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diff --git a/36691.txt b/36691.txt new file mode 100644 index 0000000..6a51535 --- /dev/null +++ b/36691.txt @@ -0,0 +1,13996 @@ +The Project Gutenberg eBook, Conversations on Natural Philosophy, in which +the Elements of that Science are Familiarly Explained, by Jane Haldimand +Marcet and Thomas P. Jones + + +This eBook is for the use of anyone anywhere 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 + + + + + +Title: Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained + + +Author: Jane Haldimand Marcet and Thomas P. Jones + + + +Release Date: July 10, 2011 [eBook #36691] + +Language: English + +Character set encoding: ISO-646-US (US-ASCII) + + +***START OF THE PROJECT GUTENBERG EBOOK CONVERSATIONS ON NATURAL +PHILOSOPHY, IN WHICH THE ELEMENTS OF THAT SCIENCE ARE FAMILIARLY +EXPLAINED*** + + +E-text prepared by Marilynda Fraser-Cunliffe, Stephen H. Sentoff, and the +Online Distributed Proofreading Team (http://www.pgdp.net) + + + +Note: Project Gutenberg also has an HTML version of this + file which includes the original illustrations. + See 36691-h.htm or 36691-h.zip: + (http://www.gutenberg.org/files/36691/36691-h/36691-h.htm) + or + (http://www.gutenberg.org/files/36691/36691-h.zip) + + + + + +CONVERSATIONS +ON +NATURAL PHILOSOPHY, + +IN WHICH +THE ELEMENTS OF THAT SCIENCE +ARE FAMILIARLY EXPLAINED. + + +_Illustrated with Plates._ + + +BY THE AUTHOR OF CONVERSATIONS ON CHEMISTRY, &c. + +WITH CORRECTIONS, IMPROVEMENTS, AND CONSIDERABLE ADDITIONS +IN THE BODY OF THE WORK; + +_Appropriate Questions, and a Glossary:_ + +BY DR. THOMAS P. JONES, +PROFESSOR OF MECHANICS, IN THE FRANKLIN INSTITUTE +OF THE STATE OF PENNSYLVANIA. + + + + + + +Philadelphia: +Published and Sold by John Grigg, +No. 9 North Fourth Street. +Stereotyped by L. Johnson. +1826. + +_Eastern District of Pennsylvania, to wit:_ + +Be it remembered, that, on the twenty-fourth day of April, in the +Fiftieth year of the Independence of the United States of America, A. D. +1826, John Grigg, of the said District, hath deposited in this office +the title of a book, the right whereof he claims as proprietor, in the +words following, to wit: + + "Conversations on Natural Philosophy, in which the Elements of + that Science are familiarly explained. Illustrated with Plates. + By the Author of Conversations on Chemistry, &c. With + Corrections, Improvements, and considerable Additions, in the + Body of the Work; appropriate Questions, and a Glossary: By Dr. + Thomas P. Jones, Professor of Mechanics, in the Franklin + Institute, of the State of Pennsylvania." + +In conformity to the Act of the Congress of the United States, entitled +"An Act for the Encouragement of Learning, by securing the Copies of +Maps, Charts, and Books, to the Authors and Proprietors of such Copies, +during the times therein mentioned;"--And also to the Act, entitled, "An +Act supplementary to an Act, entitled, 'An Act for the Encouragement of +Learning, by securing the Copies of Maps, Charts, and Books, to the +Authors and Proprietors of such Copies during the times therein +mentioned,' and extending the benefits thereof to the arts of designing, +engraving, and etching, historical and other prints." + + D. CALDWELL, + Clerk of the Eastern District of Pennsylvania. + + + + +PREFACE. + + +Notwithstanding the great number of books which are written, expressly +for the use of schools, and which embrace every subject on which +instruction is given, it is a lamentable fact, that the catalogue of +those which are well adapted to the intended purpose, is a very short +one. Almost all of them have been written, either by those who are +without experience as teachers, or by teachers, deficient in a competent +knowledge of the subjects, on which they treat. Every intelligent +person, who has devoted himself to the instruction of youth, must have +felt and deplored, the truth of these observations. + +In most instances, the improvement of a work already in use, will be +more acceptable, than one of equal merit would be, which is entirely +new; the introduction of a book into schools, being always attended with +some difficulty. + +The "Conversations on Chemistry," written by Mrs. Marcet, had obtained a +well-merited celebrity, and was very extensively adopted as a +school-book, before the publication of her "Conversations on Natural +Philosophy." This, also, has been much used for the same purpose; but, +the observation has been very general, among intelligent teachers, that, +in its execution, it is very inferior to the former work. + +The editor of the edition now presented to the public, had undertaken to +add to the work, questions, for the examination of learners; and notes, +where he deemed them necessary. He soon found, however, that the latter +undertaking would be a very unpleasant one, as he must have pointed out +at the bottom of many of the pages, the defects and mistakes in the +text; whilst numerous modes of illustration, or forms of expression, +which his experience as a teacher, had convinced him would not be clear +to the learner, must, of necessity, have remained unaltered. He +therefore determined to revise the whole work, and with the most perfect +freedom, to make such alterations in the body of it, as should, in his +opinion, best adapt it to the purpose for which it was designed. Were +the book, as it now stands, carefully compared with the original, it +would be found, that, in conformity with this determination, scarcely a +page of the latter, remains unchanged. Verbal alterations have been +made, errors, in points of fact, have been corrected; and new modes of +illustration have been introduced, whenever it was thought that those +already employed, could be improved; or when it was known, that, from +local causes, they are not familiar, in this country. + +The editor feels assured, that, in performing this task, he has rendered +the book more valuable to the teacher, and more useful to the pupil; and +he doubts not that the intelligent author of it, would prefer the mode +which has been adopted, to that which was at first proposed. + +The judicious teacher will, of course, vary the questions according to +circumstances; and those who may not employ them at all, as questions, +will still find them useful, in directing the pupil to the most +important points, in every page. + +The Glossary has been confined to such terms of science as occur in the +work; and is believed to include all those, of which a clear definition +cannot be found in our common dictionaries. + + + + +CONTENTS. + + +CONVERSATION I. + + ON GENERAL PROPERTIES OF BODIES. 9 + + INTRODUCTION. General Properties of Bodies. Impenetrability. + Extension. Figure. Divisibility. Inertia. Attraction. + Attraction of Cohesion. Density. Rarity. Heat. Attraction of + Gravitation. + + +CONVERSATION II. + + ON THE ATTRACTION OF GRAVITY. 22 + + Attraction of Gravitation, continued. Of Weight. Of the Fall of + Bodies. Of the Resistance of the Air. Of the Ascent of Light + Bodies. + + +CONVERSATION III. + + ON THE LAWS OF MOTION. 32 + + Of Motion. Of the Inertia of Bodies. Of Force to produce + Motion. Direction of Motion. Velocity, absolute and relative. + Uniform Motion. Retarded Motion. Accelerated Motion. Velocity + of Falling Bodies. Momentum. Action and Reaction equal. + Elasticity of Bodies. Porosity of Bodies. Reflected Motion. + Angles of Incidence and Reflection. + + +CONVERSATION IV. + + ON COMPOUND MOTION. 46 + + Compound Motion, the result of two opposite forces. Of + Curvilinear Motion, the result of two forces. Centre of Motion, + the point at rest, while the other parts of the body move round + it. Centre of Magnitude, the middle of a body. Centripetal + Force, that which impels a body towards a fixed central point. + Centrifugal Force, that which impels a body to fly from the + centre. Fall of Bodies in a Parabola. Centre of Gravity, the + point about which the parts balance each other. + + +CONVERSATION V. + + ON THE MECHANICAL POWERS. 54 + + Of the Power of Machines. Of the Lever in general. Of the Lever + of the first kind, having the Fulcrum between the power and the + weight. Of the Lever of the second kind, having the Weight + between the power and the fulcrum. Of the Lever of the third + kind, having the Power between the fulcrum and the weight. Of + the Pulley. Of the Wheel and Axle. Of the Inclined Plane. Of + the Wedge. Of the Screw. + + +CONVERSATION VI. + + ASTRONOMY. + + CAUSES OF THE MOTION OF THE HEAVENLY BODIES. 70 + + Of the Earth's annual motion. Of the Planets, and their motion. + Of the Diurnal motion of the Earth and Planets. + + +CONVERSATION VII. + + ON THE PLANETS. 80 + + Of the Satellites and Moons. Gravity diminishes as the Square + of the Distance. Of the Solar System. Of Comets. + Constellations, signs of the Zodiac. Of Copernicus, Newton, &c. + + +CONVERSATION VIII. + + ON THE EARTH. 91 + + Of the Terrestrial Globe. Of the Figure of the Earth. Of the + Pendulum. Of the Variation of the Seasons, and of the Length of + Days and Nights. Of the Causes of the Heat of Summer. Of Solar, + Siderial, and Equal or Mean Time. + + +CONVERSATION IX. + + ON THE MOON. 108 + + Of the Moon's Motion. Phases of the Moon. Eclipses of the Moon. + Eclipses of Jupiter's Moons. Of Latitude and Longitude. Of the + Transits of the inferior Planets. Of the Tides. + + +CONVERSATION X. + + HYDROSTATICS. + + ON THE MECHANICAL PROPERTIES OF FLUIDS. 118 + + Definition of a Fluid. Distinction between Fluids and Liquids. + Of Non-Elastic Fluids, scarcely susceptible of Compression. Of + the Cohesion of Fluids. Of their Gravitation. Of their + Equilibrium. Of their Pressure. Of Specific Gravity. Of the + Specific Gravity of Bodies heavier than Water. Of those of the + same weight as Water. Of those lighter than Water. Of the + Specific Gravity of Fluids. + + +CONVERSATION XI. + + OF SPRINGS, FOUNTAINS, &c. 128 + + Of the Ascent of Vapour and the Formation of Clouds. Of the + Formation and Fall of Rain, &c. Of the Formation of Springs. Of + Rivers and Lakes. Of Fountains. + + +CONVERSATION XII. + + PNEUMATICS. + + ON THE MECHANICAL PROPERTIES OF AIR. 136 + + Of the Spring or Elasticity of the Air. Of the Weight of the + Air. Experiments with the Air Pump. Of the Barometer. Mode of + Weighing Air. Specific Gravity of Air. Of Pumps. Description of + the Sucking Pump. Description of the Forcing Pump. + + +CONVERSATION XIII. + + ON WIND AND SOUND. 146 + + Of Wind in General. Of the Trade Wind. Of the Periodical Trade + Winds. Of the Aerial Tides. Of Sound in General. Of Sonorous + Bodies. Of Musical Sounds. Of Concord or Harmony, and Melody. + + +CONVERSATION XIV. + + ON OPTICS. 157 + + Of Luminous, Transparent, and Opaque Bodies. Of the Radiation + of Light. Of Shadows. Of the Reflection of Light. Opaque Bodies + seen only by Reflected Light. Vision Explained. Camera Obscura. + Image of Objects on the Retina. + + +CONVERSATION XV. + + OPTICS--_continued._ + + OF THE ANGLE OF VISION, AND REFLECTION OF MIRRORS. 168 + + Angle of Vision. Reflection of Plain Mirrors. Reflection of + Convex Mirrors. Reflection of Concave Mirrors. + + +CONVERSATION XVI. + + ON REFRACTION AND COLOURS. 179 + + Transmission of Light by Transparent Bodies. Refraction. + Refraction by the Atmosphere. Refraction by a Lens. Refraction + by the Prism. Of Colour from the Rays of Light. Of the Colours + of Bodies. + + +CONVERSATION XVII. + + ON THE STRUCTURE OF THE EYE, AND OPTICAL INSTRUMENTS. 195 + + Description of the Eye. Of the Image on the Retina. Refraction + by the Humours of the Eye. Of the use of Spectacles. Of the + Single Microscope. Of the Double Microscope. Of the Solar + Microscope. Magic Lanthorn. Refracting Telescope. Reflecting + Telescope. + + +GLOSSARY, 205 + + + + +CONVERSATION I. + +ON GENERAL PROPERTIES OF BODIES. + +INTRODUCTION. GENERAL PROPERTIES OF BODIES. IMPENETRABILITY. EXTENSION. +FIGURE. DIVISIBILITY. INERTIA. ATTRACTION. ATTRACTION OF COHESION. +DENSITY. RARITY. HEAT. ATTRACTION OF GRAVITATION. + + +EMILY. + +I must request your assistance, my Dear Mrs. B., in a charge which I +have lately undertaken: it is that of instructing my youngest sister, a +task, which I find proves more difficult than I had at first imagined. I +can teach her the common routine of children's lessons tolerably well; +but she is such an inquisitive little creature, that she is not +satisfied without an explanation of every difficulty that occurs to her, +and frequently asks me questions which I am at a loss to answer. This +morning, for instance, when I had explained to her that the world was +round like a ball, instead of being flat as she had supposed, and that +it was surrounded by the air, she asked me what supported it. I told her +that it required no support; she then inquired why it did not fall as +every thing else did? This I confess perplexed me; for I had myself been +satisfied with learning that the world floated in the air, without +considering how unnatural it was that so heavy a body, bearing the +weight of all other things, should be able to support itself. + +_Mrs. B._ I make no doubt, my dear, but that I shall be able to explain +this difficulty to you; but I believe that it would be almost impossible +to render it intelligible to the comprehension of so young a child as +your sister Sophia. You, who are now in your thirteenth year, may, I +think, with great propriety, learn not only the cause of this particular +fact, but acquire a general knowledge of the laws by which the natural +world is governed. + +_Emily._ Of all things, it is what I should most like to learn; but I +was afraid it was too difficult a study even at my age. + +_Mrs. B._ Not when familiarly explained: if you have patience to attend, +I will most willingly give you all the information in my power. You may +perhaps find the subject rather dry at first; but if I succeed in +explaining the laws of nature, so as to make you understand them, I am +sure that you will derive not only instruction, but great amusement from +that study. + +_Emily._ I make no doubt of it, Mrs. B.; and pray begin by explaining +why the earth requires no support; for that is the point which just now +most strongly excites my curiosity. + +_Mrs. B._ My dear Emily, if I am to attempt to give you a general idea +of the laws of nature, which is no less than to introduce you to a +knowledge of the science of natural philosophy, it will be necessary for +us to proceed with some degree of regularity. I do not wish to confine +you to the systematic order of a scientific treatise, but if we were +merely to examine every vague question that may chance to occur, our +progress would be but very slow. Let us, therefore, begin by taking a +short survey of the general properties of bodies, some of which must +necessarily be explained before I can attempt to make you understand why +the earth requires no support. + +When I speak of _bodies_, I mean substances, of whatever nature, whether +solid or fluid; and _matter_ is the general term used to denote the +substance, whatever its nature be, of which the different bodies are +composed. Thus, the wood of which this table is made, the water with +which this glass is filled, and the air which we continually breathe, +are each of them _matter_. + +_Emily._ I am very glad you have explained the meaning of the word +matter, as it has corrected an erroneous conception I had formed of it: +I thought that it was applicable to solid bodies only. + +_Mrs. B._ There are certain properties which appear to be common to all +bodies, and are hence called the _essential or inherent properties_ of +bodies; these are _Impenetrability_, _Extension_, _Figure_, +_Divisibility_, _Inertia_ and _Attraction_. These are also called the +general properties of bodies, as we do not suppose any body to exist +without them. + +By _impenetrability_ is meant the property which bodies have of +occupying a certain space, so that where one body is, another can not +be, without displacing the former; for two bodies can not exist in the +same place at the same time. A liquid may be more easily removed than a +solid body; yet it is not the less substantial, since it is as +impossible for a liquid and a solid to occupy the same space at the same +time, as for two solid bodies to do so. For instance, if you put a spoon +into a glass full of water, the water will flow over to make room for +the spoon. + +_Emily._ I understand this perfectly. Liquids are in reality as +substantial or as impenetrable as solid bodies, and they appear less so, +only because they are more easily displaced. + +_Mrs. B._ The air is a fluid differing in its nature from liquids, but +no less impenetrable. If I endeavour to fill this phial by plunging it +into this bason of water, the air, you see, rushes out of the phial in +bubbles, in order to make way for the water, for the air and the water +can not exist together in the same space, any more than two hard bodies; +and if I reverse this goblet, and plunge it perpendicularly into the +water, so that the air will not be able to escape, the water will no +longer be able to fill the goblet. + +_Emily._ But it rises some way into the glass. + +_Mrs. B._ Because the water compresses or squeezes the air into a +smaller space in the upper part of the glass; but, as long as it remains +there, no other body can occupy the same place. + +_Emily._ A difficulty has just occurred to me, with regard to the +impenetrability of solid bodies; if a nail is driven into a piece of +wood, it penetrates it, and both the wood and the nail occupy the same +space that the wood alone did before? + +_Mrs. B._ The nail penetrates between the particles of the wood, by +forcing them to make way for it; for you know that not a single atom of +wood can remain in the space which the nail occupies; and if the wood is +not increased in size by the addition of the nail, it is because wood is +a porous substance, like sponge, the particles of which may be +compressed or squeezed closer together; and it is thus that they make +way for the nail. + +We may now proceed to the next general property of bodies, _extension_. +A body which occupies a certain space must necessarily have extension; +that is to say, _length_, _breadth_ and _depth_ or thickness; these are +called the dimensions of extension: can you form an idea of any body +without them? + +_Emily._ No; certainly I can not; though these dimensions must, of +course vary extremely in different bodies. The length, breadth and depth +of a box, or of a thimble, are very different from those of a walking +stick, or of a hair. + +But is not height also a dimension of extension? + +_Mrs B._ Height and depth are the same dimension, considered in +different points of view; if you measure a body, or a space, from the +top to the bottom, you call it depth; if from the bottom upwards, you +call it height; thus the depth and height of a box are, in fact, the +same thing. + +_Emily._ Very true; a moment's consideration would have enabled me to +discover that; and breadth and width are also the same dimension. + +_Mrs. B._ Yes; the limits of extension constitute _figure_ or shape. You +conceive that a body having length, breadth and depth, can not be +without form, either symmetrical or irregular? + +_Emily._ Undoubtedly; and this property admits of almost an infinite +variety. + +_Mrs. B._ Nature has assigned regular forms to many of her productions. +The natural form of various mineral substances is that of crystals, of +which there is a great variety. Many of them are very beautiful, and no +less remarkable by their transparency or colour, than by the perfect +regularity of their forms, as may be seen in the various museums and +collections of natural history. The vegetable and animal creation +appears less symmetrical, but is still more diversified in figure than +the mineral kingdom. Manufactured substances assume the various +arbitrary forms which the art of man designs for them; and an infinite +number of irregular forms are produced by fractures and by the +dismemberment of the parts of bodies. + +_Emily._ Such as a piece of broken china, or glass? + +_Mrs. B._ Or the masses and fragments of stone, and other mineral +substances, which are dug out of the earth, or found upon its surface; +many of which, although composed of minute crystals, are in the lump of +an irregular form. + +We may now proceed to _divisibility_; that is to say, a susceptibility +of being divided into an indefinite number of parts. Take any small +quantity of matter, a grain of sand for instance, and cut it into two +parts; these two parts might be again divided, had we instruments +sufficiently fine for the purpose; and if by means of pounding, +grinding, and other similar methods, we carry this division to the +greatest possible extent, and reduce the body to its finest imaginable +particles, yet not one of the particles will be destroyed, but will each +contain as many halves and quarters, as did the whole grain. + +The dissolving of a solid body in a liquid, affords a very striking +example of the extreme divisibility of matter; when you sweeten a cup of +tea, for instance, with what minuteness the sugar must be divided to be +diffused throughout the whole of the liquid. + +_Emily._ And if you pour a few drops of red wine into a glass of water, +they immediately tinge the whole of the water, and must therefore be +diffused throughout it. + +_Mrs. B._ Exactly so; and the perfume of this lavender water will be +almost as instantaneously diffused throughout the room, if I take out +the stopper. + +_Emily._ But in this case it is only the perfume of the lavender, and +not the water itself that is diffused in the room. + +_Mrs. B._ The odour or smell of a body is part of the body itself, and +is produced by very minute particles or exhalations which escape from +the odoriferous bodies. It would be impossible that you should smell the +lavender water, if particles of it did not come in actual contact with +your nose. + +_Emily._ But when I smell a flower, I see no vapour rise from it; and +yet I perceive the smell at a considerable distance. + +_Mrs. B._ You could, I assure you, no more smell a flower, the +odoriferous particles of which did not touch your nose, than you could +taste a fruit, the flavoured particles of which did not come in contact +with your tongue. + +_Emily._ That is wonderful indeed; the particles then, which exhale from +the flower and from the lavender water, are, I suppose, too small to be +visible? + +_Mrs. B._ Certainly: you may form some idea of their extreme minuteness, +from the immense number which must have escaped in order to perfume the +whole room; and yet there is no sensible diminution of the liquid in the +phial. + +_Emily._ But the quantity must really be diminished? + +_Mrs. B._ Undoubtedly; and were you to leave the bottle open a +sufficient length of time, the whole of the water would evaporate and +disappear. But though so minutely subdivided as to be imperceptible to +any of our senses, each particle would continue to exist; for it is not +within the power of man to destroy a single particle of matter: nor is +there any reason to suppose that in nature an atom is ever annihilated. + +_Emily._ Yet, when a body is burnt to ashes, part of it, at least, +appears to be effectually destroyed: look how small is the residue of +ashes in the fire place, from all the fuel which has been consumed +within it. + +_Mrs. B._ That part of the fuel, which you suppose to be destroyed, +evaporates in the form of smoke, and vapour, and air, whilst the +remainder is reduced to ashes. A body, in burning, undergoes no doubt +very remarkable changes; it is generally subdivided; its form and colour +altered; its extension increased: but the various parts, into which it +has been separated by combustion, continue in existence, and retain all +the essential properties of bodies. + +_Emily._ But that part of a burnt body which evaporates in smoke has no +figure; smoke, it is true, ascends in columns into the air, but it is +soon so much diffused as to lose all form; it becomes indeed invisible. + +_Mrs. B._ Invisible, I allow; but we must not imagine that what we no +longer see no longer exists. Were every particle of matter that becomes +invisible annihilated, the world itself would in the course of time be +destroyed. The particles of smoke, when diffused in the air, continue +still to be particles of matter as well as when more closely united in +the form of coals: they are really as substantial in the one state as in +the other, and equally so when by their extreme subdivision they become +invisible. No particle of matter is ever destroyed: this is a principle +you must constantly remember. Every thing in nature decays and corrupts +in the lapse of time. We die, and our bodies moulder to dust; but not a +single atom of them is lost; they serve to nourish the earth, whence, +while living, they drew their support. + +The next essential property of matter is called _inertia_ or inactivity; +this word expresses the resistance which matter makes to a change from a +state of rest, to that of motion, or from a state of motion to that of +rest. Bodies are equally incapable of changing their actual state, +whether it be of motion or of rest. You know that it requires force to +put a body which is at rest in motion; an exertion of strength is also +requisite to stop a body which is already in motion. The resistance of +the body to a change of state, in either case, arises from its +_inertia_. + +_Emily._ In playing at base-ball I am obliged to use all my strength to +give a rapid motion to the ball; and when I have to catch it, I am sure +I feel the resistance it makes to being stopped. But if I did not catch +it, it would soon fall to the ground and stop of itself. + +_Mrs. B._ Matter being inert it is as incapable of stopping of itself as +it is of putting itself into motion: when the ball ceases to move, +therefore, it must be stopped by some other cause or power; but as it is +one with which you are yet unacquainted, we can not at present +investigate its effects. + +The last property which appears to be common to all bodies is +_attraction_. All bodies consist of infinitely small particles of +matter, each of which possesses the power of attracting or drawing +towards it, and uniting with any other particle sufficiently near to be +within the influence of its attraction; but in minute particles this +power extends to so very small a distance around them, that its effect +is not sensible, unless they are (or at least appear to be) in contact; +it then makes them stick or adhere together, and is hence called the +_attraction of cohesion_. Without this power, solid bodies would fall in +pieces, or rather crumble to atoms. + +_Emily._ I am so much accustomed to see bodies firm and solid, that it +never occurred to me that any power was requisite to unite the particles +of which they are composed. But the attraction of cohesion does not, I +suppose, exist in liquids; for the particles of liquids do not remain +together so as to form a body, unless confined in a vessel? + +_Mrs. B._ I beg your pardon; it is the attraction of cohesion which +holds this drop of water suspended at the end of my finger, and keeps +the minute watery particles of which it is composed united. But as this +power is stronger in proportion as the particles of bodies are more +closely united, the cohesive attraction of solid bodies is much greater +than that of fluids. + +The thinner and lighter a fluid is, the less is the cohesive attraction +of its particles, because they are further apart; and in elastic fluids, +such as air, there is no cohesive attraction among the particles. + +_Emily._ That is very fortunate; for it would be impossible to breathe +the air in a solid mass; or even in a liquid state. + +But is the air a body of the same nature as other bodies? + +_Mrs. B._ Undoubtedly, in all essential properties. + +_Emily._ Yet you say that it does not possess one of the general +properties of bodies--attraction. + +_Mrs. B._ The particles of air are not destitute of the power of +attraction, but they are too far distant from each other to be +influenced by it so as to produce cohesion: and the utmost efforts of +human art have proved ineffectual in the attempt to compress them, so as +to bring them within the sphere of each other's attraction, and make +them cohere. + +_Emily._ If so, how is it possible to prove that they are endowed with +this power? + +_Mrs. B._ The air is formed of particles precisely of the same nature as +those which enter into the composition of liquid and solid bodies, in +each of which we have a proof of their attraction. + +_Emily._ It is then, I suppose, owing to the different degrees of +cohesive attraction in different substances, that they are hard or soft, +and that liquids are thick or thin. + +_Mrs. B._ Yes; but you would express your meaning better by the term +_density_, which denotes the degree of closeness and compactness of the +particles of a body. In philosophical language, density is said to be +that property of bodies by which they contain a certain quantity of +matter, under a certain bulk or magnitude. _Rarity_ is the contrary of +density; it denotes the thinness and subtilty of bodies: thus you would +say that mercury or quicksilver was a very dense fluid; ether, a very +rare one. Those bodies which are the most dense, do not always cohere +the most strongly; lead is more dense than iron, yet its particles are +more easily separated. + +_Caroline._ But how are we to judge of the quantity of matter contained +in a certain bulk? + +_Mrs. B._ By the weight: under the same bulk bodies are said to be dense +in proportion as they are heavy. + +_Emily._ Then we may say that metals are dense bodies, wood +comparatively a rare one, &c. But, Mrs. B., when the particles of a body +are so near as to attract each other, the effect of this power must +increase as they are brought by it closer together; so that one would +suppose that the body would gradually augment in density, till it was +impossible for its particles to be more closely united. Now, we know +that this is not the case; for soft bodies, such as cork, sponge, or +butter, never become, in consequence of the increasing attraction of +their particles, as hard as iron? + +_Mrs. B._ In such bodies as cork and sponge, the particles which come in +contact are so few as to produce but a slight degree of cohesion: they +are porous bodies, which, owing to the peculiar arrangement of their +particles, abound with interstices, or pores, which separate the +particles. But there is also a fluid much more subtile than air, which +pervades all bodies, this is _heat_. Heat insinuates itself more or less +between the particles of all bodies, and forces them asunder; you may +therefore consider heat, and the attraction of cohesion, as constantly +acting in opposition to each other. + +_Emily._ The one endeavouring to rend a body to pieces, the other to +keep its parts firmly united. + +_Mrs. B._ And it is this struggle between the contending forces of heat +and attraction, which prevents the extreme degree of density which would +result from the sole influence of the attraction of cohesion. + +_Emily._ The more a body is heated then, the more its particles will be +separated. + +_Mrs. B._ Certainly: we find that bodies not only swell or dilate, but +lose their cohesion, by heat: this effect is very sensible in butter, +for instance, which expands by the application of heat, till at length +the attraction of cohesion is so far diminished that the particles +separate, and the butter becomes liquid. A similar effect is produced by +heat on metals, and all bodies susceptible of being melted. Liquids, you +know, are made to boil by the application of heat; the attraction of +cohesion then yields entirely to the repulsive power; the particles are +totally separated and converted into steam or vapour. But the agency of +heat is in no body more sensible than in air, which dilates and +contracts by its increase or diminution in a very remarkable degree. + +_Emily._ The effects of heat appear to be one of the most interesting +parts of natural philosophy. + +_Mrs. B._ That is true; but heat is so intimately connected with +chemistry, that you must allow me to defer the investigation of its +properties till you become acquainted with that science. + +To return to its antagonist, the attraction of cohesion; it is this +power which restores to vapour its liquid form, which unites it into +drops when it falls to earth in a shower of rain, which gathers the dew +into brilliant gems on the blades of grass. + +_Emily._ And I have often observed that after a shower, the water +collects into large drops on the leaves of plants; but I cannot say that +I perfectly understand how the attraction of cohesion produces this +effect. + +_Mrs. B._ Rain, when it first leaves the clouds, is not in the form of +drops, but in that of mist or vapour, which is composed of very small +watery particles; these in their descent mutually attract each other, +and those that are sufficiently near in consequence unite and form a +drop, and thus the mist is transformed into a shower. The dew also was +originally in a state of vapour, but is, by the mutual attraction of the +particles, formed into small globules on the blades of grass: in a +similar manner the rain upon the leaf collects into large drops, which +when they become too heavy for the leaf to support, fall to the ground. + +_Emily._ All this is wonderfully curious! I am almost bewildered with +surprise and admiration at the number of new ideas I have already +acquired. + +_Mrs. B._ Every step that you advance in the pursuit of natural science, +will fill your mind with admiration and gratitude towards its Divine +Author. In the study of natural philosophy, we must consider ourselves +as reading the book of nature, in which the bountiful goodness and +wisdom of God are revealed to all mankind; no study can tend more to +purify the heart, and raise it to a religious contemplation of the +Divine perfections. + +There is another curious effect of the attraction of cohesion which I +must point out to you; this is called capillary attraction. It enables +liquids to rise above their ordinary level in capillary tubes: these are +tubes, the bores of which are so extremely small that liquids ascend +within them, from the cohesive attraction between the particles of the +liquid and the interior surface of the tube. Do you perceive the water +rising in this small glass tube, above its level in the goblet of water, +into which I have put one end of it? + +_Emily._ Oh yes; I see it slowly creeping up the tube, but now it is +stationary: will it rise no higher? + +_Mrs. B._ No; because the cohesive attraction between the water and the +internal surface of the tube is now balanced by the weight of the water +within it; if the bore of the tube were narrower the water would rise +higher; and if you immerse several tubes of bores of different sizes, +you will see it rise to different heights in each of them. In making +this experiment, you should colour the water with a little red wine, in +order to render the effect more obvious. + +All porous substances, such as sponge, bread, linen, &c. may be +considered as collections of capillary tubes: if you dip one end of a +lump of sugar into water, the fluid will rise in it, and wet it +considerably above the surface of the water into which you dip it. + +_Emily._ In making tea I have often observed that effect, without being +able to account for it. + +_Mrs. B._ Now that you are acquainted with the attraction of cohesion, I +must endeavour to explain to you that of _Gravitation_, which is +probably a modification of the same power; the first is perceptible only +in very minute particles, and at very small distances; the other acts on +the largest bodies, and extends to immense distances. + +_Emily._ You astonish me: surely you do not mean to say that large +bodies attract each other? + +_Mrs. B._ Indeed I do: let us take, for example, one of the largest +bodies in nature, and observe whether it does not attract other bodies. +What is it that occasions the fall of this book, when I no longer +support it? + +_Emily._ Can it be the attraction of the earth? I thought that all +bodies had a natural tendency to fall. + +_Mrs. B._ They have a natural tendency to fall, it is true; but that +tendency is produced entirely by the attraction of the earth: the earth +being so much larger than any body on its surface, forces every body, +which is not supported, to fall upon it. + +_Emily._ If the tendency which bodies have to fall results from the +earth's attractive power, the earth itself can have no such tendency, +since it cannot attract itself, and therefore it requires no support to +prevent it from falling. Yet the idea that bodies do not fall of their +own accord, but that they are drawn towards the earth by its attraction, +is so new and strange to me, that I know not how to reconcile myself to +it. + +_Mrs. B._ When you are accustomed to consider the fall of bodies as +depending on this cause, it will appear to you as natural, and surely +much more satisfactory, than if the cause of their tendency to fall were +totally unknown. Thus you understand that all matter is attractive, from +the smallest particle to the largest mass; and that bodies attract each +other with a force proportional to the quantity of matter they contain. + +_Emily._ I do not perceive any difference between the attraction of +cohesion and that of gravitation; is it not because every particle of +matter is endowed with an attractive power, that large bodies consisting +of a great number of particles, are so strongly attractive? + +_Mrs. B._ True. There is, however, this difference between the +attraction of particles and that of masses, that the former takes place +only when the particles are contiguous, whilst the latter is exerted +when the masses are far from each other. The attraction of particles +frequently counteracts the attraction of gravitation. Of this you have +an instance in the attraction of capillary tubes, in which liquids +ascend by the attraction of cohesion, in opposition to that of gravity. +It is on this account that it is necessary that the bore of the tube +should be extremely small; for if the column of water within the tube is +not very minute, the attraction of cohesion would not be able either to +raise or support it in opposition to its gravity; because the increase +of weight, in a column of water of a given height, is much greater than +the increase in the attracting surface of the tube, when its size is +increased. + +You may observe also, that all solid bodies are enabled by the force of +the cohesive attraction of their particles to resist that of gravity, +which would otherwise disunite them, and bring them to a level with the +ground, as it does in the case of a liquid, the cohesive attraction of +which is not sufficient to enable it to resist the power of gravity. + +_Emily._ And some solid bodies appear to be of this nature, as sand, and +powder for instance: there is no attraction of cohesion between their +particles? + +_Mrs. B._ Every grain of powder, or sand, is composed of a great number +of other more minute particles, firmly united by the attraction of +cohesion; but amongst the separate grains there is no sensible +attraction, because they are not in sufficiently close contact. + +_Emily._ Yet they actually touch each other? + +_Mrs. B._ The surface of bodies is in general so rough and uneven, that +when in apparent contact, they touch each other only by a few points. +Thus, when I lay this book upon the table, the binding of which appears +perfectly smooth, so few of the particles of its under surface come in +contact with the table, that no sensible degree of cohesive attraction +takes place; for you see that it does not stick or cohere to the table, +and I find no difficulty in lifting it off. + +It is only when surfaces, perfectly flat and well polished, are placed +in contact, that the particles approach in sufficient number, and +closely enough, to produce a sensible degree of cohesive attraction. +Here are two plates of polished metal, I press their flat surfaces +together, having previously interposed a few drops of oil, to fill up +every little porous vacancy. Now try to separate them. + +_Emily._ It requires an effort beyond my strength, though there are +handles for the purpose of pulling them asunder. Is the firm adhesion of +the two plates merely owing to the attraction of cohesion? + +_Mrs. B._ There is no force more powerful, since it is by this that the +particles of the hardest bodies are held together. It would require a +weight of several pounds to separate these plates. In the present +example, however, much of the cohesive force is due to the attraction +subsisting between the metal and the oil which is interposed; as without +this, or some other fluid, the points of contact would still be +comparatively few, although we may have employed our utmost art, in +giving flat surfaces to the plates. + +_Emily._ In making a kaleidoscope, I recollect that the two plates of +glass, which were to serve as mirrors, stuck so fast together, that I +imagined some of the gum I had been using had by chance been interposed +between them; but I am now convinced that it was their own natural +cohesive attraction which produced this effect. + +_Mrs. B._ Very probably it was so; for plate-glass has an extremely +smooth, flat surface, admitting of the contact of a great number of +particles, when two plates are laid upon each other. + +_Emily._ But, Mrs. B., the cohesive attraction of some substances is +much greater than that of others; thus glue, gum and paste, cohere with +singular tenacity. + +_Mrs. B._ Bodies which differ in their natures in other respects, differ +also in their cohesive attraction; it is probable that there are no two +bodies, the particles of which attract each other with precisely the +same force. + +There are some other modifications of attraction peculiar to certain +bodies; namely, that of magnetism, of electricity, and of affinity, or +chemical attraction; but we shall confine our attention merely to the +attraction of cohesion and of gravity; the examination of the latter we +shall resume at our next meeting. + + +Questions + +1. (Pg. 10) What is intended by the term _bodies_? + +2. (Pg. 10) Is the term _matter_, restricted to substances of a +particular kind? + +3. (Pg. 10) Name those properties of bodies, which are called inherent. + +4. (Pg. 10) What is meant by impenetrability? + +5. (Pg. 10) Can a liquid be said to be impenetrable? + +6. (Pg. 11) How can you prove that air is impenetrable? + +7. (Pg. 11) If air is impenetrable, what causes the water to rise some +way into a goblet, if I plunge it into water with its mouth downward? + +8. (Pg. 11) When I drive a nail into wood, do not both the iron and the +wood occupy the same space? + +9. (Pg. 11) In how many directions, is a body said to have extension? + +10. (Pg. 11) How do we distinguish the terms height and depth? + +11. (Pg. 12) What constitutes the _figure_, or _form_ of a body? + +12. (Pg. 12) What is said respecting the form of minerals? + +13. (Pg. 12) What of the vegetable and animal creation? + +14. (Pg. 12) What of artificial, and accidental forms? + +15. (Pg. 12) What is meant by divisibility? + +16. (Pg. 12) What examples can you give, to prove that the particles of +a body are minute in the extreme? + +17. (Pg. 13) What produces the odour of bodies? + +18. (Pg. 13) How do odours exemplify the minuteness of the particles of +matter? + +19. (Pg. 13) Can matter be in any way annihilated? + +20. (Pg. 13) What becomes of the fuel, which disappears in our fires? + +21. (Pg. 14) How can that part which evaporates, be still said to +possess a substantial form? + +22. (Pg. 14) What do we mean by _inertia_? + +23. (Pg. 14) Give an example to prove that force is necessary, either to +give or to stop motion. + +24. (Pg. 14) What general power do the particles of matter exert upon +other particles? + +25. (Pg. 15) What is that species of attraction called, which keeps +bodies in a solid state? + +26. (Pg. 15) Does the attraction of cohesion exist in liquids, and how +is its existence proved? + +27. (Pg. 15) If the particles of air attract each other, why do they not +cohere? + +28. (Pg. 15) From what then do you infer that they possess attraction? + +29. (Pg. 15) How do you account for some bodies being hard and others +soft? + +30. (Pg. 16) What is meant by the term _density_? + +31. (Pg. 16) Do the most dense bodies always cohere the most strongly? + +32. (Pg. 16) How do we know that one body is more dense than another? + +33. (Pg. 16) What is there which acts in opposition to cohesive +attraction, tending to separate the particles of bodies? + +34. (Pg. 17) What would be the consequence if the repulsive power of +heat were not exerted? + +35. (Pg. 17) If we continue to increase the heat, what effects will it +produce on bodies? + +36. (Pg. 17) What body has its dimensions most sensibly affected by +change of temperature? + +37. (Pg. 17) What power restores vapours to the liquid form? + +38. (Pg. 17) What examples can you give? + +39. (Pg. 17) How are drops of rain and of dew said to be formed? + +40. (Pg. 18) What is meant by a capillary tube? + +41. (Pg. 18) What effect does attraction produce when these are immersed +in water? + +42. (Pg. 18) What is the reason that the water rises to a certain height +only? + +43. (Pg. 18) Give some familiar examples of capillary attraction. + +44. (Pg. 18) In what does _gravitation_ differ from cohesive attraction? + +45. (Pg. 18) What causes bodies near the earth's surface, to have a +tendency to fall towards it? + +46. (Pg. 19) What remarkable difference is there between the attraction +of gravitation, and that of cohesion? + +47. (Pg. 19) In what instances does the power of cohesion counteract +that of gravitation? + +48. (Pg. 19) Why will water rise to a less height, if the size of the +tube is increased? + +49. (Pg. 20) Why do not two bodies cohere, when laid upon each other? + +50. (Pg. 20) Can two bodies be made sufficiently flat to cohere with +considerable force? + +51. (Pg. 20) What is the reason that the adhesion is greater when oil is +interposed? + +52. (Pg. 21) What other modifications of attraction are there, besides +those of cohesion and of gravitation? + + + + +CONVERSATION II. + +ON THE ATTRACTION OF GRAVITY. + +ATTRACTION OF GRAVITATION, CONTINUED. OF WEIGHT. OF THE FALL OF BODIES. +OF THE RESISTANCE OF THE AIR. OF THE ASCENT OF LIGHT BODIES. + + +EMILY. + +I have related to my sister Caroline all that you have taught me of +natural philosophy, and she has been so much delighted by it, that she +hopes you will have the goodness to admit her to your lessons. + +_Mrs. B._ Very willingly; but I did not think you had any taste for +studies of this nature, Caroline. + +_Caroline._ I confess, Mrs. B., that hitherto I had formed no very +agreeable idea either of philosophy, or philosophers; but what Emily has +told me has excited my curiosity so much, that I shall be highly pleased +if you will allow me to become one of your pupils. + +_Mrs. B._ I fear that I shall not find you so tractable a scholar as +Emily; I know that you are much biased in favour of your own opinions. + +_Caroline._ Then you will have the greater merit in reforming them, Mrs. +B.; and after all the wonders that Emily has related to me, I think I +stand but little chance against you and your attractions. + +_Mrs. B._ You will, I doubt not, advance a number of objections; but +these I shall willingly admit, as they will afford an opportunity of +elucidating the subject. Emily, do you recollect the names of the +general properties of bodies? + +_Emily._ Impenetrability, extension, figure, divisibility, inertia and +attraction. + +_Mrs. B._ Very well. You must remember that these are properties common +to all bodies, and of which they cannot be deprived; all other +properties of bodies are called accidental, because they depend on the +relation or connexion of one body to another. + +_Caroline._ Yet surely, Mrs. B., there are other properties which are +essential to bodies, besides those you have enumerated. Colour and +weight, for instance, are common to all bodies, and do not arise from +their connexion with each other, but exist in the bodies themselves; +these, therefore, cannot be accidental qualities? + +_Mrs. B._ I beg your pardon; these properties do not exist in bodies +independently of their connexion with other bodies. + +_Caroline._ What! have bodies no weight? Does not this table weigh +heavier than this book; and, if one thing weighs heavier than another, +must there not be such a thing as weight? + +_Mrs. B._ No doubt: but this property does not appear to be essential to +bodies; it depends upon their connexion with each other. Weight is an +effect of the power of attraction, without which the table and the book +would have no weight whatever. + +_Emily._ I think I understand you; it is the attraction of gravity which +makes bodies heavy. + +_Mrs. B._ You are right. I told you that the attraction of gravity was +proportioned to the quantity of matter which bodies contain: now the +earth consisting of a much greater quantity of matter than any body upon +its surface, the force of its attraction must necessarily be greatest, +and must draw every thing so situated towards it; in consequence of +which, bodies that are unsupported fall to the ground, whilst those that +are supported, press upon the object which prevents their fall, with a +weight equal to the force with which they gravitate towards the earth. + +_Caroline._ The same cause then which occasions the fall of bodies, +produces their weight also. It was very dull in me not to understand +this before, as it is the natural and necessary consequence of +attraction; but the idea that bodies were not really heavy of +themselves, appeared to me quite incomprehensible. But, Mrs. B., if +attraction is a property essential to matter, weight must be so +likewise; for how can one exist without the other? + +_Mrs. B._ Suppose there were but one body existing in universal space, +what would its weight be? + +_Caroline._ That would depend upon its size; or more accurately +speaking, upon the quantity of matter it contained. + +_Emily._ No, no; the body would have no weight, whatever were its size; +because nothing would attract it. Am I not right, Mrs. B.? + +_Mrs. B._ You are: you must allow, therefore, that it would be possible +for attraction to exist without weight; for each of the particles of +which the body was composed, would possess the power of attraction; but +they could exert it only amongst themselves; the whole mass having +nothing to attract, or to be attracted by, would have no weight. + +_Caroline._ I am now well satisfied that weight is not essential to the +existence of bodies; but what have you to object to colours, Mrs. B.; +you will not, I think, deny that they really exist in the bodies +themselves. + +_Mrs. B._ When we come to treat of the subject of colours, I trust that +I shall be able to convince you, that colours are likewise accidental +qualities, quite distinct from the bodies to which they appear to +belong. + +_Caroline._ Oh do pray explain it to us now, I am so very curious to +know how that is possible. + +_Mrs. B._ Unless we proceed with some degree of order and method, you +will in the end find yourself but little the wiser for all you learn. +Let us therefore go on regularly, and make ourselves well acquainted +with the general properties of bodies before we proceed further. + +_Emily._ To return, then, to attraction, (which appears to me by far the +most interesting of them, since it belongs equally to all kinds of +matter,) it must be mutual between two bodies; and if so, when a stone +falls to the earth, the earth should rise part of the way to meet the +stone? + +_Mrs. B._ Certainly; but you must recollect that the force of attraction +is proportioned to the quantity of matter which bodies contain, and if +you consider the difference there is in that respect, between a stone +and the earth, you will not be surprised that you do not perceive the +earth rise to meet the stone; for though it is true that a mutual +attraction takes place between the earth and the stone, that of the +latter is so very small in comparison to that of the former, as to +render its effect insensible. + +_Emily._ But since attraction is proportioned to the quantity of matter +which bodies contain, why do not the hills attract the houses and +churches towards them? + +_Caroline._ What an idea, Emily! How can the houses and churches be +moved, when they are so firmly fixed in the ground! + +_Mrs. B._ Emily's question is not absurd, and your answer, Caroline, is +perfectly just; but can you tell us why the houses and churches are so +firmly fixed in the ground? + +_Caroline._ I am afraid I have answered right by mere chance; for I +begin to suspect that bricklayers and carpenters could give but little +stability to their buildings, without the aid of attraction. + +_Mrs. B._ It is certainly the cohesive attraction between the bricks and +the mortar, which enables them to build walls, and these are so strongly +attracted by the earth, as to resist every other impulse; otherwise they +would necessarily move towards the hills and the mountains; but the +lesser force must yield to the greater. There are, however, some +circumstances in which the attraction of a large body has sensibly +counteracted that of the earth. If whilst standing on the declivity of a +mountain, you hold a plumb-line in your hand, the weight will not fall +perpendicular to the earth, but incline a little towards the mountain; +and this is owing to the lateral, or sideways attraction of the +mountain, interfering with the perpendicular attraction of the earth. + +_Emily._ But the size of a mountain is very trifling, compared to the +whole earth. + +_Mrs. B._ Attraction, you must recollect, is in proportion to the +quantity of matter, and although that of the mountain, is much less than +that of the earth, it may yet be sufficient to act sensibly upon the +plumb-line which is so near to it. + +_Caroline._ Pray, Mrs. B., do the two scales of a balance hang parallel +to each other? + +_Mrs. B._ You mean, I suppose, in other words to inquire whether two +lines which are perpendicular to the earth, are parallel to each other? +I believe I guess the reason of your question; but I wish you would +endeavour to answer it without my assistance. + +_Caroline._ I was thinking that such lines must both tend by gravity to +the same point, the centre of the earth; now lines tending to the same +point cannot be parallel, as parallel lines are always at an equal +distance from each other, and would never meet. + +_Mrs. B._ Very well explained; you see now the use of your knowledge of +parallel lines: had you been ignorant of their properties, you could not +have drawn such a conclusion. This may enable you to form an idea of the +great advantage to be derived even from a slight knowledge of geometry, +in the study of natural philosophy; and if after I have made you +acquainted with the first elements, you should be tempted to pursue the +study, I would advise you to prepare yourselves by acquiring some +knowledge of geometry. This science would teach you that lines which +fall perpendicular to the surface of a sphere cannot be parallel, +because they would all meet, if prolonged to the centre of the sphere; +while lines that fall perpendicular to a plane or flat surface, are +always parallel, because if prolonged, they would never meet. + +_Emily._ And yet a pair of scales, hanging perpendicular to the earth, +appear parallel? + +_Mrs. B._ Because the sphere is so large, and the scales consequently +converge so little, that their inclination is not perceptible to our +senses; if we could construct a pair of scales whose beam would extend +several degrees, their convergence would be very obvious; but as this +cannot be accomplished, let us draw a small figure of the earth, and +then we may make a pair of scales of the proportion we please. (fig. 1. +pl. I.) + +_Caroline._ This figure renders it very clear: then two bodies cannot +fall to the earth in parallel lines? + +_Mrs. B._ Never. + +_Caroline._ The reason that a heavy body falls quicker than a light one, +is, I suppose, because the earth attracts it more strongly. + +_Mrs. B._ The earth, it is true, attracts a heavy body more than a light +one; but that would not make the one fall quicker than the other. + +_Caroline._ Yet, since it is attraction that occasions the fall of +bodies, surely the more a body is attracted, the more rapidly it will +fall. Besides, experience proves it to be so. Do we not every day see +heavy bodies fall quickly, and light bodies slowly? + +_Emily._ It strikes me, as it does Caroline, that as attraction is +proportioned to the quantity of matter, the earth must necessarily +attract a body which contains a great quantity more strongly, and +therefore bring it to the ground sooner than one consisting of a smaller +quantity. + +_Mrs. B._ You must consider, that if heavy bodies are attracted more +strongly than light ones, they require more attraction to make them +fall. Remember that bodies have no natural tendency to fall, any more +than to rise, or to move laterally, and that they will not fall unless +impelled by some force; now this force must be proportioned to the +quantity of matter it has to move: a body consisting of 1000 particles +of matter, for instance, requires ten times as much attraction to bring +it to the ground in the same space of time as a body consisting of only +100 particles. + +[Illustration: PLATE I.] + +_Caroline._ I do not understand that; for it seems to me, that the +heavier a body is, the move easily and readily it falls. + +_Emily._ I think I now comprehend it; let me try if I can explain it to +Caroline. Suppose that I draw towards me two weighty bodies, the one of +100 lbs. the other of 1000 lbs. must I not exert ten times as much +strength to draw the larger one to me, in the same space of time, as is +required for the smaller one? And if the earth draws a body of 1000 lbs. +weight to it in the same space of time that it draws a body of 100 lbs. +does it not follow that it attracts the body of 1000 lbs. weight with +ten times the force that it does that of 100 lbs.? + +_Caroline._ I comprehend your reasoning perfectly; but if it were so, +the body of 1000 lbs. weight, and that of 100 lbs. would fall with the +same rapidity; and the consequence would be, that all bodies, whether +light or heavy, being at an equal distance from the ground, would fall +to it in the same space of time: now it is very evident that this +conclusion is absurd; experience every instant contradicts it; observe +how much sooner this book reaches the floor than this sheet of paper, +when I let them drop together. + +_Emily._ That is an objection I cannot answer. I must refer it to you, +Mrs. B. + +_Mrs. B._ I trust that we shall not find it insurmountable. It is true +that, according to the laws of attraction, all bodies at an equal +distance from the earth, should fall to it in the same space of time; +and this would actually take place if no obstacle intervened to impede +their fall. But bodies fall through the air, and it is the resistance of +the air which makes bodies of different density fall with different +degrees of velocity. They must all force their way through the air, but +dense heavy bodies overcome this obstacle more easily than rarer or +lighter ones; because in the same space they contain more gravitating +particles. + +The resistance which the air opposes to the fall of bodies is +proportioned to their surface, not to their weight; the air being inert, +cannot exert a greater force to support the weight of a cannon ball, +than it does to support the weight of a ball (of the same size) made of +leather; but the cannon ball will overcome this resistance more easily, +and fall to the ground, consequently, quicker than the leather ball. + +_Caroline._ This is very clear and solves the difficulty perfectly. The +air offers the same resistance to a bit of lead and a bit of feather of +the same size; yet the one seems to meet with no obstruction in its +fall, whilst the other is evidently resisted and supported for some time +by the air. + +_Emily._ The larger the surface of a body, then, the more air it covers, +and the greater is the resistance it meets with from it. + +_Mrs. B._ Certainly: observe the manner in which this sheet of paper +falls; it floats awhile in the air, and then gently descends to the +ground. I will roll the same piece of paper up into a ball: it offers +now but a small surface to the air, and encounters therefore but little +resistance: see how much more rapidly it falls. + +The heaviest bodies may be made to float awhile in the air, by making +the extent of their surface counterbalance their weight. Here is some +gold, which is one of the most dense bodies we are acquainted with; but +it has been beaten into a very thin leaf, and offers so great an extent +of surface in proportion to its weight, that its fall, you see, is still +more retarded by the resistance of the air, than that of the sheet of +paper. + +_Caroline._ That is very curious: and it is, I suppose, upon the same +principle that a thin slate sinks in water more slowly than a round +stone. + +But, Mrs. B., if the air is a real body, is it not also subjected to the +laws of gravity? + +_Mrs. B._ Undoubtedly. + +_Caroline._ Then why does it not, like all other bodies, fall to the +ground? + +_Mrs. B._ On account of its spring or elasticity. The air is an _elastic +fluid_; and the peculiar property of elastic bodies is to resume, after +compression, their original dimensions; and you must consider the air of +which the atmosphere is composed as existing in a state of compression, +for its particles being drawn towards the earth by gravity, are brought +closer together than they would otherwise be, but the spring or +elasticity of the air by which it endeavours to resist compression, +gives it a constant tendency to expand itself, so as to resume the +dimensions it would naturally have, if not under the influence of +gravity. The air may therefore be said constantly to struggle with the +power of gravity without being able to overcome it. Gravity thus +confines the air to the regions of our globe, whilst its elasticity +prevents it from falling, like other bodies, to the ground. + +_Emily._ The air then is, I suppose, thicker, or I should rather say +more dense, near the surface of the earth, than in the higher regions +of the atmosphere; for that part of the air which is nearer the surface +of the earth must be most strongly attracted. + +_Mrs. B._ The diminution of the force of gravity, at so small a distance +as that to which the atmosphere extends (compared with the size of the +earth) is so inconsiderable as to be scarcely sensible; but the pressure +of the upper parts of the atmosphere on those beneath, renders the air +near the surface of the earth much more dense than in the upper regions. +The pressure of the atmosphere has been compared to that of a pile of +fleeces of wool, in which the lower fleeces are pressed together by the +weight of those above; these lie light and loose, in proportion as they +approach the uppermost fleece, which receives no external pressure, and +is confined merely by the force of its own gravity. + +_Emily._ I do not understand how it is that the air can be springy or +elastic, as the particles of which it is composed must, according to the +general law, attract each other; yet their elasticity, must arise from a +tendency to recede from each other. + +_Mrs. B._ Have you forgotten what I told you respecting the effects of +heat, a fluid so subtile that it readily pervades all substances, and +even in solid bodies, counteracts the attraction of cohesion? In air the +quantity of heat interposed is so great, as to cause its particles +actually to repel each other, and it is to this that we must ascribe its +elasticity; this, however, does not prevent the earth from exerting its +attraction upon the individual particles of which it consists. + +_Caroline._ It has just occurred to me that there are some bodies which +do not gravitate towards the earth. Smoke and steam, for instance, rise +instead of falling. + +_Mrs. B._ It is still gravity which produces their ascent; at least, +were that power destroyed, these bodies would not rise. + +_Caroline._ I shall be out of conceit with gravity, if it is so +inconsistent in its operations. + +_Mrs. B._ There is no difficulty in reconciling this apparent +inconsistency of effect. The air near the earth is heavier than smoke, +steam, or other vapours; it consequently not only supports these light +bodies, but forces them to rise, till they reach a part of the +atmosphere, the weight of which is not greater than their own, and then +they remain stationary. Look at this bason of water; why does the piece +of paper which I throw into it float on the surface? + +_Emily._ Because, being lighter than the water, it is supported by it. + +_Mrs. B._ And now that I pour more water into the bason, why does the +paper rise? + +_Emily._ The water being heavier than the paper, gets beneath it, and +obliges it to rise. + +_Mrs. B._ In a similar manner are smoke and vapour forced upwards by the +air; but these bodies do not, like the paper, ascend to the surface of +the fluid, because, as we observed before, the air being less dense, and +consequently lighter as it is more distant from the earth, vapours rise +only till they attain a region of air of their own density. Smoke, +indeed ascends but a very little way; it consists of minute particles of +fuel, carried up by a current of heated air, from the fire below: heat, +you recollect, expands all bodies; it consequently rarefies air, and +renders it lighter than the colder air of the atmosphere; the heated air +from the fire carries up with it vapour and small particles of the +combustible materials which are burning in the fire. When this current +of hot air is cooled by mixing with the atmosphere, the minute particles +of coal, or other combustible, fall; it is this which produces the small +black flakes which render the air, and every thing in contact with it, +in London, so dirty. + +_Caroline._ You must, however, allow me to make one more objection to +the universal gravity of bodies; which is the ascent of air balloons, +the materials of which are undoubtedly heavier than air: how, therefore, +can they be supported by it? + +_Mrs. B._ I admit that the materials of which balloons are made are +heavier than the air; but the air with which they are filled is an +elastic fluid, of a different nature from atmospheric air, and +considerably lighter; so that on the whole the balloon is lighter than +the air which it displaces, and consequently will rise, on the same +principle as smoke and vapour. Now, Emily, let me hear if you can +explain how the gravity of bodies is modified by the effect of the air? + +_Emily._ The air forces bodies which are lighter than itself to ascend; +those that are of an equal weight will remain stationary in it; and +those that are heavier will descend through it: but the air will have +some effect on these last; for if they are not much heavier, they will +with difficulty overcome the resistance they meet with in passing +through it, they will be borne up by it, and their fall will be more or +less retarded. + +_Mrs. B._ Very well. Observe how slowly this light feather falls to the +ground, while a heavier body, like this marble, overcomes the +resistance which the air makes to its descent much more easily, and its +fall is proportionally more rapid. I now throw a pebble into this tub of +water; it does not reach the bottom near so soon as if there were no +water in the tub, because it meets with resistance from the water. +Suppose that we could empty the tub, not only of water, but of air also, +the pebble would then fall quicker still, as it would in that case meet +with no resistance at all to counteract its gravity. + +Thus you see that it is not the different degrees of gravity, but the +resistance of the air, which prevents bodies of different weight from +falling with equal velocities; if the air did not bear up the feather, +it would reach the ground as soon as the marble. + +_Caroline._ I make no doubt that it is so; and yet I do not feel quite +satisfied. I wish there was any place void of air, in which the +experiment could be made. + +_Mrs. B._ If that proof will satisfy your doubts, I can give it you. +Here is a machine called an _air pump_, (fig. 2. pl. 1.) by means of +which the air may be expelled from any close vessel which is placed over +this opening, through which the air is pumped out. Glasses of various +shapes, usually called receivers, are employed for this purpose. We +shall now exhaust the air from this tall receiver which is placed over +the opening, and we shall find that bodies within it, whatever their +weight or size, will fall from the top to the bottom in the same space +of time. + +_Caroline._ Oh, I shall be delighted with this experiment; what a +curious machine! how can you put the two bodies of different weight +within the glass, without admitting the air? + +_Mrs. B._ A guinea and a feather are already placed there for the +purpose of the experiment: here is, you see, a contrivance to fasten +them in the upper part of the glass; as soon as the air is pumped out, I +shall turn this little screw, by which means the brass plates which +support them will be removed, and the two bodies will fall.--Now I +believe I have pretty well exhausted the air. + +_Caroline._ Pray let me turn the screw.