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+The Project Gutenberg EBook of The Romance of Mathematics, by P. Hampson
+
+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: The Romance of Mathematics
+       Being the Original Researches of a Lady Professor of Girtham
+       College in Polemical Science, with some Account of the Social
+       Properties of a Conic; Equations to Brain Waves; Social Forces;
+       and the Laws of Political Motion.
+
+Author: P. Hampson
+
+Release Date: August 29, 2008 [EBook #26481]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ROMANCE OF MATHEMATICS ***
+
+
+
+
+Produced by David Wilson and the Online Distributed
+Proofreading Team at https://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+
+
+
+                              THE
+                    ROMANCE OF MATHEMATICS.
+
+
+
+
+                              The
+                    Romance of Mathematics:
+
+                             BEING
+                    THE ORIGINAL RESEARCHES
+                               OF
+              A LADY PROFESSOR OF GIRTHAM COLLEGE
+                               IN
+      _Polemical Science, with some Account of the Social
+           Properties of a Conic; Equations to Brain
+               Waves; Social Forces; and the Laws
+                     of Political Motion._
+
+
+                               BY
+                       P. HAMPSON, M.A.,
+                     ORIEL COLLEGE, OXFORD.
+
+
+                            LONDON:
+               ELLIOT STOCK, 62, PATERNOSTER ROW.
+                             1886.
+
+
+
+
+INTRODUCTION.
+
+
+The lectures, essays, and other matter contained in these pages have
+been discovered recently in a well-worn desk which was formerly the
+property of a Lady Professor of Girtham College; and as they contain
+some original thoughts and investigations, they have been considered
+worthy of publication.
+
+How they came into the possession of the present writer it is not his
+intention to disclose; but inasmuch as they seemed to his unscientific
+mind to contain some important discoveries which might be useful to the
+world, he determined to investigate thoroughly the contents of the
+mysterious desk, and make the public acquainted with its profound
+treasures. He found some documents which did not refer exactly to the
+subject of 'Polemical Mathematics;' but knowing the truth of the Hindoo
+proverb, 'The words of the wise are precious, and never to be
+disregarded,' and feeling sure that this Lady Professor of Girtham
+College was entitled to that appellation, he ventured to include them in
+this volume, and felt confident that in so doing he would be carrying
+out the intention of the Authoress, had she expressed any wishes on the
+subject. In fact, as he valued the interests of the State and his own
+peace of mind, he dared not withhold any particle of that which he
+conceived would confer a lasting benefit on mankind.
+
+Internal evidence seems to show that the earlier portion of the MS. was
+written during the period when the authoress was still _in statu
+pupillari_; but her learning was soon recognised by the Collegiate
+Authorities, and she was speedily elected to a Professorship. Her
+lectures were principally devoted to the abstruse subject of Scientific
+Politics, and are worthy of the attention of all those whose high duty
+it is to regulate the affairs of the State.
+
+The Editor has been able to gather from the varied contents of the desk
+some details of the Author's life, which increase the interest which her
+words excite; and he ventures to hope that the public will appreciate
+the wisdom which created such a profound impression upon those whose
+high privilege it was to hear the lectures for the first time in the
+Hall of Girtham College.
+
+
+
+
+CONTENTS.
+
+
+  PAPER                                                             PAGE
+    I. Some Remarks on Female Education:
+
+         Cambridge Man's Powers of Application.--Torturing Ingenuity
+         of Examiners.--Slaying an Enemy.--'Concentration.'--
+         'Tangential Action.'--'Gravity'                               1
+
+   II. Lecture on the Theory of Brain Waves and the Transmigration
+       and Potentiality of Mental Forces                              15
+
+  III. The Social Properties of a Conic Section, and the Theory of
+       Polemical Mathematics:
+
+        'Circle.'--'Parabola.'--'Ellipse.' 'Eccentricity of Curves'   25
+
+   IV. The Social Properties of a Conic Section (_continued_):
+
+        'Ellipse.'--Most favoured State.--Alarming Result of
+         Suppression of House of Lords.--Analogies of Nature.--
+         Directrix.--Contact of Curves and States.--'Hyperbola.'--
+         Problems.--Radical Axis and Patriotism.--Extension of
+         Franchise to Women.--Correspondence                          39
+
+    V. Social Forces, with some Account of Polemical Kinematics:
+
+         The Use of Imagination in Scientific Discovery.--Kinetic and
+         Potential Energy.--Social Statics and Dynamics.--Attractive
+         Forces.--Cohesion.--Formation of States.--Inertia.--Dr.
+         Tyndall on Social Forces                                     71
+
+   VI. Social Forces (_continued_): Polemical Statics and Dynamics:
+
+        'Personal Equation.'--Public Opinion, how calculated.--
+         Impulsive Forces.--Friction.--Progress                       89
+
+  VII. Laws of Political Motion:
+
+         M. Auguste Comte on Political Science.--First Law of
+         Motion.--The Biology of Politics.--Stages of Growth and
+         Decay of States.--Doctrine of Nationality.--Doctrine of
+         Independence.--Law of Morality.--Ignorance of Electors and
+         Selfishness of Statesmen opposed to Action of Law.--Final
+         'Reign of Law'                                              101
+
+ VIII. The Principle of Polemical Cohesion:
+
+         Centralization.--Co-operation of States.--Marriage.--Trade
+         Unions.--International Law                                  115
+
+       Extracts from the Diary of the Lady Professor                 125
+
+       Conclusion                                                    129
+
+
+
+
+PAPER I.
+
+SOME REMARKS OF A GIRTHAM GIRL ON FEMALE EDUCATION.
+
+
+[_This essay upon Female Education was evidently written when the future
+Professor of Girtham College was still in the lowlier condition of
+studentship, before she attained that eminence for which her talents so
+justly entitled her. Its unfinished condition tends to show that it was
+probably evolved during moments of relaxation from severer studies,
+without any idea of subsequent publication._]
+
+Oh, why should I be doomed to the degradation of bearing such a foolish
+appellation! A Girtham Girl! I suppose we have to thank that fiend of
+invention who is responsible for most of the titular foibles and follies
+of mankind--artful Alliteration. The two _G_'s, people imagine, run so
+well together; and it is wonderful that they do not append some other
+delectable title, such as 'The Gushing Girl of Girtham,' or 'The Glaring
+Girl of Glittering Girtham.' O Alliteration! Alliteration! what crimes
+have been wrought in thy name! Little dost thou think of the mischief
+thou hast done, flooding the world with meaningless titles and absurd
+phrases. How canst thou talk of 'Lyrics of Loneliness,' 'Soliloquies of
+Song,' 'Pearls of the Peerage'? Why dost thou stay thine hand? We long
+for thee to enrich the world with 'Dreams of a Dotard,' the 'Dog
+Doctor's Daughters,' and other kindred works. Exercise thine art on
+these works of transcendent merit, but cease to style thy humble, but
+rebellious, servant a Girtham Girl!
+
+But what's in a name? Let the world's tongue wag. I am a student, a
+hard-working, book-devouring, never-wearied student, who burns her
+midnight oil, and drinks the strong bohea, to keep her awake during the
+long hours of toil, like any Oxford or Cambridge undergraduate. I often
+wonder whether these mighty warriors in the lists--the class lists, I
+mean--really work half so hard as we poor unfortunate 'Girls of
+Girtham.' Now that I am writing in strict confidence, so that not even
+the walls can hear the scratchings of my pen, or understand the meaning
+of all this scribbling, I beg to state that I have my serious doubts
+upon the subject; and when last I attended a soirée of the
+Anthropological Society, sounds issued forth from the windows of the
+snug college rooms, which could not be taken as evidences of profound
+and undisturbed study.
+
+Sometimes I glance at the examination papers set for these hard-working
+students, in order that they may attain the glorious degree of B.A., and
+astonish their sisters, cousins, and aunts by the display of these magic
+letters and all-resplendent hood. And again I say in strict confidence
+that if this same glorious hood does not adorn the back of each
+individual son of Alma Mater, he ought to be ashamed of himself, and not
+to fail to assume a certain less dignified, but expressive,
+three-lettered qualification. But before those Tripos Papers I bow my
+head in humble adoration. They sometimes take my breath away even to
+read the terrible excruciating things, which seem to turn one's brain
+round and round, and contort the muscles of one's face, and stop the
+pulsation of one's heart, when one tries to grasp the horrid things.
+
+Here is a fair example of the ingenuity of the hard-hearted examiners,
+who resemble the inquisitors presiding over the tortures of the rack,
+and giving the hateful machine just one turn more by way of bestowing a
+parting benediction on their miserable victims:
+
+'A uniform rod' (it is a marvellous act of mercy that the examiner
+invented it _uniform_; it is strange that its thickness did not vary in
+some complicated manner, and become a veritable birch-rod!) 'of length
+_2c_, rests in stable equilibrium' (stable! another act of leniency!),
+'with its lower end at the vertex of a cycloid whose plane is vertical'
+(why not incline it at an angle of 30°?) 'and vertex downwards, and
+passes through a small, smooth, fixed ring situated in the axis at a
+distance _b_ from the vertex. Show that if the equilibrium be slightly
+disturbed, the rod will perform small oscillations with its lower end
+on the arc of the cycloid in the time
+
+           +-------------------
+           | a{c² + 3(b - c)²}
+    4[pi]\ | ----------------- ,
+          \|    3g(b² - 4ac)
+
+where _2a_ is the length of the axis of the cycloid.'
+
+A sweet pretty problem, truly! And there are hundreds of the same
+kind--birch-rods for every back! How the examiner must have rejoiced
+when he invented this diabolical rod, with its equilibrium, its
+oscillations, its cycloid, and other tormenting accessories. And yet, I
+suppose, before my days of studentship are over, I shall be called upon
+to attack some such impregnable fortresses of mathematics, when I hope
+to be declared equal to some twentieth wrangler, if I escape the
+misfortune of sharing a portion of the 'wooden spoon.'
+
+Ah, you male sycophants! You would prevent us from competing with you;
+you would separate yourselves on your island of knowledge, and sink the
+punt which would bear us over to your privileged shore. Of all the
+twaddle--forgive me, male sycophants!--that the world has ever heard, I
+think the greatest is that which you have talked about female education.
+And the best of it is, you are so anxious about our welfare; you are so
+afraid that we should injure our health by overmuch mental exertion; you
+profess to think that our brains are not calculated to stand the strain
+of continued mental exercise; you think that competition is not good for
+the female mind; that we are too competitive by nature--too ambitious!
+Yes, we are so ambitious that we would enter the lists with those who
+are asked in Public Examinations to find the simple interest on £1,000
+for 5 years at 6¼ per cent.; so ambitious that we would compete with
+those who are requested to disclose the first aorist middle of [Greek:
+tuptô]. Oh, think of the mental strain involved in such questions! How
+it must ruin your health to find out how many times a wheel of radius 6
+feet will turn round between York and London, a distance of 200 miles!
+It is quite wonderful how your brains, my dear male sycophants, can
+stand such fearful demands upon your intelligence and industry!
+
+But you are so kind to us, so afraid of our health! Really, we are much
+obliged to you. If you married one of us, or became our guardian, or
+left us a legacy, we should then recognise your interest in us, and be
+very grateful to you for your good advice. But as matters stand, we are
+quite capable of taking care of ourselves. We will promise not to work
+too hard, if you will promise not to weary us with your paternal
+jurisdiction.
+
+But, male sycophants, I want a word with you. Why do you object to our
+taking degrees, or going in for examinations in order to qualify
+ourselves for our duties in life? You need not speak out loud if you
+would rather not. Are you not just a little afraid that we might eclipse
+you? And it is not pleasant to be beaten by a woman, is it? And then you
+profess to think that we ought to be all housewives and cooks, and
+knitters of stockings, and sewers-on of our husbands' buttons; but what
+if we have no husbands, no buttons to sew? And is it not a little
+selfish, my dear male sycophant, to wish to keep us all to yourself? to
+attend upon the wants of the lords of creation, who often distinguish
+themselves so much in the domain of science?
+
+Now, look me straight in the face (no shirking, sir!). Is it not
+jealousy--green-eyed, false-tongued jealousy--which saps your generous
+instincts, and makes you talk rubbish and nonsense about strains, and
+brains, and ambition, and the like? And if that is not hypocritical, I
+do not know what is.
+
+Well, good-day to you, male sycophant! I really have not time to indulge
+myself in scolding you any more. You are a good creature, no doubt; and
+when you have shown us what you can do, and can estimate the capacity of
+the female brain, and take a common-sense view of things, we will
+recognise your privilege to speak; and when I am the presiding genius of
+Girtham College, I will grant you the use of our hall for the purpose of
+lecturing to us on 'Women's Rights,' or, as you may prefer to entitle
+your discourse, 'Men's Wrongs.'
+
+       *       *       *       *       *
+
+Oh, this is shameful! I really am very sorry. Here have I been wasting a
+good half-hour in dreaming, and slaying an imaginary enemy with
+envenomed words and frequent dabs of ink. If I cannot concentrate my
+mind more on these mathematical researches, I fear a dreadful 'plough'
+will harrow my feelings at the end of my sojourn in these halls of
+learning.
+
+Concentration! How many of our words and ideas and thoughts are derived
+from that primal fount of all arts and sciences--mathematics! Here is
+one which owes its origin to the mathematically trained mind of some
+early philological professor, who had learnt to apply his scientific
+knowledge to the enrichment of his native tongue. He quoted to himself
+the words of the Roman poet:
+
+            'Ego cur, acquirere pauca
+    Si possum, invideor, cum lingua Catonis et Ennî
+    Sermonem patrium ditaverit, et nova rerum
+    Nomina protulerit? Licuit, semperque licebit.'
+
+His mind conceived endless figures of circles and ellipses scattered
+promiscuously over the page, defying the attempts of the student to
+reduce them to order. What must he do before he can apply his formulæ
+and equations, determine their areas, or describe their eccentric
+motion? He must reduce them to a common centre, and then he can proceed
+to calculate the abstruse problems in connection with the figures
+described. They may be the complex motions of double-star orbits, or the
+results of the impact of various projectiles on the tranquil surface of
+a pool. It matters not--the principle is the same; he must concentrate,
+and reduce to a common centre.
+
+This is the great defect of those who have no accurate mathematical
+knowledge; they cannot concentrate their minds with the same degree of
+intensity upon the work which lies before them. Their thoughts fly off
+at a tangent, as mine do very often; but then I have not been classed
+yet in the Tripos; and, O male poetical sycophant, you may be right
+after all when you say:
+
+   'O woman! in our hours of ease
+    Uncertain, coy and hard to please,
+    As variable as the noon-day shade.'
+
+Yes, as variable as the most variable quantities _x_, _y_, _z_. I, a
+student of Girtham College, blush to own that my thoughts very often fly
+off at a tangent.
+
+'Fly off at a tangent!' All hail to thee, most noble mathematical
+phrase! Here is another fine mathematical expression, plainly
+exemplifying the action of centrifugal force. The faster the wheel
+turns, the greater is the velocity of the discarded particles which fly
+off along the line, perpendicular to the radius of the circle. The world
+travels very fast now; the increased velocity of the transit of earthly
+bodies, the rate at which they live, the multiplicity of engagements,
+etc., have made the social world revolve so fast that the speed would
+have startled the torpid life of the last century. And what is the
+result? Men's thoughts fly off at a tangent; they are unable to
+concentrate their minds on any given subject; they are content with
+hasty generalisms, with short magazine articles on important subjects,
+which really require large volumes and patient study to elucidate them
+fully.
+
+What we want to do is to increase the attractive force, in order to
+prevent this tangential motion--to increase the _force of gravity_.
+
+'Well,' says the young lady who loves to revel in the 'Ghastly Secret of
+the Moated Dungeon,' or the 'Mysteries of Footlight Fancy,' 'you are
+_grave_ enough. Pray don't increase your gravity!'
+
+Thank you, gentle critic. I will, in turn, ask you one favour. Leave for
+once the 'Mysteries of Footlight Fancy;' seek to know no more 'ghastly
+secrets,' and increase _your gravity_--your mental weight; and hence
+your attraction in the eyes of all who are worth attracting will be
+marvellously increased, by understanding a little about Newton's law of
+universal gravitation, and don't fly off at a tangent.
+
+       *       *       *       *       *
+
+At the end of this portion of the MS. the editor of these papers
+discovered a photograph which, from subsequent inquiry, proved to be
+that of the accomplished authoress of the above reflections. The face
+is one of considerable beauty, with eyes as clear, steadfast, and open
+as the day. There is a degree of firmness about the mouth, but it is a
+sweet and pretty one notwithstanding; and a smile, half scornful, half
+playful, can be detected lurking about the corners of the lips, which do
+not seem altogether fitted for pronouncing hard mathematical terms and
+abstruse scientific problems. This photograph might have been the
+identical one which nearly brought an enamoured youth into grave
+difficulties by its secretion in the folds of his blotting-paper during
+examination. The said enamoured youth had evidently placed it there for
+the sake of its inspiring qualities; and it was said that all his hopes
+of gaining the hand of the fair original depended upon his passing that
+same examination. But the wakeful eye of a stern examiner had watched
+him as he turned again and again to consult the sweet face which beamed
+from beneath his blotting-paper; and he narrowly escaped expulsion from
+the Senate-house on the charge of 'cribbing.' Certainly he took a mean
+advantage of his fellow-sufferers, if this were the identical
+photograph, for it portrays a most inspiring face. Forgive us, lenient
+reader; one moment! There--thank you--we have done. And now we will
+proceed to disclose the researches and original problems which the MS.
+contains.
+
+Evidently the collegiate authorities were not slow in recognising the
+talents of the assiduous student, and elected her without much delay to
+a Professorship of Girtham. In this capacity the learned lady delivered
+several lectures, of which the second MS. contains the first of the
+series.
+
+
+
+
+PAPER II.
+
+LECTURE ON THE THEORY OF BRAIN WAVES AND THE TRANSMIGRATION
+AND POTENTIALITY OF MENTAL FORCES.
+
+
+Professors and Students of the University of Girtham, my Lords, Ladies,
+and Gentlemen,--I have the honour to bring before you this evening some
+original conceptions and discoveries which have been formulated by me
+during my researches in the boundless field of mathematical knowledge;
+and though you may be inclined at first to pronounce them as somewhat
+hastily conceived hypotheses, I hope to be able to demonstrate the
+actual truth of the propositions which I shall now endeavour to
+enunciate. It is with some feelings of diffidence that I stand before so
+august an assembly as the present; and if I were not actually convinced
+of the accuracy of my calculations, I should never have presumed to
+appear before you in the character of a lecturer. But '_Magna est
+veritas, et prævalebit_.' I cast aside maiden timidity; I clothe myself
+in the professorial robe which you have bestowed upon me, and sacrifice
+my own feelings on the altar of Truth.
+
+I have been engaged, as you are doubtless aware, for some years in the
+pursuit of mathematical research, exploring the mines of science, which
+have of late been worked very persistently, but often, like the black
+diamond mines, at a loss. Concurrently with these researches, I have
+speculated on the great social problems which perplex the minds of men,
+both individually and collectively. And I have come to the conclusion
+that the same laws hold good in both spheres of work; that methods of
+mathematical procedure are applicable to the grand social problems of
+the day and to the regulation of the mutual relations which exist
+between man and man. Take, for example, the Force of public opinion. Of
+what is it composed? It is the Resultant of all the forces which act
+upon that which is generally designated the 'Social System.' Public
+opinion is a compromise between the many elements which make up human
+society; and compromise is a purely mechanical affair, based on the
+principle of the Parallelogram of Forces. Sometimes disturbing forces
+exert their influence upon the action of Public Opinion, causing the
+system to swerve from its original course, and precipitating society
+into a course of conduct inconsistent with its former behaviour; and it
+is the duty of the Governing Body to eliminate as far as possible such
+disturbing forces, in order that society may pursue the even tenor of
+its way.
+
+Professors, we have one great problem to solve; and all questions
+social, political, scientific, or otherwise, are only fragments of that
+great problem. All truths are but different aspects of different
+applications of one and the same truth; and although they may appear
+opposed, they are not really so; and resemble lines which run in
+various directions, but lovingly meet in one centre.
+
+Now, let us take for our consideration the secret influence which men
+exert upon each other, apart from that produced by the power of speech
+(although that would come under the same general law). As
+mathematicians, you are aware that the undulatory theory of light and
+heat and sound are now accepted by scientific men as the only sure basis
+of accurate calculation. We know that the rays of light travel in waves,
+and the equation representing the waves is
+
+         a       2[pi]
+    y = --- sin ------ (vt - r),
+         r     [lambda]
+
+where _y_ is the disturbance of the ether, _a_ the initial amplitude,
+_r_ the distance from the starting-point, [lambda] the wave-length, and
+_v_ the velocity of light. Sound and heat likewise have much the same
+form of equation. Now, I maintain that the waves of thought are governed
+by the same laws, and can be determined by an equation of the same form.
+You are aware that in all these equations a certain quantity denoted by
+[lambda] appears, and varies for the different media through which the
+sound, or light, or heat passes, and which must be determined by
+experiment Now, in my equation for brain waves, the same quantity
+[lambda] appears which must be determined by the same method--by
+_experiment_. But how is this to be done? After mature deliberation and
+much careful thought, I have discovered the method for finding [lambda].
+This method is _mesmerism_. We find the ratio of brain to brain--the
+relative strength which one bears to another; and then by an application
+of our formula we can actually determine the wave of thought, and read
+the minds of our fellow-creatures. An unbounded field for reflection and
+speculation is here suggested. Like all great discoveries, the elements
+of the problem have unconsciously been utilized by many who are unable
+to account for their method of procedure. For example, thought-readers,
+mesmerists, and the like, have unconsciously been working on this
+principle, although lack of mathematical training has prevented them
+from fully mastering the details of the problem. Hence in popular minds
+a kind of mystery has hung about the actions of such people, and excited
+the curiosity of mankind.
+
+The development of this theory of brain waves may be of great practical
+utility to the world. It shows that great care ought to be exercised in
+the domain of thought, as well as that of speech. For example: A man has
+made a startling discovery, from which he expects to receive
+considerable worldly advantage. He would be careful not to disclose his
+discovery in speech to his acquaintances until his plans are
+sufficiently matured, lest they should impart it to the world, patent
+his device, and reap the reward. But while he is endeavouring to talk
+carelessly about it, the wave of thought may be travelling from brain to
+brain, suggesting the existence of the discovery; and if the conditions
+are favourable, and [lambda] sufficiently small, it is possible that the
+idea itself may be conveyed. Of course the more complicated the
+discovery, the less likely would the wave convey the conception. Or
+suppose that one of the learned professorial body of our sister
+university should conceive an attachment for a lady-student of Girtham
+College (of course a very improbable supposition!), and the infatuated
+_savant_ became somewhat jealous of another learned lecturer of the same
+college (another improbability!), the fact of his jealousy would be
+imparted to the latter by a wave of thought, and might cause
+considerable confusion in the serene course of love or science. The fact
+of the existence of the wave is indisputable. What do all the stories of
+impressions and double-sight teach us? How could the intelligence of the
+death of Professor Steele have been conveyed to his friend and
+fellow-student, Professor Tait--the one at Cambridge, the other at
+Edinburgh--were it not for the existence of some wave, which, like that
+of electricity, wings its rapid flight unobserved by human eyes? Are all
+the records of the Psychical Society only myths and legends bred of
+superstitious fancy? It were hard to suppose so.
+
+But if, gentlemen, and ladies especially, you wish to keep your secret
+discoveries to yourselves, watch over your thoughts as well as your
+words; for my researches prove, and the universal experience of mankind
+corroborates the fact, that some portion of your inmost thoughts and
+secret desires are understood by your neighbours (especially when
+[lambda] is small!); that they travel along the waves which I have
+attempted to indicate; and if you would desire to extend your influence
+in the world, probe the secret instincts of mankind, and prevent
+yourself from being deceived and wronged--study the art and science of
+Brain Waves.
+
+       *       *       *       *       *
+
+The following verses of rather doubtful merit were found in connection
+with the previous MS. They were evidently written by a different hand;
+but inasmuch as they were deemed worthy of preservation by the learned
+owner of the sealed desk, we venture to publish them. They are closely
+connected with the previous lecture, and were evidently composed by an
+admirer of the fair lecturer who did not share her love for scientific
+research.
+
+    Wavelet,[1] wing thy airy flight;
+      Let thine amplitude be great;
+    Tell her all my thoughts to-night,
+      How I long to know my fate.
+
+    All the fields of Mathematics
+      I have roamed at her decree;
+    From Binomial and Quadratics,
+      To the strange hyperbole.[2]
+
+    I have soared through Differential,
+      Deeply drunk of Finite Boole;[3]
+    Though its breath is pestilential,
+      Reeking of the hateful School.
+
+    I have tried to shape a Conic,
+      Vainly read the Calculus;
+    But my feebleness is chronic,
+      _Morbus Mathematicus_.
+
+    All my curves are cardioidal;
+      I confuse my _x_ and _y_s,
+    Which they say is suicidal;
+      And my tutor vainly sighs.
+
+    Wavelet, tell her how I love her,
+      As she mounts her learned throne;
+    And that love I hope may cover
+      All the failings which I own.
+
+    Wavelet, cry to her for pity;
+      Bid her end this bitter woe;
+    I might do something 'in the city,'
+      But never pass my Little-go.
+
+
+  [1] We presume this is addressed to an imaginary brain wave.
+
+  [2] We observe here the dash of an indignant pen, and a substituted
+      for e. But now the rhyme is spoiled. Gentle Muse, thou art
+      sacrificed by the stern hand of Mathematical Truth!
+
+  [3] Query: Does the writer refer to the learned treatise on Finite
+      Differences by Professor Boole?
+
+
+
+
+PAPER III.
+
+LECTURE ON THE SOCIAL PROPERTIES OF A CONIC SECTION,
+AND THE THEORY OF POLEMICAL MATHEMATICS.
+
+
+Most Learned Professors and Students of this University,--From the
+interest manifested in my first lecture, I conclude that my method of
+investigation has not proved altogether unsatisfactory to you, and I
+hope ere long to produce certain investigations which will probably
+startle you, and revolutionize the current thought of the age. The
+application of mathematics to the study of Social Science and Political
+Government has curiously enough escaped the attention of those who ought
+to be most conversant with these matters. I shall endeavour to prove in
+the present lecture that the relations between individuals and the
+Government are similar to those which mathematical knowledge would lead
+us to postulate, and to explain on scientific principles the various
+convulsions which sometimes agitate the social and political world.
+
+Indeed, by this method we shall be able to prophesy the future of states
+and nations, having given certain functions and peculiarities
+appertaining to them, just as easily as we can foretell the exact day
+and hour of an eclipse of the moon or sun. In order to do this, we must
+first determine the _social properties of a conic section_.
+
+For the benefit of the unlearned and ignorant, I will first state that a
+cone is a solid figure described by the revolution of a right-angled
+triangle about one of the sides containing the right angle, which
+remains fixed. The fixed side is called the axis of the cone. Conic
+sections are obtained by cutting the cone by planes. It may easily be
+proved that if the angle between the cutting plane and the axis be equal
+to the angle between the axis and the revolving side of the triangle
+which generates the cone, the section described on the surface of the
+cone is a parabola; if the former angle be greater than the latter, the
+curve will be an ellipse; and if less, the section will be a hyperbola.
+
+But the simplest conic section is, of course, a circle, which is formed
+by a plane at right angles to the axis of the cone; and the simplest
+circle is that formed by a plane passing through the apex of the cone.
+All this is simple mathematics; and let beginners consult more
+elementary treatises than this one to satisfy themselves on these
+points. But if they will assume these things to be true, they will know
+quite enough for our present purpose. The simplest conic section of all
+has been proved to be a _point_. Now, this represents the simplest and
+original form of society, a _single family_. 'It is not good for man to
+be alone' was the first observation made by the wise Creator upon the
+rational creature whom He had introduced into Paradise as its lord.
+Marriage is the rudiment of all social life, from which all others
+spring, out of which all others are developed. Around the parents'
+knees soon cluster a group of children, and in their relation to each
+other we discern the earliest forms of law and discipline--the bonds by
+which society is held together. When the children grow up, separate
+households are formed; and then the multiplication of families, the
+congregating of men together for purposes of security and mutual
+advantages in division of labour; and thus is gradually formed a state,
+which is only the development of the family--the king representing the
+parent, and ruling on the same principle.
+
+Mathematically speaking, our plane no longer passes through the apex.
+The point represented the single family; but keeping the plane
+horizontal, we move it along the axis, the sections will become
+_circles_, which represent mathematically the next simplest form of
+society, where the centre is the seat of government, which is connected
+with each individual member of the social circle by equal radii. The
+social property of a circle is that of a monarchical government in its
+purest and simplest form. The larger the circle becomes (_i.e._, the
+further you move the plane from the apex), the greater the distance
+between the individual and the monarch. Therefore, the more independent
+the monarchy becomes, and the less influence do individuals possess over
+the ruling power. Hence, we may infer that as years roll on, the
+government will become more despotic; but the stability of the country
+diminished, and probably some individual particle, when sufficiently
+withdrawn from the attraction of the central head, will begin to revolve
+on its own account, and spontaneously generate a government of its own.
+We may, therefore, conclude from mathematical reasoning that an
+unlimited monarchy, though advantageous for small states, is not a safe
+form of government for a large or populous country, inasmuch as the
+people do not derive much benefit from the sovereign; the mutual
+attraction, which ought to exist in a flourishing state between the
+ruler and the ruled, is weakened; and the isolation of the monarch
+tends to make him still more despotic. As a practical example of the
+truth of the foregoing statement, I may mention the present condition of
+Russia, which shows that the result of an unlimited monarchy, in a large
+and unwieldy social circle, is such as we should have reasonably
+expected from mathematical investigations.
+
+Invariably, under the circumstances which I have described, the country
+will become disorganized; the sovereign will cease to have any power
+over the people, and the country will become a chaos, without order,
+influence, or power.
+
+When the centre of a conic section moves along the axis of the curve to
+infinity, banished by the mutual consent of the individual particles
+which compose the curve, or the nation, a figure is formed, called a
+_parabola_. This is the curve which the most erratic bodies in the
+universe describe in space, as they rush along at a speed inconceivable
+to human minds, and are supposed to produce all kinds of mischief and
+injury to the worlds whose courses they wend their way among.
+
+This curve, then, represents the position which the nation assumes when
+the constituted monarchy, the centre of the system, has been _banished
+to infinity_. A revolution has occurred; the monarch has been dethroned;
+and it is not hard to see that the same erratic course which the comet
+pursues in its flight, is observable with respect to the social system
+which is represented by a parabola. We observe with eager scrutiny the
+wanderings of these erratic comets. They appear suddenly with their
+vapoury tails; sometimes they shine upon us with their soft, silvery
+light, brilliant as another moon; sometimes they stand afar off in the
+distant skies, and deign not to approach our steady-going earth, which
+pursues its regular course day by day, and year by year. Then, after a
+few days' coy inspection of our planet from different points of view,
+they fly to other remote parts of the universe, and do not condescend to
+show themselves again for a hundred years or so. Such is the erratic
+conduct of a heavenly body whose course is regulated by a parabolic
+curve.
+
+We may look for similar eccentric behaviour on the part of a community,
+nation, or state, whose centre is at infinity, whose constitution has
+been violently disturbed, and whose monarchy is situated in the far-off
+regions of unlimited space. The erratic course of Republican rule is
+proverbial. There is no stability, no regularity. To-day we may observe
+its brilliancy, which seems to laugh at and eclipse the sombre shining
+of more steady and enduring worlds; but ere to-morrow's moon has risen,
+it may have vanished into the regions of eternal night, and we look for
+its bright shining light in the councils of the nations, but it has
+ceased to shed its rays, and we are disappointed. Sometimes it is asked,
+with fear and trembling: 'What would be the effect if our earth were to
+come in contact with the tail of a comet? Should we be destroyed by the
+collision, and our ponderous world cease to be?' But we are assured
+that no such disastrous results would follow. We have already passed
+through the tails of many comets, but we have not discovered any
+inconvenient change in our ordinary mode of procedure. It is probable
+that the comet's tail is composed of no solid substance.
+
+We may therefore infer by analogy that a Republican State would not
+offer any powerful resistance if it were to come into collision with a
+nation possessing a more settled form of government. A shower of
+meteoric stones, like passing fireworks, might take place; but beyond
+that nothing would occur to excite the fear, or arouse the energies of
+the more favoured nation. As an example of the weakness of a Republican
+State I may mention France. There we see an industrious race of people,
+endowed with many natural gifts and graces, a country rich and
+productive; and yet, owing to the unsettled nature of its government,
+all these natural advantages are neutralized; its course amongst the
+nations is erratic in the extreme, a spectacle of feeble
+administration; and it would offer no more resistance to a colliding
+Power than the empty vacuum of a comet's tail. This example will
+demonstrate to you the truth of our theory with regard to the
+instability of a social system which is geometrically represented by a
+parabolic curve.
+
+We will now turn from this picture of insecurity and unrest to another
+figure which possesses most advantageous social properties. I refer to
+the ellipse. An ellipse is a curve formed by the section of a cone by a
+plane surface inclined at an angle to the vertical axis of the cone,
+greater than the angle between the axis and the generating line.
+
+Now, this is a curve which possesses most attractive properties. It is
+the curve which the earth and other planetary orbs describe around the
+centre of the solar system, as if nature intended that we should take
+this figure as a guide in choosing the most advantageous social system.
+It possesses a centre, C, in view of all the particles which compose the
+curve, and connected with them by close ties. It has two foci, S and
+S', fixed points, by the aid of which we may trace the curve.
+
+In the interpretation of this figure, the centre of the curve represents
+the throne of monarchy. There is no tendency here to revolutionize the
+State, to banish the ruling power, and institute a Republican form of
+government; but inasmuch as we saw the weakness of an absolute monarchy
+in large and populous States, as represented by the circle, the wisdom
+of an elliptical social system has ordained that there shall be two
+foci, or houses of representatives of the people, who shall assist in
+regulating the progress of the nation. Here we have a limited monarchy;
+the throne is supported by the representatives of the people; and the
+nearer these foci of the nation are to the centre (_i.e._, in
+mathematical language, the less the _eccentricity_ of the curve), the
+more perfect the system becomes--the greater the happiness of the
+community.
+
+In cases where the _eccentricity_ becomes very great, the beauty of the
+curve is destroyed, and ultimately the ellipse is merged into one
+straight line. Most learned Professors, here we have a terrible warning
+of the awful result of too much eccentricity. Whether we regard the life
+of the nation or of the individual, let all bear in mind this alarming
+fact, that eccentricity of thought, habit, or behaviour may result, as
+in the case of this unfortunate ellipse, which once presented such fair
+and promising proportions to the student's admiring gaze, in the
+'sinister effacement of a man,' or the gradual absorption of a State
+into an uninteresting thing 'which lies evenly between its extreme
+points.'
+
+The great examples of Bacon, of Milton, of Newton, of Locke, and of
+others, happen to be directly opposed to the popular inference that
+eccentricity and thoughtlessness of conduct are the necessary
+accompaniments of talent, and the sure indications of genius. I am
+indebted to Lacon for that reflection. You may point to Byron, or
+Savage, or Rousseau, and say, 'Were not these eccentric people
+talented?' 'Certainly,' I answer; 'but would they not have been better
+and greater men if they had been less eccentric--if they had restrained
+their caprice, and controlled their passions?' Do not imagine, my young
+students of this university, that by being eccentric you will therefore
+become great men and women of genius. The world will not give you credit
+for being brilliant because you affect the extravagances which sometimes
+accompany genius. Some of you ladies, I perceive, have adopted a
+peculiar form of dress, half male, half female; or, to be more correct,
+three-fourths male, and one-fourth female. Do not imagine that you will
+thus attain to the highest honours in this university by your
+eccentricity, unless your talents are hid beneath your short-cut hair,
+and brains are working hard under your college head-gear. As well might
+we expect to find that all females who wear sage-green and extravagant
+æsthetic costumes are really born artists and future Royal Academicians.
+It is apparent that many aspirers to fame and talent are eager to
+exhibit their eccentricities to the gaze of the world, in order that
+they may persuade the multitude that they possess the genius of which
+eccentricity is falsely supposed to be the outward sign.
+
+I may remark in passing that the eccentricity of a parabolic curve is
+always _unity_. What does this prove? You will remember that a
+Republican State is represented by a parabola. Therefore, however such a
+nation may strive to alter its condition, and secure a settled form of
+government, its eccentricity will always remain the same. It will always
+be erratic, peculiar, unsettled; and this conclusion substantiates our
+previous proposition with regard to the condition of a social system
+represented by a parabola.
+
+With regard to other advantages afforded by an elliptical social system,
+we will defer the consideration of this important subject until my next
+lecture.
+
+
+
+
+PAPER IV.
+
+THE SOCIAL PROPERTIES OF A CONIC SECTION,
+AND THE THEORY OF POLEMICAL MATHEMATICS--(_continued_).
+
+
+Most learned Professors and Students of this University,--You have
+already gathered from my preceding lecture my method of procedure in the
+investigation of the corresponding properties of curves and States. You
+have perceived that we have here the elements of a new science, which
+may be extended indefinitely, and applied to the various departments of
+self-government and State control. This new science of polemical
+mathematics is in itself an extension of the _principle of continuity_,
+for the discovery of which Poncelet is so justly renowned. We can prove
+by geometry that the properties of one figure may be derived from those
+of another which corresponds to it; and the new science teaches us that
+if we can represent, by projection or otherwise, a society of particles
+or individuals on a plane surface, the properties of the State so
+represented are analogous to the properties of the curve with which it
+corresponds. It is only possible for me to touch upon the elements of
+the science in these lectures, but I hope to arouse an interest in these
+somewhat unusual complications and curious problems, that you may
+hereafter make further discoveries in this unexplored region of
+knowledge, and that the world may reap the benefit of your labours and
+abstruse studies. I have already, in my previous lecture, touched upon
+the social properties of the parabola, and examined the constitution of
+erratic curves and eccentric nations. It is my intention to-day to speak
+of similar problems which arise with reference to elliptical States.
+
+But, first, let me answer an objection which may have occurred to your
+minds. Am I wrong in my calculations in attributing too much to the
+power and usefulness of forms of government? Does the well-being and
+happiness of a nation depend on the government, or upon the individuals
+who compose the nation? Most assuredly, I assert, they rest upon the
+former. Men love their country when the good of every particular man is
+comprehended in the public prosperity; they undertake hazard and labour
+for the government when it is justly administered. When the welfare of
+every citizen is the care of the ruling power, men do not spare their
+persons or their purses for the sake of their country and the support of
+their sovereign. But where selfish aims are manifest in Court or
+Parliament, the people care not for State officials who are indifferent
+to their country's weal; they become selfish too; Liberty hides her
+head, and shakes off the dust of her feet ere she leaves that doomed
+land, and the stability, welfare, and prosperity of that country cease.
+
+I might refer you to many a stained page of national history in order to
+prove this. Compare the closing chapters of the life of the Roman empire
+with the record of the brave deeds of its ancient warriors and valorous
+statesmen. Grecian preeminence and virtue died when liberty expired. I
+agree with Sidney when he writes that it is absurd to impute this to the
+change of times; for time changes nothing, and nothing was changed in
+those times but the government, and that changed all things. These are
+his words: 'As a man begets a man, and a beast a beast, that society of
+men which constitutes a government upon the foundation of justice,
+virtue, and the common good, will always have men to promote those ends;
+and that which intends the advancement of one man's desires and vanity
+will abound in those that will foment them.' I may not, therefore, be
+altogether wrong in attributing the prosperity and well-being of a
+nation to the form of government which it possesses.
+
+We will now proceed to the consideration of the social advantages which
+an elliptical State affords. This is the form of government and social
+position which we, as a nation, at present enjoy; and from mathematical
+considerations I am of opinion that it is the best, and hope that no
+change will ever be made in our constitution. You may remember that I
+have previously stated that an ellipse has a centre and two foci, in
+view of all the particles which compose the curve, and connected with
+them by close ties. The centre, in the projected figure, represents the
+monarchy, which is limited; and the government is carried on by the aid
+of the two houses of representatives of the people, depicted in the
+projection by the two foci.
+
+Now the social advantages of the ellipse are given by the fact that the
+sum of the distances of any point from the foci is always constant. No
+particle is left out in the cold; no one does not possess the advantages
+of a social government. Though his distance may be far from the Upper
+House, he has the advantage of nearness to the Lower, and _vice versâ_.
+The sum of the distances is constant. The extinction of one focus, the
+House of Lords, for example, would create a complete disorganization of
+the whole system: the other focus would set up a powerful magnetic
+attraction, and a curious bulb-shaped curve would be evolved, very
+different from the beautiful symmetrical form which the original figure
+presented to the eye. The centre of the system would be disturbed; and
+it is probable that ere long it would disappear along the axis and be
+vanished to infinity. Thus the curve would become a parabola. This is
+the alarming result of the extinction of one focus. Abolish the House of
+Lords, and you will soon find that the Throne will be disturbed; the
+State will become disorganized; the nation will become confused by the
+magnetic force of the Lower House, uncounteracted by any other
+attraction; and very soon a complete revolution of the whole system
+will set in: the monarch will be dethroned, and a Republican form of
+government, with all the eccentricities of a parabolic course, will take
+the place of a more orderly and settled constitution. This is a plain
+deduction from our mathematical investigations; and it behoves all our
+statesmen, our philosophers and great men, our fellow-citizens and the
+humblest artisans in our manufacturing towns, to weigh well this
+alarming result of the abolition of that House which has been threatened
+with destruction; and to ascertain for themselves the truths upon which
+my proposition and reasoning rest.
+
+I have already observed that the fact that the earth's orbit and that of
+other planets are in the form of ellipses; that the curvature of the
+earth is nearly the same, ought to guide us in choosing this particular
+curve as a model of the projection of a complete and most advantageous
+social system.
+
+The circle described on the major axis of an ellipse, is called the
+_auxiliary circle_, and affords much assistance in the investigation of
+the properties of an ellipse. As we have already shown, the circle
+represents the simplest form of monarchical government. Hence, if we
+compare the form of government represented by an ellipse (_i.e._, such
+as we now enjoy) with that of a system where the king is the only
+governing power, we may obtain great assistance in solving complicated
+political problems.
+
+In all conics there is a straight line called the 'directrix,' which
+represents in social or polemical science the laws of the nation, and
+plays a prominent part in the mutual relations of the individual
+particles. For instance, in the case of the parabola, the distance of
+any particle from the directrix is equal to its distance from the focus.
+
+From this we may conclude that if an individual deviates at all from the
+path which the laws (or, directrix) indicate, if he does not show true
+respect to the decrees of the focal government, and preserve the true
+position between them, directly he is found deviating from his course,
+he is quickly banished to a less enlightened sphere. In an ellipse there
+is less likelihood of his straying away from the course which the
+directrix points out, on account of the two-fold guidance which he
+receives from the two foci.
+
+The following curious problem may be noticed. If a parabola roll on
+another parabola, their vertices coinciding, the focus of the first
+traces out the directrix of the second.
+
+Here we come to the consideration of the international relationship of
+States. Two nations have the same form of government (in this example
+this form is Republican); their policies coincide: we may conclude from
+this proposition that the course which the government of one nation will
+pursue, will be that which is prescribed by the laws of the other.
+
+The subject of the contact of curves presents many interesting problems
+with reference to Polemical Science, and may be extended indefinitely.
+It is well known that there are different orders of contact, which are
+designated as the _first_, _second_, or _third_ order. This last order
+may be termed the 'marriage of curves,' cemented by the osculating
+circle, or 'wedding-ring;' and when two nations have contact of the
+third order, they have formed a very close alliance, and by calculation
+we can obtain the _radius of curvature_, or size of the wedding-ring, by
+means of which they may be united.
+
+The theory and nature of contact constitute a branch of our newly
+discovered science which we commend to the careful consideration of
+those who have undertaken the difficult and perplexing study of
+international law. Alas! too many States refuse this friendly contact,
+and, consequently, _cut_ each other, instead of blending in sweet
+accord. Their peace is at best an armed neutrality; and if they have
+contact of only the _first_ or _second_ order, we can prove
+mathematically that they are sure to intersect in some other point or
+points; and divergence of policy and disturbed relations are the
+results. Contact of the _third, or highest, order_ is the only safe
+position for two allied, or contiguous, States.
+
+With your permission I will add a few words to those I have already
+uttered with regard to the directrix. As necessary as the directrix is
+to the curve, so are the corresponding laws to the State. I will prove
+this fact by a few examples. English people have laws, and know how to
+obey them; therefore their numbers increase; they thrive and are
+prosperous. A friendly critic of another nation has said that the reason
+why Englishmen rule the world, is because they know how to obey. On the
+other hand, the gipsies have no laws; hence they become fewer and less
+powerful. What is the condition of all tribes and nations which are not
+governed by laws? They invariably remain poor and miserable. They are in
+want of a directrix; and if we could supplement the gift with foci and
+centre, they would soon emerge from their savage condition, and become
+more civilized.
+
+I have omitted to mention the hyperbolic form of government. The curve
+formed by the intersection of the surface of a cone with a plane will be
+a hyperbola, when the inclination of the cutting plane to the axis of
+the cone is less than the constant angle which the generating line forms
+with the axis. It is manifest that the plane will thus intersect the
+higher cone, and produce the figure which is known to mathematicians as
+the hyperbola.
+
+We may hence deduce the following property of the corresponding
+hyperbolic State. We take cognizance of that higher cone with which the
+mundane affairs of the lower cone are closely connected. As an example
+of this system we may mention the vast temporal rule and power of the
+Papal Throne, which formerly exercised such marvellous sway over the
+nations of Europe. By an appeal to a Higher Authority than that of
+earthly kings and potentates was this rule exercised; but its hyperbolic
+form is fast passing away, and degenerating into that of a circle with
+indefinitely small radius. We shall not, therefore, discuss the complex
+polemical problems which a hyperbolic State suggests.
+
+I will now mention a few problems which are easily capable of proof, and
+deduce from them the necessary conclusions which must follow when we
+apply our newly discovered principles of polemical science.
