ornament +are pressed by stamps into the clay of the cope while it is +soft. These iron copes can be bolted down to a plate under +the core, and therefore do not require to be sunk so deep +in the ground, provided only proper care is taken to get a +high enough head of melted metal above the bell, or else it +is certain to be of bad specific gravity, and probably porous +in a casting of any considerable size, as in the top of the +first Westminster bell, where the metal ran short. I was +told by an old bell-founder that the core should not be strong +enough to resist the contraction of the bell in cooling, +or the strain injures the tone. Small bells are generally +cast in sand, like iron, from models, and not in loam +moulds made by sweeps. Bells are always cast mouth +downwards, so that the sound-bow, which is by far the +most important part, may have the best chance of being +sound by having the greatest pressure of metal on it. The +importance of this was illustrated by Lord Rosse's experiments +with large cast iron crucibles for melting speculum +metal in, which were always porous in the bottom, which is +their most important part, until he had them cast with their +mouths upwards. + +Bell-metal melts\index{Bell-metal!melting point of} at a temperature far below that of the +copper, as is usual with the alloys of one easy-melting +metal. Small bits will melt in a common house fire. It is +melted in a reverberatory furnace, in which the fire is at +one end of a long shallow trough which holds the metal, and +the flame is drawn over it to reach the chimney at the other +end, and is reverberated down upon it from a `bridge' or +a low roof over the trough. The different founders use +different fuel as well as different ways of moulding. At Whitechapel +they confessed that they still use wood. I suppose +the old founders used charcoal, as I understand they +%-----File: 382.png----------------------------------------------- +%-----Folio: 367-------------------------------------------------- +do in Russia, which is probably far better, because wood +contains so much moisture that it takes much longer to get +the requisite heat up with it, and it is notoriously a bad +thing to keep the metal long melted getting up the heat. +At Woolwich they have given up using wood for that +reason, and use coal or coke in melting gun-metal\index{Gun metal}, which is +bell-metal with much less tin in it. Warner and Taylor +use coal. In order to test this as far as possible, I gave +to Warner and Mears the same pattern for a bell of about +$12$~cwt.\ for the two new churches at Doncaster; and the +result was very decidedly in favour of the coal-cast bell; +but whether from that cause or some other difference in the +general management of the casting, of course I cannot say. +Most of the metal of Mears's Westminster bell was nine +times as long in the furnace as Warner's (which however I +suspect was run too soon), and was also much longer +running into the mould than either that bell or Great Paul. +I have no doubt that that slow running contributed to its +unsoundness. Lord Rosse specially mentions the importance +of quick running of large speculums, which again are bell-metal +with a higher quantity of tin. + +\subsection[Mending cracked bells.]{Mending cracked bells.}\markboth{MENDING CRACKS IMPOSSIBLE.}{MENDING CRACKS IMPOSSIBLE.}\label{subsec:Mending_cracked_bells.}\index{Bells!cracked, incurable}\index{Cracked bells!cannot be mended}\index{Mending cracked bells impossible}---Whenever a bell of any +importance cracks, there invariably follows a flood of suggestions, +public and private, for mending it: generally by +`cutting out the crack' in some way or other. And as there +exists in some persons what is called colour-blindness by the +world at large, so there are persons to whom a bell so +divided, and others apparently to whom a bell with a deep +crack in it, sounds (at least, they say it does) no worse +than when it was whole, though to other people's ears the +tone is generally altered several notes, or is made otherwise +intolerably bad. Another way of mending, which is continually +being reinvented, is by what is called burning the +parts together; \textit{i.e.}\ cutting the crack wide enough to let +hot metal be poured in and through, which is done until the +%-----File: 383.png----------------------------------------------- +%-----Folio: 368-------------------------------------------------- +constant application of it partially melts the faces of the +division, and then the running is stopped and left to cool. +This may \textit{perhaps} answer in very thin bells, though the +cracking of one of Sir C.~Barry's gun-metal hands\index{Barry, Sir C.!his Westminster clock hands} which +were put together in that way is not very encouraging even +for much thinner castings; and the contraction, and consequent +tension of the metal, would most likely crack the bell +again as soon as it is rung. There is no evidence that I can +learn, of any bell as large as a common church bell having +been successfully treated in this way yet. And if the bell +has cracked from any radical defect, as both the Westminster +bells did, it is absurd to think of mending it, even if it were +otherwise possible; for the same defect would make it crack +again. + +\begin{figure}[htbp] +\centering +\caption{\sc New Bell Crown} +\includegraphics[width=0.9\textwidth]{images/fig81.png} +\label{fig81} +\end{figure} + +\subsection[New bell crown.]{New bell crown.}\markboth{NEW BELL CROWN.}{NEW BELL CROWN.}\label{subsec:New_bell_crown.}\index{Beckett, Sir E.!new bell-crown}\index{New bell-crown, Sir E.~Beckett's}---Church bells used\index{Bell-crown!common} always to be hung +by $6$ long ears, called `canons,'\index{Canons of bells} which cut a large piece out +of the stock, and weakened it very much. They were not +set radially, and the iron bolt which carries the clapper was +cast into the bell. Consequently when a bell got worn in +one place it could not be turned without a new stock and a +great deal of trouble. Several plans to cure this had been +proposed, but none of them were satisfactory; and I\index{Bell-crown!Sir E.~Beckett's} had the +Westminster bells and some others made with a top like a +mushroom\index{Bell-crown!mushroom-shape} or button embraced by a collar in two pieces, +%-----File: 384.png------------------------------------------- +%-----Folio: 369---------------------------------------------- +or by bolts with heads of proper shape surrounded by a ring, +which may advantageously be connected with the gudgeons +or pivots. But the founders complained (unduly, I think) +of this ironwork being expensive, and so I invented another +crown, with $4$ short and thick canons, which will be understood +from figure~\ref{fig81}. It has been generally adopted by +Messrs.~Warner. Mr.~Taylor\index{Bell-crown!Taylor's}\label{taylor} uses $6$ very short canons, and +in many cases, with my approval, none at all, but only a +thick crown with $6$ bolt-holes through it, as at p.~\pageref{fig80}. I +believe canons are of no use. In all these plans the clapper +bolt goes through a round hole in the bell, but a square or +octagonal hole in the stock. By placing the bolts (of my +plan) each with one leg in the stock, or two of them inside +and the other two outside of the stock, you may get $4$ +different pairs of places for the clapper to strike, with the +same stock and without any cutting of it, and the stock itself +is far less cut into and weakened than by the usual canons, +which are necessarily taller. The Doncaster bells were the +first peal made in this way. + +On the old plan too, the clapper bolt\label{bolt} is always cast into +the bell, and must be cut off and a new one stuck on in +some way, to turn the bell at all, which is an awkward job, +and postpones the turning of bells for years after it ought +to be done. And in connexion with that, it is another +advantage of this plan, that it enables the clapper bolt to be +adjusted both for length and position, which cannot be done +when they are cast in. The length of that bolt ought to be +more or less according as the bell is hung more or less high +in the stock, in order to bring the point of suspension of the +clapper below the gudgeons or pivots of the bell, without +which it will not swing or strike properly; and again, if the +bolt is cast in a little on one side, the clapper will not strike +true, and the time between the blows will be unequal, which +makes it impossible to ring the bells truly. If some such +plan as this had existed in old times, whereby a bell could +%-----File: 385.png---------------------------------------------- +%-----Folio: 370------------------------------------------------- +easily be turned in the stock, many a fine old bell would +now be alive which got cracked from being constantly +struck in one place, and so worn too thin. These four +short and thick canons are moreover much stronger and +less liable to crack than the usual six thinner and longer +ones. + +Opinions differ whether large bells should be what is +called `tucked up\index{Bells!tucking up@`tucking up'}\label{tuck}\index{Tuck@`Tucking-up' of bells}\markboth{TUCKING-UP OF BELLS.}{TUCKING-UP OF BELLS.