--I declare, they both reached +the bottom at the same instant! Did you see, Emily, the feather appeared +as heavy as the guinea? + +_Emily._ Exactly; and fell just as quickly. How wonderful this is! what +a number of entertaining experiments might be made with this machine! + +_Mrs. B._ No doubt there are a great many; but we shall reserve them to +elucidate the subjects to which they relate: if I had not explained to +you why the guinea, and the feather fell with equal velocity, you would +not have been so well pleased with the experiment. + +_Emily._ I should have been as much surprised, but not so much +interested; besides, experiments help to imprint on the memory the facts +they are intended to illustrate; it will be better therefore for us to +restrain our curiosity, and wait for other experiments in their proper +places. + +_Caroline._ Pray by what means is this receiver exhausted of its air? + +_Mrs. B._ You must learn something of mechanics in order to understand +the construction of a pump. At our next meeting, therefore, I shall +endeavour to make you acquainted with the laws of motion, as an +introduction to that subject. + + +Questions + +1. (Pg. 22) What are those properties of bodies called, which are not +common to all? + +2. (Pg. 23) Why are they so called? + +3. (Pg. 23) What is the cause of weight in bodies? + +4. (Pg. 23) What is the reason that all bodies near to the surface of +the earth, are drawn towards it? + +5. (Pg. 24) If attraction is the cause of weight, could you suppose it +possible for a body to possess the former and not the latter property? + +6. (Pg. 24) When a stone falls to the ground, in which of the two bodies +does the power of attraction exist? + +7. (Pg. 24) If the attraction be mutual, why does not the earth approach +the stone, as much as the stone approaches the earth? + +8. (Pg. 24) If attraction be in proportion to the mass, why does not a +hill, draw towards itself, a house placed near it? + +9. (Pg. 25) How can the attraction of a mountain be rendered sensible? + +10. (Pg. 25) Why cannot two lines which are perpendicular to the surface +of the earth be parallel to each other? + +11. (Pg. 26) Draw a small figure of the earth to exemplify this, as in +fig. 1. plate 1. + +12. (Pg. 27) If bodies were not resisted by the air, those which are +light, would fall as quickly as those which are heavy, how can you +account for this? + +13. (Pg. 27) What then is the reason that a book, and a sheet of paper, +let fall from the same height, will not reach the ground in the same +time? + +14. (Pg. 28) What then will be the effect of increasing the surface of a +body? + +15. (Pg. 28) What could you do to a sheet of paper, to make it fall +quickly, and why? + +16. (Pg. 28) Inform me how a very dense body may be made to float in the +air? + +17. (Pg. 28) The air is a real body, why does it not fall to the ground? + +18. (Pg. 29) The air is more dense near the surface of the earth, and +decreases in density as you ascend, how is this accounted for, and to +what is it compared? + +19. (Pg. 29) What is it which causes the particles of air to recede from +each other, and seems to destroy their mutual attraction? + +20. (Pg. 29) Smoke and vapour ascend in the atmosphere, how can you +reconcile this with gravitation? + +21. (Pg. 30) How would you illustrate this by the floating of a piece of +paper on water? + +22. (Pg. 30) Does smoke rise to a great height in the air, and if not, +what prevents its so doing? + +23. (Pg. 30) What limits the height to which vapours rise? + +24. (Pg. 30) Of what does smoke consist? + +25. (Pg. 30) Air balloons are formed of heavy materials, how will you +account for their rising in the air? + +26. (Pg. 30) What influence does the air exert, on bodies less dense +than itself, on those of equal, and on those of greater density? + +27. (Pg. 31) If the air could be entirely removed, what influence would +this have upon the falling of heavy and light bodies? + +28. (Pg. 31) How could this be exemplified by means of the air pump? + + + + +CONVERSATION III. + +ON THE LAWS OF MOTION. + +OF MOTION. OF THE INERTIA OF BODIES. OF FORCE TO PRODUCE MOTION. +DIRECTION OF MOTION. VELOCITY, ABSOLUTE AND RELATIVE. UNIFORM MOTION. +RETARDED MOTION. ACCELERATED MOTION. VELOCITY OF FALLING BODIES. +MOMENTUM. ACTION AND REACTION EQUAL. ELASTICITY OF BODIES. POROSITY OF +BODIES. REFLECTED MOTION. ANGLES OF INCIDENCE AND REFLECTION. + + +MRS. B. + +The science of mechanics is founded on the laws of motion; it will +therefore be necessary to make you acquainted with these laws before we +examine the mechanical powers. Tell me, Caroline, what do you understand +by the word motion? + +_Caroline._ I think I understand it perfectly, though I am at a loss to +describe it. Motion is the act of moving about, of going from one place +to another, it is the contrary of remaining at rest. + +_Mrs. B._ Very well. Motion then consists in a change of place; a body +is in motion whenever it is changing its situation with regard to a +fixed point. + +Now since we have observed that one of the general properties of bodies +is inertia, that is, an entire passiveness, either with regard to +motion or rest, it follows that a body cannot move without being put +into motion; the power which puts a body into motion is called _force_; +thus the stroke of the hammer is the force which drives the nail; the +pulling of the horse that which draws the carriage, &c. Force then is +the cause which produces motion. + +_Emily._ And may we not say that gravity is the force which occasions +the fall of bodies? + +_Mrs. B._ Undoubtedly. I have given you the most familiar illustrations +in order to render the explanation clear; but since you seek for more +scientific examples, you may say that cohesion is the force which binds +the particles of bodies together, and heat that which drives them +asunder. + +The motion of a body acted upon by a single force, is always in a +straight line, and in the direction in which it received the impulse. + +_Caroline._ That is very natural; for as the body is inert, and can move +only because it is impelled, it will move only in the direction in which +it is impelled. The degree of quickness with which it moves, must, I +suppose, also depend upon the degree of force with which it is impelled. + +_Mrs. B._ Yes; the rate at which a body moves, or the shortness of the +time which it takes to move from one place to another, is called its +velocity; and it is one of the laws of motion, that the velocity of the +moving body is proportional to the force by which it is put in motion. +We must distinguish between absolute and relative velocity. + +The velocity of a body is called _absolute_, if we consider the motion +of the body in space, without any reference to that of other bodies. +When, for instance, a horse goes fifty miles in ten hours, his velocity +is five miles an hour. + +The velocity of a body is termed _relative_, when compared with that of +another body which is itself in motion. For instance, if one man walks +at the rate of a mile an hour, and another at the rate of two miles an +hour, the relative velocity of the latter is double that of the former; +but the absolute velocity of the one is one mile, and that of the other +two miles an hour. + +_Emily._ Let me see if I understand it--The relative velocity of a body +is the degree of rapidity of its motion compared with that of another +body; thus if one ship sail three times as far as another ship in the +same space of time, the velocity of the former is equal to three times +that of the latter. + +_Mrs. B._ The general rule may be expressed thus: the velocity of a +body is measured by the space over which it moves, divided by the time +which it employs in that motion: thus if you travel one hundred miles in +twenty hours, what is your velocity in each hour? + +_Emily._ I must divide the space, which is one hundred miles, by the +time, which is twenty hours, and the answer will be five miles an hour. +Then, Mrs. B., may we not reverse this rule, and say that the time is +equal to the space divided by the velocity; since the space, one hundred +miles, divided by the velocity, five miles per hour, gives twenty hours +for the time? + +_Mrs. B._ Certainly; and we may say also that the space is equal to the +velocity multiplied by the time. Can you tell me, Caroline, how many +miles you will have travelled, if your velocity is three miles an hour, +and you travel six hours? + +_Caroline._ Eighteen miles; for the product of 3 multiplied by 6, is 18. + +_Mrs. B._ I suppose that you understand what is meant by the terms +_uniform_, _accelerated_ and _retarded_ motion. + +_Emily._ I conceive uniform motion to be that of a body whose motion is +regular, and at an equal rate throughout; for instance a horse that goes +an equal number of miles every hour. But the hand of a watch is a much +better example, as its motion is so regular as to indicate the time. + +_Mrs. B._ You have a right idea of uniform motion; but it would be more +correctly expressed by saying, that the motion of a body is uniform when +it passes over equal spaces in equal times. Uniform motion is produced +by a force having acted on a body once and having ceased to act; as, for +instance, the stroke of a bat on a ball. + +_Caroline._ But the motion of a ball is not uniform; its velocity +gradually diminishes till it falls to the ground. + +_Mrs. B._ Recollect that the ball is inert, and has no more power to +stop, than to put itself in motion; if it falls, therefore, it must be +stopped by some force superior to that by which it was projected, and +which destroys its motion. + +_Caroline._ And it is no doubt the force of gravity which counteracts +and destroys that of projection; but if there were no such power as +gravity, would the ball never stop? + +_Mrs. B._ If neither gravity nor any other force, such as the resistance +of the air, opposed its motion, the ball, or even a stone thrown by the +hand, would proceed onwards in a right line, and with a uniform velocity +for ever. + +_Caroline._ You astonish me! I thought that it was impossible to +produce perpetual motion? + +_Mrs. B._ Perpetual motion cannot be produced by art, because gravity +ultimately destroys all motion that human power can produce. + +_Emily._ But independently of the force of gravity, I cannot conceive +that the little motion I am capable of giving to a stone would put it in +motion for ever. + +_Mrs. B._ The quantity of motion you communicate to the stone would not +influence its duration; if you threw it with little force it would move +slowly, for its velocity you must remember, will be proportional to the +force with which it is projected; but if there is nothing to obstruct +its passage, it will continue to move with the same velocity, and in the +same direction as when you first projected it. + +_Caroline._ This appears to me quite incomprehensible; we do not meet +with a single instance of it in nature. + +_Mrs. B._ I beg your pardon. When you come to study the motion of the +celestial bodies, you will find that _nature_ abounds with examples of +perpetual motion; and that it conduces as much to the harmony of the +system of the universe, as the prevalence of it on the surface of the +earth, would to the destruction of all our comforts. The wisdom of +Providence has therefore ordained insurmountable obstacles to perpetual +motion here below; and though these obstacles often compel us to contend +with great difficulties, yet these appear necessary to that order, +regularity and repose, so essential to the preservation of all the +various beings of which this world is composed. + +Now can you tell me what is _retarded motion_? + +_Caroline._ Retarded motion is that of a body which moves every moment +slower and slower: thus when I am tired with walking fast, I slacken my +pace; or when a stone is thrown upwards, its velocity is gradually +diminished by the power of gravity. + +_Mrs. B._ Retarded motion is produced by some force acting upon the body +in a direction opposite to that which first put it in motion: you who +are an animated being, endowed with power and will, may slacken your +pace, or stop to rest when you are tired; but inert matter is incapable +of any feeling of fatigue, can never slacken its pace, and never stop, +unless retarded or arrested in its course by some opposing force; and as +it is the laws of inert bodies of which mechanical philosophy treats, I +prefer your illustration of the stone retarded in its ascent. Now +Emily, it is your turn; what is _accelerated motion_? + +_Emily._ Accelerated motion, I suppose, takes place when the velocity of +a body is increased; if you had not objected to our giving such active +bodies as ourselves as examples, I should say that my motion is +accelerated if I change my pace from walking to running. I cannot think +of any instance of accelerated motion in inanimate bodies; all motion of +inert matter seems to be retarded by gravity. + +_Mrs. B._ Not in all cases; for the power of gravitation sometimes +produces accelerated motion; for instance, a stone falling from a +height, moves with a regularly accelerated motion. + +_Emily._ True; because the nearer it approaches the earth, the more it +is attracted by it. + +_Mrs. B._ You have mistaken the cause of its accelerated motion; for +though it is true that the force of gravity increases as a body +approaches the earth, the difference is so trifling at any small +distance from its surface, as not to be perceptible. + +Accelerated motion is produced when the force which put a body in +motion, continues to act upon it during its motion, so that its velocity +is continually increased. When a stone falls from a height, the impulse +which it receives from gravitation in the first instant of its fall, +would be sufficient to bring it to the ground with a uniform velocity: +for, as we have observed, a body having been once acted upon by a force, +will continue to move with a uniform velocity; but the stone is not +acted upon by gravity merely at the first instant of its fall; this +power continues to impel it during the whole time of its descent, and it +is this continued impulse which accelerates its motion. + +_Emily._ I do not quite understand that. + +_Mrs. B._ Let us suppose that the instant after you have let a stone +fall from a high tower, the force of gravity were annihilated; the body +would nevertheless continue to move downwards, for it would have +received a first impulse from gravity; and a body once put in motion +will not stop unless it meets with some obstacle to impede its course; +in this case its velocity would be uniform, for though there would be no +obstacle to obstruct its descent, there would be no force to accelerate +it. + +_Emily._ That is very clear. + +_Mrs. B._ Then you have only to add the power of gravity constantly +acting on the stone during its descent, and it will not be difficult to +understand that its motion will become accelerated, since the gravity +which acts on the stone at the very first instant of its descent, will +continue in force every instant, till it reaches the ground. Let us +suppose that the impulse given by gravity to the stone during the first +instant of its descent, be equal to one; the next instant we shall find +that an additional impulse gives the stone an additional velocity, equal +to one; so that the accumulated velocity is now equal to two; the +following instant another impulse increases the velocity to three, and +so on till the stone reaches the ground. + +_Caroline._ Now I understand it; the effects of preceding impulses +continue, whilst gravity constantly adds new ones, and thus the velocity +is perpetually increased. + +_Mrs. B._ Yes; it has been ascertained, both by experiment, and +calculations which it would be too difficult for us to enter into, that +heavy bodies near the surface of the earth, descending from a height by +the force of gravity, fall sixteen feet the first second of time, three +times that distance in the next, five times in the third second, seven +times in the fourth, and so on, regularly increasing their velocities in +the proportion of the odd numbers 1, 3, 5, 7, 9, &c. according to the +number of seconds during which the body has been falling. + +_Emily._ If you throw a stone perpendicularly upwards, is it not the +same length of time in ascending, that it is in descending? + +_Mrs. B._ Exactly; in ascending, the velocity is diminished by the force +of gravity; in descending, it is accelerated by it. + +_Caroline._ I should then imagine that it would fall, quicker than it +rose? + +_Mrs. B._ You must recollect that the force with which it is projected, +must be taken into the account; and that this force is overcome and +destroyed by gravity, before the body begins to fall. + +_Caroline._ But the force of projection given to a stone in throwing it +upwards, cannot always be equal to the force of gravity in bringing it +down again; for the force of gravity is always the same, whilst the +degree of impulse given to the stone is optional; I may throw it up +gently, or with violence. + +_Mrs. B._ If you throw it gently, it will not rise high; perhaps only +sixteen feet, in which case it will fall in one second of time. Now it +is proved by experiment, that an impulse requisite to project a body +sixteen feet upwards, will make it ascend that height in one second; +here then the times of the ascent and descent are equal. But supposing +it be required to throw a stone twice that height, the force must be +proportionally greater. + +You see then, that the impulse of projection in throwing a body upwards, +is always equal to the action of the force of gravity during its +descent; and that whether the body rises to a greater or less distance, +these two forces balance each other. + +I must now explain to you what is meant by the _momentum_ of bodies. It +is the force, or power, with which a body in motion, strikes against +another body. The momentum of a body is the product of its _quantity of +matter_, multiplied by its _quantity of motion_; in other words, its +weight multiplied by its velocity. + +_Caroline._ The quicker a body moves, the greater, no doubt, must be the +force which it would strike against another body. + +_Emily._ Therefore a light body may have a greater momentum than a +heavier one, provided its velocity be sufficiently increased; for +instance, the momentum of an arrow shot from a bow, must be greater than +that of a stone thrown by the hand. + +_Caroline._ We know also by experience, that the heavier a body is, the +greater is its force; it is not therefore difficult to understand, that +the whole power, or momentum of a body, must be composed of these two +properties, its weight and its velocity: but I do not understand why +they should be _multiplied_, the one by the other; I should have +supposed that the quantity of matter, should have been _added_ to the +quantity of motion? + +_Mrs. B._ It is found by experiment, that if the weight of a body is +represented by the number 3, and its velocity also by 3, its momentum +will be represented by 9, not by 6, as would be the case, were these +figures added, instead of being multiplied together. + +_Emily._ I think that I now understand the reason of this; if the +quantity of matter is increased three-fold, it must require three times +the force to move it with the same velocity; and then if we wish to give +it three times the velocity, it will again require three times the force +to produce that effect, which is three times three, or nine; which +number therefore, would represent the momentum. + +_Caroline._ I am not quite sure that I fully comprehend what is +intended, when weight, and velocity, are represented by numbers alone; I +am so used to measure space by yards and miles, and weight by pounds and +ounces, that I still want to associate them together in my mind. + +_Mrs. B._ This difficulty will be of very short duration: you have only +to be careful, that when you represent weights and velocities by +numbers, the denominations or values of the weights and spaces, must not +be changed. Thus, if we estimate the weight of one body in ounces, the +weight of others with which it is compared, must be estimated in ounces, +and not in pounds; and in like manner, in comparing velocities, we must +throughout, preserve the same standards both of space and of time; as +for instance, the number of feet in one second, or of miles in one hour. + +_Caroline._ I now understand it perfectly, and think that I shall never +forget a thing which you have rendered so clear. + +_Mrs. B._ I recommend it to you to be very careful to remember the +definition of the momentum of bodies, as it is one of the most important +points in mechanics: you will find that it is from opposing velocity, to +quantity of matter, that machines derive their powers. + +The _reaction_ of bodies, is the next law of motion which I must explain +to you. When a body in motion strikes against another body, it meets +with resistance from it; the resistance of the body at rest will be +equal to the blow struck by the body in motion; or to express myself in +philosophical language, _action_ and _reaction_ will be equal, and in +opposite directions. + +_Caroline._ Do you mean to say, that the action of the body which +strikes, is returned with equal force by the body which receives the +blow? + +_Mrs. B._ Exactly. + +_Caroline._ But if a man strike another on the face with his fist, he +surely does not receive as much pain by the reaction, as he inflicts by +the blow? + +_Mrs. B._ No; but this is simply owing to the knuckles, having much less +feeling than the face. + +Here are two ivory balls suspended by threads, (plate 1. fig. 3.) draw +one of them, A, a little on one side,--now let it go;--it strikes, you +see, against the other ball B, and drives it off, to a distance equal to +that through which the first ball fell; but the motion of A is stopped; +because when it struck B, it received in return a blow equal to that it +gave, and its motion was consequently destroyed. + +_Emily._ I should have supposed, that the motion of the ball A was +destroyed, because it had communicated all its motion to B. + +_Mrs. B._ It is perfectly true, that when one body strikes against +another, the quantity of motion communicated to the second body, is lost +by the first; but this loss proceeds from the reaction of the body which +is struck. + +Here are six ivory balls hanging in a row, (fig. 4.) draw the first out +of the perpendicular, and let it fall against the second. You see none +of the balls except the last, appear to move, this flies off as far as +the first ball fell; can you explain this? + +_Caroline._ I believe so. When the first ball struck the second, it +received a blow in return, which destroyed its motion; the second ball, +though it did not appear to move, must have struck against the third; +the reaction of which set it at rest; the action of the third ball must +have been destroyed by the reaction of the fourth, and so on till motion +was communicated to the last ball, which, not being reacted upon, flies +off. + +_Mrs. B._ Very well explained. Observe, that it is only when bodies are +elastic, as these ivory balls are, and when their masses are equal, that +the stroke returned is equal to the stroke given, and that the striking +body loses all its motion. I will show you the difference with these two +balls of clay, (fig. 5.) which are not elastic; when you raise one of +these, D, out of the perpendicular, and let it fall against the other, +E, the reaction of the latter, on account of its not being elastic, is +not sufficient to destroy the motion of the former; only part of the +motion of D will be communicated to E, and the two balls will move on +together to _d_ and _e_, which is not so great a distance as that +through which D fell. + +Observe how useful reaction is in nature. Birds in flying strike the air +with their wings, and it is the reaction of the air, which enables them +to rise, or advance forwards; reaction being always in a contrary +direction to action. + +_Caroline._ I thought that birds might be lighter than the air, when +their wings were expanded, and were by that means enabled to fly. + +_Mrs. B._ When their wings are spread, this does not alter their weight, +but they are better supported by the air, as they cover a greater extent +of surface; yet they are still much too heavy to remain in that +situation, without continually flapping their wings, as you may have +noticed when birds hover over their nests: the force with which their +wings strike against the air, must equal the weight of their bodies, in +order that the reaction of the air, may be able to support that weight; +the bird will then remain stationary. If the stroke of the wings is +greater than is required merely to support the bird, the reaction of the +air will make it rise; if it be less, it will gently descend; and you +may have observed the lark, sometimes remaining with its wings extended, +but motionless; in this state it drops quietly into its nest. + +_Caroline._ This is indeed a beautiful effect of the law of reaction! +But if flying is merely a mechanical operation, Mrs. B., why should we +not construct wings, adapted to the size of our bodies, fasten them to +our shoulders, move them with our arms, and soar into the air? + +_Mrs. B._ Such an experiment has been repeatedly attempted, but never +with success; and it is now considered as totally impracticable. The +muscular power of birds, is incomparably greater in proportion to their +weight, than that of man; were we therefore furnished with wings +sufficiently large to enable us to fly, we should not have strength to +put them in motion. + +In swimming, a similar action is produced on the water, to that on the +air, in flying; in rowing, also, you strike the water with the oars, in +a direction opposite to that in which the boat is required to move, and +it is the reaction of the water on the oars which drives the boat along. + +_Emily._ You said, that it was in elastic bodies only, that the whole +motion of one body, would be communicated to another; pray what bodies +are elastic, besides the air? + +_Mrs. B._ In speaking of the air, I think we defined elasticity to be a +property, by means of which bodies that are compressed, return to their +former state. If I bend this cane, as soon as I leave it at liberty, it +recovers its former position; if I press my finger upon your arm, as +soon as I remove it, the flesh, by virtue of its elasticity, rises and +destroys the impression I made. Of all bodies, the air is the most +eminent for this property, and it has thence obtained the name of an +elastic fluid. Hard bodies are in the next degree elastic; if two ivory, +or hardened steel balls are struck together, the parts at which they +touch, will be flattened; but their elasticity will make them +instantaneously resume their former shape. + +_Caroline._ But when two ivory balls strike against each other, as they +constantly do on a billiard table, no mark or impression is made by the +stroke. + +_Mrs. B._ I beg your pardon; you cannot, it is true, perceive any mark, +because their elasticity instantly destroys all trace of it. + +Soft bodies, which easily retain impressions, such as clay, wax, tallow, +butter, &c. have very little elasticity; but of all descriptions of +bodies, liquids are the least elastic. + +_Emily._ If sealing-wax were elastic, instead of retaining the +impression of a seal, it would resume a smooth surface, as soon as the +weight of the seal was removed. But pray what is it that produces the +elasticity of bodies? + +_Mrs. B._ There is great diversity of opinion upon that point, and I +cannot pretend to decide which approaches nearest to the truth. +Elasticity implies susceptibility of compression, and the susceptibility +of compression depends upon the porosity of bodies; for were there no +pores or spaces between the particles of matter of which a body is +composed, it could not be compressed. + +_Caroline._ That is to say, that if the particles of bodies were as +close together as possible, they could not be squeezed closer. + +_Emily._ Bodies then, whose particles are most distant from each other, +must be most susceptible of compression, and consequently most elastic; +and this you say is the case with air, which is perhaps the least dense +of all bodies? + +_Mrs. B._ You will not in general find this rule hold good; for liquids +have scarcely any elasticity, whilst hard bodies are eminent for this +property, though the latter are certainly of much greater density than +the former; elasticity implies, therefore, not only a susceptibility of +compression, but depends upon the power possessed by the body, of +resuming its former state after compression, in consequence of the +peculiar arrangement of its particles. + +_Caroline._ But surely there can be no pores in ivory and metals, Mrs. +B.; how then can they be susceptible of compression? + +_Mrs. B._ The pores of such bodies are invisible to the naked eye, but +you must not thence conclude that they have none; it is, on the +contrary, well ascertained that gold, one of the most dense of all +bodies, is extremely porous; and that these pores are sufficiently large +to admit water when strongly compressed, to pass through them. This was +shown by a celebrated experiment made many years ago at Florence. + +_Emily._ If water can pass through gold, there must certainly be pores +or interstices which afford it a passage; and if gold is so porous, what +must other bodies be, which are so much less dense than gold! + +_Mrs. B._ The chief difference in this respect, is I believe, that the +pores in some bodies are larger than in others; in cork, sponge and +bread, they form considerable cavities; in wood and stone, when not +polished, they are generally perceptible to the naked eye; whilst in +ivory, metals, and all varnished and polished bodies, they cannot be +discerned. To give you an idea of the extreme porosity of bodies, sir +Isaac Newton conjectured that if the earth were so compressed as to be +absolutely without pores, its dimensions might possibly not be more than +a cubic inch. + +_Caroline._ What an idea! Were we not indebted to sir Isaac Newton for +the theory of attraction, I should be tempted to laugh at him for such a +supposition. What insignificant little creatures we should be! + +_Mrs. B._ If our consequence arose from the size of our bodies, we +should indeed be but pigmies, but remember that the mind of Newton was +not circumscribed by the dimensions of its envelope. + +_Emily._ It is, however, fortunate that heat keeps the pores of matter +open and distended, and prevents the attraction of cohesion from +squeezing us into a nut-shell. + +_Mrs. B._ Let us now return to the subject of reaction, on which we have +some further observations to make. It is because reaction is in its +direction opposite to action, that _reflected motion_ is produced. If +you throw a ball against the wall, it rebounds; this return of the ball +is owing to the reaction of the wall against which it struck, and is +called _reflected motion_. + +_Emily._ And I now understand why balls filled with air rebound better +than those stuffed with bran or wool; air being most susceptible of +compression and most elastic, the reaction is more complete. + +_Caroline._ I have observed that when I throw a ball straight against +the wall, it returns straight to my hand; but if I throw it obliquely +upwards, it rebounds still higher, and I catch it when it falls. + +_Mrs. B._ You should not say straight, but perpendicularly against the +wall; for straight is a general term for lines in all directions which +are neither curved nor bent, and is therefore equally applicable to +oblique or perpendicular lines. + +_Caroline._ I thought that perpendicularly meant either directly upwards +or downwards? + +_Mrs. B._ In those directions lines are perpendicular to the earth. A +perpendicular line has always a reference to something towards which it +is perpendicular; that is to say, that it inclines neither to the one +side or the other, but makes an equal angle on every side. Do you +understand what an angle is? + +_Caroline._ Yes, I believe so: it is the space contained between two +lines meeting in a point. + +_Mrs. B._ Well then, let the line A B (plate 2. fig. 1.) represent the +floor of the room, and the line C D that in which you throw a ball +against it; the line C D, you will observe, forms two angles with the +line A B, and those two angles are equal. + +_Emily._ How can the angles be equal, while the lines which compose them +are of unequal length? + +_Mrs. B._ An angle is not measured by the length of the lines, but by +their opening, or the space between them. + +_Emily._ Yet the longer the lines are, the greater is the opening +between them. + +_Mrs. B._ Take a pair of compasses and draw a circle over these spaces, +making the angular point the centre. + +_Emily._ To what extent must I open the compasses? + +_Mrs. B._ You may draw the circle what size you please, provided that it +cuts the lines of the angles we are to measure. All circles, of whatever +dimensions, are supposed to be divided into 360 equal parts, called +degrees; the opening of an angle, being therefore a portion of a circle, +must contain a certain number of degrees: the larger the angle the +greater is the number of degrees, and two angles are said to be equal, +when they contain an equal number of degrees. + +_Emily._ Now I understand it. As the dimension of an angle depends upon +the number of degrees contained between its lines, it is the opening, +and not the length of its lines, which determines the size of the angle. + +_Mrs. B._ Very well: now that you have a clear idea of the dimensions of +angles, can you tell me how many degrees are contained in the two angles +formed by one line falling perpendicularly on another, as in the figure +I have just drawn? + +_Emily._ You must allow me to put one foot of the compasses at the point +of the angles, and draw a circle round them, and then I think I shall be +able to answer your question: the two angles are together just equal to +half a circle, they contain therefore 90 degrees each; 90 degrees being +a quarter of 360. + +_Mrs. B._ An angle of 90 degrees or one-fourth of a circle is called a +right angle, and when one line is perpendicular to another, and distant +from its ends, it forms, you see, (fig. 1.) a right angle on either +side. Angles containing more than 90 degrees are called obtuse angles, +(fig. 2.) and those containing less than 90 degrees are called acute +angles, (fig. 3.) + +_Caroline._ The angles of this square table are right angles, but those +of the octagon table are obtuse angles; and the angles of sharp pointed +instruments are acute angles. + +[Illustration: PLATE II.] + +_Mrs. B._ Very well. To return now to your observation, that if a ball +is thrown obliquely against the wall, it will not rebound in the same +direction; tell me, have you ever played at billiards? + +_Caroline._ Yes, frequently; and I have observed that when I push the +ball perpendicularly against the cushion, it returns in the same +direction; but when I send it obliquely to the cushion, it rebounds +obliquely, but on an opposite side; the ball in this latter case +describes an angle, the point of which is at the cushion. I have +observed too, that the more obliquely the ball is struck against the +cushion, the more obliquely it rebounds on the opposite side, so that a +billiard player can calculate with great accuracy in what direction it +will return. + +_Mrs. B._ Very well. This figure (fig. 4. plate 2.) represents a +billiard table; now if you draw a line A B from the point where the ball +A strikes perpendicular to the cushion, you will find that it will +divide the angle which the ball describes into two parts, or two angles; +the one will show the obliquity of the direction of the ball in its +passage towards the cushion, the other its obliquity in its passage back +from the cushion. The first is called _the angle of incidence_, the +other _the angle of reflection_; and these angles are always equal, if +the bodies are perfectly elastic. + +_Caroline._ This then is the reason why, when I throw a ball obliquely +against the wall, it rebounds in an opposite oblique direction, forming +equal angles of incidence and of reflection. + +_Mrs. B._ Certainly; and you will find that the more obliquely you throw +the ball, the more obliquely it will rebound. + +We must now conclude; but I shall have some further observations to make +upon the laws of motion, at our next meeting. + + +Questions + +1. (Pg. 32) On what is the science of mechanics founded? + +2. (Pg. 32) In what does motion consist? + +3. (Pg. 33) What is the consequence of inertia, on a body at rest? + +4. (Pg. 33) What do we call that which produces motion? + +5. (Pg. 33) Give some examples. + +6. (Pg. 33) What may we say of gravity, of cohesion, and of heat, as +forces? + +7. (Pg. 33) How will a body move, if acted on by a single force? + +8. (Pg. 33) What is the reason of this? + +9. (Pg. 33) What do we intend by the term velocity, and to what is it +proportional? + +10. (Pg. 33) Velocity is divided into absolute and relative; what is +meant by absolute velocity? + +11. (Pg. 33) How is relative velocity distinguished? + +12. (Pg. 34) How do we measure the velocity of a body? + +13. (Pg. 34) The time? + +14. (Pg. 34) The space? + +15. (Pg. 34) What is uniform motion? and give an example. + +16. (Pg. 34) How is uniform motion produced? + +17. (Pg. 34) A ball struck by a bat gradually loses its motion; what +causes produce this effect? + +18. (Pg. 35) If gravity did not draw a projected body towards the earth, +and the resistance of the air were removed, what would be the +consequence? + +19. (Pg. 35) In this case would not a great degree of force be required +to produce a continued motion? + +20. (Pg. 35) What is retarded motion? + +21. (Pg. 35) Give some examples. + +22. (Pg. 36) What is accelerated motion? + +23. (Pg. 36) Give an example. + +24. (Pg. 36) Explain the mode in which gravity operates in producing +this effect. + +25. (Pg. 37) What number of feet will a heavy body descend in the first +second of its fall, and at what rate will its velocity increase? + +26. (Pg. 37) What is the difference in the time of the ascent and +descent, of a stone, or other body thrown upwards? + +27. (Pg. 37) By what reasoning is it proved that there is no difference? + +28. (Pg. 38) What is meant by the momentum of a body? + +29. (Pg. 38) How do we ascertain the momentum? + +30. (Pg. 38) How may a light body have a greater momentum than one which +is heavier? + +31. (Pg. 38) Why must we _multiply_ the weight and velocity together in +order to find the momentum? + +32. (Pg. 39) When we represent weight and velocity by numbers, what must +we carefully observe? + +33. (Pg. 39) Why is it particularly important, to understand the nature +of momentum? + +34. (Pg. 39) What is meant by reaction, and what is the rule respecting +it? + +35. (Pg. 39) How is this exemplified by the ivory balls represented in +plate 1. fig. 3? + +36. (Pg. 40) Explain the manner in which the six balls represented in +fig. 4, illustrate this fact. + +37. (Pg. 40) What must be the nature of bodies, in which the whole +motion is communicated from one to the other? + +38. (Pg. 40) What is the result if the balls are not elastic, and how is +this explained by fig. 5? + +39. (Pg. 40) How will reaction assist us in explaining the flight of a +bird? + +40. (Pg. 40) How must their wings operate in enabling them to remain +stationary, to rise, and to descend? + +41. (Pg. 41) Why cannot a man fly by the aid of wings? + +42. (Pg. 41) How does reaction operate in enabling us to swim, or to row +a boat? + +43. (Pg. 41) What constitutes elasticity? + +44. (Pg. 41) Give some examples. + +45. (Pg. 41) What name is given to air, and for what reason? + +46. (Pg. 41) What hard bodies are mentioned as elastic? + +47. (Pg. 41) Do elastic bodies exhibit any indentation after a blow? and +why not? + +48. (Pg. 42) What do we conclude from elasticity respecting the contact +of the particles of a body? + +49. (Pg. 42) Are those bodies always the most elastic, which are the +least dense? + +50. (Pg. 42) Give examples to prove that this is not the case. + +51. (Pg. 42) All bodies are believed to be porous, what is said on this +subject respecting gold? + +52. (Pg. 43) What conjecture was made by sir Isaac Newton, respecting +the porosity of bodies in general? + +53. (Pg. 43) If you throw an elastic body against a wall, it will +rebound; what is this occasioned by, and what is this return motion +called? + +54. (Pg. 43) What do we mean by a perpendicular line? + +55. (Pg. 43) What is an angle? + +56. (Pg. 43) What is represented by fig. 1. plate 2? + +57. (Pg. 44) Have the length of the lines which meet in a point, any +thing to do with the measurement of an angle? + +58. (Pg. 44) What use can we make of compasses in measuring an angle? + +59. (Pg. 44) Into what number of parts do we suppose a whole circle +divided, and what are these parts called? + +60. (Pg. 44) When are two angles said to be equal? + +61. (Pg. 44) Upon what does the dimension of an angle depend? + +62. (Pg. 44) What number of degrees, and what portion of a circle is +there in a right angle? + +63. (Pg. 44) How must one line be situated on another to form two right +angles? (fig. 1.) + +64. (Pg. 44) Figure 2 represents an angle of more than 90 degrees, what +is that called? + +65. (Pg. 44) What are those of less than 90 degrees called as in fig. 3? + +66. (Pg. 45) If you make an elastic ball strike a body at right angles, +how will it return? + +67. (Pg. 45) How if it strikes obliquely? + +68. (Pg. 45) Explain by fig. 4 what is meant by the angles of incidence +and of reflection. + + + + +CONVERSATION IV. + +ON COMPOUND MOTION. + +COMPOUND MOTION, THE RESULT OF TWO OPPOSITE FORCES. OF CURVILINEAR +MOTION, THE RESULT OF TWO FORCES. CENTRE OF MOTION, THE POINT AT REST +WHILE THE OTHER PARTS OF THE BODY MOVE ROUND IT. CENTRE OF MAGNITUDE, +THE MIDDLE OF A BODY. CENTRIPETAL FORCE, THAT WHICH IMPELS A BODY +TOWARDS A FIXED CENTRAL POINT. CENTRIFUGAL FORCE, THAT WHICH IMPELS A +BODY TO FLY FROM THE CENTRE. FALL OF BODIES IN A PARABOLA. CENTRE OF +GRAVITY, THE POINT ABOUT WHICH THE PARTS BALANCE EACH OTHER. + + +MRS. B. + +I must now explain to you the nature of compound motion. Let us suppose +a body to be struck by two equal forces in opposite directions, how will +it move? + +_Emily._ If the forces are equal, and their directions are in exact +opposition to each other, I suppose the body would not move at all. + +_Mrs. B._ You are perfectly right; but suppose the forces instead of +acting upon the body in direct opposition to each other, were to move in +lines forming an angle of ninety degrees, as the lines Y A, X A, (fig. +5. plate 2.) and were to strike the ball A, at the same instant; would +it not move? + +_Emily._ The force X alone, would send it towards B, and the force Y +towards C; and since these forces are equal, I do not know how the body +can obey one impulse rather than the other; and yet I think the ball +would move, because as the two forces do not act in direct opposition, +they cannot entirely destroy the effect of each other. + +_Mrs. B._ Very true; the ball therefore will not follow the direction of +either of the forces, but will move in a line between them, and will +reach D in the same space of time, that the force X would have sent it +to B, and the force Y would have sent it to C. Now if you draw two +lines, one from B, parallel to A C, and the other from C, parallel to A +B, they will meet in D, and you will form a square; the oblique line +which the body describes, is called the diagonal of the square. + +_Caroline._ That is very clear, but supposing the two forces to be +unequal, that the force X, for instance, be twice as great as the force +Y? + +_Mrs. B._ Then the force X, would drive the ball twice as far as the +force Y, consequently you must draw the line A B (fig. 6.) twice as long +as the line A C, the body will in this case move to D; and if you draw +lines from the points B and C, exactly as directed in the last example, +they will meet in D, and you will find that the ball has moved in the +diagonal of a rectangle. + +_Emily._ Allow me to put another case. Suppose the two forces are +unequal, but do not act on the ball in the direction of a right angle, +but in that of an acute angle, what will result? + +_Mrs. B._ Prolong the lines in the directions of the two forces, and you +will soon discover which way the ball will be impelled; it will move +from A to D, in the diagonal of a parallelogram, (fig. 7.) Forces acting +in the direction of lines forming an obtuse angle, will also produce +motion in the diagonal of a parallelogram. For instance, if the body set +out from B, instead of A, and was impelled by the forces X and Y, it +would move in the dotted diagonal B C. + +We may now proceed to curvilinear motion: this is the result of two +forces acting on a body; by one of which, it is projected forward in a +right line; whilst by the other, it is drawn or impelled towards a fixed +point. For instance, when I whirl this ball, which is fastened to my +hand with a string, the ball moves in a circular direction, because it +is acted on by two forces; that which I give it, which represents the +force of projection, and that of the string which confines it to my +hand. If, during its motion you were suddenly to cut the string, the +ball would fly off in a straight line; being released from that +confinement which caused it to move round a fixed point, it would be +acted on by one force only; and motion produced by one force, you know, +is always in a right line. + +_Caroline._ This circular motion, is a little more difficult to +comprehend than compound motion in straight lines. + +_Mrs. B._ You have seen how the water is thrown off from a grindstone, +when turned rapidly round; the particles of the stone itself have the +same tendency, and would also fly off, was not their attraction of +cohesion, greater than that of water. And indeed it sometimes happens, +that large grindstones fly to pieces from the rapidity of their motion. + +_Emily._ In the same way, the rim and spokes of a wheel, when in rapid +motion, would be driven straight forwards in a right line, were they not +confined to a fixed point, round which they are compelled to move. + +_Mrs. B._ Very well. You must now learn to distinguish between what is +called the _centre_ of motion, and the _axis_ of motion; the former +being considered as a point, the latter as a line. + +When a body, like the ball at the end of the string, revolves in a +circle, the centre of the circle is called the centre of its motion, and +the body is said to revolve in a plane; because a line extended from the +revolving body, to the centre of motion, would describe a plane, or flat +surface. + +When a body revolves round itself, as a ball suspended by a string, and +made to spin round, or a top spinning on the floor, whilst it remains on +the same spot; this revolution is round an imaginary line passing +through the body, and this line is called its axis of motion. + +_Caroline._ The axle of a grindstone, is then the axis of its motion; +but is the centre of motion always in the middle of a body? + +_Mrs. B._ No, not always. The middle point of a body, is called its +centre of magnitude, or position, that is, the centre of its mass or +bulk. Bodies have also another centre, called the centre of gravity, +which I shall explain to you; but at present we must confine ourselves +to the axis of motion. This line you must observe remains at rest, +whilst all the other parts of the body move around it; when you spin a +top, the axis is stationary, whilst every other part is in motion round +it. + +_Caroline._ But a top generally has a motion forwards besides its +spinning motion; and then no point within it can be at rest? + +_Mrs. B._ What I say of the axis of motion, relates only to circular +motion; that is to say, motion round a line, and not to that which a +body may have at the same time in any other direction. There is one +circumstance to which you must carefully attend; namely, that the +further any part of a body is from the axis of motion, the greater is +its velocity: as you approach that line, the velocity of the parts +gradually diminish till you reach the axis of motion, which is perfectly +at rest. + +_Caroline._ But, if every part of the same body did not move with the +same velocity, that part which moved quickest, must be separated from +the rest of the body, and leave it behind? + +_Mrs. B._ You perplex yourself by confounding the idea of circular +motion, with that of motion in a right line; you must think only of the +motion of a body round a fixed line, and you will find, that if the +parts farthest from the centre had not the greatest velocity, those +parts would not be able to keep up with the rest of the body, and would +be left behind. Do not the extremities of the vanes of a windmill move +over a much greater space, than the parts nearest the axis of motion? +(plate 3. fig. 1.) The three dotted circles represent the paths in which +three different parts of the vanes move, and though the circles are of +different dimensions, each of them is described in the same space of +time. + +_Caroline._ Certainly they are; and I now only wonder, that we neither +of us ever made the observation before: and the same effect must take +place in a solid body, like the top in spinning; the most bulging part +of the surface must move with the greatest rapidity. + +_Mrs. B._ The force which draws a body towards a centre, round which it +moves, is called the _centripetal_ force; and that force, which impels a +body to fly from the centre, is called the _centrifugal_ force; when a +body revolves round a centre, these two forces constantly balance each +other; otherwise the revolving body would either approach the centre or +recede from it, according as the one or the other prevailed. + +_Caroline._ When I see any body moving in a circle, I shall remember, +that it is acted on by two forces. + +_Mrs. B._ Motion, either in a circle, an ellipsis, or any other +curve-line, must be the result of the action of two forces; for you +know, that the impulse of one single force, always produces motion in a +right line. + +_Emily._ And if any cause should destroy the centripetal force, the +centrifugal force would alone impel the body, and it would, I suppose, +fly off in a straight line from the centre to which it had been +confined. + +_Mrs. B._ It would not fly off in a right line from the centre; but in a +right line in the direction in which it was moving, at the instant of +its release; if a stone, whirled round in a sling, gets loose at the +point A, (plate 3. fig. 2.) it flies off in the direction A B; this line +is called a _tangent_, it touches the circumference of the circle, and +forms a right angle with a line drawn from that point of the +circumference to the centre of the circle C. + +_Emily._ You say, that motion in a curve-line, is owing to two forces +acting upon a body; but when I throw this ball in a horizontal +direction, it describes a curve-line in falling; and yet it is only +acted upon by the force of projection; there is no centripetal force to +confine it, or produce compound motion. + +_Mrs. B._ A ball thus thrown, is acted upon by no less than three +forces; the force of projection, which you communicate to it; the +resistance of the air through which it passes, which diminishes its +velocity, without changing its direction; and the force of gravity, +which finally brings it to the ground. The power of gravity, and the +resistance of the air, being always greater than any force of projection +we can give a body, the latter is gradually overcome, and the body +brought to the ground; but the stronger the projectile force, the longer +will these powers be in subduing it, and the further the body will go +before it falls. + +_Caroline._ A shot fired from a cannon, for instance, will go much +further, than a stone projected by the hand. + +_Mrs. B._ Bodies thus projected, you observe, describe a curve-line in +their descent; can you account for that? + +_Caroline._ No; I do not understand why it should not fall in the +diagonal of a square. + +_Mrs. B._ You must consider that the force of projection is strongest +when the ball is first thrown; this force, as it proceeds, being +weakened by the continued resistance of the air, the stone, therefore, +begins by moving in a horizontal direction; but as the stronger powers +prevail, the direction of the ball will gradually change from a +horizontal, to a perpendicular line. _Projection_ alone, would drive the +ball A, to B, (fig. 3.) _gravity_ would bring it to C; therefore, when +acted on in different directions, by these two forces, it moves between, +gradually inclining more and more to the force of gravity, in proportion +as this accumulates; instead therefore of reaching the ground at D, as +you suppose it would, it falls somewhere about E. + +_Caroline._ It is precisely so; look Emily, as I throw this ball +directly upwards, how gravity and the resistance of the air conquer +projection. Now I will throw it upwards obliquely: see, the force of +projection enables it, for an instant, to act in opposition to that of +gravity; but it is soon brought down again. + +_Mrs. B._ The curve-line which the ball has described, is called in +geometry a _parabola_; but when the ball is thrown perpendicularly +upwards, it will descend perpendicularly; because the force of +projection, and that of gravity, are in the same line of direction. + +[Illustration: PLATE III.] + +We have noticed the centres of magnitude, and of motion; but I have not +yet explained to you, what is meant by the _centre of gravity_; it is +that point in a body, about which all the parts exactly balance each +other; if therefore that point be supported, the body will not fall. Do +you understand this? + +_Emily._ I think so; if the parts round about this point have an equal +tendency to fall, they will be in equilibrium, and as long as this point +is supported, the body cannot fall. + +_Mrs. B._ Caroline, what would be the effect, were the body supported in +any other single point? + +_Caroline._ The surrounding parts no longer balancing each other, the +body, I suppose, would fall on the side at which the parts are heaviest. + +_Mrs. B._ Infallibly; whenever the centre of gravity is unsupported, the +body must fall. This sometimes happens with an overloaded wagon winding +up a steep hill, one side of the road being more elevated than the +other; let us suppose it to slope as is described in this figure, (plate +3. fig. 4.) we will say, that the centre of gravity of this loaded wagon +is at the point A. Now your eye will tell you, that a wagon thus +situated, will overset; and the reason is, that the centre of gravity A, +is not supported; for if you draw a perpendicular line from it to the +ground at C, it does not fall under the wagon within the wheels, and is +therefore not supported by them. + +_Caroline._ I understand that perfectly; but what is the meaning of the +other point B? + +_Mrs. B._ Let us, in imagination take off the upper part of the load; +the centre of gravity will then change its situation, and descend to B, +as that will now be the point about which the parts of the less heavily +laden wagon will balance each other. Will the wagon now be upset? + +_Caroline._ No, because a perpendicular line from that point falls +within the wheels at D, and is supported by them; and when the centre of +gravity is supported, the body will not fall. + +_Emily._ Yet I should not much like to pass a wagon in that situation, +for, as you see, the point D is but just within the left wheel; if the +right wheel was raised, by merely passing over a stone, the point D +would be thrown on the outside of the left wheel, and the wagon would +upset. + +_Caroline._ A wagon, or any carriage whatever, will then be most firmly +supported, when the centre of gravity falls exactly between the wheels; +and that is the case in a level road. + +_Mrs. B._ The centre of gravity of the human body, is a point somewhere +in a line extending perpendicularly through the middle of it, and as +long as we stand upright, this point is supported by the feet; if you +lean on one side, you will find that you no longer stand firm. A +rope-dancer performs all his feats of agility, by dexterously supporting +his centre of gravity; whenever he finds that he is in danger of losing +his balance, he shifts the heavy pole which he holds in his hands, in +order to throw the weight towards the side that is deficient; and thus +by changing the situation of the centre of gravity, he restores his +equilibrium. + +_Caroline._ When a stick is poised on the tip of the finger, is it not +by supporting its centre of gravity? + +_Mrs. B._ Yes; and it is because the centre of gravity is not supported, +that spherical bodies roll down a slope. A sphere being perfectly round, +can touch the slope but by a single point, and that point cannot be +perpendicularly under the centre of gravity, and therefore cannot be +supported, as you will perceive by examining this figure. (fig. 5. plate +3.) + +_Emily._ So it appears: yet I have seen a cylinder of wood roll up a +slope; how is that contrived? + +_Mrs. B._ It is done by plugging or loading one side of the cylinder +with lead, as at B, (fig. 5. plate 3.) the body being no longer of a +uniform density, the centre of gravity is removed from the middle of the +body to some point in or near the lead, as that substance is much +heavier than wood; now you may observe that should this cylinder roll +down the plane, as it is here situated, the centre of gravity must rise, +which is impossible; the centre of gravity must always descend in +moving, and will descend by the nearest and readiest means, which will +be by forcing the cylinder up the slope, until the centre of gravity is +supported, and then it stops. + +_Caroline._ The centre of gravity, therefore, is not always in the +middle of a body. + +_Mrs. B._ No, that point we have called the centre of magnitude; when +the body is of an uniform density, and of a regular form, as a cube, or +sphere, the centres of gravity and of magnitude are in the same point; +but when one part of the body is composed of heavier materials than +another, the centre of gravity can no longer correspond with the centre +of magnitude. Thus you see the centre of gravity of this cylinder +plugged with lead, cannot be in the same spot as the centre of +magnitude. + +_Emily._ Bodies, therefore, consisting but of one kind of substance, as +wood, stone, or lead, and whose densities are consequently uniform, must +stand more firmly, and be more difficult to overset, than bodies +composed of a variety of substances, of different densities, which may +throw the centre of gravity on one side. + +_Mrs. B._ That depends upon the situation of the materials; if those +which are most dense, occupy the lower part, the stability will be +increased, as the centre of gravity will be near the base. But there is +another circumstance which more materially affects the firmness of their +position, and that is their form. Bodies that have a narrow base are +easily upset, for if they are a little inclined, their centre of gravity +is no longer supported, as you may perceive in fig. 6. + +_Caroline._ I have often observed with what difficulty a person carries +a single pail of water; it is owing, I suppose, to the centre of gravity +being thrown on one side; and the opposite arm is stretched out to +endeavour to bring it back to its original situation; but a pail hanging +to each arm is carried with less difficulty, because they balance each +other, and the centre of gravity remains supported by the feet. + +_Mrs. B._ Very well; I have but one more remark to make on the centre of +gravity, which is, that when two bodies are fastened together by an +inflexible rod, they are to be considered as forming but one body; if +the two bodies be of equal weight, the centre of gravity will be in the +middle of the line which unites them, (fig. 7.) but if one be heavier +than the other, the centre of gravity will be proportionally nearer the +heavy body than the light one. (fig. 8.) If you were to carry a rod or +pole with an equal weight fastened at each end of it, you would hold it +in the middle of the rod, in order that the weights should balance each +other; whilst if the weights were unequal, you would hold it nearest the +greater weight, to make them balance each other. + +_Emily._ And in both cases we should support the centre of gravity; and +if one weight be very considerably larger than the other, the centre of +gravity will be thrown out of the rod into the heaviest weight. (fig. +9.) + +_Mrs. B._ Undoubtedly. + + +Questions + +1. (Pg. 46) If a body be struck by two equal forces in opposite +directions, what will be the result? + +2. (Pg. 46) What is fig. 5. plate 2. intended to represent? + +3. (Pg. 47) How would the ball move, and how would you represent the +direction of its motion? + +4. (Pg. 47) What is supposed respecting the forces represented in fig. +6? + +5. (Pg. 47) How would the body move if so impelled? + +6. (Pg. 47) If the forces are unequal and not at right angles, how would +the body move, as illustrated by fig. 7? + +7. (Pg. 47) How must a body be acted on, to produce motion in a curve, +and what example is given? + +8. (Pg. 48) When is a body said to revolve in a plane, and what is meant +by the centre of motion? + +9. (Pg. 48) What is intended by the axis of motion, and what are +examples? + +10. (Pg. 48) What is the middle point of a body called? + +11. (Pg. 48) What is said of the axis of motion, whilst the body is +revolving? + +12. (Pg. 48) When a body revolves on an axis, do all its parts move with +equal velocity? + +13. (Pg. 49) How is this explained by fig. 1. plate 3? + +14. (Pg. 49) What are the two forces called which cause a body to move +in a curve; and what proportion do these two forces bear to each other +when a body revolves round a centre? + +15. (Pg. 49) If the centripetal force were destroyed, how would a body +be carried by the centrifugal? + +16. (Pg. 50) Explain what is meant by a _tangent_, as shown in fig. 2. +plate 3. + +17. (Pg. 50) What forces impede a body thrown horizontally? + +18. (Pg. 50) Give the reason why a body so projected, falls in a curve. +(fig. 3. plate 3.) + +19. (Pg. 51) The curve in which it falls, is not a part of a true +circle: what is it denominated? + +20. (Pg. 51) What is the _centre of gravity_ defined to be? + +21. (Pg. 51) What results from supporting, or not supporting the centre +of gravity? + +22. (Pg. 51) What is intended to be explained by fig. 4. plate 3? + +23. (Pg. 51) What would be the effect of taking off the upper portion of +the load? + +24. (Pg. 52) When will a carriage stand most firmly? + +25. (Pg. 52) What is said of the centre of gravity of the human body, +and how does a rope dancer preserve his equilibrium? + +26. (Pg. 52) Why cannot a sphere remain at rest on an inclined plane? +(fig. 5. plate 3.) + +27. (Pg. 52) A cylinder of wood, may be made to rise to a small distance +up an inclined plane. How may this be effected? (fig. 5. plate 3.) + +28. (Pg. 53) When do we find the centres of gravity, and of magnitude in +different points? + +29. (Pg. 53) What influence will the density of the parts of a body +exert upon its stability? + +30. (Pg. 53) What other circumstance materially affects the firmness of +position? (fig. 6. plate 3.) + +31. (Pg. 53) Why is it more easy to carry a weight in each hand, than in +one only? + +32. (Pg. 53) What is said respecting two bodies united by an inflexible +rod? + +33. (Pg. 53) What is fig. 7, plate 3, intended to illustrate? What fig. +8; what fig. 9? + + + + +CONVERSATION V. + +ON THE MECHANICAL POWERS. + +OF THE POWER OF MACHINES. OF THE LEVER IN GENERAL. OF THE LEVER OF THE +FIRST KIND, HAVING THE FULCRUM BETWEEN THE POWER AND THE WEIGHT. OF THE +LEVER OF THE SECOND KIND, HAVING THE WEIGHT BETWEEN THE POWER AND THE +FULCRUM. OF THE LEVER OF THE THIRD KIND, HAVING THE POWER BETWEEN THE +FULCRUM AND THE WEIGHT. + + +MRS. B. + +We may now proceed to examine the mechanical powers; they are six in +number: The _lever_, the _pulley_, the _wheel_ and _axle_, the _inclined +plane_, the _wedge_ and the _screw_; one or more of which enters into +the composition of every machine. + +A mechanical power is an instrument by which the effect of a given force +is increased, whilst the force remains the same. + +In order to understand the power of a machine, there are four things to +be considered. 1st. The power that acts: this consists in the effort of +men or horses, of weights, springs, steam, &c. + +2dly. The resistance which is to be overcome by the power: this is +generally a weight to be moved. The power must always be superior to the +resistance, otherwise the machine could not be put in motion. + +_Caroline._ If for instance the resistance of a carriage was greater +than the strength of the horses employed to draw it, they would not be +able to make it move. + +_Mrs. B._ 3dly. We are to consider the support or prop, or as it is +termed in mechanics, the _fulcrum_; this you may recollect is the point +upon which the body turns when in motion; and lastly, the respective +velocities of the power, and of the resistance. + +_Emily._ That must in general depend upon their respective distances +from the fulcrum, or from the axis of motion; as we observed in the +motion of the vanes of the windmill. + +_Mrs. B._ We shall now examine the power of the lever. The _lever is an +inflexible rod or bar, moveable about a fulcrum, and having forces +applied to two or more points on it_. For instance, the steel rod to +which these scales are suspended is a lever, and the point in which it +is supported, the fulcrum, or centre of motion; now, can you tell me why +the two scales are in equilibrium? + +_Caroline._ Being both empty, and of the same weight, they balance each +other. + +_Emily._ Or, more correctly speaking, because the centre of gravity +common to both, is supported. + +_Mrs. B._ Very well; and where is the centre of gravity of this pair of +scales? (fig. 1. plate 4.) + +_Emily._ You have told us that when two bodies of equal weight were +fastened together, the centre of gravity was in the middle of the line +that connected them; the centre of gravity of the scales must therefore +be supported by the fulcrum F of the lever which unites the two scales, +and which is the centre of motion. + +_Caroline._ But if the scales contained different weights, the centre of +gravity would no longer be in the fulcrum of the lever, but remove +towards that scale which contained the heaviest weight; and since that +point would no longer be supported, the heavy scale would descend, and +out-weigh the other. + +_Mrs. B._ True; but tell me, can you imagine any mode by which bodies of +different weights can be made to balance each other, either in a pair of +scales, or simply suspended to the extremities of the lever? for the +scales are not an essential part of the machine; they have no mechanical +power, and are used merely for the convenience of containing the +substance to be weighed. + +_Caroline._ What! make a light body balance a heavy one? I cannot +conceive that possible. + +_Mrs. B._ The fulcrum of this pair of scales (fig. 2.) is moveable, you +see; I can take it off the beam, and fasten it on again in another part; +this part is now become the fulcrum, but it is no longer in the centre +of the lever. + +_Caroline._ And the scales are no longer true; for that which hangs on +the longest side of the lever descends. + +_Mrs. B._ The two parts of the lever divided by the fulcrum, are called +its arms; you should therefore say the longest arm, not the longest side +of the lever. + +Your observation is true that the balance is now destroyed; but it will +answer the purpose of enabling you to comprehend the power of a lever, +when the fulcrum is not in the centre. + +_Emily._ This would be an excellent contrivance for those who cheat in +the weight of their goods; by making the fulcrum a little on one side, +and placing the goods in the scale which is suspended to the longest arm +of the lever, they would appear to weigh more than they do in reality. + +_Mrs. B._ You do not consider how easily the fraud would be detected; +for on the scales being emptied they would not hang in equilibrium. If +indeed the scale on the shorter arm was made heavier, so as to balance +that on the longer, they would appear to be true, whilst they were +really false. + +_Emily._ True; I did not think of that circumstance. But I do not +understand why the longest arm of the lever should not be in equilibrium +with the other? + +_Caroline._ It is because the momentum in the longest, is greater than +in the shortest arm; the centre of gravity, therefore, is no longer +supported. + +_Mrs. B._ You are right, the fulcrum is no longer in the centre of +gravity; but if we can contrive to make the fulcrum in its present +situation become the centre of gravity, the scales will again balance +each other; for you recollect that the centre of gravity is that point +about which every part of the body is in equilibrium. + +_Emily._ It has just occurred to me how this may be accomplished; put a +great weight into the scale suspended to the shortest arm of the lever, +and a smaller one into that suspended to the longest arm. Yes, I have +discovered it--look Mrs. B., the scale on the shortest arm will carry 3 +lbs., and that on the longest arm only one, to restore the balance. +(fig. 3.) + +_Mrs. B._ You see, therefore, that it is not so impracticable as you +imagined, to make a heavy body balance a light one; and this is in fact +the means by which you observed that an imposition in the weight of +goods might be effected, as a weight of ten or twelve ounces, might thus +be made to balance a pound of goods. If you measure both arms of the +lever, you will find that the length of the longer arm, is three times +that of the shorter; and that to produce an equilibrium, the weights +must bear the same proportion to each other, and that the greater +weight, must be on the shorter arm. Let us now take off the scales, that +we may consider the lever simply; and in this state you see that the +fulcrum is no longer the centre of gravity, because it has been removed +from the middle of the lever; but it is, and must ever be, the centre of +motion, as it is the only point which remains at rest, while the other +parts move about it. + +[Illustration: PLATE IV.] + +_Caroline._ The arms of the lever being different in length, it now +exactly resembles the steelyards, with which articles are so frequently +weighed. + +_Mrs. B._ It may in fact be considered as a pair of steelyards, by which +the same power enables us to ascertain the weight of different articles, +by simply increasing the distance of the power from the fulcrum; you +know that the farther a body is from the axis of motion, the greater is +its velocity. + +_Caroline._ That I remember, and understand perfectly. + +_Mrs. B._ You comprehend then, that the extremity of the longest arm of +a lever, must move with greater velocity than that of the shortest arm, +and that its momentum is greater in proportion. + +_Emily._ No doubt, because it is farthest from the centre of motion. And +pray, Mrs. B., when my brothers play at _see-saw_, is not the plank on +which they ride, a kind of lever? + +_Mrs. B._ Certainly; the log of wood which supports it from the ground +is the fulcrum, and those who ride, represent the power and the +resistance at the ends of the lever. And have you not observed that when +those who ride are of equal weight, the plank must be supported in the +middle, to make the two arms equal; whilst if the persons differ in +weight, the plank must be drawn a little farther over the prop, to make +the arms unequal, and the lightest person, who may be supposed to +represent the power, must be placed at the extremity of the longest arm. + +_Caroline._ That is always the case when I ride on a plank with my +youngest brother; I have observed also that the lightest person has the +best ride, as he moves both further and quicker; and I now understand +that it is because he is more distant from the centre of motion. + +_Mrs. B._ The greater velocity with which your little brother moves, +renders his momentum equal to yours. + +_Caroline._ Yes; I have the most weight, he the greatest velocity; so +that upon the whole our momentums are equal. But you said, Mrs. B., that +the power should be greater than the resistance, to put the machine in +motion; how then can the plank move if the momentums of the persons who +ride are equal? + +_Mrs. B._ Because each person at his descent touches and pushes against +the ground with his feet; the reaction of which gives him an impulse +which produces the motion; this spring is requisite to destroy the +equilibrium of the power and the resistance, otherwise the plank would +not move. Did you ever observe that a lever describes the arc of a +circle in its motion? + +_Emily._ No; it appears to me to rise and descend perpendicularly; at +least I always thought so. + +_Mrs. B._ I believe I must make a sketch of you and your brother riding +on a plank, in order to convince you of your error. (fig. 4. plate 4.) +You may now observe that a lever can move only round the fulcrum, since +that is the centre of motion; it would be impossible for you to rise +perpendicularly, to the point A; or for your brother to descend in a +straight line, to the point B; you must in rising, and he in descending, +describe arcs of your respective circles. This drawing shows you also +how much superior his velocity must be to yours; for if you could swing +quite round, you would each complete your respective circles, in the +same time. + +_Caroline._ My brother's circle being much the largest, he must +undoubtedly move the quickest. + +_Mrs. B._ Now tell me, do you think that your brother could raise you as +easily without the aid of a lever? + +_Caroline._ Oh no, he could not lift me off the ground. + +_Mrs. B._ Then I think you require no further proof of the power of a +lever, since you see what it enables your brother to perform. + +_Caroline._ I now understand what you meant by saying, that in +mechanics, velocity is opposed to weight, for it is my brother's +velocity which overcomes my weight. + +_Mrs. B._ You may easily imagine, what enormous weights may be raised by +levers of this description, for the longer, when compared with the +other, that arm is to which the power is applied, the greater will be +the effect produced by it; because the greater is the velocity of the +power compared to that of the weight. + +Levers are of three kinds; in the first the fulcrum is between the power +and the weight. + +_Caroline._ This kind then comprehends the several levers you have +described. + +_Mrs. B._ Yes, when in levers of the first kind, the fulcrum is equally +distant from the power and the weight, as in the balance, there will be +an equilibrium, when the power and the weight are equal to each other; +it is not then a mechanical power, for nothing can in this case be +gained by velocity; the two arms of the lever being equal, the velocity +of their extremities must be so likewise. The balance is therefore of no +assistance as a mechanical power, although it is extremely useful in +estimating the respective weights of bodies. + +But when (fig. 5.) the fulcrum F of a lever is not equally distant from +the power and the weight, and the power P acts at the extremity of the +longest arm, it may be less than the weight W; its deficiency being +compensated by its superior velocity, as we observed in the _see-saw_. + +_Emily._ Then when we want to lift a great weight, we must fasten it to +the shortest arm of a lever, and apply our strength to the longest arm? + +_Mrs. B._ If the case will admit of your putting the end of the lever +under the resisting body, no fastening will be required; as you will +perceive, when a nail is drawn by means of a hammer, which, though bent, +is a lever of the first kind; the handle being the longest arm, the +point on which it rests, the fulcrum, and the distance from that to the +part which holds the nail, the short arm. But let me hear, Caroline, +whether you can explain the action of this instrument, which is composed +of two levers united in one common fulcrum. + +_Caroline._ A pair of scissors! + +_Mrs. B._ You are surprised; but if you examine their construction, you +will discover that it is the power of the lever, that assists us in +cutting with scissors. + +_Caroline._ Yes; I now perceive that the point at which the two levers +are screwed together, is the fulcrum; the power of the fingers is +applied to the handles, and the article to be cut, is the resistance; +therefore, the longer the handles, and the shorter the points of the +scissors, the more easily you cut with them. + +_Emily._ That I have often observed, for when I cut paste-board or any +hard substance, I always make use of that part of the scissors nearest +the screw or rivet, and I now understand why it increases the power of +cutting; but I confess that I never should have discovered scissors to +have been double levers; and pray are not snuffers levers of a similar +description? + +_Mrs. B._ Yes, and most kinds of pincers; the great power of which +consists in the great relative length of the handles. + +Did you ever notice the swingle-tree of a carriage to which the horses +are attached when drawing? + +_Emily._ O yes; this is a lever of the first kind, but the fulcrum being +in the middle, the horses should draw with equal power, whatever may be +their strength. + +_Mrs. B._ That is generally the case, but it is evident that by making +one arm longer than the other, it might be adapted to horses of unequal +strength. + +_Caroline._ And of what nature are the other two kinds of levers? + +_Mrs. B._ In levers of the second kind, the weight, instead of being at +one end, is situated between the power and the fulcrum, (fig. 6.) + +_Caroline._ The weight and the fulcrum have here changed places; and +what advantage is gained by this kind of lever? + +_Mrs. B._ In moving it, the velocity of the power must necessarily be +greater than that of the weight, as it is more distant from the centre +of the motion. Have you ever seen your brother move a snow-ball by means +of a strong stick, when it became too heavy for him to move without +assistance? + +_Caroline._ Oh yes; and this was a lever of the second kind, (fig. 7.) +the end of the stick, which he thrusts under the ball, and which rests +on the ground, becomes the fulcrum; the ball is the weight to be moved, +and the power his hands, applied to the other end of the lever. In this +instance there is a great difference in the length of the arms of the +lever; for the weight is almost close to the fulcrum. + +_Mrs. B._ And the advantage gained is proportional to this difference. +The most common example that we have of levers of the second kind, is in +the doors of our apartments. + +_Emily._ The hinges represent the fulcrum, our hands the power applied +to the other end of the lever; but where is the weight to be moved? + +_Mrs. B._ The door is the weight, which in this example occupies the +whole of the space between the power and the fulcrum. Nut crackers are +double levers of this kind: the hinge is the fulcrum, the nut the +resistance, and the hands the power. + +In levers of the third kind (fig. 8.) the fulcrum is again at one +extremity, the weight or resistance at the other, and the power is +applied between the fulcrum and the resistance. + +_Emily._ The fulcrum, the weight, or the power, then, each in its turn, +occupies some part of the lever between its extremities. But in this +third kind of lever, the weight being farther than the power from the +centre of motion, the difficulty of raising it seems increased rather +than diminished. + +_Mrs. B._ That is very true; a lever of this kind is therefore never +used, unless absolutely necessary, as is the case in raising a ladder in +order to place it against a wall; the man who raises it cannot place his +hands on the upper part of the ladder, the power, therefore, is +necessarily placed much nearer to the fulcrum than to the weight. + +_Caroline._ Yes, the hands are the power, the ground the fulcrum, and +the upper part of the ladder the weight. + +_Mrs. B._ Nature employs this kind of lever in the structure of the +human frame. In lifting a weight with the hand, the lower part of the +arm becomes a lever of the third kind; the elbow is the fulcrum, the +muscles of the fleshy part of the arm, the power; and as these are +nearer to the elbow than to the hand, it is necessary that their power +should exceed the weight to be raised. + +_Emily._ Is it not surprising that nature should have furnished us with +such disadvantageous levers? + +_Mrs. B._ The disadvantage, in respect to power, is more than +counterbalanced by the convenience resulting from this structure of the +arm; and it is that no doubt which is best adapted to enable it to +perform its various functions. + +There is one rule which applies to every lever, which is this: In order +to produce an equilibrium, the power must bear the same proportion to +the weight, as the length of the shorter arm does to that of the longer; +as was shown by Emily with the weights of 1 _lb._ and of 3 _lb._ Fig. 3. +plate 4. + +We have dwelt so long on the lever, that we must reserve the examination +of the other mechanical powers, to our next interview. + + +Questions + +1. (Pg. 54) How many mechanical powers are there, and what are they +named? + +2. (Pg. 54) What