+
+1. 'If from any point in a straight line a pair of tangents be drawn to
+an ellipse, the chords of contact will pass through a fixed point.'
+
+I will not trouble you with the proof of this proposition, as it is
+evident to all mathematicians, and can easily be demonstrated. But mark
+well the deductions, when we interpret this mathematical language in
+correct polemical terms. A State, through various convulsions of its
+own, has merged into a condition represented by a straight line, having
+lost its symmetry, its beauty, its curvilinear proportion. An individual
+unhappily situated in this unfortunate community regards with longing
+eyes the prosperous condition of those who enjoy the social advantages
+of a settled form of government, and other blessings which accompany
+elliptical jurisdiction and laws. [Two tangents are drawn to an
+ellipse.] No matter where the individual may be in the unhappy envious
+straight line, the result of his reflection will be the same.
+Sympathetic chords are drawn, joining the points of contact of the
+tangents with the curve; they all pass through a fixed point. All these
+conclusions of the various individuals on the straight line will be the
+same. All are of opinion that the elliptical form is the best; and they
+mourn in secret over the sad events which have occurred in their own
+national life, their eccentricity, their lawlessness, when they see the
+advantages which their more staid and sober-minded neighbours so freely
+enjoy.
+
+2. The normal at any point of an ellipse bisects the angle between the
+focal distances of that point.
+
+The normal is the perpendicular from the point on the major axis; it is
+the line of thought directed by the observance of just laws and rules.
+Hence this proposition shows that the individual citizen, when guided by
+sound judgment, regards with equal favour and entire approval the
+existence of both foci, or Houses of Legislature. He considers that both
+are necessary to his comfort, and the right regulation of the State's
+welfare. He cares not for the _abnormal_ condition of those who talk as
+if the existence of either House were unnecessary to his country's weal,
+and bestows a pitying glance on those wandering lights, or disturbed
+erratic governments, which do not possess the advantages which from
+experience he has learned to love and to respect. No matter what his
+condition may be, the same opinions are held by all classes, all ranks
+and degrees; and if a self-opinionated particle think otherwise, he ought
+to be transferred to a less enlightened sphere, and migrate to a
+parabolic state, or uninteresting straight line. And when he has changed
+his location, he will look back on his old home and old surroundings
+with longing eyes and an aching heart, thinking of the blessings he has
+lost by his own rash act. This can be proved mathematically. He looks
+for an ideal state of society, leaps after the shadow his fancy has
+depicted; and when he finds himself outside his former state, he looks
+back with longing eyes at the once-scorned focus. What is the focus of a
+perpendicular on the tangent of an ellipse from any external point? Can
+it not be proved to be a _circle_? That is to say, he will be more
+conservative than ever. He would like to return to a primitive form of
+government. Farewell to his wild schemes and revolutionary measures!
+Farewell to his disestablishments, abolitions, and suppressions! The
+throne and government have new attractions in his eyes; loyalty, a new
+feeling, asserts its benign influence; and if he could return to his
+former position, his normal conduct would be straighter than ever, for
+by sad experience he has learned the value of those things which he once
+despised.
+
+But we need not depend upon one proof alone. Exactly the same result may
+be obtained from the well-known proposition which states that 'the angle
+between the tangent from any external point and the focal distance is
+equal to the angle between the other tangent and the focal distance.'
+
+3. The same opinions are often held by individuals in quite different
+walks and classes of life. Let these individuals be represented by
+points on an ellipse. Join these, and we have a system of parallel
+chords. Draw a straight line through the middle points of these chords,
+and lo! it will always pass through the centre. This shows that the
+central thought of all people is directed to the sovereign--that
+_loyalty_ is inherent in the hearts of those who recognise elliptical
+laws.
+
+I will conclude this lecture with a few remarks on the nature and
+properties of the _radical axis_. This name was first given, I believe,
+by M. Gaultier, of Tours, and for a full account of its nature I refer
+you to the _Journal de l'École Polytechnique_, xvi., 1813. The radical
+axis of two circles is the line perpendicular to the line joining the
+centres, from any point of which the tangents to the circles are equal.
+Let us suppose that one circle becomes a point, and that this point is
+situated on the circumference of the first circle. What is the result?
+The radical axis becomes the tangent to the circle. Hence we may
+conclude that in a social system of monarchical government the radical
+axis is perpendicular to the line attaching the individual with the
+monarch. Therefore we may conclude that the radical axis indicates a
+tendency of particles, or individuals, to fly off at a tangent, at right
+angles to the connecting-link between the individual and the king. When
+any motion takes place, this is evident, and this tendency is called
+centrifugal force. Sad is it for the State when this force is called
+into play, and the radical axis is a standing menace to the stability of
+States and nations. The only way to counteract its baneful, disturbing
+influence is to increase the attraction of the monarch on the
+individual, which nullifies the former force, and prevents further
+mischief. This is the method which nature itself adopts in the motions
+of the planetary worlds; the attraction of the sun prevents any
+disturbance which might be caused in the course of the planets by the
+action of centrifugal force, and nature suggests this plan for our
+adoption. Increase the attraction of the Throne; rigidly connect each
+individual by the strong chords of affection, advantage and utility with
+the ruling power; and then, though the radical axis may be there, it
+will cease to indicate any motion along it, it will not prevail over the
+counteracting influence of loyalty, and the stability of the social
+system and the happiness of the individuals will be the results.
+
+                 'I would serve my King,
+    Serve him with all my fortune here at home,
+    And serve him with my person in the wars;
+    Watch for him, fight for him, bleed for him, die for him,
+    As every true-born subject ought.'
+
+This, most noble professors, is the language of true patriotic loyalty.
+Let the monarch be loved and loving, let the laws be just and equal,
+happy will be the people, prosperous the realm. There are those who
+counsel different things, and preach sedition and the breaking-up of
+laws; but those who advocate such doctrines lack that judicial
+mathematical training which we, students and professors of Girtham
+College, have acquired. If polemical mathematics, the science of the
+future, should become more widely studied; if its results were
+disseminated far and wide; above all, if the proper position which women
+ought to occupy in the counsels of the nation were assigned to them, we
+should hear less of these wild schemes and foolish theories, and the
+influence of women would tend greatly to promote the stability and
+security of the State.
+
+Why, let me ask, should woman be excluded from that position which is so
+justly hers? from those duties which she can discharge so faithfully? It
+has been said that if we wish to know the political and moral condition
+of a State, we must ask what rank women hold in it. We are told that
+women have more strength in their looks than men have in their laws.
+Why, then, do men debar her from those fields of occupation wherein she
+may labour for the nation's good, and use her influence, which they
+acknowledge to be great, in those callings wherein she may most easily
+benefit the State, and the country she so ardently loves?
+
+At some future time I hope to speak more fully on this subject; and in
+concluding this lecture, I will remark that English politics need a
+leavening influence which will counteract the evil tendencies and
+corrupt theories which, in spite of our advantageous social system, at
+present exist; and this leavening influence will be best produced by
+the admission of those into the counsels of the nation who are
+acknowledged to have a benign and healthy influence--the women of
+England. Let women have their proper share in the government of the
+country, and I have no fear lest we shall preserve our elliptical
+constitution, and all the advantages which we at present enjoy.
+
+       *       *       *       *       *
+
+[Editorial Note.]--In the bundle of papers which contained the foregoing
+lectures, some letters of great interest were found, which show that the
+fame of the learned Lady Professor of Girtham College had already gone
+abroad, and attracted the attention of the leading statesmen of the day.
+It is to be regretted that the answers to these letters are not
+forthcoming, as it might be proved from them that the science of
+polemical mathematics has already influenced the minds of our
+legislators in their conduct of affairs at home and abroad. The
+following letter is of unique interest, and may be taken as evidence of
+the favourable impression which this new science has made on the mind of
+one of our greatest thinkers and statesmen:
+
+
+                    Downing Street,
+                            May, 18--
+
+My dear Lady Professor,--The report of the amazing results of your
+scientific researches has reached me, and I congratulate you most
+heartily on the originality and acumen which you have displayed in your
+investigations. A new light has dawned upon our country. Instead of
+groping in the darkness of political warfare, ensnared by party ties and
+jealousies, the statesmen of the future will be able to calculate and
+determine the correct course with mathematical precision and perfect
+accuracy. No one can dispute the truth of a proposition in Euclid, or
+the genuineness of Newton's laws; and if your method enables men to
+calculate and determine the correct political course of action, to solve
+political problems as easily as exponential equations, why--then adieu
+to the bickerings of party, the querulous complaints of the Opposition!
+Nay, joy to the Ministry! There will be no Opposition! Our statesmen
+will be able to guide the great ship of the State by means of charts
+which know no error; and they will resemble an association of savants
+met together to determine the exact moment of the transit of Venus, or
+to examine the degree of density of a comet's tail.
+
+This condition of Parliamentary procedure is much to be desired; you
+have shown how such an ideal state of things may be obtained. In the
+name of the Government I thank you for your endeavours on behalf of your
+country's welfare, and look forward to a further development of your
+admirably conceived system. As in the domain of ordinary science there
+are complex questions which defy the acumen of the philosopher; so in
+polemical science there may be questions which present the same
+difficulties and complications. But as the first are daily yielding
+before the persevering attacks of the mathematician, so I doubt not
+polemical science will soon overcome the various problems which may
+arise.
+
+But it is mainly on my own account that I venture to address you. I
+desire to consult you with regard to certain matters--political
+complications--which have recently occupied the attention of Her
+Majesty's Ministers. By the help of your new science, can you aid us
+in our deliberations? Of course, I am writing to you in _strict
+confidence_, and beg that you will keep this communication profoundly
+secret. I fear that would be a hard task for many of your sex, who do
+not possess your knowledge and powers of mind; but I have great
+confidence in your discretion.
+
+These are the problems which are presented to us for solution:
+
+1. Some members of the Cabinet are secretly in favour of Protection, and
+the country is rather stirred by the question. Can you, from your
+knowledge of the contact of curves and nations, help us to determine
+what course we ought to take with regard to Spain, for example? Are the
+principles of Adam Smith mathematically correct?
+
+2. I observe that England is represented mathematically by an ellipse.
+Are we right in assuming that Ireland is a portion of that ellipse? Or,
+on the other hand, in our chart of nations, must we describe that
+troublesome country as a rotating parabola, or complex figure,
+altogether outside our more favoured State?
+
+3. Do you consider, from your minute observation of our social system,
+that the form of our elliptical government is gradually undergoing a
+change, and that a revolutionary parabolic tendency is observable in the
+action of individual particles?
+
+4. Is it not possible that the differences in the policy of the various
+nations of Europe; the difficulties which beset the carrying out of
+international law; the jealousies, quarrels, and rivalries of States
+might disappear, if the same form of government (_i.e._, elliptical)
+were adopted in each?
+
+If you will kindly favour Her Majesty's Ministers with your opinion on
+these questions, they will owe you a debt of gratitude, which they, as
+representatives of the nation, will do their utmost to repay.
+
+With every good wish for your further success in the regions of
+polemical science,
+
+          I beg to remain,
+              My dear Lady Professor,
+                  Your faithful servant,
+                        +----------------------+
+                        |                      |
+                        |         [4]          |
+                        |                      |
+                        +----------------------+
+
+
+[Editorial Note.]--The next letter is not of quite the same pleasing
+nature as the foregoing, and shows that it is impossible to please
+everyone, even if that happy consummation were desirable. This letter
+was evidently called forth by some remarks which the learned Lady
+Professor had made in her third lecture with reference to eccentricity
+in dress. Our readers will recollect that the professor pointed out that
+an extravagant 'bloomer' costume--half male, half female--was no more a
+sign of genius than æsthetic dresses, always betokened the artist.[5]
+This latter statement evidently gave great offence to the members of a
+society which called itself the 'Æsthetic and Dress Improvement
+Association,' and the following letter is the result of one of their
+solemn conclaves:
+
+
+                    Oscar Villa, South Kensington,
+                            June, 18--.
+
+The Secretary of the Æsthetic and Dress Improvement Association presents
+his compliments to the Lady Professor of Girtham College, and begs to
+contradict emphatically her statements with regard to a subject upon
+which she is evidently in entire and lamentable ignorance, and to
+protest against her aspersions upon the artistic studies of this and
+kindred societies. He begs to state that true æsthetes are _not_
+eccentric (they leave that to lady professors and her Philistine
+followers); that to dress becomingly is one of the principal objects of
+life, and that true greatness is achieved as much by the study of the
+art of dress as by any other noble pursuit or graceful accomplishment.
+Are not Horatio Postlethwaite, Leonara Saffronia Gillan, Vandyke
+Smithson entitled to greatness? And yet their laurels have been won
+solely by the art of dress. Perhaps the lady professor has never read
+'Sartor Resartus'! In conclusion, he would ask the Lady Professor to
+refrain from casting obloquy upon the work of the Association which he
+has the honour to represent; to prevail upon her pupils to abandon the
+unfeminine attire which some of them have assumed, contrary to the first
+principles of art; to array themselves in flowing robes of sage-green
+and other choice colours (patterns enclosed), and to study art, instead
+of absurd mathematics, which no one can understand, and do no one any
+good.
+
+     (Approved by the Committee of the Æsthetic and Dress
+      Improvement Association.)
+      June, 18--.
+
+
+[Editorial Note.]--The next letter, written by a pupil of the Lady
+Professor, requires no explanation, and speaks for itself.
+
+
+                    Jesus College, Cambridge,
+                            March, 18--.
+
+My dear Tutor,
+
+You will be glad to hear that after superhuman exertions I have at last
+succeeded in passing my Little-go, and I am eternally grateful to you
+for all you have done for me. I should never have got through if it had
+not been for you. All the coaches in Cambridge would never have managed
+it, but you drove me through in a canter. And why? I never could make up
+my mind to work for them; but when I coached with you, you made me like
+it. I almost revelled in the Binomial when you wrote it out for me; and
+then I could not help listening to you; and you looked so grieved when I
+would not learn, and made me feel such a brute; so somehow or other you
+drove some mathematics into my head, and I pulled through. By-the-bye, I
+think you must have tried the 'brain wave' dodge with the examiners, as
+five out of the six propositions in Euclid, which you told me to get up
+specially, were set! I wish I could read people's thoughts; can you read
+mine? If I were a Don, or a Fellow, or something, I would advise the
+University to have some lady professors like you to teach the men,
+instead of some of these sleepy old tutors. It would be a great
+improvement, and I am sure we should get through a great deal more work.
+
+They have given me a place in the Jesus Eight, which I shall take now
+that I am released from your professorial ban, and have time for rowing.
+But I don't half like giving up mathematics. You see, I have grown fond
+of the study. Do you think you could make a wrangler of me? At any rate,
+I should like to come to your lectures again. May I?
+
+                    Your Grateful Pupil.
+                         *     *     *
+
+
+  [4] It is to be regretted that this letter has evidently fallen
+      into the hands of some autograph collector, who has ruthlessly
+      cut off the signature; but the reader will easily determine,
+      after careful perusal of the document, from whose pen it emanated.
+
+  [5] Cf. page 36.
+
+
+
+
+PAPER V.
+
+A LECTURE UPON SOCIAL FORCES, WITH SOME ACCOUNT OF POLEMICAL KINEMATICS.
+
+
+Most noble Professors and Students of Girtham College,--Since last 'I
+wandered 'twixt the pole and heavenly hinges, 'mongst encentricals,
+centres, concentricks, circles, and epicycles,' like the great
+Albumazar, and found them full of life and wisdom for the guidance of
+our States and laws, I have turned my attention to the Applied
+Mathematics, in order to determine what other truths this shaft may
+yield.
+
+The strength of all sciences, according to Bacon, consists in their
+harmony; and it is truly marvellous how perfect this harmony is, if our
+ears are tuned aright to hear it. We have observed how the beautiful
+and regular laws of curves and cones correspond to the social laws of
+States and nations, guiding them as if by word of counsel, admonishing
+them on what principle they ought to regulate their governments and
+inter-relations. We have seen that the laws which govern thought and
+light and sound are almost identical, and that harmony pervades not
+merely the ordinary sciences, but extends her benign influence over
+these newly discovered fields of scientific research, which I claim to
+have discovered.
+
+All this may appear at first sight surprising; but the real philosopher,
+who knows that all kinds of truth are intimately connected, will receive
+such revelations of science with satisfaction rather than astonishment;
+for this new science, which has opened itself out before me, is only an
+extension of other well-known laws and discoveries which have come down
+to us from the remote past.
+
+If my investigations should appear to you, most noble professors,
+somewhat novel and imaginary, remember the maxim of the sage, that in
+the infancy of science there is no speculation which does not merit
+careful examination; and the most remote and fanciful explanations of
+facts have often been found the true ones. Perhaps some
+'self-opinionated particle' (I speak mathematically) may have been
+inclined to laugh at our theories and discoveries, as the wise fools of
+the day laughed at Kepler and his laws; but time has changed the world's
+laughter into praise, and a century hence our discoveries may rank among
+the achievements of modern science. As Cicero says, 'Time obliterates
+the fictions of opinions, but confirms the decisions of nature.'
+
+I have not shunned, most noble professors, to enlist Imagination under
+the banner of Geometry; for I am fully persuaded that it is a powerful
+organ of knowledge, and is as much needed by the mathematician as by the
+poet or novelist. It is, I fear, often banished with too much haste from
+the fields of intellectual research by those who take upon themselves to
+give laws to philosophy. We need imagination to form an hypothesis; and
+without hypotheses science would soon become a lifeless and barren
+study, a horse-in-the-mill affair ever strolling round and round,
+unconscious of the grinding corn. In my previous investigations my
+imagination pictured the symmetry of curves and States; the hypothesis
+followed that the laws which regulated them were identical, and you have
+observed how the supposition was confirmed by our subsequent
+calculations.
+
+In this lecture I propose to examine some of the forces which exist in
+our social system, and shall endeavour to estimate them by methods of
+mathematical procedure and analogical reasoning. We will begin with the
+old definition of Force as _that which puts matter into motion, or which
+stops, or changes, a motion once commenced_. When a mass is in motion,
+it has a capacity for doing work, which is called _Energy_; and when
+this energy is caused by the motion of a body it is called Kinetic
+Energy (in mathematical language KE = ½ MV²). Another form of kinetic
+energy is called Potential Energy, which is in reality the capacity of a
+body for doing work _owing to its position_. For example we may take an
+ordinary eight-day clock. When the weights are wound up, they have a
+certain amount of potential energy stored up, which will counteract the
+friction of the wheels and the resistance of the air on the pendulum.
+Or, again, we have the example of a water-wheel: first the water in the
+reservoir, being higher than the wheel, has an amount of potential
+energy. This is converted into kinetic energy in striking against the
+paddles, and after this we have potential energy again produced by the
+action of the fly-wheel.
+
+By the principle of conservation of energy, if we consider the whole
+universe, not our planet alone (for its heat and energy are continually
+diminished to some slight degree), we find that _no energy is lost_.
+
+Force is recognised as acting in two ways: in _Statics_, so as to compel
+rest, or to prevent change of motion; and in _Kinetics_, so as to
+produce or to change motion; and the whole science which investigates
+the action of force is called _Dynamics_.
+
+All this is of course pure mathematics, and I have made these elementary
+observations for the benefit of my younger hearers, the students of this
+University. My grave and reverend seniors will pardon, I am sure, the
+repetition of facts well known to them for the sake of those who are
+less informed than themselves.
+
+Now before I proceed further, I will endeavour to point out that these
+elementary truths of physical science hold good in our social system.
+Each individual is a mass, acted on by numerous forces, capable of
+'doing work,' which work can be measured and his velocity calculated.
+Some individuals have a vast _potential energy_; that is to say, from
+their position and station in the social system, they have a power which
+is capable of producing work which a less exalted individual has not.
+Like the weights in an eight-day clock, or the water in a reservoir,
+they have a capacity for doing work, owing to the position to which
+they have been raised. How vast the influence of a Primate or a Premier,
+a General or a King! And yet their power is chiefly potential energy,
+arising from the position they occupy, not from the individuals
+themselves. Schiller has described this in poetical language, which,
+strange to say, is mathematically correct:
+
+   'Yes, there's a patent of nobility
+      Above the meanness of our common state;
+    With what they _do_ the vulgar natures buy
+      Their titles; and with what they _are_, the _great_.'
+
+Other forces may have raised these men to their exalted positions; but
+their influence is due to their height, their potential energy. Placed
+on a lower level, they would cease to have that power. How calm the
+dignity of this potential rank! The water in the reservoir is scarcely
+ruffled or disturbed, as if unconscious of its power; when it has lost
+its force it rushes along with a sullen murmur and a roar, howling and
+hissing and boiling in endless torture, until--
+
+   'It gains a safer bed, and steals at last
+    Along the mazes of the quiet vale.'
+
+So the vulgar crowd rushes on, with plenty of kinetic force, making
+noise enough and looking very busy; while those who seem to sleep in
+calm forgetfulness, exercise their potential energy, and do the real
+work of turning the great engine of the State.
+
+There are attractive and repulsive forces (more commonly the latter, the
+cynic will say) in our social system, but each individual is the centre
+of various forces acting upon him. In nature all matter possesses the
+force of gravity, and whatever the size of two particles may be, they
+mutually attract each other. The earth attracts the moon; the moon
+attracts the earth. A stone thrown up into the air exercises an
+infinitesimal force upon the earth; so in the social system every
+individual, however small and insignificant he may be, exercises some
+attractive force upon his neighbour. There is no one in the world who
+does not exercise some influence for good or for evil upon his fellows.
+
+The force of _cohesion_ is manifest in society as in nature, that force,
+I mean, which resists the separation of a body's particles. Different
+bodies possess different powers of cohesion, _e.g._, the cohesion of
+chalk is far less than that of flint embedded in it; even the same body
+possesses different powers of cohesion in different directions, _e.g._,
+it is easier to split wood in the direction of the fibres than
+perpendicular to them. If by our old principle of continuity we change
+the words 'bodies' into 'States' or 'individuals,' we shall see that the
+same laws hold good in social science as in natural philosophy.
+
+These are a few analogous laws which I have taken almost at random; but
+it must strike the most casual listener to my remarks that it is
+wondrous strange that men, regarded as social beings, should possess the
+same qualities, and be governed by the same laws, as the rest of
+_matter_. As Bishop Butler says, 'the force of analogy consists in the
+frequency of the supposed analogous facts, and the real resemblance of
+the things compared.' It appeals to the reasoning faculty, and may form
+a solid argument. Hence, if we can prove the similarity of various laws
+and conditions, we may not be wrong in assuming by analogy the identity
+of those laws and conditions.
+
+I have stated my case in this manner in order to convince the
+gainsayers, if any such there be, and to banish any doubts or
+questionings which may have arisen in your minds. I will now proceed
+with some further investigations, full of the most profound interest
+and importance.
+
+Doubtless many of the lady-students present are in the habit of
+welcoming peaceful evening in with a potent draught of 'the cup which
+cheers but not inebriates;' and as men are great flatterers (for
+imitation is the greatest flattery), I believe the male portion of my
+audience have been known to follow that excellent example. Some perhaps
+are in the habit of burning the midnight oil, and keep their eyes open
+by means of this fruit of the hermit's pious zeal, endowed by high
+omnipotence with the power of hindering sleep;[6] but that practice I
+do not advise, as that delicate portion of our system, the nerves,
+especially of women, often becomes injured by such stimulating doses.
+However, you will have observed (if you do not follow the modern
+pernicious fashion of taking tea without sugar) that numerous bubbles
+are formed upon the surface of the liquid. After a few moments these
+unite into one central mass of bubbles by the force of mutual
+attraction.
+
+It appears from considerations which are detailed in works on physical
+astronomy, that two particles of matter placed at any sensible distance
+apart attract each other with a force directly proportional to the
+product of their masses, and inversely proportional to the square of
+their distance.
+
+Now, suppose that we have a number of circular masses situated upon a
+plane surface, they will attract each other with a force which may be
+determined with exactitude; and the greater the masses the greater the
+force. We will now apply this to polemical science. The agricultural
+settlement is the first stage in the civilization and formation of a
+State. How did this arise? First, a single family immigrated to some
+uncultivated parts of the country, perhaps accompanied by others, who
+formed a little colony. Other settlements were made in other parts of
+the land; and thus the country became overspread with these detached and
+separate communities. An eminent writer declares that these settlements
+can be traced in the beginnings of every race which has made progress;
+that they were characteristic of those races in Greece and Italy, in
+Asia and Africa, which grew into the opulent and famous cities in which
+so much in the early history of civilization was developed. The colonies
+of England have been formed in the same way, just as in olden time
+England itself was occupied when the Roman power ceased.
+
+These settlements correspond to the circular masses situated on the
+plane surface; they were quite separate from each other, each having its
+own laws, its own headman or ruler, its own assembly or parish council.
+But as time elapsed, the force of mutual attraction set in; by degrees
+these separate settlements were drawn together by force which increased
+in proportion as the settlements increased; until at last one united
+kingdom was formed under one king, governed by uniform laws and
+regulations. The bubbles have blended, the circles have come together,
+and one large circle or other curve is the result. This may be called
+the _Law of Social Attraction_. In accordance with the results of one
+of my previous lectures, I have taken the circle as representing the
+simplest form of government, which figure, in the case of the elementary
+settlements, must have been small.
+
+Many of you, most noble professors, are doubtless accustomed to make
+experiments with the microscope. I will suggest a simple one, which
+illustrates very forcibly what I am endeavouring to show you. Take some
+particles of copper, and scatter them at intervals over the surface of
+an object-glass, and pour some sulphuric acid upon the glass. Now, what
+is the result? A beautiful network of apparently golden texture spreads
+itself gradually over the whole area of the glass. Steadily it pursues
+its way, and the result is beautiful to behold. The minute particles of
+copper were the original settlements scattered over the land; the
+sulphuric acid the civilizing agent; and the final picture of a united
+civilized homogeneous nation is well represented by the progressive and
+finally glorious network of gold. This example is of course outside our
+present subject, but it serves as a beautiful illustration.
+
+As an instance of the attractive force exercised by small communities
+upon each other, I may mention the united kingdom of Germany, which is
+composed of numerous small States and nations, which have been drawn
+together by the power of mutual attraction. Until recently they were
+each self-contained, separate constitutions, with their own kings and
+forms of government; but the attracting force, assisted by forces from
+without, has proved too much for them, and the great and powerful united
+kingdom of Germany is the result.
+
+But why, you may ask, have not the people in Hindustan united in the
+same way? There the agricultural settlements remain as they did ages
+ago; separate petty chieftains rule under the all-governing power of
+England. Why have they not united?
+
+To this objection I reply that there is in social science, as in Nature,
+a _vis inertia_; that is to say, there is a tendency in matter to remain
+at rest if unmoved by any external agency, and also of persisting to
+move, after it has once been set in motion. The _vis inertia_ of some
+bodies is greater than that of others, and depends upon their weight
+and density. Now it so happens that the moral _vis inertia_ of the
+Hindustani is very great, hence their tendency to amalgamation is
+small. They remain in the state in which they happen to be.
+
+On the other hand the inertia of Englishmen is small, of Englishwomen
+smaller, and therefore their power of combining is greater. Here let me
+observe that the quality of inertia is one which ought to be removed as
+far as possible from each social system. Inertia was regarded as a
+capital crime by the Egyptians. Solon ordained that inert persons should
+be put to death, and not contaminate the community. As savages bury
+living men, so does inertia practise the same barbarous custom upon
+States and individuals. Observe the putrid state of inert water, the
+clear and sparkling beauty of the moving stream, bearing away by the
+force of its own motion aught that might contaminate it. Men more often
+resemble the stagnant water than the rivulet. A healthy social state
+enforces labour by natural laws, and banishes inertia as much as
+possible from the system. If the principles of some noisy English
+politicians were fully carried out, and all things made '_free_,'
+inertia would be increased, and listless indolence pervade the masses of
+our countrymen. I may say that inertia is not entirely unknown in our
+sister University of Cambridge.
+
+The existence of social forces is supported by the testimony of Dr.
+Tyndall, who plainly recognises their power, though he does not attempt
+to expound their origin. 'Thoughtful minds are driven to seek, in the
+interaction of social forces, the genesis and development of man's moral
+nature. If they succeed in their search--and I think they are sure to
+succeed--social duty would be raised to a higher level of significance,
+and the deepening sense of social duty would, it is to be hoped, lessen,
+if not obliterate, the strife and heart-burnings which now beset and
+disguise our social life.' I accept with gratification Dr. Tyndall's
+conclusions: to determine, examine, trace, calculate these social forces
+which exercise such a powerful influence on our characters, our lives,
+our customs, which produce the greatness of the State, or drag it down
+with irresistible strength from its pinnacle of glory to an abyss of
+degradation; to estimate such forces is the great and noble object of
+our lectures and researches in this University. Prosecute, most noble
+professors, your studies in this direction with all the energy of your
+enlightened intellects, and there is yet hope that this new science,
+which I have endeavoured to sketch out, however feebly, may be the means
+of saving our beloved nation from degradation and ruin, and raising her
+to a higher level of glory and honour. I hope to continue the subject of
+social forces in my next lecture.
+
+
+  [6] A Chinese legend relates that a pious hermit, who in his
+      watchings and prayers had often been overtaken by sleep, so
+      that his eyelids closed, in holy wrath against the weakness
+      of the flesh, cut them off, and threw them on the ground. But
+      a god caused a tea-shrub to spring out of them, the leaves of
+      which exhibit the form of an eyelid bordered with lashes, and
+      possess the gift of hindering sleep.--Dr. Ure.
+
+
+
+
+PAPER VI.
+
+ON SOCIAL FORCES (_continued_)--POLEMICAL STATICS AND DYNAMICS.
+
+
+Most Noble Professors and Students of Girtham,--We have embarked upon
+a stormy sea of speculation, on a voyage of grand discovery, and the
+dangerous waves of adverse criticism, and the deceptive under-current of
+prejudice, often make the steersman's lot by no means an enviable one.
+But our vessel is sound and perfectly equipped, and therefore I do not
+fear to guide her across the great unknown.
+
+It may have occurred to you that the problems which present themselves
+for solution in social science are far more difficult and complicated
+than those which arise in ordinary mathematics. That is undoubtedly the
+case; but this extra degree of difficulty is due to the fact that we
+make no assumptions; we take the things as they really are, not as they
+are assumed to be. In physical science, if we take into consideration
+the resistance of the air, the curvature of the earth, the rigid
+connection which exists between particles in the same body, and a host
+of other things which are often conveniently neglected in elementary
+works, how complicated the various problems become! So we must not be
+surprised at some of the difficulties which occur in social science, as
+nothing is neglected; the whole problem is before us, and having solved
+it we need not make allowances for any falsely assumed _data_.
+
+It is possible that other professors of this science may come to
+slightly different conclusions to those which I have arrived at. That
+is only to be expected, because their original observations may have
+slightly varied. But in physical science allowances are made for
+different observers. In astronomy, for example, we find the value of the
+'Personal Equation.' One observer on looking through the telescope may
+take the meridian of a star rather differently from another watcher of
+the heavenly bodies, and the _personal equation_ is used to make
+allowances for this quickness, or slowness, of observation. So in social
+science there must be a personal equation too, and our object ought to
+be, in the ordinary affairs of life as well as in the higher duties of
+scientific action, to make our personal equation as small as possible.
+But until the old proverb, '_Quot homines, tot sententiæ_,' has ceased
+to have any meaning, there will be abundant need of this most useful aid
+to accuracy.
+
+The close connection which exists between social forces and material
+forces is plainly shown by the doctrine of the conservation of energy.
+'This doctrine,' says Dr. Tyndall, 'recognises in the material universe
+a constant sum of power made up of items among which the most Protean
+fluctuations are incessantly going on. It is as if the body of nature
+were alive, the thrill and interchange of its energies resembling those
+of an organism. The parts of the stupendous whole shift and change,
+augment and diminish, appear and disappear; while the total of which
+they are the parts remains quantitatively immutable, _plus_ accompanies
+_minus_, gain accompanies loss, no item varying in the slightest degree
+without an absolutely equal change of some other item in the opposite
+direction.' So do the forces in the social world ebb and flow, rise and
+fall, carrying on the same universal law which regulates the energy of
+material force.
+
+I will now proceed to enumerate some of those forces which exercise such
+a powerful influence on society.
+
+First, let us take the force of _Public Opinion_, which seems to
+exercise a relentless sway over the minds and manners of men. This is a
+very subtle and secret force, which is most difficult to trace, and
+resembles electricity in the science of physics. We cannot see it, but
+are only able to judge of its power by its results. Its point of
+application is not in the individual, but in the collection of
+individuals who make up the social system; and it is, in reality, the
+resultant of, or the compromise between, the various elementary forces
+which make up human society. Yes, compromise is a purely mechanical
+affair, based on the principle of the parallelogram of forces; and as
+public opinion is the result of a compromise, we may calculate its
+force. For example: 'It is required to know the state of public opinion
+in the matter of politics, when the results of a General Election show
+that the Conservatives are to the Liberals as 10 : 9.'
+
+Let OC be the direction of the Conservative force.
+
+Let OL be that of the Liberal.
+
+Then by _data_ OC : OL :: 10 : 9.
+
+[Illustration]
+
+Complete the parallelogram, and join OP.
+
+Then OP represents the force of public opinion in magnitude and
+direction.
+
+N.B.--The direction of OL is determined by the amount of deviation of
+the policy of the Liberals from that of the Conservatives.
+
+As in physical, so in social science, impulsive forces sometimes act,
+and effectually disturb our system and our calculations. Public opinion
+is very liable to the action of disturbing forces. Panic is an impulsive
+force, which defies the power of the most learned professors of social
+science to determine its magnitude and direction. Some strange
+unforeseen catastrophe--the fascination caused by a brilliant and
+unscrupulous orator, a cruel wrong, a blind revenge for real or
+imaginary injustice--will sometimes rouse one element of passion latent
+in the vast body of public opinion; so that it breaks with all that
+hitherto restrained and balanced it, and precipitates society into a
+course of conduct inconsistent with its former behaviour, and bloodshed,
+revolution, the breaking-up of laws, are the terrible results of panic
+or revengeful passion.
+
+Society is, as it were, split up by the terrible action of such
+impulsive forces, just as wood is split up by the repeated blows of the
+hatchet. It is, therefore, the duty of statesmen to increase the power
+or force of cohesion, to strengthen the fibres of the State, so that the
+force of such impulsive blows may not be felt, nor disturb the
+continuity of the framework of the State. If such measures had been
+adopted in the neighbouring country of France, much misery might have
+been avoided, and the terrible revolutions which have so frequently
+convulsed her social system entirely prevented.
+
+_Friction_ is another disturbing element in our calculations, and
+although it may be made a useful servant, it is a bad master in
+mathematics, as in polemics. Without the aid of friction, progress would
+be impossible. For example: Take the case of a man with perfectly smooth
+skates on perfectly hard, smooth ice; he would be unable to reach the
+land unless he had provided himself with some stones, by throwing which
+he would just be able to get to his destination by a backward motion.
+The engine would be unable to proceed on its iron road if it were not
+for friction. The same is true in polemical science: the government of
+the country would not be able to be carried on under our present
+conditions if it were not for _party friction_. But suppose it increased
+indefinitely, party friction becomes party _obstruction_; and the engine
+of the State would no longer proceed smoothly and evenly along its
+appointed course at the rate of sixty miles an hour, but would resemble
+an old-fashioned coach, up to its axle-trees in mud, its motion
+altogether stopped by the action of party friction.
+
+We have seen that forces have two ways of acting: that of compelling
+rest and that of producing motion. In statics forces act so as to
+prevent any change of motion, or disturb the body's original position.
+In kinetics, on the contrary, the power is recognised as acting so as to
+produce or change a body's motion. Now, in polemical science we have
+these two ways of considering the action of forces. There is the
+_statical_ or _conservative_ force, which compels rest, which seeks
+security, stability, and peace, and is not ardently devoted to change.
+It reduces the system to equilibrium. There are, of course, two kinds of
+equilibrium--_stable_ and _unstable_--according as the social and
+political system is in a healthy or unhealthy state. If a body is in
+stable equilibrium, and any slight motion takes place, the body will
+return immediately to its former position; but if in unstable, it will
+decline further and further away from its original position, and be
+entirely upset. So a healthy and sound conservative equilibrium is not
+disturbed by outside forces, and the State will resume its former
+position of stability and rest when the opposing force is withdrawn. But
+an unhealthy and insecure conservatism is as easily disturbed as an egg
+balanced on its narrow end.
+
+The kinetics of society, that is to say the Radical way of estimating
+force, is the party of motion, generally supposed to be the 'party of
+progress.' It has therefore many attractions in the eyes of those who
+delight in motion, speed, and rushing about. To run at full speed, to
+feel the keen air upon one's face, to experience the delightful
+sensation of freedom of will, and limb, are joys which cannot be denied.
+Such exercise is beneficial to the system, bodily or political. Motion
+is the life of all things; it is characteristic of nature; it adores
+nature; because it is an emblem and characteristic of life. The
+ceaseless rolling of the ocean waves, the swaying of the trees, the
+bending of the flowers, the waving of the corn, all these fill us with
+pleasure; whereas a flat uninteresting plain, unrelieved by the motion
+of terrestrial objects, is depressing to the spirit. So there is much to
+be said in favour of motion, and Carlyle has defined progress as 'living
+movement.' And men love this 'living movement,' and take up the
+Laureate's cry:
+
+               'Forward, forward, let us range,
+    Let the great world spin for ever down the ringing
+                Grooves of change.'
+
+But, after all, there is a danger in this everlasting motion. We cannot
+tell whither this progress may lead. It may be along a safe sure road;
+but perchance a precipice may open out before us; and rejoicing in the
+acceleration of our velocity, with eyes intent upon some distant heights
+of glory and ambition, we may not discover our danger until it is too
+late to stop, and a terrible plunge into an unknown abyss of turmoil and
+tumultuous waves is the alarming result of an unguarded policy of
+unrestrained 'progress.' I recall to my mind the quaint words of Holmes
+which aptly illustrate my contention.
+
+   'If the wild filly, "Progress", thou would'st ride,
+    Have young companions ever at thy side;
+    But wouldst thou stride the staunch old mare, "Success,"
+    Go with thine elders, though they please thee less.'
+
+Progress and success do not always go together hand in hand; and while
+motion is essential to life, it is not always safe to urge a country
+forward at too great a speed; and security and stability are quite as
+important to the nation's life as actual progress.
+
+There are other impulsive forces which act occasionally in the sphere
+of politics, and which baffle all our calculations, and exclude
+scientific considerations of the polemical problems which arise.
+_Ambition_ is such an impulsive force, and when the rulers of the people
+are actuated by it, and struggle for money, place, and power, politics
+is degraded from its position as a science, and it becomes impossible to
+estimate the result of forces so generated.
+
+In my next lecture I propose to treat the important subject of the Laws
+which govern States and Governments, and which regulate, generate, and
+control the social forces which we have seen at work in the body
+politic.
+
+
+
+
+PAPER VII.
+
+LAWS OF POLITICAL MOTION.
+
+
+Since the last time I had the honour of addressing you on polemical
+matters, I have met with a passage in the writings of M. Auguste Comte
+which afforded me much pleasure. It seemed to be the one word for which
+I had been waiting, and confirmed many of my own impressions and
+speculations. He lays down two propositions: first, that the
+constructive politics of the future must be based on the history of the
+past; and second, that political science is a composite study, and
+presupposes the complete apprehension of every branch of science,
+beginning with the physical, such as astronomy, and ending with the
+moral, such as ethics and sociology. M. Comte evidently does not regard
+as a vain dream and imaginative speculation the theory that it will be
+possible for statesmen to calculate a policy, and to determine a course
+of action by purely scientific considerations. May I entertain the hope
+that in this university, where all branches of physical science have
+found a home, and are studied by most able and learned professors, the
+science of politics may be pursued under most favourable circumstances?
+I trust that each professor will bring before me the results of their
+deliberations, and contribute to the growth of this particular science
+for which our university has already become deservedly famous.
+
+My present lecture is devoted to the important consideration of _Law_.
+At first sight it may appear to you that the wills and passions of
+mankind are so diverse and unknowable, that it would be absurd to
+suppose that they can be calculated, or rendered amenable to any law.
+But Professor Amos has pointed out that in proportion as we examine
+history, and compare the actions present and past of different nations
+and states, the more uniform does human nature appear; the more
+calculable the actions, sentiments, and emotions of large masses of
+people. As we have already stated, the difficulties of the study are not
+likely to deter the professors of Girtham College from the pursuit of
+any particular branch of science.
+
+_A priori_ we might suppose from analogy that these polemical laws
+existed, as there is no department of nature which is not governed by
+law. It is an essential feature in nature, and also in government. What
+is political economy but the study of certain laws of nature? These were
+first discovered by Adam Smith, and have since been traced and estimated
+by such men as Ricardo, the two Mills, Professor Cairnes, Jevons, and
+many others. Moreover, our physical constitutions are governed by laws,
+which physicians have determined, and which it is perilous to resist.
+Our moral constitution is also governed by laws, which evidently exist,
+although it is difficult to find them out. But the nation is only an
+assemblage of individuals; and since individuals are so governed, it is
+only natural to suppose that the nation, composed of individuals, is so
+constituted and controlled. And not only is that true, but we shall see
+that polemical laws are as permanent and universal, as invariable and
+irreversible, as the laws of nature which regulate the courses of the
+heavenly bodies, and raise the tides, or depress the sandstone hills.
+
+We may notice first the preponderant impulse observable in a nation's
+life in favour of supporting existing facts and institutions; and every
+reformer has discovered the difficulty and danger of changing or
+opposing the customs and habits of the people. As a wheel will travel
+most smoothly along a well-worn groove, whereby friction is diminished,
+so there is a natural national tendency always to run along those paths
+with which the habits and customs of the people have made them familiar.
+This law is nothing else than Newton's first law of motion, which is
+quite as applicable to human masses as to lifeless matter. The tendency
+of matter to remain at rest, if unmoved by any external agency, and of
+persisting to move after it has once been set in motion, is a
+conservative tendency; and is as true in political science as in any
+other.
+
+The special branch of our science, which we may call the _Biology of
+Politics_, shows how absolute is the domain of law in polemical matters.
+The law of human life is that men are born, grow, become strong and
+vigorous, and then decay and die. This is the law of life, to which we
+must all yield an enforced obedience. This same law is observed to be at
+work in the heavenly bodies; and astronomy shows us that planets are
+born, flourish, and at length die, just as our human bodies do. The moon
+is, as you may have observed, a dead planet, such as our earth may be
+some day. The same growth and decay are also manifest in national life.
+First, there is the birth of the nation, which sometimes lies a long
+time in a dormant state, and then wakes up to life and energy. China and
+Russia are examples of dormant States, just waking from a long sleep of
+childishness and ignorance. The next stage is the strong an healthy
+period of its existence, which England is at present enjoying; and then,
+after various stages of gradual decline, we come to the senile period of
+national life, when every energy and faculty, every national feeling and
+power of invention, are completely exhausted. As an example of this
+depressing condition, we may mention Turkey and several of the effete
+States of South America. Sometimes, when life is nearly extinct in the
+human body, physicians have made use of the power of galvanism, in order
+to revive the dying energies. This process of galvanizing a State into
+life was tried by Lord Palmerston and others on the worn-out frame of
+Turkey. But such attempts can only meet with partial and transitory
+success; and where the loss of national power and faculty betokens the
+senile period of the nation's existence, it is vain to attempt to
+restore its former life and energy. The study of the biology of
+politics presents many interesting and important details in this special
+branch of knowledge; and I commend this part of our subject to the
+special attention of the professor of physiology. The law of development
+is observable in nations as in nature. Recent scientific discoveries
+have tended to take away all ideas of _chance_ in the workings of
+nature, and have substituted _law_ instead of it. It would be
+unscientific and incorrect to speak of the world being formed by the
+'fortuitous concourse of atoms.' So we cannot speak of a State being
+generated in this manner. Laws--economical, geographical,
+natural--preside over the formation of States and nations, and produce
+their further development.
+
+The laws of political motion occupy the same prominent place in our new
+science as Newton's laws do in ordinary dynamics. These are very
+important in calculating the positions which various States will occupy
+in the future. First, we have the _doctrine of nationality_, which
+prevented the progress of Austria into Italy, and of the Bourbons in
+Naples, and produced the amalgamation of the small German States in the
+great empire of Germany. The second law of political motion is the
+doctrine of the _independence_ of all true States, and the equality of
+all States to each other. This had its growth in feudalism; and all the
+chief wars of modern times have been the result of the efforts of nature
+to establish this law of independence. The doctrine of intervention is a
+modification of the preceding law, and is applicable when the law of
+necessity demands its use, such as the restoration of order after
+protracted anarchy, the abolition of slave trade, etc. The third law is
+the _law of morality_. Just as for each man there exists a _right_ and a
+_wrong_; just as _duty_ and _conscience_ are certain elements in his
+daily motion, which dictate his course of action, although he may chose
+to neglect them; so a nation is bound by the same moral laws which
+govern the individual; and a nation errs if it transgresses them.
+Christianity is the agent which has produced so powerful an influence
+in making men obey the dictates of conscience and walk in the path of
+duty; and I read with thankfulness the conclusion of Mr. Amos, that
+Christianity has triumphed quite as much in moralizing secular politics
+as it has in the sphere of individual life.
+
+       *       *       *       *       *
+
+These are some of the principal laws of motion which I have observed at
+work in various States and nations. Inasmuch as political science
+embraces, in addition to the physical sciences, all those branches which
+are contained in ethics, economics, jurisprudence, sociology and others,
+the laws of each are generally applicable to the whole grand subject of
+which my lectures treat. Other general laws may be deduced, and have
+been enumerated in my previous lectures, from the social properties of
+curves and conics; and when our researches are complete we may hope to
+produce a code of laws for the guidance of our statesmen which maybe of
+immense use in determining the policies of the future. Already there is
+strong evidence that the affairs of this country are being conducted on
+sound scientific principles, rather than by any species of guess-work or
+haphazard contrivances. The use of history is recognised as extremely
+important in determining a future line of conduct; and statesmen are in
+the habit of endeavouring to find from their study of the past what is
+the logical sequence of events. Just as mathematicians endeavour to
+determine the law of a series of figures, and having found the law, can
+write down the next, and the next, _ad infinitum_; so scientific
+politicians may be able soon to establish the various laws of a series
+of events, and calculate their course of actions. That there is
+considerable progress in this direction is manifest by the value which
+they place upon statistics, and their continued use of this important
+information.