} in the stock,' or the top of the bell made +higher than the `pivots or gudgeons.' The advantage of it +evidently is that it diminishes the centrifugal force, or sideway +strain of the bell on the frame; and if friction were out +of the way it would of course make the bell easier to raise +and ring. But friction is \textit{not} out of the question; and as a +bell in swing is in effect a pendulum, and not (as I have +even heard bell-founders represent it) a body lifted by a +steady pull like a lever, it may very easily happen that a +certain amount of friction on the pivots may make it impossible +to make the bell pendulum swing through $360^\circ$ by any +practicable force that can be applied to it at the beginning +of its motion, which is the only time when the rope acts +upon it. The Rev.~Mr.~Taylor\index{Taylor, Rev.~W.!and the York bell} told me, that a bell of about +$52$~cwt.\ at Hereford, which he and some other boys used to +raise and set (\textit{i.e.}\ ring till it stands mouth upwards) was +made unraisable by them by being re-hung, and at the same +time `tucked up;' and so confident was he of the mistake +of this mode of hanging, that he offered to fill Mears's great +bad bell at York with beer if \textit{any number} of men could set it, +and they never could, as \textit{Browne's History of York Minster} +also testifies. + +There is moreover a remarkable difference in the facility +of tolling\index{Tolling of bells}, according as the bell is hung\index{Hanging bells} low or high. I +can toll the two largest bells of Doncaster Church together, +weighing $2\frac12$ tons, one with each hand, whereas it is +difficult to make a high-hung bell toll at all. At the same +time, it is true that the largest bells of a peal, where the +%-----File: 386.png---------------------------------------------- +%-----Folio: 371------------------------------------------------- +tenor is above $30$~cwt., can hardly be rung with the others, +unless they are somewhat tucked up, though it makes them +`rise false,' or with the clapper striking the low side of the +bell and lying on it, and the men have to go up and set them +right before ringing (and they will keep so), otherwise +there is a risk of cracking the bells, and they do not sound +so well. The reason why heavy bells in peals must be +rather tucked up is that otherwise their momentum is so +great that no man can check them, so as to keep time; but +this would not apply to a single bell. + +I am surprised that very large bells, say above $2$~tons, +are not hung\index{Bell-hanging} on friction rollers\index{Friction rollers!for bells}\index{Hanging bells!on friction rollers}\index{Rollers, friction}\markboth{FRICTION ROLLERS PROPOSED.}{FRICTION ROLLERS PROPOSED.}---\textit{i.e.}\ so much of the circumference +of a friction wheel as = the circumference of the +gudgeon or pivot of the bell. Of course brasses\index{Brasses for bell gudgeons} must be +put to keep the gudgeons in their place, against the side +swing. And, by the way, let me say a word here to warn +those whom it may concern, that if the smaller bells of a +peal jump out of their brasses when they are new, it is +because the gudgeons are not sunk deep enough. I have +known that happen several times. Of course the founders +denied that that was the reason, but as I cured it by +getting deeper brasses, the denial was worth nothing. + +I\index{Beckett, Sir E.!plan for Great Paul} recommended rollers of about $2\frac12$~in.\ diameter in annular +bushes round the $6$~inch pivots of \label{gphang}Great Paul\index{Bells!St.~Peter's, and Montreal, and Great Paul}\index{Bells in peals!Great Paul}\index{Great Paul of London}, like +bicycle bearings on balls. Swinging that bell through only $60^\circ$ +from the vertical (the most that is proposed) is equivalent to +sliding $18$~tons $6$~inches rapidly at every swing. Even +tolling it is equivalent to sliding that weight an inch forwards +and an inch backwards at every pull. Tolling consequently +takes three men now. (See p.~\pageref{add371}\label{371add}.) + + +\subsection[Tolling-levers.]{Tolling-levers.}\markboth{TOLLING-LEVERS.}{TOLLING-LEVERS.}\label{subsec:Tolling-levers.}\index{Bell-tolling}\index{Tolling levers}---The great Worcester bell is hung, by +my advice, on wedge-shaped rolling gudgeons, only round +instead of sharp, to enable it to be tolled almost without +friction, by a long lever; for the tower would not bear it in +full swing; and it went so easily that the Rev.~H.~T.~Ellacombe, +then 80 years old, tolled it with one hand. But for +%-----File: 387.png---------------------------------------------- +%-----Folio: 372------------------------------------------------- +all practical purposes it answers equally well to toll it by a +short lever, or shank, projecting from the top of the clapper, +and pulled by a slight rope; which is a very good plan for +all bells which the tower is either too small or too weak to +bear swinging. If a double lever is used with two ropes +one for each hand, you may ring as rapidly as the bell +itself would sound when swinging about `frame-high,' or +half-way up. See such a lever at p.~\pageref{fig80} for one side. + +A few years ago I\index{Beckett, Sir E.!plan for hanging small bells} introduced a mode of hanging chapel +and school bells,\index{Hanging bells!chapel and schools bells} \textit{i.e.}\ single bells from $1$ to $4$~cwt., or $18$ to +$28$~in.\ wide, so as to swing lengthways in the plane of the +wall, instead of across it. A bell of very moderate weight +will soon pull an ordinary wall to pieces if rung in full swing +across it. The bells in `bell gables' can hardly ever be +safely rung for that reason, but only tolled. Mr.~Taylor has +introduced an ingenious plan for ringing small school bells +without the risk of the rope being carried over, by putting +it to a crank in the iron axis which serves for the stock of +such small bells: you may then ring the bell `over' as often +as you like, and the rope always keeps right. + + +\subsection[Bell-ropes.]{Bell-ropes.}\markboth{BELL-ROPES GENERALLY TOO THICK.}{BELL-ROPES GENERALLY TOO THICK.}\label{subsec:Bell-ropes.}\index{Bell ropes}---I said just now that some people fancy a +bell is hauled up like a dead weight on a lever, and not swung +up as a pendulum; and they forget still more, that the measure +of the strength required for a rope is that of the man +who has to pull it, and has nothing to do with the weight +of the bell. A small bell can be `raised' in a few pulls, +while a large one takes many, but in either case the ringer +may be exerting his full strength, though in fact no man +does in raising small bells; and therefore \textit{some} difference in +thickness of the ropes should be allowed. But experienced +ringers know too well that inexperienced rope-makers always +make the ropes much too thick\index{Bell ropes!generally too thick}, though probably not many +ringers have reflected on the proposition that it is their force +used in pulling, and not the weight of the bells, that determines +the thickness of the ropes---allowing reasonably for +%-----File: 388.png------------------------------------------------ +%-----Folio: 373--------------------------------------------------- +wear, and for some greater force being used upon the large +bells. + +The great superiority of tone of bells ringing in full swing\index{Bells!sound best swinging}\index{Swinging, effect of, on the sound of bells} +over tolling, and even of tolling over striking by a clock +hammer, has been often noticed, but never yet accounted +for. I think the explanation is this. It is now well known +that the note of an approaching source of sound like a railway +whistle is sharper than when it is receding, because the +velocity of transit is added to, or subtracted from, the +velocity of vibration which fixes the notes. (The analogy of +light to this has been made use of by Mr.~Huggins, in one of +the greatest astronomical discoveries of late, to determine +the velocity of approach or recession of the stars, as is +explained in my Astronomy\index{Astronomy without Mathematics@`Astronomy without Mathematics'!referred to}.) The bell in full swing, while +it also vibrates from the blow, is always sending out vibrations +of slightly different velocity in each direction, and so +varying its own note a little. I remember a gentleman +trying to persuade the Institute of Architects that bells +sound as well stationary as swinging, and he illustrated it +with a common dinner bell; which by the way a servant of +experience always swings as far as he can. Everybody +exclaimed immediately that he had refuted himself. The +motion in tolling is probably too small to vary the note +sensibly, but the inevitable variation of a man's pull makes +it less monotonous than the unvarying lift of a clock hammer, +or of any chiming machinery, a melancholy and miserable +substitute for a set of ringers, only justifiable as a precaution +against strikes---of the men, I mean. Even that hardly +justifies it. + +\subsection[Ellacombe's chiming hammers.]{Ellacombe's chiming hammers.}\markboth{CHIMING AND RINGING.}{CHIMING AND RINGING.}\label{subsec:Ellacombe's_chiming_hammers.}\index{Chiming hammers!Ellacombe's}\index{Ellacombe, Rev.~H.