is a mechanical power defined to be? + +3. (Pg. 54) What four particulars must be observed? + +4. (Pg. 54) Upon what will the velocities depend? + +5. (Pg. 55) What is a lever? + +6. (Pg. 55) Give a familiar example. + +7. (Pg. 55) When and why do the scales balance each other, and where is +their centre of gravity? (fig. 1. plate 4.) + +8. (Pg. 55) Why would they not balance with unequal weights? + +9. (Pg. 55) Were the fulcrum removed from the middle of the beam what +would result? + +10. (Pg. 55) What do we mean by the arms of a lever? + +11. (Pg. 56) How may a pair of scales be false, and yet appear to be +true? + +12. (Pg. 56) If the fulcrum be removed from the centre of gravity, how +may the equilibrium be restored? + +13. (Pg. 56) How is this exemplified by fig. 3. plate 4? + +14. (Pg. 56) What proportion must the weights bear to the lengths of the +arms? + +15. (Pg. 57) On what principle do we weigh with a pair of steelyards, +and what will be the difference in the motion of the extremities of such +a lever? + +16. (Pg. 58) How is this exemplified by fig. 4. plate 4? + +17. (Pg. 58) What line is described by the ends of a lever? fig. 4. +plate 4. + +18. (Pg. 58) How many kinds are there; and in the first how is the +fulcrum situated? + +19. (Pg. 58) When may the fulcrum be so situated that this lever is not +a mechanical power, and why? + +20. (Pg. 59) What is represented by fig. 5. plate 4? + +21. (Pg. 59) Give a familiar example of the use of a lever of the first +kind. + +22. (Pg. 59) In what instruments are two such levers combined? + +23. (Pg. 59) How may two horses of unequal strength, be advantageously +coupled in a carriage? + +24. (Pg. 60) Describe a lever of the second kind. (Fig. 6. plate 4.) + +25. (Pg. 60) What is represented in fig. 7. plate 4, and in what +proportion does this lever gain power? + +26. (Pg. 60) What is said respecting a door? + +27. (Pg. 60) Describe a lever of the third kind. + +28. (Pg. 60) In what instance do we use this? + +29. (Pg. 61) What remarks are made on its employment in the limbs of +animals? + +30. (Pg. 61) What are the conditions of equilibrium in every lever? + + + + +CONVERSATION V. + +CONTINUED. + +ON THE MECHANICAL POWERS. + +OF THE PULLEY. OF THE WHEEL AND AXLE. OF THE INCLINED PLANE. OF THE +WEDGE. OF THE SCREW. + + +MRS. B. + +The pulley is the second mechanical power we are to examine. You both, I +suppose, have seen a pulley? + +_Caroline._ Yes, frequently: it is a circular, and flat piece of wood or +metal, with a string which runs in a groove round it: by means of which, +a weight may be pulled up; thus pulleys are used for drawing up +curtains. + +_Mrs. B._ Yes; but in that instance the pulleys are fixed; that is, they +retain their places, and merely turn round on their axis; these do not +increase the power to raise the weights, as you will perceive by this +figure. (plate 5. fig. 1.) Observe that the fixed pulley is on the same +principle as the lever of a pair of scales, in which the fulcrum F being +in the centre of gravity, the power P and the weight W, are equally +distant from it, and no advantage is gained. + +_Emily._ Certainly; if P represents the power employed to raise the +weight W, the power must be greater than the weight in order to move it. +But of what use then is a fixed pulley in mechanics? + +_Mrs. B._ Although it does not increase the power, it is frequently +useful for altering its direction. A single fixed pulley enables us to +draw a curtain up, by pulling the string connected with it downwards; +and we should be at a loss to accomplish this simple operation without +its assistance. + +_Caroline._ There would certainly be some difficulty in ascending to the +head of the curtain, in order to draw it up. Indeed I now recollect +having seen workmen raise weights to a considerable height by means of a +fixed pulley, which saved them the trouble of going up themselves. + +_Mrs. B._ The next figure represents a pulley which is not fixed; (fig. +2.) and thus situated, you will perceive that it affords us mechanical +assistance. + +A is a moveable pulley; that is, one which is attached to the weight to +be raised, and which consequently moves up or down with it. There is +also a fixed pulley D, which is only of use to change the direction of +the power P. Now it is evident that the velocity of the power, will be +double that of the weight W; for if the rope be pulled at P, until the +pulley A ascends with the weight to the fixed pulley D, then both parts +of the rope, C and B, must pass over the fixed pulley, and consequently +the hand at P, will have descended through a space equal to those two +parts; but the weight will have ascended only one half of that distance. + +_Caroline._ That I understand: if P drew the string but one inch, the +weight would be raised only half an inch, because it would shorten the +strings B and C half an inch each, and consequently the pulley with the +weight attached to it, can be raised only half an inch. + +_Emily._ But I do not yet understand the advantage of moveable pulleys; +they seem to me to increase rather than diminish the difficulty of +raising weights, since you must draw the string double the length that +you raise the weight; whilst with a single pulley, or without any +pulley, the weight is raised as much as the string is shortened. + +_Mrs. B._ The advantage of a moveable pulley consists in dividing the +difficulty; we must, it is true, draw twice the length of the string, +but then only half the strength is required that would be necessary to +raise the weight without the assistance of a moveable pulley. + +_Emily._ So that the difficulty is overcome in the same manner as it +would be, by dividing the weight into two equal parts, and raising them +successively. + +_Mrs. B._ Exactly. You must observe, that with a moveable pulley the +velocity of the power, is double that of the weight; since the power P +(fig. 2.) moves two inches whilst the weight W moves one inch; therefore +the power need not be more than half the weight, to make their momentums +equal. + +_Caroline._ Pulleys act then on the same principle as the lever; the +deficiency of weight in the power, being compensated by its superior +velocity, so as to make their momentums equal. + +_Mrs. B._ You will find, that all gain of power in mechanics is founded +on the same principle. + +_Emily._ But may it not be objected to pulleys, that a longer time is +required to raise a weight by their aid, than without it? for what you +gain in power, you lose in time. + +_Mrs. B._ That, my dear, is the fundamental law in mechanics: it is the +case with the lever, as well as the pulley; and you will find it to be +so with all the other mechanical powers. + +_Caroline._ I do not see any advantage in the mechanical powers then, if +what we gain by them in one way, is lost in another. + +_Mrs. B._ Since we are not able to increase our natural strength is not +any instrument of obvious utility, by means of which we may reduce the +resistance or weight of any body, to the level of that strength? This +the mechanical powers enable us to accomplish. It is true, as you +observe, that it requires a sacrifice of time to attain this end, but +you must be sensible how very advantageously it is exchanged for power. +If one man by his natural strength could raise one hundred pounds only, +it would require five such men to raise five hundred pounds; and if one +man performs this by the help of a suitable engine, there is then no +actual loss of time; as he does the work of five men, although he is +five times as long in its accomplishment. + +You can now understand, that the greater the number of moveable pulleys +connected by a string, the more easily the weight is raised; as the +difficulty is divided amongst the number of strings, or rather of parts +into which the string is divided, by the pulleys. Two, or more pulleys +thus connected, form what is called a tackle, or system of pulleys. +(fig. 3.) You may have seen them suspended from cranes to raise goods +into warehouses. + +_Emily._ When there are two moveable pulleys, as in the figure you have +shown to us, (fig. 3.) there must also be two fixed pulleys, for the +purpose of changing the direction of the string, and then the weight is +supported by four strings, and of course, each must bear only one fourth +part of the weight. + +_Mrs. B._ You are perfectly correct, and the rule for estimating the +power gained by a system of pulleys, is to count the number of strings +by which the weight is supported; or, which amounts to the same thing, +to multiply the number of moveable pulleys by two. + +In shipping, the advantages of both an increase of power, and a change +of direction, by means of pulleys, are of essential importance: for the +sails are raised up the masts by the sailors on deck, from the change of +direction which the pulley effects, and the labour is facilitated by the +mechanical power of a combination of pulleys. + +[Illustration: PLATE V.] + +_Emily._ But the pulleys on ship-board do not appear to me to be united +in the manner you have shown us. + +_Mrs. B._ They are, I believe, generally connected as described in +figure 4, both for nautical, and a variety of other purposes; but in +whatever manner pulleys are connected by a single string, the mechanical +power is the same. + +The third mechanical power, is the wheel and axle. Let us suppose (plate +6. fig. 5) the weight W, to be a bucket of water in a well, which we +raise by winding round the axle the rope, to which it is attached; if +this be done without a wheel to turn the axle, no mechanical assistance +is received. The axle without a wheel is as impotent as a single fixed +pulley, or a lever, whose fulcrum is in the centre: but add the wheel to +the axle, and you will immediately find the bucket is raised with much +less difficulty. The velocity of the circumference of the wheel is as +much greater than that of the axle, as it is further from the centre of +motion; for the wheel describes a great circle in the same space of time +that the axle describes a small one, therefore the power is increased in +the same proportion as the circumference of the wheel is greater than +that of the axle. If the velocity of the wheel is twelve times greater +than that of the axle, a power twelve times less than the weight of the +bucket, would balance it; and a small increase would raise it. + +_Emily._ The axle acts the part of the shorter arm of the lever, the +wheel that of the longer arm. + +_Caroline._ In raising water, there is commonly, I believe, instead of a +wheel attached to the axle, only a crooked handle, which answers the +purpose of winding the rope round the axle, and thus raising the bucket. + +_Mrs. B._ In this manner (fig. 6;) now if you observe the dotted circle +which the handle describes in winding up the rope, you will perceive +that the branch of the handle A, which is united to the axle, represents +the spoke of a wheel, and answers the purpose of an entire wheel; the +other branch B affords no mechanical aid, merely serving as a handle to +turn the wheel. + +Wheels are a very essential part of most machines; they are employed in +various ways; but, when fixed to the axle, their mechanical power is +always the same: that is, as the circumference of the wheel exceeds that +of the axle, so much will the energy of the power be increased. + +_Caroline._ Then the larger the wheel, in proportion to the axle, the +greater must be its effect? + +_Mrs. B._ Certainly. If you have ever seen any considerable mills or +manufactures, you must have admired the immense wheel, the revolution of +which puts the whole of the machinery into motion; and though so great +an effect is produced by it, a horse or two has sufficient power to turn +it; sometimes a stream of water is used for that purpose, but of late +years, a steam-engine has been found both the most powerful and the most +convenient mode of turning the wheel. + +_Caroline._ Do not the vanes of a windmill represent a wheel, Mrs. B.? + +_Mrs. B._ Yes; and in this instance we have the advantage of a +gratuitous force, the wind, to turn the wheel. One of the great benefits +resulting from the use of machinery is, that it gives us a sort of +empire over the powers of nature, and enables us to make them perform +the labour which would otherwise fall to the lot of man. When a current +of wind, a stream of water, or the expansive force of steam, performs +our task, we have only to superintend and regulate their operations. + +The fourth mechanical power is the inclined plane; this is generally +nothing more than a plank placed in a sloping direction, which is +frequently used to facilitate the raising of weights, to a small height, +such as the rolling of hogsheads or barrels into a warehouse. It is not +difficult to understand, that a weight may much more easily be rolled up +a slope than it can be raised the same height perpendicularly. But in +this, as well as the other mechanical powers, the facility is purchased +by a loss of time (fig. 7;) for the weight, instead of moving directly +from A to C, must move from B to C, and as the length of the plane is to +its height, so much is the resistance of the weight diminished. + +_Emily._ Yes; for the resistance, instead of being confined to the short +line A C, is spread over the long line B C. + +_Mrs. B._ The wedge, which is the next mechanical power, is usually +viewed as composed of two inclined planes (fig. 8:) you may have seen +wood-cutters use it to cleave wood. The resistance consists in the +cohesive attraction of the wood, or any other body which the wedge is +employed to separate; the advantage gained by this power is differently +estimated by philosophers; but one thing is certain, its power is +increased, in proportion to the decrease of its thickness, compared with +its length. The wedge is a very powerful instrument, but it is always +driven forward by blows from a hammer, or some other body having +considerable momentum. + +_Emily._ The wedge, then, is rather a compound than a distinct +mechanical power, since it is not propelled by simple pressure, or +weight, like the other powers. + +_Mrs. B._ It is so. All cutting instruments are constructed upon the +principle of the inclined plane, or the wedge: those that have but one +edge sloped, like the chisel, may be referred to the inclined plane; +whilst the axe, the hatchet, and the knife, (when used to split asunder) +are used as wedges. + +_Caroline._ But a knife cuts best when it is drawn across the substance +it is to divide. We use it thus in cutting meat, we do not chop it to +pieces. + +_Mrs. B._ The reason of this is, that the edge of a knife is really a +very fine saw, and therefore acts best when used like that instrument. + +The screw, which is the last mechanical power, is more complicated than +the others. You will see by this figure, (fig. 9.) that it is composed +of two parts, the screw and the nut. The screw S is a cylinder, with a +spiral protuberance coiled round it, called the thread; the nut N is +perforated to receive the screw, and the inside of the nut has a spiral +groove, made to fit the spiral thread of the screw. + +_Caroline._ It is just like this little box, the lid of which screws on +the box as you have described; but what is this handle L which projects +from the nut? + +_Mrs. B._ It is a lever, which is attached to the nut, without which the +screw is never used as a mechanical power. The power of the screw, +complicated as it appears, is referable to one of the most simple of the +mechanical powers; which of them do you think it is? + +_Caroline._ In appearance, it most resembles the wheel and axle. + +_Mrs. B._ The lever, it is true, has the effect of a wheel, as it is the +means by which you turn the nut, or sometimes the screw, round; but the +lever is not considered as composing a part of the screw, though it is +true, that it is necessarily attached to it. + +_Emily._ The spiral thread of the screw resembles, I think, an inclined +plane: it is a sort of slope, by means of which the nut ascends more +easily than it would do if raised perpendicularly; and it serves to +support it when at rest. + +_Mrs. B._ Very well: if you cut a slip of paper in the form of an +inclined plane, and wind it round your pencil, which will represent the +cylinder, you will find that it makes a spiral line, corresponding to +the spiral protuberance of the screw. (Fig. 10.) + +_Emily._ Very true; the nut then ascends an inclined plane, but ascends +it in a spiral, instead of a straight line: the closer the threads of +the screw, the more easy the ascent: it is like having shallow, instead +of steep steps to ascend. + +_Mrs. B._ Yes; excepting that the nut takes no steps, as it gradually +winds up or down; then observe, that the closer the threads of the +screw, the less is its ascent in turning round, and the greater is its +power; so that we return to the old principle,--what is saved in power +is lost in time. + +_Emily._ Cannot the power of the screw be increased also, by lengthening +the lever attached to the nut? + +_Mrs. B._ Certainly. The screw, with the addition of the lever, forms a +very powerful machine, employed either for compression or to raise heavy +weights. It is used by book-binders, to press the leaves of books +together; it is used also in cider and wine presses, in coining, and for +a variety of other purposes. + +_Emily._ Pray, Mrs. B., by what rule do you estimate the power of the +screw? + +_Mrs. B._ By measuring the circumference of the circle, which the end of +the lever would form in one whole revolution, and comparing this with +the distance from the centre of one thread of the screw, to that of its +next contiguous turn; for whilst the lever travels that whole distance, +the screw rises or falls only through the distance from one coil to +another. + +_Caroline._ I think that I have sometimes seen the lever attached to the +screw, and not to the nut, as it is represented in the figure. + +_Mrs. B._ This is frequently done, but it does not in any degree affect +the power of the instrument. + +All machines are composed of one or more of these six mechanical powers +we have examined; I have but one more remark to make to you relative to +them, which is, that friction in a considerable degree diminishes their +force: allowance must therefore always be made for it, in the +construction of machinery. + +_Caroline._ By friction, do you mean one part of the machine rubbing +against another part contiguous to it? + +_Mrs. B._ Yes; friction is the resistance which bodies meet with in +rubbing against each other; there is no such thing as perfect smoothness +or evenness in nature; polished metals, though they wear that appearance +more than most other bodies, are far from really possessing it; and +their inequalities may frequently be perceived through a good magnifying +glass. When, therefore, the surfaces of the two bodies come in contact, +the prominent parts of the one, will often fall into the hollow parts of +the other, and occasion more or less resistance to motion. + +_Caroline._ But if a machine is made of polished metal, as a watch for +instance, the friction must be very trifling? + +_Mrs. B._ In proportion as the surfaces of bodies are well polished, the +friction is doubtless diminished; but it is always considerable, and it +is usually computed to destroy one-third of the power of a machine. Oil +or grease is used to lessen friction: it acts as a polish, by filling up +the cavities of the rubbing surfaces, and thus making them slide more +easily over each other. + +_Caroline._ Is it for this reason that wheels are greased, and the locks +and hinges of doors oiled? + +_Mrs. B._ Yes; in these instances the contact of the rubbing surfaces is +so close, and they are so constantly in use, that they require to be +frequently oiled, or a considerable degree of friction is produced. + +There are two kinds of friction; the first is occasioned by the rubbing +of the surfaces of bodies against each other, the second, by the rolling +of a circular body; as that of a carriage wheel upon the ground: the +friction resulting from the first is much the most considerable, for +great force is required to enable the sliding body to overcome the +resistance which the asperities of the surfaces in contact oppose to its +motion, and it must be either lifted over, or break through them; +whilst, in the second kind of friction, the rough parts roll over each +other with comparative facility; hence it is, that wheels are often used +for the sole purpose of diminishing the resistance from friction. + +_Emily._ This is one of the advantages of carriage wheels, is it not? + +_Mrs. B._ Yes; and the larger the circumference of the wheel the more +readily it can overcome any considerable obstacles, such as stones, or +inequalities in the road. When, in descending a steep hill, we fasten +one of the wheels, we decrease the velocity of the carriage, by +increasing the friction. + +_Caroline._ That is to say, by converting the rolling friction into the +rubbing friction. And when you had casters put to the legs of the table, +in order to move it more easily, you changed the rubbing into the +rolling friction. + +_Mrs. B._ There is another circumstance which we have already noticed, +as diminishing the motion of bodies, and which greatly affects the +power of machines. This is the resistance of the medium, in which a +machine is worked. All fluids, whether elastic like air, or non-elastic +like water and other liquids, are called mediums; and their resistance +is proportioned to their density; for the more matter a body contains, +the greater the resistance it will oppose to the motion of another body +striking against it. + +_Emily._ It would then be much more difficult to work a machine under +water than in the air? + +_Mrs. B._ Certainly, if a machine could be worked in _vacuo_, and +without friction, it would not be impeded, but this is unattainable; a +considerable reduction of power must therefore be allowed for, from +friction and the resistance of the medium. + +We shall here conclude our observations on the mechanical powers. At our +next meeting I shall endeavour to give you an explanation of the motion +of the heavenly bodies. + + +Questions + +31. (Pg. 62) Describe a pulley, and its use. + +32. (Pg. 62) What is meant by a fixed pulley and why is not power gained +by its employment? (fig. 1. plate 5.) + +33. (Pg. 62) Of what use is the fixed pulley? + +34. (Pg. 63) How is the power gained by a moveable pulley, explained by +means of fig. 2. plate 5? + +35. (Pg. 63) What proportion must the power bear to the weight in fig. +2, that their momentums may be equal? + +36. (Pg. 64) What is a fundamental law as respects power and time? + +37. (Pg. 64) If to gain power we must lose time, what advantage do we +derive from the mechanical powers? + +38. (Pg. 64) What name is given to two or more pulleys connected by one +string? + +39. (Pg. 64) How do we estimate the power gained by a system of pulleys? + +40. (Pg. 65) What is represented by fig. 5. plate 5? + +41. (Pg. 65) How does the wheel operate in increasing power? + +42. (Pg. 65) How is this compared with the lever? + +43. (Pg. 65) How does a handle fixed to an axle, represent a wheel, fig. +6? + +44. (Pg. 65) How could we increase the power in this instrument? + +45. (Pg. 66) What other forces besides the power of men, do we employ to +move machines? + +46. (Pg. 66) What will serve as an example of an inclined plane? + +47. (Pg. 66) In what proportion does it gain power? (fig. 7.) + +48. (Pg. 66) To what is the wedge compared? (fig. 8.) + +49. (Pg. 66) How does its power increase? + +50. (Pg. 67) Why is it rather a compound than a simple power? + +51. (Pg. 67) What common instruments act upon the principle of the +inclined plane, or the wedge? + +52. (Pg. 67) Why does a knife cut best when drawn across? + +53. (Pg. 67) The screw has two essential parts; what are they? + +54. (Pg. 67) What other instrument is used to turn the screw? + +55. (Pg. 67) How can you compare the screw with an inclined plane? Fig. +10. + +56. (Pg. 68) By what two means may the power of the screw be increased? + +57. (Pg. 68) How do we estimate the power gained by the screw? + +58. (Pg. 68) Is the lever always attached to the nut, as in the figure? + +59. (Pg. 68) What is said respecting the composition of all machines, +and for what must allowance always be made in estimating their power? + +60. (Pg. 69) What is meant by friction, and what causes it? + +61. (Pg. 69) How may friction be diminished? + +62. (Pg. 69) Friction is of two kinds, what are they? + +63. (Pg. 69) For what purpose are wheels often used? + +64. (Pg. 69) When is the friction of a carriage wheel changed from the +rolling to the rubbing friction? + +65. (Pg. 70) What is a medium, and in what proportion does it diminish +motion? + +66. (Pg. 70) Under what circumstances must a body be placed, in order to +move without impediment? + + + +CONVERSATION VI. + +CAUSES OF THE MOTION OF THE HEAVENLY BODIES. + +OF THE EARTH'S ANNUAL MOTION. OF THE PLANETS AND THEIR MOTION. OF THE +DIURNAL MOTION OF THE EARTH AND PLANETS. + + +CAROLINE. + +I am come to you to-day quite elated with the spirit of opposition, Mrs. +B.; for I have discovered such a powerful objection to your theory of +attraction, that I doubt whether even your conjuror Newton, with his +magic wand of gravitation, will be able to dispel it. + +_Mrs. B._ Well, my dear, pray what is this weighty objection? + +[Illustration: PLATE VI.] + +_Caroline._ You say that the earth revolves in its orbit round the sun +once in a year, and that bodies attract in proportion to the quantity of +matter they contain; now we all know the sun to be much larger than the +earth: why, therefore does it not draw the earth into itself; you will +not, I suppose, pretend to say that we are falling towards the sun? + +_Emily._ However plausible your objection appears, Caroline, I think you +place too much reliance upon it: when any one has given such convincing +proofs of sagacity and wisdom as Sir Isaac Newton, when we find that his +opinions are universally received and adopted, is it to be expected that +any objection we can advance should overturn them? + +_Caroline._ Yet I confess that I am not inclined to yield implicit faith +even to opinions of the great Newton: for what purpose are we endowed +with reason, if we are denied the privilege of making use of it, by +judging for ourselves. + +_Mrs. B._ It is reason itself which teaches us, that when we, novices in +science, start objections to theories established by men of knowledge +and wisdom, we should be diffident rather of our own than of their +opinion. I am far from wishing to lay the least restraint on your +questions; you cannot be better convinced of the truth of a system, than +by finding that it resists all your attacks, but I would advise you not +to advance your objections with so much confidence, in order that the +discovery of their fallacy may be attended with less mortification. In +answer to that you have just proposed, I can only say, that the earth +really is attracted by the sun. + +_Caroline._ Take care, at least, that we are not consumed by him, Mrs. +B. + +_Mrs. B._ We are in no danger; but Newton, our magician, as you are +pleased to call him, cannot extricate himself from this difficulty +without the aid of some cabalistical figures, which I must draw for him. + +Let us suppose the earth, at its creation, to have been projected +forwards into universal space: we know that if no obstacle impeded its +course it would proceed in the same direction, and with a uniform +velocity for ever. In fig. 1. plate 6, A represents the earth, and S the +sun. We shall suppose the earth to be arrived at the point in which it +is represented in the figure, having a velocity which would carry it on +to B in the space of one month; whilst the sun's attraction would bring +it to C in the same space of time. Observe that the two forces of +projection and attraction do not act in opposition, but perpendicularly, +or at a right angle to each other. Can you tell me now, how the earth +will move? + +_Emily._ I recollect your teaching us that a body acted upon by two +forces perpendicular to each other, would move in the diagonal of a +parallelogram; if, therefore, I complete the parallelogram, by drawing +the lines C D, B D, the earth will move in the diagonal A D. + +_Mrs. B._ A ball struck by two forces acting perpendicularly to each +other, it is true, moves in the diagonal of a parallelogram; but you +must observe that the force of attraction is continually acting upon our +terrestrial ball, and producing an incessant deviation from its course +in a right line, which converts it into that of a curve-line; every +point of which may be considered as constituting the diagonal of an +infinitely small parallelogram. + +Let us retain the earth a moment at the point D, and consider how it +will be affected by the combined action of the two forces in its new +situation. It still retains its tendency to fly off in a straight line; +but a straight line would now carry it away to F, whilst the sun would +attract it in the direction D S; how then will it proceed? + +_Emily._ It will go on in a curve-line, in a direction between that of +the two forces. + +_Mrs. B._ In order to know exactly what course the earth will follow, +draw another parallelogram similar to the first, in which the line D F +describes the force of projection, and the line D S that of attraction; +and you will find that the earth will proceed in the curve-line D G. + +_Caroline._ You must now allow me to draw a parallelogram, Mrs. B. Let +me consider in what direction will the force of projection now impel the +earth. + +_Mrs. B._ First draw a line from the earth to the sun representing the +force of attraction; then describe the force of projection at a right +angle to it. + +_Caroline._ The earth will then move in the curve G I, of the +parallelogram G H I K. + +_Mrs. B._ You recollect that a body acted upon by two forces, moves +through a diagonal, in the same time that it would have moved through +one of the sides of the parallelogram, were it acted upon by one force +only. The earth has passed through the diagonals of these three +parallelograms, in the space of three months, and has performed one +quarter of a circle; and on the same principle it will go on till it has +completed the whole of the circle. It will then recommence a course, +which it has pursued ever since it first issued from the hand of its +Creator, and which there is every reason to suppose it will continue to +follow, as long as it remains in existence. + +_Emily._ What a grand and beautiful effect resulting from so simple a +cause! + +_Caroline._ It affords an example, on a magnificent scale, of the +curvilinear motion, which you taught us in mechanics. The attraction of +the sun is the centripetal force, which confines the earth to a centre; +and the impulse of projection, the centrifugal force, which impels the +earth to quit the sun, and fly off in a tangent. + +_Mrs. B._ Exactly so. A simple mode of illustrating the effect of these +combined forces on the earth, is to cut a slip of card in the form of a +carpenter's square, as A, B, C; (fig. 2. plate 6.) the point B will be a +right angle, the sides of the square being perpendicular to each other; +after having done this you are to describe a small circle at the angular +point B, representing the earth, and to fasten the extremity of one of +the legs of the square to a fixed point A, which we shall consider as +the sun. Thus situated, the two sides of the square will represent both +the centrifugal and centripetal forces; A B, representing the +centripetal, and B C, the centrifugal force; if you now draw it round +the fixed point, you will see how the direction of the centrifugal force +varies, constantly forming a tangent to the circle in which the earth +moves, as it is constantly at a right angle with the centripetal force. + +_Emily._ The earth then, gravitates towards the sun, without the +slightest danger either of approaching nearer, or receding further from +it. How admirably this is contrived! If the two forces which produce +this curved motion, had not been so accurately adjusted, one would +ultimately have prevailed over the other, and we should either have +approached so near the sun as to have been burnt, or have receded so far +from it as to have been frozen. + +_Mrs. B._ What will you say, my dear, when I tell you, that these two +forces are not, in fact, so proportioned as to produce circular motion +in the earth? We actually revolve round the sun in an elliptical or oval +orbit, the sun being situated in one of the foci or centres of the oval, +so that the sun is at some periods much nearer to the earth, than at +others. + +_Caroline._ You must explain to us, at least, in what manner we avoid +the threatened destruction. + +_Mrs. B._ Let us suppose that when the earth is at A, (fig. 3.) its +projectile force should not have given it a velocity sufficient to +counterbalance that of gravity, so as to enable these powers conjointly +to carry it round the sun in a circle; the earth, instead of describing +the line A C, as in the former figure, will approach nearer the sun in +the line A B. + +_Caroline._ Under these circumstances, I see not what is to prevent our +approaching nearer and nearer the sun, till we fall into it: for its +attraction increases as we advance towards it, and produces an +accelerated velocity in the earth, which increases the danger. + +_Mrs. B._ There is another seeming danger, of which you are not aware. +Observe, that as the earth approaches the sun, the direction of its +projectile force is no longer perpendicular to that of its attraction, +but inclines more nearly to it. When the earth reaches that part of its +orbit at B, the force of projection would carry it to D, which brings it +nearer the sun instead of bearing it away from it. + +_Emily._ If, then, we are driven by one power, and drawn by the other to +this centre of destruction, how is it possible for us to escape? + +_Mrs. B._ A little patience, and you will find that we are not without +resource. The earth continues approaching the sun with a uniformly +increasing accelerated motion, till it reaches the point E; in what +direction will the projectile force now impel it? + +_Emily._ In the direction E F. Here then the two forces act +perpendicularly to each other, the lines representing them forming a +right angle, and the earth is situated just as it was in the preceding +figure; therefore, from this point, it should revolve round the sun in a +circle. + +_Mrs. B._ No, all the circumstances do not agree. In motion round a +centre, you recollect that the centrifugal force increases with the +velocity of the body, or in other words, the quicker it moves the +stronger is its tendency to fly off in a right line. When the earth, +therefore, arrives at E, its accelerated motion will have so far +increased its velocity, and consequently its centrifugal force, that the +latter will prevail over the force of attraction, and force the earth +away from the sun till it reaches G. + +_Caroline._ It is thus then that we escape from the dangerous vicinity +of the sun; and in proportion as we recede from it, the force of its +attraction, and, consequently, the velocity of the earth's motion, are +diminished. + +_Mrs. B._ Yes. From G the direction of projection is towards H, that of +attraction towards S, and the earth proceeds between them with a +uniformly retarded motion, till it has completed its revolution. Thus +you see that the earth travels round the sun, not in a circle, but an +ellipsis, of which the sun occupies one of the _foci_; and that in its +course, the earth alternately approaches and recedes from it, without +any danger of being either swallowed up, or being entirely carried away +from it. + +_Caroline._ And I observe, that what I apprehended to be a dangerous +irregularity, is the means by which the most perfect order and harmony +are produced. + +_Emily._ The earth travels then at a very unequal rate, its velocity +being accelerated as it approaches the sun, and retarded as it recedes +from it. + +_Mrs. B._ It is mathematically demonstrable, that, in moving round a +point towards which it is attracted, a body passes over equal areas, in +equal times. The whole of the space contained within the earth's orbit, +is in fig. 4, divided into a number of areas or surfaces; 1, 2, 3, 4, +&c. all of which are of equal dimensions, though of very different +forms; some of them, you see, are long and narrow, others broad and +short: but they each of them contain an equal quantity of space. An +imaginary line drawn from the centre of the earth to that of the sun, +and keeping pace with the earth in its revolution, passes over equal +areas in equal times; that is to say, if it is a month going from A to +B, it will be a month going from B to C, and another from C to E, and so +on; and the areas A B S, B C S, C E S, will be equal to each other, +although the lines A B, B C, C E, are unequal. + +_Caroline._ What long journeys the earth has to perform in the course of +a month, in one part of her orbit, and how short they are in the other +part! + +_Mrs. B._ The inequality is not so considerable as appears in this +figure; for the earth's orbit is not so eccentric as it is there +described; and in reality, differs but little from a circle: that part +of the earth's orbit nearest the sun is called its _perihelion_, that +part most distant from the sun, its _aphelion_; and the earth is above +three millions of miles nearer the sun at its perihelion than at its +aphelion. + +_Emily._ I think I can trace a consequence from these different +situations of the earth; are not they the cause of summer and winter? + +_Mrs. B._ On the contrary, during the height of summer, the earth is in +that part of its orbit which is most distant from the sun, and it is +during the severity of winter, that it approaches nearest to it. + +_Emily._ That is very extraordinary; and how then do you account for the +heat being greatest, when we are most distant from the sun? + +_Mrs. B._ The difference of the earth's distance from the sun in summer +and winter, when compared with its total distance from the sun, is but +inconsiderable. The earth, it is true, is above three millions of miles +nearer the sun in winter than in summer; but that distance, however +great it at first appears, sinks into insignificance in comparison with +95 millions of miles, which is our mean distance from the sun. The +change of temperature, arising from this difference, would scarcely be +sensible, even were it not completely overpowered by other causes which +produce the variations of the seasons; but these I shall defer +explaining, till we have made some further observations on the heavenly +bodies. + +_Caroline._ And should not the sun appear smaller in summer, when it is +so much further from us? + +_Mrs. B._ It actually does, when accurately measured; but the apparent +difference in size, is, I believe, not perceptible to the naked eye. + +_Emily._ Then, since the earth moves with the greatest velocity in that +part of its orbit in which it is nearest the sun, it must have completed +its journey through that half of its orbit, in a shorter time than +through the other? + +_Mrs. B._ Yes, it is about seven days longer performing the summer-half +of its orbit, than the winter-half; and the summers are consequently +seven days longer in the northern, than they are in the southern +hemisphere. + +The revolution of all the planets round the sun, is the result of the +same causes, and is performed in the same manner, as that of the earth. + +_Caroline._ Pray what are the planets? + +_Mrs. B._ They are those celestial bodies, which revolve like our earth, +about the sun; they are supposed to resemble the earth also in many +other respects; and we are led by analogy, to suppose them to be +inhabited worlds. + +_Caroline._ I have heard so, but do you not think such an opinion too +great a stretch of the imagination? + +_Mrs. B._ Some of the planets are proved to be larger than the earth; it +is only their immense distance from us, which renders their apparent +dimensions so small. Now, if we consider them as enormous globes, +instead of small twinkling spots, we shall be led to suppose that the +Almighty would not have created them merely for the purpose of giving us +a little light in the night, as it was formerly imagined; and we should +find it more consistent with our ideas of the Divine wisdom and +beneficence, to suppose that these celestial bodies should be created +for the habitation of beings, who are, like us, blessed by his +providence. Both in a moral, as well as a physical point of view, it +appears to me more rational to consider the planets as worlds revolving +round the sun; and the fixed stars as other suns, each of them attended +by their respective system of planets, to which they impart their +influence. We have brought our telescopes to such a degree of +perfection, that from the appearances which the moon exhibits when seen +through them, we have very good reason to conclude that it is a +habitable globe: for though it is true that we cannot discern its towns +and people, we can plainly perceive its mountains and valleys: and some +astronomers have gone so far as to imagine that they discovered +volcanos. + +_Emily._ If the fixed stars are suns, with planets revolving round them, +why should we not see those planets as well as their suns? + +_Mrs. B._ In the first place, we conclude that the planets of other +systems (like those of our own) are much smaller than the suns which +give them light; therefore at a distance so great as to make the suns +appear like fixed stars, the planets would be quite invisible. Secondly, +the light of the planets being only reflected light, is much more feeble +than that of the fixed stars. There is exactly the same difference as +between the light of the sun and that of the moon; the first being a +fixed star, the second a planet. + +_Emily._ But the planets appear to us as bright as the fixed stars, and +these you tell us are suns like our own; why then do we not see them by +daylight, when they must be just as luminous as they are in the night? + +_Mrs. B._ Both are invisible from the same cause: their light is so +faint, compared to that of the sun, that it is entirely effaced by it: +the light emitted by the fixed stars may probably be as great as that of +our sun, at an equal distance; but they being so much more remote, it +is diffused over a greater space, and is in consequence proportionally +lessened. + +_Caroline._ True; I can see much better by the light of a candle that is +near me, than by that of one at a great distance. But I do not +understand what makes the planets shine? + +_Mrs. B._ What is that which makes the gilt buttons on your brothers +coat shine? + +_Caroline._ The sun. But if it was the sun which made the planets shine, +we should see them in the day-time, when the sun shone upon them; or if +the faintness of their light prevented our seeing them in the day, we +should not see them at all, for the sun cannot shine upon them in the +night. + +_Mrs. B._ There you are in error. But in order to explain this to you, I +must first make you acquainted with the various motions of the planets. + +You know, that according to the laws of attraction, the planets +belonging to our system all gravitate towards the sun; and that this +force, combined with that of projection, will occasion their revolution +round the sun, in orbits more or less elliptical, according to the +proportion which these two forces bear to each other. + +But the planets have also another motion: they revolve upon their axis. +The axis of a planet is an imaginary line which passes through its +centre, and on which it turns; and it is this motion which produces day +and night. It is day on that side of the planet which faces the sun; and +on the opposite side, which remains in darkness, it is night. Our earth, +which we consider as a planet, is 24 hours in performing one revolution +on its axis; in that period of time, therefore, we have a day and a +night; hence this revolution is called the earth's diurnal or daily +motion; and it is this revolution of the earth from west to east which +produces an apparent motion of the sun, moon and stars, in a contrary +direction. + +Let us now suppose ourselves to be beings independent of any planet, +travelling in the skies, and looking upon the earth from a point as +distant from it as from other planets. + +_Caroline._ It would not be flattering to us, its inhabitants, to see it +make so insignificant an appearance. + +_Mrs. B._ To those accustomed to contemplate it in this light, it could +never appear more glorious. We are taught by science to distrust +appearances; and instead of considering the fixed stars and planets as +little points, we look upon them either as brilliant suns, or habitable +worlds; and we consider the whole together as forming one vast and +magnificent system, worthy of the Divine hand by which it was created. + +_Emily._ I can scarcely conceive the idea of this immensity of creation; +it seems too sublime for our imagination;--and to think that the +goodness of Providence extends over millions of worlds throughout a +boundless universe--Ah! Mrs. B., it is we only who become trifling and +insignificant beings in so magnificent a creation! + +_Mrs. B._ This idea should teach us humility, but without producing +despondency. The same Almighty hand which guides these countless worlds +in their undeviating course, conducts with equal perfection, the blood +as it circulates through the veins of a fly, and opens the eye of the +insect to behold His wonders. Notwithstanding this immense scale of +creation, therefore, we need not fear that we shall be disregarded or +forgotten. + +But to return to our station in the skies. We were, if you recollect, +viewing the earth at a great distance, in appearance a little star, one +side illumined by the sun, the other in obscurity. But would you believe +it, Caroline, many of the inhabitants of this little star imagine that +when that part which they inhabit is turned from the sun, darkness +prevails throughout the universe, merely because it is night with them; +whilst, in reality, the sun never ceases to shine upon every planet. +When, therefore, these little ignorant beings look around them during +their night, and behold all the stars shining, they cannot imagine why +the planets, which are dark bodies, should shine; concluding, that since +the sun does not illumine themselves, the whole universe must be in +darkness. + +_Caroline._ I confess that I was one of these ignorant people; but I am +now very sensible of the absurdity of such an idea. To the inhabitants +of the other planets, then, we must appear as a little star? + +_Mrs. B._ Yes, to those which revolve round our sun; for since those +which may belong to other systems, (and whose existence is only +hypothetical) are invisible to us, it is probable that we also are +invisible to them. + +_Emily._ But they may see our sun as we do theirs, in appearance a fixed +star? + +_Mrs. B._ No doubt; if the beings who inhabit those planets are endowed +with senses similar to ours. By the same rule we must appear as a moon +to the inhabitants of our moon; but on a larger scale, as the surface of +the earth is about thirteen times as large as that of the moon. + +_Emily._ The moon, Mrs. B., appears to move in a different direction, +and in a different manner from the stars? + +_Mrs. B._ I shall defer the explanation of the motion of the moon till +our next interview, as it would prolong our present lesson too much. + + +Questions + +1. (Pg. 71) What revolution does the earth perform in a year? + +2. (Pg. 71) Had the earth received a projectile force only, at the time +of its creation, how would it have moved? + +3. (Pg. 72) What do the lines A B, and A C, represent in fig. 1. plate +6? + +4. (Pg. 72) What have you been taught respecting a body acted upon by +two forces at right angles with each other? + +5. (Pg. 72) How does the force of gravity change the diagonal into a +curved line? + +6. (Pg. 72) Describe the operation of the forces of projection and of +gravity as illustrated by the parallelograms in the figure? + +7. (Pg. 72) What is the law respecting the time required for motion in +the diagonal? + +8. (Pg. 73) What portion of a year is represented by the three diagonals +in the figure? + +9. (Pg. 73) How will what you have learned respecting motion in a curve, +apply to the earth's motion? + +10. (Pg. 73) In what form are you directed to cut a piece of card to aid +in illustrating the two forces acting upon the earth? + +11. (Pg. 73) How must you apply it to this purpose? (fig. 2. plate 6.) + +12. (Pg. 73) If these two forces did not exactly balance each other, +what would result? + +13. (Pg. 73) Does the earth revolve in a circular orbit? + +14. (Pg. 73) What results from its motion in an ellipsis? + +15. (Pg. 74) What is represented by the lines A C, A B, in fig. 3. plate +6? + +16. (Pg. 74) Were the projectile force to carry the earth from B to D, +(fig. 3.) what would result? + +17. (Pg. 74) When it has arrived at E, what angle will be formed by the +lines representing the two forces? + +18. (Pg. 74) What effect will the accelerated motion then produce? + +19. (Pg. 75) What is the form of the earth's orbit, and what +circumstances produce this form? + +20. (Pg. 75) What is the consequence as regards the regularity of the +earth's motion? + +21. (Pg. 75) What law governs as regards the spaces passed over, and how +is this explained by fig. 4. plate 6? + +22. (Pg. 75) What is meant by _perihelion_, and by _aphelion_? + +23. (Pg. 75) What is the difference of the distance of the earth from +the sun, in these two points? + +24. (Pg. 76) At what season of the year is it nearest to, and at what +furthest from the sun? + +25. (Pg. 76) What is the mean distance of the earth from the sun? + +26. (Pg. 76) Why is but little effect produced, as regards temperature, +by the change of distance? + +27. (Pg. 76) Has it any influence on the sun's apparent size? + +28. (Pg. 76) Are the summer and winter, half years, of the same length; +what is their difference, and what is the cause? + +29. (Pg. 76) What are the planets? + +30. (Pg. 77) What circumstances render it probable that they are +habitable globes? + +31. (Pg. 77) What is believed respecting the fixed stars? + +32. (Pg. 77) What discoveries have been made in the moon? + +33. (Pg. 77) What prevents our seeing the planets, if there are any, +which revolve round the fixed stars? + +34. (Pg. 77) What prevents our seeing the stars and planets in the +day-time? + +35. (Pg. 78) What other motions have the earth and planets, besides that +in their orbits? + +36. (Pg. 78) What is the imaginary line called, round which they +revolve? + +37. (Pg. 78) How does this occasion night and day? + +38. (Pg. 78) In what direction does the earth turn upon its axis, and +what apparent motion of the sun, moon, and stars is thereby produced? + +39. (Pg. 79) What must be the appearance of the earth to an inhabitant +of one of the planets? + +40. (Pg. 79) What the appearance of the sun to the inhabitants of +planets in other systems? + +41. (Pg. 79) What the appearance of the earth to an inhabitant of the +moon? + + + + +CONVERSATION VII. + +OF THE PLANETS. + +OF THE SATELLITES OR MOONS. GRAVITY DIMINISHES AS THE SQUARE OF THE +DISTANCE. OF THE SOLAR SYSTEM. OF COMETS. CONSTELLATIONS, SIGNS OF THE +ZODIAC. OF COPERNICUS, NEWTON, &c. + + +MRS. B. + +The planets are distinguished into primary and secondary. Those which +revolve immediately about the sun are called primary. Many of these are +attended in their course by smaller planets, which, revolve round them: +these are called secondary planets, satellites, or moons. Such is our +moon which accompanies the earth, and is carried with it round the sun. + +_Emily._ How then can you reconcile the motion of the secondary planets +to the laws of gravitation; for the sun is much larger than any of the +primary planets; and is not the power of gravity proportional to the +quantity of matter? + +_Caroline._ Perhaps the sun, though much larger, may be less dense than +the planets. Fire you know, is very light, and it may contain but little +matter, though of great magnitude. + +_Mrs. B._ We do not know of what kind of matter the sun is made; but we +may be certain, that since it is the general centre of attraction of our +system of planets, it must be the body which contains the greatest +quantity of matter in that system. + +You must recollect, that the force of attraction is not only +proportional to the quantity of matter, but to the degree of proximity +of the attractive body: this power is weakened by being diffused, and +diminishes as the distance increases. + +_Emily._ Then if a planet was to lose one-half of its quantity of +matter, it would lose one half of its attractive power; and the same +effect would be produced by removing it to twice its former distance +from the sun; that I understand. + +_Mrs. B._ Not so perfectly as you imagine. You are correct as respects +the diminution in size, because the attractive force is in the same +proportion as the quantity of matter; but were you to remove a planet to +double its former distance, it would retain but one-fourth part of its +gravitating force; for attraction decreases not in proportion to the +simple increase of the distance, but as the squares of the distances +increase. + +_Caroline._ I do not exactly comprehend what is meant by the squares, in +this case, although I know very well what is in general intended by a +square. + +_Mrs. B._ By the square of a number we mean the product of a number, +multiplied by itself; thus two, multiplied by two, is four, which is +therefore the square of two; in like manner the square of three, is +nine, because three multiplied by three, gives that product. + +_Emily._ Then if one planet is three times more distant from the sun +than another, it will be attracted with but one-ninth part of the force; +and if at four times the distance, with but one-sixteenth, sixteen being +the square of four? + +_Mrs. B._ You are correct; the rule is, that _the attractive force is in +the inverse proportion of the square of the distance_. And it is easily +demonstrated by the mathematics, that the same is the case with every +power that emanates from a centre; as for example, the light from the +sun, or from any other luminous body, decreases in its intensity at the +same rate. + +_Caroline._ Then the more distant planets, move much slower in their +orbits; for their projectile force must be proportioned to that of +attraction? But I do not see how this accounts for the motion of the +secondary, round the primary planets, in preference to moving round the +sun? + +_Emily._ Is it not because the vicinity of the primary planets, renders +their attraction stronger than that of the sun? + +_Mrs. B._ Exactly so. But since the attraction between bodies is +mutual, the primary planets are also attracted by the satellites which +revolve round them. The moon attracts the earth, as well as the earth +the moon; but as the latter is the smaller body, her attraction is +proportionally less; therefore, neither the earth revolves round the +moon, nor the moon round the earth; but they both revolve round a point, +which is their common centre of gravity, and which is as much nearer to +the earth than to the moon, as the gravity of the former exceeds that of +the latter. + +_Emily._ Yes, I recollect your saying, that if two bodies were fastened +together by a wire or bar, their common centre of gravity would be in +the middle of the bar, provided the bodies were of equal weight; and if +they differed in weight, it would be nearer the larger body. If then, +the earth and moon had no projectile force which prevented their mutual +attraction from bringing them together, they would meet at their common +centre of gravity. + +_Caroline._ The earth then has a great variety of motion, it revolves +round the sun, round its own axis, and round the point towards which the +moon attracts it. + +_Mrs. B._ Just so; and this is the case with every planet which is +attended by satellites. The complicated effect of this variety of +motions, produces certain irregularities, which, however, it is not +necessary to notice at present, excepting to observe that they +eventually correct each other, so that no permanent derangement exists. + +The planets act on the sun, in the same manner as they are themselves +acted on by their satellites; for attraction, you must remember, is +always mutual; but the gravity of the planets (even when taken +collectively) is so trifling compared with that of the sun, that were +they all placed on the same side of that luminary, they would not cause +him to move so much as one-half of his diameter towards them, and the +common centre of gravity, would still remain within the body of the sun. +The planets do not, therefore, revolve round the centre of the sun, but +round a point at a small distance from its centre, about which the sun +also revolves. + +_Emily._ I thought the sun had no motion? + +_Mrs. B._ You were mistaken; for besides that round the common centre of +gravity, which I have just mentioned, which is indeed very +inconsiderable, he revolves on his axis in about 25 days; this motion is +ascertained by observing certain spots which disappear, and reappear +regularly at stated times. + +[Illustration: PLATE VII.] + +_Caroline._ A planet has frequently been pointed out to me in the +heavens; but I could not perceive that its motion differed from that of +the fixed stars, which only appear to move. + +_Mrs. B._ The great distance of the planets, renders their apparent +motion so slow, that the eye is not sensible of their progress in their +orbits, unless we watch them for some considerable length of time: but +if you notice the nearness of a planet to any particular fixed star, you +may in a few nights perceive that it has changed its distance from it, +whilst the stars themselves always retain their relative situations. The +most accurate idea I can give you of the situation and motion of the +planets in their orbits, will be by the examination of this diagram, +(plate 7. fig. 1.) representing the solar system, in which you will find +every planet, with its orbit delineated. + +_Emily._ But the orbits here are all circular, and you said that they +were elliptical. The planets appear too, to be moving round the centre +of the sun; whilst you told us that they moved round a point at a little +distance from thence. + +_Mrs. B._ The orbits of the planets are so nearly circular, and the +common centre of gravity of the solar system, so near the centre of the +sun, that these deviations are too small to be represented. The +dimensions of the planets, in their proportion to each other, you will +find delineated in fig. 2. + +Mercury is the planet nearest the sun; his orbit is consequently +contained within ours; his vicinity to the sun, prevents our frequently +seeing him, so that very accurate observations cannot be made upon +Mercury. He performs his revolution round the sun in about 87 days, +which is consequently the length of his year. The time of his rotation +on his axis is not known; his distance from the sun is computed to be 37 +millions of miles, and his diameter 3180 miles. The heat of this planet +is supposed to be so great, that water cannot exist there but in a state +of vapour, and that even quicksilver would be made to boil. + +_Caroline._ Oh, what a dreadful climate! + +_Mrs. B._ Though we could not live there, it may be perfectly adapted to +other beings, destined to inhabit it; or he who created it may have so +modified the heat, by provisions of which we are ignorant, as to make it +habitable even by ourselves. + +Venus, the next in the order of planets, is 68 millions of miles from +the sun: she revolves about her axis in 23 hours and 21 minutes, and +goes round the sun in 244 days, 17 hours. The orbit of Venus is also +within ours; during nearly one-half of her course in it, we see her +before sun-rise, and she is then called the morning star; in the other +part of her orbit she rises later than the sun. + +_Caroline._ In that case we cannot see her, for she must rise in the day +time? + +_Mrs. B._ True; but when she rises later than the sun, she also sets +later; so that we perceive her approaching the horizon after sun-set: +she is then called Hesperus, or the evening star. Do you recollect those +beautiful lines of Milton? + + Now came still evening on, and twilight gray + Had in her sober livery all things clad; + Silence accompanied; for beast and bird, + They to their grassy couch, these to their nests + Were slunk, all but the wakeful nightingale; + She all night long her amorous descant sung; + Silence was pleas'd; now glowed the firmament + With living sapphires. Hesperus that led + The starry host, rode brightest, till the moon + Rising in clouded majesty, at length + Apparent queen unveil'd her peerless light, + And o'er the dark her silver mantle threw. + +The planet next to Venus is the Earth, of which we shall soon speak at +full length. At present I shall only observe that we are 95 millions of +miles distant from the sun, that we perform our annual revolution in 365 +days 5 hours and 49 minutes; and are attended in our course by a single +moon. + +Next follows Mars. He can never come between us and the sun, like +Mercury and Venus; his motion is, however, very perceptible, as he may +be traced to different situations in the heavens; his distance from the +sun is 144 millions of miles; he turns round his axis in 24 hours and 39 +minutes; and he performs his annual revolution, in about 687 of our +days: his diameter is 4120 miles. Then follow four very small planets, +Juno, Ceres, Pallas and Vesta, which have been recently discovered, but +whose dimensions, and distances from the sun, have not been very +accurately ascertained. They are generally called asteroids. + +Jupiter is next in order: this is the largest of all the planets. He is +about 490 millions of miles from the sun, and completes his annual +period in nearly 12 of our years. He turns round his axis in about ten +hours. He is above 1200 times as big as our earth; his diameter is +86,000 miles. The respective proportions of the planets cannot, +therefore, you see, be conveniently delineated in a diagram. He is +attended by four moons. + +The next planet is Saturn, whose distance from the sun, is about 900 +millions of miles; his diurnal rotation is performed in 10 hours and a +quarter: his annual revolution is nearly 30 of our years. His diameter +is 79,000 miles. This planet is surrounded by a luminous ring, the +nature of which, astronomers are much at a loss to conjecture: he has +seven moons. Lastly, we observe the planet Herschel, discovered by Dr. +Herschel, by whom it was named the Georgium Sidus, and which is attended +by six moons. + +_Caroline._ How charming it must be in the distant planets, to see +several moons shining at the same time; I think I should like to be an +inhabitant of Jupiter or Saturn. + +_Mrs. B._ Not long I believe. Consider what extreme cold must prevail in +a planet, situated as Saturn is, at nearly ten times the distance at +which we are from the sun. Then his numerous moons are far from making +so splendid an appearance as ours; for they can reflect only the light +which they receive from the sun; and both light, and heat, decrease in +the same ratio or proportion to the distances, as gravity. Can you tell +me now how much more light we enjoy than Saturn? + +_Caroline._ The square of ten is a hundred; therefore, Saturn has a +hundred times less--or to answer your question exactly, we have a +hundred times more light and heat, than Saturn--this certainly does not +increase my wish to become one of the poor wretches who inhabit that +planet. + +_Mrs. B._ May not the inhabitants of Mercury, with equal plausibility, +pity us for the insupportable coldness of our situation; and those of +Jupiter and Saturn for our intolerable heat? The Almighty power which +created these planets, and placed them in their several orbits, has no +doubt peopled them with beings, whose bodies are adapted to the various +temperatures and elements, in which they are situated. If we judge from +the analogy of our own earth, or from that of the great and universal +beneficence of Providence, we must conclude this to be the case. + +_Caroline._ Are not comets, in some respects similar to planets? + +_Mrs. B._ Yes, they are; for by the reappearance of some of them, at +stated times, they are known to revolve round the sun; but in orbits so +extremely eccentric, that they disappear for a great number of years. If +they are inhabited, it must be by a species of beings very different, +not only from the inhabitants of this, but from those of any of the +other planets, as they must experience the greatest vicissitudes of heat +and cold; one part of their orbit being so near the sun, that their +heat, when there, is computed to be greater than that of red-hot iron; +in this part of its orbit, the comet emits a luminous vapour, called the +tail, which it gradually loses as it recedes from the sun; and the comet +itself totally disappears from our sight, in the more distant parts of +its orbit, which extends considerably beyond that of the furthest +planet. + +The number of comets belonging to our system cannot be ascertained, as +some of them are several centuries before they make their reappearance. +The number that are known by their regular reappearance is, I believe, +only three, although their whole number is very considerable. + +_Emily._ Pray, Mrs. B., what are the constellations? + +_Mrs. B._ They are the fixed stars; which the ancients, in order to +recognise them, formed into groups, and gave the names of the figures, +which you find delineated on the celestial globe. In order to show their +proper situations in the heavens, they should be painted on the internal +surface of a hollow sphere, from the centre of which you should view +them; you would then behold them as they appear to be situated in the +heavens. The twelve constellations, called the signs of the zodiac, are +those which are so situated, that the earth, in its annual revolution, +passes directly between them, and the sun. Their names are Aries, +Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, +Capricornus, Aquarius, Pisces; the whole occupying a complete circle, or +broad belt, in the heavens, called the zodiac. (plate 8. fig. 1.) Hence, +a right line drawn from the earth, and passing through the sun, would +reach one of these constellations, and the sun is said to be in that +constellation at which the line terminates: thus, when the earth is at +A, the sun would appear to be in the constellation or sign Aries; when +the earth is at B, the sun would appear in Cancer; when the earth was at +C, the sun would be in Libra; and when the earth was at D, the sun would +be in Capricorn. You are aware that it is the real motion of the earth +in its orbit, which gives to the sun this apparent motion through the +signs. This circle, in which the sun thus appears to move, and which +passes through the middle of the zodiac, is called the ecliptic. + +_Caroline._ But many of the stars in these constellations appear beyond +the zodiac. + +[Illustration: PLATE VIII.] + +_Mrs. B._ We have no means of ascertaining the distance of the fixed +stars. When, therefore, they are said to be in the zodiac, it is merely +implied that they are situated in that direction, and that they shine +upon us through that portion of the heavens, which we call the zodiac. + +_Emily._ But are not those large bright stars, which are called stars of +the first magnitude, nearer to us, than those small ones which we can +scarcely discern? + +_Mrs. B._ It may be so; or the difference of size and brilliancy of the +stars may proceed from their difference of dimensions; this is a point +which astronomers are not enabled to determine. Considering them as +suns, I see no reason why different suns should not vary in dimensions, +as well as the planets belonging to them. + +_Emily._ What a wonderful and beautiful system this is, and how +astonishing to think that every fixed star may probably be attended by a +similar train of planets! + +_Caroline._ You will accuse me of being very incredulous, but I cannot +help still entertaining some doubts, and fearing that there is more +beauty than truth in this system. It certainly may be so; but there does +not appear to me to be sufficient evidence to prove it. It seems so +plain and obvious that the earth is motionless, and that the sun and +stars revolve round it;--your solar system, you must allow, is directly +in opposition to the evidence of our senses. + +_Mrs. B._ Our senses so often mislead us, that we should not place +implicit reliance upon them. + +_Caroline._ On what then can we rely, for do we not receive all our +ideas through the medium of our senses? + +_Mrs. B._ It is true that they are our primary source of knowledge; but +the mind has the power of reflecting, judging, and deciding upon the +ideas received by the organs of sense. This faculty, which we call +reason, has frequently proved to us, that our senses are liable to err. +If you have ever sailed on the water, with a very steady breeze, you +must have seen the houses, trees, and every object on the shore move, +while you were sailing. + +_Caroline._ I remember thinking so, when I was very young; but I now +know that their motion is only apparent. It is true that my reason, in +this case, corrects the error of my sight. + +_Mrs. B._ It teaches you, that the apparent motion of the objects on +shore, proceeds from your being yourself moving, and that you are not +sensible of your own motion, because you meet with no resistance. It is +only when some obstacle impedes our motion, that we are conscious of +moving; and if you were to close your eyes when you were sailing on +calm water, with a steady wind, you would not perceive that you moved, +for you could not feel it, and you could see it only by observing the +change of place of the objects on shore. So it is with the motion of the +earth: every thing on its surface, and the air that surrounds it, +accompanies it in its revolution; it meets with no resistance: +therefore, like the crew of a vessel sailing with a fair wind, in a calm +sea, we are insensible of our motion. + +_Caroline._ But the principal reason why the crew of a vessel in a calm +sea do not perceive their motion, is, because they move exceedingly +slow, while the earth, you say, revolves with great velocity. + +_Mrs. B._ It is not because they move slowly, but because they move +steadily, and meet with no irregular resistances, that the crew of a +vessel do not perceive their motion; for they would be equally +insensible to it, with the strongest wind, provided it were steady, that +they sailed with it, and that it did not agitate the water; but this +last condition, you know, is not possible, for the wind will always +produce waves which offer more or less resistance to the vessel, and +then the motion becomes sensible, because it is unequal. + +_Caroline._ But, granting this, the crew of a vessel have a proof of +their motion, which the inhabitants of the earth cannot have,--the +apparent motion of the objects on shore, or their having passed from one +place to another. + +_Mrs. B._ Have we not a similar proof of the earth's motion, in the +apparent motion of the sun and stars? Imagine the earth to be sailing +round its axis, and successively passing by every star, which, like the +objects on land, we suppose to be moving instead of ourselves. I have +heard it observed by an aerial traveller in a balloon, that the earth +appears to sink beneath the balloon, instead of the balloon rising above +the earth. + +It is a law which we discover throughout nature, and worthy of its great +Author, that all its purposes are accomplished by the most simple means; +and what reason have we to suppose this law infringed, in order that we +may remain at rest, while the sun and stars move round us; their regular +motions, which are explained by the laws of attraction, on the first +supposition, would be unintelligible on the last, and the order and +harmony of the universe be destroyed. Think what an immense circuit the +sun and stars would make daily, were their apparent motions, real. We +know many of them, to be bodies more considerable than our earth; for +our eyes vainly endeavour to persuade us, that they are little +brilliants sparkling in the heavens; while science teaches us that they +are immense spheres, whose apparent dimensions are diminished by +distance. Why then should these enormous globes daily traverse such a +prodigious space, merely to prevent the necessity of our earth's +revolving on its axis? + +_Caroline._ I think I must now be convinced. But you will, I hope, allow +me a little time to familiarise to myself, an idea so different from +that which I have been accustomed to entertain. And pray, at what rate +do we move? + +_Mrs. B._ The motion produced by the revolution of the earth on its +axis, is about seventeen miles a minute, to an inhabitant on the +equator. + +_Emily._ But does not every part of the earth move with the same +velocity? + +_Mrs. B._ A moment's reflection would convince you of the contrary: a +person at the equator must move quicker than one situated near the +poles, since they both perform a revolution in 24 hours. + +_Emily._ True, the equator is farthest from the axis of motion. But in +the earth's revolution round the sun, every part must move with equal +velocity? + +_Mrs. B._ Yes, about a thousand miles a minute. + +_Caroline._ How astonishing!