+
+There are a few great evils in our present system which are strongly
+opposed to any scientific methods in politics; and in the interests of
+the country as well as those of science they ought to be removed. One
+great evil is the want of political and scientific knowledge on the part
+of the electors, who are in the habit of choosing their representatives
+on personal grounds, or party considerations, rather than on sound
+principles of political science. All this is opposed to any idea of law.
+Owing to the ignorance of the electors they fall an easy prey to
+adventurers and unprincipled politicians, who make all kinds of specious
+promises, tempt them with all manner of baits, and make self-interest
+instead of the welfare of the State the principle of voting. Selfishness
+is the ruin of social life and intercourse, the destroyer of all
+happiness, peace, and mutual trust in family life or in society. It is
+the root of most of the faults, vices, and crimes in the individual; and
+who can tell the endless disasters which will befall the State, where
+selfishness is the chief motive-power of the electors and the elected? A
+selfish statesman, one who goes into Parliament to gain his own ends and
+forward his own personal interests, is a disgrace to society--
+
+   'Feeling himself, his own low self, the whole,
+    When he by sacred sympathy might make
+    The whole one self. Self, that no alien knows!
+    Self, far diffused as fancy's wing can travel!
+    Self, spreading still, oblivious of its own,
+    Yet all of all possessing!'
+
+I have said that the ignorance of the electorate makes them an easy prey
+to such men; and until they have learnt to detect the false from the
+true, until they become acquainted with the elements of political
+science, and have been taught that their own selfish interests are not
+the highest aims of social government, it is vain to hope for a
+reasonable method of regulating the affairs of the nation, based upon
+logical laws and scientific principles.
+
+And how is this work of educating the electors to be accomplished? Not,
+I maintain, by furious speeches and rhetorical displays; not by bribery,
+baits and banter; but by patient, never-ceasing labour, by lectures on
+history and science, by individual instruction, is the great work to be
+accomplished upon which the security and stability of the country
+depend.
+
+Then we may hope that the 'Reign of Law' in polemical science may be
+ushered in with the joyful acclamations of an enlightened and united
+people, and its benign influence extend from the throne of the monarch
+and the council-chamber of his ministers to the hearth of the cottager.
+Politicians will rule by law; policies be calculated by laws; people
+vote by law; and then methinks I see in my mind (to use the words of the
+blind old poet) a noble and puissant nation rousing herself like a
+strong man after sleep, and shaking her invincible locks; methinks I see
+her as an eagle, renewing her mighty youth, and kindling her undazzled
+eyes at the full mid-day beam; purging and unsealing her long-abused
+sight at the fountain itself of heavenly radiance; while the whole noise
+of timorous and flocking birds flutter about amazed at what she means.
+Such is the glorious vision of the 'Reign of Law.' Let it be the
+business of every Englishman and Englishwoman to arrange the framework
+of our social and political system, that law may have an uninterrupted
+sway; then shall we be a united, prosperous, and contented people, and
+the reign of lawless agitators, bribery-mongers, and counterfeit
+statesmen will have passed away into the oblivion and obscurity of a
+more suitable but less favoured region.
+
+
+
+
+PAPER VIII.
+
+ON THE PRINCIPLE OF POLEMICAL COHESION.
+
+
+In my previous lectures I have had occasion to mention the principle of
+cohesion; but it plays so vital a part in the constitution of States and
+their relations to each other that I consider it advisable to devote
+this lecture entirely to it.
+
+This is a large and comprehensive subject, and embraces such principles
+as the Centralization of States; the Co-operation of States; Monogamic
+Marriage; Unions; Free Trade, and many others equally important. We have
+already noticed that cohesion is a well-known property of matter; that
+its influence is not confined to the regions of physical sciences; and
+that it is the manifest duty of all governments to increase the force
+of cohesion.
+
+Various methods have been tried to accomplish this purpose. The
+principle of Feudalism was one of the earliest attempts to produce the
+cohesion of the nation; and, in an elementary condition of society, it
+was partly successful. The theories of 'Divine Right' and 'Social
+Contract' were other methods which have been adopted; and the unity of
+the Christian Church has been the great means of producing the cohesion
+of the State in olden times; and its aid may be again required for the
+same beneficent object in future complications and social disruptions.
+
+But it is always advantageous in scientific pursuits to go back to first
+principles; and we will adopt that method in our present investigations.
+The social unit is the family; the multiplication of families makes the
+tribe; the multiplication of tribes makes the State; and, therefore, we
+shall not be far wrong if we consider the family tie as the first
+principle of political cohesion. I am in agreement with several learned
+thinkers upon this subject when I say that marriage is a most important
+political factor; and as marriage cannot take place without women, it is
+evident that women play a very important part in promoting the cohesion
+of the State.
+
+This prominent position was duly assigned to women by one of our
+greatest political philosophers, M. Auguste Comte, who strongly opposed
+the fatal fallacy of ancient political systems, which greatly
+overestimated the powers of men, and depreciated those of women. If the
+superiority of bodily strength be the sole cause of greatness in
+political and intellectual pursuits, then, most noble lords of creation,
+we yield to you the palm--you are our masters in this respect. But if,
+on the other hand, it can be shown that physical strength is not a
+requisite for great achievements in these occupations; if the powers of
+endurance, elasticity, adaptability, nervous energy, and patience are
+quite as needful as mere animal strength; then we women are quite as
+capable, and indeed more capable than men, for achieving political
+greatness. In the 'good old days,' when the law of might was right, and
+the strongest arm was the most powerful machinery in the government of
+the country, women were compelled naturally to occupy a less prominent
+position in the conduct of the affairs of the nation; and for centuries
+they have been degraded by a dominating tradition, and supposed
+incapable of performing duties for which they were mentally well suited.
+But those militant days are past. Animal strength and brute force are no
+longer needed in the councils of the nation; and the time has arrived
+when women should cease to be oppressed by the disparaging, illogical
+deductions of former generations, and when their assistance ought to be
+invoked in the great work of promoting the nation's welfare.
+
+I have stated that marriage is an important political factor; and,
+therefore, women have always occupied a primary, though obscure, part in
+political affairs. The cohesion of the State has been produced by the
+secret influence of family life. But it may be asked, What kind of
+marriage is most conducive to national cohesion? This question has been
+carefully and conclusively answered by a learned scientific writer, who
+shows that polygamic marriage never exists in an advanced state, as
+instanced by the history of Judaism and Mohammedanism; that a strict
+form of monogamic marriage is essential to political greatness and true
+progress in civilization. The cohesion of the State is destroyed by
+polygamy, and by any system which relaxes the binding nature of the
+marriage tie. 'Domestic disorganization is a sure augury of political
+disruption.'
+
+Cohesion, the essential property of all rightly constituted nations, is
+often in danger of being lost when the State is geographically very
+large, or when local interests have greater power than the attractive
+force of the central government. To obviate this evil, the method of
+centralization has been adopted with satisfactory results, as in the
+case of the United States of America, and Germany.
+
+By this means the local authorities are brought into close relationship
+with the central head, and the centrifugal influences of independent
+interests and customs are counteracted by the force of central
+attraction. Centralization increases the importance of the whole body,
+and, like the pendulum of a clock, regulates the movements of the whole
+State. In some cases it tends to make the government despotic, when the
+local governments are entirely under the control of the central; and
+every enactment, and scheme, and plan checked and supervised by the
+chief officers of the State. Such was the system adopted in France by
+Napoleon III. But cohesion without the enforcement of a hard and rigid
+connection, a general supervision without severe tyrannical
+jurisdiction, are the best methods of securing the unity of composite
+States.
+
+But the force of cohesion is evidently at work in the nation apart from
+centralization. Men who have a community of interests unite together
+for the purposes of strength and mutual assistance. They combine for the
+sake of securing means of support in sickness, and form benefit
+societies, such as the Order of Oddfellows or Foresters. This force of
+cohesion has produced trade unions, and similar institutions which exist
+for the purpose of protecting a common interest, and giving expression
+to the concurrent opinions of the members. These have their legitimate
+use in every civilized State, in spite of some of the disadvantages
+which follow in their train. There are, of course, opposed interests in
+every community: _attractive_ forces, which produce trade unions,
+guilds, corporations, companies, and the like; and _repulsive_ forces,
+which result from the opposed interests of employers and employed,
+landlords and tenants, and similar pairs of different classes in the
+community. As time goes on, and the State advances with it, these forces
+will gain in strength; the cohesion of classes will become greater;
+association will grow as naturally as the bubbles form on the surface
+of our evening beverage. It is a law of nature, and therefore cannot be
+resisted. But the repulsive forces will be no less strong, and to
+calculate the resultant of these contending interests will be the
+problem for practical statesmen to solve.
+
+The force of cohesion is also evidently at work, not only in individual
+States, but also amongst the nations of Europe, and of the world. That
+is to say, there is an evident desire for co-operation on the part of
+those nations who have attained to the highest degree of civilization
+and internal cohesion. International law is based on the principle of
+cohesion, and every day it is gaining power and favour in the eyes of
+our leading statesmen. The doctrine of Free Trade, which, if universally
+adopted, would be of the greatest service to mankind, results from a
+desire for co-operation; and whatever evils may result from one-sided
+Free Trade in this country at the present time, there can be no doubt
+that ultimately the complete system will be adopted.
+
+Sad is the fate of a nation when the force of cohesion is weakened. The
+first revolution in France is a proof of this assertion; there was no
+cohesion, no common faith, or loyalty to the throne and Government; and
+indeed the Government, which was rotten to the core, was hardly likely
+to awake any feelings of loyalty and respect; and therefore the social
+disruption which followed was only a natural sequence of events, and was
+prophesied with the accuracy with which an astronomer can foretell an
+eclipse. But that is not all; when the cohesion of the State is
+destroyed, it takes a long time to restore the action of the force; and,
+as in the case of France, further disruption is sure to take place.
+
+In this lecture I have already enumerated some of the ways in which this
+force acts; there are doubtless others which will suggest themselves to
+you. But I contend that the prosperity of the State, and the peace of
+the world, depend upon cohesion. Let this be your work, most noble
+professors, to promote the action of this helpful and life-giving
+force. Promote, as far as in you lies, the sacred union of family life.
+Encourage the generous feelings of true loyalty and patriotism amongst
+the people of this realm of England; counsel our statesmen with regard
+to the primary necessity of national cohesion, and the advantages of
+international co-operation; and your work will be blessed; your names
+will rank with those heroes of the sword and of the pen who have raised
+our beloved country to her present pinnacle of greatness and prosperity;
+and your memory will live in the hearts of your grateful countrymen.
+
+
+[Editorial Note.]--We regret to state that the various MSS. in the
+sealed desk are nearly exhausted, and are therefore compelled to present
+the series of lectures on polemical studies in an incomplete form. But
+we had the good fortune to light upon a brief diary which discloses some
+interesting information with regard to the Author's life and
+occupations. We append a few extracts:
+
+
+
+
+Extracts from the Author's Diary.
+
+
+_June 3rd_.--Arnold called again to-day--the fifth time during the last
+fortnight! His attention is rather overpowering, and wastes much of my
+valuable time. He says he hates science--the heathen!--and wants me to
+lecture in classics. He affirms that mathematics are dry and hard--too
+hard for women, and tend to make them unsympathetic and critically
+severe. I am afraid I was rather severe with him. But really he is very
+trying, and always seems to talk like a Greek chorus in the most
+profound platitudes. Arnold is a classical tutor at Clare College. My
+old pupil is getting on famously. Poor fellow! he seems quite oppressed
+with his work. But he is making great progress, and sticks to his books
+like--a student of Girtham College!
+
+_June 4th_.--Lectured on the Scientific Basis of Blackstone's
+Commentaries; afterwards received pupils until 1 p.m. Really Blanch
+S---- is more tiresome than ever. It appears that she has taken up with
+a young undergraduate of King's, and there is no prospect of any
+improvement in her work unless this nonsense is terminated. How foolish
+some of my sex are, in spite of their improved opportunities! I blush
+for them! Arnold has sent me a copy of Robert Browning's 'Belaustion,'
+in order to make me like classics, and give up science. Misguided young
+man! He has written some tolerable verses on the fly-leaf; but I have no
+intention of playing Belaustion to his 'entranced youth.' These are his
+verses:
+
+   'My lady dear, if I may call you so,
+    For you are dearer than all else beside,
+    I know the love you bear to golden verse,
+    To golden thoughts enshrined in classic lore,
+    To all that's beautiful; so here I send
+    Some echoes of the songs of ancient days,
+    Attuned and chanted by an English bard,
+    Who fires one's old love for the rolling lines
+    Of youthful Hellas; may your cultured ear
+    Receive, and gladly welcome his sweet song.
+    And while we revel in the poet's dream,
+    And hear his actors speak, we'll play our parts.
+    You, sweet Belaustion on the temple-steps,
+    Taking your captors captive by your voice;
+    And I, the youth who, more entranced than all,
+    Was bound by fetters that he would not loose;
+    And so we'll play our part. What say you, dear?'
+
+_June 6th_.--Have just seen our new Professor of Physics, Amelia
+Cordial, who is an excellent woman, and well suited for the high office
+which she holds. She has told me of the foolish conduct of Lady Mary,
+who is evidently of opinion that the professorial mantle ought to have
+fallen on her shoulders. Really, this jealousy in the ranks of the
+learned is most disgraceful; and the bickerings which arise from
+disappointed ambition, the envyings and silly quarrels, are the weak
+places in our female collegiate system.
+
+Such good news! The wrangler list is just out, and my hard-working pupil
+is _bracketed twelfth!_ This is really delightful, and abundantly repays
+us for all our hard toil. But really I have not found working with him
+distasteful; he is such an excellent pupil, so painstaking and eager,
+that I have quite looked forward to his coming, and found him much more
+interesting than some of these foolish maidens. But I almost dread
+seeing him. He will be so elated and overpoweringly grateful, whereas I
+ought to be grateful to him for all his work for me; for I am sure he
+would never have gone in for the Tripos if I had not persuaded him.
+Well, I wonder why he does not come to tell me of his triumph.
+
+_June 7th_.--_It_ has come! and I half expected it. My eager pupil
+writes with all the energy and love of his noble nature to ask me to be
+his wife! He says _that_ is all he cares for, and only values his
+Honours as a step to a higher honour and dignity, that of gaining my
+love and being my husband. All this is very nice to read; but a terribly
+difficult problem is placed before me for solution. I do indeed love
+this dear, good fellow--no one could help doing so, I am sure; but do I
+not love science more? There is a stringent regulation in this
+University that no one shall occupy the position of professor who is
+bound by any domestic ties or cares. All married women are excluded. If
+I say 'Yes,' I must resign my high position, leave this beloved college,
+give no more lectures to entranced audiences. In the interests of
+science, ought I to refuse, and sacrifice my heart's affections for the
+cause of mathematics? But if I say 'No,' I must give up--_him_;
+sacrifice his happiness too, and blight his life. Was ever anyone so
+perplexed? Science, aid thine obedient servant! May I not determine this
+vital question by thine all-pervading light?...
+
+       *       *       *       *       *
+
+[Editorial Note.]--We had just arrived at this exciting moment in the
+life of the learned and accomplished lady whose writings form the
+subject of these pages--a moment when love and science were trembling in
+the balance--when a footstep was heard upon the stairs leading to our
+study, and ere we could secrete our MS. the door was opened, and a
+well-known voice exclaimed:
+
+'I do not know why you should have become so studious lately, Ernest,
+and why you should refuse to take me into your confidence. You spend
+hours and hours in this room all by yourself, writing away, and never
+say a word to me about the subject of your literary work. There was a
+time when things were different, and you were not so slow in availing
+yourself of my help, and asking my advice.'
+
+We murmured something about taking up the pen which had been laid aside
+by a far abler hand, and our deep gratitude for past assistance in our
+work, which could never be forgotten.
+
+'And do you think that I cannot help you now?' our visitor replied, in a
+very injured tone of voice. 'Is the old power dead, because it has not
+recently been used? Ernest, I think you very ungrateful not to confide
+in me. Come, tell me what you are writing.'
+
+A suggestion about the proverbial curiosity of women rose to our lips,
+but died away without utterance. In the meantime, her eyes wandered over
+our study-table strewed with papers, and lighted upon the well-worn
+desk.
+
+'Why, Ernest, where did you find this? My dear old desk, which has been
+lost ever so long! I do believe you have been ransacking its contents!
+Why did you not tell me that you had found it? What are you doing with
+my papers, sir?'
+
+The mischief was out! We tried to explain that the world ought not to be
+deprived of that which would benefit mankind; that the peace and
+prosperity of the country might be sacrificed if it were deprived of
+these discoveries of science, which were calculated to secure such
+beneficial results.
+
+At length we gained our point, and obtained the full sanction of the
+late Lady Professor of Girtham College to publish her papers. Thus her
+obedient pupil is enabled to repay his late instructress for all her
+kindness to him, and in some measure to compensate the scientific and
+political world for the loss of one of its most original investigators
+in the regions of polemical studies, which, not without a struggle, she
+resigned when she deigned to become his wife.
+
+
+THE END.
+
+
+
+
+_Elliot Stock, Paternoster Row, London._
+
+
+
+
+
+End of Project Gutenberg's The Romance of Mathematics, by P. Hampson
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+<pre>
+
+The Project Gutenberg EBook of The Romance of Mathematics, by P. Hampson
+
+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: The Romance of Mathematics
+       Being the Original Researches of a Lady Professor of Girtham
+       College in Polemical Science, with some Account of the Social
+       Properties of a Conic; Equations to Brain Waves; Social Forces;
+       and the Laws of Political Motion.
+
+Author: P. Hampson
+
+Release Date: August 29, 2008 [EBook #26481]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ROMANCE OF MATHEMATICS ***
+
+
+
+
+Produced by David Wilson and the Online Distributed
+Proofreading Team at https://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+</pre>
+
+
+
+
+<hr class="pg" />
+
+
+
+<div class="frontmatter">
+<h3 class="pgbrk noscr"><a name="png.001" id="png.001"></a><span class="ns">[</span><span
+ class="pgmark">i</span><span class="ns">]<br
+ /></span><small>THE</small><br
+ />ROMANCE OF MATHEMATICS.</h3>
+
+<h1><a name="png.003" id="png.003"></a><span class="ns">[</span><span
+ class="pgmark">iii</span><span class="ns">]<br
+ /></span><small>THE</small><br
+ />Romance of Mathematics:</h1>
+
+<h2><small>BEING</small><br
+ />THE ORIGINAL RESEARCHES<br
+ /><small>OF</small><br
+ /><img src="images/ladyprof.png" width="500" height="43"
+ alt="A Lady Professor of Girtham College" title="" /><br
+ /><small>IN</small></h2>
+
+<h4><i>Polemical Science, with some Account of the Social<br
+ />Properties of a Conic; Equations to Brain<br
+ />Waves; Social Forces; and the Laws<br
+ />of Political Motion.</i></h4>
+
+<h3><small>BY</small><br
+ /><big>P. HAMPSON, M.A.,</big><br
+ /><small>ORIEL COLLEGE, OXFORD.</small></h3>
+
+<h4>LONDON:<br
+ />ELLIOT STOCK, 62, PATERNOSTER ROW.<br
+ />1886.</h4>
+
+</div>
+
+
+
+
+<div class="main">
+<h2><a name="png.005" id="png.005"></a><span class="ns">[</span><span
+ class="pgmark">v</span><span class="ns">]<br
+ /></span>INTRODUCTION.</h2>
+
+
+<p class="noindent"><span class="smc">The</span> lectures, essays, and other matter
+contained in these pages have been discovered
+recently in a well-worn desk which
+was formerly the property of a Lady Professor
+of Girtham College; and as they
+contain some original thoughts and investigations,
+they have been considered
+worthy of publication.</p>
+
+<p>How they came into the possession of
+the present writer it is not his intention to
+disclose; but inasmuch as they seemed to
+his unscientific mind to contain some important
+discoveries which might be useful to
+the world, he determined to investigate
+thoroughly the contents of the mysterious
+desk, and make the public acquainted with
+its profound treasures. He found some
+documents which did not refer exactly to
+the subject of &lsquo;Polemical Mathematics;&rsquo;
+but knowing the truth of the Hindoo
+<a name="png.006" id="png.006"></a><span class="ns">[</span><span
+ class="pgmark">vi</span><span class="ns">]
+ </span>proverb, &lsquo;The words of the wise are
+precious, and never to be disregarded,&rsquo;
+and feeling sure that this Lady Professor
+of Girtham College was entitled to that
+appellation, he ventured to include them
+in this volume, and felt confident that in
+so doing he would be carrying out the
+intention of the Authoress, had she expressed
+any wishes on the subject. In
+fact, as he valued the interests of the State
+and his own peace of mind, he dared not
+withhold any particle of that which he
+conceived would confer a lasting benefit
+on mankind.</p>
+
+<p>Internal evidence seems to show that
+the earlier portion of the MS. was written
+during the period when the authoress was
+still <i>in statu pupillari</i>; but her learning
+was soon recognised by the Collegiate
+Authorities, and she was speedily elected
+to a Professorship. Her lectures were
+principally devoted to the abstruse subject
+of Scientific Politics, and are worthy of the
+attention of all those whose high duty it is
+to regulate the affairs of the State.</p>
+
+<p class="pgbrk">The Editor has been able to gather from
+<a name="png.007" id="png.007"></a><span class="ns">[</span><span
+ class="pgmark">vii</span><span class="ns">]
+ </span>the varied contents of the desk some
+details of the Author&#8217;s life, which increase
+the interest which her words excite; and
+he ventures to hope that the public will
+appreciate the wisdom which created such
+a profound impression upon those whose
+high privilege it was to hear the lectures
+for the first time in the Hall of Girtham
+College.</p>
+
+
+
+
+
+
+<h2><a name="png.009" id="png.009"></a><span class="ns">[</span><span
+ class="pgmark">ix</span><span class="ns">]<br
+ /></span>CONTENTS.</h2>
+
+<hr class="tb" />
+
+<table class="toc" summary="Table of Contents">
+<tr><td><small>PAPER</small></td><td></td><td class="pg"><small>PAGE</small></td></tr>
+
+<tr><td class="cn">I.</td><td class="chap">Some Remarks on Female Education:</td></tr>
+
+<tr><td></td><td class="details">
+Cambridge Man&#8217;s Powers of Application.&mdash;Torturing
+Ingenuity of
+Examiners.&mdash;Slaying an Enemy.&mdash;&lsquo;Concentration.&rsquo;&mdash;&lsquo;Tangential
+Action.&rsquo;&mdash;&lsquo;Gravity&rsquo;</td>
+<td class="pg"><a href="#png.013">1</a></td></tr>
+
+<tr><td class="cn">II.</td><td class="chap">Lecture on the Theory of
+Brain Waves and the Transmigration
+and Potentiality
+of Mental Forces</td><td class="pg"><a href="#png.027">15</a></td></tr>
+
+<tr><td class="cn">III.</td><td class="chap">The Social Properties of a Conic
+Section, and the Theory of
+Polemical Mathematics:</td></tr>
+
+<tr><td></td><td class="details">
+&lsquo;Circle.&rsquo;&mdash;&lsquo;Parabola.&rsquo;&mdash;&lsquo;Ellipse.&rsquo;
+&lsquo;Eccentricity of Curves&rsquo;</td><td class="pg"><a href="#png.037">25</a></td></tr>
+
+<tr><td class="cn"><a name="png.010" id="png.010"></a><span class="ns">[</span><span
+ class="pgmark">x</span><span class="ns">]<br
+ /></span>IV.</td><td class="chap">The Social Properties of a Conic
+Section (<i>continued</i>):</td></tr>
+
+<tr><td></td><td class="details">
+&lsquo;Ellipse.&rsquo;&mdash;Most favoured State.&mdash;Alarming
+Result of Suppression of
+House of Lords.&mdash;Analogies of
+Nature.&mdash;Directrix.&mdash;Contact of
+Curves and States.&mdash;&lsquo;Hyperbola.&rsquo;&mdash;Problems.&mdash;Radical
+Axis and Patriotism.&mdash;Extension
+of Franchise to
+Women.&mdash;<span class="smc">Correspondence </span></td><td class="pg"><a href="#png.051">39</a></td></tr>
+
+<tr><td class="cn">V.</td><td class="chap">Social Forces, with some Account
+of Polemical Kinematics:</td></tr>
+
+<tr><td></td><td class="details">
+The Use of Imagination in Scientific
+Discovery.&mdash;Kinetic and Potential
+Energy.&mdash;Social Statics and
+Dynamics.&mdash;Attractive Forces.&mdash;Cohesion.&mdash;Formation
+of States.&mdash;Inertia.&mdash;Dr.
+Tyndall on Social
+Forces</td><td class="pg"><a href="#png.083">71</a></td></tr>
+
+<tr><td class="cn">VI.</td><td class="chap">Social Forces (<i>continued</i>): Polemical
+Statics and Dynamics:</td></tr>
+
+<tr><td></td><td class="details">
+&lsquo;Personal Equation.&rsquo;&mdash;Public
+Opinion, how calculated.&mdash;Impulsive
+Forces.&mdash;Friction.&mdash;Progress</td><td class="pg"><a href="#png.101">89</a></td></tr>
+
+<tr><td class="cn"><a name="png.011" id="png.011"></a><span class="ns">[</span><span
+ class="pgmark">xi</span><span class="ns">]<br
+ /></span>VII.</td><td class="chap">Laws of Political Motion:</td></tr>
+
+<tr><td></td><td class="details">
+M. Auguste Comte on Political
+Science.&mdash;First Law of Motion.&mdash;The
+Biology of Politics.&mdash;Stages of
+Growth and Decay of States.&mdash;Doctrine
+of Nationality.&mdash;Doctrine of
+Independence.&mdash;Law of Morality.&mdash;Ignorance
+of Electors and Selfishness
+of Statesmen opposed to Action of
+Law.&mdash;Final &lsquo;Reign of Law&rsquo;</td><td class="pg"><a href="#png.113">101</a></td></tr>
+
+<tr><td class="cn">VIII.</td><td class="chap">The Principle of Polemical Cohesion:</td></tr>
+
+<tr><td></td><td class="details">
+Centralization.&mdash;Co-operation of
+States.&mdash;Marriage.&mdash;Trade Unions.&mdash;International
+Law</td><td class="pg"><a href="#png.127">115</a></td></tr>
+
+<tr><td></td><td class="chap">Extracts from the Diary of the
+Lady Professor</td><td class="pg"><a href="#png.137">125</a></td></tr>
+
+<tr><td></td><td class="chap">Conclusion</td><td class="pg"><a href="#png.141">129</a></td></tr>
+
+</table>
+
+
+
+
+
+<h2><a name="png.013" id="png.013"></a><span class="ns">[</span><span
+ class="pgmark">1</span><span class="ns">]<br
+ /></span>PAPER I.</h2>
+
+<h3>SOME REMARKS OF A GIRTHAM GIRL ON
+FEMALE EDUCATION.</h3>
+
+
+<p><small>[<i>This essay upon Female Education was evidently
+written when the future Professor of Girtham
+College was still in the lowlier condition of studentship,
+before she attained that eminence for which
+her talents so justly entitled her. Its unfinished
+condition tends to show that it was probably
+evolved during moments of relaxation from severer
+studies, without any idea of subsequent publication.</i>]</small></p>
+
+<p class="noindent above2"><span class="smc">Oh</span>, why should I be doomed to the
+degradation of bearing such a foolish
+appellation! A Girtham Girl! I suppose
+we have to thank that fiend of invention
+who is responsible for most of the titular
+foibles and follies of mankind&mdash;artful Alliteration.
+The two <em>G</em>&#8217;s, people imagine,
+run so well together; and it is wonderful
+that they do not append some other delectable
+title, such as &lsquo;The Gushing Girl of
+Girtham,&rsquo; or &lsquo;The Glaring Girl of Glittering
+<a name="png.014" id="png.014"></a><span class="ns">[</span><span
+ class="pgmark">2</span><span class="ns">]
+ </span>Girtham.&rsquo; O Alliteration! Alliteration!
+what crimes have been wrought in thy
+name! Little dost thou think of the mischief
+thou hast done, flooding the world
+with meaningless titles and absurd phrases.
+How canst thou talk of &lsquo;Lyrics of
+Loneliness,&rsquo; &lsquo;Soliloquies of Song,&rsquo; &lsquo;Pearls
+of the Peerage&rsquo;? Why dost thou stay
+thine hand? We long for thee to enrich
+the world with &lsquo;Dreams of a Dotard,&rsquo;
+the &lsquo;Dog Doctor&#8217;s Daughters,&rsquo; and other
+kindred works. Exercise thine art on these
+works of transcendent merit, but cease to
+style thy humble, but rebellious, servant a
+Girtham Girl!</p>
+
+<p>But what&#8217;s in a name? Let the world&#8217;s
+tongue wag. I am a student, a hard-working,
+book-devouring, never-wearied student,
+who burns her midnight oil, and drinks the
+strong bohea, to keep her awake during
+the long hours of toil, like any Oxford or
+Cambridge undergraduate. I often wonder
+whether these mighty warriors in the lists&mdash;the
+class lists, I mean&mdash;really work half
+so hard as we poor unfortunate &lsquo;Girls of
+Girtham.&rsquo; Now that I am writing in strict
+<a name="png.015" id="png.015"></a><span class="ns">[</span><span
+ class="pgmark">3</span><span class="ns">]
+ </span>confidence, so that not even the walls can
+hear the scratchings of my pen, or understand
+the meaning of all this scribbling, I
+beg to state that I have my serious doubts
+upon the subject; and when last I attended
+a soirée of the Anthropological
+Society, sounds issued forth from the
+windows of the snug college rooms, which
+could not be taken as evidences of profound
+and undisturbed study.</p>
+
+<p>Sometimes I glance at the examination
+papers set for these hard-working students,
+in order that they may attain the glorious
+degree of B.A., and astonish their sisters,
+cousins, and aunts by the display of these
+magic letters and all-resplendent hood.
+And again I say in strict confidence that
+if this same glorious hood does not adorn
+the back of each individual son of Alma
+Mater, he ought to be ashamed of himself,
+and not to fail to assume a certain
+less dignified, but expressive, three-lettered
+qualification. But before those Tripos
+Papers I bow my head in humble adoration.
+They sometimes take my breath
+away even to read the terrible excruciating
+<a name="png.016" id="png.016"></a><span class="ns">[</span><span
+ class="pgmark">4</span><span class="ns">]
+ </span>things, which seem to turn one&#8217;s brain
+round and round, and contort the muscles
+of one&#8217;s face, and stop the pulsation of
+one&#8217;s heart, when one tries to grasp the
+horrid things.</p>
+
+<p>Here is a fair example of the ingenuity
+of the hard-hearted examiners, who resemble
+the inquisitors presiding over the
+tortures of the rack, and giving the hateful
+machine just one turn more by way of
+bestowing a parting benediction on their
+miserable victims:</p>
+
+<p>&lsquo;A uniform rod&rsquo; (it is a marvellous act
+of mercy that the examiner invented it
+<em>uniform</em>; it is strange that its thickness
+did not vary in some complicated manner,
+and become a veritable birch-rod!) &lsquo;of
+length 2<i>c</i>, rests in stable equilibrium&rsquo;
+(stable! another act of leniency!), &lsquo;with
+its lower end at the vertex of a cycloid
+whose plane is vertical&rsquo; (why not incline
+it at an angle of 30°?) &lsquo;and vertex downwards,
+and passes through a small, smooth,
+fixed ring situated in the axis at a distance
+<i>b</i> from the vertex. Show that if the equilibrium
+be slightly disturbed, the rod will
+<a name="png.017" id="png.017"></a><span class="ns">[</span><span
+ class="pgmark">5</span><span class="ns">]
+ </span>perform small oscillations with its lower
+end on the arc of the cycloid in the time</p>
+
+<table class="math" summary="4[pi]sqrt(a{c^2+3(b-c)^2}/3g(b^2-4ac))">
+<tr><td rowspan="2">4&pi;</td><td rowspan="2"><big class="enorm">&radic;</big></td>
+<td class="dfrac"><i>a</i>{<i>c</i>&sup2; + 3(<i>b - c</i>)&sup2;}</td><td rowspan="2">,</td></tr>
+<tr><td class="dfrac">3<i>g</i>(<i>b</i>&sup2; - 4<i>ac</i>)</td></tr>
+</table>
+
+<p class="noindent">where 2<i>a</i> is the length
+of the axis of the cycloid.&rsquo;</p>
+
+<p>A sweet pretty problem, truly! And
+there are hundreds of the same kind&mdash;birch-rods
+for every back! How the
+examiner must have rejoiced when he
+invented this diabolical rod, with its equilibrium,
+its oscillations, its cycloid, and
+other tormenting accessories. And yet, I
+suppose, before my days of studentship
+are over, I shall be called upon to attack
+some such impregnable fortresses of mathematics,
+when I hope to be declared equal
+to some twentieth wrangler, if I escape
+the misfortune of sharing a portion of the
+&lsquo;wooden spoon.&rsquo;</p>
+
+<p>Ah, you male sycophants! You would
+prevent us from competing with you; you
+would separate yourselves on your island
+of knowledge, and sink the punt which
+would bear us over to your privileged
+shore. Of all the twaddle&mdash;forgive me,
+male sycophants!&mdash;that the world has ever
+<a name="png.018" id="png.018"></a><span class="ns">[</span><span
+ class="pgmark">6</span><span class="ns">]
+ </span>heard, I think the greatest is that which
+you have talked about female education.
+And the best of it is, you are so anxious
+about our welfare; you are so afraid that
+we should injure our health by overmuch
+mental exertion; you profess to think that
+our brains are not calculated to stand the
+strain of continued mental exercise; you
+think that competition is not good for the
+female mind; that we are too competitive
+by nature&mdash;too ambitious! Yes, we are
+so ambitious that we would enter the
+lists with those who are asked in Public
+Examinations to find the simple interest
+on £1,000 for 5&nbsp;years at 6¼ per cent.;
+so ambitious that we would compete with
+those who are requested to disclose the
+first aorist middle of <i title="Greek: tuptô">&tau;&upsilon;&pi;&tau;&omega;</i>. Oh, think of
+the mental strain involved in such questions!
+How it must ruin your health to
+find out how many times a wheel of radius
+6&nbsp;feet will turn round between York and
+London, a distance of 200 miles! It is
+quite wonderful how your brains, my dear
+male sycophants, can stand such fearful demands
+upon your intelligence and industry!</p>
+
+<p><a name="png.019" id="png.019"></a><span class="ns">[</span><span
+ class="pgmark">7</span><span class="ns">]<br
+ /></span>But you are so kind to us, so afraid of
+our health! Really, we are much obliged
+to you. If you married one of us, or
+became our guardian, or left us a legacy,
+we should then recognise your interest in
+us, and be very grateful to you for your
+good advice. But as matters stand, we
+are quite capable of taking care of ourselves.
+We will promise not to work too
+hard, if you will promise not to weary us
+with your paternal jurisdiction.</p>
+
+<p>But, male sycophants, I want a word
+with you. Why do you object to our
+taking degrees, or going in for examinations
+in order to qualify ourselves for our
+duties in life? You need not speak out
+loud if you would rather not. Are you
+not just a little afraid that we might eclipse
+you? And it is not pleasant to be beaten
+by a woman, is it? And then you profess
+to think that we ought to be all housewives
+and cooks, and knitters of stockings,
+and sewers-on of our husbands&#8217; buttons;
+but what if we have no husbands, no
+buttons to sew? And is it not a little
+selfish, my dear male sycophant, to wish
+<a name="png.020" id="png.020"></a><span class="ns">[</span><span
+ class="pgmark">8</span><span class="ns">]
+ </span>to keep us all to yourself? to attend upon
+the wants of the lords of creation, who
+often distinguish themselves so much in
+the domain of science?</p>
+
+<p>Now, look me straight in the face (no
+shirking, sir!). Is it not jealousy&mdash;green-eyed,
+false-tongued jealousy&mdash;which saps
+your generous instincts, and makes you
+talk rubbish and nonsense about strains,
+and brains, and ambition, and the like?
+And if that is not hypocritical, I do not
+know what is.</p>
+
+<p>Well, good-day to you, male sycophant!
+I really have not time to indulge myself in
+scolding you any more. You are a good
+creature, no doubt; and when you have
+shown us what you can do, and can estimate
+the capacity of the female brain, and
+take a common-sense view of things, we
+will recognise your privilege to speak;
+and when I am the presiding genius of
+Girtham College, I will grant you the use
+of our hall for the purpose of lecturing to us
+on &lsquo;Women&#8217;s Rights,&rsquo; or, as you may prefer
+to entitle your discourse, &lsquo;Men&#8217;s Wrongs.&rsquo;</p>
+
+<p class="tbstars">* * * * *</p>
+
+<p><a name="png.021" id="png.021"></a><span class="ns">[</span><span
+ class="pgmark">9</span><span class="ns">]<br
+ /></span>Oh, this is shameful! I really am very
+sorry. Here have I been wasting a good
+half-hour in dreaming, and slaying an
+imaginary enemy with envenomed words
+and frequent dabs of ink. If I cannot
+concentrate my mind more on these
+mathematical researches, I fear a dreadful
+&lsquo;plough&rsquo; will harrow my feelings at the end
+of my sojourn in these halls of learning.</p>
+
+<p>Concentration! How many of our
+words and ideas and thoughts are derived
+from that primal fount of all arts and
+sciences&mdash;mathematics! Here is one
+which owes its origin to the mathematically
+trained mind of some early philological
+professor, who had learnt to apply
+his scientific knowledge to the enrichment
+of his native tongue. He quoted to
+himself the words of the Roman poet:</p>
+
+<div class="stanza">
+<div class="indent6">&lsquo;Ego cur, acquirere pauca</div>
+<div>Si possum, invideor, cum lingua Catonis et Ennî</div>
+<div>Sermonem patrium ditaverit, et nova rerum</div>
+<div>Nomina protulerit? Licuit, semperque licebit.&rsquo;</div>
+</div>
+
+<p>His mind conceived endless figures of
+circles and ellipses scattered promiscuously
+over the page, defying the attempts of the
+<a name="png.022" id="png.022"></a><span class="ns">[</span><span
+ class="pgmark">10</span><span class="ns">]
+ </span>student to reduce them to order. What
+must he do before he can apply his
+formulæ and equations, determine their
+areas, or describe their eccentric motion?
+He must reduce them to a common
+centre, and then he can proceed to
+calculate the abstruse problems in connection
+with the figures described. They
+may be the complex motions of double-star
+orbits, or the results of the impact of
+various projectiles on the tranquil surface
+of a pool. It matters not&mdash;the principle
+is the same; he must concentrate, and
+reduce to a common centre.</p>
+
+<p>This is the great defect of those who
+have no accurate mathematical knowledge;
+they cannot concentrate their minds with
+the same degree of intensity upon the
+work which lies before them. Their
+thoughts fly off at a tangent, as mine do
+very often; but then I have not been
+classed yet in the Tripos; and, O male
+poetical sycophant, you may be right after
+all when you say:</p>
+
+<div class="stanza">
+<div>&lsquo;O woman! in our hours of ease</div>
+<div>Uncertain, coy and hard to please,</div>
+<div>As variable as the noon-day shade.&rsquo;</div>
+</div>
+
+<p class="noindent"><a name="png.023" id="png.023"></a><span class="ns">[</span><span
+ class="pgmark">11</span><span class="ns">]<br
+ /></span>Yes, as variable as the most variable
+quantities <i>x</i>, <i>y</i>, <i>z</i>. I, a student of Girtham
+College, blush to own that my thoughts
+very often fly off at a tangent.</p>
+
+<p>&lsquo;Fly off at a tangent!&rsquo; All hail to
+thee, most noble mathematical phrase!
+Here is another fine mathematical expression,
+plainly exemplifying the action
+of centrifugal force. The faster the
+wheel turns, the greater is the velocity of
+the discarded particles which fly off along
+the line, perpendicular to the radius of
+the circle. The world travels very fast
+now; the increased velocity of the transit
+of earthly bodies, the rate at which they
+live, the multiplicity of engagements,
+etc., have made the social world revolve
+so fast that the speed would have startled
+the torpid life of the last century. And
+what is the result? Men&#8217;s thoughts fly off
+at a tangent; they are unable to concentrate
+their minds on any given subject;
+they are content with hasty generalisms,
+with short magazine articles on important
+subjects, which really require large volumes
+and patient study to elucidate them fully.</p>
+
+<p><a name="png.024" id="png.024"></a><span class="ns">[</span><span
+ class="pgmark">12</span><span class="ns">]<br
+ /></span>What we want to do is to increase the
+attractive force, in order to prevent this
+tangential motion&mdash;to increase the <em>force of
+gravity</em>.</p>
+
+<p>&lsquo;Well,&rsquo; says the young lady who loves
+to revel in the &lsquo;Ghastly Secret of the
+Moated Dungeon,&rsquo; or the &lsquo;Mysteries of
+Footlight Fancy,&rsquo; &lsquo;you are <em>grave</em> enough.
+Pray don&#8217;t increase your gravity!&rsquo;</p>
+
+<p>Thank you, gentle critic. I will, in
+turn, ask you one favour. Leave for once
+the &lsquo;Mysteries of Footlight Fancy;&rsquo; seek
+to know no more &lsquo;ghastly secrets,&rsquo; and
+increase <em>your gravity</em>&mdash;your mental
+weight; and hence your attraction in the
+eyes of all who are worth attracting will be
+marvellously increased, by understanding
+a little about Newton&#8217;s law of universal
+gravitation, and don&#8217;t fly off at a tangent.</p>
+
+<hr class="tb" />
+
+<p>At the end of this portion of the MS.
+the editor of these papers discovered a
+photograph which, from subsequent inquiry,
+proved to be that of the accomplished
+authoress of the above reflections.
+<a name="png.025" id="png.025"></a><span class="ns">[</span><span
+ class="pgmark">13</span><span class="ns">]
+ </span>The face is one of considerable beauty,
+with eyes as clear, steadfast, and open as
+the day. There is a degree of firmness
+about the mouth, but it is a sweet and
+pretty one notwithstanding; and a smile,
+half scornful, half playful, can be detected
+lurking about the corners of the lips,
+which do not seem altogether fitted for
+pronouncing hard mathematical terms and
+abstruse scientific problems. This photograph
+might have been the identical one
+which nearly brought an enamoured youth
+into grave difficulties by its secretion in
+the folds of his blotting-paper during
+examination. The said enamoured youth
+had evidently placed it there for the sake
+of its inspiring qualities; and it was said
+that all his hopes of gaining the hand of
+the fair original depended upon his passing
+that same examination. But the
+wakeful eye of a stern examiner had
+watched him as he turned again and
+again to consult the sweet face which
+beamed from beneath his blotting-paper;
+and he narrowly escaped expulsion from
+the Senate-house on the charge of
+<a name="png.026" id="png.026"></a><span class="ns">[</span><span
+ class="pgmark">14</span><span class="ns">]
+ </span>&lsquo;cribbing.&rsquo; Certainly he took a mean advantage
+of his fellow-sufferers, if this were the
+identical photograph, for it portrays a
+most inspiring face. Forgive us, lenient
+reader; one moment! There&mdash;thank you&mdash;we
+have done. And now we will proceed
+to disclose the researches and original
+problems which the MS. contains.</p>
+
+<p class="pgbrk">Evidently the collegiate authorities were
+not slow in recognising the talents of the
+assiduous student, and elected her without
+much delay to a Professorship of
+Girtham. In this capacity the learned
+lady delivered several lectures, of which
+the second MS. contains the first of the
+<ins class="TN" title="Transcriber's note:
+  original reads 'eries'">series</ins>.</p>
+
+
+
+
+<h2><a name="png.027" id="png.027"></a><span class="ns">[</span><span
+ class="pgmark">15</span><span class="ns">]<br
+ /></span>PAPER II.</h2>
+
+<h3>LECTURE ON THE THEORY OF BRAIN WAVES
+AND THE TRANSMIGRATION AND POTENTIALITY
+OF MENTAL FORCES.</h3>
+
+
+<p class="noindent"><span class="smc">Professors and Students of the
+University of Girtham, my Lords,
+Ladies, and Gentlemen</span>,&mdash;I have the
+honour to bring before you this evening
+some original conceptions and discoveries
+which have been formulated by me during
+my researches in the boundless field of
+mathematical knowledge; and though you
+may be inclined at first to pronounce
+them as somewhat hastily conceived hypotheses,
+I hope to be able to demonstrate
+the actual truth of the propositions which
+I shall now endeavour to enunciate. It
+is with some feelings of diffidence that I
+stand before so august an assembly as the
+present; and if I were not actually
+<a name="png.028" id="png.028"></a><span class="ns">[</span><span
+ class="pgmark">16</span><span class="ns">]
+ </span>convinced of the accuracy of my calculations,
+I should never have presumed to appear
+before you in the character of a lecturer.
+But &lsquo;<i>Magna est veritas, et prævalebit</i>.&rsquo;
+I cast aside maiden timidity; I
+clothe myself in the professorial robe which
+you have bestowed upon me, and sacrifice
+my own feelings on the altar of Truth.</p>
+
+<p>I have been engaged, as you are doubtless
+aware, for some years in the pursuit
+of mathematical research, exploring the
+mines of science, which have of late been
+worked very persistently, but often, like
+the black diamond mines, at a loss. Concurrently
+with these researches, I have
+speculated on the great social problems
+which perplex the minds of men, both
+individually and collectively. And I have
+come to the conclusion that the same
+laws hold good in both spheres of work;
+that methods of mathematical procedure
+are applicable to the grand social problems
+of the day and to the regulation
+of the mutual relations which exist
+between man and man. Take, for
+example, the Force of public opinion. Of
+<a name="png.029" id="png.029"></a><span class="ns">[</span><span
+ class="pgmark">17</span><span class="ns">]
+ </span>what is it composed? It is the Resultant
+of all the forces which act upon that
+which is generally designated the &lsquo;Social
+System.&rsquo; Public opinion is a compromise
+between the many elements which make
+up human society; and compromise is a
+purely mechanical affair, based on the
+principle of the Parallelogram of Forces.