~T.!his chiming hammers}---There is however a +less objectionable mode of chiming by one man, with a set +of separate clappers fixed below the bells, temporarily tied +up very near them, so that a small pull of the rope makes +the clapper strike. This was invented by Mr.~Ellacombe, +and is fully described in his large book on bells, and in some +%-----File: 389.png------------------------------------------------ +%-----Folio: 374--------------------------------------------------- +smaller ones. Not that even this is to be compared to +genuine chiming by tolling the bells themselves, for they are +stationary, and those clappers are necessarily too small to +bring out the full tone. In this way however, a skilful man +can play tunes, whereas in ordinary chiming or ringing a +bell can only change one place at a time: e.g.\ the greatest +change that can follow 1 2 3 4 5 6 7 8 is 2 1 4 3 6 5 8 7. +I do not profess to teach the art of ringing, or to deal with +the interesting and complicated subject of change-ringing, +which is quite enough to have a book to itself; and there +are several\index{Bell-ringing!books on}, by Captain J.~E.~Acland Troyte\index{Troyte on bell-ringing}, and by Mr.~Jasper +\index{Snowdon's books on bell-ringing}Snowdon, of Old Bank Chambers, Leeds. I will +only say that ringing `the tenor behind,' \textit{i.e.}\ ringing the +changes only on the other bells, always sounds much better +than ringing the tenor in the changes, though ringers think +more of it as a feat. One man can ring a very heavy bell +`behind,' which would require two to ring in, as its time has +then to be altered continually. Also, when two men are +required, it tries their wind much less, and it requires only +one rope, for one to take the `fore stroke' only, and the +other the `back stroke' only, though it is hardly ever +done. + +\subsection[Stays and sliders.]{Stays and sliders.}\markboth{STAYS AND SLIDERS.}{STAYS AND SLIDERS.}\label{subsec:Stays_and_sliders.}\index{Bell-hanging!stays and sliders for}\index{Stays and sliders of bells}---The stay is a strong piece of wood, +about as long as the radius of the wheel, bolted to the stock +and pointing upwards, so that when the bell is swung right +up, the stay points downwards and rests against a stop there. +But if that stop were fixed, the bell could not reach quite the +vertical position, at least in one direction of the swing. +Therefore the stop is a sliding bar, which lies low enough to +clear the wheel and clapper, and it has play enough in its +own bed near the stay to allow the bell to go just beyond +the vertical both ways; and so a small portion of its weight +is borne by the stay and slider when it is `set,' or so +resting, until it is pulled off again by the rope and swung the +other way. Sometimes the stay has to be put by the wheel, +%-----File: 390.png------------------------------------------------ +%-----Folio: 375--------------------------------------------------- +on account of clock hammers at the other side, but generally +it is at the other end of the stock. + +After a long struggle with bell-founders and their hangers, +I\index{Beckett, Sir E.!improved stays and sliders} got the practice introduced of striking the bed or board in +which the slider runs as an arc of a circle from the +gudgeon as a centre, instead of leaving it flat, which the +smallest knowledge of mechanics will show anybody must +produce a grinding action between the stay and the slider. +Moreover, sliders were generally much too heavy, which +increased the friction and the cost of breaking. A slider +need be little more than a common stick, and can be +replaced almost for nothing in a few minutes, whereas the +breaking of a stay is a more serious matter, as many a +learner of bell-ringing knows. At the lower end (away +from the stay) it need only lie loosely in a hole; its weight +and slope will keep it there without a pin. Stays can hardly +be too strong, and should always go through a strong iron +loop, and not be merely bolted to the stock, which weakens +them, and gives more leverage for breaking. Boards should +be put over the sliders to keep the grease off, which increases +rather than diminishes their friction; black lead is the thing +to diminish it on wood. + +\subsection[The Gudgeons]{The Gudgeons,}\markboth{THE GUDGEONS.}{THE GUDGEONS.}\label{subsec:The_Gudgeons,}\index{Bells, gudgeons}\index{Gudgeons of bells}\ or pivots on which the bells swing, are +often made too short, under an erroneous idea that that +diminishes the friction, which it does not, and may in fact +increase it, because if the pressure on each particle of surface +is too great, it squeezes out the oil, and the metals come in +contact, which it is the object of oil or grease to prevent. +Besides that, short gudgeons tend to twist the beams. They +should not be less than $2$~in.\ long and $1$~in.\ thick for the +smallest bells in a peal, and rather longer and much thicker +for the large ones. I think they should be of steel. +And it should be specified that the `brasses'\index{Brasses for bell gudgeons} in which they +run are to be $19$ copper to $5$ tin, for the reason given at +p.~\pageref{195}. The brasses should be large, to allow for wearing +%-----File: 391.png------------------------------------------------% +%-----Folio: 376---------------------------------------------------% +\index{Moore, Holmes, and Mackenzie, bell-founders}%couldn't find ref on page% +down, and for firm fixing in the beams. All the ironwork +should be well painted, except the gudgeons; and the +woodwork too, though it hardly ever is, which is very bad +economy in the long run. But oak should not be painted +very soon. + +\subsection[Clappers]{Clappers}\markboth{CLAPPERS.}{CLAPPERS.}\label{subsec:Clappers}\index{Bells!clappers}\index{Clappers}\ should be hung by or on wooden blocks, and +not with a mere piece of leather inside an iron strap, which +soon wears away, and leaves the two irons in contact, and +they are sure to be rusty by that time. Thick bells of +course require heavier clappers than thin ones. I remember +a very good bell of Warner's remained unsold in the 1851 +Exhibition, and long after, merely because it was very thick +(copied from the 3rd Bow bell) and had too small a clapper. +I happened to try it with a large one which was lying loose, +and bought it immediately for a chapel for which I had been +asked to get one. All nuts connected with clappers should +be either double or keyed on with wire, or they will shake +loose and come off. + +\subsection[Iron stocks and frames]{Iron stocks and frames}\markboth{IRON STOCKS AND FRAMES.}{IRON STOCKS AND FRAMES.}\label{subsec:Iron_stocks_and_frames}\index{Bells!stocks}\index{Iron stocks and frames for bells}\ are now coming into general +use, especially for heavy bells. They have great advantage +in point of durability, if kept properly painted; and the +bells are much easier to ring, owing to the ironwork not +being subject, like wood, to constant swelling or shrinking +with every atmospheric change. They are made in two +shapes---A frames and $\mathrm{H}$ frames: the former being preferable +for light peals, and the latter for heavy bells. + +The weight and rigidity of these massive frames of iron +and steel cause them to absorb, as it were, nearly all the +vibration, if the bells are properly hung; and when built +into the walls they form excellent crop-braces for the +strengthening of the tower. + +The iron frames, etc., at Beverley and Exeter are excellent +examples. + +Frames constructed partly of iron and partly of oak are +to be avoided. +%-----File: 392.png------------------------------------------------ +%-----Folio: 377--------------------------------------------------- + +\subsection[Bell-frames,]{Bell-frames,}\markboth{BELL-FRAMES.}{BELL-FRAMES.}\label{subsec:Bell-frames,}\index{Bell frames}\index{Bells!frames}\index{Frames!for bells, and fixing}\ like most other things nowadays, are +generally starved of proper bulk. I do not see my way to +laying down any rule for the thicknesses of the beams, as +they must vary so much according to the weights of the +bells. The beams of the smallest bells ought never to be +less than $5$~in.\ wide, and $10$~in.