--and that it should be possible for us to +be insensible of such a rapid motion. You would not tell me this sooner, +Mrs. B., for fear of increasing my incredulity. + +Before the time of Newton, was not the earth supposed to be in the +centre of the system, and the sun, moon, and stars to revolve round it? + +_Mrs. B._ This was the system of Ptolemy, in ancient times; but as long +ago as the beginning of the sixteenth century it was generally +discarded, and the solar system, such as I have shown you, was +established by the celebrated astronomer Copernicus, and is hence called +the Copernican system. But the theory of gravitation, the source from +which this beautiful and harmonious arrangement flows, we owe to the +powerful genius of Newton, who lived at a much later period, and who +demonstrated its truth. + +_Emily._ It appears, indeed, far less difficult to trace by observation +the motion of the planets, than to divine by what power they are +impelled and guided. I wonder how the idea of gravitation could first +have occurred to sir Isaac Newton? + +_Mrs. B._ It is said to have been occasioned by a circumstance from +which one should little have expected so grand a theory to have arisen. + +During the prevalence of the plague in the year 1665, Newton retired +into the country to avoid the contagion: when sitting one day in an +orchard, he observed an apple fall from a tree, and was led to consider +what could be the cause which brought it to the ground. + +_Caroline._ If I dared to confess it, Mrs. B., I should say that such an +inquiry indicated rather a deficiency than a superiority of intellect. I +do not understand how any one can wonder at what is so natural and so +common. + +_Mrs. B._ It is the mark of superior genius to find matter for wonder, +observation, and research, in circumstances which, to the ordinary mind, +appear trivial, because they are common; and with which they are +satisfied, because they are natural; without reflecting that nature is +our grand field of observation, that within it, is contained our whole +store of knowledge; in a word, that to study the works of nature, is to +learn to appreciate and admire the wisdom of God. Thus, it was the +simple circumstance of the fall of an apple, which led to the discovery +of the laws upon which the Copernican system is founded; and whatever +credit this system had obtained before, it now rests upon a basis from +which it cannot be shaken. + +_Emily._ This was a most fortunate apple, and more worthy to be +commemorated than all those that have been sung by the poets. The apple +of discord for which the goddesses contended; the golden apples by which +Atalanta won the race; nay, even the apple which William Tell shot from +the head of his son, cannot be compared to this! + + +Questions + +1. (Pg. 80) Into what two classes are the planets divided, and how are +they distinguished? + +2. (Pg. 80) By what reasoning do you prove that the sun contains a +greater quantity of matter than any other body in the system? + +3. (Pg. 81) What two circumstances govern the force with which bodies +attract each other? + +4. (Pg. 81) Were a planet removed to double its former distance from the +sun, what would be the effect upon its attractive force? + +5. (Pg. 81) Why would it be reduced to one-fourth? + +6. (Pg. 81) What is meant by the square of a number, and what examples +can you give? + +7. (Pg. 81) What then would be the effect of removing it to three, or +four times its former distance? + +8. (Pg. 81) How is the rule upon this subject expressed? + +9. (Pg. 81) Does this apply to any power excepting gravitation? + +10. (Pg. 81) How is it that a secondary planet revolves round its +primary, and is not drawn off by the sun? + +11. (Pg. 82) What is said respecting the revolution of the moon, and of +the earth, round a common centre of gravity? + +12. (Pg. 82) By what law in mechanics is this explained? + +13. (Pg. 82) What motions then has the earth, and are these remarks +confined to it alone? + +14. (Pg. 82) What effect have the planets upon the sun, and what is said +of the common centre of gravity of the system? + +15. (Pg. 83) What other motion has the sun, and how is it proved? + +16. (Pg. 83) How may you observe the motion of a planet, by means of a +fixed star? + +17. (Pg. 83) What is represented by fig. 1. plate 7? + +18. (Pg. 83) Why are the orbits represented as circular? + +19. (Pg. 83) In what order do the planets increase in size as +represented, fig. 2. plate 7? + +20. (Pg. 83) What are we told respecting Mercury? + +21. (Pg. 84) What respecting Venus? + +22. (Pg. 84) When does Venus become a morning, and when an evening star? + +23. (Pg. 84) What is said of the Earth? + +24. (Pg. 84) What of Mars? + +25. (Pg. 84) What four small planets follow next? + +26. (Pg. 85) What is said of Jupiter? + +27. (Pg. 85) What of Saturn? + +28. (Pg. 85) What of Herschel? + +29. (Pg. 85) Why do we conclude that the moons of Saturn afford less +light than ours? + +30. (Pg. 85) In what proportion will the light and heat at Saturn be +diminished, and why? + +31. (Pg. 86) What do the comets resemble, and what is remarkable in +their orbits? + +32. (Pg. 86) What is said of the number of comets? + +33. (Pg. 86) What is a constellation? + +34. (Pg. 86) How are the twelve constellations, or signs, called the +zodiac, situated? + +35. (Pg. 86) Name them. + +36. (Pg. 86) What is meant by the sun being in a sign? + +37. (Pg. 86) What causes the apparent change of the sun's place? + +38. (Pg. 87) The stars appear of different magnitudes, by what may this +be caused? + +39. (Pg. 87) We are not sensible of the motion of the earth; what fact +is mentioned to illustrate this point? + +40. (Pg. 87) What does this teach us? + +41. (Pg. 88) Would the slowness, or the rapidity of the motion, if +steady, produce any sensible difference? + +42. (Pg. 88) If we do not feel the motion of the earth, how may we be +convinced of its reality? + +43. (Pg. 89) Were we to deny the motion of the earth upon its axis, what +must we admit respecting the heavenly bodies? + +44. (Pg. 89) What distance is an inhabitant on the equator carried in a +minute by the diurnal motion of the earth? + +45. (Pg. 89) Why is not the velocity every where equally great? + +46. (Pg. 89) What distance does the earth travel in a minute, in its +revolution round the sun? + +47. (Pg. 89) What was formerly supposed respecting the motion of all the +heavenly bodies? + +48. (Pg. 89) What do we mean by the Copernican system, and what is said +respecting Copernicus and Newton? + +49. (Pg. 90) What circumstance is said to have given rise to the +speculations of Newton, on the subject of gravitation? + + + + +CONVERSATION VIII. + +ON THE EARTH. + +OF THE TERRESTRIAL GLOBE. OF THE FIGURE OF THE EARTH. OF THE PENDULUM. +OF THE VARIATION OF THE SEASONS, AND OF THE LENGTH OF DAYS AND NIGHTS. +OF THE CAUSES OF THE HEAT OF SUMMER. OF SOLAR, SIDERIAL, AND EQUAL OR +MEAN TIME. + + +MRS. B. + +As the earth is the planet in which we are the most particularly +interested, it is my intention this morning, to explain to you the +effects resulting from its annual, and diurnal motions; but for this +purpose, it will be necessary to make you acquainted with the +terrestrial globe: you have not either of you, I conclude, learnt the +use of the globes? + +_Caroline._ No; I once indeed, learnt by heart, the names of the lines +marked on the globe, but as I was informed they were only imaginary +divisions, they did not appear to me worthy of much attention, and were +soon forgotten. + +_Mrs. B._ You supposed, then, that astronomers had been at the trouble +of inventing a number of lines, to little purpose. It will be impossible +for me to explain to you the particular effects of the earth's motion, +without your having acquired a knowledge of these lines: in plate 8. +fig. 2. you will find them all delineated: and you must learn them +perfectly, if you wish to make any proficiency in astronomy. + +_Caroline._ I was taught them at so early an age, that I could not +understand their meaning; and I have often heard you say, that the only +use of words, was to convey ideas. + +_Mrs. B._ A knowledge of these lines, would have conveyed some idea of +the manner in which they were designed to divide the globe into parts; +although the use of these divisions, might at that time, have been too +difficult for you to understand. Childhood is the season, when +impressions on the memory are most strongly and most easily made: it is +the period at which a large stock of terms should be treasured up, the +precise application of which we may learn when the understanding is more +developed. It is, I think, a very mistaken notion, that children should +be taught such things only, as they can perfectly understand. Had you +been early made acquainted with the terms which relate to figure and +motion, how much it would have facilitated your progress in natural +philosophy. I have been obliged to confine myself to the most common and +familiar expressions, in explaining the laws of nature; although I am +convinced that appropriate and scientific terms, might have conveyed +more precise and accurate ideas, had you been prepared to understand +them. + +_Emily._ You may depend upon our carefully learning the names of these +lines, Mrs. B.; but before we commit them to memory, will you have the +goodness to explain them to us? + +_Mrs. B._ Most willingly. This figure of a globe, or sphere, represents +the earth; the line which passes through its centre, and on which it +turns, is called its axis, and the two extremities of the axis A and B, +are the poles, distinguished by the names of the north and the south +pole. The circle C D, which divides the globe into two equal parts +between the poles, and equally distant from them, is called the equator, +or equinoctial line; that part of the globe to the north of the equator, +is the northern hemisphere; that part to the south of the equator, the +southern hemisphere. The small circle E F, which surrounds the north +pole, is called the arctic circle; that G H, which surrounds the south +pole, the antarctic circle; these are also called polar circles. There +are two circles, intermediate between the polar circles and the equator; +that to the north I K, called the tropic of Cancer; that to the south, L +M, called the tropic of Capricorn. Lastly, this circle, L K, which +divides the globe into two equal parts, crossing the equator and +extending northward as far as the tropic of Cancer, and southward as far +as the tropic of Capricorn, is called the ecliptic. The delineation of +the ecliptic on the terrestrial globe is not without danger of conveying +false ideas; for the ecliptic (as I have before said) is an imaginary +circle in the heavens, passing through the middle of the zodiac, and +situated in the plane of the earth's orbit. + +_Caroline._ I do not understand the meaning of the plane of the earth's +orbit. + +_Mrs. B._ A plane, is an even flat surface. Were you to bend a piece of +wire, so as to form a hoop, you might then stretch a piece of cloth, or +paper over it, like the head of a drum; this would form a flat surface, +which might be called the plane of the hoop. Now the orbit of the earth, +is an imaginary circle, surrounding the sun, and you can readily imagine +a plane extending from one side of this circle to the other, filling +up its whole area: such a plane would pass through the centre of the +sun, dividing it into hemispheres. You may then imagine this plane +extended beyond the limits of the earth's orbit, on every side, until it +reached those fixed stars which form the signs of the zodiac; passing +through the middle of these signs, it would give you the place of that +imaginary circle in the heavens, call the ecliptic; which is the sun's +apparent path. Let fig. 1. plate 9, represent such a plane, S the sun, E +the earth with its orbit, and A B C D the ecliptic passing through the +middle of the zodiac. + +[Illustration: PLATE IX.] + +_Emily._ If the ecliptic relates only to the heavens, why is it +described upon the terrestrial globe? + +_Mrs. B._ It is convenient for the demonstration of a variety of +problems in the use of the globes; and besides, the obliquity of this +circle to the equator is rendered more conspicuous by its being +described on the same globe; and the obliquity of the ecliptic shows how +much the earth's axis is inclined to the plane of its orbit. But to +return to fig. 2. plate 8. + +The spaces between the several parallel circles on the terrestrial globe +are called zones: that which is comprehended between the tropics is +distinguished by the name of the torrid zone; the spaces which extend +from the tropics to the polar circles, the north and south temperate +zones; and the spaces contained within the polar circles, the frigid +zones. By the term zone is meant a belt, or girdle, the frigid zones, +however, are not belts, but circles, extending 23-1/2 degrees from their +centres, the poles. + +The several lines which, you observe to be drawn from one pole to the +other, cutting the equator at right angles, are called meridians; the +number of these is unlimited, as a line passing through any place, +directly to the poles, is called the meridian of that place. When any +one of these meridians is exactly opposite to the sun, it is mid-day, or +twelve o'clock in the day, at all the places situated any where on that +meridian; and, at the places situated on the opposite meridian, it is +consequently midnight. + +_Emily._ To places situated equally distant from these two meridians, it +must then be six o'clock. + +_Mrs. B._ Yes; if they are to the east of the sun's meridian it is six +o'clock in the afternoon, because they will have previously passed the +sun; if to the west, it is six o'clock in the morning, and that meridian +will be proceeding towards the sun. + +Those circles which divide the globe into two equal parts, such as the +equator and the ecliptic, are called greater circles; to distinguish +them from those which divide it into two unequal parts, as the tropics, +and polar circles, which are called lesser circles. All circles, you +know, are imagined to be divided into 360 equal parts, called degrees, +and degrees are again divided into 60 equal parts, called minutes. The +diameter of a circle is a right line drawn across it, and passing +through its centre; were you, for instance, to measure across this round +table, that would give you its diameter; but were you to measure all +round the edge of it, you would then obtain its circumference. + +Now Emily, you may tell me exactly how many degrees are contained in a +meridian? + +_Emily._ A meridian, reaching from one pole to the other, is half a +circle, and must therefore contain 180 degrees. + +_Mrs. B._ Very well; and what number of degrees are there from the +equator to one of the poles? + +_Caroline._ The equator being equally distant from either pole, that +distance must be half of a meridian, or a quarter of the circumference +of a circle, and contain 90 degrees. + +_Mrs. B._ Besides the usual division of circles into degrees, the +ecliptic is divided into twelve equal parts, called signs, which bear +the name of the constellations through which this circle passes in the +heavens. The degrees measured on the meridians from the equator, either +towards the north, or towards the south, are called degrees of latitude, +of which there may be 90; those measured from east to west, either on +the equator, or any of the lesser circles, are called degrees of +longitude, of which there may be 180; these lesser circles are also +called parallels of latitude. Of these parallels there may be any +number; a circle drawn from east to west, at any distance from the +equator, will always be parallel to it, and is therefore called a +parallel of latitude. + +_Emily._ The degrees of longitude must then vary in length, according +to the dimensions of the circle on which they are reckoned; those, for +instance, at the polar circles, will be considerably smaller than those +at the equator? + +_Mrs. B._ Certainly; since the degrees of circles of different +dimensions do not vary in number, they must necessarily vary in length. +The degrees of latitude, you may observe, never vary in length; for the +meridians on which they are reckoned are all of the same dimensions. + +_Emily._ And of what length is a degree of latitude? + +_Mrs. B._ Sixty geographical miles, which is equal to 69-1/2 English +statute miles; or about one-sixth more than a common mile. + +_Emily._ The degrees of longitude at the equator, must then be of the +same dimensions, with a degree of latitude. + +_Mrs. B._ They would, were the earth a perfect sphere; but it is not +exactly such, being somewhat protuberant about the equator, and +flattened towards the poles. This form proceeds from the superior action +of the centrifugal power at the equator, and as this enlarges the +circle, it must, in the same proportion, increase the length of the +degrees of longitude measured on it. + +_Caroline._ I thought I had understood the centrifugal force perfectly, +but I do not comprehend its effects in this instance. + +_Mrs. B._ You know that the revolution of the earth on its axis, must +give to every particle a tendency to fly off from the centre, that this +tendency is stronger, or weaker, in proportion to the velocity with +which the particle moves; now a particle situated near to one of the +poles, makes one rotation in the same space of time as a particle at the +equator; the latter, therefore, having a much larger circle to describe, +travels proportionally faster, consequently the centrifugal force is +much stronger at the equator than in the polar regions: it gradually +decreases as you leave the equator and approach the poles, at which +points the centrifugal force, entirely ceases. Supposing, therefore, the +earth to have been originally in a fluid state, the particles in the +torrid zone would recede much farther from the centre than those in the +frigid zones; thus the polar regions would become flattened, and those +about the equator elevated. + +As a large portion of the earth is covered with water, the Creator gave +to it the form, denominated an _oblate spheroid_, otherwise the polar +regions would have been without water, and those about the equator, +would have been buried several miles below the surface of the ocean. + +_Caroline._ I did not consider that the particles in the neighbourhood +of the equator, move with greater velocity than those about the poles; +this was the reason I could not understand you. + +_Mrs. B._ You must be careful to remember, that those parts of a body +which are farthest from the centre of motion, must move with the +greatest velocity: the axis of the earth is the centre of its diurnal +motion, and the equatorial regions the parts most distant from the axis. + +_Caroline._ My head then moves faster than my feet; and upon the summit +of a mountain, we are carried round quicker than in a valley? + +_Mrs. B._ Certainly; your head is more distant from the centre of motion +than your feet; the mountain-top than the valley; and the more distant +any part of a body is from the centre of motion, the larger is the +circle it will describe, and the greater therefore must be its velocity. + +_Emily._ I have been reflecting, that if the earth is not a perfect +circle---- + +_Mrs. B._ A sphere you mean, my dear: a circle is a round line, every +part of which is equally distant from the centre; a sphere or globe is a +round body, the surface of which is every where equally distant from the +centre. + +_Emily._ If, then, the earth is not a perfect sphere, but prominent at +the equator, and depressed at the poles, would not a body weigh heavier +at the equator than at the poles? For the earth being thicker at the +equator, the attraction of gravity perpendicularly downwards must be +stronger. + +_Mrs. B._ Your reasoning has some plausibility, but I am sorry to be +obliged to add, that it is quite erroneous; for the nearer any part of +the surface of a body is to the centre of attraction, the more strongly +it is attracted; because it is then nearest to the whole mass of +attracting matter. In regard to its effects, you might consider the +whole power of gravity, as placed at the centre of attraction. + +_Emily._ But were you to penetrate deep into the earth, would gravity +increase as you approached the centre? + +_Mrs. B._ Certainly not; I am referring only to any situation on the +surface of the earth. Were you to penetrate into the interior, the +attraction of the parts above you, would counteract that of the parts +beneath you, and consequently diminish the power of gravity in +proportion as you approach the centre; and if you reached that point, +being equally attracted by the parts all around you, the effects of +gravity would cease, and you would be without weight. + +_Emily._ Bodies, then, should weigh less at the equator than at the +poles, since they are more distant from the centre of gravity in the +former than in the latter situation? + +_Mrs. B._ And this is really the case; but the difference of weight +would be scarcely sensible, were it not augmented by another +circumstance. + +_Caroline._ And what is this singular circumstance, which seems to +disturb the laws of nature? + +_Mrs. B._ One that you are well acquainted with, as conducing more to +the preservation than the destruction of order,--the centrifugal force. +This we have just observed to be strongest at the equator; and as it +tends to drive bodies from the centre, it is necessarily opposed to, and +must lessen the power of gravity, which attracts them towards the +centre. We accordingly find that bodies weigh lightest at the equator, +where the centrifugal force is greatest; and heaviest at the poles, +where this power is least: the weight being diminished at the equator, +by both the causes mentioned. + +_Caroline._ Has the experiment been made in these different situations? + +_Mrs. B._ Louis XIV. of France, sent philosophers both to the equator, +and to Lapland, for this purpose: the severity of the climate, and +obstruction from the ice, have hitherto rendered every attempt to reach +the pole abortive; but the difference of gravity at the equator, and in +Lapland is very perceptible. + +_Caroline._ Yet I do not comprehend how the difference of weight could +be ascertained, for if the body under trial decreased in weight, the +weight which was opposed to it in the opposite scale must have +diminished in the same proportion. For instance, if a pound of sugar did +not weigh so heavy at the equator as at the poles, the leaden pound +which served to weigh it, would not be so heavy either; therefore they +would still balance each other, and the different force of gravity could +not be ascertained by this means. + +_Mrs. B._ Your observation is perfectly just: the difference of gravity +in bodies situated at the poles, and at the equator, cannot be +ascertained by weighing them; a pendulum was therefore used for that +purpose. + +_Caroline._ What, the pendulum of a clock? how could that answer the +purpose? + +_Mrs. B._ A pendulum consists of a line, or rod, to one end of which a +weight is attached, and by the other end it is suspended to a fixed +point, about which it is made to vibrate. When not in motion, a +pendulum, obeying the general law of attraction, hangs like a plumb +line, perpendicular to the surface of the earth, but if you raise the +pendulum, gravity will bring it back to its perpendicular position. It +will, however, not remain stationary there, for the momentum it has +acquired during its descent, will impel it onwards, and if unobstructed, +it will rise on the opposite side to an equal height; from thence it is +brought back by gravity, and is again forced upwards, by the impulse of +its momentum. + +_Caroline._ If so, the motion of a pendulum would be perpetual, and I +thought you said, that there was no perpetual motion on the earth. + +_Mrs. B._ The motion of a pendulum is opposed by the resistance of the +air in which it vibrates, and by the friction of the part by which it is +suspended: were it possible to remove these obstacles, the motion of a +pendulum would be perpetual, and its vibrations perfectly regular; each +being of equal distance, and performed in equal times. + +_Emily._ That is the natural result of the uniformity of the power which +produces these vibrations, for the force of gravity being always the +same, the velocity of the pendulum must consequently be uniform. + +_Caroline._ No, Emily, you are mistaken; the force is not every where +the same, and therefore the effect will not be so either. I have +discovered it, Mrs. B.; since the force of gravity is less at the +equator than at the poles, the vibrations of the pendulum will be slower +at the former place than at the latter. + +_Mrs. B._ You are perfectly right, Caroline; it was by this means that +the difference of gravity was discovered, and the true figure of the +earth ascertained. + +_Emily._ But how do they contrive to regulate their time in the +equatorial and polar regions? for, since in our part of the earth the +pendulum of a clock vibrates exactly once in a second, if it vibrates +faster at the poles, and slower at the equator, the inhabitants must +regulate their clocks in a manner different from us. + +_Mrs. B._ The only alteration required is to lengthen the pendulum in +one case, and to shorten it in the other; for the velocity of the +vibrations of a pendulum depends on its length; and when it is said that +a pendulum vibrates quicker at the pole than at the equator, it is +supposed to be of the same length. A pendulum which vibrates seconds in +this latitude is about 39-1/7 inches long. In order to vibrate at the +equator in the same space of time, it must be somewhat shorter; and at +the poles, it must be proportionally lengthened. + +The vibrations of a pendulum, resemble the descent of a body on an +inclined plane, and are produced by the same cause; now you must +recollect, that the greater the perpendicular height of such a plane, in +proportion to its length, the more rapid will be the descent of the +body; a short pendulum ascends to a greater height than a larger one, in +vibrating a given distance, and of course its descent must be more +rapid. + +I shall now, I think, be able to explain to you the cause of the +variation of the seasons, and the difference in the length of the days +and nights in those seasons; both effects resulting from the same cause. + +In moving round the sun, the axis of the earth is not perpendicular to +the plane of its orbit. Supposing this round table to represent the +plane of the earth's orbit, and this little globe, the earth; through +this I have passed a wire, representing its axis and poles. In moving +round the table, I do not hold the wire perpendicular to it, but +obliquely. + +_Emily._ Yes, I understand, the earth does not go round the sun in an +upright position, its axis is slanting or oblique; and, it of course, +forms an angle with a line drawn perpendicular to the plane of the +earth's orbit. + +_Mrs. B._ All the lines, which you learnt in your last lesson, are +delineated on this little globe; you must consider the ecliptic as +representing the plane of the earth's orbit; and the equator, which +crosses the ecliptic in two places, then shows the degree of obliquity +of the axis of the earth; which amounts to 23-1/2 degrees, very nearly. +The points in which the ecliptic intersects the equator, are called the +equinoctial points. + +But I believe I shall render the effects of the obliquity of the earth's +axis clearer to you, by the revolution of the little globe round a +candle, which shall represent the sun. (Plate IX. fig. 2.) + +As I now hold it, at A, you see it in the situation in which it is in +the midst of summer, or what is called the summer solstice, which is on +the 21st of June. + +_Emily._ You hold the wire awry, I suppose, in order to show that the +axis of the earth is not upright? + +_Mrs. B._ Yes; in summer, the north pole is inclined towards the sun. In +this season, therefore, the northern hemisphere enjoys much more of his +rays than the southern. The sun, you see, now shines over the whole of +the north frigid zone, and notwithstanding the earth's diurnal +revolution, which I imitate by twirling the ball on the wire, it will +continue to shine upon it as long as it remains in this situation, +whilst the south frigid zone is at the same time completely in darkness. + +_Caroline._ That is very strange; I never before heard that there was +constant day or night in any part of the world! How much happier the +inhabitants of the north frigid zone must be than those of the southern; +the first enjoy uninterrupted day, while the last are involved in +perpetual darkness. + +_Mrs. B._ You judge with too much precipitation; examine a little +further, and you will find, that the two frigid zones share an equal +fate. + +We shall now make the earth set off from its position in the summer +solstice, and carry it round the sun; observe that the pole is always +inclined in the same direction, and points to the same spot in the +heavens. There is a fixed star situated near that spot, which is hence +called the north polar star. Now let us stop the earth at B, and examine +it in its present situation; it has gone through one quarter of its +orbit, and is arrived at that point at which the ecliptic cuts, or +crosses, the equator, and which is called the autumnal equinox. + +_Emily._ The sun now shines from one pole to the other, just as it would +constantly do, if the axis of the earth were perpendicular to its orbit. + +_Mrs. B._ Because the inclination of the axis is now neither towards the +sun, nor in the contrary direction; at this period of the year, the days +and nights are equal in every part of the earth. But the next step she +takes in her orbit, you see, involves the north pole in darkness, whilst +it illumines that of the south; this change was gradually preparing as I +moved the earth from summer to autumn; the arctic circle, which was at +first entirely illumined, began to have short nights, which increased as +the earth approached the autumnal equinox; and the instant it passed +that point, the long night of the north pole commences, and the south +pole begins to enjoy the light of the sun. We shall now make the earth +proceed in its orbit, and you may observe that as it advances, the days +shorten and the nights lengthen, throughout the northern hemisphere, +until it arrives at the winter solstice, on the 21st of December, when +the north frigid zone is entirely in darkness, and the southern has +uninterrupted daylight. + +[Illustration: PLATE X.] + +_Caroline._ Then, after all, the sun which I thought so partial, confers +his favours equally on all. + +_Mrs. B._ Not so either: the inhabitants of the torrid zone have much +more heat than we have, as the sun's rays fall perpendicularly twice in +the course of a year, on every place within the tropics, while they +shine more or less obliquely on the rest of the world, and almost +horizontally at the poles; for during their long day of six months, the +sun moves round their horizon without either rising or setting; the only +observable difference, is that it is more elevated by a few degrees at +mid-day, than at midnight. + +_Emily._ To a person placed in the temperate zone, in the situation in +which we are in England, the sun will shine neither so obliquely as it +does on the poles, nor vertically as at the equator; but its rays will +fall upon him more obliquely in autumn, and winter, than in summer. + +_Caroline._ And therefore, the inhabitants of the temperate zones, will +not have merely one day, and one night, in the year, as happens at the +poles, nor will they have equal days, and equal nights, as at the +equator; but their days and nights will vary in length, at different +times of the year, according as their respective poles incline towards, +or from the sun, and the difference will be greater in proportion to +their distance from the equator. + +_Mrs. B._ We shall now follow the earth through the other half of her +orbit, and you will observe, that now exactly the same changes take +place in the southern hemisphere, as those we have just remarked in the +northern. Day commences at the south pole, when night sets in at the +north pole; and in every other part of the southern hemisphere the days +are longer than the nights, while, on the contrary, our nights are +longer than our days. When the earth arrives at the vernal equinox, D, +where the ecliptic again cuts the equator, on the 21st of March, she is +situated, with respect to the sun, exactly in the same position, as in +the autumnal equinox; and the only difference with respect to the +earth, is, that it is now autumn in the southern hemisphere, whilst it +is spring with us. + +_Caroline._ Then the days and nights are again every where equal. + +_Mrs. B._ Yes, for the half of the globe which is enlightened, extends +exactly from one pole to the other, the sun has just risen to the north +pole, and is just setting to the south pole; but in every other part of +the globe, the day and night is of twelve hours length; hence the word +equinox, which is derived from the Latin, meaning equal night. + +As our summer advances, the days lengthen in the northern hemisphere, +and shorten in the southern, till the earth reaches the summer solstice, +when the north frigid zone is entirely illumined, and the southern is in +complete darkness; and we have now brought the earth again to the spot +from whence we first accompanied her. + +_Emily._ This is indeed a most satisfactory explanation of the cause of +the different lengths of our days and nights, and of the variation of +the seasons; and the more I learn, the more I admire the simplicity of +means by which such wonderful effects are produced. + +_Mrs. B._ I know not which is most worthy of our admiration, the causes, +or the effects of the earth's revolution round the sun. The mind can +find no object of contemplation more sublime, than the course of this +magnificent globe, impelled by the combined powers of projection and +attraction, to roll in one invariable course, around the source of light +and heat: and what can be more delightful than the beneficent effects of +this vivifying power on its attendant planet. It is at once the grand +principle which animates and fecundates nature. + +_Emily._ There is one circumstance in which this little ivory globe +appears to me to differ from the earth; it is not quite dark on that +side of it which is turned from the candle, as is the case with the +earth when neither moon nor stars are visible. + +_Mrs. B._ This is owing to the light of the candle, being reflected by +the walls of the room, on every part of the globe, consequently that +side of the globe, on which the candle does not directly shine, is not +in total darkness. Now the skies have no walls to reflect the sun's +light on that side of our earth which is in darkness. + +_Caroline._ I beg your pardon, Mrs. B., I think that the moon, and +stars, answer the purpose of walls in reflecting the sun's light to us +in the night. + +_Mrs. B._ Very well, Caroline; that is to say, the moon and planets; +for the fixed stars, you know, shine by their own light. + +_Emily._ You say, that the superior heat of the equatorial parts of the +earth, arises from the rays falling perpendicularly on those regions, +whilst they fall obliquely on these more northern regions; now I do not +understand why perpendicular rays should afford more heat than oblique +rays. + +_Caroline._ You need only hold your hand perpendicularly over the +candle, and then hold it sideways obliquely, to be sensible of the +difference. + +_Emily._ I do not doubt the fact, but I wish to have it explained. + +_Mrs. B._ You are quite right; if Caroline had not been satisfied with +ascertaining the fact, without understanding it, she would not have +brought forward the candle as an illustration; the reason why you feel +so much more heat if you hold your hand perpendicularly over the candle, +than if you hold it sideways, is because a stream of heated vapour +constantly ascends from the candle, or any other burning body, which +being lighter than the air of the room, does not spread laterally but +rises perpendicularly, and this led you to suppose that the rays were +hotter in the latter direction. Had you reflected, you would have +discovered that rays issuing from the candle sideways, are no less +perpendicular to your hand when held opposite to them, than the rays +which ascend when your hand is held over them. + +The reason why the sun's rays afford less heat when in an oblique +direction, than when perpendicular, is because fewer of them fall upon +an equal portion of the earth; this will be understood better by +referring to plate 10. fig. 1, which represents two equal portions of +the sun's rays, shining upon different parts of the earth. Here it is +evident, that the same quantity of rays fall on the space A B, as fall +on the space B C; and as A B is less than B C, the heat and light will +be much stronger in the former than in the latter; A B, you see, +represents the equatorial regions, where the sun shines perpendicularly; +and B C, the temperate and frozen climates, where his rays fall more +obliquely. + +_Emily._ This accounts not only for the greater heat of the equatorial +regions, but for the greater heat of our summers, as the sun shines less +obliquely in summer than in winter. + +_Mrs. B._ This you will see exemplified in figure 2, in which the earth +is represented, as it is situated on the 21st of June, and England +receives less oblique, and consequently a greater number of rays, than +at any other season; and figure 3, shows the situation of England on the +21st of December, when the rays of the sun fall most obliquely upon her. +But there is also another reason why oblique rays give less heat, than +perpendicular rays; which is, that they have a greater portion of the +atmosphere to traverse; and though it is true, that the atmosphere is +itself a transparent body, freely admitting the passage of the sun's +rays, yet it is always loaded more or less with dense and foggy vapour, +which the rays of the sun cannot easily penetrate; therefore, the +greater the quantity of atmosphere the sun's rays have to pass through +in their way to the earth, the less heat they will retain when they +reach it. This will be better understood, by referring to fig. 4. The +dotted line round the earth, describes the extent of the atmosphere, and +the lines which proceed from the sun to the earth, the passage of two +equal portions of the sun's rays, to the equatorial and polar regions; +the latter you see, from its greater obliquity, passes through a greater +extent of atmosphere. + +_Caroline._ And this, no doubt, is the reason why the sun, in the +morning and in the evening, gives so much less heat, than at mid-day. + +_Mrs. B._ The diminution of heat, morning and evening, is certainly +owing to the greater obliquity of the sun's rays; and they are also +affected by the other, both the cause, which I have just explained to +you; the difficulty of passing through a foggy atmosphere is perhaps +more particularly applicable to them, as mist and vapours are prevalent +about the time of sunrise and sunset. But the diminished obliquity of +the sun's rays, is not the sole cause of the heat of summer; the length +of the days greatly conduces to it; for the longer the sun is above the +horizon, the more heat he will communicate to the earth. + +_Caroline._ Both the longest days, and the most perpendicular rays, are +on the 21st of June; and yet the greatest heat prevails in July and +August. + +_Mrs. B._ Those parts of the earth which are once heated, retain the +heat for some length of time, and the additional heat they receive, +occasions an elevation of temperature, although the days begin to +shorten, and the sun's rays to fall more obliquely. For the same reason, +we have generally more heat at three o'clock in the afternoon, than at +twelve, when the sun is on the meridian. + +_Emily._ And pray, have the other planets the same vicissitudes of +seasons, as the earth? + +_Mrs. B._ Some of them more, some less, according as their axes deviate +more or less from the perpendicular, to the plane of their orbits. The +axis of Jupiter, is nearly perpendicular to the plane of his orbit; the +axes of Mars, and of Saturn, are each, inclined at angles of about sixty +degrees; whilst the axis of Venus is believed to be elevated only +fifteen or twenty degrees above her orbit; the vicissitudes of her +seasons must therefore be considerably greater than ours. For further +particulars respecting the planets, I shall refer you to Bonnycastle's +Introduction to Astronomy. + +I have but one more observation to make to you, relative to the earth's +motion; which is, that although we have but 365 days and nights in the +year, she performs 366 complete revolutions on her axis, during that +time. + +_Caroline._ How is that possible? for every complete revolution must +bring the same place back to the sun. It is now just twelve o'clock, the +sun is, therefore, on our meridian; in twenty-four hours will it not +have returned to our meridian again, and will not the earth have made a +complete rotation on its axis? + +_Mrs. B._ If the earth had no progressive motion in its orbit whilst it +revolves on its axis, this would be the case; but as it advances almost +a degree westward in its orbit, in the same time that it completes a +revolution eastward on its axis, it must revolve nearly one degree more +in order to bring the same meridian back to the sun. + +_Caroline._ Oh, yes! it will require as much more of a second revolution +to bring the same meridian back to the sun, as is equal to the space the +earth has advanced in her orbit; that is, nearly a degree; this +difference is, however, very little. + +_Mrs. B._ These small daily portions of rotation, are each equal to the +three hundred and sixty-fifth part of a circle, which at the end of the +year amounts to one complete rotation. + +_Emily._ That is extremely curious. If the earth then, had no other than +its diurnal motion, we should have 366 days in the year. + +_Mrs. B._ We should have 366 days in the same period of time that we now +have 365; but if we did not revolve round the sun, we should have no +natural means of computing years. + +You will be surprised to hear, that if time is calculated by the stars +instead of the sun, the irregularity which we have just noticed does not +occur, and that one complete rotation of the earth on its axis, brings +the same meridian back to any fixed star. + +_Emily._ That seems quite unaccountable; for the earth advances in her +orbit with regard to the fixed stars, the same as with regard to the +sun. + +_Mrs. B._ True, but then the distance of the fixed stars is so immense, +that our solar system is in comparison to it but a spot, and the whole +extent of the earth's orbit but a point; therefore, whether the earth +remain stationary, or whether it revolved in its orbit during its +rotation on its axis, no sensible difference would be produced with +regard to the fixed stars. One complete revolution brings the same +meridian back to the same fixed star; hence the fixed stars appear to go +round the earth in a shorter time than the sun by three minutes +fifty-six seconds of time. + +_Caroline._ These three minutes fifty-six seconds is the time which the +earth takes to perform the additional three hundred and sixty-fifth part +of the circle, in order to bring the same meridian back to the sun. + +_Mrs. B._ Precisely. Hence the stars gain every day three minutes +fifty-six seconds on the sun, which makes them rise that portion of time +earlier every day. + +When time is calculated by the stars it is called sidereal time; when by +the sun, solar, or apparent time. + +_Caroline._ Then a sidereal day is three minutes fifty-six seconds +shorter, than a solar day of twenty-four hours. + +_Mrs. B._ I must also explain to you what is meant by a sidereal year. + +The common year, called the solar or tropical year, containing 365 days, +five hours, forty-eight minutes and fifty-two seconds, is measured from +the time the sun sets out from one of the equinoxes, or solstices, till +it returns to the same again; but this year is completed, before the +earth has finished one entire revolution in its orbit. + +_Emily._ I thought that the earth performed one complete revolution in +its orbit, every year; what is the reason of this variation? + +_Mrs. B._ It is owing to the spheroidal figure of the earth. The +elevation about the equator produces much the same effect as if a +similar mass of matter, collected in the form of a moon, revolved round +the equator. When this moon acted on the earth, in conjunction with, or +in opposition to the sun, variations in the earth's motion would be +occasioned, and these variations produce what is called the precession +of the equinoxes. + +[Illustration: PLATE XI.] + +_Emily._ What does that mean? I thought the equinoctial points, were +fixed points in the heavens, in which the equator cuts the ecliptic. + +_Mrs. B._ These points are not quite fixed, but have an apparently +retrograde motion, among the signs of the zodiac; that is to say, +instead of being at every revolution in the same place, they move +backwards. Thus if the vernal equinox is at A, (fig. 1. plate XI.) the +autumnal one, will be at B, instead of C, and the following vernal +equinox, at D, instead of at A, as would be the case if the equinoxes +were stationary, at opposite points of the earth's orbit. + +_Caroline._ So that when the earth moves from one equinox to the other, +though it takes half a year to perform the journey, it has not travelled +through half its orbit. + +_Mrs. B._ And, consequently, when it returns again to the first equinox, +it has not completed the whole of its orbit. In order to ascertain when +the earth has performed an entire revolution in its orbit, we must +observe when the sun returns in conjunction with any fixed star; and +this is called a sidereal year. Supposing a fixed star situated at E, +(fig. 1. plate XI.) the sun would not appear in conjunction with it, +till the earth had returned to A, when it would have completed its +orbit. + +_Emily._ And how much longer is the sidereal, than the solar year? + +_Mrs. B._ Only twenty minutes; so that the variation of the equinoctial +points is very inconsiderable. I have given them a greater extent in the +figure, in order to render them sensible. + +In regard to time, I must further add, that the earth's diurnal motion +on an inclined axis, together with its annual revolution in an elliptic +orbit, occasions so much complication in its motion, as to produce many +irregularities; therefore the true time cannot be measured by the +apparent place of the sun. A perfectly correct clock, would in some +parts of the year be before the sun, and in other parts after it. There +are but four periods in which the sun and a perfect clock would agree, +which is the 15th of April, the 16th of June, the 23d of August, and the +24th of December. + +_Emily._ And is there any considerable difference between solar time, +and true time? + +_Mrs. B._ The greatest difference amounts to between fifteen and sixteen +minutes. Tables of equation are constructed for the purpose of pointing +out, and correcting these differences between solar time and equal or +mean time, which is the denomination given by astronomers, to true time. + + +Questions + +1. (Pg. 92) What does the line A B, (fig. 2 plate 8.) represent, and +what are its extremities called? + +2. (Pg. 92) What is meant by the equator, and how is it situated? + +3. (Pg. 92) There are two hemispheres; how are they named and +distinguished? + +4. (Pg. 92) What are the circles near the poles called? + +5. (Pg. 92) What do the lines I K, and L M, represent? + +6. (Pg. 92) What circle is in part represented by the line L K? + +7. (Pg. 92) Against what mistake must you guard respecting this line? + +8. (Pg. 92) What is meant by a plane, and how could one be represented? + +9. (Pg. 93) Describe what is intended by the plane of the earth's orbit. + +10. (Pg. 93) Extending this plane to the fixed stars, what circle would +it form, and among what particular stars would it be found? + +11. (Pg. 93) What is fig. 1. plate 9, designed to represent? + +12. (Pg. 93) The ecliptic does not properly belong to the earth, for +what purpose then is it described on the terrestrial globe? + +13. (Pg. 93) What does the obliquity of the ecliptic to the equator +serve to show? + +14. (Pg. 93) Within what limits do you find the torrid zone? + +15. (Pg. 93) What two zones are there between the torrid, and the two +frigid zones? + +16. (Pg. 93) Where are the frigid zones situated? + +17. (Pg. 93) What is meant by the term zone; and are the frigid zones +properly so called? + +18. (Pg. 93) How do meridian lines extend, and what is meant by the +meridian of a place? + +19. (Pg. 93) What is said of the meridian to which the sun is opposite, +and where is it then midnight? + +20. (Pg. 94) What hour is it then, at places exactly half way between +these meridians? + +21. (Pg. 94) How are greater and lesser circles distinguished? + +22. (Pg. 94) What part of a circle is a degree, and how are these +further divided? + +23. (Pg. 94) What is the diameter, and what the circumference of a +circle, and what proportion do they bear to each other? + +24. (Pg. 94) What part of a circle is a meridian? + +25. (Pg. 94) How many degrees are there between the equator and the +poles? + +26. (Pg. 94) Into what parts, besides degrees, is the ecliptic divided? + +27. (Pg. 94) How are degrees of latitude measured, and to what number do +they extend? + +28. (Pg. 94) On what circles are degrees of longitude measured, and to +what number do they extend? + +29. (Pg. 94) What is a parallel of latitude? + +30. (Pg. 95) Degrees of longitude vary in length; what is the cause of +this? + +31. (Pg. 95) What is the length of a degree of latitude, and why do not +these vary? + +32. (Pg. 95) What causes the equator to be somewhat larger than a great +circle passing through the poles, and what effect has this on degrees of +longitude measured on the equator? + +33. (Pg. 95) What is the cause of this form being given to the earth? + +34. (Pg. 96) What would have been a consequence of the centrifugal +force, had the earth been a perfect sphere? + +35. (Pg. 96) A body situated at the poles, is attracted more forcibly +than if placed at the equator, what is the reason? + +36. (Pg. 97) What effect would be produced upon the gravity of a body, +were it placed beneath the surface of the earth, and what supposing it +at its centre? + +37. (Pg. 97) What two circumstances combine, to lessen the weight of a +body on the equator? + +38. (Pg. 97) Why could not this be proved by weighing a body at the +poles, and at the equator? + +39. (Pg. 98) What is a pendulum? + +40. (Pg. 98) What causes it to vibrate? + +41. (Pg. 98) Why are not its vibrations perpetual? + +42. (Pg. 98) Two pendulums of the same length, will not, in different +latitudes, perform their vibrations in equal times, what is the cause of +this? + +43. (Pg. 98) To what use has this property of the pendulum been applied? + +44. (Pg. 99) What change must be made in pendulums situated at the +equator and at the poles, to render their vibrations equal? + +45. (Pg. 99) What do the vibrations of a pendulum resemble, and why will +it vibrate more rapidly if shortened? + +46. (Pg. 99) In the revolution of the earth round the sun, what is the +position of its axis? + +47. (Pg. 99) How much is the axis of the earth inclined, and with what +line does it form this angle? + +48. (Pg. 99) What is represented by fig. 2, plate 9? + +49. (Pg. 100) How is the north pole inclined in the middle of our +summer, and what effect has this on the north frigid zone? + +50. (Pg. 100) In what direction does the north pole always point? + +51. (Pg. 100) What is shown by the position of the earth at B, in the +figure? + +52. (Pg. 100) How does the sun then shine at the poles, and what is the +effect on the days and nights? + +53. (Pg. 101) When the earth has passed the autumnal equinox, what +changes take place at the poles, and also in the whole northern and +southern hemispheres? + +54. (Pg. 101) Why is the heat greatest within the torrid zone? + +55. (Pg. 101) How does the sun appear at the poles, during the period of +day there? + +56. (Pg. 101) In what will the days and nights differ in the temperate +zone, from those at the poles, and at the equator? + +57. (Pg. 102) Trace the earth from the winter solstice to the vernal +equinox, and inform me what changes take place. + +58. (Pg. 102) What takes place at the time of the vernal equinox, and +what is meant by the term? + +59. (Pg. 102) In proceeding from the vernal equinox to the summer +solstice, what changes take place? + +60. (Pg. 103) From what cause arises the superior heat of the equatorial +regions? + +61. (Pg. 103) Why should oblique rays afford less heat than those which +are perpendicular? + +62. (Pg. 103) How is this explained by fig. 1. plate 10? + +63. (Pg. 103) How do you account for the superior heat of summer, and +how is this exemplified in fig. 2 and 3, plate 10? + +64. (Pg. 104) What other cause lessens the intensity of oblique rays? + +65. (Pg. 104) How is this explained by fig. 4? + +66. (Pg. 104) What causes conspire to lessen the solar heat in the +morning and evening? + +67. (Pg. 104) The greatest heat of summer is after the solstice, and the +greatest heat of the day, after 12 o'clock, although the sun's rays are +then most direct, how is this accounted for? + +68. (Pg. 105) Is there any change of seasons in the other planets? + +69. (Pg. 105) What is said respecting the axes of Jupiter, of Mars, and +of Saturn? + +70. (Pg. 105) In 365 days, how many times does the earth revolve on its +axis? + +71. (Pg. 105) How is this accounted for? + +72. (Pg. 105) Do the fixed stars require the same time as the sun, to +return to the same meridian? + +73. (Pg. 106) How is this accounted for? + +74. (Pg. 106) What is meant by the solar and the sidereal day? + +75. (Pg. 106) What is the difference in time between them? + +76. (Pg. 106) What is the length of the tropical year? + +77. (Pg. 107) The solar year is completed before the earth has made a +complete revolution in its orbit, by what is this caused? + +78. (Pg. 107) What is this called, and what is represented respecting it +by fig. 1, plate 11? + +79. (Pg. 107) By what means can we ascertain the period of a complete +revolution of the earth in its orbit, as illustrated by the fixed star +E, in fig. 1? + +80. (Pg. 107) What difference is there in the length of the solar and +sidereal year? + +81. (Pg. 107) Why can we not always ascertain the true time by the +apparent place of the sun? + +82. (Pg. 108) What would be the greatest difference between solar, and +true time, as indicated by a perfect clock? + + + + +CONVERSATION IX. + +ON THE MOON. + +OF THE MOON'S MOTION. PHASES OF THE MOON. ECLIPSES OF THE MOON. ECLIPSES +OF JUPITER'S MOONS. OF LATITUDE AND LONGITUDE. OF THE TRANSITS OF THE +INFERIOR PLANETS. OF THE TIDES. + + +MRS. B. + +We shall, to-day, confine our attention to the moon, which offers many +interesting phenomena. + +The moon revolves round the earth in the space of about twenty-nine days +and a half; in an orbit, the plane of which is inclined upwards of five +degrees to that of the earth; she accompanies us in our revolution round +the sun. + +_Emily._ Her motion then must be of a complicated nature; for as the +earth is not stationary, but advances in her orbit, whilst the moon goes +round her, the moon, in passing round the sun, must proceed in a sort of +scolloped circle. + +_Mrs. B._ That is true; and there are also other circumstances which +interfere with the simplicity, and regularity of the moon's motion, but +which are too intricate for you to understand at present. + +The moon always presents the same face to us, by which it is evident +that she turns but once upon her axis, while she performs a revolution +round the earth; so that the inhabitants of the moon have but one day, +and one night, in the course of a lunar month. + +_Caroline._ We afford them, however, the advantage of a magnificent moon +to enlighten their long nights. + +_Mrs. B._ That advantage is put partial; for since we always see the +same hemisphere of the moon, the inhabitants of that hemisphere alone, +can perceive us. + +_Caroline._ One half of the moon then enjoys our light, while the other +half has constantly nights of darkness. If there are any astronomers in +those regions, they would doubtless be tempted to visit the other +hemisphere, in order to behold so grand a luminary as we must appear to +them. But, pray, do they see the earth under all the changes, which the +moon exhibits to us? + +_Mrs. B._ Exactly so. These changes are called the phases of the moon, +and require some explanation. In fig. 2, plate 11, let us say, that S +represents the sun, E the earth, and A B C D E F G H, the moon, in +different parts of her orbit. When the moon is at A, her dark side being +turned towards the earth, we shall not see her as at _a_; but her +disappearance is of very short duration, and as she advances in her +orbit, we perceive her under the form of a new moon: when she has gone +through one eighth of her orbit at B, one quarter of her enlightened +hemisphere will be turned towards the earth, and she will then appear +horned as at _b_; when she has performed one quarter of her orbit, she +shows us one half of her enlightened side, as at _c_, and this is called +her first quarter; at _d_ she is said to be gibbous, and at _e_ the +whole of the enlightened side appears to us, and the moon is at full. As +she proceeds in her orbit, she becomes again gibbous, and her +enlightened hemisphere turns gradually away from us, until she arrives +at G, which is her third quarter; proceeding thence she completes her +orbit and disappears, and then again resumes her form of a new moon, and +passes successively, through the same changes. + +When the moon is new, she is said to be in conjunction with the sun, as +they are then both in the same direction from the earth; at the time of +full moon, she is said to be in opposition, because she and the sun, are +at opposite sides of the earth; at the time of her first and third +quarters, she is said to be in her quadratures, because she is then +one-fourth of a circle, or 90 deg., from her conjunction, or the period +of new moon. + +_Emily._ Are not the eclipses of the sun produced by the moon passing +between the sun and the earth? + +_Mrs. B._ Yes; when the moon passes between the sun and the earth, she +intercepts his rays, or, in other words, casts a shadow on the earth, +then the sun is eclipsed, and daylight gives place to darkness, while +the moon's shadow is passing over us. + +When, on the contrary, the earth is between the sun and the moon, it is +we who intercept the sun's rays, and cast a shadow on the moon; she is +then said to be eclipsed, and disappears from our view. + +_Emily._ But as the moon goes round the earth every month, she must be, +once during that time, between the earth and the sun; and the earth must +likewise be once between the sun and the moon, and yet we have not a +solar and a lunar eclipse every month? + +_Mrs. B._ I have already informed you, that the orbits of the earth and +moon are not in the same plane, but cross or intersect each other; and +the moon generally passes either above or below that of the earth, when +she is in conjunction with the sun, and does not therefore intercept its +rays, and produce an eclipse; for this can take place only when the moon +is in, or near her nodes, which is the name given to those two points in +which her orbit crosses that of the earth; eclipses cannot happen at any +other time, because it is then only, that they are both in a right line +with the sun. + +_Emily._ And a partial eclipse of the moon takes place, I suppose, when, +in passing by the earth, she is not sufficiently above or below the +shadow, to escape it entirely? + +_Mrs. B._ Yes, one edge of her disk then dips into the shadow, and is +eclipsed; but as the earth is larger than the moon, when eclipses happen +precisely at the nodes, they are not only total, but last for upwards of +three hours. + +[Illustration: PLATE XII.] + +A total eclipse of the sun rarely occurs, and when it happens, the total +darkness is confined to one particular part of the earth, the diameter +of the shadow not exceeding 180 miles; evidently showing that the moon +is smaller than the sun, since she cannot entirely hide it from the +earth. In fig. 1, plate 12, you will find a solar eclipse described; S +is the sun, M the moon, and E the earth; and the moon's shadow, you see, +is not large enough to cover the earth. The lunar eclipses, on the +contrary, are visible from every part of the earth, where the moon is +above the horizon; and we discover, by the length of time which the moon +is passing through the earth's shadow, that it would be sufficient to +eclipse her totally, were she many times her actual size; it follows, +therefore, that the earth is much larger than the moon. + +In fig. 2, S represents the sun, which pours forth rays of light in +straight lines, in every direction. E is the earth, and M the moon. Now +a ray of light coming from one extremity of the sun's disk, in the +direction A B, will meet another, coming from the opposite extremity, in +the direction C B; the shadow of the earth cannot therefore extend +beyond B; as the sun is larger than the earth, the shadow of the latter +is conical, or in the figure of a sugar loaf; it gradually diminishes, +and is much smaller than the earth where the moon passes through it, and +yet we find the moon to be, not only totally eclipsed, but to remain for +a considerable length of time in darkness, and hence we are enabled to +ascertain its real dimensions. + +_Emily._ When the moon eclipses the sun to us, we must be eclipsed to +the moon? + +_Mrs. B._ Certainly; for if the moon intercepts the sun's rays, and +casts a shadow on us, we must necessarily disappear to the moon, but +only partially, as in fig. 1. + +_Caroline._ There must be a great number of eclipses in the distant +planets, which have so many moons? + +_Mrs. B._ Yes, few days pass without an eclipse taking place; for among +the number of satellites, one or the other of them are continually +passing either between their primary and the sun; or between the planet, +and each other. Astronomers are so well acquainted with the motion of +the planets, and their satellites, that they have calculated not only +the eclipses of our moon, but those of Jupiter, with such perfect +accuracy, that it has afforded a means of ascertaining the longitude. + +_Caroline._ But is it not very easy to find both the latitude and +longitude of any place by a map or globe? + +_Mrs. B._ If you know where you are situated, there is no difficulty in +ascertaining the latitude or longitude of the place, by referring to a +map; but supposing that you had been a length of time at sea, +interrupted in your course by storms, a map would afford you very little +assistance in discovering where you were. + +_Caroline._ Under such circumstances, I confess I should be equally at a +loss to discover either latitude, or longitude. + +_Mrs. B._ The latitude is usually found by taking the altitude of the +sun at mid-day; that is to say, the number of degrees that it is +elevated above the horizon, for the sun appears more elevated as we +approach the equator, and less as we recede from it. + +_Caroline._ But unless you can see the sun, how can you take its +altitude? + +_Mrs. B._ When it is too cloudy to see the sun, the latitude is +sometimes found at night, by the polar star; the north pole of the +earth, points constantly towards one particular part of the heavens, in +which a star is situated, called the Polar star: this star is visible on +clear nights, from every part of the northern hemisphere; the altitude +of the polar star, is therefore the same number of degrees, as that of +the pole; the latitude may also be determined by observations made on +any of the fixed stars: the situation therefore of a vessel at sea, with +regard to north and south, is easily ascertained. The difficulty is, +respecting east and west, that is to say, its longitude. As we have no +eastern poles from which we can reckon our distance, some particular +spot, or line, must be fixed upon for that purpose. The English, reckon +from the meridian of Greenwich, where the royal observatory is situated; +in French maps, you will find that the longitude is reckoned from the +meridian of Paris. + +The rotation of the earth on its axis in 24 hours from west to east, +occasions, you know, an apparent motion of the sun and stars in a +contrary direction, and the sun appears to go round the earth in the +space of 24 hours, passing over fifteen degrees, or a twenty-fourth part +of the earth's circumference every hour; therefore, when it is twelve +o'clock in London, it is one o'clock in any place situated fifteen +degrees to the east of London, as the sun must have passed the meridian +of that place, an hour before he reaches that of London. For the same +reason it is eleven o'clock in any place situated fifteen degrees to the +west of London, as the sun will not come to that meridian till an hour +later. + +If then the captain of a vessel at sea, could know precisely what was +the hour at London, he could, by looking at his watch, and comparing it +with the hour at the spot in which he was, ascertain the longitude. + +_Emily._ But if he had not altered his watch, since he sailed from +London, it would indicate the hour it then was in London. + +_Mrs. B._ True; but in order to know the hour of the day at the spot in +which he is, the captain of a vessel regulates his watch by the sun when +it reaches the meridian. + +_Emily._ Then if he had two watches, he might keep one regulated daily, +and leave the other unaltered; the former would indicate the hour of the +place in which he was situated, and the latter the hour at London; and +by comparing them together, he would be able to calculate his longitude. + +_Mrs. B._ You have discovered, Emily, a mode of finding the longitude, +which I have the pleasure to tell you, is universally adopted: watches +of a superior construction, called chronometers, or time-keepers, are +used for this purpose, and are now made with such accuracy, as not to +vary more than four or five seconds in a whole year; but the best +watches are liable to imperfections, and should the time-keeper go too +fast or too slow, there would be no means of ascertaining the error; +implicit reliance, cannot consequently be placed upon them. + +Recourse, therefore, is sometimes had to the eclipses of Jupiter's +satellites. A table is made, of the precise time at which the several +moons are eclipsed to a spectator at London; when they appear eclipsed +to a spectator in any other spot, he may, by consulting the table, know +what is the hour at London; for the eclipse is visible at the same +moment, from whatever place on the earth it is seen. He has then only to +look at his watch, which he regulates by the sun, and which therefore +points out the hour of the place in which he is, and by observing the +difference of time there, and at London, he may immediately determine +his longitude. + +Let us suppose, that a certain moon of Jupiter is always eclipsed at six +o'clock in the evening; and that a man at sea consults his watch, and +finds that it is ten o'clock at night, where he is situated, at the +moment the eclipse takes place, what will be his longitude? + +_Emily._ That is four hours later than in London: four times fifteen +degrees, make 60; he would, therefore, be sixty degrees east of London, +for the sun must have passed his meridian before it reaches that of +London. + +_Mrs. B._ For this reason the hour is always later than in London, when +the place is east longitude, and earlier when it is west longitude. Thus +the longitude can be ascertained whenever the eclipses of Jupiter's +moons are visible. + +_Caroline._ But do not the primary planets, sometimes eclipse the sun +from each other, as they pass round in their orbits? + +_Mrs. B._ They must of course sometimes pass between each other and the +sun, but as their shadows never reach each other, they hide so little of +his light, that the term eclipse is not in this case used; this +phenomenon is called a transit. The primary planets do not any of them +revolve in the same plane, and the times of their revolution round the +sun is considerable, it therefore but rarely happens that they are at +the same time, in conjunction with the sun, and in their nodes. It is +evident also, that a planet must be inferior (that is within the orbit +of another) in order to its apparently passing over the disk of the sun. +Mercury, and Venus, have sometimes passed in a right line between us, +and the sun, but being at so great a distance from us, their shadows did +not extend so far as the earth; no darkness was therefore produced on +any part of our globe; but the planet appeared like a small black spot, +passing across the sun's disk. + +It was by the last transit of Venus, that astronomers were enabled to +calculate, with some degree of accuracy, the distance of the earth from +the sun, and the dimensions of the latter. + +_Emily._ I have heard that the tides are affected by the moon, but I +cannot conceive what influence it can have on them. + +_Mrs. B._ They are produced by the moon's attraction, which draws up the +waters of that part of the ocean over which the moon passes, so as to +cause it to stand considerably higher than the surrounding parts. + +_Caroline._ Does attraction act on water more powerfully than on land? I +should have thought it would have been just the contrary, for land is +certainly a more dense body than water? + +_Mrs B._ Tides do not arise from water being more strongly attracted +than land, for this certainly is not the case; but the cohesion of +fluids, being much less than that of solid bodies, they more easily +yield to the power of gravity; in consequence of which, the waters +immediately below the moon, are drawn up by it, producing a full tide, +or what is commonly called, high water, at the spot where it happens. So +far, the theory of the tides is not difficult to understand. + +_Caroline._ On the contrary, nothing can be more simple; the waters, in +order to rise up under the moon, must draw the waters from the opposite +side of the globe, and occasion ebb-tide, or low water, in those parts. + +_Mrs. B._ You draw your conclusion rather too hastily, my dear; for +according to your theory, we should have full tide only once in about +twenty-four hours, that is, every time that we were below the moon, +while we find that in this time we have two tides, and that it is high +water with us, and with our antipodes, at the same time. + +_Caroline._ Yet it must be impossible for the moon to attract the sea in +opposite parts of the globe, and in opposite directions, at the same +time. + +_Mrs. B._ This opposite tide, is rather more difficult to explain, than +that which is immediately beneath the moon; with a little attention, +however, I hope I shall be able to make you understand the explanation +which has been given of it, by astronomers. It must be confessed, +however, that the theory upon this subject, is attended with some +difficulties. You recollect that the earth and the moon mutually attract +each other, but do you suppose that every part of the earth is equally +attracted by the moon? + +_Emily._ Certainly not; you have taught us that the force of attraction +decreases, with the increase of distance, and therefore that part of the +earth which is farthest from the moon, must be attracted less +powerfully, than that to which she is nearest. + +_Mrs. B._ This fact will aid us in the explanation which I am about to +give to you. + +In order to render the question more simple, let us suppose the earth to +be every where covered by the ocean, as represented in (fig. 3. pl. 12.) +M is the moon, A B C D the earth. Now the waters on the surface of the +earth, about A, being more strongly attracted than any other part, will +be elevated: the attraction of the moon at B and C being less, and at D +least of all. The high tide at A, is accounted for from the direct +attraction of the moon; to produce this the waters are drawn from B and +C, where it will consequently be low water. At D, the attraction of the +moon being considerably decreased, the waters are left relatively high, +which height is increased, by the centrifugal force of the earth being +greater at D than at A, in consequence of its greater distance from the +common centre of gravity X, between the earth and the moon. + +_Emily._ The tide A, then, is produced by the moon's attraction, and the +tide D, is produced by the centrifugal force, and increased by the +feebleness of the moon's attraction, in those parts. + +_Caroline._ And when it is high water at A and D, it is low water at B +and C: now I think I comprehend the nature of the tides, though I +confess it is not quite so easy as I at first thought. + +But, Mrs. B., why does not the sun produce tides, as well as the moon; +for its attraction is greater than that of the moon? + +_Mrs. B._ It would be at an equal distance, but our vicinity to the +moon, makes her influence more powerful. The sun has, however, a +considerable effect on the tides, and increases or diminishes them as it +acts in conjunction with, or in opposition to the moon. + +_Emily._ I do not quite understand that. + +_Mrs. B._ The moon is a month in going round the earth; twice during +that time, therefore, at full and at change, she is in the same +direction as the sun; both, then act in conjunction on the earth, and +produce very great tides, called spring tides, as represented in fig. 4, +at A and B; but when the moon is at the intermediate parts of her orbit, +that is in her quadratures, the sun, instead of affording assistance, +weakens her power, by acting in opposition to it; and smaller tides are +produced, called neap tides, as represented at M, in fig. 5. + +_Emily._ I have often observed the difference of these tides, when I +have been at the sea side. + +But since attraction is mutual between the moon and the earth, we must +produce tides in the moon; and these must be more considerable in +proportion as our planet is larger. And yet the moon does not appear of +an oval form. + +_Mrs. B._ You must recollect, that in order to render the explanation of +the tides clearer, we suppose the whole surface of the earth to be +covered with the ocean; but that is not really the case, either with the +earth or the moon, and the land which intersects the water, destroys the +regularity of the effect. Thus, in flowing up rivers, in passing round +points of land, and into bays and inlets, the water is obstructed, and +high water must happen much later, than would otherwise be the case. + +_Caroline._ True; we may, however, be certain that whenever it is high +water, the moon is immediately over our heads. + +_Mrs. B._ Not so either; for as a similar effect is produced on that +part of the globe immediately beneath the moon, and on that part most +distant from it, it cannot be over the heads of the inhabitants of both +those situations, at the same time. Besides, as the orbit of the moon is +very nearly parallel to that of the earth, she is never vertical, but to +the inhabitants of the torrid zone. + +_Caroline._ In the torrid zone, then, I hope you will grant that the +moon is immediately over, or opposite the spots where it is high water? + +_Mrs. B._ I cannot even admit that; for the ocean naturally partaking of +the earth's motion, in its rotation from west to east, the moon, in +forming a tide, has to contend against the eastern motion of the waves. +All matter, you know, by its inertia, makes some resistance to a change +of state; the waters, therefore, do not readily yield to the attraction +of the moon, and the effect of her influence is not complete, till three +hours after she has passed the meridian, where it is full tide. + +When a body is impelled by any force, its motion may continue, after the +impelling force ceases to act: this is the case with all projectiles. A +stone thrown from the hand, continues its motion for a length of time, +proportioned to the force given to it: there is a perfect analogy +between this effect, and the continued rise of the water, after the moon +has passed the meridian at any particular place. + +_Emily._ Pray what is the reason that the tide is three-quarters of an +hour later every day? + +_Mrs. B._ Because it is twenty-four hours and three-quarters before the +same meridian, on our globe, returns beneath the moon. The earth +revolves on its axis in about twenty-four hours; if the moon were +stationary, therefore, the same part of our globe would, every +twenty-four hours, return beneath the moon; but as during our daily +revolution, the moon advances in her orbit, the earth must make more +than a complete rotation, in order to bring the same meridian opposite +the moon: we are three-quarters of an hour in overtaking her. The tides, +therefore, are retarded, for the same reason that the moon rises later +by three-quarters of an hour, every day. + +We have now, I think, concluded the observations I had to make to you on +the subject of astronomy; at our next interview, I shall attempt to +explain to you the elements of hydrostatics. + + +Questions + +1. (Pg. 108) In what time does the moon revolve round the earth? what is +the inclination of her orbit? and how does she accompany the earth? + +2. (Pg. 108) As the moon revolves round the earth, and also accompanies +it in its annual revolution, in what form would you draw the moon's +orbit? + +3. (Pg. 109) What causes the moon always to present the same face to the +earth, and what must be the length of a day and night to its +inhabitants? + +4. (Pg. 109) Can the earth be seen from every part of the moon, and will +it always exhibit the same appearance? + +5. (Pg. 109) What are the changes of the moon called? + +6. (Pg. 109) How are these changes explained by fig. 2. plate 11? + +7. (Pg. 109) What is meant by her first quarter? + +8. (Pg. 109) What by her being horned, and her being gibbous? + +9. (Pg. 109) What by her being full? + +10. (Pg. 109) What by her third quarter? + +11. (Pg. 110) What is meant by her conjunction?