+Sometimes disturbing forces exert their
+influence upon the action of Public
+Opinion, causing the system to swerve
+from its original course, and precipitating
+society into a course of conduct inconsistent
+with its former behaviour; and it
+is the duty of the Governing Body to
+eliminate as far as possible such disturbing
+forces, in order that society may
+pursue the even tenor of its way.</p>
+
+<p>Professors, we have one great problem
+to solve; and all questions social, political,
+scientific, or otherwise, are only
+fragments of that great problem. All
+truths are but different aspects of different
+applications of one and the same truth;
+and although they may appear opposed,
+they are not really so; and resemble
+<a name="png.030" id="png.030"></a><span class="ns">[</span><span
+ class="pgmark">18</span><span class="ns">]
+ </span>lines which run in various directions, but
+lovingly meet in one centre.</p>
+
+<p>Now, let us take for our consideration
+the secret influence which men exert upon
+each other, apart from that produced by
+the power of speech (although that would
+come under the same general law). As
+mathematicians, you are aware that the
+undulatory theory of light and heat and
+sound are now accepted by scientific men
+as the only sure basis of accurate calculation.
+We know that the rays of light
+travel in waves, and the equation representing
+the waves is</p>
+
+<table class="math" summary="y = a/r sin(2[pi]/[lambda]) (vt-r)">
+<tr><td rowspan="2"><i>y</i> = </td><td><i>a</i></td><td rowspan="2"> sin </td>
+<td>2&pi;</td><td rowspan="2"> (<i>vt - r</i>),</td></tr>
+<tr><td class="dfrac"><i>r</i></td><td class="dfrac">&lambda;</td></tr>
+</table>
+
+<p class="noindent">where <i>y</i> is the disturbance of the ether,
+<i>a</i> the initial amplitude, <i>r</i> the distance
+from the starting-point, &lambda; the wave-length,
+and <i>v</i> the velocity of light. Sound and
+heat likewise have much the same form
+of equation. Now, I maintain that the
+waves of thought are governed by the
+same laws, and can be determined by
+an equation of the same form. You are
+<a name="png.031" id="png.031"></a><span class="ns">[</span><span
+ class="pgmark">19</span><span class="ns">]
+ </span>aware that in all these equations a certain
+quantity denoted by &lambda; appears, and varies
+for the different media through which the
+sound, or light, or heat passes, and which
+must be determined by experiment Now,
+in my equation for brain waves, the same
+quantity &lambda; appears which must be determined
+by the same method&mdash;by <em>experiment</em>.
+But how is this to be done? After
+mature deliberation and much careful
+thought, I have discovered the method for
+finding &lambda;. This method is <em>mesmerism</em>.
+We find the ratio of brain to brain&mdash;the
+relative strength which one bears to
+another; and then by an application of
+our formula we can actually determine the
+wave of thought, and read the minds of
+our fellow-creatures. An unbounded field
+for reflection and speculation is here suggested.
+Like all great discoveries, the
+elements of the problem have unconsciously
+been utilized by many who are
+unable to account for their method of
+procedure. For example, thought-readers,
+mesmerists, and the like, have unconsciously
+been working on this principle,
+<a name="png.032" id="png.032"></a><span class="ns">[</span><span
+ class="pgmark">20</span><span class="ns">]
+ </span>although lack of mathematical training
+has prevented them from fully mastering
+the details of the problem. Hence in
+popular minds a kind of mystery has
+hung about the actions of such people,
+and excited the curiosity of mankind.</p>
+
+<p>The development of this theory of brain
+waves may be of great practical utility to
+the world. It shows that great care ought
+to be exercised in the domain of thought,
+as well as that of speech. For example:
+A man has made a startling discovery,
+from which he expects to receive considerable
+worldly advantage. He would be
+careful not to disclose his discovery in
+speech to his acquaintances until his plans
+are sufficiently matured, lest they should
+impart it to the world, patent his device,
+and reap the reward. But while he is
+endeavouring to talk carelessly about it,
+the wave of thought may be travelling
+from brain to brain, suggesting the existence
+of the discovery; and if the conditions
+are favourable, and &lambda; sufficiently
+small, it is possible that the idea itself
+may be conveyed. Of course the more
+<a name="png.033" id="png.033"></a><span class="ns">[</span><span
+ class="pgmark">21</span><span class="ns">]
+ </span>complicated the discovery, the less likely
+would the wave convey the conception.
+Or suppose that one of the learned professorial
+body of our sister university
+should conceive an attachment for a lady-student
+of Girtham College (of course a
+very improbable supposition!), and the
+infatuated <i>savant</i> became somewhat jealous
+of another learned lecturer of the same
+college (another improbability!), the fact
+of his jealousy would be imparted to the
+latter by a wave of thought, and might
+cause considerable confusion in the serene
+course of love or science. The fact of
+the existence of the wave is indisputable.
+What do all the stories of impressions and
+double-sight teach us? How could the
+intelligence of the death of Professor
+Steele have been conveyed to his friend
+and fellow-student, Professor Tait&mdash;the
+one at Cambridge, the other at Edinburgh&mdash;were
+it not for the existence of some
+wave, which, like that of electricity, wings
+its rapid flight unobserved by human eyes?
+Are all the records of the Psychical Society
+only myths and legends bred of
+<a name="png.034" id="png.034"></a><span class="ns">[</span><span
+ class="pgmark">22</span><span class="ns">]
+ </span>superstitious fancy? It were hard to suppose
+so.</p>
+
+<p>But if, gentlemen, and ladies especially,
+you wish to keep your secret discoveries
+to yourselves, watch over your thoughts as
+well as your words; for my researches
+prove, and the universal experience of
+mankind corroborates the fact, that some
+portion of your inmost thoughts and secret
+desires are understood by your neighbours
+(especially when &lambda; is small!); that they
+travel along the waves which I have attempted
+to indicate; and if you would
+desire to extend your influence in the
+world, probe the secret instincts of mankind,
+and prevent yourself from being
+deceived and wronged&mdash;study the art and
+science of Brain Waves.</p>
+
+<hr class="tb" />
+
+<p>The following verses of rather doubtful
+merit were found in connection with the
+previous MS. They were evidently written
+by a different hand; but inasmuch as they
+were deemed worthy of preservation by
+<a name="png.035" id="png.035"></a><span class="ns">[</span><span
+ class="pgmark">23</span><span class="ns">]
+ </span>the learned owner of the sealed desk, we
+venture to publish them. They are closely
+connected with the previous lecture, and
+were evidently composed by an admirer
+of the fair lecturer who did not share her
+love for scientific research.</p>
+
+<div class="stanza">
+<div>Wavelet,<sup><a href="#fn.1" name="fna.1" id="fna.1">1</a></sup> wing thy airy flight;</div>
+<div class="indent">Let thine amplitude be great;</div>
+<div>Tell her all my thoughts to-night,</div>
+<div class="indent">How I long to know my fate.</div>
+
+<div class="newverse"><br class="ns"
+/>All the fields of Mathematics</div>
+<div class="indent">I have roamed at her decree;</div>
+<div>From Binomial and Quadratics,</div>
+<div class="indent">To the strange hyperbole.<sup><a href="#fn.2" name="fna.2" id="fna.2">2</a></sup></div>
+
+<div class="newverse"><br class="ns"
+/>I have soared through Differential,</div>
+<div class="indent">Deeply drunk of Finite Boole;<sup><a href="#fn.3" name="fna.3" id="fna.3">3</a></sup></div>
+<div>Though its breath is pestilential,</div>
+<div class="indent">Reeking of the hateful School.</div>
+
+<div class="newverse"><br class="ns"
+/>I have tried to shape a Conic,</div>
+<div class="indent">Vainly read the Calculus;</div>
+<div>But my feebleness is chronic,</div>
+<div class="indent"><i>Morbus Mathematicus</i>.</div>
+
+<div class="newverse"><br class="ns"
+/><a name="png.036" id="png.036"></a><span class="ns">[</span><span
+ class="pgmark">24</span><span class="ns">]<br
+ /></span>All my curves are cardioidal;</div>
+<div class="indent">I confuse my <i>x</i> and <i>y</i>s,</div>
+<div>Which they say is suicidal;</div>
+<div class="indent">And my tutor vainly sighs.</div>
+
+<div class="newverse"><br class="ns"
+/>Wavelet, tell her how I love her,</div>
+<div class="indent">As she mounts her learned throne;</div>
+<div>And that love I hope may cover</div>
+<div class="indent">All the failings which I own.</div>
+
+<div class="newverse"><br class="ns"
+/>Wavelet, cry to her for pity;</div>
+<div class="indent">Bid her end this bitter woe;</div>
+<div>I might do something &lsquo;in the city,&rsquo;</div>
+<div class="indent">But never pass my Little-go.</div>
+</div>
+
+<hr class="footnote" />
+<div class="footnote">
+<p><a href="#fna.1" name="fn.1" id="fn.1">1</a> We presume this is addressed to an imaginary
+brain wave.</p>
+
+<p><a href="#fna.2" name="fn.2" id="fn.2">2</a> We observe here the dash of an indignant pen,
+and a substituted for e. But now the rhyme is
+spoiled. Gentle Muse, thou art sacrificed by the
+stern hand of Mathematical Truth!</p>
+
+<p><a href="#fna.3" name="fn.3" id="fn.3">3</a> Query: Does the writer refer to the learned
+treatise on Finite Differences by Professor Boole?</p>
+</div>
+
+
+
+<h2><a name="png.037" id="png.037"></a><span class="ns">[</span><span
+ class="pgmark">25</span><span class="ns">]<br
+ /></span>PAPER III.</h2>
+
+<h3>LECTURE ON THE SOCIAL PROPERTIES OF
+A CONIC SECTION, AND THE THEORY OF
+POLEMICAL MATHEMATICS.</h3>
+
+
+<p class="noindent"><span class="smc">Most Learned Professors and Students
+of this University</span>,&mdash;From the
+interest manifested in my first lecture, I
+conclude that my method of investigation
+has not proved altogether unsatisfactory
+to you, and I hope ere long to produce
+certain investigations which will probably
+startle you, and revolutionize the current
+thought of the age. The application of
+mathematics to the study of Social
+Science and Political Government has
+curiously enough escaped the attention of
+those who ought to be most conversant
+with these matters. I shall endeavour to
+prove in the present lecture that the
+relations between individuals and the
+Government are similar to those which
+<a name="png.038" id="png.038"></a><span class="ns">[</span><span
+ class="pgmark">26</span><span class="ns">]
+ </span>mathematical knowledge would lead us
+to postulate, and to explain on scientific
+principles the various convulsions which
+sometimes agitate the social and political
+world.</p>
+
+<p>Indeed, by this method we shall be able
+to prophesy the future of states and
+nations, having given certain functions and
+peculiarities appertaining to them, just as
+easily as we can foretell the exact day and
+hour of an eclipse of the moon or sun. In
+order to do this, we must first determine
+the <em>social properties of a conic section</em>.</p>
+
+<p>For the benefit of the unlearned and
+ignorant, I will first state that a cone is
+a solid figure described by the revolution
+of a right-angled triangle about one of the
+sides containing the right angle, which
+remains fixed. The fixed side is called
+the axis of the cone. Conic sections are
+obtained by cutting the cone by planes.
+It may easily be proved that if the angle
+between the cutting plane and the axis be
+equal to the angle between the axis and
+the revolving side of the triangle which
+generates the cone, the section described
+<a name="png.039" id="png.039"></a><span class="ns">[</span><span
+ class="pgmark">27</span><span class="ns">]
+ </span>on the surface of the cone is a parabola;
+if the former angle be greater than the
+latter, the curve will be an ellipse; and if
+less, the section will be a hyperbola.</p>
+
+<p>But the simplest conic section is, of
+course, a circle, which is formed by a plane
+at right angles to the axis of the cone;
+and the simplest circle is that formed
+by a plane passing through the apex of the
+cone. All this is simple mathematics;
+and let beginners consult more elementary
+treatises than this one to satisfy themselves
+on these points. But if they will
+assume these things to be true, they will
+know quite enough for our present
+purpose. The simplest conic section
+of all has been proved to be a <em>point</em>.
+Now, this represents the simplest and
+original form of society, a <em>single family</em>.
+&lsquo;It is not good for man to be alone&rsquo;
+was the first observation made by the
+wise Creator upon the rational creature
+whom He had introduced into
+Paradise as its lord. Marriage is the
+rudiment of all social life, from which
+all others spring, out of which all others
+<a name="png.040" id="png.040"></a><span class="ns">[</span><span
+ class="pgmark">28</span><span class="ns">]
+ </span>are developed. Around the parents&#8217; knees
+soon cluster a group of children, and in
+their relation to each other we discern the
+earliest forms of law and discipline&mdash;the
+bonds by which society is held together.
+When the children grow up, separate
+households are formed; and then the
+multiplication of families, the congregating
+of men together for purposes of security
+and mutual advantages in division of
+labour; and thus is gradually formed a
+state, which is only the development of
+the family&mdash;the king representing the
+parent, and ruling on the same principle.</p>
+
+<p>Mathematically speaking, our plane no
+longer passes through the apex. The
+point represented the single family;
+but keeping the plane horizontal, we
+move it along the axis, the sections
+will become <em>circles</em>, which represent
+mathematically the next simplest form of
+society, where the centre is the seat of
+government, which is connected with each
+individual member of the social circle by
+equal radii. The social property of a
+circle is that of a monarchical government
+<a name="png.041" id="png.041"></a><span class="ns">[</span><span
+ class="pgmark">29</span><span class="ns">]
+ </span>in its purest and simplest form. The
+larger the circle becomes (<i>i.e.</i>, the further
+you move the plane from the apex), the
+greater the distance between the individual
+and the monarch. Therefore, the more
+independent the monarchy becomes, and
+the less influence do individuals possess
+over the ruling power. Hence, we may
+infer that as years roll on, the government
+will become more despotic; but the
+stability of the country diminished, and
+probably some individual particle, when
+sufficiently withdrawn from the attraction
+of the central head, will begin to revolve
+on its own account, and spontaneously
+generate a government of its own. We
+may, therefore, conclude from mathematical
+reasoning that an unlimited monarchy,
+though advantageous for small states, is
+not a safe form of government for a large
+or populous country, inasmuch as the
+people do not derive much benefit from
+the sovereign; the mutual attraction,
+which ought to exist in a flourishing state
+between the ruler and the ruled, is
+weakened; and the isolation of the
+<a name="png.042" id="png.042"></a><span class="ns">[</span><span
+ class="pgmark">30</span><span class="ns">]
+ </span>monarch tends to make him still more
+despotic. As a practical example of the
+truth of the foregoing statement, I may
+mention the present condition of Russia,
+which shows that the result of an unlimited
+monarchy, in a large and unwieldy
+social circle, is such as we should have
+reasonably expected from mathematical
+investigations.</p>
+
+<p>Invariably, under the circumstances
+which I have described, the country will
+become disorganized; the sovereign will
+cease to have any power over the people,
+and the country will become a chaos,
+without order, influence, or power.</p>
+
+<p>When the centre of a conic section
+moves along the axis of the curve to
+infinity, banished by the mutual consent
+of the individual particles which compose
+the curve, or the nation, a figure is formed,
+called a <em>parabola</em>. This is the curve
+which the most erratic bodies in the
+universe describe in space, as they rush
+along at a speed inconceivable to human
+minds, and are supposed to produce all
+kinds of mischief and injury to the
+<a name="png.043" id="png.043"></a><span class="ns">[</span><span
+ class="pgmark">31</span><span class="ns">]
+ </span>worlds whose courses they wend their way
+among.</p>
+
+<p>This curve, then, represents the position
+which the nation assumes when the constituted
+monarchy, the centre of the system,
+has been <em>banished to infinity</em>. A revolution
+has occurred; the monarch has been
+dethroned; and it is not hard to see that
+the same erratic course which the comet
+pursues in its flight, is observable with
+respect to the social system which is
+represented by a parabola. We observe
+with eager scrutiny the wanderings of
+these erratic comets. They appear suddenly
+with their vapoury tails; sometimes
+they shine upon us with their soft, silvery
+light, brilliant as another moon; sometimes
+they stand afar off in the distant
+skies, and deign not to approach our
+steady-going earth, which pursues its
+regular course day by day, and year by
+year. Then, after a few days&#8217; coy inspection
+of our planet from different
+points of view, they fly to other remote
+parts of the universe, and do not condescend
+to show themselves again for a
+<a name="png.044" id="png.044"></a><span class="ns">[</span><span
+ class="pgmark">32</span><span class="ns">]
+ </span>hundred years or so. Such is the erratic
+conduct of a heavenly body whose course
+is regulated by a parabolic curve.</p>
+
+<p>We may look for similar eccentric behaviour
+on the part of a community,
+nation, or state, whose centre is at infinity,
+whose constitution has been violently
+disturbed, and whose monarchy is
+situated in the far-off regions of unlimited
+space. The erratic course of Republican
+rule is proverbial. There is no stability,
+no regularity. To-day we may observe its
+brilliancy, which seems to laugh at and
+eclipse the sombre shining of more
+steady and enduring worlds; but ere to-morrow&#8217;s
+moon has risen, it may have
+vanished into the regions of eternal night,
+and we look for its bright shining light in
+the councils of the nations, but it has
+ceased to shed its rays, and we are disappointed.
+Sometimes it is asked, with
+fear and trembling: &lsquo;What would be the
+effect if our earth were to come in contact
+with the tail of a comet? Should we be
+destroyed by the collision, and our ponderous
+world cease to be?&rsquo; But we are
+<a name="png.045" id="png.045"></a><span class="ns">[</span><span
+ class="pgmark">33</span><span class="ns">]
+ </span>assured that no such disastrous results
+would follow. We have already passed
+through the tails of many comets, but we
+have not discovered any inconvenient
+change in our ordinary mode of procedure.
+It is probable that the comet&#8217;s
+tail is composed of no solid substance.</p>
+
+<p>We may therefore infer by analogy that
+a Republican State would not offer any
+powerful resistance if it were to come into
+collision with a nation possessing a more
+settled form of government. A shower of
+meteoric stones, like passing fireworks,
+might take place; but beyond that
+nothing would occur to excite the fear,
+or arouse the energies of the more
+favoured nation. As an example of the
+weakness of a Republican State I may
+mention France. There we see an industrious
+race of people, endowed with
+many natural gifts and graces, a country
+rich and productive; and yet, owing to
+the unsettled nature of its government, all
+these natural advantages are neutralized;
+its course amongst the nations is erratic
+in the extreme, a spectacle of feeble
+<a name="png.046" id="png.046"></a><span class="ns">[</span><span
+ class="pgmark">34</span><span class="ns">]
+ </span>administration; and it would offer no more
+resistance to a colliding Power than the
+empty vacuum of a comet&#8217;s tail. This
+example will demonstrate to you the truth
+of our theory with regard to the instability
+of a social system which is geometrically
+represented by a parabolic curve.</p>
+
+<p>We will now turn from this picture of
+insecurity and unrest to another figure
+which possesses most advantageous social
+properties. I refer to the ellipse. An
+ellipse is a curve formed by the section
+of a cone by a plane surface inclined at
+an angle to the vertical axis of the cone,
+greater than the angle between the axis
+and the generating line.</p>
+
+<p>Now, this is a curve which possesses
+most attractive properties. It is the curve
+which the earth and other planetary orbs
+describe around the centre of the solar
+system, as if nature intended that we
+should take this figure as a guide in
+choosing the most advantageous social
+system. It possesses a centre, C, in view
+of all the particles which compose the
+curve, and connected with them by close
+<a name="png.047" id="png.047"></a><span class="ns">[</span><span
+ class="pgmark">35</span><span class="ns">]
+ </span>ties. It has two foci, S and S', fixed
+points, by the aid of which we may trace
+the curve.</p>
+
+<p>In the interpretation of this figure, the
+centre of the curve represents the throne
+of monarchy. There is no tendency here
+to revolutionize the State, to banish the
+ruling power, and institute a Republican
+form of government; but inasmuch as we
+saw the weakness of an absolute monarchy
+in large and populous States, as represented
+by the circle, the wisdom of an
+elliptical social system has ordained that
+there shall be two foci, or houses of
+representatives of the people, who shall
+assist in regulating the progress of the
+nation. Here we have a limited monarchy;
+the throne is supported by the representatives
+of the people; and the nearer these
+foci of the nation are to the centre (<i>i.e.</i>,
+in mathematical language, the less the
+<em>eccentricity</em> of the curve), the more perfect
+the system becomes&mdash;the greater the
+happiness of the community.</p>
+
+<p>In cases where the <em>eccentricity</em> becomes
+very great, the beauty of the curve is
+<a name="png.048" id="png.048"></a><span class="ns">[</span><span
+ class="pgmark">36</span><span class="ns">]
+ </span>destroyed, and ultimately the ellipse is
+merged into one straight line. Most
+learned Professors, here we have a terrible
+warning of the awful result of too much
+eccentricity. Whether we regard the life
+of the nation or of the individual, let all
+bear in mind this alarming fact, that
+eccentricity of thought, habit, or behaviour
+may result, as in the case of this unfortunate
+ellipse, which once presented such
+fair and promising proportions to the
+student&#8217;s admiring gaze, in the &lsquo;sinister
+effacement of a man,&rsquo; or the gradual absorption
+of a State into an uninteresting
+thing &lsquo;which lies evenly between its extreme
+points.&rsquo;</p>
+
+<p>The great examples of Bacon, of Milton,
+of Newton, of Locke, and of others,
+happen to be directly opposed to the
+popular inference that eccentricity and
+thoughtlessness of conduct are the necessary
+accompaniments of talent, and the
+sure indications of genius. I am indebted
+to Lacon for that reflection. You may
+point to Byron, or Savage, or Rousseau,
+and say, &lsquo;Were not these eccentric people
+<a name="png.049" id="png.049"></a><span class="ns">[</span><span
+ class="pgmark">37</span><span class="ns">]
+ </span>talented?&rsquo; &lsquo;Certainly,&rsquo; I answer; &lsquo;but
+would they not have been better and
+greater men if they had been less eccentric&mdash;if
+they had restrained their caprice,
+and controlled their <ins class="TN" title="Transcriber's note:
+ original lacks closing quote">passions?&rsquo;</ins> Do not
+imagine, my young students of this university,
+that by being eccentric you will
+therefore become great men and women
+of genius. The world will not give you
+credit for being brilliant because you affect
+the extravagances which sometimes accompany
+genius. Some of you ladies, I
+perceive, have adopted a peculiar form of
+dress, half male, half female; or, to be
+more correct, three-fourths male, and one-fourth
+female. Do not imagine that you
+will thus attain to the highest honours in
+this university by your eccentricity, unless
+your talents are hid beneath your short-cut
+hair, and brains are working hard under
+your college head-gear. As well might we
+expect to find that all females who wear
+sage-green and extravagant æsthetic costumes
+are really born artists and future
+Royal Academicians. It is apparent that
+many aspirers to fame and talent are eager
+<a name="png.050" id="png.050"></a><span class="ns">[</span><span
+ class="pgmark">38</span><span class="ns">]
+ </span>to exhibit their eccentricities to the gaze
+of the world, in order that they may persuade
+the multitude that they possess the
+genius of which eccentricity is falsely supposed
+to be the outward sign.</p>
+
+<p>I may remark in passing that the eccentricity
+of a parabolic curve is always <em>unity</em>.
+What does this prove? You will remember
+that a Republican State is represented by
+a parabola. Therefore, however such a
+nation may strive to alter its condition,
+and secure a settled form of government,
+its eccentricity will always remain the
+same. It will always be erratic, peculiar,
+unsettled; and this conclusion substantiates
+our previous proposition with regard
+to the condition of a social system represented
+by a parabola.</p>
+
+<p class="pgbrk">With regard to other advantages afforded
+by an elliptical social system, we will defer
+the consideration of this important
+subject until my next lecture.</p>
+
+
+
+
+
+<h2><a name="png.051" id="png.051"></a><span class="ns">[</span><span
+ class="pgmark">39</span><span class="ns">]<br
+ /></span>PAPER IV.</h2>
+
+<h3>THE SOCIAL PROPERTIES OF A CONIC
+SECTION, AND THE THEORY OF POLEMICAL
+MATHEMATICS&mdash;(<i>continued</i>).</h3>
+
+
+<p class="noindent"><span class="smc">Most learned Professors and Students
+of this University</span>,&mdash;You have already
+gathered from my preceding lecture my
+method of procedure in the investigation
+of the corresponding properties of curves
+and States. You have perceived that we
+have here the elements of a new science,
+which may be extended indefinitely, and
+applied to the various departments of self-government
+and State control. This new
+science of polemical mathematics is in
+itself an extension of the <em>principle of continuity</em>,
+for the discovery of which Poncelet
+is so justly renowned. We can prove by
+geometry that the properties of one figure
+may be derived from those of another
+<a name="png.052" id="png.052"></a><span class="ns">[</span><span
+ class="pgmark">40</span><span class="ns">]
+ </span>which corresponds to it; and the new
+science teaches us that if we can represent,
+by projection or otherwise, a society of
+particles or individuals on a plane surface,
+the properties of the State so represented
+are analogous to the properties of the
+curve with which it corresponds. It is
+only possible for me to touch upon the
+elements of the science in these lectures,
+but I hope to arouse an interest in these
+somewhat unusual complications and
+curious problems, that you may hereafter
+make further discoveries in this unexplored
+region of knowledge, and that the world
+may reap the benefit of your labours and
+abstruse studies. I have already, in my
+previous lecture, touched upon the social
+properties of the parabola, and examined
+the constitution of erratic curves and
+eccentric nations. It is my intention
+to-day to speak of similar problems
+which arise with reference to elliptical
+States.</p>
+
+<p>But, first, let me answer an objection
+which may have occurred to your minds.
+<a name="png.053" id="png.053"></a><span class="ns">[</span><span
+ class="pgmark">41</span><span class="ns">]
+ </span>Am I wrong in my calculations in attributing
+too much to the power and usefulness
+of forms of government? Does the
+well-being and happiness of a nation depend
+on the government, or upon the
+individuals who compose the nation?
+Most assuredly, I assert, they rest upon
+the former. Men love their country when
+the good of every particular man is comprehended
+in the public prosperity; they
+undertake hazard and labour for the
+government when it is justly administered.
+When the welfare of every citizen is the
+care of the ruling power, men do not
+spare their persons or their purses for the
+sake of their country and the support of
+their sovereign. But where selfish aims
+are manifest in Court or Parliament, the
+people care not for State officials who are
+indifferent to their country&#8217;s weal; they
+become selfish too; Liberty hides her head,
+and shakes off the dust of her feet ere she
+leaves that doomed land, and the stability,
+welfare, and prosperity of that country
+cease.</p>
+
+<p><a name="png.054" id="png.054"></a><span class="ns">[</span><span
+ class="pgmark">42</span><span class="ns">]<br
+ /></span>I might refer you to many a stained
+page of national history in order to prove
+this. Compare the closing chapters of the
+life of the Roman empire with the record
+of the brave deeds of its ancient warriors
+and valorous statesmen. Grecian preeminence
+and virtue died when liberty
+expired. I agree with Sidney when he
+writes that it is absurd to impute this to
+the change of times; for time changes
+nothing, and nothing was changed in
+those times but the government, and that
+changed all things. These are his words:
+&lsquo;As a man begets a man, and a beast a
+beast, that society of men which constitutes
+a government upon the foundation
+of justice, virtue, and the common good,
+will always have men to promote those
+ends; and that which intends the advancement
+of one man&#8217;s desires and
+vanity will abound in those that will
+foment them.&rsquo; I may not, therefore, be
+altogether wrong in attributing the prosperity
+and well-being of a nation to the
+form of government which it possesses.</p>
+
+<p><a name="png.055" id="png.055"></a><span class="ns">[</span><span
+ class="pgmark">43</span><span class="ns">]<br
+ /></span>We will now proceed to the consideration
+of the social advantages which an
+elliptical State affords. This is the form
+of government and social position which
+we, as a nation, at present enjoy; and
+from mathematical considerations I am
+of opinion that it is the best, and hope
+that no change will ever be made in our
+constitution. You may remember that I
+have previously stated that an ellipse has
+a centre and two foci, in view of all the
+particles which compose the curve, and
+connected with them by close ties. The
+centre, in the projected figure, represents
+the monarchy, which is limited; and the
+government is carried on by the aid of
+the two houses of representatives of the
+people, depicted in the projection by the
+two foci.</p>
+
+<p>Now the social advantages of the ellipse
+are given by the fact that the sum of the
+distances of any point from the foci is
+always constant. No particle is left out
+in the cold; no one does not possess
+the advantages of a social government.
+<a name="png.056" id="png.056"></a><span class="ns">[</span><span
+ class="pgmark">44</span><span class="ns">]
+ </span>Though his distance may be far from the
+Upper House, he has the advantage of
+nearness to the Lower, and <i>vice versâ</i>. The
+sum of the distances is constant. The
+extinction of one focus, the House of
+Lords, for example, would create a complete
+disorganization of the whole system:
+the other focus would set up a powerful
+magnetic attraction, and a curious bulb-shaped
+curve would be evolved, very
+different from the beautiful symmetrical
+form which the original figure presented
+to the eye. The centre of the system
+would be disturbed; and it is probable
+that ere long it would disappear along the
+axis and be vanished to infinity. Thus
+the curve would become a parabola. This
+is the alarming result of the extinction of
+one focus. Abolish the House of Lords,
+and you will soon find that the Throne
+will be disturbed; the State will become
+disorganized; the nation will become
+confused by the magnetic force of the
+Lower House, uncounteracted by any other
+attraction; and very soon a complete
+<a name="png.057" id="png.057"></a><span class="ns">[</span><span
+ class="pgmark">45</span><span class="ns">]
+ </span>revolution of the whole system will set
+in: the monarch will be dethroned, and
+a Republican form of government, with all
+the eccentricities of a parabolic course,
+will take the place of a more orderly and
+settled constitution. This is a plain
+deduction from our mathematical investigations;
+and it behoves all our statesmen,
+our philosophers and great men, our
+fellow-citizens and the humblest artisans
+in our manufacturing towns, to weigh well
+this alarming result of the abolition of
+that House which has been threatened
+with destruction; and to ascertain for
+themselves the truths upon which my proposition
+and reasoning rest.</p>
+
+<p>I have already observed that the fact
+that the earth&#8217;s orbit and that of other
+planets are in the form of ellipses; that
+the curvature of the earth is nearly the
+same, ought to guide us in choosing this
+particular curve as a model of the projection
+of a complete and most advantageous
+social system.</p>
+
+<p>The circle described on the major axis of
+<a name="png.058" id="png.058"></a><span class="ns">[</span><span
+ class="pgmark">46</span><span class="ns">]
+ </span>an ellipse, is called the <em>auxiliary circle</em>, and
+affords much assistance in the investigation
+of the properties of an ellipse. As
+we have already shown, the circle represents
+the simplest form of monarchical
+government. Hence, if we compare the
+form of government represented by an
+ellipse (<i>i.e.</i>, such as we now enjoy) with
+that of a system where the king is the only
+governing power, we may obtain great
+assistance in solving complicated political
+problems.</p>
+
+<p>In all conics there is a straight line
+called the &lsquo;directrix,&rsquo; which represents in
+social or polemical science the laws of the
+nation, and plays a prominent part in the
+mutual relations of the individual particles.
+For instance, in the case of the parabola,
+the distance of any particle from the
+directrix is equal to its distance from the
+focus.</p>
+
+<p>From this we may conclude that if an
+individual deviates at all from the path
+which the laws (or, directrix) indicate, if
+he does not show true respect to the
+<a name="png.059" id="png.059"></a><span class="ns">[</span><span
+ class="pgmark">47</span><span class="ns">]
+ </span>decrees of the focal government, and
+preserve the true position between them,
+directly he is found deviating from his
+course, he is quickly banished to a less
+enlightened sphere. In an ellipse there
+is less likelihood of his straying away from
+the course which the directrix points out,
+on account of the two-fold guidance which
+he receives from the two foci.</p>
+
+<p>The following curious problem may be
+noticed. If a parabola roll on another
+parabola, their <ins class="TN" title="Transcriber's note:
+ original reads 'virtices'">vertices</ins> coinciding, the
+focus of the first traces out the directrix
+of the second.</p>
+
+<p>Here we come to the consideration of
+the international relationship of States.
+Two nations have the same form of
+government (in this example this form is
+Republican); their policies coincide: we
+may conclude from this proposition that
+the course which the government of one
+nation will pursue, will be that which is
+prescribed by the laws of the other.</p>
+
+<p>The subject of the contact of curves
+presents many interesting problems with
+<a name="png.060" id="png.060"></a><span class="ns">[</span><span
+ class="pgmark">48</span><span class="ns">]
+ </span>reference to Polemical Science, and may
+be extended indefinitely. It is well known
+that there are different orders of contact,
+which are designated as the <em>first</em>, <em>second</em>,
+or <em>third</em> order. This last order may be
+termed the &lsquo;marriage of curves,&rsquo; cemented
+by the osculating circle, or &lsquo;wedding-ring;&rsquo;
+and when two nations have contact
+of the third order, they have formed a
+very close alliance, and by calculation we
+can obtain the <em>radius of curvature</em>, or size
+of the wedding-ring, by means of which
+they may be united.</p>
+
+<p>The theory and nature of contact constitute
+a branch of our newly discovered
+science which we commend to the careful
+consideration of those who have undertaken
+the difficult and perplexing study of
+international law. Alas! too many States
+refuse this friendly contact, and, consequently,
+<em>cut</em> each other, instead of
+blending in sweet accord. Their peace is
+at best an armed neutrality; and if they
+have contact of only the <em>first</em> or <em>second</em>
+order, we can prove mathematically that
+<a name="png.061" id="png.061"></a><span class="ns">[</span><span
+ class="pgmark">49</span><span class="ns">]
+ </span>they are sure to intersect in some other
+point or points; and divergence of policy
+and disturbed relations are the results.
+Contact of the <em>third, or highest, order</em> is
+the only safe position for two allied, or
+contiguous, States.</p>
+
+<p>With your permission I will add a few
+words to those I have already uttered
+with regard to the directrix. As necessary
+as the directrix is to the curve, so are
+the corresponding laws to the State. I
+will prove this fact by a few examples.
+English people have laws, and know how
+to obey them; therefore their numbers
+increase; they thrive and are prosperous.
+A friendly critic of another nation has
+said that the reason why Englishmen
+rule the world, is because they know how
+to obey. On the other hand, the gipsies
+have no laws; hence they become fewer
+and less powerful. What is the condition
+of all tribes and nations which are not
+governed by laws? They invariably
+remain poor and miserable. They are in
+want of a directrix; and if we could
+<a name="png.062" id="png.062"></a><span class="ns">[</span><span
+ class="pgmark">50</span><span class="ns">]
+ </span>supplement the gift with foci and centre, they
+would soon emerge from their savage condition,
+and become more civilized.</p>
+
+<p>I have omitted to mention the hyperbolic
+form of government. The curve
+formed by the intersection of the surface
+of a cone with a plane will be a hyperbola,
+when the inclination of the cutting
+plane to the axis of the cone is less than
+the constant angle which the generating
+line forms with the axis. It is manifest
+that the plane will thus intersect the
+higher cone, and produce the figure
+which is known to mathematicians as
+the hyperbola.</p>
+
+<p>We may hence deduce the following
+property of the corresponding hyperbolic
+State. We take cognizance of that higher
+cone with which the mundane affairs of
+the lower cone are closely connected. As
+an example of this system we may mention
+the vast temporal rule and power of the
+Papal Throne, which formerly exercised
+such marvellous sway over the nations of
+Europe.  By an appeal to a Higher
+<a name="png.063" id="png.063"></a><span class="ns">[</span><span
+ class="pgmark">51</span><span class="ns">]
+ </span>Authority than that of earthly kings and
+potentates was this rule exercised; but its
+hyperbolic form is fast passing away, and
+degenerating into that of a circle with
+indefinitely small radius. We shall not,
+therefore, discuss the complex polemical
+problems which a hyperbolic State
+suggests.</p>
+
+<p>I will now mention a few problems
+which are easily capable of proof, and
+deduce from them the necessary conclusions
+which must follow when we apply
+our newly discovered principles of polemical
+science.</p>
+
+<p>1. &lsquo;If from any point in a straight line
+a pair of tangents be drawn to an ellipse,
+the chords of contact will pass through a
+fixed point.&rsquo;</p>
+
+<p>I will not trouble you with the proof of
+this proposition, as it is evident to all
+mathematicians, and can easily be demonstrated.
+But mark well the deductions,
+when we interpret this mathematical language
+in correct polemical terms. A State,
+through various convulsions of its own,
+<a name="png.064" id="png.064"></a><span class="ns">[</span><span
+ class="pgmark">52</span><span class="ns">]
+ </span>has merged into a condition represented
+by a straight line, having lost its symmetry,
+its beauty, its curvilinear proportion.
+An individual unhappily situated
+in this unfortunate community regards
+with longing eyes the prosperous condition
+of those who enjoy the social advantages
+of a settled form of government, and other
+blessings which accompany elliptical jurisdiction
+and laws. [Two tangents are
+drawn to an ellipse.] No matter where
+the individual may be in the unhappy
+envious straight line, the result of his reflection
+will be the same. Sympathetic
+chords are drawn, joining the points of
+contact of the tangents with the curve;
+they all pass through a fixed point. All
+these conclusions of the various individuals
+on the straight line will be the same. All
+are of opinion that the elliptical form is
+the best; and they mourn in secret over
+the sad events which have occurred in
+their own national life, their eccentricity,
+their lawlessness, when they see the
+advantages which their more staid and
+sober-minded neighbours so freely enjoy.</p>
+
+<p><a name="png.065" id="png.065"></a><span class="ns">[</span><span
+ class="pgmark">53</span><span class="ns">]<br
+ /></span>2. The normal at any point of an ellipse
+bisects the angle between the focal distances
+of that point.</p>
+
+<p>The normal is the perpendicular from
+the point on the major axis; it is the line
+of thought directed by the observance of
+just laws and rules. Hence this proposition
+shows that the individual citizen,
+when guided by sound judgment, regards
+with equal favour and entire approval the
+existence of both foci, or Houses of Legislature.
+He considers that both are necessary
+to his comfort, and the right regulation
+of the State&#8217;s welfare. He cares not for
+the <em>abnormal</em> condition of those who talk
+as if the existence of either House were
+unnecessary to his country&#8217;s weal, and
+bestows a pitying glance on those wandering
+lights, or disturbed erratic governments,
+which do not possess the advantages
+which from experience he has learned to
+love and to respect. No matter what his
+condition may be, the same opinions are
+held by all classes, all ranks and degrees;
+and if a <ins class="TN" title="Transcriber's note:
+ original reads 'self-opiniated'">self-opinionated</ins> particle think otherwise,
+he ought to be transferred to a less
+<a name="png.066" id="png.066"></a><span class="ns">[</span><span
+ class="pgmark">54</span><span class="ns">]
+ </span>enlightened sphere, and migrate to a parabolic
+state, or uninteresting straight line.
+And when he has changed his location,
+he will look back on his old home and
+old surroundings with longing eyes and an
+aching heart, thinking of the blessings he
+has lost by his own rash act. This can
+be proved mathematically. He looks for
+an ideal state of society, leaps after the
+shadow his fancy has depicted; and when
+he finds himself outside his former state,
+he looks back with longing eyes at the
+once-scorned focus. What is the focus of
+a perpendicular on the tangent of an
+ellipse from any external point? Can it
+not be proved to be a <em>circle</em>? That is to
+say, he will be more conservative than
+ever. He would like to return to a primitive
+form of government. Farewell to his
+wild schemes and revolutionary measures!
+Farewell to his disestablishments, abolitions,
+and suppressions! The throne and
+government have new attractions in his
+eyes; loyalty, a new feeling, asserts its
+benign influence; and if he could return
+<a name="png.067" id="png.067"></a><span class="ns">[</span><span
+ class="pgmark">55</span><span class="ns">]
+ </span>to his former position, his normal conduct
+would be straighter than ever, for
+by sad experience he has learned the
+value of those things which he once
+despised.</p>
+
+<p>But we need not depend upon one
+proof alone. Exactly the same result may
+be obtained from the well-known proposition
+which states that &lsquo;the angle between
+the tangent from any external point and
+the focal distance is equal to the angle
+between the other tangent and the focal
+distance.&rsquo;</p>
+
+<p>3. The same opinions are often held
+by individuals in quite different walks and
+classes of life. Let these individuals be
+represented by points on an ellipse. Join
+these, and we have a system of parallel
+chords. Draw a straight line through the
+middle points of these chords, and lo! it
+will always pass through the centre. This
+shows that the central thought of all people
+is directed to the sovereign&mdash;that <em>loyalty</em>
+is inherent in the hearts of those who
+recognise elliptical laws.</p>
+
+<p><a name="png.068" id="png.068"></a><span class="ns">[</span><span
+ class="pgmark">56</span><span class="ns">]<br
+ /></span>I will conclude this lecture with a few
+remarks on the nature and properties of
+the <em>radical axis</em>. This name was first
+given, I believe, by M.&nbsp;Gaultier, of Tours,
+and for a full account of its nature I refer
+you to the <cite>Journal de l&#8217;École Polytechnique</cite>,
+xvi., 1813. The radical axis of two circles
+is the line perpendicular to the line joining
+the centres, from any point of which
+the tangents to the circles are equal. Let
+us suppose that one circle becomes a point,
+and that this point is situated on the circumference
+of the first circle. What is
+the result? The radical axis becomes
+the tangent to the circle. Hence we
+may conclude that in a social system of
+monarchical government the radical axis
+is perpendicular to the line attaching the
+individual with the monarch. Therefore
+we may conclude that the radical axis
+indicates a tendency of particles, or individuals,
+to fly off at a tangent, at right
+angles to the connecting-link between the
+individual and the king. When any motion
+takes place, this is evident, and this
+<a name="png.069" id="png.069"></a><span class="ns">[</span><span
+ class="pgmark">57</span><span class="ns">]
+ </span>tendency is called centrifugal force. Sad is
+it for the State when this force is called
+into play, and the radical axis is a standing
+menace to the stability of States and
+nations. The only way to counteract its
+baneful, disturbing influence is to increase
+the attraction of the monarch on the individual,
+which nullifies the former force,
+and prevents further mischief. This is the
+method which nature itself adopts in the
+motions of the planetary worlds; the attraction
+of the sun prevents any disturbance
+which might be caused in the course
+of the planets by the action of centrifugal
+force, and nature suggests this plan for
+our adoption. Increase the attraction of
+the Throne; rigidly connect each individual
+by the strong chords of affection, advantage
+and utility with the ruling power;
+and then, though the radical axis may be
+there, it will cease to indicate any motion
+along it, it will not prevail over the counteracting
+influence of loyalty, and the stability
+of the social system and the happiness of
+the individuals will be the results.</p>
+
+<div class="stanza">
+<div class="indent6"><a name="png.070" id="png.070"></a><span class="ns">[</span><span
+ class="pgmark">58</span><span class="ns">]<br
+ /></span>&lsquo;I would serve my King,</div>
+<div>Serve him with all my fortune here at home,</div>
+<div>And serve him with my person in the wars;</div>
+<div>Watch for him, fight for him, bleed for him, die for him,</div>
+<div>As every true-born subject ought.&rsquo;</div>
+</div>
+
+<p class="noindent">This, most noble professors, is the language
+of true patriotic loyalty. Let the
+monarch be loved and loving, let the
+laws be just and equal, happy will be the
+people, prosperous the realm. There are
+those who counsel different things, and
+preach sedition and the breaking-up of
+laws; but those who advocate such doctrines
+lack that judicial mathematical
+training which we, students and professors
+of Girtham College, have acquired. If
+polemical mathematics, the science of the
+future, should become more widely studied;
+if its results were disseminated far and
+wide; above all, if the proper position
+which women ought to occupy in the
+counsels of the nation were assigned to
+them, we should hear less of these wild
+schemes and foolish theories, and the influence
+of women would tend greatly to
+<a name="png.071" id="png.071"></a><span class="ns">[</span><span
+ class="pgmark">59</span><span class="ns">]
+ </span>promote the stability and security of the
+State.</p>
+
+<p>Why, let me ask, should woman be
+excluded from that position which is so
+justly hers? from those duties which she
+can discharge so faithfully? It has been
+said that if we wish to know the political
+and moral condition of a State, we must
+ask what rank women hold in it. We are
+told that women have more strength in
+their looks than men have in their laws.
+Why, then, do men debar her from those
+fields of occupation wherein she may
+labour for the nation&#8217;s good, and use her
+influence, which they acknowledge to be
+great, in those callings wherein she may
+most easily benefit the State, and the
+country she so ardently loves?</p>
+
+<p>At some future time I hope to speak
+more fully on this subject; and in concluding
+this lecture, I will remark that
+English politics need a leavening influence
+which will counteract the evil tendencies
+and corrupt theories which, in spite of our
+advantageous social system, at present
+<a name="png.072" id="png.072"></a><span class="ns">[</span><span
+ class="pgmark">60</span><span class="ns">]
+ </span>exist; and this leavening influence will be
+best produced by the admission of those
+into the counsels of the nation who are
+acknowledged to have a benign and healthy
+influence&mdash;the women of England. Let
+women have their proper share in the
+government of the country, and I have
+no fear lest we shall preserve our elliptical
+constitution, and all the advantages which
+we at present enjoy.</p>
+
+<hr class="tb" />
+
+<p>[<span class="smc">Editorial Note.</span>]&mdash;In the bundle of
+papers which contained the foregoing
+lectures, some letters of great interest
+were found, which show that the fame
+of the learned Lady Professor of Girtham
+College had already gone abroad, and
+attracted the attention of the leading
+statesmen of the day. It is to be regretted
+that the answers to these letters
+are not forthcoming, as it might be proved
+from them that the science of polemical
+mathematics has already influenced the
+minds of our legislators in their conduct
+<a name="png.073" id="png.073"></a><span class="ns">[</span><span
+ class="pgmark">61</span><span class="ns">]
+ </span>of affairs at home and abroad. The
+following letter is of unique interest, and
+may be taken as evidence of the favourable
+impression which this new science
+has made on the mind of one of our
+greatest thinkers and statesmen:</p>
+
+<p class="address"><small>Downing Street,</small></p>
+<p class="date"><small>May, 18&mdash;</small></p>
+
+<p><span class="smc">My dear Lady Professor</span>,&mdash;The
+report of the amazing results of your
+scientific researches has reached me, and
+I congratulate you most heartily on the
+originality and acumen which you have
+displayed in your investigations. A new
+light has dawned upon our country.