\ deep, and of the large +ones for a peal with a tenor about $30$~cwt., not less than +$9 \times 12$, and the lower beams should be always a little +wider than the upper ones. It is also specially important +to have the diagonal trusses very deep, particularly under the +heavy bells. Dove-tailing and any cutting away of the +beams should be avoided as much as possible, by using +`bed-bolts' and iron \textsf{T} pieces bolted on at all weak corners. +The upper beams should also be bolted to the lower by long +diagonal bolts, set the opposite way to the trusses. + +And now I have to correct one of the most common errors +about frame-fixing. It is quite true that the upper beams +should not touch the walls, unless the walls are very thick +and strong. But if they must touch anywhere, for want of +room, they should touch close, and in fact tight\index{Bell frames!bottom should fit tight to walls}\label{walls}, all along the +beam, so as to avoid anything like battering. The lower +beams should always do so, or be somehow connected with +the walls as firmly as possible. The notion that they should +not is an extraordinary piece of architectural ignorance. +Either the whole frame\label{framearrange} must float about on the floor under +the swing of the bells, or it must be fixed to the floor; and +if it is fixed, the horizontal thrust must ultimately go to the +walls, pulling the floor or its beams against them anyhow; +and it is much better to make this connection firm at once, +and avoid all chance of battering. + +All the elasticity takes place between the upper frame and +the lower, and it acts like carriage springs, and the pressure is +diffused over the walls as well as it can be, if the lower frame +is tight. The oscillation of towers under ringing is merely +due to the elasticity of the whole mass of stonework; and +%-----File: 393.png----------------------------------------------- +%-----Folio: 378-------------------------------------------------- +though they sometimes move enough to make the little call-bell +from the church into the belfry almost ring by accumulated +vibrations, the actual motion of the tower is too small +to see, except perhaps with a fixed telescope. The idea of +preventing it by building up a frame from the ground within +the tower is ludicrous\label{folly}, though some architects do not know +it, or that such frames have always at last to be wedged +against the walls of the bell-chamber. + +Another `vulgar error' about bell-frames is that bells +swinging at right angles\index{Bell frames!their arrangement} to each other tend to correct each +other's swinging thrust upon the frame and tower; whereas +every mathematician knows that that is exactly the position +in which the thrusts cannot the least neutralise each other. +Besides that, it has the effect of making the ends of some +beams thrust against the gudgeons of other bells, and so +occasionally binds them tight. I was assured by a bell-founder's +foreman, before making the first frame on the +parallel plan (for the cathedral at Fredericton, which also +had the first gravity escapement clock), that `all experience +was against such a plan.' I said, I should like to be referred +to some frames of that kind which were proved by experience +not to answer. His reply was, `O, nobody ever thought +of making such a frame.' That total absence of experience +of the very thing in question is what so-called practical men +mean by experience---and many other people too. + +The following is the plan which I\index{Beckett, Sir E.!plan for bell frames} prescribed for Doncaster +and the others mentioned at p.~\pageref{donc}. All the bells swing +north and south: $2$, $1$, $8$, $7$, are on the south side, and +$3$, $4$, $5$, $6$, on the north; all the beams going through, except +the one on the west side of $8$ and $5$, which is divided, and +overlapped and bolted together, so as to make the tenor pit +wider than the 5th by the thickness of that beam, and the +treble pit as much narrower than the 4th. The east and west +beams are only notched on to the others and bolted, not +halved or cut away as usual. There should always be long +%-----File: 394.png----------------------------------------------- +%-----Folio: 379-------------------------------------------------- +bolts nearly vertical, but oblique, holding the upper and +lower beams together the opposite way to the diagonal struts +which carry the weight, because the mortices always get +loose, but the bolts can be tightened from time to time. In +this frame the ropes can fall in a very good and wide circle, +in one or two ways which will be obvious; and in large +towers such as those, there is also room for the entrance; +indeed in all but Croydon you can go all round the frame. + +But when the tower is only just large enough to hold +the frame, it is expedient to adopt some other and inferior +plan, in which the bells cannot all swing parallel, in order to +avoid having the ropes too close to the walls for the men +to stand behind them; for leading them down obliquely +in troughs increases the friction and labour of ringing. +It may be taken as a rule that a peal of $8$ bells hung +properly on beams of proper thickness requires a frame +nearly $4$ times the width of the tenor, both ways; and one +of $6$ bells requires rather more than $3$ times the width of +the tenor. In hanging $10$ or $12$, some space may be saved +by making a few of the smaller bells swing at right angles +to the others; but it should only be the small ones. When +the large ones all swing parallel, they are sure never to be +thrusting all one way twice together; and as it is only an +accumulation of similar vibrations that could affect the tower, +they are certain on the whole to escape that effect, and in a +great measure to neutralise each other, though of course +not completely. + +\subsection[Clappering.]{Clappering.}\markboth{BELLS CRACKED BY CLAPPERING.}{BELLS CRACKED BY CLAPPERING.}\label{subsec:Clappering.}\index{Clappering cracks bells@`Clappering' cracks bells}\index{Cracked bells!clappering causes}---It is still necessary to warn clergymen and +churchwardens against allowing the lazy and pernicious +practice of `clappering,' \textit{i.e.}\ tying the bell-rope to the +clapper, and pulling it instead of the bell. More bells have +been cracked in that way than by all other causes together, +and there is not the least excuse for it, as any man may +learn to toll a bell in one lesson, and the work of doing it +is nothing, for the bell moves so little that it seems +%-----File: 395.png----------------------------------------------- +%-----Folio: 380-------------------------------------------------- +wonderful that the clapper should strike it; but they both +act as pendulums which a very small impulse will keep up, +and the blow being elastic loses very little of the force. +Bells are consequently much easier to toll when they are +not tucked up in the stock, because they act more like a +pendulum and less like a grindstone; in fact, it is difficult to +set a much tucked-up bell tolling, though easy to keep it +up afterwards. The only safe way of allowing bells to be +clappered is to fix a separate pulley in the floor under +the bell with a thin rope, in such a position that no pulling +of the rope over the pulley can hold the clapper against +or very near the bell, so that it must depend entirely on the +swing given to it by the rope. + +\subsection[Specifications.]{Specifications.}\markboth{SPECIFICATION FOR A PEAL OF LARGE BELLS.}{SPECIFICATION FOR A PEAL OF LARGE BELLS.}\label{subsec:Specifications.}\index{Bells!specifications for}\index{Peal of large bells, specification for}\index{Specifications!for bells}---As I gave a specification for large +clocks, I will do the same for bells, so far as any one model +can serve for a variety of cases. I add however some +variations and notes to explain them, which will enable anybody +with the least understanding of such things to make +out a specification for the peal he wants. And first, I +remark that specifications should always be silent about +notes\index{Notes of bells!should not be prescribed}, and stick to diameters and weights. Most of the bad +peals in the kingdom, except those by utterly bad bell-founders, +are greatly due to people demanding low notes +for low prices; and besides that, there are so many uncertainties +about notes, even with bells of very nearly the same +dimensions, that it leads to nothing but confusion to specify +anything about them. Suppose then a specification is +wanted for a peal of ten bells, intended to be as good as +possible, and of no unusual weight: it should be as follows:--- +\begin{enumerate} +\item The founder to make, and hang complete for ringing, +a peal of $10$ bells in perfect tune; the tenor to be $60$~inches +wide (or more, if you like, up to $67$ or $68$). The $4$ or $5$ +largest bells to be a $13$th of the diameter in thickness; +and the smaller ones to increase gradually up to the treble, +which is not to exceed a $10$th of its diameter in thickness. +%-----File: 396.png----------------------------------------------- +%-----Folio: 381-------------------------------------------------- + +For $8$ bells, the $4$ largest to be a $13$th, increasing up to +an $11$th in the treble; and for $6$ bells, the $3$ largest to be a +$13$th, and the treble may be an $11$th, or a $12$th. + +\item The bells are to be of the shape described in this +book as to their `sweep,' and all to have independent +clapper bolts going through a round hole in the crown, and +through the stock. The larger bells to have no canons, and +the smaller bells low canons, if any. The bells are all to +consist of pure copper and tin only, in the proportions of $13$ +to $4$, and are to be guaranteed as perfect castings, homogeneous, +and free from porosity or other defects. (I should +mention that those superficial marks called seams are of no +consequence, though of course a casting looks better without +them; but the slightest visible porosity in the smoothest +bell is a fatal mark of unsound casting, though a bell-founder +should find any number of brass-founders and +engineers to swear that it is not, as I know that Mears was +prepared to do about Big Ben, before Dr.~Percy's examination +of the `taster' cut out of it (see p.