--what by her being in +opposition?--what by her quadratures? + +12. (Pg. 110) By what are eclipses of the sun caused? + +13. (Pg. 110) What causes eclipses of the moon? + +14. (Pg. 110) What is meant by the moon's nodes? + +15. (Pg. 110) Why do not eclipses happen at every new and full moon? + +16. (Pg. 110) What causes partial eclipses of the moon? + +17. (Pg. 110) When the moon is exactly in one of her nodes, what length +of time will she be eclipsed? + +18. (Pg. 110) Are total eclipses of the sun frequent, and when they +happen what is their extent? + +19. (Pg. 111) What does this prove respecting the size of the moon? + +20. (Pg. 111) What is shown in fig. 1, plate 12? + +21. (Pg. 111) How are lunar eclipses visible, and what is proved by +their duration? + +22. (Pg. 111) What is illustrated by fig. 2, plate 12? + +23. (Pg. 111) What remark is made respecting those planets which have +several moons? + +24. (Pg. 111) What use is made of the eclipses of the satellites of +Jupiter? + +25. (Pg. 112) How is the latitude of a place usually found? + +26. (Pg. 112) By what other means may latitude be found? + +27. (Pg. 112) From what is longitude reckoned? + +28. (Pg. 112) How does the rotation of the earth upon its axis, govern +the time at different places? + +29. (Pg. 113) What two circumstances, if known, will enable you to find +your longitude from a given place? + +30. (Pg. 113) By what means may a captain find the time at London, and +in the place where his ship may be? + +31. (Pg. 113) How may the eclipses of Jupiter's satellites be used to +find the longitude? + +32. (Pg. 113) Give an example. + +33. (Pg. 114) How will you know whether the longitude is east or west? + +34. (Pg. 114) What is meant by the transit of a planet? + +35. (Pg. 114) Why can we see transits of Venus and Mercury only? + +36. (Pg. 114) By what are tides caused? + +37. (Pg. 114) Why is not a similar effect produced on the land? + +38. (Pg. 115) In what two parts of the world is it high water at the +same time? + +39. (Pg. 115) What circumstances respecting the decrease of attraction +are taken into account, in explaining the tides? + +40. (Pg. 115) How are the high tides at A and D, and the low ones at B +and C, in fig. 3. pl. 12, accounted for? + +41. (Pg. 116) Has the sun any influence on the tides, and why is it less +than that of the moon? + +42. (Pg. 116) What is meant by spring tides, and how are they produced? + +43. (Pg. 116) What by neap tides, and how are they caused? + +44. (Pg. 116) What circumstances affect the time of the tide in rivers, +bays, &c.? + +45. (Pg. 117) Why in the open ocean, is it high water, some hours after +the moon has passed the meridian? + +46. (Pg. 117) Why are the tides three-quarters of an hour later every +day? + + + + +CONVERSATION X. + +ON THE MECHANICAL PROPERTIES OF FLUIDS. + +DEFINITION OF A FLUID. DISTINCTION BETWEEN FLUIDS AND LIQUIDS. OF +NON-ELASTIC FLUIDS. SCARCELY SUSCEPTIBLE OF COMPRESSION. OF THE COHESION +OF FLUIDS. OF THEIR GRAVITATION. OF THEIR EQUILIBRIUM. OF THEIR +PRESSURE. OF SPECIFIC GRAVITY. OF THE SPECIFIC GRAVITY OF BODIES HEAVIER +THAN WATER. OF THOSE OF THE SAME WEIGHT AS WATER. OF THOSE LIGHTER THAN +WATER. OF THE SPECIFIC GRAVITY OF FLUIDS. + + +MRS. B. + +We have hitherto confined our attention to the mechanical properties of +solid bodies, which have been illustrated, and, I hope, thoroughly +impressed upon your memory, by the conversations we have subsequently +had, on astronomy. It will now be necessary for me to give you some +account of the mechanical properties of fluids--a science which, when +applied to liquids, is divided into two parts, hydrostatics and +hydraulics. Hydrostatics, treats of the weight and pressure of fluids; +and hydraulics, of the motion of fluids, and the effects produced by +this motion. A fluid is a substance which yields to the slightest +pressure. If you dip your hand into a basin of water, you are scarcely +sensible of meeting with any resistance. + +_Emily._ The attraction of cohesion is then, I suppose, less powerful in +fluids, than in solids? + +_Mrs. B._ Yes; fluids, generally speaking, are bodies of less density +than solids. From the slight cohesion, of the particles of fluids, and +the facility with which they slide over each other, it is inferred, that +they have but a slight attraction for each other, and that this +attraction is equal, in every position of their particles, and therefore +produces no resistance to a perfect freedom of motion among themselves. + +_Caroline._ Pray what is the distinction between a fluid and a liquid? + +_Mrs. B._ Liquids comprehend only one class of fluids. There is another +class, distinguished by the name of elastic fluids, or gases, which +comprehends the air of the atmosphere, and all the various kinds of air +with which you will become acquainted, when you study chemistry. Their +mechanical properties we shall examine hereafter, and confine our +attention this morning, to those of liquids, or non-elastic fluids. + +Water, and liquids in general, are scarcely susceptible of being +compressed, or squeezed into a smaller space, than that which they +naturally occupy. Such, however, is the extreme minuteness of their +particles, that by strong compression, they sometimes force their way +through the pores of the substance which confines them. This was shown +by a celebrated experiment, made at Florence many years ago. A hollow +globe of gold was filled with water, and on its being submitted to great +pressure, the water was seen to exude through the pores of the gold, +which it covered with a fine dew. Many philosophers, however, think that +this experiment is too much relied upon, as it does not appear that it +has ever been repeated; it is possible, therefore, that there may have +been some source of error, which was not discovered by the +experimenters. Fluids, appear to gravitate more freely, than solid +bodies; for the strong cohesive attraction of the particles of the +latter, in some measure counteracts the effect of gravity. In this +table, for instance, the cohesion of the particles of wood, enables four +slender legs to support a considerable weight. Were the cohesion +destroyed, or, in other words, the wood converted into a fluid, no +support could be afforded by the legs, for the particles no longer +cohering together, each would press separately and independently, and +would be brought to a level with the surface of the earth. + +_Emily._ This want of cohesion is then the reason why fluids can never +be formed into figures, or maintained in heaps; for though it is true +the wind raises water into waves, they are immediately afterwards +destroyed by gravity, and water always finds its level. + +_Mrs. B._ Do you understand what is meant by the level, or equilibrium +of fluids? + +_Emily._ I believe I do, though I feel rather at a loss to explain it. +Is not a fluid level when its surface is smooth and flat, as is the case +with all fluids, when in a state of rest? + +_Mrs. B._ Smooth, if you please, but not flat; for the definition of the +equilibrium of a fluid is, that every part of the surface is equally +distant from the point to which they gravitate, that is to say, from the +centre of the earth; hence the surface of all fluids must be spherical, +not flat, since they will partake of the spherical form of the globe. +This is very evident in large bodies of water, such as the ocean, but +the sphericity of small bodies of water, is so trifling, that their +surfaces appear flat. + +This level, or equilibrium of fluids, is the natural result of their +particles gravitating independently of each other; for when any particle +of a fluid, accidentally finds itself elevated above the rest, it is +attracted down to the level of the surface of the fluid, and the +readiness with which fluids yield to the slightest impression, will +enable the particle by its weight, to penetrate the surface of the +fluid, and mix with it. + +_Caroline._ But I have seen a drop of oil, float on the surface of +water, without mixing with it. + +_Mrs. B._ They do not mix, because their particles repel each other, and +the oil rises to the surface, because oil is a lighter liquid than +water. If you were to pour water over it, the oil would still rise, +being forced up by the superior gravity of the water. Here is an +instrument called a spirit-level, (fig. 1, plate 13.) which is +constructed upon the principle of the equilibrium of fluids. It consists +of a short tube A B, closed at both ends, and containing a little water, +or more commonly some spirits: it is so nearly filled, as to leave only +a small bubble of air; when the tube is perfectly horizontal, this +bubble will occupy the middle of it, but when not perfectly horizontal, +the water runs to the lower, and the bubble of air or spirit rises to +the upper end; by this instrument, the level of any situation, to which +we apply it, may be ascertained. + +From the strong cohesion of their particles, you may therefore consider +solid bodies as gravitating in masses, while every particle of a fluid +may be considered as separate, and gravitating independently of each +other. Hence the resistance of a fluid, is considerably less, than that +of a solid body; for the resistance of the particles, acting separately, +is more easily overcome. + +_Emily._ A body of water, in falling, does certainly less injury than a +solid body of the same weight. + +_Mrs. B._ The particles of fluids, acting thus independently, press +against each other in every direction, not only downwards, but upwards, +and laterally or sideways; and in consequence of this equality of +pressure, every particle remains at rest, in the fluid. If you agitate +the fluid, you disturb this equality of pressure, and the fluid will +not rest, till its equilibrium is restored. + +[Illustration: PLATE XIII.] + +_Caroline._ The pressure downwards is very natural; it is the effect of +gravity; one particle, weighing upon another, presses on it; but the +pressure sideways, and particularly the pressure upwards, I cannot +understand. + +_Mrs. B._ If there were no lateral pressure, water would not run out of +an opening on the side of a vessel. If you fill a vessel with sand, it +will not continue to run out of such an opening, because there is +scarcely any lateral pressure among its particles. + +_Emily._ When water runs out of the side of a vessel, is it not owing to +the weight of the water, above the opening? + +_Mrs. B._ If the particles of fluids were arranged in regular columns, +thus, (fig. 2.) there would be no lateral pressure, for when one +particle is perpendicularly above the other, it can only press +downwards; but as it must continually happen, that a particle presses +between two particles beneath, (fig. 3.) these last, must suffer a +lateral pressure. + +_Emily._ The same as when a wedge is driven into a piece of wood, and +separates the parts, laterally. + +_Mrs. B._ Yes. The lateral pressure proceeds, therefore, entirely from +the pressure downwards, or the weight of the liquid above; and +consequently, the lower the orifice is made in the vessel, the greater +will be the velocity of the water rushing out of it. Here is a vessel of +water (fig. 5.), with three stop cocks at different heights; we shall +open them, and you will see with what different degrees of velocity, the +water issues from them. Do you understand this, Caroline? + +_Caroline._ Oh yes. The water from the upper spout, receiving but a +slight pressure, on account of its vicinity to the surface, flows but +gently; the second cock, having a greater weight above it, the water is +forced out with greater velocity, whilst the lowest cock, being near the +bottom of the vessel, receives the pressure of almost the whole body of +water, and rushes out with the greatest impetuosity. + +_Mrs. B._ Very well; and you must observe, that as the lateral pressure, +is entirely owing to the pressure downwards, it is not affected by the +horizontal dimensions of the vessel, which contains the water, but +merely by its depth; for as every particle acts independently of the +rest, it is only the column of particles immediately above the orifice, +that can weigh upon, and press out the water. + +_Emily._ The breadth and width of the vessel then, can be of no +consequence in this respect. The lateral pressure on one side, in a +cubical vessel, is, I suppose, not so great as the pressure downwards +upon the bottom. + +_Mrs. B._ No; in a cubical vessel, the pressure downwards will be double +the lateral pressure on one side; for every particle at the bottom of +the vessel is pressed upon, by a column of the whole depth of the fluid, +whilst the lateral pressure diminishes from the bottom upwards to the +surface, where the particles have no pressure. + +_Caroline._ And from whence proceeds the pressure of fluids upwards? +that seems to me the most unaccountable, as it is in direct opposition +to gravity. + +_Mrs. B._ And yet it is in consequence of their pressure downwards. +When, for example, you pour water into a tea-pot, the water rises in the +spout, to a level with the water in the pot. The particles of water at +the bottom of the pot, are pressed upon by the particles above them; to +this pressure they will yield, if there is any mode of making way for +the superior particles, and as they cannot descend, they will change +their direction, and rise in the spout. + +Suppose the tea-pot to be filled with columns of particles of water, +similar to that described in fig. 4., the particle 1, at the bottom, +will be pressed laterally by the particle 2, and by this pressure be +forced into the spout, where, meeting with the particle 3, it presses it +upwards, and this pressure will be continued from 3 to 4, from 4 to 5, +and so on, till the water in the spout, has risen to a level with that +in the pot. + +_Emily._ If it were not for this pressure upwards, forcing the water to +rise in the spout, the equilibrium of the fluid would be destroyed. + +_Caroline._ True; but then a tea-pot is wide and large, and the weight +of so great a body of water as the pot will contain, may easily force up +and support so small a quantity, as will fill the spout. But would the +same effect be produced, if the spout and the pot, were of equal +dimensions? + +_Mrs. B._ Undoubtedly it would. You may even reverse the experiment, by +pouring water into the spout, and you will find that the water will rise +in the pot, to a level with that in the spout; for the pressure of the +small quantity of water in the spout, will force up and support, the +larger quantity in the pot. In the pressure upwards, as well as that +laterally, you see that the force of pressure, depends entirely on the +height, and is quite independent of the horizontal dimensions of the +fluid. + +As a tea-pot is not transparent, let us try the experiment by filling +this large glass goblet, by means of this narrow tube, (fig. 6.) + +_Caroline._ Look, Emily, as Mrs. B. fills it, how the water rises in the +goblet, to maintain an equilibrium with that in the tube. + +Now, Mrs. B., will you let me fill the tube, by pouring water into the +goblet? + +_Mrs. B._ That is impossible. However, you may try the experiment, and I +doubt not that you will be able to account for its failure. + +_Caroline._ It is very singular, that if so small a column of water as +is contained in the tube, can force up and support the whole contents of +the goblet; that the weight of all the water in the goblet, should not +be able to force up the small quantity required to fill the tube:--oh, I +see now the reason, the water in the goblet, cannot force that in the +tube above its level, and as the end of the tube, is considerably higher +than the goblet, it can never be filled by pouring water into the +goblet. + +_Mrs. B._ And if you continue to pour water into the goblet when it is +full, the water will run over, instead of rising above its level in the +tube. + +I shall now explain to you the meaning of the _specific gravity_ of +bodies. + +_Caroline._ What! is there another species of gravity, with which we are +not yet acquainted? + +_Mrs. B._ No: the specific gravity of a body, means simply its weight, +compared with that of another body, of the same size. When we say, that +substances, such as lead, and stones, are heavy, and that others, such +as paper and feathers, are light, we speak comparatively; that is to +say, that the first are heavy, and the latter light, in comparison with +the generality of substances in nature. Would you call wood, and chalk, +light or heavy bodies? + +_Caroline._ Some kinds of wood are heavy, certainly, as oak and +mahogany; others are light, as cedar and poplar. + +_Emily._ I think I should call wood in general, a heavy body; for cedar +and poplar, are light, only in comparison to wood of a heavier +description. I am at a loss to determine whether chalk should be ranked +as a heavy, or a light body; I should be inclined to say the former, if +it was not that it is lighter than most other minerals. I perceive that +we have but vague notions of light and heavy. I wish there was some +standard of comparison, to which we could refer the weight of all other +bodies. + +_Mrs. B._ The necessity of such a standard, has been so much felt, that +a body has been fixed upon for this purpose. What substance do you think +would be best calculated to answer this end? + +_Caroline._ It must be one generally known, and easily obtained; lead or +iron, for instance. + +_Mrs. B._ The metals, would not answer the purpose well, for several +reasons; they are not always equally compact, and they are rarely quite +pure; two pieces of iron, for instance, although of the same size, might +not, from the causes mentioned, weigh exactly alike. + +_Caroline._ But, Mrs. B., if you compare the weight, of equal quantities +of different bodies, they will all be alike. You know the old saying, +that a pound of feathers, is as heavy as a pound of lead? + +_Mrs. B._ When therefore we compare the weight of different kinds of +bodies, it would be absurd to take quantities of equal _weight_, we must +take quantities of equal _bulk_; pints or quarts, not ounces or pounds. + +_Caroline._ Very true; I perplexed myself by thinking that quantity +referred to weight, rather than to measure. It is true, it would be as +absurd to compare bodies of the same size, in order to ascertain which +was largest, as to compare bodies of the same weight, in order to +discover which was heaviest. + +_Mrs. B._ In estimating the specific gravity of bodies, therefore, we +must compare equal bulks, and we shall find that their specific gravity, +will be proportional to their weights. The body which has been adopted +as a standard of reference, is distilled, or rain water. + +_Emily._ I am surprised that a fluid should have been chosen for this +purpose, as it must necessarily be contained in some vessel, and the +weight of the vessel, will require to be deducted. + +_Mrs. B._ You will find that the comparison will be more easily made +with a fluid, than with a solid; and water you know can be every where +obtained. In order to learn the specific gravity of a solid body, it is +not necessary to put a certain measure of it in one scale, and an equal +measure of water into the other scale: but simply to weigh the body +under trial, first in air, and then in water. If you weigh a piece of +gold, in a glass of water, will not the gold displace just as much +water, as is equal to its own bulk? + +_Caroline._ Certainly, where one body is, another cannot be at the same +time; so that a sufficient quantity of water must be removed, in order +to make way for the gold. + +_Mrs. B._ Yes, a cubic inch of water, to make room for a cubic inch of +gold; remember that the bulk, alone, is to be considered; the weight, +has nothing to do with the quantity of water displaced, for an inch of +gold, does not occupy more space, and therefore will not displace more +water, than an inch of ivory, or any other substance, that will sink in +water. + +Well, you will perhaps be surprised to hear that the gold will weigh +less in water, than it did out of it? + +_Emily._ And for what reason? + +_Mrs. B._ On account of the upward pressure of the particles of water, +which in some measure supports the gold, and by so doing, diminishes its +weight. If the body immersed in water, was of the same weight as that +fluid, it would be wholly supported by it, just as the water which it +displaces, was supported, previous to its making way for the solid body. +If the body is heavier than the water, it cannot be wholly supported by +it; but the water will offer some resistance to its descent. + +_Caroline._ And the resistance which water offers to the descent of +heavy bodies immersed in it, (since it proceeds from the upward pressure +of the particles of the fluid,) must in all cases, I suppose, be the +same? + +_Mrs. B._ Yes: the resistance of the fluid, is proportioned to the bulk, +and not to the weight, of the body immersed in it; all bodies of the +same size, therefore, lose the same quantity of their weight in water. +Can you form any idea what this loss will be? + +_Emily._ I should think it would be equal to the weight of the water +displaced; for, since that portion of the water was supported before the +immersion of the solid body, an equal weight of the solid body, will be +supported. + +_Mrs. B._ You are perfectly right; a body weighed in water, loses just +as much of its weight, as is equal to that of the water it displaces; so +that if you were to put the water displaced, into the scale to which the +body is suspended, it would restore the balance. + +You must observe, that when you weigh a body in water, in order to +ascertain its specific gravity, you must not sink the dish of the +balance in the water; but either suspend the body to a hook at the +bottom of the dish, or else take off the dish, and suspend to the arm of +the balance a weight to counterbalance the other dish, and to this +attach the solid to be weighed, (fig. 7.) Now suppose that a cubic inch +of gold, weighed 19 ounces out of water, and lost one ounce of its +weight by being weighed in water, what would be its specific gravity? + +_Caroline._ The cubic inch of water it displaced, must weigh that one +ounce; and as a cubic inch of gold, weighs 19 ounces, gold is 19 times, +as heavy as water. + +_Emily._ I recollect having seen a table of the comparative weights of +bodies, in which gold appeared to me to be estimated at 19 thousand +times, the weight of water. + +_Mrs. B._ You misunderstood the meaning of the table. In the estimation +you allude to, the weight of water was reckoned at 1000. You must +observe, that the weight of a substance when not compared to that of any +other, is perfectly arbitrary; and when water is adopted as a standard, +we may denominate its weight by any number we please; but then the +weight of all bodies tried by this standard, must be signified by +proportional numbers. + +_Caroline._ We may call the weight of water, for example, one, and then +that of gold, would be nineteen; or if we choose to call the weight of +water 1000, that of gold would be 19,000. In short, specific gravity, +means how many times more a body weighs, than an equal bulk of water. + +_Mrs. B._ It is rather the weight of a body compared with a portion of +water equal to it in bulk; for the specific gravity of many substances, +is less than that of water. + +_Caroline._ Then you cannot ascertain the specific gravity of such +substances, in the same manner as that of gold; for a body that is +lighter than water, will float on its surface, without displacing any of +it. + +_Mrs. B._ If a body were absolutely without weight, it is true that it +would not displace a drop of water, but the bodies we are treating of, +have all some weight, however small; and will, therefore, displace some +quantity. If the body be lighter than water, it will not sink to a level +with its surface, and therefore it will not displace so much water as is +equal to its bulk; but only so much, as is equal to its weight. A ship, +you must have observed, sinks to some depth in water, and the heavier it +is laden, the deeper it sinks, as it always displaces a quantity of +water, equal to its own weight. + +_Caroline._ But you said just now, that in the immersion of gold, the +bulk, and not the weight of body, was to be considered. + +_Mrs. B._ That is the case with all substances which are heavier than +water; but since those which are lighter, do not displace so much as +their own bulk, the quantity they displace is not a test of their +specific gravity. + +In order to obtain the specific gravity of a body which is lighter than +water, you must attach to it a heavy one, whose specific gravity is +known, and immerse them together; the specific gravity of the lighter +body, may then be easily calculated from observing the loss of weight it +produces, in the heavy body. + +_Emily._ But are there not some bodies which have exactly the same +specific gravity as water? + +_Mrs. B._ Undoubtedly; and such bodies will remain at rest in whatever +situation they are placed in water. Here is a piece of wood which I have +procured, because it is of a kind which is precisely the weight of an +equal bulk of water; in whatever part of this vessel of water you place +it, you will find that it will remain stationary. + +_Caroline._ I shall first put it at the bottom; from thence, of course, +it cannot rise, because it is not lighter than water. Now I shall place +it in the middle of the vessel; it neither rises nor sinks, because it +is neither lighter nor heavier than the water. Now I will lay it on the +surface of the water; but there it sinks a little--what is the reason of +that, Mrs. B.? + +_Mrs. B._ Since it is not lighter than the water, it cannot float upon +its surface; since it is not heavier than water, it cannot sink below +its surface: it will sink therefore, only till the upper surface of both +bodies are on a level, so that the piece of wood is just covered with +water. If you poured a few drops of water into the vessel, (so gently as +not to give them momentum) they would mix with the water at the surface, +and not sink lower. + +_Caroline._ I now understand the reason, why, in drawing up a bucket of +water out of a well, the bucket feels so much heavier when it rises +above the surface of the water in the well; for whilst you raise it in +the water, the water within the bucket being of the same specific +gravity as the water on the outside, will be wholly supported by the +upward pressure of the water beneath the bucket, and consequently very +little force will be required to raise it; but as soon as the bucket +rises to the surface of the well, you immediately perceive the increase +of weight. + +_Emily._ And how do you ascertain the specific gravity of fluids? + +_Mrs. B._ By means of an hydrometer; this instrument is made of various +materials, and in different forms, one of which I will show you. It +consists of a thin brass ball A, (fig. 8, plate 13.) with a graduated +tube B, and the specific gravity of the liquid, is estimated by the +depth to which the instrument sinks in it, or by the weight required to +sink it to a given depth. There is a small bucket C, suspended at the +lower end, and also a little dish on the graduated tube; into either of +these, small weights may be put, until the instrument sinks in the +fluid, to a mark on the tube B; the amount of weight necessary for this, +will enable you to discover the specific gravity of the fluid. + +I must now take leave of you; but there remain yet many observations to +be made on fluids: we shall, therefore, resume this subject at our next +interview. + + +Questions + +1. (Pg. 118) What are the two divisions of the science which treats of +the mechanical properties of liquids? + +2. (Pg. 118) Of what do hydrostatics and hydraulics treat? + +3. (Pg. 118) What is a fluid defined to be? + +4. (Pg. 118) From what is fluidity supposed to arise? + +5. (Pg. 118) Into what two classes are fluids divided? + +6. (Pg. 119) What is said of the incompressibility of liquids, and what +experiment is related? + +7. (Pg. 119) Ought this experiment to be considered as conclusive? + +8. (Pg. 119) Why do fluids appear to gravitate more freely than solids? + +9. (Pg. 120) When is a fluid said to be in equilibrium? + +10. (Pg. 120) What is there in the nature of a fluid, which causes it to +seek this level? + +11. (Pg. 120) What circumstances occasion oil to float upon water? + +12. (Pg. 120) What is the nature and use of the instrument represented +in fig. 1, plate 13? + +13. (Pg. 120) What difference is there in the gravitation of solid +masses, and of fluids? + +14. (Pg. 121) What results as regards the pressure of fluids? + +15. (Pg. 121) How is this illustrated by fig. 2, 3, plate 13? + +16. (Pg. 121) From what does the lateral pressure proceed? and to what +is it proportioned, as exemplified in fig. 5, plate 13? + +17. (Pg. 122) Has the extent of the surface of a fluid, any effect upon +its pressure downwards? + +18. (Pg. 122) What will be the difference between the pressure upon the +bottom, and upon one side of a cubical vessel? + +19. (Pg. 122) What occasions the upward pressure, and how is it +explained by fig. 4, plate 13? + +20. (Pg. 123) How could the equilibrium of fluids be exemplified by +pouring water in at the spout of a tea-pot? + +21. (Pg. 123) How by the apparatus represented at fig. 6, plate 13? + +22. (Pg. 123) What is meant by the specific gravity of a body? + +23. (Pg. 123) What do we in common mean by calling a body heavy, or +light? + +24. (Pg. 124) Why would not the metals answer to compare other bodies +with? + +25. (Pg. 124) What must be supposed equal in estimating the specific +gravity of a body? + +26. (Pg. 124) What has been adopted as a standard for comparison? + +27. (Pg. 125) What is the first step in ascertaining the specific +gravity of a solid? + +28. (Pg. 125) What quantity of water will the solid displace? + +29. (Pg. 125) Why will a solid weigh less in water than in air, and to +what will the loss of weight be equal? + +30. (Pg. 126) What is the arrangement represented by fig. 7, plate 13? + +31. (Pg. 126) What is stated of gold as an example? + +32. (Pg. 126) In comparing a body with water, this is sometimes called +1000, what must be observed? + +33. (Pg. 126) What quantity of water is displaced, by a body floating +upon its surface? + +34. (Pg. 127) How can you find the specific gravity of a solid which is +lighter than water? + +35. (Pg. 127) What is observed of a body whose specific gravity is the +same as that of water? + +36. (Pg. 127) What is the reason that in drawing a bucket of water from +a well, its weight is not perceived until it rises above the surface? + +37. (Pg. 128) Describe the instrument represented by fig. 8, plate 13, +and also how, and for what it is used? + + + + +CONVERSATION XI. + +OF SPRINGS, FOUNTAINS, &c. + +OF THE ASCENT OF VAPOUR AND THE FORMATION OF CLOUDS. OF THE FORMATION +AND FALL OF RAIN, &c. OF THE FORMATION OF SPRINGS. OF RIVERS AND LAKES. +OF FOUNTAINS. + + +CAROLINE. + +There is a question I am very desirous of asking you, respecting fluids, +Mrs. B., which has often perplexed me. What is the reason that the great +quantity of rain which falls upon the earth and sinks into it, does not, +in the course of time, injure its solidity? The sun and the wind, I +know, dry the surface, but they have no effect on the interior parts, +where there must be a prodigious accumulation of moisture. + +_Mrs. B._ Do you not know, that, in the course of time, all the water +which sinks into the ground, rises out of it again? It is the same +water which successively forms seas, rivers, springs, clouds, rain, and +sometimes hail, snow and ice. If you will take the trouble of following +it through these various changes, you will understand why the earth is +not yet drowned, by the quantity of water which has fallen upon it, +since its creation; and you will even be convinced, that it does not +contain a single drop more water now, than it did at that period. + +Let us consider how the clouds were originally formed. When the first +rays of the sun warmed the surface of the earth, the heat, by separating +the particles of water, rendered them lighter than the air. This, you +know, is the case with steam or vapour. What then ensues? + +_Caroline._ When lighter than the air, it will naturally rise; and now I +recollect your telling us in a preceding lesson, that the heat of the +sun transformed the particles of water into vapour; in consequence of +which, it ascended into the atmosphere, where it formed clouds. + +_Mrs. B._ We have then already followed water through two of its +transformations; from water it becomes vapour, and from vapour clouds. + +_Emily._ But since this watery vapour is lighter than the air, why does +it not continue to rise; and why does it unite again, to form clouds? + +_Mrs. B._ Because the atmosphere diminishes in density, as it is more +distant from the earth. The vapour, therefore, which the sun causes to +exhale, not only from seas, rivers, and lakes, but likewise from the +moisture on the land, rises till it reaches a region of air of its own +specific gravity; and there, you know, it will remain stationary. By the +frequent accession of fresh vapour, it gradually accumulates, so as to +form those large bodies of vapour, which we call clouds: and the +particles, at length uniting, become too heavy for the air to support, +and fall to the ground. + +_Caroline._ They do fall to the ground, certainly, when it rains; but, +according to your theory, I should have imagined, that when the clouds +became too heavy, for the region of air in which they were situated, to +support them, they would descend, till they reached a stratum of air of +their own weight, and not fall to the earth; for as clouds are formed of +vapour, they cannot be so heavy as the lowest regions of the atmosphere, +otherwise the vapour would not have risen. + +_Mrs. B._ If you examine the manner in which the clouds descend, it will +obviate this objection. In falling, several of the watery particles +come within the sphere of each other's attraction, and unite in the form +of a drop of water. The vapour thus transformed into a shower, is +heavier than any part of the atmosphere, and consequently descends to +the earth. + +_Caroline._ How wonderfully curious! + +_Mrs. B._ It is impossible to consider any part of nature attentively, +without being struck with admiration at the wisdom it displays; and I +hope you will never contemplate these wonders, without feeling your +heart glow with admiration and gratitude, towards their bounteous +Author. Observe, that if the waters were never drawn out of the earth, +all vegetation would be destroyed by the excess of moisture; if, on the +other hand, the plants were not nourished and refreshed by occasional +showers, the drought would be equally fatal to them. If the clouds +constantly remained in a state of vapour, they might, as you remarked, +descend into a heavier stratum of the atmosphere, but could never fall +to the ground; or were the power of attraction more than sufficient to +convert the vapour into drops, it would transform the cloud into a mass +of water, which, instead of nourishing, would destroy the produce of the +earth. + +Water then ascends in the form of vapour, and descends in that of rain, +snow, or hail, all of which ultimately become water. Some of this falls +into the various bodies of water on the surface of the globe, the +remainder upon the land. Of the latter, part reascends in the form of +vapour, part is absorbed by the roots of vegetables, and part descends +into the earth, where it forms springs. + +_Emily._ Is there then no difference between rain water, and spring +water? + +_Mrs. B._ They are originally the same; but that portion of rain water +which goes to supply springs, dissolves a number of foreign particles, +which it meets with in its passage through the various soils it +traverses. + +_Caroline._ Yet spring water is more pleasant to the taste, appears more +transparent, and, I should have supposed, would have been more pure than +rain water. + +_Mrs. B._ No; excepting distilled water, rain water is the most pure we +can obtain; it is its purity which renders it insipid; whilst the +various salts and different ingredients, dissolved in spring water, give +it a species of flavour, which habit renders agreeable; these salts do +not, in any degree, affect its transparency; and the filtration it +undergoes, through gravel and sand, cleanses it from all foreign +matter, which it has not the power of dissolving. + +_Emily._ How is it that the rain water does not continue to descend by +its gravity, instead of collecting together, and forming springs? + +_Mrs. B._ When rain falls on the surface of the earth, it continues +making its way downwards through the pores and crevices in the ground. +When several drops meet in their subterraneous passage, they unite and +form a little rivulet; this, in its progress, meets with other rivulets +of a similar description, and they pursue their course together within +the earth, till they are stopped by some substance, such as rock, or +clay, which they cannot penetrate. + +_Caroline._ But you say that there is some reason to believe that water +can penetrate even the pores of gold, and it cannot meet with a +substance more dense? + +_Mrs. B._ But if water penetrate the pores of gold, it is only when +under a strong compressive force, as in the Florentine experiment; now +in its passage towards the centre of the earth, it is acted upon by no +other power than gravity, which is not sufficient to make it force its +way, even through a stratum of clay. This species of earth, though not +remarkably dense, being of great tenacity, will not admit the particles +of water to pass. When water encounters any substance of this nature, +therefore, its progress is stopped, and it is diffused through the +porous earth, and sometimes the pressure of the accumulating waters, +forms a bed, or reservoir. This will be more clearly explained by fig. +9, plate 13, which represents a section, of the interior of a hill or +mountain. A, is a body of water, such as I have described, which, when +filled up as high as B, (by the continual accession of water it receives +from the ducts or rivulets _a_, _a_, _a_, _a_,) finds a passage out of +the cavity, and, impelled by gravity, it runs on, till it makes its way +out of the ground at the side of the hill, and there forms a spring, C. + +_Caroline._ Gravity impels downwards towards the centre of the earth; +and the spring in this figure runs in an horizontal direction. + +_Mrs. B._ Not entirely. There is some declivity from the reservoir, to +the spot where the water issues out of the ground; and gravity, you +know, will bring bodies down an inclined plane, as well as in a +perpendicular direction. + +_Caroline._ But though the spring may descend, on first issuing, it must +afterwards rise to reach the surface of the earth; and that is in direct +opposition to gravity. + +_Mrs. B._ A spring can never rise above the level of the reservoir +whence it issues; it must, therefore, find a passage to some part of the +surface of the earth, that is lower, or nearer the centre, than the +reservoir. It is true that, in this figure, the spring rises in its +passage from B to C; but this, I think, with a little reflection, you +will be able to account for. + +_Emily._ Oh, yes; it is owing to the pressure of fluids upwards; and the +water rises in the duct, upon the same principle as it rises in the +spout of a tea-pot; that is to say, in order to preserve an equilibrium +with the water in the reservoir. Now I think I understand the nature of +springs: the water will flow through a duct, whether ascending or +descending, provided it never rises higher than the reservoir. + +_Mrs. B._ Water may thus be conveyed to every part of a town, and to the +upper part of the houses, if it is originally brought from a height, +superior to any to which it is conveyed. Have you never observed, when +the pavements of the streets have been mending, the pipes which serve as +ducts for the conveyance of the water through the town? + +_Emily._ Yes, frequently; and I have remarked that when any of these +pipes have been opened, the water rushes upwards from them, with great +velocity; which, I suppose, proceeds from the pressure of the water in +the reservoir, which forces it out. + +_Caroline._ I recollect having once seen a very curious glass, called +Tantalus's cup; it consists of a goblet, containing a small figure of a +man, and whatever quantity of water you pour into the goblet, it never +rises higher than the breast of the figure. Do you know how that is +contrived? + +_Mrs. B._ It is by means of a syphon, or bent tube, which is concealed +in the body of the figure. This tube rises through one of the legs, as +high as the breast, and there turning, descends through the other leg, +and from thence through the foot of the goblet, where the water runs +out. (fig. 1, plate 14.) When you pour water into the glass A, it must +rise in the syphon B, in proportion as it rises in the glass; and when +the glass is filled to a level with the upper part of the syphon, the +water will run out through the other leg of the figure, and will +continue running out, as fast as you pour it in; therefore the glass can +never fill any higher. + +_Emily._ I think the new well that has been made at our country-house, +must be of that nature. We had a great scarcity of water, and my father +has been at considerable expense to dig a well; after penetrating to a +great depth, before water could be found, a spring was at length +discovered, but the water rose only a few feet above the bottom of the +well; and sometimes it is quite dry. + +[Illustration: PLATE XIV.] + +_Mrs. B._ This has, however, no analogy to Tantalus's cup; but is owing +to the very elevated situation of your country-house. + +_Emily._ I believe I guess the reason. There cannot be a reservoir of +water near the summit of a hill; as in such a situation, there will not +be a sufficient number of rivulets formed, to supply one; and without a +reservoir, there can be no spring. In such situations, therefore, it is +necessary to dig very deep, in order to meet with a spring; and when we +give it vent, it can rise only as high as the reservoir from whence it +flows, which will be but little, as the reservoir must be situated at +some considerable depth below the summit of the hill. + +_Caroline._ Your explanation appears very clear and satisfactory; but I +can contradict it from experience. At the very top of a hill, near our +country-house, there is a large pond, and, according to your theory, it +would be impossible there should be springs in such a situation to +supply it with water. Then you know that I have crossed the Alps, and I +can assure you, that there is a fine lake on the summit of Mount Cenis, +the highest mountain we passed over. + +_Mrs. B._ Were there a lake on the summit of Mount Blanc, which is the +highest of the Alps, it would indeed be wonderful. But that on Mount +Cenis, is not at all contradictory to our theory of springs; for this +mountain is surrounded by others, much more elevated, and the springs +which feed the lake must descend from reservoirs of water, formed in +those mountains. This must also be the case with the pond on the top of +the hill; there is doubtless some more considerable hill in the +neighbourhood, which supplies it with water. + +_Emily._ I comprehend perfectly, why the water in our well never rises +high: but I do not understand why it should occasionally be dry. + +_Mrs. B._ Because the reservoir from which it flows, being in an +elevated situation, is but scantily supplied with water; after a long +drought, therefore, it may be drained, and the spring dry, till the +reservoir be replenished by fresh rains. It is not uncommon to see +springs flow with great violence in wet seasons, which at other times, +are perfectly dry. + +_Caroline._ But there is a spring in our grounds, which more frequently +flows in dry, than in wet weather; how is that to be accounted for? + +_Mrs. B._ The spring, probably, comes from a reservoir at a great +distance, and situated very deep in the ground: it is, therefore, some +length of time before the rain reaches the reservoir; and another +considerable portion must elapse, whilst the water is making its way, +from the reservoir, to the surface of the earth; so that the dry weather +may probably have succeeded the rains, before the spring begins to flow; +and the reservoir may be exhausted, by the time the wet weather sets in +again. + +_Caroline._ I doubt not but this is the case, as the spring is in a very +low situation, therefore, the reservoir may be at a great distance from +it. + +_Mrs. B._ Springs which do not constantly flow, are called intermitting, +and are occasioned by the reservoir being imperfectly supplied. +Independently of the situation, this is always the case, when the duct, +or ducts, which convey the water into the reservoir, are smaller than +those which carry it off. + +_Caroline._ If it runs out, faster than it runs in, it will of course +sometimes be empty. Do not rivers also, derive their source from +springs? + +_Mrs. B._ Yes, they generally take their source in mountainous +countries, where springs are most abundant. + +_Caroline._ I understood you that springs were more rare, in elevated +situations. + +_Mrs. B._ You do not consider that mountainous countries, abound equally +with high, and low situations. Reservoirs of water, which are formed in +the bosoms of mountains, generally find a vent, either on their +declivity, or in the valley beneath; while subterraneous reservoirs, +formed in a plain, can seldom find a passage to the surface of the +earth, but remain concealed, unless discovered by digging a well. When a +spring once issues at the surface of the earth, it continues its course +externally, seeking always a lower ground, for it can no longer rise. + +_Emily._ Then what is the consequence, if the spring, or, as I should +now rather call it, the rivulet, runs into a situation, which is +surrounded by higher ground? + +_Mrs. B._ Its course is stopped; the water accumulates, and it forms a +pool, pond, or lake, according to the dimensions of the body of water. +The lake of Geneva, in all probability, owes its origin to the Rhone, +which passes through it: if, when the river first entered the valley, +which now forms the bed of the Lake, it found itself surrounded by +higher grounds, its waters would there accumulate, till they rose to a +level with that part of the valley, where the Rhone now continues its +course beyond the Lake, and from whence it flows through valleys, +occasionally forming other small lakes, till it reaches the sea. + +_Emily._ And are not fountains, of the nature of springs? + +_Mrs. B._ Exactly. A fountain is conducted perpendicularly upwards, by +the spout or adjutage A, through which it flows; and it will rise nearly +as high as the reservoir B, from whence it proceeds. (Plate 14. fig. 2.) + +_Caroline._ Why not quite as high? + +_Mrs. B._ Because it meets with resistance from the air, in its ascent; +and its motion is impeded by friction against the spout, where it rushes +out. + +_Emily._ But if the tube through which the water rises be smooth, can +there be any friction? especially with a fluid, whose particles yield to +the slightest impression. + +_Mrs. B._ Friction, (as we observed in a former lesson,) may be +diminished by polishing, but can never be entirely destroyed; and though +fluids, are less susceptible of friction, than solid bodies, they are +still affected by it. Another reason why a fountain will not rise so +high as its reservoir, is, that as all the water which spouts up, has to +descend again, it in doing so, presses, or strikes against the under +parts, and forces them sideways, spreading the column into a head, and +rendering it both wider, and shorter, than it otherwise would be. + +At our next meeting, we shall examine the mechanical properties of the +air, which being an elastic fluid, differs in many respects, from +liquids. + + +Questions + +1. (Pg. 129) Why do not the frequent rains, fill the earth with water? + +2. (Pg. 129) Why will vapour rise? to what height will it ascend, and +what will it form? + +3. (Pg. 129) How may drops of rain be formed? + +4. (Pg. 130) What becomes of the water after it has fallen to the earth? + +5. (Pg. 130) What is the difference between rain water, and that from +springs? + +6. (Pg. 130) Why is rain more pure than spring water? + +7. (Pg. 130) Why is spring water more agreeable to the palate? + +8. (Pg. 131) What causes the water to collect and form springs? + +9. (Pg. 131) Why cannot water penetrate through clay? + +10. (Pg. 131) What is represented by fig. 9, plate 13? + +11. (Pg. 132) How can you account for its rising upwards, as represented +at C? + +12. (Pg. 132) In conveying water by means of pipes, how must the +reservoir be situated? + +13. (Pg. 132) What is the instrument called, which is represented in +plate 14, fig. 1,--and how does it operate? + +14. (Pg. 133) Why are wells rarely well supplied with water, in elevated +situations? + +15. (Pg. 133) When water is found in elevated situations, whence is it +supplied? + +16. (Pg. 133) Wells and springs, at some periods well supplied, fail at +others; how is this accounted for? + +17. (Pg. 134) Some springs flow abundantly in dry weather, which +occasionally fail in wet weather, how may this be explained? + +18. (Pg. 134) What is meant by intermitting springs? + +19. (Pg. 134) Whence do rivers, in general, derive their water? + +20. (Pg. 134) Why do springs abound more in mountainous, than in level +countries? + +21. (Pg. 135) How are lakes formed? + +22. (Pg. 135) What causes water to rise in fountains, and how is this +explained by figure 2, plate 14? + +23. (Pg. 135) Why will not the fountain rise to the height of the water +in the reservoir? + + + + +CONVERSATION XII. + +ON THE MECHANICAL PROPERTIES OF AIR. + +OF THE SPRING OR ELASTICITY OF THE AIR. OF THE WEIGHT OF THE AIR. +EXPERIMENTS WITH THE AIR PUMP. OF THE BAROMETER. MODE OF WEIGHING AIR. +SPECIFIC GRAVITY OF AIR. OF PUMPS. DESCRIPTION OF THE SUCKING PUMP. +DESCRIPTION OF THE FORCING PUMP. + + +MRS. B. + +At our last meeting we examined the properties of fluids in general, and +more particularly of such as are called non-elastic fluids, or liquids. + +There is another class of fluids, distinguished by the name of aeriform, +or elastic fluids, the principal of which is the air we breathe, which +surrounds the earth, and is called the atmosphere. + +_Emily._ There are then other kinds of air, besides the atmosphere? + +_Mrs. B._ Yes; a great variety; but they differ only in their chemical, +and not in their mechanical properties; and as it is the latter we are +to examine, we shall not at present inquire into their composition, but +confine our attention to the mechanical properties of elastic fluids in +general. + +_Caroline._ And from whence arises this difference, between elastic, and +non-elastic fluids? + +_Mrs. B._ There is no attraction of cohesion, between the particles of +elastic fluids; so that the expansive power of heat, has no adversary to +contend with, but gravity; any increase of temperature, therefore, +expands elastic fluids considerably, and a diminution, proportionally +condenses them. + +The most essential point, in which air, differs from other fluids is in +its spring or elasticity; that is to say, its power of increasing, or +diminishing in bulk, accordingly as it is more, or less, compressed: a +power of which I have informed you, liquids are almost wholly deprived. + +_Emily._ I think I understand the elasticity of the air very well from +what you formerly said of it; but what perplexes me is, its having +gravity; if it is heavy, and we are surrounded by it, why do we not feel +its weight? + +_Caroline._ It must be impossible to be sensible of the weight of such +infinitely small particles, as those of which the air is composed: +particles which are too small to be seen, must be too light to be felt. + +_Mrs. B._ You are mistaken, my dear; the air is much heavier than you +imagine; it is true, that the particles which compose it, are small; but +then, reflect on their quantity: the atmosphere extends in height, a +great number of miles from the earth, and its gravity is such, that a +man of middling stature, is computed (when the air is heaviest) to +sustain the weight of about 14 tons. + +_Caroline._ Is it possible! I should have thought such a weight would +have crushed any one to atoms. + +_Mrs. B._ That would, indeed, be the case, if it were not for the +equality of the pressure, on every part of the body; but when thus +diffused, we can bear even a much greater weight, without any +considerable inconvenience. In bathing we support the weight and +pressure of the water, in addition to that of the atmosphere; but +because this pressure is equally distributed over the body, we are +scarcely sensible of it; whilst if your shoulders, your head, or any +particular part of your frame, were loaded with the additional weight of +a hundred pounds, you would soon sink under the fatigue. Besides this, +our bodies contain air, the spring of which, counterbalances the weight +of the external air, and renders us insensible of its pressure. + +_Caroline._ But if it were possible to relieve me from the weight of the +atmosphere, should I not feel more light and agile? + +_Mrs. B._ On the contrary, the air within you, meeting with no external +pressure to restrain its elasticity, would distend your body, and at +length bursting some of the parts which confined it, put a period to +your existence. + +_Caroline._ This weight of the atmosphere, then, which I was so +apprehensive would crush me, is, in reality, essential to my +preservation. + +_Emily._ I once saw a person cupped, and was told that the swelling of +the part under the cup, was produced by taking away from that part, the +pressure of the atmosphere; but I could not understand how this pressure +produced such an effect. + +_Mrs. B._ The air pump affords us the means of making a great variety of +interesting experiments, on the weight, and pressure of the air: some +of them you have already seen. Do you not recollect, that in a vacuum +produced within the air pump, substances of various weights, fell to the +bottom in the same time; why does not this happen in the atmosphere? + +_Caroline._ I remember you told us it was owing to the resistance which +light bodies meet with, from the air, during their fall. + +_Mrs. B._ Or, in other words, to the support which they received from +the air, and which prolonged the time of their fall. Now, if the air +were destitute of weight, how could it support other bodies, or retard +their fall? + +I shall now show you some other experiments, which illustrate, in a +striking manner, both the weight, and elasticity of air. I shall tie a +piece of bladder over this glass receiver, which, you will observe, is +open at the top as well as below. + +_Caroline._ Why do you wet the bladder first? + +_Mrs. B._ It expands by wetting, and contracts in drying; it is also +more soft and pliable when wet, so that I can make it fit better, and +when dry, it will be tighter. We must hold it to the fire in order to +dry it; but not too near, lest it should burst by sudden contraction. +Let us now fix it on the air pump, and exhaust the air from underneath +it--you will not be alarmed if you hear a noise? + +_Emily._ It was as loud as the report of a gun, and the bladder is +burst! Pray explain how the air is concerned in this experiment. + +_Mrs. B._ It is the effect of the weight of the atmosphere, on the upper +surface of the bladder, when I had taken away the air from the under +surface, so that there was no longer any reaction to counterbalance the +pressure of the atmosphere, on the receiver. You observed how the +bladder was pressed inwards, by the weight of the external air, in +proportion as I exhausted the receiver: and before a complete vacuum was +formed, the bladder, unable to sustain the violence of the pressure, +burst with the explosion you have just heard. + +I shall now show you an experiment, which proves the expansion of the +air, contained within a body, when it is relieved from the pressure of +the external air. You would not imagine that there was any air contained +within this shrivelled apple, by its appearance; but take notice of it +when placed within a receiver, from which I shall exhaust the air. + +_Caroline._ How strange! it grows quite plump, and looks like a +fresh-gathered apple. + +_Mrs. B._ But as soon as I let the air again into the receiver, the +apple, you see, returns to its shrivelled state. When I took away the +pressure of the atmosphere, the air within the apple, expanded, and +swelled it out; but the instant the atmospheric air was restored, the +expansion of the internal air, was checked and repressed, and the apple +shrunk to its former dimensions. + +You may make a similar experiment with this little bladder, which you +see is perfectly flaccid, and appears to contain no air: in this state I +shall tie up the neck of the bladder, so that whatever air remains +within it, may not escape, and then place it under the receiver. Now +observe, as I exhaust the receiver, how the bladder distends; this +proceeds from the great dilatation of the small quantity of air, which +was enclosed within the bladder, when I tied it up; but as soon as I let +the air into the receiver, that which the bladder contains, condenses +and shrinks into its small compass, within the folds of the bladder. + +_Emily._ These experiments are extremely amusing, and they afford clear +proofs, both of the weight, and elasticity of the air; but I should like +to know, exactly, how much the air weighs. + +_Mrs. B._ A column of air reaching to the top of the atmosphere, and +whose base is a square inch, weighs about 15 lbs. therefore, every +square inch of our bodies, sustains a weight of 15 lbs.: and if you wish +to know the weight of the whole of the atmosphere, you must reckon how +many square inches there are on the surface of the globe, and multiply +them by 15. + +_Emily._ But can we not ascertain the weight of a small quantity of air? + +_Mrs. B._ With perfect ease. I shall exhaust the air from this little +bottle, by means of the air pump: and having emptied the bottle of air, +or, in other words, produced a vacuum within it, I secure it by turning +this screw adapted to its neck: we may now find the exact weight of this +bottle, by putting it into one of the scales of a balance. It weighs, +you see, just two ounces; but when I turn the screw, so as to admit the +air into the bottle, the scale which contains it, preponderates. + +_Caroline._ No doubt the bottle filled with air, is heavier than the +bottle void of air; and the additional weight required to bring the +scales again to a balance, must be exactly that of the air which the +bottle now contains. + +_Mrs. B._ That weight, you see, is almost two grains. The dimensions of +this bottle, are six cubic inches. Six cubic inches of air, therefore, +at the temperature of this room, weighs nearly 2 grains. + +_Caroline._ Why do you observe the temperature of the room, in +estimating the weight of the air? + +_Mrs. B._ Because heat rarefies air, and renders it lighter; therefore +the warmer the air is, which you weigh, the lighter it will be. + +If you should now be desirous of knowing the specific gravity of this +air, we need only fill the same bottle, with water, and thus obtain the +weight of an equal quantity of water--which you see is 1515 grs.; now by +comparing the weight of water, to that of air, we find it to be in the +proportion of about 800 to 1. + +As you are acquainted with decimal arithmetic, you will understand what +I mean, when I tell you, that water being called 1000, the specific +gravity of air, will be 1.2. + +I will show you another instance, of the weight of the atmosphere, which +I think will please you: you know what a barometer is? + +_Caroline._ It is an instrument which indicates the state of the +weather, by means of a tube of quicksilver; but how, I cannot exactly +say. + +_Mrs. B._ It is by showing the weight of the atmosphere, which has great +influence on the weather. The barometer, is an instrument extremely +simple in its construction. In order that you may understand it, I will +show you how it is made. I first fill with mercury, a glass tube A B, +(fig. 3, plate 14.) about three feet in length, and open only at one +end; then stopping the open end, with my finger, I immerse it in a cup +C, containing a little mercury. + +_Emily._ Part of the mercury which was in the tube, I observe, runs down +into the cup; but why does not the whole of it subside, for it is +contrary to the law of the equilibrium of fluids, that the mercury in +the tube, should not descend to a level with that in the cup? + +_Mrs. B._ The mercury that has fallen from the tube, into the cup, has +left a vacant space in the upper part of the tube, to which the air +cannot gain access; this space is therefore a perfect vacuum; the +mercury in the tube, is relieved from the pressure of the atmosphere, +whilst that in the cup, remains exposed to it. + +_Caroline._ Oh, now I understand it; the pressure of the air on the +mercury in the cup, forces it to rise in the tube, where there is not +any air to counteract the external pressure. + +_Emily._ Or rather supports the mercury in the tube, and prevents it +from falling. + +_Mrs. B._ That comes to the same thing; for the power that can support +mercury in a vacuum, would also make it ascend, when it met with a +vacuum. + +Thus you see, that the equilibrium of the mercury is destroyed, only to +preserve the general equilibrium of fluids. + +_Caroline._ But this simple apparatus is, in appearance, very unlike a +barometer. + +_Mrs. B._ It is all that is essential to a barometer. The tube and the +cup, or a cistern of mercury, are fixed on a board, for the convenience +of suspending it; the brass plate on the upper part of the board, is +graduated into inches, and tenths of inches, for the purpose of +ascertaining the height at which the mercury stands in the tube; and the +small moveable metal plate, serves to show that height, with greater +accuracy. + +_Emily._ And at what height, will the weight of the atmosphere sustain +the mercury? + +_Mrs. B._ About 28 or 29 inches, as you will see by this barometer; but +it depends upon the weight of the atmosphere, which varies much, in +different states of the weather. The greater the pressure of the air on +the mercury in the cup, the higher it will ascend in the tube. Now can +you tell me whether the air is heavier, in wet, or in dry weather? + +_Caroline._ Without a moment's reflection, the air must be heaviest in +wet weather. It is so depressing, and makes one feel so heavy, while in +fine weather, I feel as light as a feather, and as brisk as a bee. + +_Mrs. B._ Would it not have been better to have answered with a moment's +reflection, Caroline? It would have convinced you, that the air must be +heaviest in dry weather; for it is then, that the mercury is found to +rise in the tube, and consequently, the mercury in the cup, must be most +pressed by the air. + +_Caroline._ Why then does the air feel so heavy, in bad weather? + +_Mrs. B._ Because it is less salubrious, when impregnated with damp. The +lungs, under these circumstances, do not play so freely, nor does the +blood circulate so well; thus obstructions are frequently occasioned in +the smaller vessels, from which arise colds, asthmas, agues, fevers, &c. + +_Emily._ Since the atmosphere diminishes in density, in the upper +regions, is not the air more rare, upon a hill, than in a plain; and +does the barometer indicate this difference? + +_Mrs. B._ Certainly. This instrument, is so exact in its indications, +that it is used for the purpose of measuring the height of mountains, +and of estimating the elevation of balloons; the mercury descending in +the tube, as you ascend to a greater height. + +_Emily._ And is no inconvenience experienced, from the thinness of the +air, in such elevated situations? + +_Mrs. B._ Oh, yes; frequently. It is sometimes oppressive, from being +insufficient for respiration; and the expansion which takes place, in +the more dense air contained within the body, is often painful: it +occasions distention, and sometimes causes the bursting of the smaller +blood-vessels, in the nose, and ears. Besides in such situations, you +are more exposed, both to heat, and cold; for though the atmosphere is +itself transparent, its lower regions, abound with vapours, and +exhalations, from the earth, which float in it, and act in some degree +as a covering, which preserves us equally from the intensity of the +sun's rays, and from the severity of the cold. + +_Caroline._ Pray, Mrs. B., is not the thermometer constructed on the +same principles as the barometer? + +_Mrs. B._ Not at all. The rise and fall of the fluid in the thermometer, +is occasioned by the expansive power of heat, and the condensation +produced by cold: the air has no access to it. An explanation of it +would, therefore, be irrelevant to our present subject. + +_Emily._ I have been reflecting, that since it is the weight of the +atmosphere, which supports the mercury, in the tube of a barometer, it +would support a column of any other fluid, in the same manner. + +_Mrs. B._ Certainly; but as mercury, is heavier than all other fluids, +it will support a higher column, of any other fluid; for two fluids are +in equilibrium, when their height varies, inversely as their densities. +We find the weight of the atmosphere, is equal to sustaining a column of +water, for instance, of no less than 32 feet above its level. + +_Caroline._ The weight of the atmosphere, is then, as great as that of a +body of water of 32 feet in height. + +_Mrs. B._ Precisely; for a column of air, of the height of the +atmosphere, is equal to a column of water of about 32 feet, or one of +mercury, of from 28 to 29 inches. + +The common pump, is dependent on this principle. By the act of pumping, +the pressure of the atmosphere is taken off the water, which, in +consequence, rises. + +The body of a pump, consists of a large tube or pipe, whose lower end is +immersed in the water which it is designed to raise. A kind of stopper, +called a piston, is fitted to this tube, and is made to slide up and +down it, by means of a metallic rod, fastened to the centre of the +piston. + +_Emily._ Is it not similar to the syringe, or squirt, with which you +first draw in, and then force out water? + +_Mrs. B._ It is; but you know that we do not wish to force the water out +of the pump, at the same end of the pipe, at which we draw it in. The +intention of a pump, is to raise water from a spring, or well; the pipe +is, therefore, placed perpendicularly over the water, which enters it at +the lower extremity, and it issues at a horizontal spout, towards the +upper part of the pump; to effect this, there are, besides the piston, +two contrivances called valves. The pump, therefore, is rather a more +complicated piece of machinery, than the syringe. + +_Caroline._ Pray, Mrs. B., is not the leather, which covers the opening, +in the lower board of a pair of bellows, a kind of valve? + +_Mrs. B._ It is, valves are made in various forms; any contrivance, +which allows a fluid to pass in one direction, and prevents its return, +is called a valve; that of the bellows, and of the common pump, resemble +each other, exactly. You can now, I think, understand the structure of +the pump. + +Its various parts, are delineated in this figure: (fig. 4. plate 14.) A +B is the pipe, or body of the pump, P the piston, V a valve, or little +door in the piston, which, opening upwards, admits the water to rise +through it, but prevents its returning, and Y, is a similar valve, +placed lower down in the body of the pump; H is the handle, which in +this model, serves to work the piston. + +When the pump is in a state of inaction, the two valves are closed by +their own weight; but when, by working the handle of the pump, the +piston ascends; it raises a column of air which rested upon it, and +produces a vacuum, between the piston, and the lower valve Y; the air +beneath this valve, which is immediately over the surface of the water, +consequently expands, and forces its way through it; the water, then, +relieved from the pressure of the air, ascends into the pump. A few +strokes of the handle, totally excludes the air from the body of the +pump, and fills it with water, which, having passed through both the +valves, runs out at the spout. + +_Caroline._ I understand this perfectly. When the piston is elevated, +the air, and the water, successively rise in the pump, for the same +reason as the mercury, rises in the barometer. + +_Emily._ I thought that water was drawn up into a pump, by suction, in +the same manner as water may be sucked through a straw. + +_Mrs. B._ It is so, into the body of the pump; for the power of suction, +is no other than that of producing a vacuum over one part of the liquid, +into which vacuum the liquid is forced, by the pressure of the +atmosphere, on another part. The action of sucking through a straw, +consists in drawing in, and confining the breath, so as to produce a +vacuum in the mouth; in consequence of which, the air within the straw, +rushes into the mouth, and is followed by the liquid, into which, the +lower end of the straw, is immersed. The principle, you see, is the +same, and the only difference consists in the mode of producing a +vacuum. In suction, the muscular powers answer the purpose of the piston +and valve. + +_Emily._ Water cannot, then, be raised by a pump, above 32 feet; for the +pressure of the atmosphere will not sustain a column of water, above +that height. + +_Mrs. B._ I beg your pardon. It is true that there must never be so +great a distance as 32 feet, from the level of the water in the well, to +the valve in the piston, otherwise the water would not rise through that +valve; but when once the water has passed that opening, it is no longer +the pressure of air on the reservoir, which makes it ascend; it is +raised by lifting it up, as you would raise it in a bucket, of which the +piston formed the bottom. This common pump is, therefore, called the +sucking, or lifting pump, as it is constructed on both these principles. +The rod to which the piston is attached, must be made sufficiently long, +to allow the piston to be within 32 feet of the surface of the water in +the well, however deep it may be. There is another sort of pump, called +the forcing pump: it consists of a forcing power, added to the sucking +part of the pump. This additional power, is exactly on the principle of +the syringe: by raising the piston, you draw the water into the pump, +and by causing it to descend, you force the water out. + +_Caroline._ But the water must be forced out at the upper part of the +pump; and I cannot conceive how that can be done by the descent of the +piston. + +_Mrs. B._ Figure 5, plate 14, will explain the difficulty. The large +pipe, A B, represents the sucking part of the pump, which differs from +the lifting pump, only in its piston P, being unfurnished with a valve, +in consequence of which the water cannot rise above it. When, therefore, +the piston descends, it shuts the valve Y, and forces the water (which +has no other vent) into the pipe D: this is likewise furnished with a +valve V, which, opening upwards, admits the water to pass, but prevents +its return. + +The water, is thus first raised in the pump, and then forced into the +pipe, by the alternate ascending, and descending motion of the piston, +after a few strokes of the handle to fill the pipe, from whence the +water issues at the spout. + +_Emily._ Does not the air pump, which you used in the experiments, on +pneumatics, operate upon the same principles as the sucking pump? + +_Mrs. B._ Exactly. The air pump which I used (plate 1, fig. 2,) has two +hollow, brass cylinders, called barrels, which are made perfectly true. +In each of those barrels, there is a piston; these are worked up, and +down, by the same handle; the pistons, are furnished with valves, +opening upwards, like those of the common pump: there are valves also, +placed at the lower part of each barrel, which open upwards; there are +therefore two pumps, united to produce the same effect: two tubes, +connect these barrels with the plate, upon which I placed the receivers, +which were to be exhausted. + +_Emily._ I now understand how the air pump acts; the receiver contains +air, which is exhausted, just as it is by the common pump, before the +water begins to rise. + +_Mrs. B._ Having explained the mechanical properties of air, I think it +is now time to conclude our lesson. When next we meet, I shall give you +some account of wind, and of sound, which will terminate our +observations on elastic fluids. + +_Caroline._ And I shall run into the garden, to have the pleasure of +pumping, now that I understand the construction of a pump. + +_Mrs. B._ And, to-morrow, I hope you will be able to tell me, whether it +is a forcing, or a common lifting pump. + + +Questions + +1. (Pg. 136) Into what two kinds are fluids divided? + +2. (Pg. 136) There are different kinds of elastic fluids, in what +properties are they alike, and in what do they differ? + +3. (Pg. 136) In what particular do elastic, differ from non-elastic, +fluids? + +4. (Pg. 136) What is meant by the elasticity of air? + +5. (Pg. 137) What is said respecting the weight of the atmosphere? + +6. (Pg. 137) Why do we not feel the pressure of the air? + +7. (Pg. 137) What would be the effect of relieving us from atmospheric +pressure? + +8. (Pg. 138) How may the weight of the air be shown by the aid of the +air pump, and a piece of bladder? + +9. (Pg. 138) How is this explained? + +10. (Pg. 138) How may its elasticity be exhibited, by an apple, and by a +bladder? + +11. (Pg. 139) What is the absolute weight of a given column of +atmospheric air, and how could its whole pressure upon the earth be +ascertained? + +12. (Pg. 139) How can the weight of a small bulk of air be found? + +13. (Pg. 140) In ascertaining the weight of air, we take account of its +temperature--Why? + +14. (Pg. 140) How could you ascertain the specific gravity of air, and +what would it be? + +15. (Pg. 140) What are the essential parts of a barometer, as +represented plate 14, fig. 3? + +16. (Pg. 141) What sustains the mercury in the tube? + +17. (Pg. 141) Of what use are the divisions in the upper part of the +instrument? + +18. (Pg. 141) To what height will the mercury rise, and what occasions +this height to vary? + +19. (Pg. 141) When is the mercury highest, in wet, or in dry weather? + +20. (Pg. 141) What occasions the sensation of oppression, in damp +weather? + +21. (Pg. 142) Why will the barometer indicate the height of mountains, +or of balloons? + +22. (Pg. 142) Is any inconvenience experienced by persons ascending to +great heights, and from what cause? + +23. (Pg. 142) What occasions the rise and fall of the mercury, in a +thermometer? + +24. (Pg. 142) To what height will the pressure of the atmosphere raise a +column of water? + +25. (Pg. 142) What governs the difference between the height of the +mercury, and of the water? + +26. (Pg. 143) How does the common pump, raise water from a well? + +27. (Pg. 143) What is meant by a piston? + +28. (Pg. 143) Describe the construction, and use, of a valve. + +29. (Pg. 143) What are the parts of the pump, as represented, fig. 4, +plate 14.? + +30. (Pg. 144) How do these parts act, in raising the water? + +31. (Pg. 144) In what does that which is commonly called suction, +consist? + +32. (Pg. 144) How must the piston be situated in the pump? + +33. (Pg. 144) What other kind of pump is described? + +34. (Pg. 145) How is the forcing pump constructed, as shown in plate 14, +fig. 5? + +35. (Pg. 145) Describe the construction and operation of the air pump, +(fig. 2, plate 1.) + + + + +CONVERSATION XIII. + +ON WIND AND SOUND. + +OF WIND IN GENERAL. OF THE TRADE-WIND. OF THE PERIODICAL TRADE-WINDS. OF +THE AERIAL TIDES. OF SOUNDS IN GENERAL. OF SONOROUS BODIES. OF MUSICAL +SOUNDS. OF CONCORD OR HARMONY, AND MELODY. + + +MRS. B. + +Well, Caroline, have you ascertained what kind of pump you have in your +garden? + +_Caroline._ I think it must be merely a lifting pump, because no more +force is required to raise the handle than is necessary to lift its +weight; and as in a forcing pump, by raising the handle, you force the +water into the smaller pipe, the resistance the water offers, must +require an exertion of strength, to overcome it. + +_Mrs. B._ I make no doubt you are right; for lifting pumps, being simple +in their construction, are by far the most common. + +I have promised to-day to give you some account of the nature of wind. +Wind is nothing more than the motion of a stream, or current of air, +generally produced by a partial change of temperature in the atmosphere; +for when any one part is more heated than the rest, that part is +rarefied, the air in consequence rises, and the equilibrium is +destroyed. When this happens, there necessarily follows a motion of the +surrounding air towards that part, in order to restore it; this spot, +therefore, receives winds from every quarter. Those who live to the +north of it, experience a north wind; those to the south, a south +wind:--do you comprehend this? + +_Caroline._ Perfectly. But what sort of weather must those people have, +who live on the spot, where these winds meet and interfere? + +_Mrs. B._ They have most commonly turbulent and boisterous weather, +whirlwinds, hurricanes, rain, lightning, thunder, &c. This stormy +weather occurs most frequently in the torrid zone, where the heat is +greatest: the air being more rarefied there, than in any other part of +the globe, is lighter, and consequently, ascends; whilst the air from +the north and south, is continually flowing in, to restore the +equilibrium. + +_Caroline._ This motion of the air, would produce a regular and constant +north wind, to the inhabitants of the northern hemisphere; and a south +wind, to those of the southern hemisphere, and continual storms at the +equator, where these two adverse winds would meet. + +_Mrs. B._ These winds do not meet, for they each change their direction +before they reach the equator. The sun, in moving over the equatorial +regions from east to west, rarefies the air as it passes, and causes the +denser eastern air to flow westwards, in order to restore the +equilibrium, thus producing a regular east wind, about the equator. + +_Caroline._ The air from the west, then, constantly goes to meet the +sun, and repair the disturbance which his beams have produced in the +equilibrium of the atmosphere. But I wonder how you will reconcile these +various winds, Mrs. B.; you first led me to suppose there was a constant +struggle between opposite winds at the equator, producing storm and +tempest; but now I hear of one regular invariable wind, which must +naturally be attended by calm weather. + +_Emily._ I think I comprehend it: do not these winds from the north and +south, combine with the easterly wind about the equator, and form, what +are called, the trade-winds? + +_Mrs. B._ Just so, my dear. The composition of the two winds, north and +east, produces a constant north-east wind; and that of the two winds, +south and east, produces a regular south-east wind; these winds extend +to about thirty degrees on each side of the equator, the regions further +distant from it, experiencing only their respective northerly and +southerly winds. + +_Caroline._ But, Mrs. B., if the air is constantly flowing from the +poles, to the torrid zone, there must be a deficiency of air, in the +polar regions? + +_Mrs. B._ The light air about the equator, which expands, and rises into +the upper regions of the atmosphere, ultimately flows from thence, back +to the poles, to restore the equilibrium: if it were not for this +resource, the polar, atmospheric regions, would soon be exhausted by the +stream of air, which, in the lower strata of the atmosphere, they are +constantly sending towards the equator. + +_Caroline._ There is then a sort of circulation of air in the +atmosphere; the air in the lower strata, flowing from the poles towards +the equator, and in the upper strata, flowing back from the equator, +towards the poles. + +_Mrs. B._ Exactly; I can show you an example of this circulation, on a +smaller scale. The air of this room, being more rarefied, than the +external air, a wind or current of air is pouring in from the crevices +of the windows and doors, to restore the equilibrium; but the light air, +with which the room is filled, must find some vent, in order to make way +for the heavy air that enters. If you set the door a-jar, and hold a +candle near the upper part of it, you will find that the flame will be +blown outwards, showing that there is a current of air flowing out from +the upper part of the room.