+Instead of groping in the darkness of
+political warfare, ensnared by party ties
+and jealousies, the statesmen of the future
+will be able to calculate and determine the
+correct course with mathematical precision
+and perfect accuracy. No one can
+dispute the truth of a proposition in
+Euclid, or the genuineness of Newton&#8217;s
+laws; and if your method enables men to
+<a name="png.074" id="png.074"></a><span class="ns">[</span><span
+ class="pgmark">62</span><span class="ns">]
+ </span>calculate and determine the correct political
+course of action, to solve political
+problems as easily as exponential equations,
+why&mdash;then adieu to the bickerings
+of party, the querulous complaints of the
+Opposition! Nay, joy to the Ministry!
+There will be no Opposition! Our statesmen
+will be able to guide the great ship of
+the State by means of charts which know
+no error; and they will resemble an
+association of savants met together to
+determine the exact moment of the
+transit of Venus, or to examine the degree
+of density of a comet&#8217;s tail.</p>
+
+<p>This condition of Parliamentary procedure
+is much to be desired; you have
+shown how such an ideal state of things
+may be obtained. In the name of the
+Government I thank you for your endeavours
+on behalf of your country&#8217;s
+welfare, and look forward to a further
+development of your admirably conceived
+system. As in the domain of ordinary
+science there are complex questions
+which defy the acumen of the philosopher;
+<a name="png.075" id="png.075"></a><span class="ns">[</span><span
+ class="pgmark">63</span><span class="ns">]
+ </span>so in polemical science there may be
+questions which present the same difficulties
+and complications. But as the first
+are daily yielding before the persevering
+attacks of the mathematician, so I doubt
+not polemical science will soon overcome
+the various problems which may
+arise.</p>
+
+<p>But it is mainly on my own account
+that I venture to address you. I desire
+to consult you with regard to certain
+matters&mdash;political complications&mdash;which
+have recently occupied the attention of
+Her Majesty&#8217;s Ministers. By the help of
+your new science, can you aid us in our
+deliberations? Of course, I am writing
+to you in <em>strict confidence</em>, and beg that you
+will keep this communication profoundly
+secret. I fear that would be a hard task
+for many of your sex, who do not possess
+your knowledge and powers of mind;
+but I have great confidence in your discretion.</p>
+
+<p>These are the problems which are
+presented to us for solution:</p>
+
+<p><a name="png.076" id="png.076"></a><span class="ns">[</span><span
+ class="pgmark">64</span><span class="ns">]<br
+ /></span>1. Some members of the Cabinet are
+secretly in favour of Protection, and the
+country is rather stirred by the question.
+Can you, from your knowledge of the
+contact of curves and nations, help us to
+determine what course we ought to take
+with regard to Spain, for example? Are
+the principles of Adam Smith mathematically
+correct?</p>
+
+<p>2. I observe that England is represented
+mathematically by an ellipse.  Are we
+right in assuming that Ireland is a portion
+of that ellipse? Or, on the other hand,
+in our chart of nations, must we describe
+that troublesome country as a rotating
+parabola, or complex figure, altogether outside
+our more favoured State?</p>
+
+<p>3. Do you consider, from your minute
+observation of our social system, that the
+form of our elliptical government is
+gradually undergoing a change, and that
+a revolutionary parabolic tendency is
+observable in the action of individual
+particles?</p>
+
+<p>4. Is it not possible that the differences
+<a name="png.077" id="png.077"></a><span class="ns">[</span><span
+ class="pgmark">65</span><span class="ns">]
+ </span>in the policy of the various nations of
+Europe; the difficulties which beset the
+carrying out of international law; the
+jealousies, quarrels, and rivalries of
+States might disappear, if the same form
+of government (<i>i.e.</i>, elliptical) were adopted
+in each?</p>
+
+<p>If you will kindly favour Her Majesty&#8217;s
+Ministers with your opinion on these
+questions, they will owe you a debt of
+gratitude, which they, as representatives of
+the nation, will do their utmost to repay.</p>
+
+<p>With every good wish for your further
+success in the regions of polemical science,</p>
+
+<p class="sig1">I beg to remain,</p>
+<p class="sig2">My dear Lady Professor,</p>
+<p class="sig3">Your faithful servant,</p>
+<div class="cutout">
+<p class="cutbordertop"><img src="images/tuc.png" width="201" height="11"
+ alt="" title="" /></p>
+<sup><a href="#fn.4" name="fna.4" id="fna.4">4</a></sup>
+<p class="cutborderbot"><img src="images/cut.png" width="201" height="11"
+ alt="" title="" /></p>
+</div>
+
+<p><ins class="TN" title="Transcriber's note:
+ original lacks closing bracket">[<span class="smc">Editorial Note.</span>]</ins>&mdash;The next letter
+is not of quite the same pleasing nature
+as the foregoing, and shows that it is
+<a name="png.078" id="png.078"></a><span class="ns">[</span><span
+ class="pgmark">66</span><span class="ns">]
+ </span>impossible to please everyone, even if that
+happy consummation were desirable. This
+letter was evidently called forth by some
+remarks which the learned Lady Professor
+had made in her third lecture with reference
+to eccentricity in dress. Our
+readers will recollect that the professor
+pointed out that an extravagant &lsquo;bloomer&rsquo;
+costume&mdash;half male, half female&mdash;was no
+more a sign of genius than æsthetic
+dresses, always betokened the artist.<sup><a href="#fn.5" name="fna.5" id="fna.5">5</a></sup>
+This latter statement evidently gave great
+offence to the members of a society
+which called itself the &lsquo;Æsthetic and
+Dress Improvement Association,&rsquo; and
+the following letter is the result of one of
+their solemn conclaves:</p>
+
+<p class="address"><small>Oscar Villa, South Kensington,</small></p>
+<p class="date"><small>June, 18&mdash;.</small></p>
+
+<p>The Secretary of the Æsthetic and
+Dress Improvement Association presents
+his compliments to the Lady Professor of
+Girtham College, and begs to contradict
+emphatically her statements with regard
+<a name="png.079" id="png.079"></a><span class="ns">[</span><span
+ class="pgmark">67</span><span class="ns">]
+ </span>to a subject upon which she is evidently
+in entire and lamentable ignorance, and
+to protest against her aspersions upon
+the artistic studies of this and kindred
+societies. He begs to state that true
+æsthetes are <em>not</em> eccentric (they leave that
+to lady professors and her Philistine followers);
+that to dress becomingly is one
+of the principal objects of life, and that
+true greatness is achieved as much by the
+study of the art of dress as by any other
+noble pursuit or graceful accomplishment.
+Are not Horatio Postlethwaite, Leonara
+Saffronia Gillan, Vandyke Smithson entitled
+to greatness? And yet their laurels
+have been won solely by the art of dress.
+Perhaps the lady professor has never read
+&lsquo;Sartor Resartus&rsquo;! In conclusion, he
+would ask the Lady Professor to refrain
+from casting obloquy upon the work of
+the Association which he has the honour
+to represent; to prevail upon her pupils
+to abandon the unfeminine attire which
+some of them have assumed, contrary to
+the first principles of art; to array themselves
+in flowing robes of sage-green and
+<a name="png.080" id="png.080"></a><span class="ns">[</span><span
+ class="pgmark">68</span><span class="ns">]
+ </span>other choice colours (patterns enclosed),
+and to study art, instead of absurd mathematics,
+which no one can understand, and
+do no one any good.</p>
+
+<p class="hangsig">
+(Approved by the Committee of the
+Æsthetic and Dress Improvement
+Association.)</p>
+<p class="hangsig"><small>June, 18&mdash;.</small></p>
+
+
+<p class="above2"><ins class="TN" title="Transcriber's note:
+ original showed period outside bracket">[<span class="smc">Editorial Note.</span>]</ins>&mdash;The next letter,
+written by a pupil of the Lady Professor,
+requires no explanation, and speaks for
+itself.</p>
+
+
+<p class="address"><small>Jesus College, Cambridge,</small></p>
+<p class="date"><small>March, 18&mdash;.</small></p>
+
+<p class="smc">My dear Tutor,</p>
+
+<p>You will be glad to hear that after
+superhuman exertions I have at last succeeded
+in passing my Little-go, and I am
+eternally grateful to you for all you have
+done for me. I should never have got
+through if it had not been for you. All
+the coaches in Cambridge would never
+have managed it, but you drove me
+through in a canter. And why? I never
+could make up my mind to work for them;
+<a name="png.081" id="png.081"></a><span class="ns">[</span><span
+ class="pgmark">69</span><span class="ns">]
+ </span>but when I coached with you, you made
+me like it. I almost revelled in the
+Binomial when you wrote it out for me;
+and then I could not help listening to
+you; and you looked so grieved when I
+would not learn, and made me feel such
+a brute; so somehow or other you drove
+some mathematics into my head, and I
+pulled through. By-the-bye, I think you
+must have tried the &lsquo;brain wave&rsquo; dodge
+with the examiners, as five out of the six
+propositions in Euclid, which you told me
+to get up specially, were set! I wish I
+could read people&#8217;s thoughts; can you read
+mine? If I were a Don, or a Fellow, or
+something, I would advise the University
+to have some lady professors like you to
+teach the men, instead of some of these
+sleepy old tutors. It would be a great
+improvement, and I am sure we should
+get through a great deal more work.</p>
+
+<p>They have given me a place in the Jesus
+Eight, which I shall take now that I am
+released from your professorial ban, and
+have time for rowing. But I don&#8217;t half
+like giving up mathematics. You see, I
+<a name="png.082" id="png.082"></a><span class="ns">[</span><span
+ class="pgmark">70</span><span class="ns">]
+ </span>have grown fond of the study. Do you
+think you could make a wrangler of me?
+At any rate, I should like to come to your
+lectures again. May I?</p>
+
+<p class="sig2 smc">Your Grateful Pupil.</p>
+<p class="sig3 anon">* * *</p>
+
+
+<hr class="footnote" />
+<div class="footnote">
+<p><a href="#fna.4" name="fn.4" id="fn.4">4</a> It is to be regretted that this letter has evidently
+fallen into the hands of some autograph
+collector, who has ruthlessly cut off the signature;
+but the reader will easily determine, after careful perusal
+of the document, from whose pen it emanated.</p>
+
+<p><a href="#fna.5" name="fn.5" id="fn.5">5</a> Cf. page <a class="nopad" href="#png.048">36</a>.</p>
+</div>
+
+
+
+<h2><a name="png.083" id="png.083"></a><span class="ns">[</span><span
+ class="pgmark">71</span><span class="ns">]<br
+ /></span>PAPER V.</h2>
+
+<h3>A LECTURE UPON SOCIAL FORCES, WITH
+SOME ACCOUNT OF POLEMICAL KINEMATICS.</h3>
+
+
+<p><span class="smc">Most noble Professors and Students
+of Girtham College</span>,&mdash;Since last &lsquo;I
+wandered &#8217;twixt the pole and heavenly
+hinges, &#8217;mongst encentricals, centres, concentricks,
+circles, and epicycles,&rsquo; like the
+great Albumazar, and found them full of
+life and wisdom for the guidance of our
+States and laws, I have turned my attention
+to the Applied Mathematics, in order
+to determine what other truths this shaft
+may yield.</p>
+
+<p>The strength of all sciences, according
+to Bacon, consists in their harmony; and
+it is truly marvellous how perfect this
+harmony is, if our ears are tuned aright to
+hear it.  We have observed how the
+<a name="png.084" id="png.084"></a><span class="ns">[</span><span
+ class="pgmark">72</span><span class="ns">]
+ </span>beautiful and regular laws of curves and
+cones correspond to the social laws of
+States and nations, guiding them as if by
+word of counsel, admonishing them on
+what principle they ought to regulate
+their governments and inter-relations. We
+have seen that the laws which govern
+thought and light and sound are almost
+identical, and that harmony pervades not
+merely the ordinary sciences, but extends
+her benign influence over these newly
+discovered fields of scientific research,
+which I claim to have discovered.</p>
+
+<p>All this may appear at first sight surprising;
+but the real philosopher, who
+knows that all kinds of truth are intimately
+connected, will receive such revelations
+of science with satisfaction rather
+than astonishment; for this new science,
+which has opened itself out before me, is
+only an extension of other well-known
+laws and discoveries which have come
+down to us from the remote past.</p>
+
+<p>If my investigations should appear to
+you, most noble professors, somewhat novel
+and imaginary, remember the maxim of
+<a name="png.085" id="png.085"></a><span class="ns">[</span><span
+ class="pgmark">73</span><span class="ns">]
+ </span>the sage, that in the infancy of science
+there is no speculation which does not
+merit careful examination; and the most
+remote and fanciful explanations of facts
+have often been found the true ones.
+Perhaps some &lsquo;self-opinionated particle&rsquo;
+(I speak mathematically) may have been
+inclined to laugh at our theories and discoveries,
+as the wise fools of the day
+laughed at Kepler and his laws; but time
+has changed the world&#8217;s laughter into
+praise, and a century hence our discoveries
+may rank among the achievements of
+modern science. As Cicero says, &lsquo;Time
+obliterates the fictions of opinions, but
+confirms the decisions of nature.&rsquo;</p>
+
+<p>I have not shunned, most noble professors,
+to enlist Imagination under the
+banner of Geometry; for I am fully persuaded
+that it is a powerful organ of
+knowledge, and is as much needed by the
+mathematician as by the poet or novelist.
+It is, I fear, often banished with too much
+haste from the fields of intellectual research
+by those who take upon themselves
+to give laws to philosophy. We need
+<a name="png.086" id="png.086"></a><span class="ns">[</span><span
+ class="pgmark">74</span><span class="ns">]
+ </span>imagination to form an hypothesis; and
+without hypotheses science would soon
+become a lifeless and barren study, a
+horse-in-the-mill affair ever strolling round
+and round, unconscious of the grinding
+corn. In my previous investigations my
+imagination pictured the symmetry of
+curves and States; the hypothesis followed
+that the laws which regulated them were
+identical, and you have observed how the
+supposition was confirmed by our subsequent
+calculations.</p>
+
+<p>In this lecture I propose to examine
+some of the forces which exist in our
+social system, and shall endeavour to
+estimate them by methods of mathematical
+procedure and analogical reasoning.
+We will begin with the old definition
+of Force as <em>that which puts matter into
+motion, or which stops, or changes, a
+motion once commenced</em>. When a mass
+is in motion, it has a capacity for doing
+work, which is called <em>Energy</em>; and when
+this energy is caused by the motion of a
+body it is called Kinetic Energy (in
+mathematical language <span class="nw">KE = ½ MV&sup2;</span>).
+<a name="png.087" id="png.087"></a><span class="ns">[</span><span
+ class="pgmark">75</span><span class="ns">]
+ </span>Another form of kinetic energy is called
+Potential Energy, which is in reality the
+capacity of a body for doing work <em>owing
+to its position</em>. For example we may take
+an ordinary eight-day clock. When the
+weights are wound up, they have a certain
+amount of potential energy stored up,
+which will counteract the friction of the
+wheels and the resistance of the air on
+the pendulum. Or, again, we have the
+example of a water-wheel: first the water
+in the reservoir, being higher than the
+wheel, has an amount of potential energy.
+This is converted into kinetic energy in
+striking against the paddles, and after this
+we have potential energy again produced
+by the action of the fly-wheel.</p>
+
+<p>By the principle of conservation of
+energy, if we consider the whole universe,
+not our planet alone (for its heat and
+energy are continually diminished to some
+slight degree), we find that <em>no energy is lost</em>.</p>
+
+<p>Force is recognised as acting in two
+ways: in <em>Statics</em>, so as to compel rest, or
+to prevent change of motion; and in
+<em>Kinetics</em>, so as to produce or to change
+<a name="png.088" id="png.088"></a><span class="ns">[</span><span
+ class="pgmark">76</span><span class="ns">]
+ </span>motion; and the whole science which investigates
+the action of force is called
+<em>Dynamics</em>.</p>
+
+<p>All this is of course pure mathematics,
+and I have made these elementary observations
+for the benefit of my younger
+hearers, the students of this University.
+My grave and reverend seniors will pardon,
+I am sure, the repetition of facts well
+known to them for the sake of those who
+are less informed than themselves.</p>
+
+<p>Now before I proceed further, I will
+endeavour to point out that these elementary
+truths of physical science hold good
+in our social system. Each individual is
+a mass, acted on by numerous forces,
+capable of &lsquo;doing work,&rsquo; which work can
+be measured and his velocity calculated.
+Some individuals have a vast <em>potential
+energy</em>; that is to say, from their position
+and station in the social system, they have
+a power which is capable of producing
+work which a less exalted individual has
+not. Like the weights in an eight-day
+clock, or the water in a reservoir, they
+have a capacity for doing work, owing to
+<a name="png.089" id="png.089"></a><span class="ns">[</span><span
+ class="pgmark">77</span><span class="ns">]
+ </span>the position to which they have been
+raised. How vast the influence of a
+Primate or a Premier, a General or a
+King! And yet their power is chiefly
+potential energy, arising from the position
+they occupy, not from the individuals
+themselves. Schiller has described this in
+poetical language, which, strange to say, is
+mathematically correct:</p>
+
+<div class="stanza">
+<div>&lsquo;Yes, there&#8217;s a patent of nobility</div>
+<div class="indent">Above the meanness of our common state;</div>
+<div>With what they <em>do</em> the vulgar natures buy</div>
+<div class="indent">Their titles; and with what they <em>are</em>, the <em>great</em>.&rsquo;</div>
+</div>
+
+<p>Other forces may have raised these men
+to their exalted positions; but their influence
+is due to their height, their potential
+energy. Placed on a lower level, they
+would cease to have that power. How
+calm the dignity of this potential rank!
+The water in the reservoir is scarcely
+ruffled or disturbed, as if unconscious of
+its power; when it has lost its force it
+rushes along with a sullen murmur and a
+roar, howling and hissing and boiling in
+endless torture, until&mdash;</p>
+
+<div class="stanza">
+<div>&lsquo;It gains a safer bed, and steals at last</div>
+<div>Along the mazes of the quiet vale.&rsquo;</div>
+</div>
+
+<p><a name="png.090" id="png.090"></a><span class="ns">[</span><span
+ class="pgmark">78</span><span class="ns">]<br
+ /></span>So the vulgar crowd rushes on, with
+plenty of kinetic force, making noise
+enough and looking very busy; while
+those who seem to sleep in calm forgetfulness,
+exercise their potential energy, and
+do the real work of turning the great
+engine of the State.</p>
+
+<p>There are attractive and repulsive forces
+(more commonly the latter, the cynic will
+say) in our social system, but each individual
+is the centre of various forces acting
+upon him. In nature all matter possesses
+the force of gravity, and whatever the
+size of two particles may be, they mutually
+attract each other. The earth attracts the
+moon; the moon attracts the earth. A
+stone thrown up into the air exercises an
+infinitesimal force upon the earth; so in
+the social system every individual, however
+small and insignificant he may be,
+exercises some attractive force upon his
+neighbour. There is no one in the world
+who does not exercise some influence for
+good or for evil upon his fellows.</p>
+
+<p>The force of <em>cohesion</em> is manifest in
+society as in nature, that force, I mean,
+<a name="png.091" id="png.091"></a><span class="ns">[</span><span
+ class="pgmark">79</span><span class="ns">]
+ </span>which resists the separation of a body&#8217;s
+particles. Different bodies possess different
+powers of cohesion, <i>e.g.</i>, the cohesion
+of chalk is far less than that of flint embedded
+in it; even the same body possesses
+different powers of cohesion in different
+directions, <i>e.g.</i>, it is easier to split wood in
+the direction of the fibres than perpendicular
+to them. If by our old principle
+of continuity we change the words &lsquo;bodies&rsquo;
+into &lsquo;States&rsquo; or &lsquo;individuals,&rsquo; we shall see
+that the same laws hold good in social
+science as in natural philosophy.</p>
+
+<p>These are a few analogous laws which I
+have taken almost at random; but it must
+strike the most casual listener to my
+remarks that it is wondrous strange that
+men, regarded as social beings, should
+possess the same qualities, and be governed
+by the same laws, as the rest of <em>matter</em>. As
+Bishop Butler says, &lsquo;the force of analogy
+consists in the frequency of the supposed
+analogous facts, and the real resemblance
+of the things compared.&rsquo; It appeals to
+the reasoning faculty, and may form a solid
+argument. Hence, if we can prove the
+<a name="png.092" id="png.092"></a><span class="ns">[</span><span
+ class="pgmark">80</span><span class="ns">]
+ </span>similarity of various laws and conditions, we
+may not be wrong in assuming by analogy
+the identity of those laws and conditions.</p>
+
+<p>I have stated my case in this manner in
+order to convince the gainsayers, if any
+such there be, and to banish any doubts
+or questionings which may have arisen
+in your minds. I will now proceed with
+some further investigations, full of the
+most profound interest and importance.</p>
+
+<p>Doubtless many of the lady-students
+present are in the habit of welcoming
+peaceful evening in with a potent draught
+of &lsquo;the cup which cheers but not
+inebriates;&rsquo; and as men are great
+flatterers (for imitation is the greatest
+flattery), I believe the male portion of my
+audience have been known to follow that
+excellent example. Some perhaps are in
+the habit of burning the midnight oil, and
+keep their eyes open by means of this
+fruit of the hermit&#8217;s pious zeal, endowed
+by high omnipotence with the power of
+hindering sleep;<sup><a href="#fn.6" name="fna.6" id="fna.6">6</a></sup> but that practice I do
+<a name="png.093" id="png.093"></a><span class="ns">[</span><span
+ class="pgmark">81</span><span class="ns">]
+ </span>not advise, as that delicate portion of our
+system, the nerves, especially of women,
+often becomes injured by such stimulating
+doses. However, you will have observed
+(if you do not follow the modern pernicious
+fashion of taking tea without sugar)
+that numerous bubbles are formed upon
+the surface of the liquid. After a few
+moments these unite into one central
+mass of bubbles by the force of mutual
+attraction.</p>
+
+<p>It appears from considerations which
+are detailed in works on physical astronomy,
+that two particles of matter placed at
+any sensible distance apart attract each other
+with a force directly proportional to the product
+of their masses, and inversely proportional
+to the square of their distance.</p>
+
+<p>Now, suppose that we have a number
+of circular masses situated upon a plane
+<a name="png.094" id="png.094"></a><span class="ns">[</span><span
+ class="pgmark">82</span><span class="ns">]
+ </span>surface, they will attract each other with a
+force which may be determined with
+exactitude; and the greater the masses
+the greater the force. We will now apply
+this to polemical science. The agricultural
+settlement is the first stage in the
+civilization and formation of a State.
+How did this arise? First, a single family
+immigrated to some uncultivated parts
+of the country, perhaps accompanied by
+others, who formed a little colony. Other
+settlements were made in other parts of
+the land; and thus the country became
+overspread with these detached and separate
+communities. An eminent writer
+declares that these settlements can be
+traced in the beginnings of every race
+which has made progress; that they were
+characteristic of those races in Greece and
+Italy, in Asia and Africa, which grew into
+the opulent and famous cities in which so
+much in the early history of civilization
+was developed. The colonies of England
+have been formed in the same way, just
+as in olden time England itself was occupied
+when the Roman power ceased.</p>
+
+<p><a name="png.095" id="png.095"></a><span class="ns">[</span><span
+ class="pgmark">83</span><span class="ns">]<br
+ /></span>These settlements correspond to the
+circular masses situated on the plane
+surface; they were quite separate from
+each other, each having its own laws, its
+own headman or ruler, its own assembly
+or parish council. But as time elapsed,
+the force of mutual attraction set in;
+by degrees these separate settlements
+were drawn together by force which increased
+in proportion as the settlements
+increased; until at last one united kingdom
+was formed under one king, governed
+by uniform laws and regulations. The
+bubbles have blended, the circles have
+come together, and one large circle or
+other curve is the result. This may be
+called the <em>Law of Social Attraction</em>. In
+accordance with the results of one of my
+previous lectures, I have taken the circle
+as representing the simplest form of
+government, which figure, in the case of
+the elementary settlements, must have
+been small.</p>
+
+<p>Many of you, most noble professors,
+are doubtless accustomed to make experiments
+with the microscope. I will
+<a name="png.096" id="png.096"></a><span class="ns">[</span><span
+ class="pgmark">84</span><span class="ns">]
+ </span>suggest a simple one, which illustrates
+very forcibly what I am endeavouring to
+show you. Take some particles of copper,
+and scatter them at intervals over the
+surface of an object-glass, and pour some
+sulphuric acid upon the glass. Now, what
+is the result? A beautiful network of
+apparently golden texture spreads itself
+gradually over the whole area of the
+glass. Steadily it pursues its way, and
+the result is beautiful to behold. The
+minute particles of copper were the original
+settlements scattered over the land;
+the sulphuric acid the civilizing agent;
+and the final picture of a united civilized
+homogeneous nation is well represented
+by the progressive and finally glorious
+network of gold. This example is of
+course outside our present subject, but it
+serves as a beautiful illustration.</p>
+
+<p>As an instance of the attractive force
+exercised by small communities upon each
+other, I may mention the united kingdom
+of Germany, which is composed of numerous
+small States and nations, which have
+been drawn together by the power of
+<a name="png.097" id="png.097"></a><span class="ns">[</span><span
+ class="pgmark">85</span><span class="ns">]
+ </span>mutual attraction. Until recently they
+were each self-contained, separate constitutions,
+with their own kings and forms of
+government; but the attracting force,
+assisted by forces from without, has
+proved too much for them, and the great
+and powerful united kingdom of Germany
+is the result.</p>
+
+<p>But why, you may ask, have not the
+people in Hindustan united in the same
+way? There the agricultural settlements
+remain as they did ages ago; separate
+petty chieftains rule under the all-governing
+power of England. Why have they
+not united?</p>
+
+<p>To this objection I reply that there is
+in social science, as in Nature, a <i>vis inertia</i>;
+that is to say, there is a tendency in
+matter to remain at rest if unmoved by
+any external agency, and also of persisting
+to move, after it has once been set in
+motion. The <i>vis <ins class="TN" title="Transcriber's note:
+ original reads 'inetiar'">inertia</ins></i> of some bodies
+is greater than that of others, and depends
+upon their weight and density. Now it
+so happens that the moral <i>vis inertia</i> of
+the Hindustani is very great, hence their
+<a name="png.098" id="png.098"></a><span class="ns">[</span><span
+ class="pgmark">86</span><span class="ns">]
+ </span>tendency to amalgamation is small. They
+remain in the state in which they happen
+to be.</p>
+
+<p>On the other hand the inertia of Englishmen
+is small, of Englishwomen smaller,
+and therefore their power of combining
+is greater. Here let me observe that the
+quality of inertia is one which ought to be
+removed as far as possible from each
+social system. Inertia was regarded as a
+capital crime by the Egyptians. Solon
+ordained that inert persons should be put
+to death, and not contaminate the community.
+As savages bury living men, so
+does inertia practise the same barbarous
+custom upon States and individuals.
+Observe the putrid state of inert water,
+the clear and sparkling beauty of the
+moving stream, bearing away by the force
+of its own motion aught that might contaminate
+it. Men more often resemble
+the stagnant water than the rivulet. A
+healthy social state enforces labour by
+natural laws, and banishes inertia as much
+as possible from the system. If the
+principles of some noisy English
+<a name="png.099" id="png.099"></a><span class="ns">[</span><span
+ class="pgmark">87</span><span class="ns">]
+ </span>politicians were fully carried out, and all
+things made &lsquo;<em>free</em>,&rsquo; inertia would be increased,
+and listless indolence pervade the
+masses of our countrymen. I may say
+that inertia is not entirely unknown in our
+sister University of Cambridge.</p>
+
+<p>The existence of social forces is supported
+by the testimony of Dr. Tyndall,
+who plainly recognises their power, though
+he does not attempt to expound their
+origin. &lsquo;Thoughtful minds are driven to
+seek, in the interaction of social forces,
+the genesis and development of man&#8217;s
+moral nature. If they succeed in their
+search&mdash;and I think they are sure to
+succeed&mdash;social duty would be raised to
+a higher level of significance, and the
+deepening sense of social duty would, it
+is to be hoped, lessen, if not obliterate,
+the strife and heart-burnings which now
+beset and disguise our social life.&rsquo; I
+accept with gratification Dr. Tyndall&#8217;s
+conclusions: to determine, examine, trace,
+calculate these social forces which exercise
+such a powerful influence on our characters,
+our lives, our customs, which produce the
+<a name="png.100" id="png.100"></a><span class="ns">[</span><span
+ class="pgmark">88</span><span class="ns">]
+ </span>greatness of the State, or drag it down
+with irresistible strength from its pinnacle
+of glory to an abyss of degradation; to
+estimate such forces is the great and noble
+object of our lectures and researches in
+this University. Prosecute, most noble
+professors, your studies in this direction
+with all the energy of your enlightened
+intellects, and there is yet hope that this
+new science, which I have endeavoured to
+sketch out, however feebly, may be the
+means of saving our beloved nation from
+degradation and ruin, and raising her to
+a higher level of glory and honour. I
+hope to continue the subject of social
+forces in my next lecture.</p>
+
+
+<hr class="footnote" />
+<div class="footnote">
+<p><a href="#fna.6" name="fn.6" id="fn.6">6</a> A Chinese legend relates that a pious hermit,
+who in his watchings and prayers had often been
+overtaken by sleep, so that his eyelids closed, in
+holy wrath against the weakness of the flesh, cut
+them off, and threw them on the ground. But a
+god caused a tea-shrub to spring out of them, the
+leaves of which exhibit the form of an eyelid bordered
+with lashes, and possess the gift of hindering
+sleep.&mdash;Dr.&nbsp;<span class="smc">Ure</span>.</p>
+</div>
+
+
+
+
+<h2><a name="png.101" id="png.101"></a><span class="ns">[</span><span
+ class="pgmark">89</span><span class="ns">]<br
+ /></span>PAPER VI.</h2>
+
+<h3>ON SOCIAL FORCES (<i>continued</i>)&mdash;POLEMICAL
+STATICS AND DYNAMICS.</h3>
+
+
+<p class="noindent"><span class="smc">Most Noble Professors and Students
+of Girtham</span>,&mdash;We have embarked upon a
+stormy sea of speculation, on a voyage of
+grand discovery, and the dangerous waves
+of adverse criticism, and the deceptive
+under-current of prejudice, often make the
+steersman&#8217;s lot by no means an enviable
+one. But our vessel is sound and perfectly
+equipped, and therefore I do not fear to
+guide her across the great unknown.</p>
+
+<p>It may have occurred to you that the
+problems which present themselves for
+solution in social science are far more
+difficult and complicated than those which
+arise in ordinary mathematics. That is
+undoubtedly the case; but this extra
+degree of difficulty is due to the fact that
+<a name="png.102" id="png.102"></a><span class="ns">[</span><span
+ class="pgmark">90</span><span class="ns">]
+ </span>we make no assumptions; we take the
+things as they really are, not as they are
+assumed to be. In physical science, if
+we take into consideration the resistance
+of the air, the curvature of the earth, the
+rigid connection which exists between
+particles in the same body, and a host of
+other things which are often conveniently
+neglected in elementary works, how complicated
+the various problems become!
+So we must not be surprised at some of
+the difficulties which occur in social
+science, as nothing is neglected; the whole
+problem is before us, and having solved it
+we need not make allowances for any
+falsely assumed <i>data</i>.</p>
+
+<p>It is possible that other professors of
+this science may come to slightly different
+conclusions to those which I have arrived
+at. That is only to be expected, because
+their original observations may have
+slightly varied. But in physical science
+allowances are made for different observers.
+In astronomy, for example, we find the
+value of the &lsquo;Personal Equation.&rsquo; One
+observer on looking through the telescope
+<a name="png.103" id="png.103"></a><span class="ns">[</span><span
+ class="pgmark">91</span><span class="ns">]
+ </span>may take the meridian of a star rather
+differently from another watcher of the
+heavenly bodies, and the <em>personal equation</em>
+is used to make allowances for this
+quickness, or slowness, of observation.
+So in social science there must be a
+personal equation too, and our object
+ought to be, in the ordinary affairs of life
+as well as in the higher duties of scientific
+action, to make our personal equation as
+small as possible. But until the old
+proverb, &lsquo;<i>Quot homines, tot sententiæ</i>,&rsquo; has
+ceased to have any meaning, there will be
+abundant need of this most useful aid to
+accuracy.</p>
+
+<p>The close connection which exists between
+social forces and material forces is
+plainly shown by the doctrine of the conservation
+of energy. &lsquo;This doctrine,&rsquo; says
+Dr. Tyndall, &lsquo;recognises in the material
+universe a constant sum of power made
+up of items among which the most Protean
+fluctuations are incessantly going on. It
+is as if the body of nature were alive, the
+thrill and interchange of its energies resembling
+those of an organism. The
+<a name="png.104" id="png.104"></a><span class="ns">[</span><span
+ class="pgmark">92</span><span class="ns">]
+ </span>parts of the stupendous whole shift and
+change, augment and diminish, appear and
+disappear; while the total of which they
+are the parts remains quantitatively immutable,
+<em>plus</em> accompanies <em>minus</em>, gain
+accompanies loss, no item varying in the
+slightest degree without an absolutely
+equal change of some other item in the
+opposite direction.&rsquo; So do the forces in
+the social world ebb and flow, rise and
+fall, carrying on the same universal law
+which regulates the energy of material
+force.</p>
+
+<p>I will now proceed to enumerate some
+of those forces which exercise such a
+powerful influence on society.</p>
+
+<p>First, let us take the force of <em>Public
+Opinion</em>, which seems to exercise a relentless
+sway over the minds and manners of
+men. This is a very subtle and secret
+force, which is most difficult to trace, and
+resembles electricity in the science of
+physics. We cannot see it, but are only
+able to judge of its power by its results.
+Its point of application is not in the individual,
+but in the collection of individuals
+<a name="png.105" id="png.105"></a><span class="ns">[</span><span
+ class="pgmark">93</span><span class="ns">]
+ </span>who make up the social system; and it is,
+in reality, the resultant of, or the compromise
+between, the various elementary
+forces which make up human society.
+Yes, compromise is a purely mechanical
+affair, based on the principle of the parallelogram
+of forces; and as public opinion
+is the result of a compromise, we may
+calculate its force. For example: &lsquo;It is
+required to know the state of public
+opinion in the matter of politics, when
+the results of a General Election show
+that the Conservatives are to the Liberals
+as <span class="nw">10 : 9</span>.&rsquo;</p>
+
+<p>Let OC be the direction of the Conservative
+force.</p>
+
+<p>Let OL be that of the Liberal.</p>
+
+<p>Then by <i>data</i> <span class="nw">OC : OL :: 10 : 9</span>.</p>
+
+<p class="ctr"><img src="images/illus-105.png" width="270" height="110"
+  alt="Diagram: parallelogram with leading diagonal" title="" /></p>
+
+<p>Complete the parallelogram, and join
+OP.</p>
+
+<p><a name="png.106" id="png.106"></a><span class="ns">[</span><span
+ class="pgmark">94</span><span class="ns">]<br
+ /></span>Then OP represents the force of public
+opinion in magnitude and direction.</p>
+
+<p>N.B.&mdash;The direction of OL is determined
+by the amount of deviation of the
+policy of the Liberals from that of the
+Conservatives.</p>
+
+<p>As in physical, so in social science,
+impulsive forces sometimes act, and effectually
+disturb our system and our calculations.
+Public opinion is very liable to
+the action of disturbing forces. Panic is
+an impulsive force, which defies the power
+of the most learned professors of social
+science to determine its magnitude and
+direction. Some strange unforeseen catastrophe&mdash;the
+fascination caused by a brilliant
+and unscrupulous orator, a cruel wrong, a
+blind revenge for real or imaginary injustice&mdash;will
+sometimes rouse one element of
+passion latent in the vast body of public
+opinion; so that it breaks with all that
+hitherto restrained and balanced it, and
+precipitates society into a course of conduct
+inconsistent with its former behaviour,
+and bloodshed, revolution, the breaking-up
+of laws, are the terrible results of panic
+or revengeful passion.</p>
+
+<p><a name="png.107" id="png.107"></a><span class="ns">[</span><span
+ class="pgmark">95</span><span class="ns">]<br
+ /></span>Society is, as it were, split up by the
+terrible action of such impulsive forces,
+just as wood is split up by the repeated
+blows of the hatchet. It is, therefore, the
+duty of statesmen to increase the power
+or force of cohesion, to strengthen the
+fibres of the State, so that the force of
+such impulsive blows may not be felt, nor
+disturb the continuity of the framework
+of the State. If such measures had been
+adopted in the neighbouring country of
+France, much misery might have been
+avoided, and the terrible revolutions which
+have so frequently convulsed her social
+system entirely prevented.</p>
+
+<p><em>Friction</em> is another disturbing element
+in our calculations, and although it may
+be made a useful servant, it is a bad
+master in mathematics, as in polemics.
+Without the aid of friction, progress would
+be impossible. For example: Take the
+case of a man with perfectly smooth skates
+on perfectly hard, smooth ice; he would
+be unable to reach the land unless he had
+provided himself with some stones, by
+throwing which he would just be able to
+<a name="png.108" id="png.108"></a><span class="ns">[</span><span
+ class="pgmark">96</span><span class="ns">]
+ </span>get to his destination by a backward
+motion. The engine would be unable to
+proceed on its iron road if it were not for
+friction. The same is true in polemical
+science: the government of the country
+would not be able to be carried on under
+our present conditions if it were not for <em>party
+friction</em>. But suppose it increased indefinitely,
+party friction becomes party <em>obstruction</em>;
+and the engine of the State would no
+longer proceed smoothly and evenly along
+its appointed course at the rate of sixty
+miles an hour, but would resemble an old-fashioned
+coach, up to its axle-trees in
+mud, its motion altogether stopped by the
+action of party friction.</p>
+
+<p>We have seen that forces have two ways
+of acting: that of compelling rest and
+that of producing motion. In statics
+forces act so as to prevent any change
+of motion, or disturb the body&#8217;s original
+position. In kinetics, on the contrary,
+the power is recognised as acting so as
+to produce or change a body&#8217;s motion.
+Now, in polemical science we have these
+two ways of considering the action of
+<a name="png.109" id="png.109"></a><span class="ns">[</span><span
+ class="pgmark">97</span><span class="ns">]
+ </span>forces. There is the <em>statical</em> or <em>conservative</em>
+force, which compels rest, which seeks
+security, stability, and peace, and is not
+ardently devoted to change. It reduces
+the system to equilibrium. There are, of
+course, two kinds of equilibrium&mdash;<em>stable</em>
+and <em>unstable</em>&mdash;according as the social
+and political system is in a healthy or
+unhealthy state. If a body is in stable
+equilibrium, and any slight motion takes
+place, the body will return immediately to
+its former position; but if in unstable, it
+will decline further and further away from
+its original position, and be entirely upset.
+So a healthy and sound conservative equilibrium
+is not disturbed by outside forces,
+and the State will resume its former
+position of stability and rest when the
+opposing force is withdrawn. But an unhealthy
+and insecure conservatism is as
+easily disturbed as an egg balanced on its
+narrow end.</p>
+
+<p>The kinetics of society, that is to say
+the Radical way of estimating force, is
+the party of motion, generally supposed
+to be the &lsquo;party of progress.&rsquo; It has
+<a name="png.110" id="png.110"></a><span class="ns">[</span><span
+ class="pgmark">98</span><span class="ns">]
+ </span>therefore many attractions in the eyes
+of those who delight in motion, speed,
+and rushing about. To run at full speed,
+to feel the keen air upon one&#8217;s face, to
+experience the delightful sensation of
+freedom of will, and limb, are joys which
+cannot be denied. Such exercise is beneficial
+to the system, bodily or political.
+Motion is the life of all things; it is
+characteristic of nature; it adores nature;
+because it is an emblem and characteristic
+of life. The ceaseless rolling of the ocean
+waves, the swaying of the trees, the bending
+of the flowers, the waving of the corn,
+all these fill us with pleasure; whereas a
+flat uninteresting plain, unrelieved by the
+motion of terrestrial objects, is depressing
+to the spirit. So there is much to be said
+in favour of motion, and Carlyle has
+defined progress as &lsquo;living movement.&rsquo;
+And men love this &lsquo;living movement,&rsquo; and
+take up the Laureate&#8217;s cry:</p>
+
+<div class="stanza">
+<div class="indent6">&lsquo;Forward, forward, let us range,</div>
+<div>Let the great world spin for ever down the ringing</div>
+<div class="indent6">Grooves of change.&rsquo;</div>
+</div>
+
+<p class="noindent">But, after all, there is a danger in this
+<a name="png.111" id="png.111"></a><span class="ns">[</span><span
+ class="pgmark">99</span><span class="ns">]
+ </span>everlasting motion. We cannot tell
+whither this progress may lead. It may
+be along a safe sure road; but perchance
+a precipice may open out before us; and
+rejoicing in the acceleration of our
+velocity, with eyes intent upon some
+distant heights of glory and ambition, we
+may not discover our danger until it is too
+late to stop, and a terrible plunge into an
+unknown abyss of turmoil and tumultuous
+waves is the alarming result of an unguarded
+policy of unrestrained &lsquo;progress.&rsquo; I recall
+to my mind the quaint words of Holmes
+which aptly illustrate my contention.</p>
+
+<div class="stanza">
+<div>&lsquo;If the wild filly, &ldquo;Progress&rdquo;, thou would&#8217;st ride,</div>
+<div>Have young companions ever at thy side;</div>
+<div>But wouldst thou stride the staunch old mare, &ldquo;Success,&rdquo;</div>
+<div>Go with thine elders, though they please thee less.&rsquo;</div>
+</div>
+
+<p>Progress and success do not always go
+together hand in hand; and while motion
+is essential to life, it is not always safe to
+urge a country forward at too great a
+speed; and security and stability are quite
+as important to the nation&#8217;s life as actual
+progress.</p>
+
+<p>There are other impulsive forces which
+<a name="png.112" id="png.112"></a><span class="ns">[</span><span
+ class="pgmark">100</span><span class="ns">]
+ </span>act occasionally in the sphere of politics,
+and which baffle all our calculations, and
+exclude scientific considerations of the
+polemical problems which arise. <em>Ambition</em>
+is such an impulsive force, and when the
+rulers of the people are actuated by it,
+and struggle for money, place, and power,
+politics is degraded from its position as a
+science, and it becomes impossible to
+estimate the result of forces so generated.</p>
+
+<p class="pgbrk">In my next lecture I propose to treat
+the important subject of the Laws which
+govern States and Governments, and
+which regulate, generate, and control the
+social forces which we have seen at work
+in the body politic.</p>
+
+
+
+
+
+<h2><a name="png.113" id="png.113"></a><span class="ns">[</span><span
+ class="pgmark">101</span><span class="ns">]<br
+ /></span>PAPER VII.</h2>
+
+<h3>LAWS OF POLITICAL MOTION.</h3>
+
+
+<p class="noindent"><span class="smc">Since</span> the last time I had the honour of
+addressing you on polemical matters, I
+have met with a passage in the writings of
+M.&nbsp;Auguste Comte which afforded me
+much pleasure. It seemed to be the one
+word for which I had been waiting, and
+confirmed many of my own impressions
+and speculations. He lays down two
+propositions: first, that the constructive
+politics of the future must be based on the
+history of the past; and second, that
+political science is a composite study, and
+presupposes the complete apprehension of
+every branch of science, beginning with
+the physical, such as astronomy, and
+ending with the moral, such as ethics and
+sociology. M. Comte evidently does not
+regard as a vain dream and imaginative
+<a name="png.114" id="png.114"></a><span class="ns">[</span><span
+ class="pgmark">102</span><span class="ns">]
+ </span>speculation the theory that it will be
+possible for statesmen to calculate a
+policy, and to determine a course of
+action by purely scientific considerations.
+May I entertain the hope that in this
+university, where all branches of physical
+science have found a home, and are
+studied by most able and learned professors,
+the science of politics may be
+pursued under most favourable circumstances?
+I trust that each professor will
+bring before me the results of their
+deliberations, and contribute to the growth
+of this particular science for which our
+university has already become deservedly
+famous.</p>
+
+<p>My present lecture is devoted to the
+important consideration of <em>Law</em>. At first
+sight it may appear to you that the wills
+and passions of mankind are so diverse
+and unknowable, that it would be absurd
+to suppose that they can be calculated, or
+rendered amenable to any law. But Professor
+Amos has pointed out that in proportion
+as we examine history, and compare
+the actions present and past of different
+<a name="png.115" id="png.115"></a><span class="ns">[</span><span
+ class="pgmark">103</span><span class="ns">]
+ </span>nations and states, the more uniform does
+human nature appear; the more calculable
+the actions, sentiments, and emotions of
+large masses of people. As we have
+already stated, the difficulties of the study
+are not likely to deter the professors of
+Girtham College from the pursuit of any
+particular branch of science.</p>
+
+<p><i>A priori</i> we might suppose from analogy
+that these polemical laws existed, as there
+is no department of nature which is not
+governed by law. It is an essential feature
+in nature, and also in government.