~\pageref{taster}). Also an inequality +in thickness round the bell, such as Great Peter of +York has, is equally fatal, and is not a `perfect casting.') + +\item The clappers to be hung with wooden blocks, not iron +and leather (for the leather soon wears out). The tenor +clapper to be a $90$th of the weight of the bell, and the others +to increase upwards, to about a $30$th for a treble a $10$th of its +diameter thick, and a $36$th for an $11$th, and a $40$th for a $12$th. +All nuts connected with the clappers to be keyed on, or else +double nuts (or they will shake loose). + +\item The brasses\index{Brasses for bell gudgeons} to be of $19$ copper to $5$ tin, and none to +have less than $1\frac12$~in.\ of metal on each side of the hole, +and the holes to be deep enough to prevent the small bells +from jumping, and to have at least $2$~inches of metal +below the hole. They are to be boxed over with wood to +keep out dust. [Metal tops always get torn off and stolen.] + +\item The gudgeons to be of steel, and to run from +%-----File: 397.png----------------------------------------------- +%-----Folio: 382-------------------------------------------------- +$2$~in.\ to $2\frac12$~in.\ long in the brass, and $1\frac12$~in.\ thick for a +bell of $30$ to $35$~cwt. (It is difficult to define the thickness +farther, and the fault is more generally in making them too +short than too thin.) They are to be fixed so that they will +keep themselves quite true in the stock. (The founders +have different ways of doing this, and I do not like to +prescribe any one absolutely, but I must say that Taylor's +plan is the best I have yet seen. The old one is very rough +indeed, and cannot be relied on to keep them either true or +firm.) + +\item The stays to go through iron loops bolted to the +stocks, the bottom only of the stay having a bolt through it, +and to be so strong that the slider may break rather than +the stay. The sliders to run in circular beds, traced from +the gudgeon, which are to be covered over to protect them +from grease dropping (which makes wood stick, though it +makes metals run). + +\item The wheels are all to have at least $4$ side stays to +keep them true. (The founders will never put more than +two unless they are made, and others have always to be +added in a year or two.) The wheels to be wide enough +and deep enough to prevent the ropes from slipping (a +source of frequent accidents, and always arising from bad +or untrue wheels; in fact wheels, like everything else now, +are generally made too flimsy; but I do not see how to +define their dimensions in a specification, nor indeed many +other things which can only be judged of by a competent +eye when they are done). + +\item The frame to be of English oak,\footnote{See, however, what is said about iron +frames on p.~\pageref{subsec:Iron_stocks_and_frames}.} and the founders to +state the dimensions of the beams. (This will at any rate +be useful in comparing tenders, which otherwise are deceptive.) +The wood must be perfectly dry before using, and if +joints get loose afterwards, the founder will be held responsible +for all expense incurred in consequence. The beams +are to be cut into by mortices as little as possible, and iron +%-----File: 398.png----------------------------------------------- +%-----Folio: 383-------------------------------------------------- +\textbf{T} pieces, and bed-bolts to be used instead, or in addition. +The diagonal struts especially are to be deep, and diagonal +bolts inclined the other way are to be used also. + +\item The \textit{bottom }of the frame to fit tight against the walls, +if it is about the width of the tower (see p.~\pageref{folly}), and if not, +to be strongly bolted to the great beams below; the position +of which the architect should be made to settle with the +bell-founder beforehand, if the tower or the floor is new; +and also to arrange for having two floors between the ringers +and the bells, with gravel or small stones on the lower one, +if they are very close together (see p.~\pageref{floor}). All the large +bells, as far as possible, to swing either north and south or +east and west, and not across each other. + +\item The tender to state the probable weight of each bell, +and maximum of the whole peal (the word `about' not to +be allowed there), and the founder will be paid for no excess +beyond that maximum. The tender also to state the cost +of frame and hangings separately, besides the price per +cwt.\ for the bells, and all other expenses, as far as they +can be estimated. (Recasting of old bells is always +charged at two guineas a cwt.\ whatever is the price of new +metal, see p.~\pageref{price}.) + +\item The whole of the work to be subject to the approval +of some competent person or persons, not being in the trade, +to be appointed by the [committee], who may require any +experiments to be made which they may think fit for testing +the bells. + +\item All the iron and woodwork to be painted\index{Painting!bell frames and wheels} twice, and +the frame also after a year, with Carson's anticorrosive paint. +(It is very odd that nothing will induce people to paint +their bell-frames. They leave them exposed to damp, and +frost, and heat, and see them cracking all over worse and +worse yearly, and then they are surprised at having to +spend three times as much as the painting would have cost, +in repairs after a few years. It is said not to be expedient +%-----File: 399.png----------------------------------------------- +%-----Folio: 384-------------------------------------------------- +to paint oak immediately, and for that reason only I have +allowed the year for it.) +\end{enumerate} + +\subsection[Bell-towers.]{Bell-towers.}\markboth{MODERN TOWERS TOO SMALL.}{ARCHITECTS DESTROY BELFRIES.}\label{subsec:Bell-towers.}\index{Bell-towers}---I proceed to notice a few things relating +to bells which are more the business of architects than bell-founders, +except that architects\index{Architects!ignore bells and clocks}\index{Church towers and architects} nowadays rather think it +their business to ignore everything that has to be done in a +building after they have left it. I have known plenty of +cases where they knew perfectly well that it was intended to +have peals of bells and clocks, and yet have built costly +towers without condescending to learn, either by reading or +inquiry, what provisions should be made, or even what +dimensions were required. That they may have the less +excuse, and that those who want church bells may have some +idea of what their architects ought to do, I will give the +following information as the result of my own experience; +and I am probably the only person living who has the +experience of designing both bells and clocks, and the towers +in which they are to be placed. + +It\label{bellplan} follows from what I said before about bell-frames, that +the smallest tower fit for even a small peal of $6$ bells, should +be $11$~ft.\ square inside\index{Bell-towers!construction and size for bells}; and the smallest for a very moderate +peal of $8$ should be $16$. Even these sizes make the ropes +hang closer to the walls than they ought to do, and therefore +they are much better somewhat larger. Very few \textit{old} +towers with $8$ bells are so small as $16$~ft.; they are much +more frequently $20$, and those with $6$ bells at least $14$. In +what is called \textit{A Book on Building}, I have shown how +much narrower modern towers generally are than old +ones; but I am only now dealing with them as campaniles, +which in fact they always are, without reference to +architectural reasons in the same direction. Of course when +$10$ or $12$ bells are intended, the towers should be larger +still, certainly not less than $22$ and $24$~ft.\ square inside. + +There is also another reason for it. Bells sound much +better in a large chamber than a small one. Anyone who +%-----File: 400.png----------------------------------------------- +%-----Folio: 385-------------------------------------------------- +has heard the Doncaster bells will hardly believe that the +three bells in All Saints' Church, Margaret Street, are +repetitions by the same founders of the 1st, 4th, and tenor +of Doncaster. But the Doncaster bell-chamber is $23$~ft.