--Now place the candle on the floor, close by +the door, and you will perceive, by the inclination of the flame, that +there is also a current of air, setting into the room. + +_Caroline._ It is just so; the upper current is the warm light air, +which is driven out to make way for the stream of cold dense air, which +enters the room lower down. + +_Mrs. B._ Besides the general, or trade-winds, there are others, which +are called periodical, because they blow in contrary directions, at +particular periods. + +_Emily._ I have heard, Mrs. B., that the periodical winds, called, in +the torrid zone, the sea and land breezes, blow towards the land, in the +day time, and towards the sea, at night: what is the reason of that? + +_Mrs. B._ The land reflects into the atmosphere, a much greater quantity +of the sun's rays, than the water; therefore, that part of the +atmosphere which is over the land, is more heated and rarefied, than +that which is over the sea: this occasions the wind to set in upon the +land, as we find that it regularly does on the coast of Guinea, and +other countries in the torrid zone. There, they have only the sea +breeze, but on the islands, they have, in general, both a land and sea +breeze, the latter being produced in the way described; whilst at night, +during the absence of the sun, the earth cools, and the air is +consequently condensed, and flows from the land, towards the sea, +occasioning the land breeze. + +_Emily._ I have heard much of the violent tempests, occasioned by the +breaking up of the monsoons; are not they also regular trade-winds? + +_Mrs. B._ They are called periodical trade-winds, as they change their +course every half year. This variation is produced by the earth's +annual course round the sun; the north pole being inclined towards that +luminary one half of the year, the south pole, the other half. During +the summer of the northern hemisphere, the countries of Arabia, Persia, +India, and China, are much heated, and reflect great quantities of the +sun's rays into the atmosphere, by which it becomes extremely rarefied, +and the equilibrium consequently destroyed. In order to restore it, the +air from the equatorial southern regions, where it is colder, (as well +as from the colder northern parts,) must necessarily have a motion +towards those parts. The current of air from the equatorial regions, +produces the trade-winds for the first six months, in all the seas +between the heated continent of Asia, and the equator. The other six +months, when it is summer in the southern hemisphere, the ocean and +countries towards the southern tropic are most heated, and the air over +those parts, more rarefied: then the air about the equator alters its +course, and flows exactly in an opposite direction. + +_Caroline._ This explanation of the monsoons is very curious; but what +does their breaking up mean? + +_Mrs. B._ It is the name given by sailors to the shifting of the +periodical winds; they do not change their course suddenly, but by +degrees, as the sun moves from one hemisphere, to the other: this change +is usually attended by storms and hurricanes, very dangerous for +shipping; so that those seas are seldom navigated at the season of the +equinoxes. + +_Emily._ I think I understand the winds in the torrid zone perfectly +well; but what is it that occasions the great variety of winds, which +occur in the temperate zones? for, according to your theory, there +should be only north and south winds, in those climates. + +_Mrs. B._ Since so large a portion of the atmosphere, as is over the +torrid zone, is in continued agitation, these agitations in an elastic +fluid, which yields to the slightest impression, must extend every way, +to a great distance; the air, therefore, in all climates, will suffer +more or less perturbation, according to the situation of the country, +the position of mountains, valleys, and a variety of other causes: hence +it is easy to conceive, that almost every climate, must be liable to +variable winds; this is particularly the case in high latitudes, where +the earth is less powerfully affected by the sun's rays, than near the +equator. + +_Caroline._ I have observed, that the wind, whichever way it blows, +almost always falls about sun-set. + +_Mrs. B._ Because the rarefaction of air in the particular spot which +produces the wind, diminishes as the sun declines, and consequently the +velocity of the wind, abates. + +_Emily._ Since the air is a gravitating fluid, is it not affected by the +attraction of the moon and the sun, in the same manner as the waters? + +_Mrs. B._ Undoubtedly; but the aerial tides are as much greater than +those of water, as the density of water exceeds that of air, which, as +you may recollect, we found to be about 800 to 1. + +_Caroline._ What a prodigious protuberance that must occasion! How much +the weight of such a column of air, must raise the mercury in the +barometer! + +_Emily._ As this enormous tide of air is drawn up and supported, as it +were, by the moon, its weight and pressure, I should suppose, would be +rather diminished than increased? + +_Mrs. B._ The weight of the atmosphere is neither increased nor +diminished by the aerial tides. The moon's attraction augments the bulk, +as much as it diminishes the weight, of the column of air; these +effects, therefore, counterbalancing each other, the aerial tides do not +affect the barometer. + +_Caroline._ I do not quite understand that. + +_Mrs. B._ Let us suppose that the additional bulk of air at high tide, +raises the barometer one inch; and on the other hand, that the support +which the moon's attraction affords the air, diminishes its weight or +pressure, so as to occasion the mercury to fall one inch; under these +circumstances the mercury must remain stationary. Thus, you see, that we +can never be sensible of aerial tides by the barometer, on account of the +equality of pressure of the atmosphere, whatever be its height. + +The existence of aerial tides is not, however, hypothetical; it is proved +by the effect they produce on the apparent position of the heavenly +bodies; but this I cannot explain to you, till you understand the +properties of light. + +_Emily._ And when shall we learn them? + +_Mrs. B._ I shall first explain to you the nature of sound, which is +intimately connected with that of air; and I think at our next meeting, +we may enter upon the subject of optics. + +We have now considered the effects produced by the wide, and extended +agitation, of the air; but there is another kind of agitation, of which +the air is susceptible--a vibratory trembling motion, which, striking on +the drum of the ear, produces _sound_. + +_Caroline._ Is not sound produced by solid bodies? The voice of +animals, the ringing of bells, the music of instruments, all proceed +from solid bodies. I know of no sound but that of the wind, which is +produced by the air. + +_Mrs. B._ Sound, I assure you, results from a tremulous motion of the +air; and the sonorous bodies you enumerate, are merely the instruments +by which that peculiar species of motion, is communicated to the air. + +_Caroline._ What! when I ring this little bell, is it the air that +sounds, and not the bell? + +_Mrs. B._ Both the bell, and the air, are concerned in the production of +sound. But sound, strictly speaking, is a perception excited in the +mind, by the motion of the air, on the nerves of the ear; the air, +therefore, as well as the sonorous bodies which put it in motion, is +only the cause of sound, the immediate effect is produced by the sense +of hearing: for without this sense, there would be no sound. + +_Emily._ I can with difficulty conceive that. A person born deaf, it is +true, has no idea of sound, because he hears none; yet that does not +prevent the real existence of sound, as all those who are not deaf, can +testify. + +_Mrs. B._ I do not doubt the existence of sound, to all those who +possess the sense of hearing; but it exists neither in the sonorous +body, nor in the air, but in the mind of the person whose ear is struck, +by the vibratory motion of the air, produced by a sonorous body. Sound, +therefore, is a sensation, produced in a living body; life, is as +necessary to its existence, as it is to that of feeling or seeing. + +To convince you that sound does not exist in sonorous bodies, but that +air or some other vehicle, is necessary to its production, endeavour to +ring the little bell, after I have suspended it under a receiver in the +air pump, from which I shall exhaust the air.... + +_Caroline._ This is indeed very strange: though I agitate it so +violently, it produces but little sound. + +_Mrs. B._ By exhausting the receiver, I have cut off the communication +between the air and the bell; the latter, therefore, cannot impart its +motion, to the air. + +_Caroline._ Are you sure that it is not the glass, which covers the +bell, that prevents our hearing it? + +_Mrs. B._ That you may easily ascertain, by letting the air into the +receiver, and then ringing the bell. + +_Caroline._ Very true; I can hear it now, almost as loud, as if the +glass did not cover it; and I can no longer doubt but that air is +necessary to the production of sound. + +_Mrs. B._ Not absolutely necessary, though by far the most common +vehicle of sound. Liquids, as well as air, are capable of conveying the +vibratory motion of a sonorous body, to the organ of hearing; as sound +can be heard under water. Solid bodies also, convey sound, as I can soon +convince you by a very simple experiment. I shall fasten this string by +the middle, round the poker; now raise the poker from the ground, by the +two ends of the string, and hold one to each of your ears:--I shall now +strike the poker, with a key, and you will find that the sound is +conveyed to the ear by means of the strings, in a much more perfect +manner, than if it had no other vehicle than the air. + +_Caroline._ That it is, certainly, for I am almost stunned by the noise. +But what is a sonorous body, Mrs. B.? for all bodies are capable of +producing some kind of sound, by the motion they communicate to the air. + +_Mrs. B._ Those bodies are called sonorous, which produce clear, +distinct, regular, and durable sounds, such as a bell, a drum, musical +strings, wind instruments, &c. They owe this property to their +elasticity; for an elastic body, after having been struck, not only +returns to its former situation, but having acquired momentum by its +velocity, like the pendulum, it springs out on the opposite side. If I +draw the string A B, (fig. 6, plate 14,) which is made fast at both +ends, to C, it will not only return to its original position, but +proceed onwards, to D. + +This is its first vibration; at the end of which, it will retain +sufficient velocity to bring it to E, and back again to F, which +constitutes its second vibration; the third vibration, will carry it +only to G and H, and so on, till the resistance of the air destroys its +motion. + +The vibration of a sonorous body, gives a tremulous motion to the air +around it, very similar to the motion communicated to smooth water, when +a stone is thrown into it. This, first produces a small circular wave, +around the spot in which the stone falls; the wave spreads, and +gradually communicates its motion to the adjacent waters, producing +similar waves to a considerable extent. The same kind of waves are +produced in the air, by the motion of a sonorous body, but with this +difference, that as air, is an elastic fluid, the motion does not +consist of regularly extending waves, but of vibrations; and are +composed of a motion, forwards and backwards, similar to those of the +sonorous body. They differ also, in the one taking place in a plane, +the other, in all directions: the aerial undulations, being spherical. + +_Emily._ But if the air moves backwards, as well as forwards, how can +its motion extend so as to convey sound to a distance? + +_Mrs. B._ The first sphere of undulations, which are produced +immediately around the sonorous body, by pressing against the contiguous +air, condenses it. The condensed air, though impelled forward by the +pressure, reacts on the first set of undulations, driving them back +again. The second set of undulations which have been put in motion, in +their turn, communicate their motion, and are themselves driven back, by +reaction. Thus, there is a succession of waves in the air, corresponding +with the succession of waves in the water. + +_Caroline._ The vibrations of sound, must extend much further than the +circular waves in water, since sound is conveyed to a great distance. + +_Mrs. B._ The air is a fluid so much less dense than water, that motion +is more easily communicated to it. The report of a cannon produces +vibrations of the air, which extend to several miles around. + +_Emily._ Distant sound takes some time to reach us, since it is produced +at the moment the cannon is fired; and we see the light of the flash, +long before we hear the report. + +_Mrs. B._ The air is immediately put in motion, by the firing of a +cannon; but it requires time for the vibrations to extend to any distant +spot. The velocity of sound, is computed to be at the rate of 1142 feet +in a second. + +_Caroline._ With what astonishing rapidity the vibrations must be +communicated! But the velocity of sound varies, I suppose, with that of +the air which conveys it. If the wind sets towards us from the cannon, +we must hear the report sooner than if it set the other way. + +_Mrs. B._ The direction of the wind makes less difference in the +velocity of sound, than you would imagine. If the wind sets from us, it +bears most of the aerial waves away, and renders the sound fainter; but +it is not very considerably longer in reaching the ear, than if the wind +blew towards us. This uniform velocity of sound, enables us to determine +the distance of the object, from which it proceeds; as that of a vessel +at sea, firing a cannon, or that of a thunder cloud. If we do not hear +the thunder, till half a minute after we see the lightning, we conclude +the cloud to be at the distance of six miles and a half. + +_Emily._ Pray, how is the sound of an echo produced? + +_Mrs. B._ When the aerial vibrations meet with an obstacle, having a hard +and regular surface, such as a wall, or rock, they are reflected back to +the ear, and produce the same sound a second time; but the sound will +then appear to proceed, from the object by which it is reflected. If the +vibrations fall perpendicularly on the obstacle, they are reflected back +in the same line; if obliquely, the sound returns obliquely, in the +opposite direction, the angle of reflection being equal to the angle of +incidence. + +_Caroline._ Oh, then, Emily, I now understand why the echo of my voice +behind our house is heard so much plainer by you than it is by me, when +we stand at the opposite ends of the gravel walk. My voice, or rather, I +should say, the vibrations of air it occasions, fall obliquely on the +wall of the house, and are reflected by it, to the opposite end of the +gravel walk. + +_Emily._ Very true; and we have observed, that when we stand in the +middle of the walk, opposite the house, the echo returns to the person +who spoke. + +_Mrs. B._ Speaking-trumpets, are constructed on the principle, that +sound is reflected. The voice, instead of being diffused in the open +air, is confined within the trumpet; and the vibrations which would +otherwise spread laterally, fall against the sides of the instrument, +and are reflected from the different points of incidence, so as to +combine with those vibrations which proceed straight forwards. The +vibrations are thus forced onwards, in the direction of the trumpet, so +as greatly to increase the sound, to a person situated in that +direction. Figure 7, plate 14, will give you a clearer idea, of the +speaking-trumpet; in this, lines are drawn to represent the manner, in +which we may imagine the sound to be reflected. There is a point in +front of the trumpet, F, which is denominated its focus, because the +sound is there more intense, than at any other spot. The trumpet used by +deaf persons, acts on the same principle; although it does not equally +increase the sound. + +_Emily._ Are the trumpets used as musical instruments, also constructed +on this principle? + +_Mrs. B._ So far as their form tends to increase the sound, they are; +but, as a musical instrument, the trumpet becomes itself the sonorous +body, which is made to vibrate by blowing into it, and communicates its +vibrations to the air. + +I will attempt to give you, in a few words, some notion of the nature of +musical sounds, which, as you are fond of music, must be interesting to +you. + +If a sonorous body be struck in such a manner, that its vibrations, are +all performed in regular times, the vibrations of the air, will +correspond with them; and striking in the same regular manner on the +drum of the ear, will produce the same uniform sensation, on the +auditory nerve, and excite the same uniform idea, in the mind; or, in +other words, we shall hear one musical tone. + +But if the vibrations of the sonorous body, are irregular, there will +necessarily follow a confusion of aerial vibrations; for a second +vibration may commence, before the first is finished, meet it half way +on its return, interrupt it in its course, and produce harsh jarring +sounds, which are called _discords_. + +_Emily._ But each set of these irregular vibrations, if repeated alone, +and at equal intervals, would, I suppose, produce a musical tone? It is +only their irregular interference, which occasions discord. + +_Mrs. B._ Certainly. The quicker a sonorous body vibrates, the more +acute, or sharp, is the sound produced; and the slower the vibrations, +the more grave will be the note. + +_Caroline._ But if I strike any one note of the piano-forte, repeatedly, +whether quickly or slowly, it always gives the same tone. + +_Mrs. B._ Because the vibrations of the same string, at the same degree +of tension, are always of a similar duration. The quickness, or slowness +of the vibrations, relate to the single tones, not to the various sounds +which they may compose, by succeeding each other. Striking the note in +quick succession, produces a more frequent repetition of the tone, but +does not increase the velocity of the vibrations of the string. + +The duration of the vibrations of strings, or wires, depends upon their +length, their thickness, or weight, and their degree of tension: thus, +you find, the low bass notes are produced by long, thick, loose strings; +and the high treble notes by short, small, and tight strings. + +_Caroline._ Then, the different length, and size, of the strings of +musical instruments, serve to vary the duration of the vibrations, and +consequently, the acuteness or gravity of the notes? + +_Mrs. B._ Yes. Among the variety of tones, there are some which, sounded +together, please the ear, producing what we call harmony, or concord. +This arises from the agreement of the vibrations of the two sonorous +bodies; so that some of the vibrations of each, strike upon the ear at +the same time. Thus, if the vibrations of two strings are performed in +equal times, the same tone is produced by both, and they are said to be +in unison. + +_Emily._ Now, then, I understand why, when I tune my harp, in unison +with the piano-forte, I draw the strings tighter, if it is too low, or +loosen them, if it is too high a pitch: it is in order to bring them to +vibrate, in equal times, with the strings of the piano-forte. + +_Mrs. B._ But concord, you know, is not confined to unison; for two +different tones, harmonize in a variety of cases. When the vibrations of +one string (or other sonorous body) vibrate in double the time of +another, the second vibration of the latter, will strike upon the ear, +at the same instant, as the first vibration of the former; and this is +the concord of an octave. + +If the vibrations of two strings are as two to three, the second +vibration of the first, corresponds with the third vibration of the +latter, producing the harmony called, a fifth. + +_Caroline._ So, then, when I strike the key-note with its fifth, I hear +every second vibration of one, and every third of the other, at the same +time? + +_Mrs. B._ Yes; and the key-note, struck with the fourth, is likewise a +concord, because the vibrations, are as three to four. The vibrations of +a major third, with the key-note, are as four to five; and those of a +minor third, as five to six. + +There are other tones, which, though they cannot be struck together +without producing discord, if struck successively, give us that +succession of pleasing sounds, which is called melody. Harmony, you +perceive, arises from the combined effect of two, or more concordant +sounds, while melody, is the result of certain simple sounds, which +succeed each other. Upon these general principles, the science of music +is founded; but, I am not sufficiently acquainted with it, to enter into +it any further. + +We shall now, therefore, take leave of the subject of sound; and, at our +next interview, enter upon that of optics, in which we shall consider +the nature of light, vision, and colours. + + +Questions + +1. (Pg. 146) What is wind, and how is it generally produced? + +2. (Pg. 146) How do the winds blow, around the place where the air +becomes rarefied? + +3. (Pg. 146) What effect is likely to be produced where the winds meet? + +4. (Pg. 147) In what part of the globe is the air most rarefied, and +what is the consequence? + +5. (Pg. 147) How do these winds change their direction as they approach +the equator? + +6. (Pg. 147) How are the trade-winds produced, and how far do they +extend? + +7. (Pg. 147) How is the equilibrium in the air restored? + +8. (Pg. 148) How can contrary currents of air be shown in a room? + +9. (Pg. 148) What causes this? + +10. (Pg. 148) What is meant by a periodical wind? + +11. (Pg. 148) What occasions the land and sea breezes, and where do they +prevail? + +12. (Pg. 149) What are monsoons? + +13. (Pg. 149) How do they change, and what is the cause? + +14. (Pg. 149) What is meant by their breaking up, and what effect is in +general produced? + +15. (Pg. 149) Why is the wind most variable in high latitudes? + +16. (Pg. 150) Why is the wind apt to lessen about sunset? + +17. (Pg. 150) What effect must the sun and moon produce upon the +atmosphere, from their attraction? + +18. (Pg. 150) Why do not the aerial tides affect the barometer? + +19. (Pg. 151) How is sound produced? + +20. (Pg. 151) Does sound exist in the sonorous body, if not, what is it? + +21. (Pg. 151) By what experiment might we prove that air is the +principal vehicle of sound? + +22. (Pg. 152) What other bodies convey sound, and how can it be shown +that they do so? + +23. (Pg. 152) What is meant by a sonorous body? + +24. (Pg. 152) To what do they owe this property? + +25. (Pg. 152) How is this explained by fig. 6, plate 14? + +26. (Pg. 152) How is it illustrated by a stone thrown into water, and +how far does this illustration apply? + +27. (Pg. 153) How are the vibrations propagated? + +28. (Pg. 153) How can we prove that sound, does not travel as rapidly as +light? + +29. (Pg. 153) At what rate is sound said to travel? + +30. (Pg. 153) Is the velocity much influenced by the direction of the +wind? + +31. (Pg. 153) How will sound enable us to judge of the distance of +objects? + +32. (Pg. 154) How are echoes produced? + +33. (Pg. 154) What is the operation and effect of the speaking-trumpet +(fig. 7, plate 14)? + +34. (Pg. 155) How is a musical tone produced? + +35. (Pg. 155) What occasions discords? + +36. (Pg. 155) Upon what does the acuteness or gravity of a sound depend? + +37. (Pg. 155) Does the force, with which a string is struck, affect the +rapidity of its vibrations? + +38. (Pg. 155) How are the strings made to produce the high and low +notes? + +39. (Pg. 155) What is meant by harmony, or concord, and how is it +produced? + +40. (Pg. 156) When are strings said to be in unison? + +41. (Pg. 156) How are octaves produced? + +42. (Pg. 156) How are fifths produced? + +43. (Pg. 156) How major and minor thirds? + +44. (Pg. 156) What is meant by melody, and in what particular does it +differ from harmony? + +[Illustration: PLATE XV.] + + + + +CONVERSATION XIV. + +ON OPTICS. + +OF LUMINOUS, TRANSPARENT, AND OPAQUE BODIES. OF THE RADIATION OF LIGHT. +OF SHADOWS. OF THE REFLECTION OF LIGHT. OPAQUE BODIES SEEN ONLY BY +REFLECTED LIGHT. VISION EXPLAINED. CAMERA OBSCURA. IMAGE OF OBJECTS ON +THE RETINA. + + +CAROLINE. + +I long to begin our lesson to-day, Mrs. B., for I expect that it will be +very entertaining. + +_Mrs. B._ _Optics is that branch of philosophy, which treats of the +nature and properties of light._ It is certainly one of the most +interesting branches of Natural Philosophy, but not one of the easiest +to understand; I must, therefore, beg that you will give me your +undivided attention. + +I shall first inquire, whether you comprehend the meaning of a _luminous +body_, an _opaque body_, and a _transparent body_. + +_Caroline._ A luminous body is one that shines; an opaque.... + +_Mrs. B._ Do not proceed to the second, until we have agreed upon the +definition of the first. All bodies that shine, are not luminous; for a +luminous body is one that shines by its own light; as the sun, the fire, +a candle, &c. + +_Emily._ Polished metal then, when it shines with so much brilliancy, is +not a luminous body? + +_Mrs. B._ No, for it would be dark, if it did not receive light from a +luminous body; it belongs, therefore, to the class of dark, as well as +of opaque bodies, which comprehends all such as are neither luminous, +nor will admit the light to pass through them. + +_Emily._ And transparent bodies, are those which admit the light to pass +through them, such as glass and water. + +_Mrs. B._ You are right. Transparent, or pellucid bodies, are frequently +called mediums, because they allow the rays of light to pass through +them; and the rays which pass through, are said to be transmitted by +them. + +Light, when emanated from the sun, or any other luminous body, is +projected forward in straight lines, in every possible direction; so +that the luminous body, is not only the general centre, from whence all +the rays proceed; but every point of it, may be considered as a centre, +which radiates light in every direction. (Fig. 1, plate 15.) + +_Emily._ But do not the rays which are projected in different +directions, and cross each other, interfere, and impede each other's +course? + +_Mrs. B._ Not at all. The particles of light, are so extremely minute, +that they are never known to interfere with each other. A ray of light, +is a single line of light, projected from a luminous body; and a pencil +of rays, is a collection of rays, proceeding from any one point of a +luminous body, as fig. 2. + +_Caroline._ Is light then a substance composed of particles, like other +bodies? + +_Mrs. B._ That is a disputed point, upon which I cannot pretend to +decide. In some respects, light is obedient to the laws which govern +bodies; in others, it appears to be independent of them: thus, though +its course is guided by the laws of motion, it does not seem to be +influenced by those of gravity. It has never been discovered to have +weight, though a variety of interesting experiments have been made with +a view of ascertaining that point; but we are so ignorant of the +intimate nature of light, that an attempt to investigate it, would lead +us into a labyrinth of perplexity, if not of error; we shall, therefore, +confine our attention to those properties of light, which are well +ascertained. + +Let us return to the examination of the effects of the radiation of +light, from a luminous body. Since the rays of light are projected in +straight lines, when they meet with an opaque body through which they +are unable to pass, they are stopped short in their course; for they +cannot move in a curve line round the body. + +_Caroline._ No, certainly; for it would require some other force besides +that of projection, to produce motion in a curve line. + +_Mrs. B._ The interruption of the rays of light, by the opaque body, +produces, therefore, darkness on the opposite side of it: and if this +darkness fall upon a wall, a sheet of paper, or any object whatever, it +forms a shadow. + +_Emily._ A shadow, then, is nothing more than darkness produced by the +intervention of an opaque body, which prevents the rays of light from +reaching an object behind it. + +_Caroline._ Why then are shadows of different degrees of darkness; for +I should have supposed, from your definition of a shadow, that it would +have been perfectly black? + +_Mrs. B._ It frequently happens that a shadow is produced by an opaque +body, interrupting the course of the rays from one luminous body, while +light from another, reaches the space where the shadow is formed; in +which case, the shadow is proportionally fainter. This happens when the +opaque body is lighted by two candles: if you extinguish one of them, +the shadow will be both deeper, and more distinct. + +_Caroline._ But yet it will not be perfectly dark. + +_Mrs. B._ Because it is still slightly illuminated by light reflected +from the walls of the room, and other surrounding objects. + +You must observe, also, that when a shadow is produced by the +interruption of rays from a single luminous body, the darkness is +proportioned to the intensity of the light. + +_Emily._ I should have supposed the contrary; for as the light reflected +from surrounding objects on the shadow, must be in proportion to the +intensity of the light, the stronger the light, the more the shadow will +be illumined. + +_Mrs. B._ Your remark is perfectly just; but as we have no means of +estimating the degrees of light, and of darkness, but by comparison, the +strongest light will appear to produce the deepest shadow. Hence a total +eclipse of the sun, occasions a more sensible darkness than midnight, as +it is immediately contrasted with the strong light of noonday. + +_Caroline._ The reappearance of the sun, after an eclipse, must, by the +same contrast, appear remarkably brilliant. + +_Mrs. B._ Certainly. There are several things to be observed, in regard +to the form, and extent, of shadows. If the luminous body A (fig. 3.) is +larger than the opaque body B, the shadow will gradually diminish in +size, till it terminates in a point. + +_Caroline._ This is the case with the shadows of the earth, and the +moon; as the sun, which illumines them, is larger than either of those +bodies. And why is it not the case with the shadows of terrestrial +objects? Their shadows, far from diminishing, are always larger than the +object, and increase with the distance from it. + +_Mrs. B._ In estimating the effect of shadows, we must consider the +dimensions of the luminous body; when the luminous body is less, than +the opaque body, the shadow will increase with the distance. This will +be best exemplified, by observing the shadow of an object lighted by a +candle. + +_Emily._ I have often noticed, that the shadow of my figure, against the +wall, grows larger, as it is more distant from me, which is owing, no +doubt, to the candle that shines on me, being much smaller than myself. + +_Mrs. B._ Yes. The shadow of a figure as A, (fig. 4.) varies in size, +according to the distance of the several surfaces B C D E, on which it +is described. + +_Caroline._ I have observed, that two candles, produce two shadows from +the same object; whilst it would appear, from what you said, that they +should rather produce only half a shadow, that is to say, a very faint +one. + +_Mrs. B._ The number of lights (in different directions) while it +decreases the intensity of the shadows, increases their number, which +always corresponds with that of the lights; for each light, makes the +opaque body cast a different shadow, as illustrated by fig. 5. which +represents a ball A, lighted by three candles, B, C, D; and you observe +the light B, produces the shadow _b_, the light C, the shadow _c_, and +the light D, the shadow _d_; but neither of these shadows will be very +dark, because the light of one candle only, is intercepted by the ball; +and the spot is still illuminated by the other two. + +_Emily._ I think we now understand the nature of shadows very well; but +pray, what becomes of the rays of light, which opaque bodies arrest in +their course, and the interruption of which, is the occasion of shadows? + +_Mrs. B._ Your question leads to a very important property of light, +_Reflection_. When rays of light encounter an opaque body, they cannot +pass through it, and part of them are absorbed by it, and part are +reflected, and rebound; just as an elastic ball rebounds, when struck +against a wall. + +By reflection, we mean that the light is turned back again, through the +same medium which it had traversed in its first course. + +_Emily._ And is light, in its reflection, governed by the same laws, as +solid, elastic bodies? + +_Mrs. B._ Exactly. If a ray of light fall perpendicularly on an opaque +body, it is reflected back in the same line, towards the point whence it +proceeded. If it fall obliquely, it is reflected obliquely, but in the +opposite direction; the ray which falls upon the reflecting surface, is +called the incident ray, and that which leaves it, the reflected ray; +the angle of incidence, is always equal to the angle of reflection. You +recollect that law in mechanics? + +_Emily._ Oh yes, perfectly. + +_Mrs. B._ If you will shut the shutters, we will admit a ray of the +sun's light, through a very small aperture, and I can show you how it is +reflected. I now hold this mirror, so that the ray shall fall +perpendicularly upon it. + +_Caroline._ I see the ray which falls upon the mirror, but not that +which is reflected by it. + +_Mrs. B._ Because it is turned directly back again; and the ray of +incidence, and that of reflection, are confounded together, both being +in the same line, though in opposite directions. + +_Emily._ The ray then, which appears to us single, is really double, and +is composed of the incident ray, proceeding to the mirror, and of the +reflected ray, returning from the mirror. + +_Mrs. B._ Exactly so. We will now separate them, by holding the mirror +M, (fig. 6,) in such a manner, that the incident ray, A B, shall fall +obliquely upon it--you see the reflected ray, B C, is marching off in +another direction. If we draw a line from the point of incidence B, +perpendicularly, to the mirror, it will divide the angle of incidence, +from the angle of reflection, and you will see that they are equal. + +_Emily._ Exactly; and now, that you hold the mirror, so that the ray +falls more obliquely upon it, it is also reflected more obliquely, +preserving the equality of the angles of incidence, and of reflection. + +_Mrs. B._ It is by reflected rays only, that we see opaque objects. +Luminous bodies, send rays of light immediately to our eyes, but the +rays which they send to other bodies, are invisible to us, and are seen, +only when they are reflected by those bodies, to our eyes. + +_Emily._ But have we not just seen the ray of light, in its passage from +the sun to the mirror, and its reflections? yet, in neither case, were +those rays in a direction to enter our eyes. + +_Mrs. B._ What you saw, was the light reflected to your eyes, by small +particles of dust floating in the air, and on which the ray shone, in +its passage to, and from, the mirror. + +_Caroline._ Yet I see the sun, shining on that house yonder, as clearly +as possible. + +_Mrs. B._ Indeed you cannot see a single ray, which passes from the sun +to the house; you see, by the aid of those rays, which enter your eyes; +therefore, it is the rays which are reflected by the house, to you, and +not those which proceed directly from the sun, to the house, that render +the building visible to you. + +_Caroline._ Why then does one side of the house appear to be in +sunshine, and the other in shade? for, if I cannot see the sun shine +upon it, the whole of the house should appear in the shade. + +_Mrs. B._ That side of the house, which the sun shines upon, receives, +and reflects more light, and therefore, appears more luminous and vivid, +than the side which is in shadow; for the latter is illumined only, by +rays reflected upon it by other objects; these rays are, therefore, +twice reflected before they reach your sight; and as light is more, or +less, absorbed by the bodies it strikes upon, every time a ray is +reflected, its intensity is diminished. + +_Caroline._ Still I cannot reconcile to myself, the idea that we do not +see the sun's rays shining on objects, but only those which such objects +reflect to us. + +_Mrs. B._ I do not, however, despair of convincing you of it. Look at +that large sheet of water; can you tell why the sun appears to shine on +one part of it only? + +_Caroline._ No, indeed; for the whole of it is equally exposed to the +sun. This partial brilliancy of water, has often excited my wonder; but +it has struck me more particularly by moonlight. I have frequently +observed a vivid streak of moonshine on the sea, while the rest of the +water remained in deep obscurity, and yet there was no apparent obstacle +to prevent the moon from shining equally on every part of the water. + +_Mrs. B._ By moonlight the effect is more remarkable, on account of the +deep obscurity of the other parts of the water; while by the sun's +light, the effect is too strong for the eye to be able to observe it so +distinctly. + +_Caroline._ But, if the sun really shines on every part of that sheet of +water, why does not every part of it, reflect rays to my eyes? + +_Mrs. B._ The reflected rays, are not attracted out of their natural +course, by your eyes. The direction of a reflected ray, you know, +depends on that of the incident ray; the sun's rays, therefore, which +fall with various degrees of obliquity upon the water, are reflected in +directions equally various; some of these will meet your eyes, and you +will see them, but those which fall elsewhere, are invisible to you. + +_Caroline._ The streak of sunshine, then, which we now see upon the +water, is composed of those rays which by their reflection, happen to +fall upon my eyes? + +_Mrs. B._ Precisely. + +_Emily._ But is that side of the house yonder, which appears to be in +shadow, really illuminated by the sun, and its rays reflected another +way? + +_Mrs. B._ No; that is a different case, from the sheet of water. That +side of the house, is really in shadow; it is the west side, which the +sun cannot shine upon, till the afternoon. + +_Emily._ Those objects, then, which are illumined by reflected rays, and +those which receive direct rays from the sun, but which do not reflect +those rays towards us, appear equally in shadow? + +_Mrs. B._ Certainly; for we see them both illumined by reflected rays. +That part of the sheet of water, over which the trees cast a shadow, by +what light do you see it? + +_Emily._ Since it is not by the sun's direct rays, it must be by those +reflected on it from other objects, and which it again reflects to us. + +_Caroline._ But if we see all terrestrial objects by reflected light, +(as we do the moon,) why do they appear so bright and luminous? I should +have supposed that reflected rays, would have been dull and faint, like +those of the moon. + +_Mrs. B._ The moon reflects the sun's light, with as much vividness as +any terrestrial object. If you look at it on a clear night, it will +appear as bright as a sheet of water, the walls of a house, or any +object seen by daylight, and on which the sun shines. The rays of the +moon are doubtless feeble, when compared with those of the sun; but that +would not be a fair comparison, for the former are incident, the latter, +reflected rays. + +_Caroline._ True; and when we see terrestrial objects by moonlight, the +light has been twice reflected, and is consequently, proportionally +fainter. + +_Mrs. B._ In traversing the atmosphere, the rays, both of the sun, and +moon, lose some of their light. For though the pure air, is a +transparent medium, which transmits the rays of light freely, we have +observed, that near the surface of the earth, it is loaded with vapours +and exhalations, by which some portion of them are absorbed. + +_Caroline._ I have often noticed, that an object on the summit of a +hill, appears more distinct, than one at an equal distance in a valley, +or a plain; which is owing, I suppose, to the air being more free from +vapours in an elevated situation, and the reflected rays, being +consequently brighter. + +_Mrs. B._ That may have some sensible effect; but, when an object on the +summit of a hill, has a back ground of light sky, the contrast with the +object, makes its outline more distinct. + +_Caroline._ I now feel well satisfied, that we see opaque objects, only +by reflected rays; but I do not understand, how these rays, show us the +objects from which they proceed. + +_Mrs. B._ I shall hereafter describe the structure of the eye, very +particularly, but will now observe, that the small round spot, which is +generally called the sight of the eye, is properly denominated the +_pupil_; and that the _retina_, is an expansion of the optic nerve on +the back part of the ball of the eye, upon which, as upon a screen, the +rays fall, which enter at the pupil. The rays of light, enter at the +pupil of the eye, and proceed to the retina; and there they describe the +figure, colour, and (excepting size) form a perfect representation of +the object, from which they proceed. We shall again close the shutters, +and admit the light, through the small hole made for that purpose, and +you will see a picture, on the wall, opposite the aperture, similar to +that which is delineated on the retina of the eye. The picture is +somewhat confused, but by using a lens, to bring the rays to a focus, it +will be rendered very distinct. + +_Caroline._ Oh, how wonderful! There is an exact picture in miniature of +the garden, the gardener at work, the trees blown about by the wind. The +landscape, would be perfect, if it were not reversed; the ground, being +above, and the sky beneath. + +_Mrs. B._ It is not enough to admire, you must understand, this +phenomenon, which is called a _camera obscura_, or dark chamber; from +the necessity of darkening the room, in order to exhibit it. The camera +obscura, sometimes consists of a small box, properly fitted up, to +represent external objects. + +This picture, you now see, is produced by the rays of light, reflected +from the various objects in the garden, and which are admitted through +the hole in the window shutter. + +[Illustration: PLATE XVI.] + +The rays from the glittering weathercock, at the top of the alcove, A, +(plate 16.) represent it in this spot, _a_; for the weathercock, being +much higher than the aperture in the shutter, only a few of the rays, +which are reflected by it, in an obliquely descending direction, can +find entrance there. The rays of light, you know, always move in +straight lines; those, therefore, which enter the room, in a descending +direction, will continue their course in the same direction, and will +consequently fall upon the lower part of the wall opposite the aperture, +and represent the weathercock, reversed in that spot, instead of erect, +in the uppermost part of the landscape. + +_Emily._ And the rays of light, from the steps, (B) of the alcove, in +entering the aperture, ascend, and will describe those steps in the +highest, instead of the lowest, part of the landscape. + +_Mrs. B._ Observe, too, that the rays coming from the alcove, which is +to our left, describe it on the wall, to the right; while those, which +are reflected by the walnut tree, C D, to our right, delineate its +figure in the picture, to the left, _c d_. Thus the rays, coming in +different directions, and proceeding always in right lines, cross each +other at their entrance through the aperture; those which come from +above, proceed below, those from the right, go to the left, those from +the left, towards the right; thus every object is represented in the +picture, as occupying a situation, the very reverse of that which it +does in nature. + +_Caroline._ Excepting the flower-pot, E F, which, though its position is +reversed, has not changed its situation in the landscape. + +_Mrs. B._ The flower-pot, is directly in front of the aperture; so that +its rays, fall perpendicularly upon it, and consequently proceed +perpendicularly to the wall, where they delineate the object, directly +behind the aperture. + +_Emily._ And is it thus, that the picture of objects, is painted on the +retina of the eye? + +_Mrs. B._ Precisely. The pupil of the eye, through which the rays of +light enter, represents the aperture in the window-shutter; and the +image, delineated on the retina, is exactly similar to the picture on +the wall. + +_Caroline._ You do not mean to say, that we see only the representation +of the object, which is painted on the retina, and not the object +itself? + +_Mrs. B._ If, by sight, you understand that sense, by which the presence +of objects is perceived by the mind, through the means of the eyes, we +certainly see only the image of those objects, painted on the retina. + +_Caroline._ This appears to me quite incredible. + +_Mrs. B._ The nerves, are the only part of our frame, capable of +sensation: they appear, therefore, to be the instruments, which the mind +employs in its perceptions; for a sensation, always conveys an idea, to +the mind. Now it is known, that our nerves can be affected only by +contact; and for this reason, the organs of sense, cannot act at a +distance: for instance, we are capable of smelling only particles which +are actually in contact with the nerves of the nose. We have already +observed, that the odour of a flower consists in effluvia, composed of +very minute particles, which penetrate the nostrils, and strike upon the +olfactory nerves, which instantly convey the idea of odour to the mind. + +_Emily._ And sound, though it is said to be heard at a distance, is, in +fact, heard only when the vibrations of the air, which convey it to our +ears, strike upon the auditory nerve. + +_Caroline._ There is no explanation required, to prove that the senses +of feeling and of tasting, are excited only by contact. + +_Mrs. B._ And I hope to convince you, that the sense of sight, is so +likewise. The nerves, which constitute the sense of sight, are not +different in their nature from those of the other organs; they are +merely instruments which convey ideas to the mind, and can be affected +only on contact. Now, since real objects cannot be brought to touch the +optic nerve, the image of them is conveyed thither by the rays of light, +proceeding from real objects, which actually strike upon the optic +nerve, and form that image which the mind perceives. + +_Caroline._ While I listen to your reasoning, I feel convinced; but when +I look upon the objects around, and think that I do not see them, but +merely their image painted in my eyes, my belief is again staggered. I +cannot reconcile to myself, the idea, that I do not really see this book +which I hold in my hand, nor the words which I read in it. + +_Mrs. B._ Did it ever occur to you as extraordinary, that you never +beheld your own face? + +_Caroline._ No; because I so frequently see an exact representation of +it in the looking-glass. + +_Mrs. B._ You see a far more exact representation of objects on the +retina of your eye: it is a much more perfect mirror, than any made by +art. + +_Emily._ But is it possible, that the extensive landscape, which I now +behold from the window, should be represented on so small a space, as +the retina of the eye? + +_Mrs. B._ It would be impossible for art to paint so small and distinct +a miniature; but nature works with a surer hand, and a more delicate +pencil. That power alone, which forms the feathers of the butterfly, and +the organs of the minutest insect, can pourtray so admirable and +perfect a miniature, as that which is represented on the retina of the +eye. + +_Caroline._ But, Mrs. B., if we see only the image of objects, why do we +not see them reversed, as you showed us they were, in the camera +obscura? Is not that a strong argument against your theory? + +_Mrs. B._ Not an unanswerable one, I hope. The image on the retina, it +is true, is reversed, like that in the camera obscura; as the rays, from +the different parts of the landscape, intersect each other on entering +the pupil, in the same manner as they do, on entering the camera +obscura. The scene, however, does not excite the idea of being inverted, +because we always see an object in the direction of the rays which it +sends to us. + +_Emily._ I confess I do not understand that. + +_Mrs. B._ It is, I think, a difficult point to explain clearly. A ray +which comes from the upper part of an object, describes the image on the +lower part of the retina; but, experience having taught us, that the +direction of that ray is from above, we consider that part of the object +it represents as uppermost. The rays proceeding from the lower part of +an object, fall upon the upper part of the retina; but as we know their +direction to be from below, we see that part of the object they describe +as the lowest. + +_Caroline._ When I want to see an object above me, I look up; when an +object below me, I look down. Does not this prove that I see the objects +themselves? for if I beheld only the image, there would be no necessity +for looking up or down, according as the object was higher or lower, +than myself. + +_Mrs. B._ I beg your pardon. When you look up, to an elevated object, it +is in order that the rays reflected from it, should fall upon the retina +of your eyes; but the very circumstance of directing your eyes upwards, +convinces you that the object is elevated, and teaches you to consider +as uppermost, the image it forms on the retina, though it is, in fact, +represented in the lowest part of it. When you look down upon an object, +you draw your conclusion from a similar reasoning; it is thus that we +see all objects in the direction of the rays which reach our eyes. + +But I have a further proof in favour of what I have advanced, which, I +hope, will remove your remaining doubts: I shall, however, defer it till +our next meeting, as the lesson has been sufficiently long to-day. + + +Questions + +1. (Pg. 157) What is optics? + +2. (Pg. 157) What is meant by a luminous body? + +3. (Pg. 157) What is meant by a dark body, and what by an opaque body? + +4. (Pg. 157) What are transparent bodies? + +5. (Pg. 157) What is a medium? + +6. (Pg. 158) How is light projected from luminous bodies, and how, from +every point of such bodies, (fig. 1, plate 15?) + +7. (Pg. 158) Why do not the rays of light from different points, stop +each other's progress? + +8. (Pg. 158) What is a ray, and what a pencil of rays? fig. 2, plate 15. + +9. (Pg. 158) Do we know whether light is a substance, similar to bodies +in general? + +10. (Pg. 158) When a ray of light falls upon an opaque body, what is the +result? + +11. (Pg. 159) In what does shadow consist? + +12. (Pg. 159) Why are they, in general, but partially dark? + +13. (Pg. 159) Upon what does the intensity of a shadow depend? + +14. (Pg. 159) How are shadows affected by the size of the luminous body, +as represented in plate 15, fig. 3? + +15. (Pg. 159) When is the shadow larger than the intercepting body? + +16. (Pg. 160) What is explained by fig. 4, plate 15? + +17. (Pg. 160) What will be the effect of several lights, as in fig. 5, +plate 15? + +18. (Pg. 160) Why will neither of these shadows be very dark? + +19. (Pg. 160) What becomes of the light which falls upon an opaque body? + +20. (Pg. 160) What is meant by reflection? + +21. (Pg. 161) What is meant by the incident, and reflected rays? + +22. (Pg. 161) What is the result, when the incident ray falls +perpendicularly, and what, when it falls obliquely? + +23. (Pg. 161) What two angles are always equal in this case? + +24. (Pg. 161) To what law in mechanics, is this analogous, as +represented in fig. 4, plate 2? + +25. (Pg. 161) What is represented by fig. 6, plate 15? + +26. (Pg. 161) By what light are we enabled to see opaque, and by what, +luminous bodies? + +27. (Pg. 161) What enables us to see a ray of light in its passage, +through a darkened room? + +28. (Pg. 162) By what reasoning would you prove that an object, such, +for example, as a house, is seen by reflected light? + +29. (Pg. 162) Why may one side of such object appear more bright than +another side? + +30. (Pg. 162) How is the fact exemplified by the sun, or moon, shining +upon water? + +31. (Pg. 162) Why is this best evinced by moonlight? + +32. (Pg. 163) By what light do we see the moon, and why is it +comparatively feeble? + +33. (Pg. 163) What circumstance, renders objects seen by moonlight, +still less vivid? + +34. (Pg. 164) What is meant by the pupil of the eye? + +35. (Pg. 164) What by the retina? + +36. (Pg. 164) How do the rays of light operate on the eye in producing +vision? + +37. (Pg. 164) How may this be exemplified, in a darkened room? + +38. (Pg. 164) What is meant by a _camera obscura_? + +39. (Pg. 164) How is it explained in plate 16? + +40. (Pg. 165) Why are the objects inverted and reversed? + +41. (Pg. 165) What analogy is there between the camera obscura, and the +eye? + +42. (Pg. 165) Is it the object, or its picture on the retina, which +presents to the mind an idea of the object seen? + +43. (Pg. 166) By what organs is sensation produced, and how must these +organs be affected? + +44. (Pg. 166) How will the idea of contact, apply to objects not +touching the eye? + +45. (Pg. 167) Why do not objects appear reversed to the eye, as in the +camera obscura? + + + + +CONVERSATION XV. + +OPTICS--_continued_. + +ON THE ANGLE OF VISION, AND THE REFLECTION OF MIRRORS. + +ANGLE OF VISION. REFLECTION OF PLAIN MIRRORS. REFLECTION OF CONVEX +MIRRORS. REFLECTION OF CONCAVE MIRRORS. + + +CAROLINE. + +Well, Mrs. B., I am very impatient to hear what further proofs you have +to offer, in support of your theory. You must allow, that it was rather +provoking to dismiss us as you did at our last meeting. + +_Mrs. B._ You press so hard upon me with your objections, that you must +give me time to recruit my forces. + +Can you tell me, Caroline, why objects at a distance, appear smaller +than they really are? + +_Caroline._ I know no other reason than their distance. + +_Mrs. B._ It is a fact, that distance causes objects to appear smaller, +but to state the fact, is not to give the reason. We must refer again to +the camera obscura, to account for this circumstance; and you will find, +that the different apparent dimensions of objects at different +distances, proceed from our seeing, not the objects themselves, but +merely their image on the retina. Fig. 1, plate 17, represents a row of +trees, as viewed in the camera obscura. I have expressed the direction +of the rays, from the objects to the image, by lines. Now, observe, the +ray which comes from the top of the nearest tree, and that which comes +from the foot of the same tree, meet at the aperture, forming an angle +of about twenty-five degrees; the angle under which we see any object, +is called, the visual angle, or, angle of vision. These rays cross each +other at the aperture, forming equal angles on each side of it, and +represent the tree inverted in the camera obscura. The degrees of the +image, are considerably smaller than those of the object, but the +proportions are perfectly preserved. + +[Illustration: PLATE XVII.] + +Now, let us notice the upper and lower ray, from the most distant tree; +they form an angle of not more than twelve or fifteen degrees, and an +image of proportional dimensions. Thus, two objects of the same size, as +the two trees of the avenue, form figures of different sizes in the +camera obscura, according to their distance; or, in other words, +according to the angle of vision under which they are seen. Do you +understand this? + +_Caroline._ Perfectly. + +_Mrs. B._ Then you have only to suppose, that the representation in the +camera obscura, is similar to that on the retina. + +Now, since objects of the same magnitudes, appear to be of different +dimensions, when at different distances from us, let me ask you which it +is, that you see; the real objects, which, we know, do not vary in size, +or the images, which, we know, do vary, according to the angle of vision +under which we see them? + +_Caroline._ I must confess, that reason is in favour of the latter. But +does that chair, at the further end of the room, form an image on my +retina, much smaller than this which is close to me? they appear exactly +of the same size. + +_Mrs. B._ Our senses are imperfect, but the experience we acquire by the +sense of touch, corrects the illusions of our sight, with regard to +objects within our reach. You are so perfectly convinced, of the real +size of objects, which you can handle, that you do not attend to the +apparent difference. + +Does that house appear to you much smaller, than when you are close to +it? + +_Caroline._ No, because it is very near us. + +_Mrs. B._ And yet you can see the whole of it, through one of the +windows of this room. The image of the house on your retina must, +therefore, be smaller than that of the window through which you see it. +It is your knowledge of the real magnitude of the house which prevents +your attending to its apparent size. If you were accustomed to draw from +nature, you would be fully aware of this difference. + +_Emily._ And pray, what is the reason that, when we look up an avenue, +the trees not only appear smaller as they are more distant, but seem +gradually to approach each other, till they meet in a point? + +_Mrs. B._ Not only the trees, but the road which separates the two rows, +forms a smaller visual angle, in proportion as it is more distant from +us; therefore, the width of the road gradually diminishes, as well as +the size of the trees, till at length the road apparently terminates in +a point, at which the trees seem to meet. + +_Emily._ I am very glad to understand this, for I have lately begun to +learn perspective, which appeared to me a very dry study; but now that I +am acquainted with some of the principles on which it is founded, I +shall find it much more interesting. + +_Caroline._ In drawing a view from nature, it seems that we do not copy +the real objects, but the image they form on the retina of our eyes? + +_Mrs. B._ Certainly. In sculpture, we copy nature as she really exists; +in painting, we represent her, as she appears to us. + +We must now conclude the observations that remain to be made, on the +angle of vision. + +If the rays, proceeding from the extremities of an object, with an +ordinary degree of illumination, do not enter the eye under an angle of +more than two seconds, which is the 1-1800th part of a degree, it is +invisible. There are, consequently, two cases in which objects may be +invisible; if they are either so small, or so distant, as to form an +angle of less than two seconds of a degree. + +In like manner, if the velocity of a body does not exceed 20 degrees in +an hour, its motion is imperceptible. + +_Caroline._ A very rapid motion may then be imperceptible, provided the +distance of the moving body, is sufficiently great. + +_Mrs. B._ Undoubtedly; for the greater its distance, the smaller will be +the angle, under which its motion will appear to the eye. It is for this +reason, that the motion of the celestial bodies is invisible, although +inconceivably rapid. + +_Emily._ I am surprised, that so great a velocity as 20 degrees an hour, +should be invisible. + +_Mrs. B._ The real velocity depends upon the space comprehended in each +degree, and upon the time, in which the moving body, passes over that +space. But we can only know the extent of this space, by knowing the +distance of the moving body, from its centre of motion; for supposing +two men to set off at the same moment from A and B, (fig. 2.) to walk +each to the end of their respective lines, C and D; if they perform +their walk in the same space of time, they must have proceeded at a +very different rate; and yet to an eye situated at E, they will appear +to have moved with equal velocity, because they will both have gone +through an equal number of degrees, though over a very unequal length of +ground. The number of degrees over which a body moves in a given time, +is called its angular velocity; two bodies, you see, may have the same +angular, or apparent velocity, whilst their real velocities may differ +almost infinitely. Sight is an extremely useful sense, no doubt, but it +cannot always be relied on, it deceives us both in regard to the size +and the distance of objects; indeed, our senses would be very liable to +lead us into error, if experience did not set us right. + +_Emily._ Between the two, I think that we contrive to acquire a +tolerably accurate idea of objects. + +_Mrs. B._ At least sufficiently so, for the general purposes of life. To +convince you how requisite experience is, to correct the errors of +sight, I shall relate to you, the case of a young man, who was blind +from his infancy, and who recovered his sight at the age of fourteen, by +the operation of couching. At first, he had no idea, either of the size, +or distance of objects, but imagined that every thing he saw touched his +eyes; and it was not, till after having repeatedly felt them, and walked +from one object to another, that he acquired an idea of their respective +dimensions, their relative situations, and their distances. + +_Caroline._ The idea that objects touched his eyes, is, however, not so +absurd, as it at first appears; for if we consider that we see only the +image of objects, this image actually touches our eyes. + +_Mrs. B._ That is, doubtless, the reason of the opinion he formed, +before the sense of touch had corrected his judgment. + +_Caroline._ But since an image must be formed on the retina of each of +our eyes, why do we not see objects double? + +_Mrs. B._ The action of the rays, on the optic nerve of each eye, is so +perfectly similar, that they produce but a single sensation; the mind, +therefore, receives the same idea, from the retina of both eyes, and +conceives the object to be single. + +_Caroline._ This is difficult to comprehend, and I should think, can be +but conjectural. + +_Mrs. B._ I can easily convince you, that you have a distinct image of +an object formed on the retina of each eye. Look through the window, +with both eyes open, at some object exactly opposite to one of the +upright bars of the sash. + +_Caroline._ I now see a tree, the body of which, appears to be in a line +exactly opposite to one of the bars. + +_Mrs. B._ If you now shut your right eye, and look with the left, it +will appear to the left of the bar; then by closing the left eye, and +looking with the other, it will appear to the right of the bar. + +_Caroline._ That is true, indeed! + +_Mrs. B._ There are, evidently, two representations of the tree in +different situations, which must be owing to an image of it being formed +on each eye; if the action of the rays, therefore, on each retina, were +not so perfectly similar as to produce but one sensation, we should see +double; and we find that to be the case with some persons, who are +afflicted with a disease in one eye, which prevents the rays of light +from affecting it in the same manner as the other. + +_Emily._ Pray, Mrs. B., when we see the image of an object in a +looking-glass, why is it not inverted, as in the camera obscura, and on +the retina of the eye? + +_Mrs. B._ Because the rays do not enter the mirror by a small aperture, +and cross each other, as they do at the orifice of a camera obscura, or +the pupil of the eye. + +When you view yourself in a mirror, the rays from your eyes fall +perpendicularly upon it, and are reflected in the same line; the image +is, therefore, described behind the glass, and is situated in the same +manner as the object before it. + +_Emily._ Yes, I see that it is; but the looking-glass is not nearly so +tall as I am, how is it, therefore, that I can see the whole of my +figure in it? + +_Mrs. B._ It is not necessary that the mirror should be more than half +your height, in order that you may see the whole of your person in it, +(fig. 3.) The ray of light A B, from your eye, which falls +perpendicularly on the mirror B D, will be reflected back, in the same +line; but the ray from your feet, will fall obliquely on the mirror, for +it must ascend in order to reach it; it will, therefore, be reflected in +the line A D: and since we view objects in the direction of the +reflected rays, which reach the eye, and since the image appears at the +same distance, behind the mirror, that the object is before it, we must +continue the line A D to E, and the line C D to F, at the termination of +which, the image will be represented. + +[Illustration: PLATE XVIII.] + +_Emily._ Then I do not understand why I should not see the whole of my +person in a much smaller mirror, for a ray of light from my feet would +always reach it, though more obliquely. + +_Mrs. B._ True; but the more obliquely the ray falls on the mirror, the +more obliquely it will be reflected; the ray would, therefore, be +reflected above your head, and you could not see it. This is shown by +the dotted line (fig. 3.) + +Now stand a little to the right of the mirror, so that the rays of light +from your figure may fall obliquely on it---- + +_Emily._ There is no image formed of me in the glass now. + +_Mrs. B._ I beg your pardon, there is; but you cannot see it, because +the incident rays, falling obliquely on the mirror, will be reflected +obliquely, in the opposite direction; the angles of incidence, and +reflection, being equal. Caroline, place yourself in the direction of +the reflected rays, and tell me whether you do not see Emily's image in +the glass? + +_Caroline._ Let me consider.--In order to look in the direction of the +reflected rays, I must place myself as much to the left of the glass, as +Emily stands to the right of it.