+What is political economy but the study
+of certain laws of nature? These were
+first discovered by Adam Smith, and have
+since been traced and estimated by such
+men as Ricardo, the two Mills, Professor
+Cairnes, Jevons, and many others. Moreover,
+our physical constitutions are
+governed by laws, which physicians have
+determined, and which it is perilous to
+resist. Our moral constitution is also
+governed by laws, which evidently exist,
+although it is difficult to find them out.
+But the nation is only an assemblage of
+<a name="png.116" id="png.116"></a><span class="ns">[</span><span
+ class="pgmark">104</span><span class="ns">]
+ </span>individuals; and since individuals are
+so governed, it is only natural to suppose
+that the nation, composed of individuals,
+is so constituted and controlled. And
+not only is that true, but we shall see
+that polemical laws are as permanent and
+universal, as invariable and irreversible,
+as the laws of nature which regulate the
+courses of the heavenly bodies, and raise
+the tides, or depress the sandstone hills.</p>
+
+<p>We may notice first the preponderant
+impulse observable in a nation&#8217;s life in
+favour of supporting existing facts and
+institutions; and every reformer has
+discovered the difficulty and danger of
+changing or opposing the customs and
+habits of the people. As a wheel will
+travel most smoothly along a well-worn
+groove, whereby friction is diminished, so
+there is a natural national tendency always
+to run along those paths with which the
+habits and customs of the people have
+made them familiar. This law is nothing
+else than Newton&#8217;s first law of motion,
+which is quite as applicable to human
+masses as to lifeless matter. The
+<a name="png.117" id="png.117"></a><span class="ns">[</span><span
+ class="pgmark">105</span><span class="ns">]
+ </span>tendency of matter to remain at rest, if unmoved
+by any external agency, and of
+persisting to move after it has once been
+set in motion, is a conservative tendency;
+and is as true in political science as in
+any other.</p>
+
+<p>The special branch of our science,
+which we may call the <em>Biology of Politics</em>,
+shows how absolute is the domain of law
+in polemical matters. The law of human
+life is that men are born, grow, become
+strong and vigorous, and then decay and
+die. This is the law of life, to which
+we must all yield an enforced obedience.
+This same law is observed to be at work
+in the heavenly bodies; and astronomy
+shows us that planets are born, flourish,
+and at length die, just as our human
+bodies do. The moon is, as you may
+have observed, a dead planet, such as our
+earth may be some day. The same
+growth and decay are also manifest in
+national life. First, there is the birth of
+the nation, which sometimes lies a long
+time in a dormant state, and then wakes
+up to life and energy. China and Russia
+<a name="png.118" id="png.118"></a><span class="ns">[</span><span
+ class="pgmark">106</span><span class="ns">]
+ </span>are examples of dormant States, just
+waking from a long sleep of childishness
+and ignorance. The next stage is the
+strong an healthy period of its existence,
+which England is at present enjoying;
+and then, after various stages of gradual
+decline, we come to the senile period of
+national life, when every energy and
+faculty, every national feeling and power
+of invention, are completely exhausted.
+As an example of this depressing condition,
+we may mention Turkey and several
+of the effete States of South America.
+Sometimes, when life is nearly extinct in
+the human body, physicians have made
+use of the power of galvanism, in order to
+revive the dying energies. This process
+of galvanizing a State into life was tried
+by Lord Palmerston and others on the
+worn-out frame of Turkey. But such
+attempts can only meet with partial and
+transitory success; and where the loss of
+national power and faculty betokens the
+senile period of the nation&#8217;s existence, it
+is vain to attempt to restore its former
+life and energy. The study of the biology
+<a name="png.119" id="png.119"></a><span class="ns">[</span><span
+ class="pgmark">107</span><span class="ns">]
+ </span>of politics presents many interesting and
+important details in this special branch
+of knowledge; and I commend this part
+of our subject to the special attention of
+the professor of physiology. The law of
+development is observable in nations as
+in nature. Recent scientific discoveries
+have tended to take away all ideas of
+<em>chance</em> in the workings of nature, and have
+substituted <em>law</em> instead of it. It would
+be unscientific and incorrect to speak of
+the world being formed by the &lsquo;fortuitous
+concourse of atoms.&rsquo; So we cannot speak
+of a State being generated in this manner.
+Laws&mdash;economical, geographical, natural&mdash;preside
+over the formation of States and
+nations, and produce their further development.</p>
+
+<p>The laws of political motion occupy
+the same prominent place in our new
+science as Newton&#8217;s laws do in ordinary
+dynamics. These are very important in
+calculating the positions which various
+States will occupy in the future. First,
+we have the <em>doctrine of nationality</em>, which
+prevented the progress of Austria into
+<a name="png.120" id="png.120"></a><span class="ns">[</span><span
+ class="pgmark">108</span><span class="ns">]
+ </span>Italy, and of the Bourbons in Naples, and
+produced the amalgamation of the small
+German States in the great empire of
+Germany. The second law of political
+motion is the doctrine of the <em>independence</em>
+of all true States, and the equality
+of all States to each other. This had its
+growth in feudalism; and all the chief
+wars of modern times have been the result
+of the efforts of nature to establish this
+law of independence. The doctrine of
+intervention is a modification of the preceding
+law, and is applicable when the
+law of necessity demands its use, such as
+the restoration of order after protracted
+anarchy, the abolition of slave trade, etc.
+The third law is the <em>law of morality</em>.
+Just as for each man there exists a <em>right</em>
+and a <em>wrong</em>; just as <em>duty</em> and <em>conscience</em>
+are certain elements in his daily motion,
+which dictate his course of action,
+although he may chose to neglect them;
+so a nation is bound by the same moral
+laws which govern the individual; and
+a nation errs if it transgresses them.
+Christianity is the agent which has
+<a name="png.121" id="png.121"></a><span class="ns">[</span><span
+ class="pgmark">109</span><span class="ns">]
+ </span>produced so powerful an influence in making
+men obey the dictates of conscience and
+walk in the path of duty; and I read
+with thankfulness the conclusion of Mr.
+Amos, that Christianity has triumphed
+quite as much in moralizing secular
+politics as it has in the sphere of individual
+life.</p>
+
+<hr class="tb" />
+
+<p>These are some of the principal laws of
+motion which I have observed at work in
+various States and nations. Inasmuch as
+political science embraces, in addition to
+the physical sciences, all those branches
+which are contained in ethics, economics,
+jurisprudence, sociology and others, the
+laws of each are generally applicable to the
+whole grand subject of which my lectures
+treat. Other general laws may be deduced,
+and have been enumerated in my previous
+lectures, from the social properties of curves
+and conics; and when our researches are
+complete we may hope to produce a code
+of laws for the guidance of our statesmen
+which maybe of immense use in determining
+<a name="png.122" id="png.122"></a><span class="ns">[</span><span
+ class="pgmark">110</span><span class="ns">]
+ </span>the policies of the future. Already
+there is strong evidence that the affairs of
+this country are being conducted on sound
+scientific principles, rather than by any
+species of guess-work or haphazard contrivances.
+The use of history is recognised
+as extremely important in determining
+a future line of conduct; and statesmen
+are in the habit of endeavouring to find
+from their study of the past what is the
+logical sequence of events. Just as mathematicians
+endeavour to determine the law
+of a series of figures, and having found the
+law, can write down the next, and the next,
+<i>ad infinitum</i>; so scientific politicians may
+be able soon to establish the various laws
+of a series of events, and calculate their
+course of actions. That there is considerable
+progress in this direction is manifest
+by the value which they place upon statistics,
+and their continued use of this important
+information.</p>
+
+<p>There are a few great evils in our present
+system which are strongly opposed to any
+scientific methods in politics; and in the
+interests of the country as well as those of
+<a name="png.123" id="png.123"></a><span class="ns">[</span><span
+ class="pgmark">111</span><span class="ns">]
+ </span>science they ought to be removed. One
+great evil is the want of political and
+scientific knowledge on the part of the
+electors, who are in the habit of choosing
+their representatives on personal grounds,
+or party considerations, rather than on
+sound principles of political science. All
+this is opposed to any idea of law. Owing
+to the ignorance of the electors they fall an
+easy prey to adventurers and unprincipled
+politicians, who make all kinds of specious
+promises, tempt them with all manner of
+baits, and make self-interest instead of the
+welfare of the State the principle of voting.
+Selfishness is the ruin of social life and intercourse,
+the destroyer of all happiness,
+peace, and mutual trust in family life or in
+society. It is the root of most of the faults,
+vices, and crimes in the individual; and
+who can tell the endless disasters which
+will befall the State, where selfishness is the
+chief motive-power of the electors and the
+elected? A selfish statesman, one who goes
+into Parliament to gain his own ends and
+forward his own personal interests, is a disgrace
+to society&mdash;</p>
+
+<div class="stanza">
+<div><a name="png.124" id="png.124"></a><span class="ns">[</span><span
+ class="pgmark">112</span><span class="ns">]<br
+ /></span>&lsquo;Feeling himself, his own low self, the whole,</div>
+<div>When he by sacred sympathy might make</div>
+<div>The whole one self. Self, that no alien knows!</div>
+<div>Self, far diffused as fancy&#8217;s wing can travel!</div>
+<div>Self, spreading still, oblivious of its own,</div>
+<div>Yet all of all possessing!&rsquo;</div>
+</div>
+
+<p>I have said that the ignorance of the
+electorate makes them an easy prey to such
+men; and until they have learnt to detect
+the false from the true, until they become
+acquainted with the elements of political
+science, and have been taught that their
+own selfish interests are not the highest
+aims of social government, it is vain to
+hope for a reasonable method of regulating
+the affairs of the nation, based upon
+logical laws and scientific principles.</p>
+
+<p>And how is this work of educating the
+electors to be accomplished? Not, I
+maintain, by furious speeches and rhetorical
+displays; not by bribery, baits and
+banter; but by patient, never-ceasing
+labour, by lectures on history and science,
+by individual instruction, is the great work
+to be accomplished upon which the security
+and stability of the country depend.</p>
+
+<p class="pgbrk">Then we may hope that the &lsquo;Reign of
+<a name="png.125" id="png.125"></a><span class="ns">[</span><span
+ class="pgmark">113</span><span class="ns">]
+ </span>Law&rsquo; in polemical science may be ushered
+in with the joyful acclamations of an enlightened
+and united people, and its benign
+influence extend from the throne of the
+monarch and the council-chamber of his
+ministers to the hearth of the cottager.
+Politicians will rule by law; policies be calculated
+by laws; people vote by law; and
+then methinks I see in my mind (to use
+the words of the blind old poet) a noble
+and puissant nation rousing herself like a
+strong man after sleep, and shaking her invincible
+locks; methinks I see her as an
+eagle, renewing her mighty youth, and kindling
+her undazzled eyes at the full mid-day
+beam; purging and unsealing her long-abused
+sight at the fountain itself of
+heavenly radiance; while the whole noise
+of timorous and flocking birds flutter about
+amazed at what she means. Such is the
+glorious vision of the &lsquo;Reign of Law.&rsquo; Let
+it be the business of every Englishman and
+Englishwoman to arrange the framework of
+our social and political system, that law
+may have an uninterrupted sway; then
+shall we be a united, prosperous, and
+<a name="png.126" id="png.126"></a><span class="ns">[</span><span
+ class="pgmark">114</span><span class="ns">]
+ </span>contented people, and the reign of lawless
+agitators, bribery-mongers, and counterfeit
+statesmen will have passed away into the
+oblivion and obscurity of a more suitable
+but less favoured region.</p>
+
+
+
+
+<h2><a name="png.127" id="png.127"></a><span class="ns">[</span><span
+ class="pgmark">115</span><span class="ns">]<br
+ /></span>PAPER VIII.</h2>
+
+<h3>ON THE PRINCIPLE OF POLEMICAL COHESION.</h3>
+
+
+<p class="noindent"><span class="smc">In</span> my previous lectures I have had occasion
+to mention the principle of cohesion;
+but it plays so vital a part in the constitution
+of States and their relations to each
+other that I consider it advisable to devote
+this lecture entirely to it.</p>
+
+<p>This is a large and comprehensive
+subject, and embraces such principles as
+the Centralization of States; the Co-operation
+of States; Monogamic Marriage;
+Unions; Free Trade, and many
+others equally important. We have
+already noticed that cohesion is a well-known
+property of matter; that its
+influence is not confined to the regions of
+physical sciences; and that it is the
+<a name="png.128" id="png.128"></a><span class="ns">[</span><span
+ class="pgmark">116</span><span class="ns">]
+ </span>manifest duty of all governments to increase
+the force of cohesion.</p>
+
+<p>Various methods have been tried to
+accomplish this purpose. The principle
+of Feudalism was one of the earliest
+attempts to produce the cohesion of the
+nation; and, in an elementary condition of
+society, it was partly successful. The
+theories of &lsquo;Divine Right&rsquo; and &lsquo;Social
+Contract&rsquo; were other methods which have
+been adopted; and the unity of the
+Christian Church has been the great
+means of producing the cohesion of the
+State in olden times; and its aid may be
+again required for the same beneficent
+object in future complications and social
+disruptions.</p>
+
+<p>But it is always advantageous in scientific
+pursuits to go back to first principles; and
+we will adopt that method in our present
+investigations. The social unit is the
+family; the multiplication of families
+makes the tribe; the multiplication of
+tribes makes the State; and, therefore, we
+shall not be far wrong if we consider the
+family tie as the first principle of political
+<a name="png.129" id="png.129"></a><span class="ns">[</span><span
+ class="pgmark">117</span><span class="ns">]
+ </span>cohesion. I am in agreement with several
+learned thinkers upon this subject when
+I say that marriage is a most important
+political factor; and as marriage cannot
+take place without women, it is evident
+that women play a very important part in
+promoting the cohesion of the State.</p>
+
+<p>This prominent position was duly
+assigned to women by one of our greatest
+political philosophers, M.&nbsp;Auguste Comte,
+who strongly opposed the fatal fallacy of
+ancient political systems, which greatly
+overestimated the powers of men, and
+depreciated those of women. If the
+superiority of bodily strength be the sole
+cause of greatness in political and intellectual
+pursuits, then, most noble lords of
+creation, we yield to you the palm&mdash;you
+are our masters in this respect. But if, on
+the other hand, it can be shown that
+physical strength is not a requisite for
+great achievements in these occupations;
+if the powers of endurance, elasticity,
+adaptability, nervous energy, and patience
+are quite as needful as mere animal
+strength; then we women are quite as
+<a name="png.130" id="png.130"></a><span class="ns">[</span><span
+ class="pgmark">118</span><span class="ns">]
+ </span>capable, and indeed more capable than
+men, for achieving political greatness. In
+the &lsquo;good old days,&rsquo; when the law of
+might was right, and the strongest arm was
+the most powerful machinery in the
+government of the country, women were
+compelled naturally to occupy a less prominent
+position in the conduct of the
+affairs of the nation; and for centuries
+they have been degraded by a dominating
+tradition, and supposed incapable of
+performing duties for which they were
+mentally well suited. But those militant
+days are past. Animal strength and
+brute force are no longer needed in the
+councils of the nation; and the time has
+arrived when women should cease to be
+oppressed by the disparaging, illogical
+deductions of former generations, and
+when their assistance ought to be invoked
+in the great work of promoting the
+nation&#8217;s welfare.</p>
+
+<p>I have stated that marriage is an important
+political factor; and, therefore,
+women have always occupied a primary,
+though obscure, part in political affairs.
+<a name="png.131" id="png.131"></a><span class="ns">[</span><span
+ class="pgmark">119</span><span class="ns">]
+ </span>The cohesion of the State has been
+produced by the secret influence of
+family life. But it may be asked, What
+kind of marriage is most conducive to
+national cohesion? This question has
+been carefully and conclusively answered
+by a learned scientific writer, who shows
+that polygamic marriage never exists in an
+advanced state, as instanced by the
+history of Judaism and Mohammedanism;
+that a strict form of monogamic marriage
+is essential to political greatness and true
+progress in civilization. The cohesion of
+the State is destroyed by polygamy, and
+by any system which relaxes the binding
+nature of the marriage tie. &lsquo;Domestic
+disorganization is a sure augury of political
+disruption.&rsquo;</p>
+
+<p>Cohesion, the essential property of all
+rightly constituted nations, is often in
+danger of being lost when the State is
+geographically very large, or when local
+interests have greater power than the
+attractive force of the central government.
+To obviate this evil, the method of centralization
+has been adopted with satisfactory
+<a name="png.132" id="png.132"></a><span class="ns">[</span><span
+ class="pgmark">120</span><span class="ns">]
+ </span>results, as in the case of the United States
+of America, and Germany.</p>
+
+<p>By this means the local authorities are
+brought into close relationship with the
+central head, and the centrifugal influences
+of independent interests and customs
+are counteracted by the force of
+central attraction. Centralization increases
+the importance of the whole body, and,
+like the pendulum of a clock, regulates the
+movements of the whole State. In some
+cases it tends to make the government
+despotic, when the local governments are
+entirely under the control of the central;
+and every enactment, and scheme, and
+plan checked and supervised by the chief
+officers of the State. Such was the system
+adopted in France by Napoleon&nbsp;III.
+But cohesion without the enforcement of
+a hard and rigid connection, a general
+supervision without severe tyrannical jurisdiction,
+are the best methods of securing
+the unity of composite States.</p>
+
+<p>But the force of cohesion is evidently
+at work in the nation apart from centralization.
+Men who have a community of
+<a name="png.133" id="png.133"></a><span class="ns">[</span><span
+ class="pgmark">121</span><span class="ns">]
+ </span>interests unite together for the purposes of
+strength and mutual assistance. They
+combine for the sake of securing means
+of support in sickness, and form benefit
+societies, such as the Order of Oddfellows
+or Foresters. This force of cohesion has
+produced trade unions, and similar institutions
+which exist for the purpose of
+protecting a common interest, and giving
+expression to the concurrent opinions of
+the members. These have their legitimate
+use in every civilized State, in spite of
+some of the disadvantages which follow in
+their train. There are, of course, opposed
+interests in every community: <em>attractive</em>
+forces, which produce trade unions,
+guilds, corporations, companies, and the
+like; and <em>repulsive</em> forces, which result
+from the opposed interests of employers
+and employed, landlords and tenants, and
+similar pairs of different classes in the
+community. As time goes on, and the
+State advances with it, these forces will
+gain in strength; the cohesion of classes
+will become greater; association will grow
+as naturally as the bubbles form on the
+<a name="png.134" id="png.134"></a><span class="ns">[</span><span
+ class="pgmark">122</span><span class="ns">]
+ </span>surface of our evening beverage. It is a
+law of nature, and therefore cannot be
+resisted. But the repulsive forces will be
+no less strong, and to calculate the
+resultant of these contending interests will
+be the problem for practical statesmen to
+solve.</p>
+
+<p>The force of cohesion is also evidently
+at work, not only in individual States, but
+also amongst the nations of Europe, and
+of the world. That is to say, there is an
+evident desire for co-operation on the part
+of those nations who have attained to the
+highest degree of civilization and internal
+cohesion. International law is based on
+the principle of cohesion, and every day it
+is gaining power and favour in the eyes of
+our leading statesmen. The doctrine of
+Free Trade, which, if universally adopted,
+would be of the greatest service to mankind,
+results from a desire for co-operation;
+and whatever evils may result from one-sided
+Free Trade in this country at the
+present time, there can be no doubt that
+ultimately the complete system will be
+adopted.</p>
+
+<p><a name="png.135" id="png.135"></a><span class="ns">[</span><span
+ class="pgmark">123</span><span class="ns">]<br
+ /></span>Sad is the fate of a nation when the
+force of cohesion is weakened. The first
+revolution in France is a proof of this
+assertion; there was no cohesion, no common
+faith, or loyalty to the throne and
+Government; and indeed the Government,
+which was rotten to the core, was
+hardly likely to awake any feelings of
+loyalty and respect; and therefore the
+social disruption which followed was only
+a natural sequence of events, and was
+prophesied with the accuracy with which
+an astronomer can foretell an eclipse.
+But that is not all; when the cohesion of
+the State is destroyed, it takes a long time
+to restore the action of the force; and, as
+in the case of France, further disruption is
+sure to take place.</p>
+
+<p>In this lecture I have already enumerated
+some of the ways in which this force
+acts; there are doubtless others which
+will suggest themselves to you. But I
+contend that the prosperity of the State,
+and the peace of the world, depend upon
+cohesion. Let this be your work, most
+noble professors, to promote the action of
+<a name="png.136" id="png.136"></a><span class="ns">[</span><span
+ class="pgmark">124</span><span class="ns">]
+ </span>this helpful and life-giving force. Promote,
+as far as in you lies, the sacred
+union of family life. Encourage the
+generous feelings of true loyalty and
+patriotism amongst the people of this
+realm of England; counsel our statesmen
+with regard to the primary necessity of
+national cohesion, and the advantages of
+international co-operation; and your work
+will be blessed; your names will rank with
+those heroes of the sword and of the pen
+who have raised our beloved country to
+her present pinnacle of greatness and
+prosperity; and your memory will live in
+the hearts of your grateful countrymen.</p>
+
+<p class="above2">[<span class="smc">Editorial Note.</span>]&mdash;We regret to state
+that the various MSS. in the sealed desk
+are nearly exhausted, and are therefore
+compelled to present the series of lectures
+on polemical studies in an incomplete
+form. But we had the good fortune to
+light upon a brief diary which discloses
+some interesting information with regard
+to the Author&#8217;s life and occupations. We
+append a few extracts:</p>
+
+<h3 class="smc"><a name="png.137" id="png.137"></a><span class="ns">[</span><span
+ class="pgmark">125</span><span class="ns">]<br
+ /></span>Extracts from the Author&#8217;s Diary.</h3>
+
+
+<p><i>June 3rd</i>.&mdash;Arnold called again to-day&mdash;the
+fifth time during the last fortnight!
+His attention is rather overpowering, and
+wastes much of my valuable time. He
+says he hates science&mdash;the heathen!&mdash;and
+wants me to lecture in classics. He affirms
+that mathematics are dry and hard&mdash;too
+hard for women, and tend to make them
+unsympathetic and critically severe. I am
+afraid I was rather severe with him. But
+really he is very trying, and always seems
+to talk like a Greek chorus in the most
+profound platitudes. Arnold is a classical
+tutor at Clare College. My old pupil
+is getting on famously. Poor fellow! he
+seems quite oppressed with his work. But
+he is making great progress, and sticks
+to his books like&mdash;a student of Girtham
+College!</p>
+
+<p><i>June 4th</i>.&mdash;Lectured on the Scientific
+Basis of Blackstone&#8217;s Commentaries; afterwards
+received pupils until 1 p.m. Really
+Blanch <span class="nw">S&mdash;&mdash;</span> is more tiresome than ever.
+<a name="png.138" id="png.138"></a><span class="ns">[</span><span
+ class="pgmark">126</span><span class="ns">]
+ </span>It appears that she has taken up with a
+young undergraduate of King&#8217;s, and there
+is no prospect of any improvement in her
+work unless this nonsense is terminated.
+How foolish some of my sex are, in spite of
+their improved opportunities! I blush for
+them! Arnold has sent me a copy of Robert
+Browning&#8217;s &lsquo;Belaustion,&rsquo; in order to make
+me like classics, and give up science.
+Misguided young man! He has written
+some tolerable verses on the fly-leaf; but
+I have no intention of playing Belaustion
+to his &lsquo;entranced youth.&rsquo; These are his
+verses:</p>
+
+<div class="stanza">
+<div>&lsquo;My lady dear, if I may call you so,</div>
+<div>For you are dearer than all else beside,</div>
+<div>I know the love you bear to golden verse,</div>
+<div>To golden thoughts enshrined in classic lore,</div>
+<div>To all that&#8217;s beautiful; so here I send</div>
+<div>Some echoes of the songs of ancient days,</div>
+<div>Attuned and chanted by an English bard,</div>
+<div>Who fires one&#8217;s old love for the rolling lines</div>
+<div>Of youthful Hellas; may your cultured ear</div>
+<div>Receive, and gladly welcome his sweet song.</div>
+<div>And while we revel in the poet&#8217;s dream,</div>
+<div>And hear his actors speak, we&#8217;ll play our parts.</div>
+<div>You, sweet Belaustion on the temple-steps,</div>
+<div>Taking your captors captive by your voice;</div>
+<div>And I, the youth who, more entranced than all,</div>
+<div>Was bound by fetters that he would not loose;</div>
+<div>And so we&#8217;ll play our part. What say you, dear?&rsquo;</div>
+</div>
+
+<p><a name="png.139" id="png.139"></a><span class="ns">[</span><span
+ class="pgmark">127</span><span class="ns">]<br
+ /></span><i>June 6th</i>.&mdash;Have just seen our new
+Professor of Physics, Amelia Cordial, who
+is an excellent woman, and well suited for
+the high office which she holds. She has
+told me of the foolish conduct of Lady
+Mary, who is evidently of opinion that
+the professorial mantle ought to have
+fallen on her shoulders. Really, this
+jealousy in the ranks of the learned is
+most disgraceful; and the bickerings which
+arise from disappointed ambition, the envyings
+and silly quarrels, are the weak places
+in our female collegiate system.</p>
+
+<p>Such good news! The wrangler list is
+just out, and my hard-working pupil is
+<em>bracketed twelfth!</em> This is really delightful,
+and abundantly repays us for all our
+hard toil. But really I have not found
+working with him distasteful; he is such
+an excellent pupil, so painstaking and
+eager, that I have quite looked forward to
+his coming, and found him much more
+interesting than some of these foolish
+maidens. But I almost dread seeing him.
+He will be so elated and overpoweringly
+grateful, whereas I ought to be grateful to
+<a name="png.140" id="png.140"></a><span class="ns">[</span><span
+ class="pgmark">128</span><span class="ns">]
+ </span>him for all his work for me; for I am sure
+he would never have gone in for the Tripos
+if I had not persuaded him. Well, I
+wonder why he does not come to tell me
+of his triumph.</p>
+
+<p><i>June 7th</i>.&mdash;<em>It</em> has come! and I half
+expected it. My eager pupil writes with
+all the energy and love of his noble nature
+to ask me to be his wife! He says <em>that</em>
+is all he cares for, and only values his
+Honours as a step to a higher honour and
+dignity, that of gaining my love and being
+my husband. All this is very nice to read;
+but a terribly difficult problem is placed
+before me for solution. I do indeed love
+this dear, good fellow&mdash;no one could help
+doing so, I am sure; but do I not love
+science more? There is a stringent regulation
+in this University that no one shall
+occupy the position of professor who is
+bound by any domestic ties or cares. All
+married women are excluded. If I say
+&lsquo;Yes,&rsquo; I must resign my high position,
+leave this beloved college, give no more
+lectures to entranced audiences. In the
+interests of science, ought I to refuse, and
+<a name="png.141" id="png.141"></a><span class="ns">[</span><span
+ class="pgmark">129</span><span class="ns">]
+ </span>sacrifice my heart&#8217;s affections for the cause
+of mathematics? But if I say &lsquo;No,&rsquo; I
+must give up&mdash;<em>him</em>; sacrifice his happiness
+too, and blight his life. Was ever
+anyone so perplexed? Science, aid thine
+obedient servant! May I not determine
+this vital question by thine all-pervading
+light?&hellip;</p>
+
+<p class="tbstars">* * * * *</p>
+
+<p>[<span class="smc">Editorial Note.</span>]&mdash;We had just arrived
+at this exciting moment in the life
+of the learned and accomplished lady
+whose writings form the subject of these
+pages&mdash;a moment when love and science
+were trembling in the balance&mdash;when a
+footstep was heard upon the stairs leading
+to our study, and ere we could secrete our
+MS. the door was opened, and a well-known
+voice exclaimed:</p>
+
+<p>&lsquo;I do not know why you should have
+become so studious lately, Ernest, and
+why you should refuse to take me into
+your confidence. You spend hours and
+hours in this room all by yourself, writing
+away, and never say a word to me about
+the subject of your literary work. There
+<a name="png.142" id="png.142"></a><span class="ns">[</span><span
+ class="pgmark">130</span><span class="ns">]
+ </span>was a time when things were different, and
+you were not so slow in availing yourself
+of my help, and asking my advice.&rsquo;</p>
+
+<p>We murmured something about taking
+up the pen which had been laid aside by
+a far abler hand, and our deep gratitude
+for past assistance in our work, which could
+never be forgotten.</p>
+
+<p>&lsquo;And do you think that I cannot help
+you now?&rsquo; our visitor replied, in a very
+injured tone of voice. &lsquo;Is the old power
+dead, because it has not recently been
+used? Ernest, I think you very ungrateful
+not to confide in me. Come, tell me
+what you are writing.&rsquo;</p>
+
+<p>A suggestion about the proverbial
+curiosity of women rose to our lips, but
+died away without utterance. In the
+meantime, her eyes wandered over our
+study-table strewed with papers, and lighted
+upon the well-worn desk.</p>
+
+<p>&lsquo;Why, Ernest, where did you find this?
+My dear old desk, which has been lost
+ever so long! I do believe you have been
+ransacking its contents! Why did you
+<a name="png.143" id="png.143"></a><span class="ns">[</span><span
+ class="pgmark">131</span><span class="ns">]
+ </span>not tell me that you had found it? What
+are you doing with my papers, sir?&rsquo;</p>
+
+<p>The mischief was out! We tried to
+explain that the world ought not to be
+deprived of that which would benefit mankind;
+that the peace and prosperity of
+the country might be sacrificed if it were
+deprived of these discoveries of science,
+which were calculated to secure such beneficial
+results.</p>
+
+<p>At length we gained our point, and obtained
+the full sanction of the late Lady
+Professor of Girtham College to publish
+her papers. Thus her obedient pupil is
+enabled to repay his late instructress for
+all her kindness to him, and in some
+measure to compensate the scientific and
+political world for the loss of one of its
+most original investigators in the regions
+of polemical studies, which, not without a
+struggle, she resigned when she deigned
+to become his wife.</p>
+
+<p class="ctr above4"><small>THE END.</small></p>
+
+</div>
+
+<p class="ctr above4 pgbrk"><small><i>Elliot Stock, Paternoster Row, London.</i></small></p>
+
+<hr class="pg" />
+
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's The Romance of Mathematics, by P. Hampson
+
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+</body>
+</html>
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@@ -0,0 +1,2794 @@
+The Project Gutenberg EBook of The Romance of Mathematics, by P. Hampson
+
+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: The Romance of Mathematics
+       Being the Original Researches of a Lady Professor of Girtham
+       College in Polemical Science, with some Account of the Social
+       Properties of a Conic; Equations to Brain Waves; Social Forces;
+       and the Laws of Political Motion.
+
+Author: P. Hampson
+
+Release Date: August 29, 2008 [EBook #26481]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE ROMANCE OF MATHEMATICS ***
+
+
+
+
+Produced by David Wilson and the Online Distributed
+Proofreading Team at https://www.pgdp.net (This file was
+produced from images generously made available by The
+Internet Archive/Canadian Libraries)
+
+
+
+
+
+
+
+
+
+                              THE
+                    ROMANCE OF MATHEMATICS.
+
+
+
+
+                              The
+                    Romance of Mathematics:
+
+                             BEING
+                    THE ORIGINAL RESEARCHES
+                               OF
+              A LADY PROFESSOR OF GIRTHAM COLLEGE
+                               IN
+      _Polemical Science, with some Account of the Social
+           Properties of a Conic; Equations to Brain
+               Waves; Social Forces; and the Laws
+                     of Political Motion._
+
+
+                               BY
+                       P. HAMPSON, M.A.,
+                     ORIEL COLLEGE, OXFORD.
+
+
+                            LONDON:
+               ELLIOT STOCK, 62, PATERNOSTER ROW.
+                             1886.
+
+
+
+
+INTRODUCTION.
+
+
+The lectures, essays, and other matter contained in these pages have
+been discovered recently in a well-worn desk which was formerly the
+property of a Lady Professor of Girtham College; and as they contain
+some original thoughts and investigations, they have been considered
+worthy of publication.
+
+How they came into the possession of the present writer it is not his
+intention to disclose; but inasmuch as they seemed to his unscientific
+mind to contain some important discoveries which might be useful to the
+world, he determined to investigate thoroughly the contents of the
+mysterious desk, and make the public acquainted with its profound
+treasures. He found some documents which did not refer exactly to the
+subject of 'Polemical Mathematics;' but knowing the truth of the Hindoo
+proverb, 'The words of the wise are precious, and never to be
+disregarded,' and feeling sure that this Lady Professor of Girtham
+College was entitled to that appellation, he ventured to include them in
+this volume, and felt confident that in so doing he would be carrying
+out the intention of the Authoress, had she expressed any wishes on the
+subject. In fact, as he valued the interests of the State and his own
+peace of mind, he dared not withhold any particle of that which he
+conceived would confer a lasting benefit on mankind.
+
+Internal evidence seems to show that the earlier portion of the MS. was
+written during the period when the authoress was still _in statu
+pupillari_; but her learning was soon recognised by the Collegiate
+Authorities, and she was speedily elected to a Professorship. Her
+lectures were principally devoted to the abstruse subject of Scientific
+Politics, and are worthy of the attention of all those whose high duty
+it is to regulate the affairs of the State.
+
+The Editor has been able to gather from the varied contents of the desk
+some details of the Author's life, which increase the interest which her
+words excite; and he ventures to hope that the public will appreciate
+the wisdom which created such a profound impression upon those whose
+high privilege it was to hear the lectures for the first time in the
+Hall of Girtham College.
+
+
+
+
+CONTENTS.
+
+
+  PAPER                                                             PAGE
+    I. Some Remarks on Female Education:
+
+         Cambridge Man's Powers of Application.--Torturing Ingenuity
+         of Examiners.--Slaying an Enemy.--'Concentration.'--
+         'Tangential Action.'--'Gravity'                               1
+
+   II. Lecture on the Theory of Brain Waves and the Transmigration
+       and Potentiality of Mental Forces                              15
+
+  III. The Social Properties of a Conic Section, and the Theory of
+       Polemical Mathematics:
+
+        'Circle.'--'Parabola.'--'Ellipse.' 'Eccentricity of Curves'   25
+
+   IV. The Social Properties of a Conic Section (_continued_):
+
+        'Ellipse.'--Most favoured State.--Alarming Result of
+         Suppression of House of Lords.--Analogies of Nature.--
+         Directrix.--Contact of Curves and States.--'Hyperbola.'--
+         Problems.--Radical Axis and Patriotism.--Extension of
+         Franchise to Women.--Correspondence                          39
+
+    V. Social Forces, with some Account of Polemical Kinematics:
+
+         The Use of Imagination in Scientific Discovery.--Kinetic and
+         Potential Energy.--Social Statics and Dynamics.--Attractive
+         Forces.--Cohesion.--Formation of States.--Inertia.--Dr.
+         Tyndall on Social Forces                                     71
+
+   VI. Social Forces (_continued_): Polemical Statics and Dynamics:
+
+        'Personal Equation.'--Public Opinion, how calculated.--
+         Impulsive Forces.--Friction.--Progress                       89
+
+  VII. Laws of Political Motion:
+
+         M. Auguste Comte on Political Science.--First Law of
+         Motion.--The Biology of Politics.--Stages of Growth and
+         Decay of States.--Doctrine of Nationality.--Doctrine of
+         Independence.--Law of Morality.--Ignorance of Electors and
+         Selfishness of Statesmen opposed to Action of Law.--Final
+         'Reign of Law'                                              101
+
+ VIII. The Principle of Polemical Cohesion:
+
+         Centralization.--Co-operation of States.--Marriage.--Trade
+         Unions.--International Law                                  115
+
+       Extracts from the Diary of the Lady Professor                 125
+
+       Conclusion                                                    129
+
+
+
+
+PAPER I.
+
+SOME REMARKS OF A GIRTHAM GIRL ON FEMALE EDUCATION.
+
+
+[_This essay upon Female Education was evidently written when the future
+Professor of Girtham College was still in the lowlier condition of
+studentship, before she attained that eminence for which her talents so
+justly entitled her. Its unfinished condition tends to show that it was
+probably evolved during moments of relaxation from severer studies,
+without any idea of subsequent publication._]
+
+Oh, why should I be doomed to the degradation of bearing such a foolish
+appellation! A Girtham Girl! I suppose we have to thank that fiend of
+invention who is responsible for most of the titular foibles and follies
+of mankind--artful Alliteration. The two _G_'s, people imagine, run so
+well together; and it is wonderful that they do not append some other
+delectable title, such as 'The Gushing Girl of Girtham,' or 'The Glaring
+Girl of Glittering Girtham.' O Alliteration! Alliteration! what crimes
+have been wrought in thy name! Little dost thou think of the mischief
+thou hast done, flooding the world with meaningless titles and absurd
+phrases. How canst thou talk of 'Lyrics of Loneliness,' 'Soliloquies of
+Song,' 'Pearls of the Peerage'? Why dost thou stay thine hand? We long
+for thee to enrich the world with 'Dreams of a Dotard,' the 'Dog
+Doctor's Daughters,' and other kindred works. Exercise thine art on
+these works of transcendent merit, but cease to style thy humble, but
+rebellious, servant a Girtham Girl!
+
+But what's in a name? Let the world's tongue wag. I am a student, a
+hard-working, book-devouring, never-wearied student, who burns her
+midnight oil, and drinks the strong bohea, to keep her awake during the
+long hours of toil, like any Oxford or Cambridge undergraduate. I often
+wonder whether these mighty warriors in the lists--the class lists, I
+mean--really work half so hard as we poor unfortunate 'Girls of
+Girtham.' Now that I am writing in strict confidence, so that not even
+the walls can hear the scratchings of my pen, or understand the meaning
+of all this scribbling, I beg to state that I have my serious doubts
+upon the subject; and when last I attended a soiree of the
+Anthropological Society, sounds issued forth from the windows of the
+snug college rooms, which could not be taken as evidences of profound
+and undisturbed study.
+
+Sometimes I glance at the examination papers set for these hard-working
+students, in order that they may attain the glorious degree of B.A., and
+astonish their sisters, cousins, and aunts by the display of these magic
+letters and all-resplendent hood. And again I say in strict confidence
+that if this same glorious hood does not adorn the back of each
+individual son of Alma Mater, he ought to be ashamed of himself, and not
+to fail to assume a certain less dignified, but expressive,
+three-lettered qualification. But before those Tripos Papers I bow my
+head in humble adoration. They sometimes take my breath away even to
+read the terrible excruciating things, which seem to turn one's brain
+round and round, and contort the muscles of one's face, and stop the
+pulsation of one's heart, when one tries to grasp the horrid things.
+
+Here is a fair example of the ingenuity of the hard-hearted examiners,
+who resemble the inquisitors presiding over the tortures of the rack,
+and giving the hateful machine just one turn more by way of bestowing a
+parting benediction on their miserable victims:
+
+'A uniform rod' (it is a marvellous act of mercy that the examiner
+invented it _uniform_; it is strange that its thickness did not vary in
+some complicated manner, and become a veritable birch-rod!) 'of length
+_2c_, rests in stable equilibrium' (stable! another act of leniency!),
+'with its lower end at the vertex of a cycloid whose plane is vertical'
+(why not incline it at an angle of 30 degrees?) 'and vertex downwards,
+and passes through a small, smooth, fixed ring situated in the axis at a
+distance _b_ from the vertex. Show that if the equilibrium be slightly
+disturbed, the rod will perform small oscillations with its lower end on
+the arc of the cycloid in the time
+
+           +---------------------
+           | a{c^2 + 3(b - c)^2}
+    4[pi]\ | ------------------- ,
+          \|    3g(b^2 - 4ac)
+
+where _2a_ is the length of the axis of the cycloid.'
+
+A sweet pretty problem, truly! And there are hundreds of the same
+kind--birch-rods for every back! How the examiner must have rejoiced
+when he invented this diabolical rod, with its equilibrium, its
+oscillations, its cycloid, and other tormenting accessories. And yet, I
+suppose, before my days of studentship are over, I shall be called upon
+to attack some such impregnable fortresses of mathematics, when I hope
+to be declared equal to some twentieth wrangler, if I escape the
+misfortune of sharing a portion of the 'wooden spoon.'
+
+Ah, you male sycophants! You would prevent us from competing with you;
+you would separate yourselves on your island of knowledge, and sink the
+punt which would bear us over to your privileged shore. Of all the
+twaddle--forgive me, male sycophants!--that the world has ever heard, I
+think the greatest is that which you have talked about female education.
+And the best of it is, you are so anxious about our welfare; you are so
+afraid that we should injure our health by overmuch mental exertion; you
+profess to think that our brains are not calculated to stand the strain
+of continued mental exercise; you think that competition is not good for
+the female mind; that we are too competitive by nature--too ambitious!
+Yes, we are so ambitious that we would enter the lists with those who
+are asked in Public Examinations to find the simple interest on 1,000
+pounds for 5 years at 6-1/4 per cent.; so ambitious that we would
+compete with those who are requested to disclose the first aorist middle
+of [Greek: tupto]. Oh, think of the mental strain involved in such
+questions! How it must ruin your health to find out how many times a
+wheel of radius 6 feet will turn round between York and London, a
+distance of 200 miles! It is quite wonderful how your brains, my dear
+male sycophants, can stand such fearful demands upon your intelligence
+and industry!
+
+But you are so kind to us, so afraid of our health! Really, we are much
+obliged to you. If you married one of us, or became our guardian, or
+left us a legacy, we should then recognise your interest in us, and be
+very grateful to you for your good advice. But as matters stand, we are
+quite capable of taking care of ourselves. We will promise not to work
+too hard, if you will promise not to weary us with your paternal
+jurisdiction.
+
+But, male sycophants, I want a word with you. Why do you object to our
+taking degrees, or going in for examinations in order to qualify
+ourselves for our duties in life? You need not speak out loud if you
+would rather not. Are you not just a little afraid that we might eclipse
+you? And it is not pleasant to be beaten by a woman, is it? And then you
+profess to think that we ought to be all housewives and cooks, and
+knitters of stockings, and sewers-on of our husbands' buttons; but what
+if we have no husbands, no buttons to sew? And is it not a little
+selfish, my dear male sycophant, to wish to keep us all to yourself? to
+attend upon the wants of the lords of creation, who often distinguish
+themselves so much in the domain of science?
+
+Now, look me straight in the face (no shirking, sir!). Is it not
+jealousy--green-eyed, false-tongued jealousy--which saps your generous
+instincts, and makes you talk rubbish and nonsense about strains, and
+brains, and ambition, and the like? And if that is not hypocritical, I
+do not know what is.
+
+Well, good-day to you, male sycophant! I really have not time to indulge
+myself in scolding you any more. You are a good creature, no doubt; and
+when you have shown us what you can do, and can estimate the capacity of
+the female brain, and take a common-sense view of things, we will
+recognise your privilege to speak; and when I am the presiding genius of
+Girtham College, I will grant you the use of our hall for the purpose of
+lecturing to us on 'Women's Rights,' or, as you may prefer to entitle
+your discourse, 'Men's Wrongs.'
+
+       *       *       *       *       *
+
+Oh, this is shameful! I really am very sorry. Here have I been wasting a
+good half-hour in dreaming, and slaying an imaginary enemy with
+envenomed words and frequent dabs of ink. If I cannot concentrate my
+mind more on these mathematical researches, I fear a dreadful 'plough'
+will harrow my feelings at the end of my sojourn in these halls of
+learning.
+
+Concentration! How many of our words and ideas and thoughts are derived
+from that primal fount of all arts and sciences--mathematics! Here is
+one which owes its origin to the mathematically trained mind of some
+early philological professor, who had learnt to apply his scientific
+knowledge to the enrichment of his native tongue. He quoted to himself
+the words of the Roman poet:
+
+            'Ego cur, acquirere pauca
+    Si possum, invideor, cum lingua Catonis et Enni
+    Sermonem patrium ditaverit, et nova rerum
+    Nomina protulerit? Licuit, semperque licebit.'
+
+His mind conceived endless figures of circles and ellipses scattered
+promiscuously over the page, defying the attempts of the student to
+reduce them to order. What must he do before he can apply his formulae
+and equations, determine their areas, or describe their eccentric
+motion? He must reduce them to a common centre, and then he can proceed
+to calculate the abstruse problems in connection with the figures
+described. They may be the complex motions of double-star orbits, or the
+results of the impact of various projectiles on the tranquil surface of
+a pool. It matters not--the principle is the same; he must concentrate,
+and reduce to a common centre.
+
+This is the great defect of those who have no accurate mathematical
+knowledge; they cannot concentrate their minds with the same degree of
+intensity upon the work which lies before them. Their thoughts fly off
+at a tangent, as mine do very often; but then I have not been classed
+yet in the Tripos; and, O male poetical sycophant, you may be right
+after all when you say:
+
+   'O woman! in our hours of ease
+    Uncertain, coy and hard to please,
+    As variable as the noon-day shade.'
+
+Yes, as variable as the most variable quantities _x_, _y_, _z_. I, a
+student of Girtham College, blush to own that my thoughts very often fly
+off at a tangent.
+
+'Fly off at a tangent!' All hail to thee, most noble mathematical
+phrase! Here is another fine mathematical expression, plainly
+exemplifying the action of centrifugal force. The faster the wheel
+turns, the greater is the velocity of the discarded particles which fly
+off along the line, perpendicular to the radius of the circle. The world
+travels very fast now; the increased velocity of the transit of earthly
+bodies, the rate at which they live, the multiplicity of engagements,
+etc., have made the social world revolve so fast that the speed would
+have startled the torpid life of the last century. And what is the
+result? Men's thoughts fly off at a tangent; they are unable to
+concentrate their minds on any given subject; they are content with
+hasty generalisms, with short magazine articles on important subjects,
+which really require large volumes and patient study to elucidate them
+fully.
+
+What we want to do is to increase the attractive force, in order to
+prevent this tangential motion--to increase the _force of gravity_.
+
+'Well,' says the young lady who loves to revel in the 'Ghastly Secret of
+the Moated Dungeon,' or the 'Mysteries of Footlight Fancy,' 'you are
+_grave_ enough. Pray don't increase your gravity!'