\ square, +and Margaret Street not more than $14$, or just two-fifths +of the area. And the same at All Saints, Halifax, with +a spire $240$~feet high. The bells, a smaller peal than Burton, +could not be got into it on one level. + +Another important consideration is the windows. I have +known two cases, both in Leeds as it happened, where clock +bells had to be re-hung some feet higher up than the architects\index{Architects!often destroy belfries} +had provided, because they did not know that the bells +ought to be above the sills of the windows. Louvres\index{Bell-towers!windows should have louvres} again +are a frequent source of trouble, by being put too close or +too much overlapping, even if they are on that ugly and now +fashionable foreign plan of having a few enormously wide or +deep boards sticking out beyond the face of the mullions, +which never were in genuine English architecture. It is no +use trying to keep out snow, or even small driving rain, and +it does no harm if bell hangings are kept painted, and the +floor is made waterproof and drained. Louvres just overlapping +will keep out ordinary rain, and I am afraid cannot +be dispensed with in church towers, though they are at +Westminster, where the \label{floor}floor under the bells is flagged. It +is the custom in the eastern counties to put small clock bells +quite open on the tops of the church tower's, instead of +making the clock strike on the tenor of the peal, and they +are generally heard farther; in fact, a clock bell (if only a +clock bell) cannot be too open, as it has no hangings that +will spoil with rain if the hammer gudgeons are occasionally +oiled---or even if they are not, for a long time. + +There must be two floors between the ringers and the +bells, or they cannot hear for the noise. In most towers of +good size this can easily be done, but in low central towers +it is sometimes difficult. The plan to be adopted then is to +%-----File: 401.png----------------------------------------------- +%-----Folio: 386-------------------------------------------------- +lay a strong floor about a foot below the bell-floor by straps +from the great beams, and cover it a few inches thick with +large gravel, or broken stones (not sand), or else to fill up +the whole space between the floors with shavings, including +a box full of them for the trap door which must be left +under the great bell. I need hardly say that the great floor +beams ought to come under the beams of the bell-frame as +much as possible, and should rest on large corbels, and for +heavy peals should be strutted also from corbels lower down +This too is often neglected, and a floor made at random, and +then the bell-founder is expected to fix a firm bell-frame on a +floor not fit to carry it. + +But the worst abomination of all, committed by architects\index{Architects!often destroy belfries}\index{Belfries, their destruction by architects}\index{Church towers and architects}\label{archdestroy}\markboth{CHURCH TOWERS.}{ARCHITECTS DESTROY BELFRIES.} +and church restorers, is the destroying of the belfry (\textit{i.e.}\ ringing +chamber) floor for the sake of making a `lantern'\index{Lantern towers difficult for bell-ringing} of +the tower. This has been done, at Hereford Cathedral, Ludlow +and Boston churches, Merton College Chapel, St.~Alban's +Abbey, and divers other places. At St.~Alban's, where the +space is abundant, they have lately re-hung the bells higher +up, and so regained a ringing chamber, but not so at the +others. At Howden the ringing is done inconveniently and +dangerously from a narrow gallery round the tower, and so +it is at Merton Chapel---unless they ring from the ground +now, as the tower is practically in the ante-chapel. At +Pershore Sir G.~Scott did a better thing than a gallery, by +the converse of it, a sort of insulated floor, leaving an open +space round it except where there is a bridge to reach it. Mr.~Cattley +and I did much the same at Worcester Cathedral, +which has probably the best belfry in England on account of +the great width of the tower, $32$~ft.\ inside. The much +larger central towers of York and Lincoln do not contain the +peals of bells; they are in the smaller western towers. In +the central tower which I designed for Mr.~Bass, at Burton: +there are small spandril windows to light the space under +it, as in the grand old church of Hedon, so that the +%-----File: 402.png----------------------------------------------- +%-----Folio: 387-------------------------------------------------- +belfry floor can still be at the natural place, about the +level of the roofs of the four limbs of the church; and +it is $22$~feet high. At Doncaster there was height enough +above the lower windows of the tower. + +But this lanterning mania has destroyed some belfries +irreparably, and ringers will not ring long in dark holes +about $8$~feet high, which were only intended for the intermediate +chamber or clock room. That demon of church +destruction, under the name of restoration, Wyatt, in the +last century and early in this, pulled down the old campanile +of Salisbury, and the bells had to be sold because +nobody dared ring them in the great overloaded steeple of +the cathedral. Well might Pugin say of him, in one of his +`restored' churches, `Yes, the monster has been here!' + +Where it has become impossible to \markboth{CHURCH TOWERS OFTEN SPOILT FOR RINGING.}{CHURCH TOWERS OFTEN SPOILT FOR RINGING.}ring bells properly, the +best thing to do is at once to fit them up for chiming only, +\textit{i.e.}\ tolling with levers. Though inferior to ringing in some +respects, and much less interesting to ringers, it has a +sweeter sound, but feebler. The clappers ought to be +heavier for it, as they strike much softer: especially when +there are only $3$ or $4$ bells, chiming sounds much better +than ringing. The tolling of $3$ large bells has a very grand +sound, and the ringing of two bells only frame high, \textit{i.e.}\ swinging +up to horizontal, so that they strike quickly, has +a pleasant and lively sound. I always admire it at New +College Chapel when I visit Oxford. + +The \label{windows}\index{Windows of bell-chambers}windows of bell-chambers, and of every opening in +the tower or spire above them, should be completely covered +with strong wire netting\index{Bell-towers!windows should be caged}, which must also be kept in repair, +to keep out birds, which otherwise fill the place with sticks +and dirt, which caused the second fire at York Minster, and +the destruction of the bells. The netting should be of +about $18$ gauge woven in squares of half an inch, not in long +openings tied with thin wire, which soon perishes. + +The well-known story\index{St.~Paul's!clock heard at Windsor striking thirteen} of St.~Paul's clock being heard at +%-----File: 403.png----------------------------------------------- +%-----Folio: 388-------------------------------------------------- +Windsor striking $13$ by a sentinel who was charged with +being asleep, is often regarded as fabulous; and so it would +be in the present feeble condition of the striking. But Reid +says, in his book on clocks, that he heard it there himself +and I have heard an officer quartered there say the same +The Doncaster clock striking on a bell of only $30$~cwt.\ has +been heard $11$ miles in a very flat country. Nobody has +yet solved the problem why a wind which you can hardly +feel will make the difference of your hearing bells half a mile +or ten miles, according as the wind is with you or against. + +\subsection[The great bells of Europe]{The great bells of Europe}\markboth{THE GREAT BELLS OF EUROPE.}{THE GREAT BELLS OF EUROPE.}\label{subsec:The_great_bells_of_Europe}\index{Bells!great bells of Europe}\index{Europe, the great bells of}\ are all that remains to +notice, by which I mean those above any ordinary weight of +the tenor of a peal, which may be called $3$~tons; for there is +none except Exeter and St.~Paul's which exceeds or even +reaches that weight.\footnote{I will use the letters M, T, W, to denote the only three English +founders who have made large bells in this century, viz.: Mears\index{Mears, bell-founders!Montreal and York}, +Taylor, and Warner.} There are clock bells of $3$~tons at +the town halls of Hull (W) and Halifax (T), and one lately +made from my specification, with $4$ quarter bells, for the post +office at Adelaide (T). I cannot vouch for the accuracy of +the whole of the \hyperlink{longtable1}{following list}; indeed I am sure that some +of the figures cannot be correct, and I must warn people +against newspaper statistics of such things. For instance +even in London, the St.~Paul's clock bell still figures in +sundry books as $9$~ft.\ wide instead of $6$~ft.~$9$~in., and I have +seen the York bell credited with a greater weight than Westminster; +and if such exaggerations as these take place about +bells whose sizes and weights have been correctly published +for years in this and other books, it is evident that little +reliance can be placed on others where the weights and sizes +are plainly inconsistent. Most of the foreign ones are taken +from the small German book on bells by Otte, before noticed. +But I satisfied myself that he sometimes uses the measures +of one country and sometimes of another. I have received +%-----File: 404.png----------------------------------------------- +%-----Folio: 389-------------------------------------------------- +sections and measures of some bells from architects and +others who had measured them, and I shall be thankful for +any more, of really large bells. I give the weights of the +two great Russian ones by calculation from their size and +thickness, which is easily done, from their similarity to the +Westminster pattern. I have seen even a larger weight +than $8$~cwt.\ given for the clapper of the Paris bell; but the +$8$~cwt.\ agrees pretty well with the drawing; but if the drawing +I have of the Erfurt clapper is right it cannot be so +heavy as Otte gives it. Our clappers are of a better shape +than the foreign ones, though generally too light. + +\markboth{CHARACTER OF SOME GREAT BELLS.}{CHARACTER OF SOME GREAT BELLS.