--Now I see her image, not straight +before me, however, but before her; and it appears at the same distance +behind the glass, that she is in front of it. + +_Mrs. B._ You must recollect, that we always see objects in the +direction of the last rays, which reach our eyes. Figure 4 represents an +eye, looking at the image of a vase, reflected by a mirror; it must see +it in the direction of the ray A B, as that is the ray which brings the +image to the eye; prolong the ray to C, and in that spot will the image +appear. + +_Caroline._ I do not understand why a looking-glass reflects the rays of +light; for glass is a transparent body, which should transmit them! + +_Mrs. B._ It is not the glass that reflects the rays which form the +image you behold, but the silvering behind it; this silvering is a +compound of mercury and tin, which forms a brilliant metallic coating. +The glass acts chiefly as a transparent case, through which the rays +find an easy passage, to, and from, the quicksilver. + +_Caroline._ Why then should not mirrors be made simply of mercury? + +_Mrs. B._ Because mercury is a fluid. By amalgamating it with tinfoil, +it becomes of the consistence of paste, attaches itself to the glass, +and forms, in fact, a metallic mirror, which would be much more perfect +without its glass cover, for the purest glass is never perfectly +transparent; some of the rays, therefore, are lost during their passage +through it, by being either absorbed, or irregularly reflected. + +This imperfection of glass mirrors, has introduced the use of metallic +mirrors, for optical purposes. + +_Emily._ But since all opaque bodies reflect the rays of light, I do not +understand why they are not all mirrors. + +_Caroline._ A curious idea indeed, sister; it would be very gratifying +to see oneself in every object at which one looked. + +_Mrs. B._ It is very true that all opaque objects reflect light; but the +surface of bodies, in general, is so rough and uneven, that the +reflection from them is extremely irregular, and prevents the rays from +forming an image on the retina. This, you will be able to understand +better, when I shall explain to you the nature of vision, and the +structure of the eye. + +You may easily conceive the variety of directions in which rays would be +reflected by a nutmeg-grater, on account of the inequality of its +surface, and the number of holes with which it is pierced. All solid +bodies more or less resemble the nutmeg-grater, in these respects; and +it is only those which are susceptible of receiving a polish, that can +be made to reflect the rays with regularity. As hard bodies are of the +closest texture, the least porous, and capable of taking the highest +polish, they make the best mirrors; none, therefore, are so well +calculated for this purpose, as metals. + +_Caroline._ But the property of regular reflection, is not confined to +this class of bodies; for I have often seen myself, in a highly polished +mahogany table. + +_Mrs. B._ Certainly; but as that substance is less durable, and its +reflection less perfect, than that of metals, I believe it would seldom +be chosen, for the purpose of a mirror. + +There are three kinds of mirrors used in optics; the _plain_, or _flat_, +which are the common mirrors we have just mentioned; _convex_ mirrors, +and _concave_ mirrors. The reflection of the two latter, is very +different from that of the former. The plain mirror, we have seen, does +not alter the direction of the reflected rays, and forms an image behind +the glass, exactly similar to the object before it. A convex mirror has +the peculiar property of making the reflected rays diverge, by which +means it diminishes the image; and a concave mirror makes the rays +converge, and under certain circumstances, magnifies the image. + +_Emily._ We have a convex mirror in the drawing-room, which forms a +beautiful miniature picture of the objects in the room; and I have often +amused myself with looking at my magnified face in a concave mirror. But +I hope you will explain to us, why the one enlarges, while the other +diminishes the objects it reflects. + +_Mrs. B._ Let us begin by examining the reflection of a convex mirror. +This is formed of a portion of the exterior surface of a sphere. When +several parallel rays fall upon it, that ray only which, if prolonged, +would pass through the centre or axis of the mirror, is perpendicular to +it. In order to avoid confusion, I have, in fig. 1, plate 18, drawn only +three parallel lines, A B, C D, E F, to represent rays falling on the +convex mirror, M N; the middle ray, you will observe, is perpendicular +to the mirror, the others fall on it, obliquely. + +_Caroline._ As the three rays are parallel, why are they not all +perpendicular to the mirror? + +_Mrs. B._ They would be so to a flat mirror; but as this is spherical, +no ray can fall perpendicularly upon it which is not directed towards +the centre of the sphere. + +_Emily._ Just as a weight falls perpendicularly to the earth, when +gravity attracts it towards the centre. + +_Mrs. B._ In order, therefore, that rays may fall perpendicularly to the +mirror at B and F, the rays must be in the direction of the dotted +lines, which, you may observe, meet at the centre O of the sphere, of +which the mirror forms a portion. + +Now, can you tell me in what direction the three rays, A B, C D, E F, +will be reflected? + +_Emily._ Yes, I think so: the middle ray, falling perpendicularly on the +mirror, will be reflected in the same line: the two outer rays falling +obliquely, will be reflected obliquely to G and H; for the dotted lines +you have drawn are perpendiculars, which divide the angles of incidence +and reflection, of those two rays. + +_Mrs. B._ Extremely well, Emily: and since we see objects in the +direction of the reflected ray, we shall see the image L, which is the +point at which the reflected rays, if continued through the mirror, +would unite and form an image. This point is equally distant, from the +surface and centre of the sphere, and is called the imaginary focus of +the mirror. + +_Caroline._ Pray, what is the meaning of focus? + +_Mrs. B._ A point at which converging rays, unite. And it is in this +case, called an imaginary focus; because the rays do not really unite at +that point, but only appear to do so: for the rays do not pass through +the mirror, since they are reflected by it. + +_Emily._ I do not yet understand why an object appears smaller, when +viewed in a convex mirror. + +_Mrs. B._ It is owing to the divergence of the reflected rays. You have +seen that a convex mirror, by reflection, converts parallel rays into +divergent rays; rays that fall upon the mirror divergent, are rendered +still more so by reflection, and convergent rays are reflected either +parallel, or less convergent. If then, an object be placed before any +part of a convex mirror, as the vase A B, fig. 2, for instance, the two +rays from its extremities, falling convergent on the mirror, will be +reflected less convergent, and will not come to a focus, till they +arrive at C; then an eye placed in the direction of the reflected rays, +will see the image formed in (or rather behind) the mirror, at _a b_. + +_Caroline._ But the reflected rays, do not appear to me to converge less +than the incident rays. I should have supposed that, on the contrary, +they converged more, since they meet in a point. + +_Mrs. B._ They would unite sooner than they actually do, if they were +not less convergent than the incident rays: for observe, that if the +incident rays, instead of being reflected by the mirror, continued their +course in their original direction, they would come to a focus at D, +which is considerably nearer to the mirror than at C; the image, is, +therefore, seen under a smaller angle than the object; and the more +distant the latter is from the mirror, the smaller is the image +reflected by it. + +You will now easily understand the nature of the reflection of concave +mirrors. These are formed of a portion of the internal surface of a +hollow sphere, and their peculiar property is to converge the rays of +light. + +Can you discover, Caroline, in what direction the three parallel rays, A +B, C D, E F, are reflected, which fall on the concave mirror, M N, (fig. +3.)? + +_Caroline._ I believe I can. The middle ray is sent back in the same +line, in which it arrives, that being the direction of the axis of the +mirror; and the two others will be reflected obliquely, as they fall +obliquely on the mirror. I must now draw two dotted lines perpendicular +to their points of incidence, which will divide their angles of +incidence and reflection; and in order that those angles may be equal, +the two oblique rays must be reflected to L, where they will unite with +the middle ray. + +_Mrs. B._ Very well explained. Thus you see, that when any number of +parallel rays fall on a concave mirror, they are all reflected to a +focus: for in proportion as the rays are more distant from the axis of +the mirror, they fall more obliquely upon it, and are more obliquely +reflected; in consequence of which they come to a focus in the direction +of the axis of the mirror, at a point equally distant from the centre, +and the surface, of the sphere; and this point is not an imaginary +focus, as happens with the convex mirror, but is the true focus at which +the rays unite. + +_Emily._ Can a mirror form more than one focus, by reflecting rays? + +_Mrs. B._ Yes. If rays fall convergent on a concave mirror, (fig. 4,) +they are sooner brought to a focus, L, than parallel rays; their focus +is, therefore, nearer to the mirror M N. Divergent rays are brought to a +more distant focus than parallel rays, as in figure 5, where the focus +is at L; but what is called the true focus of mirrors, either convex or +concave, is that of parallel rays, and is equally distant from the +centre, and the surface of the spherical mirror. + +I shall now show you the real reflection of rays of light, by a metallic +concave mirror. This is one made of polished tin, which I expose to the +sun, and as it shines bright, we shall be able to collect the rays into +a very brilliant focus. I hold a piece of paper where I imagine the +focus to be situated; you may see by the vivid spot of light on the +paper, how much the rays converge: but it is not yet exactly in the +focus; as I approach the paper to that point, observe how the brightness +of the spot of light increases, while its size diminishes. + +_Caroline._ That must be occasioned by the rays approaching closer +together. I think you hold the paper just in the focus now, the light is +so small and dazzling--Oh, Mrs. B., the paper has taken fire! + +_Mrs. B._ The rays of light cannot be concentrated, without, at the same +time, accumulating a proportional quantity of heat: hence concave +mirrors have obtained the name of burning mirrors. + +_Emily._ I have often heard of the surprising effects of burning +mirrors, and I am quite delighted to understand their nature. + +_Caroline._ It cannot be the true focus of the mirror, at which the +rays of the sun unite, for as they proceed from so large a body, they +cannot fall upon the mirror parallel to each other. + +_Mrs. B._ Strictly speaking, they certainly do not. But when rays, come +from such an immense distance as the sun, they may be considered as +parallel: their point of union is, therefore, the true focus of the +mirror, and there the image of the object is represented. + +Now that I have removed the mirror out of the influence of the sun's +rays, if I place a burning taper in the focus, how will its light be +reflected? (Fig. 6.) + +_Caroline._ That, I confess, I cannot say. + +_Mrs. B._ The ray which falls in the direction of the axis of the +mirror, is reflected back in the same line; but let us draw two other +rays from the focus, falling on the mirror at B and F; the dotted lines +are perpendicular to those points, and the two rays will, therefore, be +reflected to A and E. + +_Caroline._ Oh, now I understand it clearly. The rays which proceed from +a light placed in the focus of a concave mirror fall divergent upon it, +and are reflected, parallel. It is exactly the reverse of the former +experiment, in which the sun's rays fell parallel on the mirror, and +were reflected to a focus. + +_Mrs. B._ Yes: when the incident rays are parallel, the reflected rays +converge to a focus; when, on the contrary, the incident rays proceed +from the focus, they are reflected parallel. This is an important law of +optics, and since you are now acquainted with the principles on which it +is founded, I hope that you will not forget it. + +_Caroline._ I am sure that we shall not. But, Mrs. B., you said that the +image was formed in the focus of a concave mirror; yet I have frequently +seen glass concave mirrors, where the object has been represented within +the mirror, in the same manner as in a convex mirror. + +_Mrs. B._ That is the case only, when the object is placed between the +mirror and its focus; the image then appears magnified behind the +mirror, or, as you would say, within it. + +_Caroline._ I do not understand why the image should be larger than the +object. + +_Mrs. B._ This results from the convergent property of the concave +mirror. If an object, A B, (fig. 7.) be placed between the mirror and +its focus, the rays from its extremities fall divergent on the mirror, +and on being reflected, become less divergent, as if they proceeded from +C: to an eye placed in that situation, the image will appear magnified +behind the mirror at _a b_, since it is seen under a larger angle than +the object. + +You now, I hope, understand the reflection of light by opaque bodies. At +our next meeting, we shall enter upon another property of light, no less +interesting, and which is called _refraction_. + + +Questions + +1. (Pg. 168) What is meant by the angle of vision, or the visual angle? + +2. (Pg. 169) Why do objects of the same size appear smaller when +distant, than when near? + +3. (Pg. 169) Why do not two objects, known to be equal in size, appear +to differ, when at different distances from the eye? + +4. (Pg. 169) How is this exemplified, by a house seen through a window? + +5. (Pg. 170) Why do rows of trees, forming an avenue, appear to approach +as they recede from the eye, until they eventually seem to meet? + +6. (Pg. 170) In drawing a view from nature, what do we copy? + +7. (Pg. 170) What is the difference in sculpture, in this respect? + +8. (Pg. 170) Excepting the rays from an object enter the eye, under a +certain angle, they cannot be seen; what must this angle exceed? + +9. (Pg. 170) What two circumstances may cause the angle to be so small, +as not to produce vision? + +10. (Pg. 170) Motion may be so slow as to become imperceptible, what is +said on this point? + +11. (Pg. 170) Under what circumstances may a body, moving with great +rapidity, appear to be at rest? + +12. (Pg. 170) Upon what does the real velocity of a body, depend? + +13. (Pg. 171) What must be known, to enable us to ascertain the real +space contained in a degree? + +14. (Pg. 171) What is explained by fig. 2, plate 17? + +15. (Pg. 171) What is said respecting the evidence afforded by our +senses, and how do we correct the errors into which they would lead us? + +16. (Pg. 171) An image of a visible object is formed upon the retina of +each eye, why, therefore, are not objects seen double? + +17. (Pg. 172) By what experiment can you prove that a separate image of +an object is formed in each eye? + +18. (Pg. 172) Under what circumstances are objects seen double? + +19. (Pg. 172) Why is not the image of an object inverted in the common +mirror? + +20. (Pg. 172) Your whole figure may be seen in a looking-glass, which is +not more than half your height; how is this shown in fig. 3. plate 17? + +21. (Pg. 173) Why is the image invisible to the person, when not +standing directly before the glass? + +22. (Pg. 173) In what situation may a second person see the image +reflected? + +23. (Pg. 173) In what direction will an object always appear to the eye? + +24. (Pg. 173) How is this explained by fig. 4, plate 17? + +25. (Pg. 173) What is it that reflects the rays in a looking-glass? + +26. (Pg. 174) All opaque bodies reflect some light, why do they not all +act as mirrors? + +27. (Pg. 174) What substances form the most perfect mirrors, and for +what reason? + +28. (Pg. 174) What are the three kinds of mirrors usually employed for +optical purposes? + +29. (Pg. 174) How are the rays of light affected by them? + +30. (Pg. 175) What is the form of a convex mirror, and how do parallel +rays fall upon it, as represented in fig. 1, plate 18? + +31. (Pg. 175) What is represented by the dotted line in the same figure? + +32. (Pg. 175) Explain by the figure, how the parallel rays will be +reflected. + +33. (Pg. 175) At what distance behind such a mirror, would an image, +produced by parallel rays, be formed? + +34. (Pg. 175) What is that point denominated? + +35. (Pg. 176) What is meant by a focus? + +36. (Pg. 176) Why is the point behind the mirror, called the _imaginary +focus_? + +37. (Pg. 176) Why does an object appear to be lessened by a convex +mirror, (fig. 2.)? + +38. (Pg. 176) What is a concave mirror, and what its peculiar property? + +39. (Pg. 176) How are parallel rays reflected by a concave mirror, as +explained by fig. 3, plate 18? + +40. (Pg. 177) Where is the focus of parallel rays, in a concave mirror? + +41. (Pg. 177) If rays fall on it convergent, how are they reflected? + +42. (Pg. 177) How if divergent? + +43. (Pg. 177) How, and why, may concave, become burning mirrors? + +44. (Pg. 178) Why may rays of light coming from the sun, be viewed as +parallel to each other? + +45. (Pg. 178) If a luminous body, as a burning taper, be placed in the +focus of a concave mirror, how will the rays from it, be reflected? +(fig. 6.) + +46. (Pg. 178) What fact is explained by fig. 7, plate 18? + + + + +CONVERSATION XVI. + +ON REFRACTION AND COLOURS. + +TRANSMISSION OF LIGHT BY TRANSPARENT BODIES. REFRACTION. REFRACTION BY +THE ATMOSPHERE. REFRACTION BY A LENS. REFRACTION BY THE PRISM. OF COLOUR +FROM THE RAYS OF LIGHT. OF THE COLOURS OF BODIES. + + +MRS. B. + +The refraction of light will furnish the subject of to-day's lesson. + +_Caroline._ That is a property of which I have not the faintest idea. + +_Mrs. B._ It is the effect which transparent mediums produce on light in +its passage through them. Opaque bodies, you know, reflect the rays, and +transparent bodies transmit them; but it is found, that _if a ray, in +passing from one medium, into another of different density, fall +obliquely, it is turned out of its course. The ray of light is then said +to be refracted._ + +_Caroline._ It must then be acted on by some new power, otherwise it +would not deviate from its first direction. + +_Mrs. B._ The power which causes the deviation of the ray, appears to be +the attraction of the denser medium. Let us suppose the two mediums to +be air, and water; if a ray of light passes from air, into water, it is +more strongly attracted by the latter, on account of its superior +density. + +_Emily._ In what direction does the water attract the ray? + +_Mrs. B._ The ray is attracted perpendicularly towards the water, in +the same manner in which bodies are acted upon by gravity. + +If then a ray, A B, (fig. 1, plate 19.) fall perpendicularly on water, +the attraction of the water acts in the same direction as the course of +the ray: it will not, therefore, cause a deviation, and the ray will +proceed straight on, to E. But if it fall obliquely, as the ray C B, the +water will attract it out of its course. Let us suppose the ray to have +approached the surface of a denser medium, and that it there begins to +be affected by its attraction; this attraction, if not counteracted by +some other power, would draw it perpendicularly to the water, at B; but +it is also impelled by its projectile force, which the attraction of the +denser medium cannot overcome; the ray, therefore, acted on by both +these powers, moves in a direction between them, and instead of pursuing +its original course to D, or being implicitly guided by the water to E, +proceeds towards F, so that the ray appears bent or broken. + +_Caroline._ I understand that very well; and is not this the reason that +oars appear bent in the water? + +_Mrs. B._ It is owing to the refraction of the rays, reflected by the +oar; but this is in passing from a dense, to a rare medium, for you know +that the rays, by means of which you see the oar, pass from water into +air. + +_Emily._ But I do not understand why refraction takes place, when a ray +passes from a dense into a rare medium; I should suppose that it would +be less, attracted by the latter, than by the former. + +_Mrs. B._ And it is precisely on that account that the ray is refracted. +Let the upper half of fig. 2, represent glass, and the lower half water, +let C B represent a ray, passing obliquely from the glass, into water: +glass, being the denser medium, the ray will be more strongly attracted +by that which it leaves than by that which it enters. The attraction of +the glass acts in the direction A B, while the impulse of projection +would carry the ray to F; it moves, therefore, between these directions +towards D. + +_Emily._ So that a contrary refraction takes place, when a ray passes +from a dense, into a rare medium. + +[Illustration: PLATE XIX.] + +_Mrs. B._ The rule upon this subject is this; _when a ray of light +passes from a rare into a dense medium, it is refracted towards the +perpendicular; when from a dense into a rare medium, it is refracted +from the perpendicular_. By the perpendicular is meant a line, at right +angle with the refracting surface. This may be seen in fig. 1, and +fig. 2, where the lines A E, are the perpendiculars. + +_Caroline._ But does not the attraction of the denser medium affect the +ray before it touches it? + +_Mrs. B._ The distance at which the attraction of the denser medium acts +upon a ray, is so small, as to be insensible; it appears, therefore, to +be refracted only at the point at which it passes from one medium into +the other. + +Now that you understand the principle of refraction, I will show you the +real refraction of a ray of light. Do you see the flower painted at the +bottom of the inside of this tea-cup? (Fig. 3.) + +_Emily._ Yes.--But now you have moved it just out of sight; the rim of +the cup hides it. + +_Mrs. B._ Do not stir. I will fill the cup with water, and you will see +the flower again. + +_Emily._ I do, indeed! Let me try to explain this: when you drew the cup +from me, so as to conceal the flower, the rays reflected by it, no +longer met my eyes, but were directed above them; but now that you have +filled the cup with water, they are refracted, and bent downwards when +passing out of the water, into the air, so as again to enter my eyes. + +_Mrs. B._ You have explained it perfectly: fig. 3. will help to imprint +it on your memory. You must observe that when the flower becomes visible +by the refraction of the ray, you do not see it in the situation which +it really occupies, but the image of the flower appears higher in the +cup; for as objects always appear to be situated in the direction of the +rays which enter the eye, the flower will be seen at B, in the direction +of the refracted ray. + +_Emily._ Then, when we see the bottom of a clear stream of water, the +rays which it reflects, being refracted in their passage from the water +into the air, will make the bottom appear higher than it really is. + +_Mrs. B._ And the water will consequently appear more shallow. Accidents +have frequently been occasioned by this circumstance; and boys, who are +in the habit of bathing, should be cautioned not to trust to the +apparent shallowness of water, as it will always prove deeper than it +appears. + +The refraction of light prevents our seeing the heavenly bodies in their +real situation: the light they send to us being refracted in passing +into the atmosphere, we see the sun and stars in the direction of the +refracted ray; as described in fig. 4, plate 19., the dotted line +represents the extent of the atmosphere, above a portion of the earth, E +B E: a ray of light coming from the sun S, falls obliquely on it, at A, +and is refracted to B; then, since we see the object in the direction of +the refracted ray, a spectator at B, will see an image of the sun at C, +instead of its real situation, at S. + +_Emily._ But if the sun were immediately over our heads, its rays, +falling perpendicularly on the atmosphere, would not be refracted, and +we should then see the real sun, in its true situation. + +_Mrs. B._ You must recollect that the sun, is vertical only to the +inhabitants of the torrid zone; its rays, therefore, are always +refracted, in this latitude. There is also another obstacle to our +seeing the heavenly bodies in their real situations: light, though it +moves with extreme velocity, is about eight minutes and a quarter, in +its passage from the sun to the earth; therefore, when the rays reach +us, the sun must have quitted the spot he occupied on their departure; +yet we see him in the direction of those rays, and consequently in a +situation which he had abandoned eight minutes and a quarter, before. + +_Emily._ When you speak of the sun's motion, you mean, I suppose, his +apparent motion, produced by the diurnal motion of the earth? + +_Mrs. B._ Certainly; the effect being the same, whether it is our earth, +or the heavenly bodies, which move: it is more easy to represent things +as they appear to be, than as they really are. + +_Caroline._ During the morning, then, when the sun is rising towards the +meridian, we must (from the length of time the light is in reaching us) +see an image of the sun below that spot which it really occupies. + +_Emily._ But the refraction of the atmosphere, counteracting this +effect, we may, perhaps, between the two, see the sun in its real +situation. + +_Caroline._ And in the afternoon, when the sun is sinking in the west, +refraction, and the length of time which the light is in reaching the +earth, will conspire to render the image of the sun, higher than it +really is. + +_Mrs. B._ The refraction of the sun's rays, by the atmosphere, prolongs +our days, as it occasions our seeing an image of the sun, both before he +rises, and after he sets; when below our horizon, he still shines upon +the atmosphere, and his rays are thence refracted to the earth: so +likewise we see an image of the sun, previously to his rising, the rays +that fall upon the atmosphere being refracted to the earth. + +_Caroline._ On the other hand, we must recollect that light is eight +minutes and a quarter on its journey; so that, by the time it reaches +the earth, the sun may, perhaps, have risen above the horizon. + +_Emily._ Pray, do not glass windows, refract the light? + +_Mrs. B._ They do; but this refraction would not be perceptible, were +the surfaces of the glass, perfectly flat and parallel, because, in +passing through a pane of glass, the rays suffer two refractions, which, +being in contrary directions, produce nearly the same effect as if no +refraction had taken place. + +_Emily._ I do not understand that. + +_Mrs. B:_ Fig. 5, plate 19, will make it clear to you: A A represents a +thick pane of glass, seen edgeways. When the ray B approaches the glass, +at C, it is refracted by it; and instead of continuing its course in the +same direction, as the dotted line describes, it passes through the +pane, to D; at that point returning into the air, it is again refracted +by the glass, but in a contrary direction to the first refraction, and +in consequence proceeds to E. Now you must observe that the ray B C and +the ray D E being parallel, the light does not appear to have suffered +any refraction: the apparent, differing so little from the true place of +any object, when seen through glass of ordinary thickness. + +_Emily._ So that the effect which takes place on the ray entering the +glass, is undone on its quitting it. Or, to express myself more +scientifically, when a ray of light passes from one medium into another, +and through that into the first again, the two refractions being equal, +and in opposite directions, no sensible effect is produced. + +_Caroline._ I think the effect is very sensible, for, in looking through +the glass of the window, I see objects very much distorted; articles +which I know to be straight, appear bent and broken, and sometimes the +parts seem to be separated to a distance from each other. + +_Mrs. B._ That is because common window glass is not flat, its whole +surface being uneven. Rays from any object, falling upon it under +different angles, are, consequently, refracted in various ways, and thus +produce the distortion you have observed. + +_Emily._ Is it not in consequence of refraction, that the glasses in +common spectacles, magnify objects seen through them? + +_Mrs. B._ Yes. Glasses of this description are called _lenses_; of +these, there are several kinds, the names of which it will be necessary +for you to learn. Every lens is formed of glass, ground so as to form a +segment of a sphere, on one, or both sides. They are all represented at +fig. 1, plate 20. The most common, is the _double convex_ lens, D. This +is thick in the middle, and thin at the edges, like common spectacles, +or reading glasses. A B, is a _plano-convex_ lens, being flat on one +side, and convex on the other. E is a _double concave_, being, in all +respects, the reverse of D. C is a _plano-concave_, flat on one side, +and concave on the other. F is called a _meniscus_, or _concavo-convex_, +being concave on one, and convex on the other side. A line passing +through the centre of a lens, is called its _axis_. + +_Caroline._ I should like to understand how the rays of light are +refracted, by means of a lens. + +_Mrs. B._ When parallel rays (fig. 6) fall on a double convex _lens_, +that only, which falls in the direction of the axis of the lens, is +perpendicular to the surface; the other rays, falling obliquely, are +refracted towards the axis, and will meet at a point beyond the lens, +called its _focus_. + +Of the three rays, A B C, which fall on the lens D E, the rays A and C +are refracted in their passage through it, to _a_, and _c_; and on +quitting the lens, they undergo a second refraction in the same +direction, which unites them with the ray B, at the focus F. + +_Emily._ And what is the distance of the focus, from the surface of the +lens? + +_Mrs. B._ The focal distance depends both upon the form of the lens, and +on the refracting power of the substance of which it is made: in a glass +lens, both sides of which are equally convex, the focus is situated +nearly at the centre of the sphere, of which the surface of the lens +forms a portion; it is at the distance, therefore, of the radius of the +sphere. + +The property of those lenses which have a convex surface, is to collect +the rays of light to a focus; and of those which have a concave surface, +on the contrary, to disperse them. For the rays A and C, falling on the +concave lens X Y, (fig. 7, plate 19.) instead of converging towards the +ray B, in the axis of the lens, will each be attracted towards the thick +edges of the lens, both on entering and quitting it, and will, +therefore, by the first refraction, be made to diverge to _a_, _c_, and +by the seconds, to _d_, _e_. + +[Illustration: PLATE XX.] + +_Caroline._ And lenses which have one side flat, and the other +convex, or concave, as A and B, (fig. 1, plate 20.) are, I suppose, +less powerful in their refractions? + +_Mrs. B._ Yes; the focus of the plano-convex, is at the distance of the +diameter of a sphere, of which the convex surface of the lens, forms a +portion; as represented in figure 2, plate 20. The three parallel rays, +A B C, are brought to a focus by the plano-convex lens, X Y, at F. + +_Emily._ You have not explained to us, Mrs. B., how the lens serves to +magnify objects. + +_Mrs. B._ By turning again to fig. 6, plate 19. you will readily +understand this. Let A C, be an object placed before the lens, and +suppose it to be seen by an eye at F; the ray from the point A, will be +seen in the direction F G, that from C, in the direction F H; the visual +angle, therefore, will be greatly increased, and the object must appear +larger, in proportion. + +I must now explain to you the refraction of a ray of light, by a +triangular piece of glass, called a prism. (Fig. 3.) + +_Emily._ The three sides of this glass are flat; it cannot, therefore, +bring the rays to a focus; nor do I suppose that its refraction will be +similar to that of a flat pane of glass, because it has not two sides +parallel; I cannot, therefore, conjecture what effect the refraction by +a prism, can produce. + +_Mrs. B._ The refractions of the ray, both on entering and on quitting +the prism, are in the same direction, (Fig. 3.) On entering the prism P, +the ray A is refracted from B to C, and on quitting it from C to D. In +the first instance it is refracted towards, and in the last, from the +perpendicular; each causing it to deviate in the same way, from its +original course, A B. + +I will show you this by experiment; but for this purpose it will be +advisable to close the window-shutters, and admit, through the small +aperture, a ray of light, which I shall refract, by means of this prism. + +_Caroline._ Oh, what beautiful colours are represented on the opposite +wall! There are all the colours of the rainbow, and with a brightness, I +never saw equalled. (Fig. 4, plate 20.) + +_Emily._ I have seen an effect, in some respects similar to this, +produced by the rays of the sun shining upon glass lustres; but how is +it possible that a piece of white glass can produce such a variety of +brilliant colours? + +_Mrs. B._ The colours are not formed by the prism, but existed in the +ray previously to its refraction. + +_Caroline._ Yet, before its refraction, it appeared perfectly white. + +_Mrs. B._ The white rays of the sun, are composed of rays, which, when +separated, produce all these colours, although when blended together, +they appear colourless or white. + +Sir Isaac Newton, to whom we are indebted for the most important +discoveries respecting light and colours, was the first who divided a +white ray of light, and found it to consist of an assemblage of coloured +rays, which formed an image upon the wall, such as you now see +exhibited, (fig. 4.) in which are displayed the following series of +colours: red, orange, yellow, green, blue, indigo, and violet. + +_Emily._ But how does a prism separate these coloured rays? + +_Mrs. B._ By refraction. It appears that the coloured rays have +different degrees of refrangibility; in passing through the prism, +therefore, they take different directions according to their +susceptibility of refraction. The violet rays deviate most from their +original course; they appear at one of the ends of the spectrum, A B: +contiguous to the violet, are the blue rays, being those which have +somewhat less refrangibility; then follow, in succession, the green, +yellow, orange, and lastly, the red, which are the least refrangible of +the coloured rays. + +_Caroline._ I cannot conceive how these colours, mixed together, can +become white? + +_Mrs. B._ That I cannot pretend to explain: but it is a fact that the +union of these colours, in the proportions in which they appear in the +spectrum, produce in us the idea of whiteness. If you paint a circular +piece of card, in compartments, with these seven colours, as nearly as +possible in the proportion, and of the shade exhibited in the spectrum, +and whirl it rapidly on a pin, it will appear white; as the velocity of +the motion, will have the effect of blending the colours, in the +impression which they make upon the eye. + +But a more decisive proof of the composition of a white ray is afforded, +by reuniting these coloured rays, and forming with them, a ray of white +light. + +_Caroline._ If you can take a ray of white light to pieces, and put it +together again, I shall be quite satisfied. + +_Mrs. B._ This can be done by letting the coloured rays, which have been +separated by a prism, fall upon a lens, which will converge them to a +focus; and if, when thus reunited, we find that they appear white as +they did before refraction, I hope you will be convinced that the white +rays, are a compound of the several coloured rays. The prism P, you +see, (fig. 5.) separates a ray of white light, into seven coloured rays, +and the lens L L brings them to a focus at F, where they again appear +white. + +_Caroline._ You succeed to perfection: this is indeed a most interesting +and conclusive experiment. + +_Emily._ Yet, Mrs. B., I cannot help thinking, that there may, perhaps, +be but three distinct colours in the spectrum, red, yellow, and blue; +and that the four others may consist of two of these colours blended +together; for, in painting, we find, that by mixing red and yellow, we +produce orange; with different proportions of red and blue, we make +violet or any shade of purple; and yellow, and blue, form green. Now, it +is very natural to suppose, that the refraction of a prism, may not be +so perfect as to separate the coloured rays of light completely, and +that those which are contiguous, in order of refrangibility, may +encroach on each other, and by mixing, produce the intermediate colours, +orange, green, violet, and indigo. + +_Mrs. B._ Your observation is, I believe, neither quite wrong, nor quite +right. Dr. Wollaston, who has performed many experiments on the +refraction of light, in a more accurate manner than had been previously +done, by receiving a very narrow line of light on a prism, found that it +formed a spectrum, consisting of rays of four colours only; but they +were not exactly those you have named as primitive colours, for they +consisted of red, green, blue, and violet. A very narrow line of yellow +was visible, at the limit of the red and green, which Dr. Wollaston +attributed to the overlapping of the edges of the red and green light. + +_Caroline._ But red and green mixed together, do not produce yellow? + +_Mrs. B._ Not in painting; but it may be so in the primitive rays of the +spectrum. Dr. Wollaston observed, that, by increasing the breadth of the +aperture, by which the line of light was admitted, the space occupied by +each coloured ray in the spectrum, was augmented, in proportion as each +portion encroached on the neighbouring colour, and mixed with it; so +that the intervention of orange and yellow, between the red and green, +is owing, he supposes, to the mixture of these two colours; and the blue +is blended on the one side with the green, and on the other with the +violet, forming the spectrum, as it was originally observed by Sir Isaac +Newton, and which I have just shown you. + +The rainbow, which exhibits a series of colours, so analogous to those +of the spectrum, is formed by the refraction of the sun's rays, in their +passage through a shower of rain; every drop of which acts as a prism, +in separating the coloured rays as they pass through it; the combined +effect of innumerable drops, produces the bow, which you know can be +seen, only when there are both rain, and sunshine. + +_Emily._ Pray, Mrs. B., cannot the sun's rays be collected to a focus by +a lens, in the same manner as they are by a concave mirror? + +_Mrs. B._ The same effect in concentrating the rays, is produced by the +refraction with a lens, as by the reflection from a concave mirror: in +the first, the rays pass through the glass and converge to a focus, +behind it, in the latter, they are reflected from the mirror, and +brought to a focus, before it. A lens, when used for the purpose of +collecting the sun's rays, is called a burning glass. I have before +explained to you, the manner in which a convex lens, refracts the rays, +and brings them to a focus; (fig. 6, plate 19.) as these rays contain +both light and heat, the latter, as well as the former, is refracted; +and intense heat, as well as light, will be found in the focal point. +The sun now shines very bright; if we let the rays fall on this lens, +you will perceive the focus. + +_Emily._ Oh yes: the point of union of the rays, is very luminous. I +will hold a piece of paper in the focus, and see if it will take fire. +The spot of light is extremely brilliant, but the paper does not burn? + +_Mrs. B._ Try a piece of brown paper;--that, you see, takes fire almost +immediately. + +_Caroline._ This is surprising; for the light appeared to shine more +intensely, on the white, than on the brown paper. + +_Mrs. B._ The lens collects an equal number of rays to a focus, whether +you hold the white or the brown paper, there; but the white paper +appears more luminous in the focus, because most of the rays, instead of +entering into the paper, are reflected by it; and this is the reason +that the paper does not readily take fire: whilst, on the contrary, the +brown paper, which absorbs more light and heat than it reflects, soon +becomes heated and takes fire. + +_Caroline._ This is extremely curious; but why should brown paper, +absorb more rays, than white paper? + +_Mrs. B._ I am far from being able to give a satisfactory answer to that +question. We can form but mere conjecture on this point; it is supposed +that the tendency to absorb, or reflect rays, depends on the +arrangement of the minute particles of the body, and that this diversity +of arrangement renders some bodies susceptible of reflecting one +coloured ray, and absorbing the others; whilst other bodies, have a +tendency to reflect all the colours, and others again, to absorb them +all. + +_Emily._ And how do you know which colours bodies have a tendency to +reflect, or which to absorb? + +_Mrs. B._ Because a body always appears to be of the colour which it +reflects; for, as we see only by reflected rays, it can appear of the +colour of those rays, only. + +_Caroline._ But we see all bodies of their own natural colour, Mrs. B.; +the grass and trees, green; the sky, blue; the flowers of various hues. + +_Mrs. B._ True; but why is the grass green?--because it absorbs all, +except the green rays; it is, therefore, these only which the grass and +trees reflect to our eyes, and this makes them appear green. The +flowers, in the same manner, reflect the various colours of which they +appear to us; the rose, the red rays; the violet, the blue; the jonquil, +the yellow, &c. + +_Caroline._ But these are the permanent colours of the grass and +flowers, whether the sun's rays shine on them or not. + +_Mrs. B._ Whenever you see those colours, the flowers must be illumined +by some light; and light, from whatever source it proceeds, is of the +same nature; composed of the various coloured rays which paint the +grass, the flowers, and every coloured object in nature. + +_Caroline._ But, Mrs. B., the grass is green, and the flowers are +coloured, whether in the dark, or exposed to the light? + +_Mrs. B._ Why should you think so? + +_Caroline._ It cannot be otherwise. + +_Mrs. B._ A most philosophical reason indeed! But, as I never saw them +in the dark, you will allow me to dissent from your opinion. + +_Caroline._ What colour do you suppose them to be, then, in the dark? + +_Mrs. B._ None at all; or black, which is the same thing. You can never +see objects, without light. White light is compounded of rays, from +which all the colours in nature are produced; there, therefore, can be +no colour without light; and though a substance is black, or without +colour, in the dark, it may become coloured, as soon as it becomes +visible. It is visible, indeed, only by the coloured rays which it +reflects; therefore, we can see it only when coloured. + +_Caroline._ All you say seems very true, and I know not what to object +to it; yet it appears at the same time incredible! What, Mrs. B., are we +all as black as negroes in the dark? you make me shudder at the thought. + +_Mrs. B._ Your vanity need not be alarmed at the idea, as you are +certain of never being seen, in that state. + +_Caroline._ That is some consolation, undoubtedly; but what a melancholy +reflection it is, that all nature which appears so beautifully +diversified with colours, is really one uniform mass of blackness! + +_Mrs. B._ Is nature less pleasing for being coloured, as well as +illumined, by the rays of light? and are colours less beautiful, for +being accidental, rather than essential properties of bodies? + +Providence seems to have decorated nature with the enchanting diversity +of colours, which we so much admire, for the sole purpose of beautifying +the scene, and rendering it a source of sensible gratification: it is an +ornament which embellishes nature, whenever we behold her. What reason +is there to regret, that she does not wear it when she is invisible? + +_Emily._ I confess, Mrs. B., that I have had my doubts, as well as +Caroline, though she has spared me the pains of expressing them: but I +have just thought of an experiment, which, if it succeed, will, I am +sure, satisfy us both. It is certain, that we cannot see bodies in the +dark, to know whether they have then any colour. But we may place a +coloured body in a ray of light, which has been refracted by a prism; +and if your theory is true, the body, of whatever colour it naturally +is, must appear of the colour of the ray in which it is placed; for +since it receives no other coloured rays, it can reflect no others. + +_Caroline._ Oh! that is an excellent thought, Emily; will you stand the +test, Mrs. B.? + +_Mrs. B._ I consent: but we must darken the room, and admit only the ray +which is to be refracted; otherwise, the white rays will be reflected on +the body under trial, from various parts of the room. With what do you +choose to make the experiment? + +_Caroline._ This rose: look at it, Mrs. B., and tell me whether it is +possible to deprive it of its beautiful colour? + +_Mrs. B._ We shall see.--I expose it first to the red rays, and the +flower appears of a more brilliant hue; but observe the green leaves---- + +_Caroline._ They appear neither red nor green; but of a dingy brown with +a reddish glow? + +_Mrs. B._ They cannot appear green, because they have no green rays to +reflect; neither are they red, because green bodies absorb most of the +red rays. But though bodies, from the arrangement of their particles, +have a tendency to absorb some rays, and reflect others, yet it is not +natural to suppose, that bodies are so perfectly uniform in their +arrangement, as to reflect only pure rays of one colour, and perfectly +to absorb the others; it is found, on the contrary, that a body +reflects, in great abundance, the rays which determine its colour, and +the others in a greater or less degree, in proportion as they are nearer +to or further from its own colour, in the order of refrangibility. The +green leaves of the rose, therefore, will reflect a few of the red rays, +which, blended with their natural blackness, give them that brown tinge: +if they reflected none of the red rays, they would appear perfectly +black. Now I shall hold the rose in the blue rays---- + +_Caroline._ Oh, Emily, Mrs. B. is right! look at the rose: it is no +longer red, but of a dingy blue colour. + +_Emily._ This is the most wonderful, of any thing we have yet learnt. +But, Mrs. B., what is the reason that the green leaves, are of a +brighter blue than the rose? + +_Mrs. B._ The green leaves reflect both blue and yellow rays, which +produce a green colour. They are now in a coloured ray, which they have +a tendency to reflect; they, therefore, reflect more of the blue rays +than the rose, (which naturally absorbs that colour,) and will, of +course, appear of a brighter blue. + +_Emily._ Yet, in passing the rose through the different colours of the +spectrum, the flower takes them more readily than the leaves. + +_Mrs. B._ Because the flower is of a paler hue. Bodies which reflect all +the rays, are white; those which absorb them all, are black: between +these extremes, bodies appear lighter or darker, in proportion to the +quantity of rays they reflect or absorb. This rose is of a pale red; it +approaches nearer to white than to black, and therefore, reflects rays, +more abundantly than it absorbs them. + +_Emily._ But if a rose has so strong a tendency to reflect rays, I +should imagine that it would be of a deep red colour. + +_Mrs. B._ I mean to say, that it has a general tendency to reflect rays. +Pale coloured bodies, reflect all the coloured rays to a certain degree, +their paleness, being an approach towards whiteness: but they reflect +one colour more than the rest: this predominates over the white, and +determines the colour of the body. Since, then, bodies of a pale colour, +in some degree reflect all the rays of light, in passing through the +various colours of the spectrum, they will reflect them all, with +tolerable brilliancy; but will appear most vivid, in the ray of their +natural colour. The green leaves, on the contrary, are of a dark colour, +bearing a stronger resemblance to black, than to white; they have, +therefore, a greater tendency to absorb, than to reflect rays; and +reflecting very few of any, but the blue, and yellow rays, they will +appear dingy, in passing through the other colours of the spectrum. + +_Caroline._ They must, however, reflect great quantities of the green +rays, to produce so deep a colour. + +_Mrs. B._ Deepness or darkness of colour, proceeds rather from a +deficiency, than an abundance of reflected rays. Remember, that if +bodies reflected none of the rays, they would be black; and if a body +reflects only a few green rays, it will appear of a dark green; it is +the brightness, and intensity of the colour, which show that a great +quantity of rays are reflected. + +_Emily._ A white body, then, which reflects all the rays, will appear +equally bright in all the colours of the spectrum. + +_Mrs. B._ Certainly. And this is easily proved by passing a sheet of +white paper, through the rays of the spectrum. + +White, you perceive, results from a body reflecting all the rays which +fall upon it; black, is produced, when they are all absorbed; and +colour, arises from a body possessing the power to decompose the solar +ray, by absorbing some parts, and reflecting others. + +_Caroline._ What is the reason that articles which are blue, often +appear green, by candle-light? + +_Mrs. B._ The light of a candle, is not of so pure a white as that of +the sun: it has a yellowish tinge, and when refracted by the prism, the +yellow rays predominate; and blue bodies reflect some of the yellow +rays, from their being next to the blue, in the order of refrangibility; +the superabundance of yellow rays, which is supplied by the candle, +gives to blue bodies, a greenish hue. + +_Caroline._ Candle-light must then give to all bodies, a yellowish +tinge, from the excess of yellow rays; and yet it is a common remark, +that people of a sallow complexion, appear fairer, or whiter, by +candle-light. + +_Mrs. B._ The yellow cast of their complexion is not so striking, when +every surrounding object has a yellow tinge. + +_Emily._ Pray, why does the sun appear red, through a fog? + +[Illustration: PLATE XXI.] + +_Mrs. B._ It is supposed to be owing to the rays, which are most +refrangible, being also the most easily reflected: in passing through an +atmosphere, loaded with moisture, as in foggy weather, and also in the +morning and evening, when mists prevail, the _violet_, _indigo_, _blue_, +and _green_ rays, are reflected back by the particles which load the +air; whilst the _yellow_, _orange_, and _red_ rays, being less +susceptible of reflection, pass on, and reach the eye. + +_Caroline._ And, pray, why is the sky of a blue colour? + +_Mrs. B._ You should rather say, the atmosphere; for the sky is a very +vague term, the meaning of which, it would be difficult to define, +philosophically. + +_Caroline._ But the colour of the atmosphere should be white, since all +the rays traverse it, in their passage to the earth. + +_Mrs. B._ Do not forget that the direct rays of light which pass from +the sun to the earth, do not meet our eyes, excepting when we are +looking at that luminary, and thus intercept them; in which case, you +know, that the sun appears white. The atmosphere is a transparent +medium, through which the sun's rays pass freely to the earth; but the +particles of which it is composed, also reflect the rays of light, and +it appears that they possess the property of reflecting the blue rays, +the most copiously: the light, therefore, which is reflected back into +the atmosphere, from the surface of the earth, falls upon these +particles of air, and the blue rays are returned by reflection: this +reflection is performed in every possible direction; so that whenever we +look at the atmosphere, some of these rays fall upon our eyes; hence we +see the air of a blue colour. If the atmosphere did not reflect any +rays, though the objects, on the surface of the earth, would be +illuminated, the sky would appear perfectly black. + +_Caroline._ Oh, how melancholy would that be; and how pernicious to the +sight, to be constantly viewing bright objects against a black sky. But +what is the reason that bodies often change their colour; as leaves, +which wither in autumn, or a spot of ink, which produces an iron-mould +on linen? + +_Mrs. B._ It arises from some chemical change, which takes place in the +arrangement of the component parts; by which they lose their tendency to +reflect certain colours, and acquire the power of reflecting others. A +withered leaf thus no linger reflects the blue rays; it appears, +therefore, yellow, or has a slight tendency to reflect several rays, +which produce a dingy brown colour. + +An ink spot on linen, at first absorbs all the rays; but, from the +action of soap, or of some other agent, it undergoes a chemical change, +and the spot partially regains its tendency to reflect colours, but with +a preference to reflect the yellow rays, and such is the colour of the +iron-mould. + +_Emily._ Bodies, then, far from being of the colour which they appear to +possess, are of that colour to which they have the greatest aversion, +with which they will not incorporate, but reject, and drive from them. + +_Mrs. B._ It certainly is so; though I scarcely dare venture to advance +such an opinion, whilst Caroline is contemplating her beautiful rose. + +_Caroline._ My poor rose! you are not satisfied with depriving it of +colour, but even make it have an aversion to it; and I am unable to +contradict you. + +_Emily._ Since dark bodies, absorb more solar rays than light ones, the +former should sooner be heated if exposed to the sun? + +_Mrs. B._ And they are found, by experience, to be so. Have you never +observed a black dress, to be warmer than a white one? + +_Emily._ Yes, and a white one more dazzling: the black is heated by +absorbing the rays, the white is dazzling, by reflecting them. + +_Caroline._ And this was the reason that the brown paper was burnt in +the focus of the lens, whilst the white paper exhibited the most +luminous spot, but did not take fire. + +_Mrs. B._ It was so. It is now full time to conclude our lesson. At our +next meeting, I shall give you a description of the eye. + + +Questions + +1. (Pg. 179) What is meant by the refraction of light? + +2. (Pg. 179) What is believed to be the cause of refraction? + +3. (Pg. 180) How is a ray refracted in passing obliquely from air into +water? + +4. (Pg. 180) How is this refraction explained in fig. 1, plate 19? + +5. (Pg. 180) What is fig. 2 intended to explain? + +6. (Pg. 180) What is the rule respecting refraction, by different +mediums? + +7. (Pg. 181) What is meant by the perpendicular? + +8. (Pg. 181) How does fig. 3, plate 19, elucidate the law of refraction? + +9. (Pg. 181) What will be the effect on the apparent situation of the +flower? + +10. (Pg. 181) What effect has refraction upon the apparent depth of a +stream of water? + +11. (Pg. 182) How does the atmosphere refract the rays of the sun, as +represented, fig. 4? + +12. (Pg. 182) Why have we the rays of the sun always refracted? + +13. (Pg. 182) What length of time is required for light to travel from +the sun, to the earth? + +14. (Pg. 182) What effect has this upon his apparent place? + +15. (Pg. 182) How is the length of the day affected by refraction? + +16. (Pg. 183) How are rays refracted, which fall obliquely upon a flat +pane of glass, (fig. 5, plate 19?) + +17. (Pg. 183) What is the reason that objects are distorted, when seen +through common window glass? + +18. (Pg. 184) What is meant by a lens? + +19. (Pg. 184) What are the five kinds called, represented at fig. 1, +plate 20? + +20. (Pg. 184) What is meant by the axis of a lens? + +21. (Pg. 184) How are parallel rays, refracted by the double convex +lens, fig. 6, plate 19? + +22. (Pg. 184) What is meant by the focus of a lens? + +23. (Pg. 184) What is the focal distance of parallel rays, from a double +convex lens? + +24. (Pg. 184) How are the rays refracted by a concave lens, fig. 7, +plate 19? + +25. (Pg. 185) What is the effect of one plane side in a lens? + +26. (Pg. 185) How is the focus of the plano-convex lens situated, fig. +2, plate 20? + +27. (Pg. 185) How does a convex lens magnify objects, fig. 6, plate 19? + +28. (Pg. 185) What is the article denominated which is represented at +fig. 3, plate 20? + +29. (Pg. 185) How will a ray be refracted, which enters on one side of +the prism, in the direction A B? + +30. (Pg. 185) What effect is produced by this refraction, as represented +in fig. 4, plate 20? + +31. (Pg. 186) Of what are the rays of white light said to be composed? + +32. (Pg. 186) What colours are produced? + +33. (Pg. 186) By what property, in light, does refraction enable us to +separate these different rays? + +34. (Pg. 187) What experiment may be performed with a piece of card, so +as to exemplify the compound nature of light? + +35. (Pg. 187) How can the same be shown by a lens, fig. 5. plate 20? + +36. (Pg. 187) Is it certain that there are seven primitive colours in +the spectrum? + +37. (Pg. 188) How is the rainbow produced, and what is necessary to its +production? + +38. (Pg. 188) How are the solar rays affected by a convex lens? + +39. (Pg. 188) Why is such a lens, called a burning glass? + +40. (Pg. 188) Why are bodies of a dark colour, more readily inflamed, +than those which are white? + +41. (Pg. 189) What is believed to be the reason, why some bodies absorb +more rays than others? + +42. (Pg. 189) What determines the colour of any particular body? + +43. (Pg. 189) What exemplifications are given? + +44. (Pg. 189) By what reasoning is it proved, that bodies do not retain +their colours in the dark? + +45. (Pg. 190) What proof of the truth of this theory of colours, may be +afforded by the prism? + +46. (Pg. 191) Why will green leaves, when exposed to the red ray, appear +of a dingy brown? + +47. (Pg. 191) Bodies, in general, when placed in a ray differing in +colour from their own, appear of a mixed hue, what causes this? + +48. (Pg. 191) Why will bodies of a pale, or light hue, most perfectly, +assume the different colours of the spectrum? + +49. (Pg. 192) Upon what property in a body, does the darkness of its +colour depend? + +50. (Pg. 192) Why do some bodies appear white, others black, and others +of different colours? + +51. (Pg. 192) From what cause do blue articles appear green, by +candle-light? + +52. (Pg. 193) What is believed to be the cause, of the red appearance of +the sun, through a fog, or misty atmosphere? + +53. (Pg. 193) From what is the blue colour of the sky, thought to arise? + +54. (Pg. 193) What would be the colour of the sky, did not the +atmosphere reflect light? + +55. (Pg. 193) From what cause do some bodies change their colour, as +leaves formerly green, become brown, and ink, yellow? + +56. (Pg. 194) Why is a black dress, warmer in the sunshine, than a white +one of the same texture? + + + + +CONVERSATION XVII. + +ON THE STRUCTURE OF THE EYE, AND OPTICAL INSTRUMENTS. + +DESCRIPTION OF THE EYE. OF THE IMAGE ON THE RETINA. REFRACTION BY THE +HUMOURS OF THE EYE. OF THE USE OF SPECTACLES. OF THE SINGLE MICROSCOPE. +OF THE DOUBLE MICROSCOPE. OF THE SOLAR MICROSCOPE. MAGIC LANTHORN. +REFRACTING TELESCOPE. REFLECTING TELESCOPE. + + +MRS. B. + +The body of the eye, is of a spherical form: (fig. 1. plate 21.) it has +two membranous coats, or coverings; the external one, _a a a_, is called +the sclerotica, this is commonly known under the name of the white of +the eye; it has a projection in that part of the eye which is exposed to +view, _b b_, which is called the transparent cornea, because, when +dried, it has nearly the consistence of very fine horn, and is +sufficiently transparent for the light to obtain free passage through +it. + +The second membrane which lines the cornea, and envelops the eye, is +called the choroid, _c c c_; this has an opening in front, just beneath +the cornea, which forms the pupil, or sight of the eye, _d d_, through +which the rays of light pass into the eye. The pupil is surrounded by a +coloured border called the iris, _e e_, which, by its muscular motion, +always preserves the pupil of a circular form, whether it is expanded in +the dark, or contracted by a strong light. This you will understand +better by examining fig. 2. + +_Emily._ I did not know that the pupil was susceptible of varying its +dimensions. + +_Mrs. B._ The construction of the eye is so admirable, that it is +capable of adapting itself, more or less, to the circumstances in which +it is placed. In a faint light, the pupil dilates so as to receive an +additional quantity of rays, and in a strong light, it contracts, in +order to prevent the intensity of the light from injuring the optic +nerve. Observe Emily's eyes, as she sits looking towards the windows: +the pupils appear very small, and the iris, large. Now, Emily, turn from +the light, and cover your eyes with your hand, so as entirely to exclude +it, for a few moments. + +_Caroline._ How very much the pupils of her eyes are now enlarged, and +the iris diminished! This is, no doubt, the reason why the eyes suffer +pain, when from darkness, they suddenly come into a strong light; for +the pupil being dilated, a quantity of rays must rush in, before it has +time to contract. + +_Emily._ And when we go from a strong light, into obscurity, we at first +imagine ourselves in total darkness; for a sufficient number of rays +cannot gain admittance into the contracted pupil, to enable us to +distinguish objects: but in a few minutes it dilates, and we clearly +perceive objects which were before invisible. + +_Mrs. B._ It is just so. The choroid _c c_, is embued with a black +liquor, which serves to absorb all the rays that are irregularly +reflected, and to convert the body of the eye, into a more perfect +camera obscura. When the pupil is expanded to its utmost extent, it is +capable of admitting ten times the quantity of light, that it does when +most contracted. In cats, and animals which are said to see in the dark, +the power of dilatation and contraction of the pupil, is still greater; +it is computed that the pupils of their eyes may admit one hundred times +more light at one time than at another. + +Within these coverings of the eye-ball, are contained, three transparent +substances, called humours. The first occupies the space immediately +behind the cornea, and is called the aqueous humour, _f f_, from its +liquidity and its resemblance to water. Beyond this, is situated the +crystalline humour, _g g_, so called from its clearness and +transparency: it has the form of a lens, and refracts the rays of light +in a greater degree of perfection, than any that have been constructed +by art: it is attached by two muscles, _m m_, to each side of the +choroid. The back part of the eye, between the crystalline humour and +the retina, is filled by the vitreous humour, _h h_, which derives its +name from a resemblance it is supposed to bear, to glass, or vitrified +substances. + +[Illustration: PLATE XXII.] + +The membranous coverings of the eye are intended chiefly for the +preservation of the retina, _i i_, which is by far the most important +part of the eye, as it is that which receives the impression of the +objects of sight, and conveys it to the mind. The retina is formed by +the expansion of the optic nerve, and is of a most perfect whiteness: +this nerve proceeds from the brain, enters the eye, at _n_, on the side +next the nose, and is finely spread over the interior surface of the +choroid. + +The rays of light which enter the eye, by the pupil, are refracted by +the several humours in their passage through them, and unite in a focus +on the retina. + +_Caroline._ I do not understand the use of these refracting humours: the +image of objects was represented in the camera obscura, without any such +assistance. + +_Mrs. B._ That is true; but the representation became much more strong +and distinct, when we enlarged the opening of the camera obscura, and +received the rays into it, through a lens. + +I have told you, that rays proceed from bodies in all possible +directions. We must, therefore, consider every part of an object which +sends rays to our eyes, as points from which the rays diverge, as from a +centre. + +_Emily._ These divergent rays, issuing from a single point, I believe +you told us, were called a pencil of rays? + +_Mrs. B._ Yes. Now, divergent rays, on entering the pupil, do not cross +each other; the pupil, however, is sufficiently large to admit a small +pencil of them; and these, if not refracted to a focus, by the humours, +would continue diverging after they had passed the pupil, would fall +dispersed upon the retina, and thus the image of a single point, would +be expanded over a large portion of the retina. The divergent rays from +every other point of the object, would be spread over a similar extent +of space, and would interfere and be confounded with the first; so that +no distinct image could be formed, and the representation on the retina +would be confused, both in figure and colour. Fig. 3. represents two +pencils of rays, issuing from two points of the tree, A B, and entering +the pupil C, refracted by the crystalline humour D, and forming on the +retina, at _a b_, distinct images of the spot they proceed from. Fig. 4. +differs from the preceding, merely from not being supplied with a lens; +in consequence of which, the pencils of rays are not refracted to a +focus, and no distinct image is formed on the retina. I have delineated +only the rays issuing from two points of an object, and distinguished +the two pencils in fig. 4. by describing one of them with dotted lines: +the interference of these two pencils of rays on the retina, will enable +you to form an idea of the confusion which would arise, from thousands +and millions of points, at the same instant pouring their divergent rays +upon the retina. + +_Emily._ True; but I do not yet well understand, how the refracting +humours, remedy this imperfection. + +_Mrs. B._ The refraction of these several humours, unites the whole of a +pencil of rays, proceeding from any one point of an object, to a +corresponding point on the retina, and the image is thus rendered +distinct and strong. If you conceive, in fig. 3., every point of the +tree to send forth a pencil of rays, similar to those from A B, every +part of the tree will be as accurately represented on the retina, as the +points _a b_. + +_Emily._ How admirably, how wonderfully, is this contrived! + +_Caroline._ But since the eye absolutely requires refracting humours, in +order to have a distinct representation formed on the retina, why is not +the same refraction equally necessary, for the images formed in the +camera obscura? + +_Mrs. B._ It is; excepting the aperture through which we receive the +rays into the camera obscura, is extremely small; so that but very few +of the rays diverging from a point, gain admittance; but when we +enlarged the aperture, and furnished it with a lens, you found the +landscape more perfectly represented. + +_Caroline._ I remember how obscure and confused the image was, when you +enlarged the opening, without putting in the lens. + +_Mrs. B._ Such, or very similar, would be the representation on the +retina, unassisted by the refracting humours. + +You will now be able to understand the nature of that imperfection of +sight, which arises from the eyes being too prominent. In such cases, +the crystalline humour, D, (fig. 5.) being extremely convex, refracts +the rays too much, and collects a pencil, proceeding from the object A +B, into a focus, F, before they reach the retina. From this focus, the +rays proceed, diverging, and consequently form a very confused image on +the retina, at _a b_. This is the defect in short-sighted people. + +_Emily._ I understand it perfectly. But why is this defect remedied by +bringing the object nearer to the eye, as we find to be the case with +short-sighted people? + +_Mrs. B._ The nearer you bring an object to your eye, the more divergent +the rays fall upon the crystalline humour, and consequently they are not +so soon converged to a focus: this focus, therefore, either falls upon +the retina, or at least approaches nearer to it, and the object is +proportionally distinct, as in fig. 6. + +_Emily._ The nearer, then, you bring an object to a lens, the further +the image recedes behind it. + +_Mrs. B._ Certainly. But short-sighted persons have another resource, +for objects which they can not bring near to their eyes; this is, to +place a concave lens, C D, (fig. 1, plate 22.) before the eye, in order +to increase the divergence of the rays. The effect of a concave lens, +is, you know, exactly the reverse of a convex one: it renders parallel +rays divergent, and those which are already divergent, still more so. By +the assistance of such glasses, therefore, the rays from a distant +object, fall on the pupil, as divergent as those from a less distant +object; and, with short-sighted people, they throw the image of a +distant object, back, as far as the retina. + +_Caroline._ This is an excellent contrivance, indeed. + +_Mrs. B._ And tell me, what remedy would you devise for such persons as +have a contrary defect in their sight; that is to say, who are +long-sighted, in whom the crystalline humour, being too flat, does not +refract the rays sufficiently, so that they reach the retina before they +are converged to a point? + +_Caroline._ I suppose that a contrary remedy must be applied to this +defect; that is to say, a convex lens, L M, fig. 2, to make up for the +deficiency of convexity of the crystalline humour, O P. For the convex +lens would bring the rays nearer together, so that they would fall, +either less divergent, or parallel, on the crystalline humour; and, by +being sooner converged to a focus, would fall on the retina. + +_Mrs. B._ Very well, Caroline. This is the reason why elderly people, +the humours of whose eyes are decayed by age, are under the necessity of +using convex spectacles. And when deprived of that resource, they hold +the object at a distance from their eyes, as in fig. 3, in order to +bring the focus more forward. + +_Caroline._ I have often been surprised, when my grandfather reads +without his spectacles, to see him hold the book at a considerable +distance from his eyes. But I now understand the cause; the more distant +the object is from the crystalline lens, the nearer to it, will the +image be formed. + +_Emily._ I comprehend the nature of these two opposite defects very +well; but I cannot now conceive, how any sight can be perfect: for, if +the crystalline humour is of a proper degree of convexity, to bring the +image of distant objects to a focus on the retina, it will not represent +near objects distinctly; and if, on the contrary, it is adapted to give +a clear image of near objects, it will produce a very imperfect one, of +distant objects. + +_Mrs. B._ Your observation is very good, Emily; and it is true, that +every person would be subject to one of these two defects, if we had it +not in our power to adapt the eye, to the distance of the object; it is +believed that this is accomplished, by our having a command over the +crystalline lens, so as to project it towards, or draw it back from the +object, as circumstances require, by means of the two muscles, to which +the crystalline humour is attached; so that the focus of the rays, +constantly falls on the retina, and an image is formed equally distinct, +either of distant objects, or of those which are near. + +_Caroline._ In the eyes of fishes, which are the only eyes I have ever +seen separate from the head, the cornea does not protrude, in that part +of the eye which is exposed to view. + +_Mrs. B._ The cornea of the eye of a fish is not more convex than the +rest of the ball of the eye; but to supply this deficiency, their +crystalline humour is spherical, and refracts the rays so much, that it +does not require the assistance of the cornea to bring them to a focus +on the retina. + +_Emily._ Pray, what is the reason that we cannot see an object +distinctly, if we place it very near to the eye? + +_Mrs. B._ Because the rays fall on the crystalline humour, too divergent +to be refracted to a focus on the retina; the confusion, therefore, +arising from viewing an object too near the eye, is similar to that +which proceeds from a flattened crystalline humour; the rays reach the +retina before they are collected to a focus, (fig. 4.) If it were not +for this imperfection, we should be able to see and distinguish the +parts of objects, which, from their minuteness, are now invisible to us; +for, could we place them very near the eye, the image on the retina +would be so much magnified, as to render them visible. + +_Emily._ And could there be no contrivance, to convey the rays of +objects viewed, close to the eye, so that they should be refracted to a +focus on the retina? + +_Mrs. B._ The microscope is constructed for this purpose. The single +microscope (fig. 5.) consists simply of a convex lens, commonly called a +magnifying glass; in the focus of which the object is placed, and +through which it is viewed: by this means, you are enabled to place your +eye very near to the object, for the lens A B, by diminishing the +divergence of the rays, before they enter the pupil C, makes them fall +parallel on the crystalline humour D, by which they are refracted to a +focus on the retina, at R R. + +_Emily._ This is a most admirable invention, and nothing can be more +simple; for the lens magnifies the object, merely by allowing us to +bring it nearer to the eye. + +[Illustration: PLATE XXIII.] + +_Mrs. B._ Those lenses, therefore, which have the shortest focus will +magnify the object most, because they enable us to place it nearest to +the eye. + +_Emily._ But a lens, that has the shortest focus, is most bulging or +convex; and the protuberance of the lens will prevent the eye from +approaching very near to the object. + +_Mrs. B._ This is remedied by making the lens extremely small: it may +then be spherical without occupying much space, and thus unite the +advantages of a short focus, and of allowing the eye to approach the +object. + +There is a mode of magnifying objects, without the use of a lens: if you +look through a hole, not larger than a small pin, you may place a minute +object near to the eye, and it will be distinct, and greatly enlarged. +This piece of tin has been perforated for the purpose; place it close to +your eye, and this small print before it. + +_Caroline._ Astonishing! the letters appear ten times as large as they +do without it: I cannot conceive how this effect is produced. + +_Mrs. B._ The smallness of the hole, prevents the entrance into the eye, +of those parts of every pencil of rays which diverge much; so that, +notwithstanding the nearness of the object, those rays from it, which +enter the eye, are nearly parallel, and are, therefore, brought to a +focus by the humours of the eye. + +_Caroline._ We have a microscope at home, which is a much more +complicated instrument than that you have described. + +_Mrs. B._ It is a double microscope, (fig. 6.) in which you see, not the +object A B, but a magnified image of it, _a b_. In this microscope, two +lenses are employed; the one, L M, for the purpose of magnifying the +object, is called the object-glass, the other, N O, acts on the +principle of the single microscope, and is called the eye-glass. + +There is another kind of microscope, called the solar microscope, which +is the most wonderful from its great magnifying power: in this we also +view an image formed by a lens, not the object itself. As the sun +shines, I can show you the effect of this microscope; but for this +purpose, we must close the shutters, and admit only a small portion of +light, through the hole in the window-shutter, which we used for the +camera obscura. We shall now place the object A B, (plate 23, fig. 1.) +which is a small insect, before the lens C D, and nearly at its focus: +the image E F, will then be represented on the opposite wall, in the +same manner, as the landscape was in the camera obscura; with this +difference, that it will be magnified, instead of being diminished. I +shall leave you to account for this, by examining the figure. + +_Emily._ I see it at once. The image E F is magnified, because it is +farther from the lens, than the object A B; while the representation of +the landscape was diminished, because it was nearer the lens, than the +landscape was. A lens, then, answers the purpose equally well, either +for magnifying or diminishing objects? + +_Mrs. B._ Yes: if you wish to magnify the image, you place the object +near the focus of the lens; if you wish to produce a diminished image, +you place the object at a distance from the lens, in order that the +image may be formed in, or near the focus. + +_Caroline._ The magnifying power of this microscope is prodigious: but +the indistinctness of the image, for want of light, is a great +imperfection. Would it not be clearer, if the opening in the shutter +were enlarged, so as to admit more light? + +_Mrs. B._ If the whole of the light admitted, does not fall upon the +object, the effect will only be to make the room lighter, and the image +consequently less distinct. + +_Emily._ But could you not by means of another lens, bring a large +pencil of rays to a focus on the object, and thus concentrate upon it +the whole of the light admitted? + +_Mrs. B._ Very well. We shall enlarge the opening, and place the lens X +Y (fig. 2.) in it, to converge the rays to a focus on the object A B. +There is but one thing more wanting to complete the solar microscope, +which I shall leave to Caroline's sagacity to discover. + +_Caroline._ Our microscope has a small mirror attached to it, upon a +moveable joint, which can be so adjusted as to receive the sun's rays, +and reflect them upon the object: if a similar mirror were placed to +reflect light upon the lens, would it not be a means of illuminating the +object more perfectly? + +_Mrs. B._ You are quite right. P Q (fig. 2.) is a small mirror, placed +on the outside of the window-shutter, which receives the incident rays S +S, and reflects them on the lens X Y. Now that we have completed the +apparatus, let us examine the mites on this piece of cheese, which I +place near the focus of the lens. + +_Caroline._ Oh, how much more distinct the image now is, and how +wonderfully magnified! The mites on the cheese look like a drove of pigs +scrambling over rocks. + +_Emily._ I never saw any thing so curious. Now, an immense piece of +cheese has fallen: one might imagine it an earthquake: some of the poor +mites must have been crushed; how fast they run--they absolutely seem to +gallop. + +But this microscope can be used only for transparent objects; as the +light must pass through them, to form the image on the wall? + +_Mrs. B._ Very minute objects, such as are viewed in a microscope, are +generally transparent, but when opaque objects are to be exhibited, a +mirror M N (fig. 3.) is used to reflect the light on the side of the +object next the wall: the image is then formed by light reflected from +the object, instead of being transmitted through it. + +_Emily._ Pray, is not a magic lanthorn constructed on the same +principles? + +_Mrs. B._ Yes, with this difference; the objects to be magnified, are +painted upon pieces of glass, and the light is supplied by a lamp, +instead of the sun. + +The microscope is an excellent invention to enable us to see and +distinguish objects, which are too small to be visible to the naked eye. +But there are objects, which, though not really small, appear so to us, +from their distance; to these, we cannot apply the same remedy; for when +a house is so far distant, as to be seen under the same angle as a mite +which is close to us, the effect produced on the retina is the same: the +angle it subtends is not large enough for it to form a distinct image on +the retina. + +_Emily._ Since it is impossible, in this case, to make the object +approach the eye, cannot we by means of a lens bring an image of it, +nearer to us? + +_Mrs. B._ Yes; but then the object being very distant from the focus of +the lens, the image would be too small to be visible to the naked eye. + +_Emily._ Then, why not look at the image through another lens, which +will act as a microscope, enable us to bring the image close to the eye, +and thus render it visible? + +_Mrs. B._ Very well, Emily; I congratulate you on having invented a +telescope. In figure 4, the lens C D, forms an image E F, of the object +A B; and the lens X Y, serves the purpose of magnifying that image; and +this is all that is required in a common refracting telescope. + +_Emily._ But in fig. 4, the image is not inverted on the retina, as +objects usually are: it should therefore appear to us inverted; and that +is not the case in the telescopes I have looked through. + +_Mrs. B._ When it is necessary to represent the image erect, two other +lenses are required; by which means a second image is formed, the +reverse of the first, and consequently upright. These additional glasses +are used to view terrestrial objects; for no inconvenience arises from +seeing the celestial bodies inverted. + +_Emily._ The difference between a microscope and a telescope, seems to +be this:--a microscope produces a magnified image, because the object is +nearest the lens; and a telescope produces a diminished image, because +the object is furthest from the lens. + +_Mrs. B._ Your observation applies only to the lens C D, or +object-glass, which serves to bring an image of the object nearer the +eye; for the lens X Y, or eye-glass, is, in fact, a microscope, as its +purpose is to magnify the image. + +When a very great magnifying power is required, telescopes are +constructed with concave mirrors, instead of lenses. These are called +reflecting telescopes, because the image is reflected by metallic +mirrors. Concave mirrors, you know, produce by reflection, an effect +similar to that of convex lenses, by refraction. In reflecting +telescopes, therefore, mirrors are used in order to bring the image +nearer the eye; and a lens, or eye-glass, the same as in the refracting +telescope, to magnify the image. + +The advantage of the reflecting telescope is, that mirrors whose focus +is six feet, will magnify as much as lenses of a hundred feet: an +instrument of this kind may, therefore, possess a high magnifying power, +and yet be so short, as to be readily managed. + +_Caroline._ But I thought it was the eye-glass only which magnified the +image; and that the other lens, served to bring a diminished image +nearer to the eye. + +_Mrs. B._ The image is diminished in comparison with the object, it is +true; but it is magnified, if you compare it to the dimensions of which +it would appear without the intervention of any optical instrument; and +this magnifying power is greater in reflecting, than in refracting +telescopes. + +We must now bring our observations to a conclusion, for I have +communicated to you the whole of my very limited stock of knowledge of +Natural Philosophy. If it enable you to make further progress in that +science, my wishes will be satisfied; but remember, in order that the +study of nature may be productive of happiness, it must lead to an +entire confidence in the wisdom and goodness of its bounteous Author. + + +Questions + +1. (Pg. 195) What is the form of the body of the eye? fig. 1, plate 21. + +2. (Pg. 195) What is its external coat called? + +3. (Pg. 195) What is the transparent part of this coat denominated? + +4. (Pg. 195) What is the second coat named? + +5. (Pg. 195) What opening is there in this? + +6. (Pg. 195) What is the coloured part which surrounds the pupil? + +7. (Pg. 195) The pupils dilate and contract, what purpose does this +answer? + +8. (Pg. 196) How could you observe the dilatation and contraction of the +pupils? + +9. (Pg. 196) What purpose is the choroid said to answer? + +10. (Pg. 196) In what animals is the change in the iris greatest? + +11. (Pg. 196) What are the three humours denominated, and how are they +situated? + +12. (Pg. 197) What is the part represented at _i i_, and of what does it +consist? + +13. (Pg. 197) What are the respective uses of the humours, and of the +retina? + +14. (Pg. 197) Why is it necessary the rays should be refracted? + +15. (Pg. 197) How is this illustrated by fig. 3 and 4, plate 21? + +16. (Pg. 198) What causes a person to be short-sighted? fig. 5, plate +21. + +17. (Pg. 198) Why does placing an object near the eye, enable such, to +see distinctly? fig. 6. + +18. (Pg. 199) A concave lens remedies this defect; how? fig. 1, plate +22. + +19. (Pg. 199) What is the remedy, when a person is long-sighted? fig. 2. + +20. (Pg. 199) Why does holding an object far from the eye, help such +persons? fig. 3. + +21. (Pg. 200) How is the eye said to adapt itself to distant, and to +near objects? + +22. (Pg. 200) Why are objects rendered indistinct, when placed very near +to the eye? fig. 4, plate 22. + +23. (Pg. 200) What is the single microscope, fig. 5, and how does it +magnify objects? + +24. (Pg. 201) How may objects be magnified without the aid of a lens? + +25. (Pg. 201) Why can an object, very near to the eye, be distinctly +seen, when viewed through a small hole? + +26. (Pg. 201) Describe the double microscope, as represented in fig. 6, +plate 22. + +27. (Pg. 202) How does the solar microscope, (fig. 1 plate 23.) operate? + +28. (Pg. 202) Why may minute objects be greatly magnified by this +instrument? + +29. (Pg. 202) In its more perfect form it has other appendages, as seen +in fig. 2, what are they? and what their uses? + +30. (Pg. 203) What is added when opaque objects are to be viewed? fig. +3. + +31. (Pg. 203) In what does the magic lanthorn differ from the solar +microscope? + +32. (Pg. 203) What are the use and structure of the telescope, as shown +in fig. 4? + +33. (Pg. 204) When terrestrial objects are to be viewed, why are two +additional lenses employed? + +34. (Pg. 204) What part of the telescope performs the part of a +microscope? + +35. (Pg. 204) In what does the reflecting, differ from the refracting +telescope? + +36. (Pg. 204) What advantages, do reflecting, possess over refracting +telescopes? + + + + +GLOSSARY. + + +ACCELERATED MOTION. Motion is said to be accelerated, when the velocity +is continually increasing. + +ACCIDENTAL PROPERTIES. Those properties of bodies which are liable to +change, as colour, form, &c. + +ACUTE.