+
+Thank you, gentle critic. I will, in turn, ask you one favour. Leave for
+once the 'Mysteries of Footlight Fancy;' seek to know no more 'ghastly
+secrets,' and increase _your gravity_--your mental weight; and hence
+your attraction in the eyes of all who are worth attracting will be
+marvellously increased, by understanding a little about Newton's law of
+universal gravitation, and don't fly off at a tangent.
+
+       *       *       *       *       *
+
+At the end of this portion of the MS. the editor of these papers
+discovered a photograph which, from subsequent inquiry, proved to be
+that of the accomplished authoress of the above reflections. The face
+is one of considerable beauty, with eyes as clear, steadfast, and open
+as the day. There is a degree of firmness about the mouth, but it is a
+sweet and pretty one notwithstanding; and a smile, half scornful, half
+playful, can be detected lurking about the corners of the lips, which do
+not seem altogether fitted for pronouncing hard mathematical terms and
+abstruse scientific problems. This photograph might have been the
+identical one which nearly brought an enamoured youth into grave
+difficulties by its secretion in the folds of his blotting-paper during
+examination. The said enamoured youth had evidently placed it there for
+the sake of its inspiring qualities; and it was said that all his hopes
+of gaining the hand of the fair original depended upon his passing that
+same examination. But the wakeful eye of a stern examiner had watched
+him as he turned again and again to consult the sweet face which beamed
+from beneath his blotting-paper; and he narrowly escaped expulsion from
+the Senate-house on the charge of 'cribbing.' Certainly he took a mean
+advantage of his fellow-sufferers, if this were the identical
+photograph, for it portrays a most inspiring face. Forgive us, lenient
+reader; one moment! There--thank you--we have done. And now we will
+proceed to disclose the researches and original problems which the MS.
+contains.
+
+Evidently the collegiate authorities were not slow in recognising the
+talents of the assiduous student, and elected her without much delay to
+a Professorship of Girtham. In this capacity the learned lady delivered
+several lectures, of which the second MS. contains the first of the
+series.
+
+
+
+
+PAPER II.
+
+LECTURE ON THE THEORY OF BRAIN WAVES AND THE TRANSMIGRATION
+AND POTENTIALITY OF MENTAL FORCES.
+
+
+Professors and Students of the University of Girtham, my Lords, Ladies,
+and Gentlemen,--I have the honour to bring before you this evening some
+original conceptions and discoveries which have been formulated by me
+during my researches in the boundless field of mathematical knowledge;
+and though you may be inclined at first to pronounce them as somewhat
+hastily conceived hypotheses, I hope to be able to demonstrate the
+actual truth of the propositions which I shall now endeavour to
+enunciate. It is with some feelings of diffidence that I stand before so
+august an assembly as the present; and if I were not actually convinced
+of the accuracy of my calculations, I should never have presumed to
+appear before you in the character of a lecturer. But '_Magna est
+veritas, et praevalebit_.' I cast aside maiden timidity; I clothe myself
+in the professorial robe which you have bestowed upon me, and sacrifice
+my own feelings on the altar of Truth.
+
+I have been engaged, as you are doubtless aware, for some years in the
+pursuit of mathematical research, exploring the mines of science, which
+have of late been worked very persistently, but often, like the black
+diamond mines, at a loss. Concurrently with these researches, I have
+speculated on the great social problems which perplex the minds of men,
+both individually and collectively. And I have come to the conclusion
+that the same laws hold good in both spheres of work; that methods of
+mathematical procedure are applicable to the grand social problems of
+the day and to the regulation of the mutual relations which exist
+between man and man. Take, for example, the Force of public opinion. Of
+what is it composed? It is the Resultant of all the forces which act
+upon that which is generally designated the 'Social System.' Public
+opinion is a compromise between the many elements which make up human
+society; and compromise is a purely mechanical affair, based on the
+principle of the Parallelogram of Forces. Sometimes disturbing forces
+exert their influence upon the action of Public Opinion, causing the
+system to swerve from its original course, and precipitating society
+into a course of conduct inconsistent with its former behaviour; and it
+is the duty of the Governing Body to eliminate as far as possible such
+disturbing forces, in order that society may pursue the even tenor of
+its way.
+
+Professors, we have one great problem to solve; and all questions
+social, political, scientific, or otherwise, are only fragments of that
+great problem. All truths are but different aspects of different
+applications of one and the same truth; and although they may appear
+opposed, they are not really so; and resemble lines which run in
+various directions, but lovingly meet in one centre.
+
+Now, let us take for our consideration the secret influence which men
+exert upon each other, apart from that produced by the power of speech
+(although that would come under the same general law). As
+mathematicians, you are aware that the undulatory theory of light and
+heat and sound are now accepted by scientific men as the only sure basis
+of accurate calculation. We know that the rays of light travel in waves,
+and the equation representing the waves is
+
+         a       2[pi]
+    y = --- sin ------ (vt - r),
+         r     [lambda]
+
+where _y_ is the disturbance of the ether, _a_ the initial amplitude,
+_r_ the distance from the starting-point, [lambda] the wave-length, and
+_v_ the velocity of light. Sound and heat likewise have much the same
+form of equation. Now, I maintain that the waves of thought are governed
+by the same laws, and can be determined by an equation of the same form.
+You are aware that in all these equations a certain quantity denoted by
+[lambda] appears, and varies for the different media through which the
+sound, or light, or heat passes, and which must be determined by
+experiment Now, in my equation for brain waves, the same quantity
+[lambda] appears which must be determined by the same method--by
+_experiment_. But how is this to be done? After mature deliberation and
+much careful thought, I have discovered the method for finding [lambda].
+This method is _mesmerism_. We find the ratio of brain to brain--the
+relative strength which one bears to another; and then by an application
+of our formula we can actually determine the wave of thought, and read
+the minds of our fellow-creatures. An unbounded field for reflection and
+speculation is here suggested. Like all great discoveries, the elements
+of the problem have unconsciously been utilized by many who are unable
+to account for their method of procedure. For example, thought-readers,
+mesmerists, and the like, have unconsciously been working on this
+principle, although lack of mathematical training has prevented them
+from fully mastering the details of the problem. Hence in popular minds
+a kind of mystery has hung about the actions of such people, and excited
+the curiosity of mankind.
+
+The development of this theory of brain waves may be of great practical
+utility to the world. It shows that great care ought to be exercised in
+the domain of thought, as well as that of speech. For example: A man has
+made a startling discovery, from which he expects to receive
+considerable worldly advantage. He would be careful not to disclose his
+discovery in speech to his acquaintances until his plans are
+sufficiently matured, lest they should impart it to the world, patent
+his device, and reap the reward. But while he is endeavouring to talk
+carelessly about it, the wave of thought may be travelling from brain to
+brain, suggesting the existence of the discovery; and if the conditions
+are favourable, and [lambda] sufficiently small, it is possible that the
+idea itself may be conveyed. Of course the more complicated the
+discovery, the less likely would the wave convey the conception. Or
+suppose that one of the learned professorial body of our sister
+university should conceive an attachment for a lady-student of Girtham
+College (of course a very improbable supposition!), and the infatuated
+_savant_ became somewhat jealous of another learned lecturer of the same
+college (another improbability!), the fact of his jealousy would be
+imparted to the latter by a wave of thought, and might cause
+considerable confusion in the serene course of love or science. The fact
+of the existence of the wave is indisputable. What do all the stories of
+impressions and double-sight teach us? How could the intelligence of the
+death of Professor Steele have been conveyed to his friend and
+fellow-student, Professor Tait--the one at Cambridge, the other at
+Edinburgh--were it not for the existence of some wave, which, like that
+of electricity, wings its rapid flight unobserved by human eyes? Are all
+the records of the Psychical Society only myths and legends bred of
+superstitious fancy? It were hard to suppose so.
+
+But if, gentlemen, and ladies especially, you wish to keep your secret
+discoveries to yourselves, watch over your thoughts as well as your
+words; for my researches prove, and the universal experience of mankind
+corroborates the fact, that some portion of your inmost thoughts and
+secret desires are understood by your neighbours (especially when
+[lambda] is small!); that they travel along the waves which I have
+attempted to indicate; and if you would desire to extend your influence
+in the world, probe the secret instincts of mankind, and prevent
+yourself from being deceived and wronged--study the art and science of
+Brain Waves.
+
+       *       *       *       *       *
+
+The following verses of rather doubtful merit were found in connection
+with the previous MS. They were evidently written by a different hand;
+but inasmuch as they were deemed worthy of preservation by the learned
+owner of the sealed desk, we venture to publish them. They are closely
+connected with the previous lecture, and were evidently composed by an
+admirer of the fair lecturer who did not share her love for scientific
+research.
+
+    Wavelet,[1] wing thy airy flight;
+      Let thine amplitude be great;
+    Tell her all my thoughts to-night,
+      How I long to know my fate.
+
+    All the fields of Mathematics
+      I have roamed at her decree;
+    From Binomial and Quadratics,
+      To the strange hyperbole.[2]
+
+    I have soared through Differential,
+      Deeply drunk of Finite Boole;[3]
+    Though its breath is pestilential,
+      Reeking of the hateful School.
+
+    I have tried to shape a Conic,
+      Vainly read the Calculus;
+    But my feebleness is chronic,
+      _Morbus Mathematicus_.
+
+    All my curves are cardioidal;
+      I confuse my _x_ and _y_s,
+    Which they say is suicidal;
+      And my tutor vainly sighs.
+
+    Wavelet, tell her how I love her,
+      As she mounts her learned throne;
+    And that love I hope may cover
+      All the failings which I own.
+
+    Wavelet, cry to her for pity;
+      Bid her end this bitter woe;
+    I might do something 'in the city,'
+      But never pass my Little-go.
+
+
+  [1] We presume this is addressed to an imaginary brain wave.
+
+  [2] We observe here the dash of an indignant pen, and a substituted
+      for e. But now the rhyme is spoiled. Gentle Muse, thou art
+      sacrificed by the stern hand of Mathematical Truth!
+
+  [3] Query: Does the writer refer to the learned treatise on Finite
+      Differences by Professor Boole?
+
+
+
+
+PAPER III.
+
+LECTURE ON THE SOCIAL PROPERTIES OF A CONIC SECTION,
+AND THE THEORY OF POLEMICAL MATHEMATICS.
+
+
+Most Learned Professors and Students of this University,--From the
+interest manifested in my first lecture, I conclude that my method of
+investigation has not proved altogether unsatisfactory to you, and I
+hope ere long to produce certain investigations which will probably
+startle you, and revolutionize the current thought of the age. The
+application of mathematics to the study of Social Science and Political
+Government has curiously enough escaped the attention of those who ought
+to be most conversant with these matters. I shall endeavour to prove in
+the present lecture that the relations between individuals and the
+Government are similar to those which mathematical knowledge would lead
+us to postulate, and to explain on scientific principles the various
+convulsions which sometimes agitate the social and political world.
+
+Indeed, by this method we shall be able to prophesy the future of states
+and nations, having given certain functions and peculiarities
+appertaining to them, just as easily as we can foretell the exact day
+and hour of an eclipse of the moon or sun. In order to do this, we must
+first determine the _social properties of a conic section_.
+
+For the benefit of the unlearned and ignorant, I will first state that a
+cone is a solid figure described by the revolution of a right-angled
+triangle about one of the sides containing the right angle, which
+remains fixed. The fixed side is called the axis of the cone. Conic
+sections are obtained by cutting the cone by planes. It may easily be
+proved that if the angle between the cutting plane and the axis be equal
+to the angle between the axis and the revolving side of the triangle
+which generates the cone, the section described on the surface of the
+cone is a parabola; if the former angle be greater than the latter, the
+curve will be an ellipse; and if less, the section will be a hyperbola.
+
+But the simplest conic section is, of course, a circle, which is formed
+by a plane at right angles to the axis of the cone; and the simplest
+circle is that formed by a plane passing through the apex of the cone.
+All this is simple mathematics; and let beginners consult more
+elementary treatises than this one to satisfy themselves on these
+points. But if they will assume these things to be true, they will know
+quite enough for our present purpose. The simplest conic section of all
+has been proved to be a _point_. Now, this represents the simplest and
+original form of society, a _single family_. 'It is not good for man to
+be alone' was the first observation made by the wise Creator upon the
+rational creature whom He had introduced into Paradise as its lord.
+Marriage is the rudiment of all social life, from which all others
+spring, out of which all others are developed. Around the parents'
+knees soon cluster a group of children, and in their relation to each
+other we discern the earliest forms of law and discipline--the bonds by
+which society is held together. When the children grow up, separate
+households are formed; and then the multiplication of families, the
+congregating of men together for purposes of security and mutual
+advantages in division of labour; and thus is gradually formed a state,
+which is only the development of the family--the king representing the
+parent, and ruling on the same principle.
+
+Mathematically speaking, our plane no longer passes through the apex.
+The point represented the single family; but keeping the plane
+horizontal, we move it along the axis, the sections will become
+_circles_, which represent mathematically the next simplest form of
+society, where the centre is the seat of government, which is connected
+with each individual member of the social circle by equal radii. The
+social property of a circle is that of a monarchical government in its
+purest and simplest form. The larger the circle becomes (_i.e._, the
+further you move the plane from the apex), the greater the distance
+between the individual and the monarch. Therefore, the more independent
+the monarchy becomes, and the less influence do individuals possess over
+the ruling power. Hence, we may infer that as years roll on, the
+government will become more despotic; but the stability of the country
+diminished, and probably some individual particle, when sufficiently
+withdrawn from the attraction of the central head, will begin to revolve
+on its own account, and spontaneously generate a government of its own.
+We may, therefore, conclude from mathematical reasoning that an
+unlimited monarchy, though advantageous for small states, is not a safe
+form of government for a large or populous country, inasmuch as the
+people do not derive much benefit from the sovereign; the mutual
+attraction, which ought to exist in a flourishing state between the
+ruler and the ruled, is weakened; and the isolation of the monarch
+tends to make him still more despotic. As a practical example of the
+truth of the foregoing statement, I may mention the present condition of
+Russia, which shows that the result of an unlimited monarchy, in a large
+and unwieldy social circle, is such as we should have reasonably
+expected from mathematical investigations.
+
+Invariably, under the circumstances which I have described, the country
+will become disorganized; the sovereign will cease to have any power
+over the people, and the country will become a chaos, without order,
+influence, or power.
+
+When the centre of a conic section moves along the axis of the curve to
+infinity, banished by the mutual consent of the individual particles
+which compose the curve, or the nation, a figure is formed, called a
+_parabola_. This is the curve which the most erratic bodies in the
+universe describe in space, as they rush along at a speed inconceivable
+to human minds, and are supposed to produce all kinds of mischief and
+injury to the worlds whose courses they wend their way among.
+
+This curve, then, represents the position which the nation assumes when
+the constituted monarchy, the centre of the system, has been _banished
+to infinity_. A revolution has occurred; the monarch has been dethroned;
+and it is not hard to see that the same erratic course which the comet
+pursues in its flight, is observable with respect to the social system
+which is represented by a parabola. We observe with eager scrutiny the
+wanderings of these erratic comets. They appear suddenly with their
+vapoury tails; sometimes they shine upon us with their soft, silvery
+light, brilliant as another moon; sometimes they stand afar off in the
+distant skies, and deign not to approach our steady-going earth, which
+pursues its regular course day by day, and year by year. Then, after a
+few days' coy inspection of our planet from different points of view,
+they fly to other remote parts of the universe, and do not condescend to
+show themselves again for a hundred years or so. Such is the erratic
+conduct of a heavenly body whose course is regulated by a parabolic
+curve.
+
+We may look for similar eccentric behaviour on the part of a community,
+nation, or state, whose centre is at infinity, whose constitution has
+been violently disturbed, and whose monarchy is situated in the far-off
+regions of unlimited space. The erratic course of Republican rule is
+proverbial. There is no stability, no regularity. To-day we may observe
+its brilliancy, which seems to laugh at and eclipse the sombre shining
+of more steady and enduring worlds; but ere to-morrow's moon has risen,
+it may have vanished into the regions of eternal night, and we look for
+its bright shining light in the councils of the nations, but it has
+ceased to shed its rays, and we are disappointed. Sometimes it is asked,
+with fear and trembling: 'What would be the effect if our earth were to
+come in contact with the tail of a comet? Should we be destroyed by the
+collision, and our ponderous world cease to be?' But we are assured
+that no such disastrous results would follow. We have already passed
+through the tails of many comets, but we have not discovered any
+inconvenient change in our ordinary mode of procedure. It is probable
+that the comet's tail is composed of no solid substance.
+
+We may therefore infer by analogy that a Republican State would not
+offer any powerful resistance if it were to come into collision with a
+nation possessing a more settled form of government. A shower of
+meteoric stones, like passing fireworks, might take place; but beyond
+that nothing would occur to excite the fear, or arouse the energies of
+the more favoured nation. As an example of the weakness of a Republican
+State I may mention France. There we see an industrious race of people,
+endowed with many natural gifts and graces, a country rich and
+productive; and yet, owing to the unsettled nature of its government,
+all these natural advantages are neutralized; its course amongst the
+nations is erratic in the extreme, a spectacle of feeble
+administration; and it would offer no more resistance to a colliding
+Power than the empty vacuum of a comet's tail. This example will
+demonstrate to you the truth of our theory with regard to the
+instability of a social system which is geometrically represented by a
+parabolic curve.
+
+We will now turn from this picture of insecurity and unrest to another
+figure which possesses most advantageous social properties. I refer to
+the ellipse. An ellipse is a curve formed by the section of a cone by a
+plane surface inclined at an angle to the vertical axis of the cone,
+greater than the angle between the axis and the generating line.
+
+Now, this is a curve which possesses most attractive properties. It is
+the curve which the earth and other planetary orbs describe around the
+centre of the solar system, as if nature intended that we should take
+this figure as a guide in choosing the most advantageous social system.
+It possesses a centre, C, in view of all the particles which compose the
+curve, and connected with them by close ties. It has two foci, S and
+S', fixed points, by the aid of which we may trace the curve.
+
+In the interpretation of this figure, the centre of the curve represents
+the throne of monarchy. There is no tendency here to revolutionize the
+State, to banish the ruling power, and institute a Republican form of
+government; but inasmuch as we saw the weakness of an absolute monarchy
+in large and populous States, as represented by the circle, the wisdom
+of an elliptical social system has ordained that there shall be two
+foci, or houses of representatives of the people, who shall assist in
+regulating the progress of the nation. Here we have a limited monarchy;
+the throne is supported by the representatives of the people; and the
+nearer these foci of the nation are to the centre (_i.e._, in
+mathematical language, the less the _eccentricity_ of the curve), the
+more perfect the system becomes--the greater the happiness of the
+community.
+
+In cases where the _eccentricity_ becomes very great, the beauty of the
+curve is destroyed, and ultimately the ellipse is merged into one
+straight line. Most learned Professors, here we have a terrible warning
+of the awful result of too much eccentricity. Whether we regard the life
+of the nation or of the individual, let all bear in mind this alarming
+fact, that eccentricity of thought, habit, or behaviour may result, as
+in the case of this unfortunate ellipse, which once presented such fair
+and promising proportions to the student's admiring gaze, in the
+'sinister effacement of a man,' or the gradual absorption of a State
+into an uninteresting thing 'which lies evenly between its extreme
+points.'
+
+The great examples of Bacon, of Milton, of Newton, of Locke, and of
+others, happen to be directly opposed to the popular inference that
+eccentricity and thoughtlessness of conduct are the necessary
+accompaniments of talent, and the sure indications of genius. I am
+indebted to Lacon for that reflection. You may point to Byron, or
+Savage, or Rousseau, and say, 'Were not these eccentric people
+talented?' 'Certainly,' I answer; 'but would they not have been better
+and greater men if they had been less eccentric--if they had restrained
+their caprice, and controlled their passions?' Do not imagine, my young
+students of this university, that by being eccentric you will therefore
+become great men and women of genius. The world will not give you credit
+for being brilliant because you affect the extravagances which sometimes
+accompany genius. Some of you ladies, I perceive, have adopted a
+peculiar form of dress, half male, half female; or, to be more correct,
+three-fourths male, and one-fourth female. Do not imagine that you will
+thus attain to the highest honours in this university by your
+eccentricity, unless your talents are hid beneath your short-cut hair,
+and brains are working hard under your college head-gear. As well might
+we expect to find that all females who wear sage-green and extravagant
+aesthetic costumes are really born artists and future Royal Academicians.
+It is apparent that many aspirers to fame and talent are eager to
+exhibit their eccentricities to the gaze of the world, in order that
+they may persuade the multitude that they possess the genius of which
+eccentricity is falsely supposed to be the outward sign.
+
+I may remark in passing that the eccentricity of a parabolic curve is
+always _unity_. What does this prove? You will remember that a
+Republican State is represented by a parabola. Therefore, however such a
+nation may strive to alter its condition, and secure a settled form of
+government, its eccentricity will always remain the same. It will always
+be erratic, peculiar, unsettled; and this conclusion substantiates our
+previous proposition with regard to the condition of a social system
+represented by a parabola.
+
+With regard to other advantages afforded by an elliptical social system,
+we will defer the consideration of this important subject until my next
+lecture.
+
+
+
+
+PAPER IV.
+
+THE SOCIAL PROPERTIES OF A CONIC SECTION,
+AND THE THEORY OF POLEMICAL MATHEMATICS--(_continued_).
+
+
+Most learned Professors and Students of this University,--You have
+already gathered from my preceding lecture my method of procedure in the
+investigation of the corresponding properties of curves and States. You
+have perceived that we have here the elements of a new science, which
+may be extended indefinitely, and applied to the various departments of
+self-government and State control. This new science of polemical
+mathematics is in itself an extension of the _principle of continuity_,
+for the discovery of which Poncelet is so justly renowned. We can prove
+by geometry that the properties of one figure may be derived from those
+of another which corresponds to it; and the new science teaches us that
+if we can represent, by projection or otherwise, a society of particles
+or individuals on a plane surface, the properties of the State so
+represented are analogous to the properties of the curve with which it
+corresponds. It is only possible for me to touch upon the elements of
+the science in these lectures, but I hope to arouse an interest in these
+somewhat unusual complications and curious problems, that you may
+hereafter make further discoveries in this unexplored region of
+knowledge, and that the world may reap the benefit of your labours and
+abstruse studies. I have already, in my previous lecture, touched upon
+the social properties of the parabola, and examined the constitution of
+erratic curves and eccentric nations. It is my intention to-day to speak
+of similar problems which arise with reference to elliptical States.
+
+But, first, let me answer an objection which may have occurred to your
+minds. Am I wrong in my calculations in attributing too much to the
+power and usefulness of forms of government? Does the well-being and
+happiness of a nation depend on the government, or upon the individuals
+who compose the nation? Most assuredly, I assert, they rest upon the
+former. Men love their country when the good of every particular man is
+comprehended in the public prosperity; they undertake hazard and labour
+for the government when it is justly administered. When the welfare of
+every citizen is the care of the ruling power, men do not spare their
+persons or their purses for the sake of their country and the support of
+their sovereign. But where selfish aims are manifest in Court or
+Parliament, the people care not for State officials who are indifferent
+to their country's weal; they become selfish too; Liberty hides her
+head, and shakes off the dust of her feet ere she leaves that doomed
+land, and the stability, welfare, and prosperity of that country cease.
+
+I might refer you to many a stained page of national history in order to
+prove this. Compare the closing chapters of the life of the Roman empire
+with the record of the brave deeds of its ancient warriors and valorous
+statesmen. Grecian preeminence and virtue died when liberty expired. I
+agree with Sidney when he writes that it is absurd to impute this to the
+change of times; for time changes nothing, and nothing was changed in
+those times but the government, and that changed all things. These are
+his words: 'As a man begets a man, and a beast a beast, that society of
+men which constitutes a government upon the foundation of justice,
+virtue, and the common good, will always have men to promote those ends;
+and that which intends the advancement of one man's desires and vanity
+will abound in those that will foment them.' I may not, therefore, be
+altogether wrong in attributing the prosperity and well-being of a
+nation to the form of government which it possesses.
+
+We will now proceed to the consideration of the social advantages which
+an elliptical State affords. This is the form of government and social
+position which we, as a nation, at present enjoy; and from mathematical
+considerations I am of opinion that it is the best, and hope that no
+change will ever be made in our constitution. You may remember that I
+have previously stated that an ellipse has a centre and two foci, in
+view of all the particles which compose the curve, and connected with
+them by close ties. The centre, in the projected figure, represents the
+monarchy, which is limited; and the government is carried on by the aid
+of the two houses of representatives of the people, depicted in the
+projection by the two foci.
+
+Now the social advantages of the ellipse are given by the fact that the
+sum of the distances of any point from the foci is always constant. No
+particle is left out in the cold; no one does not possess the advantages
+of a social government. Though his distance may be far from the Upper
+House, he has the advantage of nearness to the Lower, and _vice versa_.
+The sum of the distances is constant. The extinction of one focus, the
+House of Lords, for example, would create a complete disorganization of
+the whole system: the other focus would set up a powerful magnetic
+attraction, and a curious bulb-shaped curve would be evolved, very
+different from the beautiful symmetrical form which the original figure
+presented to the eye. The centre of the system would be disturbed; and
+it is probable that ere long it would disappear along the axis and be
+vanished to infinity. Thus the curve would become a parabola. This is
+the alarming result of the extinction of one focus. Abolish the House of
+Lords, and you will soon find that the Throne will be disturbed; the
+State will become disorganized; the nation will become confused by the
+magnetic force of the Lower House, uncounteracted by any other
+attraction; and very soon a complete revolution of the whole system
+will set in: the monarch will be dethroned, and a Republican form of
+government, with all the eccentricities of a parabolic course, will take
+the place of a more orderly and settled constitution. This is a plain
+deduction from our mathematical investigations; and it behoves all our
+statesmen, our philosophers and great men, our fellow-citizens and the
+humblest artisans in our manufacturing towns, to weigh well this
+alarming result of the abolition of that House which has been threatened
+with destruction; and to ascertain for themselves the truths upon which
+my proposition and reasoning rest.
+
+I have already observed that the fact that the earth's orbit and that of
+other planets are in the form of ellipses; that the curvature of the
+earth is nearly the same, ought to guide us in choosing this particular
+curve as a model of the projection of a complete and most advantageous
+social system.
+
+The circle described on the major axis of an ellipse, is called the
+_auxiliary circle_, and affords much assistance in the investigation of
+the properties of an ellipse. As we have already shown, the circle
+represents the simplest form of monarchical government. Hence, if we
+compare the form of government represented by an ellipse (_i.e._, such
+as we now enjoy) with that of a system where the king is the only
+governing power, we may obtain great assistance in solving complicated
+political problems.
+
+In all conics there is a straight line called the 'directrix,' which
+represents in social or polemical science the laws of the nation, and
+plays a prominent part in the mutual relations of the individual
+particles. For instance, in the case of the parabola, the distance of
+any particle from the directrix is equal to its distance from the focus.
+
+From this we may conclude that if an individual deviates at all from the
+path which the laws (or, directrix) indicate, if he does not show true
+respect to the decrees of the focal government, and preserve the true
+position between them, directly he is found deviating from his course,
+he is quickly banished to a less enlightened sphere. In an ellipse there
+is less likelihood of his straying away from the course which the
+directrix points out, on account of the two-fold guidance which he
+receives from the two foci.
+
+The following curious problem may be noticed. If a parabola roll on
+another parabola, their vertices coinciding, the focus of the first
+traces out the directrix of the second.
+
+Here we come to the consideration of the international relationship of
+States. Two nations have the same form of government (in this example
+this form is Republican); their policies coincide: we may conclude from
+this proposition that the course which the government of one nation will
+pursue, will be that which is prescribed by the laws of the other.
+
+The subject of the contact of curves presents many interesting problems
+with reference to Polemical Science, and may be extended indefinitely.
+It is well known that there are different orders of contact, which are
+designated as the _first_, _second_, or _third_ order. This last order
+may be termed the 'marriage of curves,' cemented by the osculating
+circle, or 'wedding-ring;' and when two nations have contact of the
+third order, they have formed a very close alliance, and by calculation
+we can obtain the _radius of curvature_, or size of the wedding-ring, by
+means of which they may be united.
+
+The theory and nature of contact constitute a branch of our newly
+discovered science which we commend to the careful consideration of
+those who have undertaken the difficult and perplexing study of
+international law. Alas! too many States refuse this friendly contact,
+and, consequently, _cut_ each other, instead of blending in sweet
+accord. Their peace is at best an armed neutrality; and if they have
+contact of only the _first_ or _second_ order, we can prove
+mathematically that they are sure to intersect in some other point or
+points; and divergence of policy and disturbed relations are the
+results. Contact of the _third, or highest, order_ is the only safe
+position for two allied, or contiguous, States.
+
+With your permission I will add a few words to those I have already
+uttered with regard to the directrix. As necessary as the directrix is
+to the curve, so are the corresponding laws to the State. I will prove
+this fact by a few examples. English people have laws, and know how to
+obey them; therefore their numbers increase; they thrive and are
+prosperous. A friendly critic of another nation has said that the reason
+why Englishmen rule the world, is because they know how to obey. On the
+other hand, the gipsies have no laws; hence they become fewer and less
+powerful. What is the condition of all tribes and nations which are not
+governed by laws? They invariably remain poor and miserable. They are in
+want of a directrix; and if we could supplement the gift with foci and
+centre, they would soon emerge from their savage condition, and become
+more civilized.
+
+I have omitted to mention the hyperbolic form of government. The curve
+formed by the intersection of the surface of a cone with a plane will be
+a hyperbola, when the inclination of the cutting plane to the axis of
+the cone is less than the constant angle which the generating line forms
+with the axis. It is manifest that the plane will thus intersect the
+higher cone, and produce the figure which is known to mathematicians as
+the hyperbola.
+
+We may hence deduce the following property of the corresponding
+hyperbolic State. We take cognizance of that higher cone with which the
+mundane affairs of the lower cone are closely connected. As an example
+of this system we may mention the vast temporal rule and power of the
+Papal Throne, which formerly exercised such marvellous sway over the
+nations of Europe. By an appeal to a Higher Authority than that of
+earthly kings and potentates was this rule exercised; but its hyperbolic
+form is fast passing away, and degenerating into that of a circle with
+indefinitely small radius. We shall not, therefore, discuss the complex
+polemical problems which a hyperbolic State suggests.
+
+I will now mention a few problems which are easily capable of proof, and
+deduce from them the necessary conclusions which must follow when we
+apply our newly discovered principles of polemical science.
+
+1. 'If from any point in a straight line a pair of tangents be drawn to
+an ellipse, the chords of contact will pass through a fixed point.'
+
+I will not trouble you with the proof of this proposition, as it is
+evident to all mathematicians, and can easily be demonstrated. But mark
+well the deductions, when we interpret this mathematical language in
+correct polemical terms. A State, through various convulsions of its
+own, has merged into a condition represented by a straight line, having
+lost its symmetry, its beauty, its curvilinear proportion. An individual
+unhappily situated in this unfortunate community regards with longing
+eyes the prosperous condition of those who enjoy the social advantages
+of a settled form of government, and other blessings which accompany
+elliptical jurisdiction and laws. [Two tangents are drawn to an
+ellipse.] No matter where the individual may be in the unhappy envious
+straight line, the result of his reflection will be the same.
+Sympathetic chords are drawn, joining the points of contact of the
+tangents with the curve; they all pass through a fixed point. All these
+conclusions of the various individuals on the straight line will be the
+same. All are of opinion that the elliptical form is the best; and they
+mourn in secret over the sad events which have occurred in their own
+national life, their eccentricity, their lawlessness, when they see the
+advantages which their more staid and sober-minded neighbours so freely
+enjoy.
+
+2. The normal at any point of an ellipse bisects the angle between the
+focal distances of that point.
+
+The normal is the perpendicular from the point on the major axis; it is
+the line of thought directed by the observance of just laws and rules.
+Hence this proposition shows that the individual citizen, when guided by
+sound judgment, regards with equal favour and entire approval the
+existence of both foci, or Houses of Legislature. He considers that both
+are necessary to his comfort, and the right regulation of the State's
+welfare. He cares not for the _abnormal_ condition of those who talk as
+if the existence of either House were unnecessary to his country's weal,
+and bestows a pitying glance on those wandering lights, or disturbed
+erratic governments, which do not possess the advantages which from
+experience he has learned to love and to respect. No matter what his
+condition may be, the same opinions are held by all classes, all ranks
+and degrees; and if a self-opinionated particle think otherwise, he ought
+to be transferred to a less enlightened sphere, and migrate to a
+parabolic state, or uninteresting straight line. And when he has changed
+his location, he will look back on his old home and old surroundings
+with longing eyes and an aching heart, thinking of the blessings he has
+lost by his own rash act. This can be proved mathematically. He looks
+for an ideal state of society, leaps after the shadow his fancy has
+depicted; and when he finds himself outside his former state, he looks
+back with longing eyes at the once-scorned focus. What is the focus of a
+perpendicular on the tangent of an ellipse from any external point? Can
+it not be proved to be a _circle_? That is to say, he will be more
+conservative than ever. He would like to return to a primitive form of
+government. Farewell to his wild schemes and revolutionary measures!
+Farewell to his disestablishments, abolitions, and suppressions! The
+throne and government have new attractions in his eyes; loyalty, a new
+feeling, asserts its benign influence; and if he could return to his
+former position, his normal conduct would be straighter than ever, for
+by sad experience he has learned the value of those things which he once
+despised.
+
+But we need not depend upon one proof alone. Exactly the same result may
+be obtained from the well-known proposition which states that 'the angle
+between the tangent from any external point and the focal distance is
+equal to the angle between the other tangent and the focal distance.'
+
+3. The same opinions are often held by individuals in quite different
+walks and classes of life. Let these individuals be represented by
+points on an ellipse. Join these, and we have a system of parallel
+chords. Draw a straight line through the middle points of these chords,
+and lo! it will always pass through the centre. This shows that the
+central thought of all people is directed to the sovereign--that
+_loyalty_ is inherent in the hearts of those who recognise elliptical
+laws.
+
+I will conclude this lecture with a few remarks on the nature and
+properties of the _radical axis_. This name was first given, I believe,
+by M. Gaultier, of Tours, and for a full account of its nature I refer
+you to the _Journal de l'Ecole Polytechnique_, xvi., 1813. The radical
+axis of two circles is the line perpendicular to the line joining the
+centres, from any point of which the tangents to the circles are equal.
+Let us suppose that one circle becomes a point, and that this point is
+situated on the circumference of the first circle. What is the result?
+The radical axis becomes the tangent to the circle. Hence we may
+conclude that in a social system of monarchical government the radical
+axis is perpendicular to the line attaching the individual with the
+monarch. Therefore we may conclude that the radical axis indicates a
+tendency of particles, or individuals, to fly off at a tangent, at right
+angles to the connecting-link between the individual and the king. When
+any motion takes place, this is evident, and this tendency is called
+centrifugal force. Sad is it for the State when this force is called
+into play, and the radical axis is a standing menace to the stability of
+States and nations. The only way to counteract its baneful, disturbing
+influence is to increase the attraction of the monarch on the
+individual, which nullifies the former force, and prevents further
+mischief. This is the method which nature itself adopts in the motions
+of the planetary worlds; the attraction of the sun prevents any
+disturbance which might be caused in the course of the planets by the
+action of centrifugal force, and nature suggests this plan for our
+adoption. Increase the attraction of the Throne; rigidly connect each
+individual by the strong chords of affection, advantage and utility with
+the ruling power; and then, though the radical axis may be there, it
+will cease to indicate any motion along it, it will not prevail over the
+counteracting influence of loyalty, and the stability of the social
+system and the happiness of the individuals will be the results.
+
+                 'I would serve my King,
+    Serve him with all my fortune here at home,
+    And serve him with my person in the wars;
+    Watch for him, fight for him, bleed for him, die for him,
+    As every true-born subject ought.'
+
+This, most noble professors, is the language of true patriotic loyalty.
+Let the monarch be loved and loving, let the laws be just and equal,
+happy will be the people, prosperous the realm. There are those who
+counsel different things, and preach sedition and the breaking-up of
+laws; but those who advocate such doctrines lack that judicial
+mathematical training which we, students and professors of Girtham
+College, have acquired. If polemical mathematics, the science of the
+future, should become more widely studied; if its results were
+disseminated far and wide; above all, if the proper position which women
+ought to occupy in the counsels of the nation were assigned to them, we
+should hear less of these wild schemes and foolish theories, and the
+influence of women would tend greatly to promote the stability and
+security of the State.
+
+Why, let me ask, should woman be excluded from that position which is so
+justly hers? from those duties which she can discharge so faithfully? It
+has been said that if we wish to know the political and moral condition
+of a State, we must ask what rank women hold in it. We are told that
+women have more strength in their looks than men have in their laws.
+Why, then, do men debar her from those fields of occupation wherein she
+may labour for the nation's good, and use her influence, which they
+acknowledge to be great, in those callings wherein she may most easily
+benefit the State, and the country she so ardently loves?
+
+At some future time I hope to speak more fully on this subject; and in
+concluding this lecture, I will remark that English politics need a
+leavening influence which will counteract the evil tendencies and
+corrupt theories which, in spite of our advantageous social system, at
+present exist; and this leavening influence will be best produced by
+the admission of those into the counsels of the nation who are
+acknowledged to have a benign and healthy influence--the women of
+England. Let women have their proper share in the government of the
+country, and I have no fear lest we shall preserve our elliptical
+constitution, and all the advantages which we at present enjoy.
+
+       *       *       *       *       *
+
+[Editorial Note.]--In the bundle of papers which contained the foregoing
+lectures, some letters of great interest were found, which show that the
+fame of the learned Lady Professor of Girtham College had already gone
+abroad, and attracted the attention of the leading statesmen of the day.
+It is to be regretted that the answers to these letters are not
+forthcoming, as it might be proved from them that the science of
+polemical mathematics has already influenced the minds of our
+legislators in their conduct of affairs at home and abroad. The
+following letter is of unique interest, and may be taken as evidence of
+the favourable impression which this new science has made on the mind of
+one of our greatest thinkers and statesmen:
+
+
+                    Downing Street,
+                            May, 18--
+
+My dear Lady Professor,--The report of the amazing results of your
+scientific researches has reached me, and I congratulate you most
+heartily on the originality and acumen which you have displayed in your
+investigations. A new light has dawned upon our country. Instead of
+groping in the darkness of political warfare, ensnared by party ties and
+jealousies, the statesmen of the future will be able to calculate and
+determine the correct course with mathematical precision and perfect
+accuracy. No one can dispute the truth of a proposition in Euclid, or
+the genuineness of Newton's laws; and if your method enables men to
+calculate and determine the correct political course of action, to solve
+political problems as easily as exponential equations, why--then adieu
+to the bickerings of party, the querulous complaints of the Opposition!
+Nay, joy to the Ministry! There will be no Opposition! Our statesmen
+will be able to guide the great ship of the State by means of charts
+which know no error; and they will resemble an association of savants
+met together to determine the exact moment of the transit of Venus, or
+to examine the degree of density of a comet's tail.
+
+This condition of Parliamentary procedure is much to be desired; you
+have shown how such an ideal state of things may be obtained. In the
+name of the Government I thank you for your endeavours on behalf of your
+country's welfare, and look forward to a further development of your
+admirably conceived system. As in the domain of ordinary science there
+are complex questions which defy the acumen of the philosopher; so in
+polemical science there may be questions which present the same
+difficulties and complications. But as the first are daily yielding
+before the persevering attacks of the mathematician, so I doubt not
+polemical science will soon overcome the various problems which may
+arise.
+
+But it is mainly on my own account that I venture to address you. I
+desire to consult you with regard to certain matters--political
+complications--which have recently occupied the attention of Her
+Majesty's Ministers. By the help of your new science, can you aid us
+in our deliberations? Of course, I am writing to you in _strict
+confidence_, and beg that you will keep this communication profoundly
+secret. I fear that would be a hard task for many of your sex, who do
+not possess your knowledge and powers of mind; but I have great
+confidence in your discretion.
+
+These are the problems which are presented to us for solution:
+
+1. Some members of the Cabinet are secretly in favour of Protection, and
+the country is rather stirred by the question. Can you, from your
+knowledge of the contact of curves and nations, help us to determine
+what course we ought to take with regard to Spain, for example? Are the
+principles of Adam Smith mathematically correct?
+
+2. I observe that England is represented mathematically by an ellipse.
+Are we right in assuming that Ireland is a portion of that ellipse? Or,
+on the other hand, in our chart of nations, must we describe that
+troublesome country as a rotating parabola, or complex figure,
+altogether outside our more favoured State?
+
+3. Do you consider, from your minute observation of our social system,
+that the form of our elliptical government is gradually undergoing a
+change, and that a revolutionary parabolic tendency is observable in the
+action of individual particles?
+
+4. Is it not possible that the differences in the policy of the various
+nations of Europe; the difficulties which beset the carrying out of
+international law; the jealousies, quarrels, and rivalries of States
+might disappear, if the same form of government (_i.e._, elliptical)
+were adopted in each?
+
+If you will kindly favour Her Majesty's Ministers with your opinion on
+these questions, they will owe you a debt of gratitude, which they, as
+representatives of the nation, will do their utmost to repay.
+
+With every good wish for your further success in the regions of
+polemical science,
+
+          I beg to remain,
+              My dear Lady Professor,
+                  Your faithful servant,
+                        +----------------------+
+                        |                      |
+                        |         [4]          |
+                        |                      |
+                        +----------------------+
+
+
+[Editorial Note.]--The next letter is not of quite the same pleasing
+nature as the foregoing, and shows that it is impossible to please
+everyone, even if that happy consummation were desirable. This letter
+was evidently called forth by some remarks which the learned Lady
+Professor had made in her third lecture with reference to eccentricity
+in dress. Our readers will recollect that the professor pointed out that
+an extravagant 'bloomer' costume--half male, half female--was no more a
+sign of genius than aesthetic dresses, always betokened the artist.[5]
+This latter statement evidently gave great offence to the members of a
+society which called itself the 'Aesthetic and Dress Improvement
+Association,' and the following letter is the result of one of their
+solemn conclaves:
+
+
+                    Oscar Villa, South Kensington,
+                            June, 18--.
+
+The Secretary of the Aesthetic and Dress Improvement Association presents
+his compliments to the Lady Professor of Girtham College, and begs to
+contradict emphatically her statements with regard to a subject upon
+which she is evidently in entire and lamentable ignorance, and to
+protest against her aspersions upon the artistic studies of this and
+kindred societies. He begs to state that true aesthetes are _not_
+eccentric (they leave that to lady professors and her Philistine
+followers); that to dress becomingly is one of the principal objects of
+life, and that true greatness is achieved as much by the study of the
+art of dress as by any other noble pursuit or graceful accomplishment.
+Are not Horatio Postlethwaite, Leonara Saffronia Gillan, Vandyke
+Smithson entitled to greatness? And yet their laurels have been won
+solely by the art of dress. Perhaps the lady professor has never read
+'Sartor Resartus'! In conclusion, he would ask the Lady Professor to
+refrain from casting obloquy upon the work of the Association which he
+has the honour to represent; to prevail upon her pupils to abandon the
+unfeminine attire which some of them have assumed, contrary to the first
+principles of art; to array themselves in flowing robes of sage-green
+and other choice colours (patterns enclosed), and to study art, instead
+of absurd mathematics, which no one can understand, and do no one any
+good.
+
+     (Approved by the Committee of the Aesthetic and Dress
+      Improvement Association.)
+      June, 18--.
+
+
+[Editorial Note.]--The next letter, written by a pupil of the Lady
+Professor, requires no explanation, and speaks for itself.
+
+
+                    Jesus College, Cambridge,
+                            March, 18--.
+
+My dear Tutor,
+
+You will be glad to hear that after superhuman exertions I have at last
+succeeded in passing my Little-go, and I am eternally grateful to you
+for all you have done for me. I should never have got through if it had
+not been for you. All the coaches in Cambridge would never have managed
+it, but you drove me through in a canter. And why? I never could make up
+my mind to work for them; but when I coached with you, you made me like
+it. I almost revelled in the Binomial when you wrote it out for me; and
+then I could not help listening to you; and you looked so grieved when I
+would not learn, and made me feel such a brute; so somehow or other you
+drove some mathematics into my head, and I pulled through. By-the-bye, I
+think you must have tried the 'brain wave' dodge with the examiners, as
+five out of the six propositions in Euclid, which you told me to get up
+specially, were set! I wish I could read people's thoughts; can you read
+mine? If I were a Don, or a Fellow, or something, I would advise the
+University to have some lady professors like you to teach the men,
+instead of some of these sleepy old tutors. It would be a great
+improvement, and I am sure we should get through a great deal more work.
+
+They have given me a place in the Jesus Eight, which I shall take now
+that I am released from your professorial ban, and have time for rowing.
+But I don't half like giving up mathematics. You see, I have grown fond
+of the study. Do you think you could make a wrangler of me? At any rate,
+I should like to come to your lectures again. May I?
+
+                    Your Grateful Pupil.
+                         *     *     *
+
+
+  [4] It is to be regretted that this letter has evidently fallen
+      into the hands of some autograph collector, who has ruthlessly
+      cut off the signature; but the reader will easily determine,
+      after careful perusal of the document, from whose pen it emanated.
+
+  [5] Cf. page 36.
+
+
+
+
+PAPER V.
+
+A LECTURE UPON SOCIAL FORCES, WITH SOME ACCOUNT OF POLEMICAL KINEMATICS.
+
+
+Most noble Professors and Students of Girtham College,--Since last 'I
+wandered 'twixt the pole and heavenly hinges, 'mongst encentricals,
+centres, concentricks, circles, and epicycles,' like the great
+Albumazar, and found them full of life and wisdom for the guidance of
+our States and laws, I have turned my attention to the Applied
+Mathematics, in order to determine what other truths this shaft may
+yield.
+
+The strength of all sciences, according to Bacon, consists in their
+harmony; and it is truly marvellous how perfect this harmony is, if our
+ears are tuned aright to hear it. We have observed how the beautiful
+and regular laws of curves and cones correspond to the social laws of
+States and nations, guiding them as if by word of counsel, admonishing
+them on what principle they ought to regulate their governments and
+inter-relations. We have seen that the laws which govern thought and
+light and sound are almost identical, and that harmony pervades not
+merely the ordinary sciences, but extends her benign influence over
+these newly discovered fields of scientific research, which I claim to
+have discovered.