}I have no doubt that some of these bells are bad ones, or +they would have a greater reputation than they have. The +Erfurt bell is the most famous of all the very large ones, +and probably that of Paris next, though there are two +opinions about that; the old Cologne and Lucerne bells I +have heard well spoken of. The new and larger Cologne\index{Bells!Cologne, cast three times}\index{Cologne bell cast three times} one +was cast three times. I have never heard it praised. On +the other hand the new Great Paul\index{Great Paul of London}\index{St.~Paul's!the great bell} was cast successfully at +once, and it seems to me as good as possible. We have +ample proof at home that large bells may be thought not +worth ringing after costing a great sum of money, or may +sound no distinct note, or may be supposed to be cracked +because they are so bad. I heard the Montreal\index{Mears, bell-founders!Montreal and York} bell before +it went out, and thought it quite as bad as York. I am +told that the bell of St.~Peter's\index{Bells!St.~Peter's, and Montreal, and Great Paul} at Rome sounds as ill as +it ought to do from its extremely bad flower-pot shape; +I have a model of it, and it is loaded also with ornaments +in high relief, which are sure to injure the sound; but the +shape is such that it is of very little consequence what the +decoration is. The Canterbury bell is struck so feebly by a +good-for-nothing modern clock that no one would suppose it +had any business in this list: nor Tom of Oxford either, if +judged only by his weak and abominable sound. See List, +over the page. + +%-----File: 405.png----------------------------------------- +%-----Folio: 390-------------------------------------------- +\clearpage\markboth{LIST OF GREAT BELLS.}{LIST OF GREAT BELLS.} +\addtolength{\textwidth}{52pt} +\begin{longtable}{|l@{\,}|@{\,}c@{\,}|c@{}c@{\,}|c@{\,}c|c@{\,}|@{\,}c@{\,}|@{\,}c@{\,}|} +\hline\index{Bells!great bells of Europe!list of their weights and sizes}\index{Europe, the great bells of}\index{Weights and sizes of bells} +Great Bells of &Date. & \multicolumn{2}{|c|}{Diameter.} & \multicolumn{2}{|c|}{Weight.} +&Note. &Thick- &Clapper or\\ +&&&&&&&ness.&Hammer.\\ +\hline\index{Table!great bells of Europe} + & &ft. &in. &tns. &cwts. & &in. &lbs. \endhead +\hline\endfoot\label{longtable1}\hypertarget{longtable1}{% +Moscow (broken)} &1734 &22 &8 &220 &0 &\dots &23 &\dots \\ +Another &1817 &18 &0 &110 &0 &\dots &18 &\dots \\ +Another &1878 &\dots &\dots &28 &13 &\dots &\dots &\dots \\ +Novogorod &\dots &\dots &\dots &31 &0 &\dots &\dots &\dots \\ +Cologne &1874 &11 &3 &25 &10 &D~flat &\dots &1530 \\ +Rouen (was) &1501 &10 &8 &17 &6 &\dots &\dots &\dots \\ +Olmutz &\dots &\dots &\dots &17 &18 &\dots &\dots &\dots \\ +Paris, Montmartre &1898 &9 &11$\frac12$&18&10 &C &9 &\dots \\ +Vienna &1711 &9 &10 &17 &14 &\dots &\dots &1600? \\ +St.~Paul's, T. &1882 &9 &6$\frac12$&16&14 &E~flat &8$\frac34$ &730 \\ +Westminster, M. &1858 &9 &0 &13 &11 &E &\dots &766 \\ +Paris, Notre Dame &1680 &8 &8 &12 &0 &F to &7$\frac12$ &900 \\[-1ex] + & & & & & &F~sharp& & \\ +Montreal, M. &1847 &8 &7 &11 &11 &\dots &8$\frac12$ &413 \\ +Sens &\dots &8 &7 &11 &0 &\dots &\dots &\dots \\ +Frankfort &1868 &8 &6$\frac12$&10&0 &E &\dots &\dots \\ +Frankfort (2nd) &1868 &6 &5 &4 &8 &A~flat &\dots &\dots \\ +Erfurt &1497 &8 &5$\frac34$&10&0 &E &7$\frac12$&1120? \\ +Erfurt (2nd) &1720 &6 &5 &4 &8 &A~flat &\dots &\dots \\ +York, M. &1845 &8 &4 &10 &15 &F~sharp &8 &405 \\ +Rheims &1570 &8 &2$\frac12$&9 &0 &F &\dots &\dots \\ +Rheims (2nd) &1849 &\dots &\dots &7 &0 &G &\dots &\dots \\ +Vienna (2nd) &\dots &\dots &\dots &10 &0? &\dots &\dots &\dots \\ +Magdeburg &1702 &8 &1$\frac12$&8 &16 &E &\dots &\dots \\ +Magdeburg (2nd) &1590 &6 &5 &5 &0 &B~flat &\dots &\dots \\ +Schaffhausen &1486 &\dots &\dots &9 &0? &\dots &\dots &\dots \\ +Lyons &\dots &\dots &\dots &8 &0? &\dots &\dots &\dots \\ +Cologne (2nd) &1448 &7 &11 &8 &0 &G &\dots &\dots \\ +Tournai &1843 &7 &9 &8 &10 &\dots &\dots &\dots \\ +Tournai (Beffroi) &1393 &6 &5$\frac34$&\dots&\dots&\dots&\dots &\dots \\ +Breslau &1507 &\dots &\dots &9 &0? &\dots &\dots &\dots \\ +Breslau (2nd) &1721 &\dots &\dots &5 &0? &\dots &\dots &\dots \\ +Amiens &1748 &\dots &\dots &9 &0? &\dots &\dots &\dots \\ +Amiens (2nd) &1736 &6 &0 &5 &0? &\dots &\dots &\dots \\ +Rennes &\dots &7 &7$\frac44$&7 &8 &F to &\dots&\dots \\[-1ex] + & & & & & &F~sharp& & \\ +Rennes (2nd) &\dots &5 &11$\frac12$&4&2 &A &\dots &\dots \\ +Marseilles &\dots &\dots &\dots &8 &0? &\dots &\dots &\dots \\ +Manchester, T. &1882 &7 &7$\frac12$&8 &3 &G &7 &458 \\ +Manchester (2nd), T. &1882 &6 &8 &5 &2 &\dots &\dots &\dots \\ +Gorlitz &1516 &\dots &\dots&8 &0? &\dots &\dots &\dots \\ +St.~Peter's, Rome &1786 &7 &6 &7 &0? &\dots &\dots &\dots \\ +Beverley, T. &1901 &7 &3 &7 &1 &G &6$\frac12$ &360 \\ +Sneeberg &\dots &7 &6 &7 &10? &\dots &\dots &\dots \\ +Cambrai &\dots &\dots &\dots&7 &15? &\dots &\dots &\dots \\ +%-----File: 406.png--------------------------------------------% +%-----Folio: 391-----------------------------------------------% +Hamburgh (St.~Nic.) &1876 & 7 &6 & 6 & 7 &\dots &\dots &\dots \\ +Nuremberg &1392 &\dots &\dots & 7 & 16? &\dots &\dots &\dots \\ +Malines &1844 & 7 &7$\frac14$& 7 & 0 &G~flat&\dots &\dots \\ +Malines (2nd) &1696 & 6 &3 & 4 & 18 &A~flat&\dots &\dots \\ +Le Mans &\dots & 7 &3 & 5 & 16 &F &\dots &\dots \\ +Lucerne &1636 &\dots &\dots & 6 & 0? &\dots &\dots &\dots \\ +Halberstadt &1457 &\dots &\dots & 6 & 0? &\dots &\dots &\dots \\ +Bale &\dots &7 &1$\frac12$& 5 & 14 &F~sharp&\dots&\dots \\ +Middleburg &\dots &7 &1$\frac12$& 5 & 8 &F~sharp&\dots&\dots \\[-1ex] + & & & & & &to G & & \\ +Rouen (Cathedral) &1852 & 7 &0$\frac12$& 6 & 0 &A~flat &\dots&\dots \\ +Rouen (Bons\`ecours) &1892 & 6 &9$\frac12$&\dots&\dots&G &\dots &\dots \\ +Rouen (St.~Hilaire) &\dots & 5 &11$\frac34$&\dots&\dots&\dots &\dots &\dots \\ +Rouen (St.~Ouen) &\dots & 5 &11 & 3 & 10?&A~flat &\dots &\dots \\ +Antwerp &1655 & 7 &0 & 5 & 12 &A~flat &\dots &\dots \\ +Antwerp (2nd) &1310 & 6 &5 & 4 & 18 & A &\dots &\dots \\ +Oxford &1680 & 7 &0 & 5 & 15?&\dots &\dots &\dots \\ +Newcastle, T. &1891 & 6 &11$\frac12$& 5 & 18 &A~flat &\dots &\dots \\ +Halle &1480 & 6 & 0 &\dots&\dots&\dots &\dots &\dots \\ +Munich &1493 & 7 & 3 & 6 & 0 &\dots &\dots &\dots \\ +Tourcoing &\dots &\dots &\dots & 6 & 0 &\dots &\dots &\dots \\ +Ghent &\dots & 6 &11$\frac12$&5 &10 &G to G &\dots &\dots \\[-1ex] + & & & & & & flat & & \\ +Ghent (2nd) &\dots & 6 & 3 &5 &0 &A to A &\dots &\dots\\[-1ex] + & & & & & &flat & & \\ +Lincoln, M. &1835 & 6 &10 &5 &8 & A &6 & 224 \\ +F\'ecamp &1878 & 6 &10 &\dots&\dots&G &\dots &\dots \\ +St.~Paul's (Old) &1716 & 6 &9$\frac12$& 5 & 2 &A and C&180 &\dots \\ +Bruges &1680 & 6 &9$\frac14$& 5 & 0 & G &\dots &\dots \\ +Leipsic &1634 & 7 &7$\frac34$& 5 & 4 & A &\dots &\dots \\ +Brussells &\dots &\dots &\dots & 7 & 0 &\dots &\dots &\dots \\ +Brussells (2nd) &\dots &\dots &\dots & 5 & 1 &\dots &\dots &\dots \\ +Coire (Protestant) &\dots & 6 &5$\frac34$& 4 & 10 &A~flat&\dots &\dots \\ +Coire (R.~C.) &\dots & 6 &1$\frac34$& 4 & 0 &A~flat&\dots &\dots \\ +Bradford, T. &1873 & 6 &5$\frac14$& 4 & 7 & A & 6 &\dots \\ +Courtrai &\dots & 6 &4 & 4 & 12 &B~flat&\dots &\dots \\ +Dantzic &1453 &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Cologne (3d) &1449 & 5 & 0 & 4 &10? &\dots &\dots &\dots \\ +Batisbon &1325 &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Brunn &1515 &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Rodiz &1814 &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Chalons &\dots &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Mariazell &1830 &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Dresden &1787 &\dots &\dots & 5 & 0? &\dots &\dots &\dots \\ +Worcester, T. &1868 & 6 &4$\frac14$& 4 & 10 &B~flat& 6 & 246 \\ +%-----File: 407.png----------------------------------------------% +%-----Folio: 392-------------------------------------------------% +Exeter (Peter) &1675 &6 &2$\frac14$& 4 &0 &A &\dots&\dots \\ +Exeter (Tenor).T &1902 &6 &0 &3 &12 &B~flat& 5 & \dots \\ +Lille (St.~Andr\`e) &\dots &\dots &\dots &4 &8 &\dots &\dots& \dots \\ +Lille (N.~D.\ de la Treille) &\dots &\dots &\dots&3 &10$\frac34$ &\dots&\dots&\dots \\ +Sydney, T. &\dots &\dots &\dots &4 &18 &\dots &\dots& \dots \\ +Merville &\dots &\dots &\dots &4 &7$\frac12$&\dots&\dots & \dots \\ +Preston, T. &1868 &6 &3 &4 &16 &B~flat& 6 & 227 \\ +Bolton, W. &1872 &6 &2 &4 &2 & B & 6 & 200 \\ +Leeds, W. &1859 &6 &2 &4 &1 & B & 6 & 200 \\ +Valetta &\dots &6 &1 &\dots&\dots&B~flat&\dots& \dots \\ +Boulogne &1800 &\dots &\dots &4 &0 &\dots &\dots& \dots \\ +Westminster(4th) &1857 &6 & 0 &3 &18 & B &5$\frac78$ & 175 \\ +\ ''\ (all W.)3rd qur.&1858&4 &6 &1 &13$\frac12$&E&4$\frac12$ & 80 \\ +\ ''\ (all W.)2nd qur.&1857&4 &0 &1 &6 &F~sharp&3$\frac78$ & 60 \\ +\ ''\ (all W.)1st qur.&1857&3 &9 &1 &1 &G~sharp&3$\frac34$ & 56 \\ +Chichester, T. &1877 &5 &10$\frac12$&3 &14 &B~flat &\dots & 142 \\ +H\^otel de Ville, Paris&\dots&\dots&\dots &3 &10 &\dots &\dots & \dots \\ +Canterbury &1762 &5 &9 &3 &10 &C &5$\frac12$ & \dots \\ +Gloucester &1400 &5 &8$\frac12$&3 &5 &C &\dots & \dots \\ +\cline{1-9} +\end{longtable} +\label{longtable2}N.B.---Many of the above weights have been calculated from measurements taken by +an experienced English bell-founder on the spot. + +\backmatter +\addtolength{\textwidth}{-52pt} +\chapter{ADDENDA.}\label{chap:ADDENDA.} +\phantomsection +\addcontentsline{toc}{section}{Addenda.