--See ANGLE. + +AIR. An elastic fluid. The atmosphere which surrounds the earth, is +generally understood by this term, but there are many kinds of air. The +term is synonymous with _Gas_. + +AIR PUMP. An instrument by which vessels may be exhausted of air. + +ALTITUDE. The height in degrees of the sun, or any heavenly body, above +the horizon. + +ANGLE. The space contained between two lines inclined to each other, and +which meet in a point. Angles are measured in degrees, upon a segment of +a circle described by placing one leg of a pair of compasses on the +angular point, and with the other, describing the segment between the +two lines. If the segment be exactly 1-4th of a circle, it is called a +_right_ angle, and contains 90 deg. If more than 1-4th of a circle, it +is an _obtuse_ angle. If less, an _acute_ angle. See plate 2. + +ANGLE OF INCIDENCE, is the space contained between a ray which falls +obliquely upon a body, and a line perpendicular to the surface of the +body, at the point where the ray falls. + +ANGLE OF REFLECTION. The space contained between a reflected ray, and a +line perpendicular to the reflecting point. + +ANGLE OF VISION, or visual angle. The space contained between lines +drawn from the extreme parts of any object, and meeting in the eye. + +ANTARCTIC CIRCLE. A circle extending round the south pole, at the +distance of 23 1-2 degrees from it. The same as the south frigid zone. + +APHELION. That part of the orbit of a planet, in which its distance from +the sun is the greatest. + +AREA. The surface enclosed between the lines which form the boundary of +any figure, whether regular or irregular. + +ARIES. See SIGN. + +ASTEROIDS. The name given to the four small planets, Ceres, Juno, +Pallas, and Vesta. + +ASTRONOMY. The science which treats of the motion and other phenomena of +the sun, the planets, the stars, and the other heavenly bodies. + +ATMOSPHERE. The air which surrounds the earth, extending to an unknown +height. Wind is this air in motion. + +ATTRACTION. A tendency in bodies to approach each other, and to exist in +contact. + +ATTRACTION OF COHESION. That attraction which causes matter to remain in +masses, preventing them from falling into powder. For this attraction to +exist, the particles must be contiguous. + +ATTRACTION OF GRAVITATION. By this attraction, masses of matter, placed +at a distance, have a tendency to approach each other. Attraction is +mutual between the sun and the planets. + +AXIS OF THE EARTH, OR OF ANY OF THE PLANETS. An imaginary line passing +through their centres, and terminating at their poles; round this their +diurnal revolutions are performed. + +AXIS OF MOTION. The imaginary line, around which all the parts of a body +revolve, when it has a spinning motion. + +AXIS OF A LENS, OR MIRROR. A line passing through the centre of a lens, +or mirror, in a direction perpendicular to its surface. + + +BALLOON. Any hollow globe. The term is generally applied to those which +are made to ascend in the air. + +BAROMETER. Commonly called a weather-glass. It has a glass tube, +containing quicksilver, which by rising and falling, indicates any +change in the pressure of the atmosphere, and thus frequently warns us +of changes in the weather. + +BODY. The same as _Matter_. It may exist in the solid, liquid, or +aeriform state; and includes every thing with which we become acquainted +by the aid of the senses. + +BURNING-GLASS, OR MIRROR. A lens, or a mirror, by which the rays of +light, and heat, are brought to a focus, so as to set bodies on fire. + + +CAMERA OBSCURA, a darkened room; or more frequently a box, admitting +light by one opening, where a lens is placed; which, bringing the rays +of light, from external objects, to a focus, presents a perfect picture +of them, in miniature. + +CAPILLARY TUBES. Tubes, the bore of which is very small. Glass tubes are +usually employed, to show the phenomenon of _capillary attraction_. +Fluids in which they are immersed, rise in such tubes above the level of +that in the containing vessel. + +CENTRE OF A CIRCLE. A point, equally distant from every part of its +circumference. + +CENTRE OF GRAVITY. That point within a body, to which all its particles +tend, and around which they exactly balance each other. A system of +bodies, as the planets, may have a common centre of gravity, around +which they revolve in their orbits; whilst each, like the earth, has its +particular centre of gravity within itself. + +CENTRE OF MOTION. That point about which the parts of a revolving body +move, which point is, itself, considered as in a state of rest. + +CENTRE OF MAGNITUDE. The middle point of any body. Suppose a globe, one +side of which is formed of lead, and the other of wood, the centres of +magnitude and of gravity, would not be in the same points. + +CENTRAL FORCES. Those which either impel a body towards, or from, a +centre of motion. + +CENTRIFUGAL. That which gives a tendency to fly from a centre. + +CENTRIPETAL. That which impels a body, towards a centre. + +CIRCLE. A figure; the periphery, or circumference of which, is every +where equally distant, from the point, called its centre. + +CIRCLE, GREAT. On the globe, or earth, is one that divides it into two +equal parts, or hemispheres. The equator, and meridian lines, are great +circles. + +CIRCLE, LESSER. Those which divide the globe into unequal parts. The +tropical, arctic and antarctic circles, and all parallels of latitude, +are lesser circles. + +CIRCUMFERENCE. The boundary line of any surface, as that which surrounds +the centre of a circle; the four sides of a square, &c. + +COMETS. Bodies which revolve round the sun, in very long ovals, +approaching him very nearly in their perihelion, but in their aphelion, +passing to a distance immeasurably great. + +COHESION. See ATTRACTION. + +COMPRESSIBLE. Capable of being forced into a smaller space. + +CONCAVE. Hollowed out; the inner surface of a watch-glass is concave, +and may represent the form of a _concave mirror_, or _lens_. + +CONVEX. Projecting, or bulging out, as the exterior surface of a +watch-glass, which may represent the form of a _convex mirror_, or +_lens_. + +CONE. A body somewhat resembling a sugar-loaf; that is, having a round +base, and sloping at the sides, until it terminates in a point. + +CONJUNCTION. When three of the heavenly bodies are in a straight or +right line, if you take either of the extreme bodies, the other two are +in conjunction with it; because a straight line drawn from it, might +pass through the centres of both, and join them together. At the time of +new moon, the moon and sun are in conjunction with the earth; and the +moon and earth, are in conjunction with the sun. + +CONSTELLATION, OR SIGN. A collection of stars. Astronomers have imagined +pictures drawn in the heavens, so as to embrace a number of contiguous +stars, and have named the group after the animal, or other article +supposed to be drawn; an individual star is generally designated by its +fancied location; as upon the ear of _Leo_, the Lion, &c. + +CONVERGENT RAYS, are those which approach each other, so as eventually +to meet in the same point. + +CRYSTALS. Bodies of a regular form, having flat surfaces, and well +defined angles. Nitre, and other salts, are familiar examples. Many +masses of matter, are composed of crystals too minute to be discerned +without glasses. + +CURVILINEAR, consisting of a line which is not straight, as a portion of +a circle, of an oval, or any curved line. + +CYLINDER. A body in the form of a roller, having flat circular ends, and +being of equal diameter throughout. + + +DEGREE. If a circle of any size be divided into 360 equal parts, each of +these parts is called a degree. One quarter of a circle contains ninety +degrees; one twelfth of a circle, thirty degrees. The actual length of a +degree, must depend upon the size of the circle. A degree upon the +equator, upon a meridian, or any great circle of the earth, is equal to +69-1/2 miles. + +Straight lines are sometimes divided into equal parts, called degrees; +but these divisions are arbitrary, bearing no relationship to the +degrees upon a circle. + +DENSITY. Closeness of texture. When two bodies are equal in bulk, that +which weighs the most, has the greatest density. + +DIAGONAL. A line drawn so as to connect two remote angles of a square, +or other four-sided figure. + +DILATATION. The act of increasing in size. Bodies in general, dilate +when heated, and contract by cooling. + +DISCORD. When the vibrations of the air, produced by two musical tones, +do not bear a certain ratio to each other, a jarring sound is produced, +which is called discord. + +DIVERGENT RAYS. Those which proceed from the same point, but are +continually receding from each other. + +DIVISIBILITY. Capability of being divided, or of having the parts +separated from each other. This is called one of the _essential +properties_ of matter; because, however minute the particles may be, +they must still contain as many halves, quarters, &c. as the largest +mass of matter. + + +ECHO. A sound reflected back, by some substance, so situated as to +produce this effect. + +ECLIPSE. The interruption of the light of the sun, or of some other +heavenly body, by the intervention of an opaque body. The moon passing +between the earth and the sun, causes an eclipse of the latter. + +ECLIPTIC. A circle in the heavens. The apparent path of the sun, through +the twelve signs of the zodiac. This is caused by the actual revolution +of the earth, round the sun. It is called the ecliptic, because eclipses +always happen in the direction of that line, from the earth. + +ELASTICITY. That property of bodies, by which they resume their +dimensions and form, when the force which changed them is removed. Air +is eminently elastic. Two ivory balls, struck together, become flattened +at the point of contact; but immediately resuming their form, they react +upon each other. + +ELLIPSIS. An oval. This figure differs from a circle, in being unequal +in its diameters, and in having two centres, or points, called its +_foci_. The orbits of the planets are all elliptical. + +EQUATOR. That imaginary line which divides the earth into northern and +southern hemispheres, and which is equally distant from each pole. + +EQUILIBRIUM. When two articles exactly balance each other, they are in +equilibrium. They may, notwithstanding, be very unequal in weight, but +they must be so situated, that, if set in motion, their momentums would +be equal. + +EQUINOX. The two periods of time at which the nights and days are every +where of equal length. The _vernal_ equinox is in March, when the sun +enters the sign _Aries_; the _autumnal_ equinox in September, when the +sun enters _Libra_. At these periods, the sun is vertical at the +equator. + +EXHALATIONS. All those articles which arise from the earth, and mixing +with the atmosphere, form vapour. + +EXPANSION. The same as dilatation, which see. + +EXTENSION. One of the essential properties of matter; that by which it +occupies some space, to the exclusion of all other matter. + + +FIGURE. All matter must exist in some form, or shape; hence figure is +deemed an essential property of matter. + +FLUID. A form of matter, in which its particles readily flow, or slide, +over each other. Airs, or gases, are called elastic fluids, because they +are readily reduced to a smaller bulk by pressure. Liquids, are +denominated non-elastic fluids, because they suffer but little +diminution of bulk, by any mechanical force. + +FOCUS. That point in which converging rays unite. + +FORCE. That power which acts upon a body, either tending to create, or +to stop motion. + +FOUNTAIN. A jet, or stream of water, forced upwards by the weight of +other water, by the elasticity of air, or some other mechanical +pressure. + +FRICTION. The rubbing of bodies together, by which their motion is +retarded. Friction may be lessened, but cannot be destroyed. + +FRIGID ZONES. The spaces or areas, contained within the arctic and +antarctic circles. + +FULCRUM. A prop. The point or axis, by which a body is supported, and +about which it is susceptible of motion. + + +GAS. Any kind of air; of these there are several. The atmosphere +consists of two kinds, mixed, or combined with each other. + +GEOMETRY. That branch of the mathematics, which treats of lines, of +surfaces, and of solids; and investigates their properties, and +proportions. + +GLOBE. A sphere, or ball. It has a point in its centre of magnitude, +from which its surface is every where equally distant. + +GRAVITY. That species of attraction which appears to be common to +matter, existing in its particles, and giving to them, and of course to +the masses which they compose, a tendency to approach each other. By +gravity a stone falls to the earth, and by it the heavenly bodies tend +towards each other. + + +HARMONY. A combination of musical sounds, produced by vibrations which +bear a certain ratio to each other; and which thence affect the mind +agreeably, when heard at the same time. Sounds not so related, produce +discord. + +HEMISPHERE. Half a sphere or globe. A plane passing through the centre +of a globe, will divide it into hemispheres. + +HORIZON. This is generally divided into _sensible_, and _rational_. The +sensible horizon is that portion of the surface of the earth, to which +our vision extends. Our rational horizon is that circle in the heavens +which bounds our vision, when on the ocean, an extended plane, or any +elevated situation. In the heavens our sensible, and our rational +horizon are the same; its plane would divide the earth into hemispheres +at 90 degrees from us; and a person standing on that part of the earth +which is directly opposite to us, would, at the same moment, see in his +horizon, the same heavenly bodies, which would be seen in ours. + +HORIZONTAL. Level; not inclined, or sloping. A perfectly round ball, +placed upon a flat surface, which is placed horizontally, will remain at +rest. + +HYDRAULICS. That science which treats of water in motion, and the means +of raising, conducting, and using it for moving machinery, or other +purposes. + +HYDROSTATICS. Treats of the weight, pressure, and equilibrium of fluids, +when in a state of rest. + +HYDROMETER. An instrument used to ascertain the specific gravity of +different fluids, which it does, by the depth to which it sinks when +floating on them. + + +IMAGE. The picture of any object which we perceive either by reflected +or refracted light. All objects which are visible, become so by forming +images on the retina. + +IMPENETRABILITY. That property of matter, by which it excludes all other +matter from occupying the same space with itself at the same time. If +two particles could exist in the same space, so also might any greater +number, and indeed all the matter in the universe, might be collected in +a single point. + +INCIDENCE. The direction in which a body, or a ray of light, moves in +its approach towards any substance, upon which it strikes. + +INCLINED PLANE. One of the six mechanical powers. Any plane surface +inclined to the horizon, may be so denominated. + +INERTIA. One of the inherent properties of matter. Want of power, or of +any active principle within itself, by which it can change its own +state, whether of motion, or of rest. + +INHERENT PROPERTIES. Those properties which are absolutely necessary to +the existence of a body; called also essential properties. All others +are denominated accidental. Colour is an accidental--extension, an +essential property of matter. + + +LATITUDE. Distance from the equator, in a direct line towards either +pole. This distance is measured in degrees and minutes. The degree of +latitude cannot exceed ninety, or one quarter of a circle. Places to the +south of the equator, are in south latitude, and those to the north, in +north latitude. + +LATITUDE, PARALLELS OF. Lines drawn upon the globe, parallel to the +equator, are so called; every place situated on such a line, has the +same latitude, because equally distant from the equator. + +LENS. A glass, ground so that one or both surfaces form segments of a +sphere, serving either to magnify, or diminish objects seen through +them. Glasses used in spectacles are lenses. + +LEVER. One of the mechanical powers. An inflexible bar of wood or metal, +supported by a fulcrum, or prop; and employed to increase the effect of +a given power. + +LIBRA. One of the twelve signs of the zodiac. That into which the sun +enters, at the autumnal equinox. + +LIGHT. That principle, by the aid of which we are able to discern all +visible objects. It is generally believed to be a substance emitted by +luminous bodies, and, exciting vision by passing into the eye. + +LONGITUDE. Distance measured in degrees and minutes, either in an +eastern, or a western direction, from any given point either on the +equator, or on a parallel of latitude. Degrees of longitude may amount +to 180, or half a circle. A degree of longitude measured upon the +equator, is of the same length with a degree of latitude; but as the +poles are approached, the degrees of longitude diminish in length, +because the circles upon which they are measured, become less. + +LUNAR. Relating to _Luna_, the moon. + +LUNATION. The time in which the moon completes its circuit. A lunar +month. + +LUMINOUS BODIES. Those which emit light from their own substance; not +shining by borrowed, or reflected light. + + +MACHINE. Any instrument, either simple or compound, by which any +mechanical effect is produced. A needle, and a clock, are both machines. + +MAGIC LANTHORN, OR LANTERN. An optical instrument, by which transparent +pictures, painted upon glass, are magnified and exhibited on a white +wall or screen, in a darkened room. The phantasmagoria, is a species of +magic lanthorn. + +MATHEMATICS. The science of numbers and of extension. Common arithmetic, +is a lower branch of the mathematics. In its higher departments, it +extends to every thing which is capable of being either numbered or +measured. + +MATTER. Substance. Every thing with which we become acquainted by the +aid of the senses; every thing however large, or however minute, which +has length, breadth, and thickness. + +MECHANICS. That science which investigates the principles, upon which +the action of every machine depends; and teaches their proper +application in overcoming resistance, and in producing motion, in all +the useful purposes to which they are applied. + +MEDIUM. In optics, is any body which transmits light. Air, water, glass, +and all other transparent bodies, are media. Medium also denotes that in +which any body moves. Air is the medium which conveys sound, and which +enables birds to fly. + +MELODY. A succession of such single musical sounds, as form a simple air +or tune. + +MERCURY. That planet which is nearest to the sun. Quicksilver, a metal, +which remains fluid at the common temperature of the atmosphere. It is +capable of being rendered solid, by intense cold. + +MERIDIAN. Midday. A meridian line, is one which extends directly from +one pole of the earth to the other; crossing the equator at right +angles. It is therefore half of a great circle. The hour of the day is +the same at every place situated on the same meridian. Longitude is +measured from any given meridian, to the opposite meridian. Places at +the same distance in degrees, to the east or west of any meridian, have +the same longitude. + +MICROSCOPE. An optical instrument, by which minute objects, are +magnified, so as to enable us to perceive and examine such as could not +be seen by the naked eye. + +MINERAL. Earths, stones, metals, salts, and in general all substances +dug out of the earth, are denominated minerals. + +MINUTE. In time, the sixtieth part of an hour. In length, the sixtieth +part of a degree. A minute of time, is an unvarying period; but a minute +in length varies in extent, with the degree of which it forms a part. +The degrees and minutes are equal in number, upon a common ring, upon +the equator of the earth, or, on any circle of the heavens. + +MIRRORS. Polished surfaces of metal, or of glass coated with metal, for +the purpose of reflecting the rays of light, and the images of objects. +Common looking-glasses, are mirrors. Those used in reflecting +telescopes, are made of metal. + +MOBILITY. Capable of being moved from one place to another. This is +accounted one of the essential properties of matter, because we cannot +conceive of its existence without this capacity. + +MOMENTUM. The force, or power, with which a body in motion acts upon any +other body, or tends to preserve its own quantity of motion. The +momentum of a body, is compounded of its quantity of matter, and its +velocity. A body weighing one pound, moving with a velocity of two miles +in a minute, will possess the same momentum with one weighing two +pounds, moving with a velocity of one mile in a minute. + +MOTION. A continued and successive change of place, either of a whole +body, or of the particles of which a body is composed; the earth in +revolving upon its axis only, would not change its place as a body, but +all the particles of which it is composed, would revolve round a common +axis of motion. In revolving in its orbit, its whole mass is constantly +occupying a new portion of space. + + +NATURAL PHILOSOPHY. That science which enquires into the laws which +govern all the natural bodies in the universe, in all their changes of +place, or of state. + +NEAP TIDES. Those tides which occur when the moon is in her quadratures, +or half way between new, and full moon; at these periods the tides are +the lowest. + +NODES. Those points in the orbit of the moon, or of a planet, where it +crosses the ecliptic or plane of the earth's orbit. When passing to the +north of the ecliptic, it is called the ascending node; when to the +south of it, the descending node. + + +OBLATE. See SPHEROID. + +OCTAGON. A figure with eight sides, and consequently with eight angles. + +OPAQUE. Not transparent; refusing a passage to the rays of light. + +OPTICS. That branch of science which treats of light, and vision. It is +generally divided into two parts. _Catoptrics_, which treats of the +reflection of light, and _Dioptrics_, which treats of its refraction. + +ORBIT. The line in which a primary planet moves in its revolution round +the sun; or a secondary planet, in its revolution round its primary. +These orbits are all elliptical, or oval. + + +PARABOLA. A particular kind of curve; that which a body describes in +rising and in falling, when thrown upwards, in any direction not +perpendicular to the horizon. + +PARALLELOGRAM. A figure with four sides, having those which are +opposite, parallel to each other. A square, an oblong square, and the +figure usually called a diamond, are Parallelograms. + +PARALLEL LINES. All lines, whether straight or curved, which are every +where at an equal distance from each other, are parallel lines. + +PARALLEL OF LATITUDE. See LATITUDE. + +PERIHELION. That part of the orbit of a planet, in which it approaches +the sun most nearly. + +PENDULUM. A body suspended by a rod, or line, so that it may vibrate, or +oscillate, backwards and forwards. Pendulums of the same length, perform +their vibrations in the same time, whatever may be their weight, and +whether the arc of vibration, be long or short. + +PERCUSSION. The striking of bodies against each other. The force of +this, depends upon the momentum of the striking body. + +PERIOD. The time required for the revolution of one of the heavenly +bodies in its orbit. + +PERPENDICULAR. Making an angle of 90 degrees with the horizon. When two +lines which meet, make an angle of 90 degrees, they are perpendicular to +each other. + +PHASES. The various appearances of the disc, or face of the moon, and of +the planets; that portion of them which we see illuminated by the rays +of the sun. + +PHENOMENON. Any natural appearance is properly so called; the term, +however, is usually applied to extraordinary appearances, as eclipses, +transits, &c. + +PISTON. That part of a pump, or other engine which is made to fit into a +hollow cylinder, or barrel; and to move up and down in it, in order to +raise water, or for any other purpose. + +PLANE. A perfectly flat surface. The plane of the orbit of a planet, is +an imaginary flat surface, extending to every part of the orbit. + +PLANET. Those bodies which revolve round the sun, in orbits nearly +circular. They are divided into _primary_, and _secondary_; these latter +are also called satellites, or moons; they revolve round the primary +planets, and accompany them in their courses round the sun. + +PLUMB-LINE. A string, or cord, by which a weight is suspended; it is +used for the purpose of finding a line perpendicular to the horizon; the +weight being always attracted towards the centre of the earth. + +PNEUMATICS. That branch of natural philosophy, which treats of the +mechanical properties of the atmosphere, or of air in general. + +POLES. The extremities of the axis of motion either of our earth, or of +any other revolving sphere. The poles of the earth have never been +visited; the regions by which they are surrounded, being obstructed by +impassable barriers of ice. + +POWER. That force which we apply to any mechanical instrument, to effect +a given purpose, is denominated power, from whatever source it may be +derived. We have the power of weights, of springs, of horses, of men, of +steam, &c. + +PRISM. The instrument usually so called, is employed in optics to +decompose the solar ray: it consists of a piece of solid glass, several +inches in length, and having three flat sides; the ends are equal in +size, and are of course triangular. + +PRECESSION OF THE EQUINOXES. Every equinox takes place a few seconds of +a degree, before the earth arrives at that part of the ecliptic in which +the preceding equinox occurred. This phenomenon is called the precession +of the equinoxes. There is consequently a gradual change of the places +of the signs of the zodiac: a fact, the discovery of which has thrown +much light on ancient chronology. + +PROJECTION. That force by which motion is given to a body, by some power +acting upon it, independently of gravity. + +PULLEY. One of the six mechanical powers. A wheel turning upon an axis, +with a line passing over it. It is the moveable pulley only, which gives +any mechanical advantage. + +PUMP. An hydraulic, or pneumatic instrument, for the purpose of raising +water, or exhausting air. + + +QUADRANT. A quarter of a circle. An instrument used to measure the +elevation of a body in degrees above the horizon. + +QUADRATURES OF THE MOON. That period in which she appears in the form of +a semicircle. She is then either in her first, or her last quarter; and +exactly half way, between the places of new, and of full moon. + + +RADIATION. The passage of light or heat in rays, or straight lines; +these being projected from every luminous, or heated point, in all +directions. + +RADIUS. The distance from the centre of a circle, to its circumference; +or one half of its diameter. In the plural denominated radii. + +RAINBOW. An appearance in the atmosphere, occasioned by the +decomposition of solar light, in its refraction, and reflection, in +passing through drops of rain. The bow can be seen, only when the sun is +near the horizon, when the back is turned towards it, and there is a +shower in the opposite direction. + +RAY. A single line of light, emitted in one direction, from any luminous +point. + +REACTION. Every body, whether in a state of motion, or at rest, tends to +remain in such state, and resists the action of any other body upon it, +with a force equal to that action. This resistance, is called its +_reaction_. + +RECEIVER. This name is applied to glass vessels of various kinds, +appertaining to the air pump, and from which the air may be exhausted. +They are made to contain, or receive, any article upon which an effect +is to be produced, by taking off the pressure of the atmosphere. + +REFRACTION, of the rays of light, is the bending of those rays, when +they pass obliquely from one medium into another of different density. A +stick held obliquely in water, appears bent or broken at the surface of +the fluid. + +REFRANGIBILITY. Capacity of being refracted. Light is decomposed by the +prism, because its component parts are refrangible in different +degrees, by the same refracting medium. + +REPULSION. The reverse of attraction. A tendency in particles, or in +masses of matter, to recede from each other. The matter of heat within a +body, appears to counteract the attraction of its particles, so as to +prevent absolute contact. + +RETINA. That part of the ball of the eye, upon which the images of +visible objects are formed; and from which, the idea of such forms, is +conveyed to the mind. + +REVOLUTION, of a planet; is either diurnal, or annual; the former, is +its turning upon its own axis; the latter, is its passage in its orbit. + + +SATELLITES. Moons, secondary planets. + +SEGMENT OF A CIRCLE. A portion, or part of a circle; called also, an arc +of a circle. + +SEMI-DIAMETER. Half the diameter. The semi-diameter of the earth, is the +distance from its surface, to its centre. + +SIDERIAL. Belonging to the stars. A siderial day, is the time required +for a star to reappear on a given meridian. A siderial year, the period +in which the sun appears to have travelled round the ecliptic, so as to +have arrived opposite to any particular star, from which his course was +calculated. + +SIGNS, or CONSTELLATIONS. Collections, or groups, of stars. Those of the +zodiac are twelve, corresponding with the twelve months in the year. In +the centre of these the ecliptic is situated. The sun appears to pass in +succession through these signs; entering the first degree of Aries, +which is accounted the first sign, about the 21st of March. + +SKY. That vast expanse, or space, in which the heavenly bodies are +situated. Its blue appearance is supposed to arise from the particles of +which the atmosphere is composed, possessing the property of reflecting +the blue rays, in greatest abundance. + +SOLAR. Appertaining to, or governed by, the sun: as the solar system, +the solar year, solar eclipses. + +SOLID. Not fluid. Having its parts connected so as to form a mass. Solid +bodies, are not absolutely so, all undoubtedly containing pores, or +spaces void of matter. + +SOLSTICES. The middle of summer and the middle of winter; those two +points in the orbit of the earth, in which its poles point most directly +towards the sun. + +SONOROUS BODIES. Those bodies which are capable of being put into a +state of vibration, so as to emit sounds. + +SPECIFIC GRAVITY. The relative weight of bodies of different species, +when the same bulk of each is taken. Water has been chosen as the +standard for comparison. If we say that the specific gravity of a body +is 6, we mean, that its weight is six times as great as that of a +portion of water, exactly equal to it in bulk. + +SPECTRUM. That appearance of differently coloured rays, which is +produced by the refraction of the solar ray, by means of a prism, is +called the prismatic spectrum; it exhibits most distinctly, and +beautifully, all the colours seen in the rainbow. + +SPHERE. A globe, or ball. + +SPHEROID. Spherical; a body approaching nearly to a sphere in its +figure. The earth, is denominated an _oblate spheroid_; it not being an +exact sphere, but flattened at the poles, so as to cause the polar +diameter to be upwards of thirty miles less than the equatorial. Oblate, +is the reverse of oblong, and means shorter in one direction, than in +another. + +SPRING TIDES. Those tides which occur at the time of new, or of full +moon. The tides then rise to a greater height than at any other period. + +SQUARE. A figure having four sides of equal length, and its angles all +right angles. + +In numbers; the product of a number multiplied into itself; thus, the +square of 3 is 9, and the square of 8 is 64. + +STAR. The _fixed_ stars are so called, because they retain their +relative situations; while the planets, by revolving in their orbits, +appear to wander amongst the fixed stars. + +SUBTEND. This term is applied to the measurement of an angle; when the +lines by which it is bounded recede but little from each other, they are +said to subtend; that is, to be contained under, a small angle. + +SUPERFICIES. The surface of any figure. Space extended in length and +width. + +SYSTEM. The mutual connexion, and dependance of things, upon each other. +The solar, or Copernican system, includes the sun, the planets, with +their moons, and the comets. + + +TANGENT. A straight line touching the circumference of a circle; but +which would not cut off any portion of it, were it extended beyond the +touching point, in both directions. + +TELESCOPE. An instrument by which distant objects may be distinctly +seen; the images of objects being brought near to the eye, and greatly +magnified. + +TEMPERATE ZONES. Those portions of the surface of the earth situated +between 23-1/2 and 66-1/2 degrees of latitude. Within these boundaries, +the sun is never vertical; nor does he ever remain, during a whole day, +below the horizon. + +THERMOMETER. An instrument for measuring the temperature of the +atmosphere, or of other bodies. + +TORRID ZONE. That portion of the earth which extends 23-1/2 degrees on +each side of the equator, to the tropical circles; within this limit, +the sun is vertical, twice in the year. + +TRANSIT. Mercury or Venus, are said to transit the sun, when they pass +between the earth and that luminary. They then appear like dark spots, +upon the face of the sun. + +TRANSPARENT. Allowing the rays of light to pass freely through. The +reverse of opaque. Glass, water, air, &c. are transparent bodies. + +TROPICS. Two circles on the globe on either hemisphere, at the distance +of 23-1/2 degrees from the equator. Beyond these circles, the sun is +never vertical: and the countries within them, are denominated tropical. + +TWILIGHT. That portion of the morning or evening, in which the light of +the sun is perceptible, although he is below the horizon. + + +VACUUM. Space void of matter. Such is supposed to be the space in which +the planets revolve. We are said to produce a vacuum, when we exhaust +the air from a receiver. + +VALVE. A part of a pump, and of some other instruments, which opens to +admit the passage of a fluid in one direction, but closes when pressed +in the opposite direction, so as to prevent the return of the fluid; a +pair of bellows is furnished with a valve. + +VAPOUR. Exhalations from fluid or solid substances, generally mixing +with the atmosphere. The most abundant, is that from water. + +VERTICAL. Exactly over our heads: ninety degrees above our horizon. + +VIBRATION. The alternate motion of a body, forwards and backwards; +swinging, as a pendulum. + +VISUAL. Belonging to vision; as the visual angle, or that angle formed +by the rays of light which enter the eye, from the extremities of any +object. + + +UNDULATION. A vibratory, or wave-like motion communicated to fluids. +Sound, is said to be propagated by the undulatory, or vibratory motion +of the air. + + +WEDGE. One of the mechanical powers; the form of the wedge is well +known. It is of extensive use; serving to rend bodies of great strength, +and to raise enormous weights. + +WHEEL AND AXLE. One of the mechanical powers, used under various +modifications. Cranes for raising weights, the wheels and pinions of +clocks and watches, windlasses, &c. are all applications of this power. + + +ZODIAC. A broad belt in the heavens, extending nearly eight degrees on +each side of the ecliptic; the planes of the orbits of all the planets +are included within this space. This belt is divided into twelve parts +or signs, each containing 30 degrees. + +These signs are: + + _Aries_; the Ram. + _Taurus_; the Bull. + _Gemini_; the Twins. + _Cancer_; the Crab. + _Leo_; the Lion. + _Virgo_; the Virgin. + _Libra_; the Scales. + _Scorpio_; the Scorpion. + _Sagittarius_; the Archer. + _Capricornus_; the Goat. + _Aquarius_; the Waterer. + _Pisces_; the Fishes. + +The first six are called northern signs; because the sun is in them, +during that half of the year, in which he is vertical to the north of +the equator; the last six, are called southern signs; because, during +his journey among them, he is vertical to the south of the equator. + +The sun enters _Aries_, at the time of the _vernal equinox_; _Cancer_, +at the _summer solstice_; _Libra_, at the _autumnal equinox_; and +_Capricornus_, at the _winter solstice_. + +The sun is said to enter a sign, when the earth in going round in its +orbit, enters the opposite sign. Thus, when the sun appears in the first +degree of _Libra_, it is in consequence of the earth having arrived +opposite to the first degree of Aries. A line then drawn from the earth, +and passing through the centre of the sun, would, if extended to the +fixed stars, touch the first degree of Libra. + +ZONE. The earth is divided into zones, or belts. See FRIGID, TEMPERATE, +and TORRID ZONES. + + + + +INDEX. + + +A. + +Air, 11, 15, 28, 50, 136. + +Air-pump, 31, 145. + +Angle, 44. + acute, 44. + obtuse, 44. + right, 44. + of incidence, 45, 154, 160, 173. + of reflection, 45, 154, 160, 173. + visual, 168, 169, 170. + +Angular velocity, 171. + +Antarctic circle, 92. + +Aphelion, 75. + +Arctic circle, 92. + +Atmosphere, 28, 104, 129, 136, 144, 150, 163. + colour of, 193. + reflection of, 193. + refraction of, 182. + +Attraction, 10, 14, 23, 25, 179. + of cohesion, 15, 19, 118. + capillary, 18. + of gravitation, 18, 23, 29, 70, 80, 96, 116, 136. + +Avenue, 170. + +Auditory nerve, 151. + +Axis, 78. + of motion, 48. + of the earth, 22, 99. + of mirrors, 176. + of a lens, 184. + + +B. + +Balloon, 30. + +Barometer, 140. + +Bass, 155. + +Bladder, 138. + +Bodies, 10. + elastic, 40. + fall of, 23, 26, 30, 36. + luminous, 157. + opaque, 157. + sonorous, 152, 155. + transparent, 157. + +Bulk, 16. + + +C. + +Camera obscura, 184, 197, 201. + +Capillary tubes, 18. + +Centre, 48. + of gravity, 48, 51, 52, 115. + of magnitude, 48, 53. + of motion, 48, 55, 115. + +Centrifugal force, 49, 72, 95, 115. + +Centripetal force, 49, 72. + +Ceres, 84. + +Circle, 44, 94. + +Circumference, 94. + +Clouds, 129. + +Colours, 23, 185. + +Comets, 86. + +Compression, 42. + +Concord, 155. + +Constellation, 86. + +Convergent rays, 175, 177. + +Crystals, 12. + +Curvilinear motion, 47, 72. + +Cylinder, 52. + + +D. + +Day, 78, 105, 106. + +Degrees, 44, 94, 99, 169, 170. + of latitude, 94, 112. + of longitude, 94, 112. + +Density, 16. + +Diagonal, 47. + +Diameter, 94. + +Discords, 155. + +Diurnal, 78. + +Divergent rays, 175, 177. + +Divisibility, 10, 12. + + +E. + +Earth, 18, 70, 84, 88, 95. + +Echo, 154. + +Eclipse, 110, 159. + +Ecliptic, 86, 92, 99. + +Elasticity, 41. + +Elastic bodies, 28, 40. + fluids, 28, 41, 118, 136. + +Ellipsis, 75. + +Equinox, 100, 107. + precession of, 107. + +Equator, 92, 99. + +Essential properties, 10. + +Exhalations, 13. + +Extension, 10, 11. + +Eye, 166, 195. + + +F. + +Fall of bodies, 24, 27, 31. + +Figure, 10, 12. + +Fluids, 118, 128. + elastic, 28, 41, 118, 136. + equilibrium of, 120, 122, 132. + non-elastic, 119. + pressure of, 121. + +Flying, 40. + +Focus, 176. + of concave mirrors, 177. + of convex mirrors, 175, 177. + of a lens, 184. + imaginary, 176. + virtual, 176. + +Force, 33. + centrifugal, 49, 72, 95, 115. + centripetal, 49, 72. + projectile, 47, 49. + of gravity, 47, 49. + +Fountains, 135. + +Friction, 68, 69, 135. + +Frigid zone, 93. + +Fulcrum, 54. + + +G. + +General properties of bodies, 10. + +Georgium Sidus, 85. + +Glass, 183. + burning, 188. + refraction of, 183. + +Gold, 119, 126. + +Gravity, 18, 23, 78, 97. + + +H. + +Harmony, 155. + +Heat, 16, 29, 103. + +Hemisphere, 92, 100. + +Herschel, 85. + +Hydraulics, 118. + +Hydrometer, 128. + +Hydrostatics, 118. + + +I. + +Image on the retina, 165, 172. + reversed, 167. + in plain mirror, 172. + in concave do. 175. + in convex do. 175. + +Impenetrability, 10. + +Inclined plane, 54, 66. + +Inertia, 10, 14, 32. + +Inherent properties, 10. + +Juno, 84. + +Jupiter, 85. + + +L. + +Lake, 133, 135. + +Latitude, 94, 112. + +Lens, 184. + concave, 184. + convex, 184. + meniscus, 184. + plano-concave, 184. + plano-convex, 184. + +Lever, 54, 55. + first kind, 58. + second kind, 60. + third kind, 60. + +Light, 157. + pencil of, 158. + of the moon, 162, 163. + absorption of, 188. + reflected, 160. + refraction of, 179. + +Liquids, 118. + +Longitude, 94, 112. + +Luminous bodies, 157. + +Lunar month, 108. + eclipse, 110. + + +M. + +Machine, 54, 66. + +Magic lanthorn, 203. + +Mars, 84. + +Matter, 10, 13. + +Mechanics, 32. + +Mediums, 157, 180. + +Melody, 156. + +Mercury, (planet) 83, 85, 114. + +Mercury, or quicksilver, 16, 140, 141. + +Meridians, 93. + +Microscope, 200. + single, 200. + double, 200. + solar, 202, 203. + +Minerals, 12. + +Minutes, 94. + +Momentum, 38, 56. + +Monsoons, 149. + +Month, lunar, 108. + +Moon, 78, 79, 80, 82, 85. + +Moonlight, 162, 163. + +Motion, 14, 32, 36. + accelerated, 36. + axis of, 48. + centre of, 48, 55. + compound, 46. + curvilinear, 47, 49. + diurnal, 78. + perpetual, 35. + retarded, 35. + reflected, 43. + uniform, 34. + +Mirrors, 172. + axis of, 176. + burning, 177. + concave, 174, 176, 209. + convex, 174, 175. + plane or flat, 172. + reflection of, 173. + + +N. + +Neap tides, 116. + +Nerves, 166. + auditory, 151, 166. + olfactory, 166. + optic, 164, 166. + +Night, 78. + +Nodes, 110. + + +O. + +Octave, 156. + +Odour, 13. + +Opaque bodies, 157, 158. + +Optics, 157. + +Orbit, 86. + + +P. + +Pallas, 84. + +Parabola, 51. + +Parallel lines, 25. + +Parallel of latitude, 94. + +Pellucid bodies, 157. + +Pencil of rays, 158. + +Pendulum, 98. + +Perihelion, 75. + +Perpendicular lines, 25. + +Phases, 109. + +Piston, 143, 145. + +Plane, 92, 93. + +Planets, 76, 81, 83. + +Poles, 92, 99, 100. + +Polar star, 100, 112. + +Porosity, 42, 126. + +Powers, mechanical, 54. + +Projection, 49, 50, 71. + +Precession of equinoxes, 107. + +Pulley, 54, 63. + +Pump, 31. + sucking and lifting, 143. + forcing, 144, 145. + air, 31, 145. + +Pupil of the eye, 164. + + +R. + +Rain, 17, 129. + +Rainbow, 188. + +Rarity, 16. + +Ray of light, 158, 179. + reflected, 160, 161. + incident, 161. + +Rays, intersecting, 165. + +Reaction, 39. + +Receiver, 31. + +Reflection of light, 160, 163. + angle of, 45, 161, 173. + of mirrors, 173. + of plane mirrors, 174. + of concave do. 174. + of convex do. 174. + +Reflected motion, 43. + +Refraction, 179, 186. + of the atmosphere, 182. + of glass, 183. + of a lens, 184. + of a prism, 185. + +Resistance, 54. + +Retina, 165. + image on, 166. + +Rivers, 134. + +Rivulets, 131. + + +S. + +Satellites, 80, 111, 113. + +Saturn, 85. + +Scales, or balance, 55. + +Screw, 54, 67. + +Shadow, 110, 111. + +Siderial time, 106. + +Sight, 165. + +Signs of the zodiac, 86, 93. + +Smoke, 14, 29. + +Solar microscope, 202. + +Solstice, 100, 102. + +Sound, 151. + acute, 155. + musical, 155. + +Space, 33. + +Specific gravity, 123. + of air, 140. + +Spectrum, 190. + +Speaking-trumpet, 154. + +Sphere, 26. + +Springs, 130. + +Spring tides, 116. + +Square, 81, 85. + +Stars, 77, 86, 102. + +Storms, 147. + +Substance, 10. + +Summer, 76, 100. + +Sun, 71, 75, 78, 162, 182. + +Swimming, 41. + +Syphon, 132. + + +T. + +Tangent, 49, 73. + +Telescope, 203, 204. + reflecting, 204. + refracting, 204. + +Temperate zone, 92, 101. + +Thermometer, 142. + +Tides, 114, 116. + neap, 116. + spring, 116. + aerial, 150. + +Time, 105, 107. + siderial, 107. + equal, 107. + solar, 107. + +Tone, 155. + +Torrid zone, 93, 147, 182. + +Transit, 114. + +Transparent bodies, 157. + +Treble and bass, 155. + +Tropics, 92. + + +V. + +Valve, 143. + +Vapour, 17, 29, 104, 129. + +Velocity, 33, 57. + +Venus, 84. + +Vesta, 84. + +Vibration, 98, 152. + +Vision, 164, 168. + +Vision, angle of, 168, 170. + double, 171. + + +U. + +Undulation, 153. + +Unison, 155. + + +W. + +Water, 118, 130. + spring, 130. + rain, 130. + level of, 120. + +Wedge, 54, 66. + +Weight, 23. + +Wheel and axle, 54, 65. + +Wind, 146. + trade, 147. + periodical, 148. + +Winter, 76, 101. + + +Y. + +Year, 107. + siderial, 107. + solar, 107. + + +Z. + +Zodiac, 86. + +Zone, 93. + torrid, 93, 147, 182. + temperate, 93, 101. + frigid, 93, 100. + + +THE END. + + + + +TO ALL TEACHERS. + +SCHOOL BOOKS. + + + + +SMILEY'S GEOGRAPHY AND ATLAS, and SACRED AND ANCIENT GEOGRAPHY FOR +SCHOOLS. + + The above works will be found useful and very valuable as works + of reference, as well as for schools. The Maps, composing the + Atlases, will be found equal in execution and correctness to + those on the most extensive scale. The author has received + numerous recommendations, among which are the following: + + Dear Sir--I have looked over your "_Easy Introduction to the + Study of Geography_," together with your "_Improved Atlas_." I + have no hesitation in declaring, that I consider them works of + peculiar merit. They do honour to your industry, research, and + talent, and I am satisfied, will facilitate the improvement of + the student in geographical science. + + With sentiments of sincere consideration, I am yours truly, + + WM. STAUGHTON, D. D. + _President of Columbia College, District of Columbia._ + + MR. THOMAS SMILEY. + _Philadelphia, Sept. 1, 1823._ + + * * * * * + + _Extract from the Minutes of the Philadelphia Academy of + Teachers._ + + _November 1, 1823._ + + Resolved unanimously, That the Academy of Teachers highly + approve the superior merits of Mr. Smiley's "_Easy Introduction + to the Study of Geography_," and the accompanying Atlas, and + cordially recommend them to the patronage of the public. + + B. MAYO, _President._ + + I. I. HITCHCOCK, _Secretary._ + + + + +THE NEW FEDERAL CALCULATOR, or SCHOLAR'S ASSISTANT. Containing the most +concise and accurate Rules for performing the operations in common +Arithmetic; together with numerous Examples under each of the Rules, +varied so as to make them conformable to almost every kind of business. +For the Use of Schools and Counting Houses. + + By Thomas T. Smiley, Teacher: author of An Easy Introduction + to the Study of Geography. Also, of Sacred Geography for the + Use of Schools. + + Among the numerous recommendations received to the work, are + the following: + + MR. JOHN GRIGG. _Phila. March 8, 1825._ + + SIR--I have examined with as much care as my time would admit, + "The New Federal Calculator," by Thomas T. Smiley. It appears + to me to be a treatise on Arithmetic of considerable merit. + There are parts in Mr. Smiley's work which are very valuable; + the rules given by him in Barter, Loss and Gain, and Exchange, + are a great desideratum in a new system or treatise on + Arithmetic, and renders his book superior to any on the subject + now in use; and when it is considered that the calculations in + the work are made in Federal Money, the only currency now known + in the United States, and that appropriate questions follow the + different rules, by which the learner can be exercised as to + his understanding of each part as he progresses; I hesitate not + to say, that, in my opinion, it is eminently calculated to + promote instruction in the science on which it treats. Mr. + Smiley deserves the thanks of the public and the encouragement + of teachers, for his attempt to simplify and improve the method + of teaching Arithmetic. I am yours respectfully, + + WM. P. SMITH, + _Preceptor of Mathematics and Natural Philosophy, + No. 152, South Tenth Street._ + + * * * * * + + SIR--I have carefully examined "The New Federal Calculator, or + Scholar's Assistant," by Thomas T. Smiley, on which you + politely requested my opinion; and freely acknowledge that I + think it better calculated for the use of the United States + schools and counting-houses than any book on the subject that I + have seen. The author's arrangement of the four primary rules + is, in my opinion, a judicious and laudable innovation, + claiming the merit of improvement; as it brings together the + rules nearest related in their nature and uses. His questions + upon the rules throughout, appear to me to be admirably + calculated to elicit the exertions of the learner. But above + all, the preference he has given to the currency of his own + country, in its numerous examples, has stamped a value upon + this little work, which I believe has not fallen to the lot of + any other book of the kind, as yet offered to the American + public. + + I am, sir, yours respectfully, + JOHN MACKAY. + + _Charleston, (S. C.) March 29, 1825._ + + * * * * * + + _From the United States Gazette._ + + Among the numerous publications of the present day, devoted to + the improvement of youth, we have noticed a new edition of + Smiley's Arithmetic, just published by J. Grigg. + + The general arrangement of this book is an improvement upon the + Arithmetics in present use, being more systematic, and + according to the affinities of different rules. The chief + advantage of the present over the first edition, is a + correction of several typographical errors, a circumstance + which will render it peculiarly acceptable to teachers. In + referring to the merits of this little work, it is proper to + mention that a greater portion of its pages are devoted to + Federal calculation, than is generally allowed in primary + works in this branch of study. The heavy tax of time and + patience which our youth are now compelled to pay to the errors + of their ancestors, by performing the various operations of + pounds, shillings, and pence, should be remitted, and we are + glad to notice that the Federal computation is becoming the + prominent practice of school arithmetic. + + In recommending Mr. Smiley's book to the notice of parents and + teachers, we believe that we invite their attention to a work + that will really prove an "assistant" to them, and a "_guide_" + to their interesting charge. + + * * * * * + + The Editors of the New York Telegraph, speaking of Smiley's + Arithmetic, observe that they have within a few days + attentively examined the above Arithmetic, and say, "We do not + hesitate to pronounce it an improvement upon every work of the + kind previously before the public; and as such, recommend its + adoption in all our Schools and Academies." + + + + +A KEY to the above Arithmetic, in which all the Examples necessary for a +Learner are wrought at large, and also Solutions given of all the +various Rules. Designed principally to facilitate the labour of +Teachers, and assist such as have not the opportunity of a tutor's aid. +By T. T. Smiley, author of the New Federal Calculator, &c. &c. + + + + +TORREY'S SPELLING BOOK, or First Book for Children. + + I have examined Mr. Jesse Torrey's "Familiar Spelling Book." I + think it a great improvement in the primitive, and not least + important branches of education, and shall introduce it into + the seminaries under my care, as one superior to any which has + yet appeared. + + IRA HILL, A. M. + + _Boonsborough, Feb. 2, 1825._ + + The increasing demand for this work is the best evidence of its + merits. + + + + +A PLEASING COMPANION FOR LITTLE GIRLS AND BOYS, blending Instruction +with Amusement; being a Selection of Interesting Stories, Dialogues, +Fables, and Poetry. Designed for the use of Primary Schools and Domestic +Nurseries. By Jesse Torrey, Jr. + + To secure the perpetuation of our republican form of government + to future generations, let Divines and Philosophers, Statesmen + and Patriots, unite their endeavours to renovate the age, by + impressing the minds of the people with the importance of + educating their _little boys and girls_. + + S. ADAMS. + + _Report of the Committee of the Philadelphia Academy of + Teachers: adopted Nov. 6, 1824._ + + The Committee, to whom was referred Mr. Jesse Torrey's + "Pleasing Companion for Little Girls and Boys," beg leave to + report, + + That they have perused the "Pleasing Companion," and have much + pleasure in pronouncing as their opinion, that it is a + compilation much better calculated for the exercise and + improvement of small children in the art of reading, and + especially in the more rare art of understanding what they + read, than the books in general use. + + All which is respectfully submitted. + + I. IRVINE HITCHCOCK, + PARDON DAVIS, + CHARLES MEAD, + _Committee_. + + A true copy from the minutes of the Academy. + + C. B. TREGO, _Secretary_. + + _Nov. 22, 1824._ + + + + +THE MORAL INSTRUCTOR AND GUIDE TO VIRTUE, by Jesse Torrey, Jr. + + Among the numerous recommendations to this valuable School + Book, are the following:-- + + _Extract of a note from the Hon. Thomas Jefferson, late + President of the United States._ + + "I thank you, sir, for the copy of your '_Moral Instructor_.' I + have read the first edition with great satisfaction, and + encouraged its reading in my family." + + * * * * * + + _Extracts of a Letter from the Hon. James Madison, late + President of the United States._ + + "Sir--I have received your letter of the 15th, with a copy of + the _Moral Instructor_. + + "I have looked enough into your little volume to be satisfied, + that both the original and selected parts contain information + and instruction which may be useful, not only to juvenile but + most other readers. + + "With friendly respects, + JAMES MADISON." + + DR. TORREY. + + * * * * * + + _From Roberts Vaux, President of the Controllers of the Public + Schools in Philadelphia._ + + "The Moral Instructor" is a valuable compilation. It appears to + be well adapted for elementary schools, and it will give me + pleasure to learn that the lessons which it contains are + furnished for the improvement of our youth generally. + + Respectfully, + ROBERTS VAUX. + + _Philadelphia, 5th month, 8 1823._ + + + + +HISTORY OF ENGLAND, from the First Invasion by Julius Caesar, to the +Accession of George the Fourth, in eighteen hundred and twenty: +comprising every Political Event worthy of remembrance; a Progressive +View of Religion, Language, and Manners; of Men eminent for their Virtue +or their Learning; their Patriotism, Eloquence, or Philosophical +Research; of the Introduction of Manufactures, and of Colonial +Establishments. With an interrogative Index, for the use of Schools. By +William Grimshaw, author of a History of the United States, &c. + +HISTORY OF THE UNITED STATES, from their first settlement as Colonies, +to the cession of Florida, in 1821: comprising every Important Political +Event; with a Progressive View of the Aborigines; Population, Religion, +Agriculture, and Commerce; of the Arts, Sciences, and Literature; +occasional Biographies of the most remarkable Colonists, Writers, and +Philosophers, Warriors, and Statesmen; and a Copious Alphabetical Index. +By William Grimshaw, author of a History of England, &c. + +Also, QUESTIONS adapted to the above History, and a KEY, adapted to the +Questions, for the use of Teachers. + + "_University of Georgia, Athens, June 4, 1825._ + + "DEAR SIR, + + "With grateful pleasure, I have read the two small volumes of + Mr. Grimshaw, (a History of England, and a History of the + United States) which you some time since placed in my hands. On + a careful perusal of them, I feel no difficulty in giving my + opinion, that they are both, as to style and sentiment, works + of uncommon merit in their kind; and admirably adapted to + excite, in youthful minds, the love of historical research. + + "With sincere wishes for the success of his literary labours, + + "I am very respectfully, your friend, + "M. WADDEL, _President_. + + "E. JACKSON, ESQ." + + * * * * * + + "D. JAUDON presents his respectful compliments to Mr. Grimshaw, + and is much obliged by his polite attention, and the handsome + compliment of his History of the United States with the + Questions and Key. + + "Mr. J. has been in the use of this book for some time; but + anticipates still more pleasure to himself, and profit to his + pupils, in future, from the help and facility which the + questions and key will afford in the study of these interesting + pages. + + "_October 10th, 1822._" + + * * * * * + + _Golgotha, P. Edwd. Va. Sep. 26, 1820._ + + "DEAR SIR, + + "MR. GRIMSHAW'S 'History of the United States,' &c. was some + time ago put into my hands by Mr. B----, who requested me to + give you my opinion as to the merits of the work. The history + of the late war is well managed by your author: it has more of + detail and interest than the former part; and I consider it + much superior to any of the many compilations on that subject, + with which the public has been favoured. It may be said of the + entire performance, that it is decidedly the best chronological + series, and the chastest historical narrative, suited to the + capacity of the juvenile mind, that has yet appeared. Its + arrangement is judicious; its style neat, always perspicuous, + and often elegant; and its principles sound. + + "American writings on men and things connected with America, + have been long needed for the young; and I am happy to find, + that Mr. Grimshaw has not only undertaken to supply this want, + but also to _Americanise_ foreign history for the use of our + schools. In a word, sir, I am so fond of American fabrics, and + so anxious to show myself humbly instrumental in giving our + youth American feeling and character whilst at school; that I + shall without hesitation recommend Mr. Grimshaw's works to my + young pupils, as introductory to more extensive historical + reading. In fine, the work is so unobjectionable, and puts so + great a mass of necessary information within the reach of + school-boys, at so cheap a rate, that I feel the highest + pleasure in recommending it to the public, and wish you + extensive sales. + + "Yours respectfully, + "WILLIAM BRANCH, JR. + + "MR. BENJAMIN WARNER, + "_Philadelphia._" + + * * * * * + + "_History of the United States, from their first settlement as + Colonies, to the Peace of Ghent, &c._ By William Grimshaw, pp. + 312, 12mo. + + "This is the third time, within the space of two years, that we + have had occasion to review a volume from the hand of Mr. + Grimshaw. He writes with great rapidity; and improves as he + advances. This is the most correctly written of all his + productions. We could wish that a person so well formed for + close, and persevering study, as he must be, might find + encouragement to devote himself to the interests of + literature." + + "Mr. G. has our thanks for the best concise and comprehensive + history of the United States which we have seen." + + _Theological Review, October, 1819._ + + * * * * * + + "_History of England, from the first Invasion by Julius Caesar, + to the Peace of Ghent, &c._ _For the use of Schools._ By + William Grimshaw. Philadelphia, 1819. Benjamin Warner. 12mo. + pp. 300. + + "We have copied so much of the title of this work, barely to + express our decided approbation of the book, and to recommend + its general introduction into schools. It is one of the best + books of the kind to be found, and is instructive even to an + adult reader. We should be pleased that teachers would rank it + among their class-books; for it is well calculated to give + correct impressions, to its readers, of the gradual progress of + science, religion, government, and many other institutions, a + knowledge of which is beneficial in the present age. Among the + many striking merits of this book, are, the perspicuity of the + narrative, and chasteness of the style. It is with no little + pleasure we have learned, that the author has prepared a + similar history _of the United States_; a work long wanted, to + fill up a deplorable chasm in the education of American youth." + + _Analectic Magazine, October, 1819._ + + * * * * * + + "_Philadelphia, 28 June, 1819._ + + "SIR--I have read with pleasure and profit your History of + England. I think it is written with perspicuity, chasteness, + and impartiality. Well written history is the best political + instructor, and under a government in which it is the blessing + of the country that the people govern, its pages should be + constantly in the hands of our youth, and lie open to the + humblest citizen in our wide-spread territories. Your book is + eminently calculated thus to diffuse this important knowledge, + and therefore entitled to extensive circulation; which I most + cordially wish. With much respect, + + "Your obedient servant, + "LANGDON CHEVES. + + "WILLIAM GRIMSHAW, ESQ." + + + + +GRIMSHAW'S IMPROVED EDITION OF GOLDSMITH'S GREECE.--Among the numerous +recommendations to this valuable School Book, are the following:-- + + Although there are many worthless School Books, there are but + few which are equally impure and inaccurate with the original + editions of Goldsmith's Histories, for the use of Schools. I + congratulate both teachers and pupils upon the appearance of + Mr. Grimshaw's edition of the "History of Greece," which has + been so completely expurgated, and otherwise corrected, as to + give it the character of a new work, admirably adapted to the + purpose for which it is intended. + + THOS. P. JONES, + _Professor of Mechanics in the Franklin Institute + of the State of Pennsylvania, and late Principal of + the North Carolina Female Academy._ + + _Philadelphia, Sept. 5, 1826._ + + * * * * * + + MR. JOHN GRIGG. + + DEAR SIR--Agreeably to your request I have examined, with + attention, "Goldsmith's Greece, revised and corrected, and a + vocabulary of proper names appended, with prosodial marks, to + assist in their pronunciation, by William Grimshaw;" and I feel + a perfect freedom to say, that the correction of numerous + grammatical and other errors, by Mr. Grimshaw, together with + the rejection of many obscene and indelicate passages improper + for the perusal of youth, gives this edition, in my opinion, a + decided preference over the editions of that work heretofore in + use. + + The Questions and Key, likewise supplied by Mr. Grimshaw to + accompany this edition, afford a facility for communicating + instruction, which will be duly appreciated by every judicious + teacher. + + I am, Sir, + Yours truly, + THOS. T. SMILEY. + + _Philadelphia, Sept. 8, 1826._ + + * * * * * + + The Editor of the United States Gazette, in speaking of this + work, says--"Goldsmith's Greece, without a revision, is not + calculated for schools; it abounds in errors, in indelicate + description, improper phrases, and is, indeed, a proof how very + badly a good author can write, if indeed there is not much room + to doubt Goldsmith ever composed the histories to which his + name is attached. Mr. Grimshaw has adopted the easy descriptive + style of that writer, retained his facts, connected his dates, + and entirely and handsomely adapted his work to the school + desk. The book of questions and the accompanying key, are + valuable additions to the work, and will be found most + serviceable to teacher and pupil. + + "From a knowledge of the book, and some acquaintance with the + wants of those for whom it was especially prepared, we + unhesitatingly recommend Grimshaw's Greece as one of the best + (in our opinion, the very best of) works of the kind that has + been offered to the public." + + + + +THE UNITED STATES SPEAKER, compiled by T. T. Smiley--preferred generally +to the Columbian Orator and Scott's Lessons, and works of that kind, by +teachers who have examined it. + + + + +GOLDSMITH'S HISTORY OF GREECE, improved by Grimshaw, with a Vocabulary +of the Proper Names contained in the work, and the Prosodial Accents, in +conformity with the Pronunciation of Lempriere--with Questions and a +Key, as above. + + + + +GRIMSHAW'S ETYMOLOGICAL DICTIONARY AND EXPOSITOR OF THE ENGLISH +LANGUAGE. + + + + + * * * * * + + + + +Transcriber's note: + + +Spelling variations where there is no obviously preferred choice have +been preserved, except as noted below. Irregularities include: "bason" +and "basin;" derivatives of "enquire" and "inquire;" "learned" and +"learnt;" "sidereal" and "siderial;" "sun-rise" and "sunrise;" "sun-set" +and "sunset." + +The original use of commas was preserved, except where explicitly +noted below. + +The original spelling of "pourtray" was preserved. + +Both Roman and Arabic numerals are used to number the plates; the text +was left as is. + +Preserved the non-standard order in the index, where U comes after V. + +Removed extra comma after "which" on page v: "about which the parts." + +Changed "Sideral" to "Siderial" on page vi: "Solar, Siderial, and +Equal." + +Added comma after "Mrs. B." on page 9: "your assistance, my Dear Mrs. +B., in a charge." + +Changed "errroneous" to "erroneous" on page 10: "an erroneous +conception." + +Added comma after "Mrs. B." twice on page 23: "Yet surely, Mrs. B., +there;" and "But, Mrs. B., if attraction." + +Added commas before and after "Mrs. B." on page 25: "Pray, Mrs. B., do." + +Changed "pullies" to "pulleys" on page 64: "a system of pulleys." + +Changed "plate 6. fig. 5" to "plate 5. fig. 5" on page 65 in the body of +the text and in the associated question, to designate the correct +figure. + +Changed "twelves" to "twelve" on page 65: "twelve times less." + +Changed "stream" to "steam" on page 66: "expansive force of steam." + +Changed "Pray Mrs. B," to "Pray, Mrs. B.," on page 68. + +Changed "nonelastic" to "non-elastic" on page 70: "non-elastic like +water." + +Removed extra comma after "one" on page 73: "one would ultimately have +prevailed." + +Changed "eliptical" to "elliptical" on page 73: "elliptical or oval +orbit." + +Changed "eclipse" to "ellipsis" on page 73: "motion in an ellipsis." + +Changed "elipsis" to "ellipsis" on page 75: "but an ellipsis." + +Changed "fig. 4 plate 3" in the question on page 75 to "fig. 4. plate 6" +to designate the correct figure. + +Changed "day-light" to "daylight" on page 77: "see them by daylight." + +Changed the second question numbered 40 to "41" from page 79. + +Changed "eliptical" to "elliptical" on page 83: "they were elliptical." + +Capitalised "Mercury" on page 83: "made upon Mercury." + +Added question mark on page 84 after "those beautiful lines of Milton." + +Removed repeated word, "it", on page 88: "provided it were steady." + +Changed "aeriform" to "aeriform" on page 136 (in versions supporting full +Latin-1 character set). + +Changed "atmospherical" to "atmospheric" on page 139: "the atmospheric +air." + +Changed "rarifies" to "rarefies" on page 140: "heat rarefies air." + +Changed "to day" to "to-day" on page 157: "our lesson to-day." + +Changed "re-appearance" to "reappearance" on page 159: "reappearance of +the sun." + +Changed question 20 to "29" on page 174 to maintain proper sequence. + +Changed "proportionably" to "proportionally" on page 198: +"proportionally distinct." + +Inserted comma after "Circle" on page 206 in the glossary entry for +"Circle, Lesser." + +Inserted period on page 207 at the end of the glossary entry for +"Cylinder." + +Changed "musisical" to "musical" on page 208 in the glossary entry for +"Harmony." + +Changed "perpendidicular" to "perpendicular" on page 211: "perpendicular +to each other." + +Changed "oppoite" to "opposite" on page 212: "the opposite direction." + +Capitalised "Aries" on page 215: "the first degree of Aries." + +Change "jr." to "Jr." in the advertisement for "A Pleasing Companion +...": "By Jesse Torrey, Jr." + + + +***END OF THE PROJECT GUTENBERG EBOOK CONVERSATIONS ON NATURAL PHILOSOPHY, +IN WHICH THE ELEMENTS OF THAT SCIENCE ARE FAMILIARLY EXPLAINED*** + + +******* This file should be named 36691.txt or 36691.zip ******* + + +This and all associated files of various formats will be found in: +http://www.gutenberg.org/dirs/3/6/6/9/36691 + + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions 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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