} +\label{addenda_start} +\subsection[Addendum to p.~\protect\pageref{199add}]{Addendum to p.~\protect\pageref{199add}.}---A powerful clock, by Messrs.~Smith +of Derby, was fixed at Beverley Minster\index{Beverley!clock} in 1902, +which is the only clock in the world striking upon bells in +two towers. The quarters chime upon the peal of $10$ bells +(tenor $41\frac12$~cwt.) in the N.W.\ tower (in strains of $12$, $20$, +$32$, and $41$ notes, at the 1st, and, 3rd, and 4th quarters +respectively), and the hour is struck upon the bell, ``Great +John'' ($7$~tons, $1$~cwt.) in the S.W.\ tower, which is exactly +in tune with the peal. For this purpose, the clock is divided; +the going part, and the chiming machine, being in the N. +%-----File: 408.png-------------------------------------------- +%-----Folio: 393----------------------------------------------- +tower (on the north face of which there is a Gothic skeleton +dial $14$~feet in diameter), and the striking train in the S. +tower. The connection is made by a rod through the +``tympanum,'' or chamber between the towers. + +\subsection[Addendum to p.~\protect\pageref{200add}]{Addendum to p.~\protect\pageref{200add}.}\label{add200}---I designed the clock at St.~Paul's +Cathedral to strike the hour on ``Great Paul,'' but +objection was taken to altering the striking from the very +inferior old ``Phelps'' bell. + +\subsection[Addendum to p.~\protect\pageref{341add}]{Addendum to p.~\protect\pageref{341add}.}\label{add341}---Since 1896, a revolution has been +brought about in the tuning\index{Tuning of bells|(} of bells, inaugurated by the +late Rev.~A.~B.~Simpson, Rector of Fittleworth and Prebendary +of Chichester. Every bell gives out several notes, +but, while the old Belgian founders (Hemony, Van den +Gheyn, etc.) endeavoured to bring these more or less nearly +into tune with each other, the task has never been achieved, +and but rarely attempted, in England or any other country, +for the past three centuries. Elaborate experiments, however, +have demonstrated its possibility, and modern science +and improved machinery enable the old methods to be +applied with greater exactness than ever before. There is +no reason now why every bell should not give out a true +and harmonious chord instead of a collection of discords. +The tone of properly tuned bells is incomparably fuller and +richer; and ordinary bells sound so thin and poor (as well +as inharmonious) by comparison, that more than one fair +average peal has already been sent to Loughborough to be +recast---Messrs.~Taylor being as yet the only founders who +have taken up the discovery. The principal examples are +the new peals of the Minster and St.~Mary's, Beverley; St.~Patrick's +Cathedral, Dublin; Holy Trinity, Hull; and +Loughborough Church, and the tenor of Exeter Cathedral. +In the N.\ tower of Beverley Minster hangs a peal of $10$ +bells (1901), the tenor of which ($41\frac12$~cwt.\ in C) was described +by Mr.~W.~W.~Starmer, \textsc{a.r.a.m.}, when lecturing +on bells before the Incorporated Society of Musicians, in +February, 1903, as an ideal example of a perfectly tuned bell. +In the S.\ tower is a Bourdon (``Great John'') of $7$~tons, $3$~cwt.\ in G, which has been tuned an exact octave below the +%-----File: 409.png------------------------------------------- +%-----Folio: 394---------------------------------------------- +sixth bell of the peal, thus satisfying the most exacting ear, +both when it is rang as a service-bell on the ceasing of the +peal, or when it follows the chimes as an hour-bell for the +clock \textit{(v.~Addendum }to p.~\pageref{199add}). During the visit of the +Yorkshire Association of Change Ringers to Beverley\index{Bells in peals!Beverley}\index{Beverley!bells} in +September, 1902, it was rung as a bass accompaniment to +the peal, with fine effect.\index{Tuning of bells|)} + +\subsection[Addendum to p.~\protect\pageref{355add}]{Addendum to p.~\protect\pageref{355add}.}\label{add355}\index{Bells in peals!large and small together, bad}---It is now, however, asserted +that this difficulty has been entirely overcome by the new +method of tuning, to prove which, a very small set of six +bells, the largest only a little over $4$~cwt., was exhibited at +the Ecclesiastical Art Exhibition in the Imperial Institute +in connection with the London Church Congress of 1899. +Canon Simpson called attention to the subject in a letter to +the \textit{Times }(Oct.~8, 1899), in which he said, ``This little +chime shows that the difficulty of small bells has been +mastered, and there can be no reason why carillons of any +size should not now be made in perfect tune.'' Messrs.~Taylor +have placed a similar miniature peal of eight in their +tower at the Loughborough Foundry. + +\subsection[Addendum to p.~\protect\pageref{362add}]{Addendum to p.~\protect\pageref{362add}.}\label{add362}---Persons who want large bells +or peals should be informed that Messrs.~Taylor of Loughborough +still use my composition of $13$ of copper to $4$ of +tin which I prescribed for the Westminster bells as +mentioned in this book. + +\subsection[Addendum to p.~\protect\pageref{371add}]{Addendum to p.~\protect\pageref{371add}.}\label{add371}---This recommendation has now +been carried out with great success. Two out of the three +largest church bells in this country, ``Great Paul'' of +London, and ``Great John'' of Beverley, have been hung +in roller-bearings\index{Friction rollers!for bells}, and in steel headstocks of horseshoe +shape, so that there is a very considerable counterpoise +above the gudgeons. They can be easily rung ``frame-high,'' +or higher, if desired, without any strain to the towers.\label{addenda_end} +%-----File: 410.png---------------------------------------------- +%-----Folio: 395------------------------------------------------- + +\chapter{APPENDIX.}\label{chap:APPENDIX.}\label{appendix} +\phantomsection +\addcontentsline{toc}{section}{Appendix.} +\subsection[Weathercocks]{Weathercocks}\label{weathercocks}\index{Weathercocks} \ (see also p.~\pageref{subsec:Weathercocks.}).---Weathercocks are so +much expected on steeples and other high roofs, and so +much within the competence of public clockmakers, and so +universally made wrong, that I add a few lines about them +and their universal defects of sticking fast (and so pointing +wrong) by day and squeaking by night, and swallowing +damp and dust, which decay them prematurely. + +The only way to make them, and avoid all this, is to join +the meeting narrower ends of two oblong sheets of copper +by copper rivets, so as to form a tube that will ride loosely +on the usual spike, and then stop the upper end of the tube +with a bell-metal plug or disc, pushed tight into the tube and +fixed with common solder, or only the edges of the tube +hammered over it, so that it will ride and spin on the top +of the spike---which is better rounded than sharp. The +other end of the double plate may be cut into any shape +you like, as pointer to the point of the compass from which +it is called E.~W.~N.~S., as usual. I have had successive +cocks of this construction in use, and perfectly successful, +for years. Two of my best makers of large clocks---viz.\ Joyce +of Whitchurch, and Smith and Sons of Derby, who +made the new St.~Paul's clock under my direction in 1893---have +offered to make them, and a firm of coppersmiths wrote +to me to the same effect, intimating that they did so already. +But my building foreman could find nothing of the kind +in shops that sell weathercocks of the usual badness, and I +have a similar complaint from a friend with a large country +house. The spike should be slightly oiled occasionally, but +not greased thickly. + +Chimney-cowls may evidently be made in the same way. +%-----File: 411.png----------------------------------------------- +%-----Folio: 396-------------------------------------------------- + + + +\index{Church clocks|see{Turret clocks}} +\index{Going barrels|see{Maintaining power}} +\index{Quarter chimes|see{Chimes}} +\index{Time, measures of|see{mean, sidereal, local}} +\index{Wheels, numbers of teeth|see{Teeth}} +\setlength{\columnsep}{35pt} +\printindex +\markboth{INDEX.}{INDEX.} +%-----Folio: 404-------------------------------------------------- +\newpage\markboth{}{}\vspace*{\stretch{1}} +\section*{THE END.} +\vspace{\stretch{1}} +\centering PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON AND BECCLES. + + +\newpage + +\small +\pagenumbering{gobble} +\begin{verbatim} + +End of Project Gutenberg's A Rudimentary Treatise on Clocks, +Watches and Bells, by Edmund Beckett + +*** END OF THIS PROJECT GUTENBERG EBOOK CLOCKS, WATCHES, BELLS *** + +*** This file should be named 17576-t.tex or 17576-t.zip *** +*** or 17576-pdf.pdf or 17576-pdf.pdf *** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/1/7/5/7/17576/ + +Updated editions will replace the previous one--the old editions will +be renamed. + +Creating the works from print editions not protected by U.S. copyright +law means that no one owns a United States copyright in these works, +so the Foundation (and you!) can copy and distribute it in the +United States without permission and without paying copyright +royalties. 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