+
+All this may appear at first sight surprising; but the real philosopher,
+who knows that all kinds of truth are intimately connected, will receive
+such revelations of science with satisfaction rather than astonishment;
+for this new science, which has opened itself out before me, is only an
+extension of other well-known laws and discoveries which have come down
+to us from the remote past.
+
+If my investigations should appear to you, most noble professors,
+somewhat novel and imaginary, remember the maxim of the sage, that in
+the infancy of science there is no speculation which does not merit
+careful examination; and the most remote and fanciful explanations of
+facts have often been found the true ones. Perhaps some
+'self-opinionated particle' (I speak mathematically) may have been
+inclined to laugh at our theories and discoveries, as the wise fools of
+the day laughed at Kepler and his laws; but time has changed the world's
+laughter into praise, and a century hence our discoveries may rank among
+the achievements of modern science. As Cicero says, 'Time obliterates
+the fictions of opinions, but confirms the decisions of nature.'
+
+I have not shunned, most noble professors, to enlist Imagination under
+the banner of Geometry; for I am fully persuaded that it is a powerful
+organ of knowledge, and is as much needed by the mathematician as by the
+poet or novelist. It is, I fear, often banished with too much haste from
+the fields of intellectual research by those who take upon themselves to
+give laws to philosophy. We need imagination to form an hypothesis; and
+without hypotheses science would soon become a lifeless and barren
+study, a horse-in-the-mill affair ever strolling round and round,
+unconscious of the grinding corn. In my previous investigations my
+imagination pictured the symmetry of curves and States; the hypothesis
+followed that the laws which regulated them were identical, and you have
+observed how the supposition was confirmed by our subsequent
+calculations.
+
+In this lecture I propose to examine some of the forces which exist in
+our social system, and shall endeavour to estimate them by methods of
+mathematical procedure and analogical reasoning. We will begin with the
+old definition of Force as _that which puts matter into motion, or which
+stops, or changes, a motion once commenced_. When a mass is in motion,
+it has a capacity for doing work, which is called _Energy_; and when
+this energy is caused by the motion of a body it is called Kinetic
+Energy (in mathematical language KE = 1/2 MV^2). Another form of kinetic
+energy is called Potential Energy, which is in reality the capacity of a
+body for doing work _owing to its position_. For example we may take an
+ordinary eight-day clock. When the weights are wound up, they have a
+certain amount of potential energy stored up, which will counteract the
+friction of the wheels and the resistance of the air on the pendulum.
+Or, again, we have the example of a water-wheel: first the water in the
+reservoir, being higher than the wheel, has an amount of potential
+energy. This is converted into kinetic energy in striking against the
+paddles, and after this we have potential energy again produced by the
+action of the fly-wheel.
+
+By the principle of conservation of energy, if we consider the whole
+universe, not our planet alone (for its heat and energy are continually
+diminished to some slight degree), we find that _no energy is lost_.
+
+Force is recognised as acting in two ways: in _Statics_, so as to compel
+rest, or to prevent change of motion; and in _Kinetics_, so as to
+produce or to change motion; and the whole science which investigates
+the action of force is called _Dynamics_.
+
+All this is of course pure mathematics, and I have made these elementary
+observations for the benefit of my younger hearers, the students of this
+University. My grave and reverend seniors will pardon, I am sure, the
+repetition of facts well known to them for the sake of those who are
+less informed than themselves.
+
+Now before I proceed further, I will endeavour to point out that these
+elementary truths of physical science hold good in our social system.
+Each individual is a mass, acted on by numerous forces, capable of
+'doing work,' which work can be measured and his velocity calculated.
+Some individuals have a vast _potential energy_; that is to say, from
+their position and station in the social system, they have a power which
+is capable of producing work which a less exalted individual has not.
+Like the weights in an eight-day clock, or the water in a reservoir,
+they have a capacity for doing work, owing to the position to which
+they have been raised. How vast the influence of a Primate or a Premier,
+a General or a King! And yet their power is chiefly potential energy,
+arising from the position they occupy, not from the individuals
+themselves. Schiller has described this in poetical language, which,
+strange to say, is mathematically correct:
+
+   'Yes, there's a patent of nobility
+      Above the meanness of our common state;
+    With what they _do_ the vulgar natures buy
+      Their titles; and with what they _are_, the _great_.'
+
+Other forces may have raised these men to their exalted positions; but
+their influence is due to their height, their potential energy. Placed
+on a lower level, they would cease to have that power. How calm the
+dignity of this potential rank! The water in the reservoir is scarcely
+ruffled or disturbed, as if unconscious of its power; when it has lost
+its force it rushes along with a sullen murmur and a roar, howling and
+hissing and boiling in endless torture, until--
+
+   'It gains a safer bed, and steals at last
+    Along the mazes of the quiet vale.'
+
+So the vulgar crowd rushes on, with plenty of kinetic force, making
+noise enough and looking very busy; while those who seem to sleep in
+calm forgetfulness, exercise their potential energy, and do the real
+work of turning the great engine of the State.
+
+There are attractive and repulsive forces (more commonly the latter, the
+cynic will say) in our social system, but each individual is the centre
+of various forces acting upon him. In nature all matter possesses the
+force of gravity, and whatever the size of two particles may be, they
+mutually attract each other. The earth attracts the moon; the moon
+attracts the earth. A stone thrown up into the air exercises an
+infinitesimal force upon the earth; so in the social system every
+individual, however small and insignificant he may be, exercises some
+attractive force upon his neighbour. There is no one in the world who
+does not exercise some influence for good or for evil upon his fellows.
+
+The force of _cohesion_ is manifest in society as in nature, that force,
+I mean, which resists the separation of a body's particles. Different
+bodies possess different powers of cohesion, _e.g._, the cohesion of
+chalk is far less than that of flint embedded in it; even the same body
+possesses different powers of cohesion in different directions, _e.g._,
+it is easier to split wood in the direction of the fibres than
+perpendicular to them. If by our old principle of continuity we change
+the words 'bodies' into 'States' or 'individuals,' we shall see that the
+same laws hold good in social science as in natural philosophy.
+
+These are a few analogous laws which I have taken almost at random; but
+it must strike the most casual listener to my remarks that it is
+wondrous strange that men, regarded as social beings, should possess the
+same qualities, and be governed by the same laws, as the rest of
+_matter_. As Bishop Butler says, 'the force of analogy consists in the
+frequency of the supposed analogous facts, and the real resemblance of
+the things compared.' It appeals to the reasoning faculty, and may form
+a solid argument. Hence, if we can prove the similarity of various laws
+and conditions, we may not be wrong in assuming by analogy the identity
+of those laws and conditions.
+
+I have stated my case in this manner in order to convince the
+gainsayers, if any such there be, and to banish any doubts or
+questionings which may have arisen in your minds. I will now proceed
+with some further investigations, full of the most profound interest
+and importance.
+
+Doubtless many of the lady-students present are in the habit of
+welcoming peaceful evening in with a potent draught of 'the cup which
+cheers but not inebriates;' and as men are great flatterers (for
+imitation is the greatest flattery), I believe the male portion of my
+audience have been known to follow that excellent example. Some perhaps
+are in the habit of burning the midnight oil, and keep their eyes open
+by means of this fruit of the hermit's pious zeal, endowed by high
+omnipotence with the power of hindering sleep;[6] but that practice I
+do not advise, as that delicate portion of our system, the nerves,
+especially of women, often becomes injured by such stimulating doses.
+However, you will have observed (if you do not follow the modern
+pernicious fashion of taking tea without sugar) that numerous bubbles
+are formed upon the surface of the liquid. After a few moments these
+unite into one central mass of bubbles by the force of mutual
+attraction.
+
+It appears from considerations which are detailed in works on physical
+astronomy, that two particles of matter placed at any sensible distance
+apart attract each other with a force directly proportional to the
+product of their masses, and inversely proportional to the square of
+their distance.
+
+Now, suppose that we have a number of circular masses situated upon a
+plane surface, they will attract each other with a force which may be
+determined with exactitude; and the greater the masses the greater the
+force. We will now apply this to polemical science. The agricultural
+settlement is the first stage in the civilization and formation of a
+State. How did this arise? First, a single family immigrated to some
+uncultivated parts of the country, perhaps accompanied by others, who
+formed a little colony. Other settlements were made in other parts of
+the land; and thus the country became overspread with these detached and
+separate communities. An eminent writer declares that these settlements
+can be traced in the beginnings of every race which has made progress;
+that they were characteristic of those races in Greece and Italy, in
+Asia and Africa, which grew into the opulent and famous cities in which
+so much in the early history of civilization was developed. The colonies
+of England have been formed in the same way, just as in olden time
+England itself was occupied when the Roman power ceased.
+
+These settlements correspond to the circular masses situated on the
+plane surface; they were quite separate from each other, each having its
+own laws, its own headman or ruler, its own assembly or parish council.
+But as time elapsed, the force of mutual attraction set in; by degrees
+these separate settlements were drawn together by force which increased
+in proportion as the settlements increased; until at last one united
+kingdom was formed under one king, governed by uniform laws and
+regulations. The bubbles have blended, the circles have come together,
+and one large circle or other curve is the result. This may be called
+the _Law of Social Attraction_. In accordance with the results of one
+of my previous lectures, I have taken the circle as representing the
+simplest form of government, which figure, in the case of the elementary
+settlements, must have been small.
+
+Many of you, most noble professors, are doubtless accustomed to make
+experiments with the microscope. I will suggest a simple one, which
+illustrates very forcibly what I am endeavouring to show you. Take some
+particles of copper, and scatter them at intervals over the surface of
+an object-glass, and pour some sulphuric acid upon the glass. Now, what
+is the result? A beautiful network of apparently golden texture spreads
+itself gradually over the whole area of the glass. Steadily it pursues
+its way, and the result is beautiful to behold. The minute particles of
+copper were the original settlements scattered over the land; the
+sulphuric acid the civilizing agent; and the final picture of a united
+civilized homogeneous nation is well represented by the progressive and
+finally glorious network of gold. This example is of course outside our
+present subject, but it serves as a beautiful illustration.
+
+As an instance of the attractive force exercised by small communities
+upon each other, I may mention the united kingdom of Germany, which is
+composed of numerous small States and nations, which have been drawn
+together by the power of mutual attraction. Until recently they were
+each self-contained, separate constitutions, with their own kings and
+forms of government; but the attracting force, assisted by forces from
+without, has proved too much for them, and the great and powerful united
+kingdom of Germany is the result.
+
+But why, you may ask, have not the people in Hindustan united in the
+same way? There the agricultural settlements remain as they did ages
+ago; separate petty chieftains rule under the all-governing power of
+England. Why have they not united?
+
+To this objection I reply that there is in social science, as in Nature,
+a _vis inertia_; that is to say, there is a tendency in matter to remain
+at rest if unmoved by any external agency, and also of persisting to
+move, after it has once been set in motion. The _vis inertia_ of some
+bodies is greater than that of others, and depends upon their weight
+and density. Now it so happens that the moral _vis inertia_ of the
+Hindustani is very great, hence their tendency to amalgamation is
+small. They remain in the state in which they happen to be.
+
+On the other hand the inertia of Englishmen is small, of Englishwomen
+smaller, and therefore their power of combining is greater. Here let me
+observe that the quality of inertia is one which ought to be removed as
+far as possible from each social system. Inertia was regarded as a
+capital crime by the Egyptians. Solon ordained that inert persons should
+be put to death, and not contaminate the community. As savages bury
+living men, so does inertia practise the same barbarous custom upon
+States and individuals. Observe the putrid state of inert water, the
+clear and sparkling beauty of the moving stream, bearing away by the
+force of its own motion aught that might contaminate it. Men more often
+resemble the stagnant water than the rivulet. A healthy social state
+enforces labour by natural laws, and banishes inertia as much as
+possible from the system. If the principles of some noisy English
+politicians were fully carried out, and all things made '_free_,'
+inertia would be increased, and listless indolence pervade the masses of
+our countrymen. I may say that inertia is not entirely unknown in our
+sister University of Cambridge.
+
+The existence of social forces is supported by the testimony of Dr.
+Tyndall, who plainly recognises their power, though he does not attempt
+to expound their origin. 'Thoughtful minds are driven to seek, in the
+interaction of social forces, the genesis and development of man's moral
+nature. If they succeed in their search--and I think they are sure to
+succeed--social duty would be raised to a higher level of significance,
+and the deepening sense of social duty would, it is to be hoped, lessen,
+if not obliterate, the strife and heart-burnings which now beset and
+disguise our social life.' I accept with gratification Dr. Tyndall's
+conclusions: to determine, examine, trace, calculate these social forces
+which exercise such a powerful influence on our characters, our lives,
+our customs, which produce the greatness of the State, or drag it down
+with irresistible strength from its pinnacle of glory to an abyss of
+degradation; to estimate such forces is the great and noble object of
+our lectures and researches in this University. Prosecute, most noble
+professors, your studies in this direction with all the energy of your
+enlightened intellects, and there is yet hope that this new science,
+which I have endeavoured to sketch out, however feebly, may be the means
+of saving our beloved nation from degradation and ruin, and raising her
+to a higher level of glory and honour. I hope to continue the subject of
+social forces in my next lecture.
+
+
+  [6] A Chinese legend relates that a pious hermit, who in his
+      watchings and prayers had often been overtaken by sleep, so
+      that his eyelids closed, in holy wrath against the weakness
+      of the flesh, cut them off, and threw them on the ground. But
+      a god caused a tea-shrub to spring out of them, the leaves of
+      which exhibit the form of an eyelid bordered with lashes, and
+      possess the gift of hindering sleep.--Dr. Ure.
+
+
+
+
+PAPER VI.
+
+ON SOCIAL FORCES (_continued_)--POLEMICAL STATICS AND DYNAMICS.
+
+
+Most Noble Professors and Students of Girtham,--We have embarked upon
+a stormy sea of speculation, on a voyage of grand discovery, and the
+dangerous waves of adverse criticism, and the deceptive under-current of
+prejudice, often make the steersman's lot by no means an enviable one.
+But our vessel is sound and perfectly equipped, and therefore I do not
+fear to guide her across the great unknown.
+
+It may have occurred to you that the problems which present themselves
+for solution in social science are far more difficult and complicated
+than those which arise in ordinary mathematics. That is undoubtedly the
+case; but this extra degree of difficulty is due to the fact that we
+make no assumptions; we take the things as they really are, not as they
+are assumed to be. In physical science, if we take into consideration
+the resistance of the air, the curvature of the earth, the rigid
+connection which exists between particles in the same body, and a host
+of other things which are often conveniently neglected in elementary
+works, how complicated the various problems become! So we must not be
+surprised at some of the difficulties which occur in social science, as
+nothing is neglected; the whole problem is before us, and having solved
+it we need not make allowances for any falsely assumed _data_.
+
+It is possible that other professors of this science may come to
+slightly different conclusions to those which I have arrived at. That
+is only to be expected, because their original observations may have
+slightly varied. But in physical science allowances are made for
+different observers. In astronomy, for example, we find the value of the
+'Personal Equation.' One observer on looking through the telescope may
+take the meridian of a star rather differently from another watcher of
+the heavenly bodies, and the _personal equation_ is used to make
+allowances for this quickness, or slowness, of observation. So in social
+science there must be a personal equation too, and our object ought to
+be, in the ordinary affairs of life as well as in the higher duties of
+scientific action, to make our personal equation as small as possible.
+But until the old proverb, '_Quot homines, tot sententiae_,' has ceased
+to have any meaning, there will be abundant need of this most useful aid
+to accuracy.
+
+The close connection which exists between social forces and material
+forces is plainly shown by the doctrine of the conservation of energy.
+'This doctrine,' says Dr. Tyndall, 'recognises in the material universe
+a constant sum of power made up of items among which the most Protean
+fluctuations are incessantly going on. It is as if the body of nature
+were alive, the thrill and interchange of its energies resembling those
+of an organism. The parts of the stupendous whole shift and change,
+augment and diminish, appear and disappear; while the total of which
+they are the parts remains quantitatively immutable, _plus_ accompanies
+_minus_, gain accompanies loss, no item varying in the slightest degree
+without an absolutely equal change of some other item in the opposite
+direction.' So do the forces in the social world ebb and flow, rise and
+fall, carrying on the same universal law which regulates the energy of
+material force.
+
+I will now proceed to enumerate some of those forces which exercise such
+a powerful influence on society.
+
+First, let us take the force of _Public Opinion_, which seems to
+exercise a relentless sway over the minds and manners of men. This is a
+very subtle and secret force, which is most difficult to trace, and
+resembles electricity in the science of physics. We cannot see it, but
+are only able to judge of its power by its results. Its point of
+application is not in the individual, but in the collection of
+individuals who make up the social system; and it is, in reality, the
+resultant of, or the compromise between, the various elementary forces
+which make up human society. Yes, compromise is a purely mechanical
+affair, based on the principle of the parallelogram of forces; and as
+public opinion is the result of a compromise, we may calculate its
+force. For example: 'It is required to know the state of public opinion
+in the matter of politics, when the results of a General Election show
+that the Conservatives are to the Liberals as 10 : 9.'
+
+Let OC be the direction of the Conservative force.
+
+Let OL be that of the Liberal.
+
+Then by _data_ OC : OL :: 10 : 9.
+
+[Illustration]
+
+Complete the parallelogram, and join OP.
+
+Then OP represents the force of public opinion in magnitude and
+direction.
+
+N.B.--The direction of OL is determined by the amount of deviation of
+the policy of the Liberals from that of the Conservatives.
+
+As in physical, so in social science, impulsive forces sometimes act,
+and effectually disturb our system and our calculations. Public opinion
+is very liable to the action of disturbing forces. Panic is an impulsive
+force, which defies the power of the most learned professors of social
+science to determine its magnitude and direction. Some strange
+unforeseen catastrophe--the fascination caused by a brilliant and
+unscrupulous orator, a cruel wrong, a blind revenge for real or
+imaginary injustice--will sometimes rouse one element of passion latent
+in the vast body of public opinion; so that it breaks with all that
+hitherto restrained and balanced it, and precipitates society into a
+course of conduct inconsistent with its former behaviour, and bloodshed,
+revolution, the breaking-up of laws, are the terrible results of panic
+or revengeful passion.
+
+Society is, as it were, split up by the terrible action of such
+impulsive forces, just as wood is split up by the repeated blows of the
+hatchet. It is, therefore, the duty of statesmen to increase the power
+or force of cohesion, to strengthen the fibres of the State, so that the
+force of such impulsive blows may not be felt, nor disturb the
+continuity of the framework of the State. If such measures had been
+adopted in the neighbouring country of France, much misery might have
+been avoided, and the terrible revolutions which have so frequently
+convulsed her social system entirely prevented.
+
+_Friction_ is another disturbing element in our calculations, and
+although it may be made a useful servant, it is a bad master in
+mathematics, as in polemics. Without the aid of friction, progress would
+be impossible. For example: Take the case of a man with perfectly smooth
+skates on perfectly hard, smooth ice; he would be unable to reach the
+land unless he had provided himself with some stones, by throwing which
+he would just be able to get to his destination by a backward motion.
+The engine would be unable to proceed on its iron road if it were not
+for friction. The same is true in polemical science: the government of
+the country would not be able to be carried on under our present
+conditions if it were not for _party friction_. But suppose it increased
+indefinitely, party friction becomes party _obstruction_; and the engine
+of the State would no longer proceed smoothly and evenly along its
+appointed course at the rate of sixty miles an hour, but would resemble
+an old-fashioned coach, up to its axle-trees in mud, its motion
+altogether stopped by the action of party friction.
+
+We have seen that forces have two ways of acting: that of compelling
+rest and that of producing motion. In statics forces act so as to
+prevent any change of motion, or disturb the body's original position.
+In kinetics, on the contrary, the power is recognised as acting so as to
+produce or change a body's motion. Now, in polemical science we have
+these two ways of considering the action of forces. There is the
+_statical_ or _conservative_ force, which compels rest, which seeks
+security, stability, and peace, and is not ardently devoted to change.
+It reduces the system to equilibrium. There are, of course, two kinds of
+equilibrium--_stable_ and _unstable_--according as the social and
+political system is in a healthy or unhealthy state. If a body is in
+stable equilibrium, and any slight motion takes place, the body will
+return immediately to its former position; but if in unstable, it will
+decline further and further away from its original position, and be
+entirely upset. So a healthy and sound conservative equilibrium is not
+disturbed by outside forces, and the State will resume its former
+position of stability and rest when the opposing force is withdrawn. But
+an unhealthy and insecure conservatism is as easily disturbed as an egg
+balanced on its narrow end.
+
+The kinetics of society, that is to say the Radical way of estimating
+force, is the party of motion, generally supposed to be the 'party of
+progress.' It has therefore many attractions in the eyes of those who
+delight in motion, speed, and rushing about. To run at full speed, to
+feel the keen air upon one's face, to experience the delightful
+sensation of freedom of will, and limb, are joys which cannot be denied.
+Such exercise is beneficial to the system, bodily or political. Motion
+is the life of all things; it is characteristic of nature; it adores
+nature; because it is an emblem and characteristic of life. The
+ceaseless rolling of the ocean waves, the swaying of the trees, the
+bending of the flowers, the waving of the corn, all these fill us with
+pleasure; whereas a flat uninteresting plain, unrelieved by the motion
+of terrestrial objects, is depressing to the spirit. So there is much to
+be said in favour of motion, and Carlyle has defined progress as 'living
+movement.' And men love this 'living movement,' and take up the
+Laureate's cry:
+
+               'Forward, forward, let us range,
+    Let the great world spin for ever down the ringing
+                Grooves of change.'
+
+But, after all, there is a danger in this everlasting motion. We cannot
+tell whither this progress may lead. It may be along a safe sure road;
+but perchance a precipice may open out before us; and rejoicing in the
+acceleration of our velocity, with eyes intent upon some distant heights
+of glory and ambition, we may not discover our danger until it is too
+late to stop, and a terrible plunge into an unknown abyss of turmoil and
+tumultuous waves is the alarming result of an unguarded policy of
+unrestrained 'progress.' I recall to my mind the quaint words of Holmes
+which aptly illustrate my contention.
+
+   'If the wild filly, "Progress", thou would'st ride,
+    Have young companions ever at thy side;
+    But wouldst thou stride the staunch old mare, "Success,"
+    Go with thine elders, though they please thee less.'
+
+Progress and success do not always go together hand in hand; and while
+motion is essential to life, it is not always safe to urge a country
+forward at too great a speed; and security and stability are quite as
+important to the nation's life as actual progress.
+
+There are other impulsive forces which act occasionally in the sphere
+of politics, and which baffle all our calculations, and exclude
+scientific considerations of the polemical problems which arise.
+_Ambition_ is such an impulsive force, and when the rulers of the people
+are actuated by it, and struggle for money, place, and power, politics
+is degraded from its position as a science, and it becomes impossible to
+estimate the result of forces so generated.
+
+In my next lecture I propose to treat the important subject of the Laws
+which govern States and Governments, and which regulate, generate, and
+control the social forces which we have seen at work in the body
+politic.
+
+
+
+
+PAPER VII.
+
+LAWS OF POLITICAL MOTION.
+
+
+Since the last time I had the honour of addressing you on polemical
+matters, I have met with a passage in the writings of M. Auguste Comte
+which afforded me much pleasure. It seemed to be the one word for which
+I had been waiting, and confirmed many of my own impressions and
+speculations. He lays down two propositions: first, that the
+constructive politics of the future must be based on the history of the
+past; and second, that political science is a composite study, and
+presupposes the complete apprehension of every branch of science,
+beginning with the physical, such as astronomy, and ending with the
+moral, such as ethics and sociology. M. Comte evidently does not regard
+as a vain dream and imaginative speculation the theory that it will be
+possible for statesmen to calculate a policy, and to determine a course
+of action by purely scientific considerations. May I entertain the hope
+that in this university, where all branches of physical science have
+found a home, and are studied by most able and learned professors, the
+science of politics may be pursued under most favourable circumstances?
+I trust that each professor will bring before me the results of their
+deliberations, and contribute to the growth of this particular science
+for which our university has already become deservedly famous.
+
+My present lecture is devoted to the important consideration of _Law_.
+At first sight it may appear to you that the wills and passions of
+mankind are so diverse and unknowable, that it would be absurd to
+suppose that they can be calculated, or rendered amenable to any law.
+But Professor Amos has pointed out that in proportion as we examine
+history, and compare the actions present and past of different nations
+and states, the more uniform does human nature appear; the more
+calculable the actions, sentiments, and emotions of large masses of
+people. As we have already stated, the difficulties of the study are not
+likely to deter the professors of Girtham College from the pursuit of
+any particular branch of science.
+
+_A priori_ we might suppose from analogy that these polemical laws
+existed, as there is no department of nature which is not governed by
+law. It is an essential feature in nature, and also in government. What
+is political economy but the study of certain laws of nature? These were
+first discovered by Adam Smith, and have since been traced and estimated
+by such men as Ricardo, the two Mills, Professor Cairnes, Jevons, and
+many others. Moreover, our physical constitutions are governed by laws,
+which physicians have determined, and which it is perilous to resist.
+Our moral constitution is also governed by laws, which evidently exist,
+although it is difficult to find them out. But the nation is only an
+assemblage of individuals; and since individuals are so governed, it is
+only natural to suppose that the nation, composed of individuals, is so
+constituted and controlled. And not only is that true, but we shall see
+that polemical laws are as permanent and universal, as invariable and
+irreversible, as the laws of nature which regulate the courses of the
+heavenly bodies, and raise the tides, or depress the sandstone hills.
+
+We may notice first the preponderant impulse observable in a nation's
+life in favour of supporting existing facts and institutions; and every
+reformer has discovered the difficulty and danger of changing or
+opposing the customs and habits of the people. As a wheel will travel
+most smoothly along a well-worn groove, whereby friction is diminished,
+so there is a natural national tendency always to run along those paths
+with which the habits and customs of the people have made them familiar.
+This law is nothing else than Newton's first law of motion, which is
+quite as applicable to human masses as to lifeless matter. The tendency
+of matter to remain at rest, if unmoved by any external agency, and of
+persisting to move after it has once been set in motion, is a
+conservative tendency; and is as true in political science as in any
+other.
+
+The special branch of our science, which we may call the _Biology of
+Politics_, shows how absolute is the domain of law in polemical matters.
+The law of human life is that men are born, grow, become strong and
+vigorous, and then decay and die. This is the law of life, to which we
+must all yield an enforced obedience. This same law is observed to be at
+work in the heavenly bodies; and astronomy shows us that planets are
+born, flourish, and at length die, just as our human bodies do. The moon
+is, as you may have observed, a dead planet, such as our earth may be
+some day. The same growth and decay are also manifest in national life.
+First, there is the birth of the nation, which sometimes lies a long
+time in a dormant state, and then wakes up to life and energy. China and
+Russia are examples of dormant States, just waking from a long sleep of
+childishness and ignorance. The next stage is the strong an healthy
+period of its existence, which England is at present enjoying; and then,
+after various stages of gradual decline, we come to the senile period of
+national life, when every energy and faculty, every national feeling and
+power of invention, are completely exhausted. As an example of this
+depressing condition, we may mention Turkey and several of the effete
+States of South America. Sometimes, when life is nearly extinct in the
+human body, physicians have made use of the power of galvanism, in order
+to revive the dying energies. This process of galvanizing a State into
+life was tried by Lord Palmerston and others on the worn-out frame of
+Turkey. But such attempts can only meet with partial and transitory
+success; and where the loss of national power and faculty betokens the
+senile period of the nation's existence, it is vain to attempt to
+restore its former life and energy. The study of the biology of
+politics presents many interesting and important details in this special
+branch of knowledge; and I commend this part of our subject to the
+special attention of the professor of physiology. The law of development
+is observable in nations as in nature. Recent scientific discoveries
+have tended to take away all ideas of _chance_ in the workings of
+nature, and have substituted _law_ instead of it. It would be
+unscientific and incorrect to speak of the world being formed by the
+'fortuitous concourse of atoms.' So we cannot speak of a State being
+generated in this manner. Laws--economical, geographical,
+natural--preside over the formation of States and nations, and produce
+their further development.
+
+The laws of political motion occupy the same prominent place in our new
+science as Newton's laws do in ordinary dynamics. These are very
+important in calculating the positions which various States will occupy
+in the future. First, we have the _doctrine of nationality_, which
+prevented the progress of Austria into Italy, and of the Bourbons in
+Naples, and produced the amalgamation of the small German States in the
+great empire of Germany. The second law of political motion is the
+doctrine of the _independence_ of all true States, and the equality of
+all States to each other. This had its growth in feudalism; and all the
+chief wars of modern times have been the result of the efforts of nature
+to establish this law of independence. The doctrine of intervention is a
+modification of the preceding law, and is applicable when the law of
+necessity demands its use, such as the restoration of order after
+protracted anarchy, the abolition of slave trade, etc. The third law is
+the _law of morality_. Just as for each man there exists a _right_ and a
+_wrong_; just as _duty_ and _conscience_ are certain elements in his
+daily motion, which dictate his course of action, although he may chose
+to neglect them; so a nation is bound by the same moral laws which
+govern the individual; and a nation errs if it transgresses them.
+Christianity is the agent which has produced so powerful an influence
+in making men obey the dictates of conscience and walk in the path of
+duty; and I read with thankfulness the conclusion of Mr. Amos, that
+Christianity has triumphed quite as much in moralizing secular politics
+as it has in the sphere of individual life.
+
+       *       *       *       *       *
+
+These are some of the principal laws of motion which I have observed at
+work in various States and nations. Inasmuch as political science
+embraces, in addition to the physical sciences, all those branches which
+are contained in ethics, economics, jurisprudence, sociology and others,
+the laws of each are generally applicable to the whole grand subject of
+which my lectures treat. Other general laws may be deduced, and have
+been enumerated in my previous lectures, from the social properties of
+curves and conics; and when our researches are complete we may hope to
+produce a code of laws for the guidance of our statesmen which maybe of
+immense use in determining the policies of the future. Already there is
+strong evidence that the affairs of this country are being conducted on
+sound scientific principles, rather than by any species of guess-work or
+haphazard contrivances. The use of history is recognised as extremely
+important in determining a future line of conduct; and statesmen are in
+the habit of endeavouring to find from their study of the past what is
+the logical sequence of events. Just as mathematicians endeavour to
+determine the law of a series of figures, and having found the law, can
+write down the next, and the next, _ad infinitum_; so scientific
+politicians may be able soon to establish the various laws of a series
+of events, and calculate their course of actions. That there is
+considerable progress in this direction is manifest by the value which
+they place upon statistics, and their continued use of this important
+information.
+
+There are a few great evils in our present system which are strongly
+opposed to any scientific methods in politics; and in the interests of
+the country as well as those of science they ought to be removed. One
+great evil is the want of political and scientific knowledge on the part
+of the electors, who are in the habit of choosing their representatives
+on personal grounds, or party considerations, rather than on sound
+principles of political science. All this is opposed to any idea of law.
+Owing to the ignorance of the electors they fall an easy prey to
+adventurers and unprincipled politicians, who make all kinds of specious
+promises, tempt them with all manner of baits, and make self-interest
+instead of the welfare of the State the principle of voting. Selfishness
+is the ruin of social life and intercourse, the destroyer of all
+happiness, peace, and mutual trust in family life or in society. It is
+the root of most of the faults, vices, and crimes in the individual; and
+who can tell the endless disasters which will befall the State, where
+selfishness is the chief motive-power of the electors and the elected? A
+selfish statesman, one who goes into Parliament to gain his own ends and
+forward his own personal interests, is a disgrace to society--
+
+   'Feeling himself, his own low self, the whole,
+    When he by sacred sympathy might make
+    The whole one self. Self, that no alien knows!
+    Self, far diffused as fancy's wing can travel!
+    Self, spreading still, oblivious of its own,
+    Yet all of all possessing!'
+
+I have said that the ignorance of the electorate makes them an easy prey
+to such men; and until they have learnt to detect the false from the
+true, until they become acquainted with the elements of political
+science, and have been taught that their own selfish interests are not
+the highest aims of social government, it is vain to hope for a
+reasonable method of regulating the affairs of the nation, based upon
+logical laws and scientific principles.
+
+And how is this work of educating the electors to be accomplished? Not,
+I maintain, by furious speeches and rhetorical displays; not by bribery,
+baits and banter; but by patient, never-ceasing labour, by lectures on
+history and science, by individual instruction, is the great work to be
+accomplished upon which the security and stability of the country
+depend.
+
+Then we may hope that the 'Reign of Law' in polemical science may be
+ushered in with the joyful acclamations of an enlightened and united
+people, and its benign influence extend from the throne of the monarch
+and the council-chamber of his ministers to the hearth of the cottager.
+Politicians will rule by law; policies be calculated by laws; people
+vote by law; and then methinks I see in my mind (to use the words of the
+blind old poet) a noble and puissant nation rousing herself like a
+strong man after sleep, and shaking her invincible locks; methinks I see
+her as an eagle, renewing her mighty youth, and kindling her undazzled
+eyes at the full mid-day beam; purging and unsealing her long-abused
+sight at the fountain itself of heavenly radiance; while the whole noise
+of timorous and flocking birds flutter about amazed at what she means.
+Such is the glorious vision of the 'Reign of Law.' Let it be the
+business of every Englishman and Englishwoman to arrange the framework
+of our social and political system, that law may have an uninterrupted
+sway; then shall we be a united, prosperous, and contented people, and
+the reign of lawless agitators, bribery-mongers, and counterfeit
+statesmen will have passed away into the oblivion and obscurity of a
+more suitable but less favoured region.
+
+
+
+
+PAPER VIII.
+
+ON THE PRINCIPLE OF POLEMICAL COHESION.
+
+
+In my previous lectures I have had occasion to mention the principle of
+cohesion; but it plays so vital a part in the constitution of States and
+their relations to each other that I consider it advisable to devote
+this lecture entirely to it.
+
+This is a large and comprehensive subject, and embraces such principles
+as the Centralization of States; the Co-operation of States; Monogamic
+Marriage; Unions; Free Trade, and many others equally important. We have
+already noticed that cohesion is a well-known property of matter; that
+its influence is not confined to the regions of physical sciences; and
+that it is the manifest duty of all governments to increase the force
+of cohesion.
+
+Various methods have been tried to accomplish this purpose. The
+principle of Feudalism was one of the earliest attempts to produce the
+cohesion of the nation; and, in an elementary condition of society, it
+was partly successful. The theories of 'Divine Right' and 'Social
+Contract' were other methods which have been adopted; and the unity of
+the Christian Church has been the great means of producing the cohesion
+of the State in olden times; and its aid may be again required for the
+same beneficent object in future complications and social disruptions.
+
+But it is always advantageous in scientific pursuits to go back to first
+principles; and we will adopt that method in our present investigations.
+The social unit is the family; the multiplication of families makes the
+tribe; the multiplication of tribes makes the State; and, therefore, we
+shall not be far wrong if we consider the family tie as the first
+principle of political cohesion. I am in agreement with several learned
+thinkers upon this subject when I say that marriage is a most important
+political factor; and as marriage cannot take place without women, it is
+evident that women play a very important part in promoting the cohesion
+of the State.
+
+This prominent position was duly assigned to women by one of our
+greatest political philosophers, M. Auguste Comte, who strongly opposed
+the fatal fallacy of ancient political systems, which greatly
+overestimated the powers of men, and depreciated those of women. If the
+superiority of bodily strength be the sole cause of greatness in
+political and intellectual pursuits, then, most noble lords of creation,
+we yield to you the palm--you are our masters in this respect. But if,
+on the other hand, it can be shown that physical strength is not a
+requisite for great achievements in these occupations; if the powers of
+endurance, elasticity, adaptability, nervous energy, and patience are
+quite as needful as mere animal strength; then we women are quite as
+capable, and indeed more capable than men, for achieving political
+greatness. In the 'good old days,' when the law of might was right, and
+the strongest arm was the most powerful machinery in the government of
+the country, women were compelled naturally to occupy a less prominent
+position in the conduct of the affairs of the nation; and for centuries
+they have been degraded by a dominating tradition, and supposed
+incapable of performing duties for which they were mentally well suited.
+But those militant days are past. Animal strength and brute force are no
+longer needed in the councils of the nation; and the time has arrived
+when women should cease to be oppressed by the disparaging, illogical
+deductions of former generations, and when their assistance ought to be
+invoked in the great work of promoting the nation's welfare.
+
+I have stated that marriage is an important political factor; and,
+therefore, women have always occupied a primary, though obscure, part in
+political affairs. The cohesion of the State has been produced by the
+secret influence of family life. But it may be asked, What kind of
+marriage is most conducive to national cohesion? This question has been
+carefully and conclusively answered by a learned scientific writer, who
+shows that polygamic marriage never exists in an advanced state, as
+instanced by the history of Judaism and Mohammedanism; that a strict
+form of monogamic marriage is essential to political greatness and true
+progress in civilization. The cohesion of the State is destroyed by
+polygamy, and by any system which relaxes the binding nature of the
+marriage tie. 'Domestic disorganization is a sure augury of political
+disruption.'
+
+Cohesion, the essential property of all rightly constituted nations, is
+often in danger of being lost when the State is geographically very
+large, or when local interests have greater power than the attractive
+force of the central government. To obviate this evil, the method of
+centralization has been adopted with satisfactory results, as in the
+case of the United States of America, and Germany.
+
+By this means the local authorities are brought into close relationship
+with the central head, and the centrifugal influences of independent
+interests and customs are counteracted by the force of central
+attraction. Centralization increases the importance of the whole body,
+and, like the pendulum of a clock, regulates the movements of the whole
+State. In some cases it tends to make the government despotic, when the
+local governments are entirely under the control of the central; and
+every enactment, and scheme, and plan checked and supervised by the
+chief officers of the State. Such was the system adopted in France by
+Napoleon III. But cohesion without the enforcement of a hard and rigid
+connection, a general supervision without severe tyrannical
+jurisdiction, are the best methods of securing the unity of composite
+States.
+
+But the force of cohesion is evidently at work in the nation apart from
+centralization. Men who have a community of interests unite together
+for the purposes of strength and mutual assistance. They combine for the
+sake of securing means of support in sickness, and form benefit
+societies, such as the Order of Oddfellows or Foresters. This force of
+cohesion has produced trade unions, and similar institutions which exist
+for the purpose of protecting a common interest, and giving expression
+to the concurrent opinions of the members. These have their legitimate
+use in every civilized State, in spite of some of the disadvantages
+which follow in their train. There are, of course, opposed interests in
+every community: _attractive_ forces, which produce trade unions,
+guilds, corporations, companies, and the like; and _repulsive_ forces,
+which result from the opposed interests of employers and employed,
+landlords and tenants, and similar pairs of different classes in the
+community. As time goes on, and the State advances with it, these forces
+will gain in strength; the cohesion of classes will become greater;
+association will grow as naturally as the bubbles form on the surface
+of our evening beverage. It is a law of nature, and therefore cannot be
+resisted. But the repulsive forces will be no less strong, and to
+calculate the resultant of these contending interests will be the
+problem for practical statesmen to solve.
+
+The force of cohesion is also evidently at work, not only in individual
+States, but also amongst the nations of Europe, and of the world. That
+is to say, there is an evident desire for co-operation on the part of
+those nations who have attained to the highest degree of civilization
+and internal cohesion. International law is based on the principle of
+cohesion, and every day it is gaining power and favour in the eyes of
+our leading statesmen. The doctrine of Free Trade, which, if universally
+adopted, would be of the greatest service to mankind, results from a
+desire for co-operation; and whatever evils may result from one-sided
+Free Trade in this country at the present time, there can be no doubt
+that ultimately the complete system will be adopted.
+
+Sad is the fate of a nation when the force of cohesion is weakened. The
+first revolution in France is a proof of this assertion; there was no
+cohesion, no common faith, or loyalty to the throne and Government; and
+indeed the Government, which was rotten to the core, was hardly likely
+to awake any feelings of loyalty and respect; and therefore the social
+disruption which followed was only a natural sequence of events, and was
+prophesied with the accuracy with which an astronomer can foretell an
+eclipse. But that is not all; when the cohesion of the State is
+destroyed, it takes a long time to restore the action of the force; and,
+as in the case of France, further disruption is sure to take place.
+
+In this lecture I have already enumerated some of the ways in which this
+force acts; there are doubtless others which will suggest themselves to
+you. But I contend that the prosperity of the State, and the peace of
+the world, depend upon cohesion. Let this be your work, most noble
+professors, to promote the action of this helpful and life-giving
+force. Promote, as far as in you lies, the sacred union of family life.
+Encourage the generous feelings of true loyalty and patriotism amongst
+the people of this realm of England; counsel our statesmen with regard
+to the primary necessity of national cohesion, and the advantages of
+international co-operation; and your work will be blessed; your names
+will rank with those heroes of the sword and of the pen who have raised
+our beloved country to her present pinnacle of greatness and prosperity;
+and your memory will live in the hearts of your grateful countrymen.
+
+
+[Editorial Note.]--We regret to state that the various MSS. in the
+sealed desk are nearly exhausted, and are therefore compelled to present
+the series of lectures on polemical studies in an incomplete form. But
+we had the good fortune to light upon a brief diary which discloses some
+interesting information with regard to the Author's life and
+occupations. We append a few extracts:
+
+
+
+
+Extracts from the Author's Diary.
+
+
+_June 3rd_.--Arnold called again to-day--the fifth time during the last
+fortnight! His attention is rather overpowering, and wastes much of my
+valuable time. He says he hates science--the heathen!--and wants me to
+lecture in classics. He affirms that mathematics are dry and hard--too
+hard for women, and tend to make them unsympathetic and critically
+severe. I am afraid I was rather severe with him. But really he is very
+trying, and always seems to talk like a Greek chorus in the most
+profound platitudes. Arnold is a classical tutor at Clare College. My
+old pupil is getting on famously. Poor fellow! he seems quite oppressed
+with his work. But he is making great progress, and sticks to his books
+like--a student of Girtham College!
+
+_June 4th_.--Lectured on the Scientific Basis of Blackstone's
+Commentaries; afterwards received pupils until 1 p.m. Really Blanch
+S---- is more tiresome than ever. It appears that she has taken up with
+a young undergraduate of King's, and there is no prospect of any
+improvement in her work unless this nonsense is terminated. How foolish
+some of my sex are, in spite of their improved opportunities! I blush
+for them! Arnold has sent me a copy of Robert Browning's 'Belaustion,'
+in order to make me like classics, and give up science. Misguided young
+man! He has written some tolerable verses on the fly-leaf; but I have no
+intention of playing Belaustion to his 'entranced youth.' These are his
+verses:
+
+   'My lady dear, if I may call you so,
+    For you are dearer than all else beside,
+    I know the love you bear to golden verse,
+    To golden thoughts enshrined in classic lore,
+    To all that's beautiful; so here I send
+    Some echoes of the songs of ancient days,
+    Attuned and chanted by an English bard,
+    Who fires one's old love for the rolling lines
+    Of youthful Hellas; may your cultured ear
+    Receive, and gladly welcome his sweet song.
+    And while we revel in the poet's dream,
+    And hear his actors speak, we'll play our parts.
+    You, sweet Belaustion on the temple-steps,
+    Taking your captors captive by your voice;
+    And I, the youth who, more entranced than all,
+    Was bound by fetters that he would not loose;
+    And so we'll play our part. What say you, dear?'
+
+_June 6th_.--Have just seen our new Professor of Physics, Amelia
+Cordial, who is an excellent woman, and well suited for the high office
+which she holds. She has told me of the foolish conduct of Lady Mary,
+who is evidently of opinion that the professorial mantle ought to have
+fallen on her shoulders. Really, this jealousy in the ranks of the
+learned is most disgraceful; and the bickerings which arise from
+disappointed ambition, the envyings and silly quarrels, are the weak
+places in our female collegiate system.
+
+Such good news! The wrangler list is just out, and my hard-working pupil
+is _bracketed twelfth!_ This is really delightful, and abundantly repays
+us for all our hard toil. But really I have not found working with him
+distasteful; he is such an excellent pupil, so painstaking and eager,
+that I have quite looked forward to his coming, and found him much more
+interesting than some of these foolish maidens. But I almost dread
+seeing him. He will be so elated and overpoweringly grateful, whereas I
+ought to be grateful to him for all his work for me; for I am sure he
+would never have gone in for the Tripos if I had not persuaded him.
+Well, I wonder why he does not come to tell me of his triumph.
+
+_June 7th_.--_It_ has come! and I half expected it. My eager pupil
+writes with all the energy and love of his noble nature to ask me to be
+his wife! He says _that_ is all he cares for, and only values his
+Honours as a step to a higher honour and dignity, that of gaining my
+love and being my husband. All this is very nice to read; but a terribly
+difficult problem is placed before me for solution. I do indeed love
+this dear, good fellow--no one could help doing so, I am sure; but do I
+not love science more? There is a stringent regulation in this
+University that no one shall occupy the position of professor who is
+bound by any domestic ties or cares. All married women are excluded. If
+I say 'Yes,' I must resign my high position, leave this beloved college,
+give no more lectures to entranced audiences. In the interests of
+science, ought I to refuse, and sacrifice my heart's affections for the
+cause of mathematics? But if I say 'No,' I must give up--_him_;
+sacrifice his happiness too, and blight his life. Was ever anyone so
+perplexed? Science, aid thine obedient servant! May I not determine this
+vital question by thine all-pervading light?...
+
+       *       *       *       *       *
+
+[Editorial Note.]--We had just arrived at this exciting moment in the
+life of the learned and accomplished lady whose writings form the
+subject of these pages--a moment when love and science were trembling in
+the balance--when a footstep was heard upon the stairs leading to our
+study, and ere we could secrete our MS. the door was opened, and a
+well-known voice exclaimed:
+
+'I do not know why you should have become so studious lately, Ernest,
+and why you should refuse to take me into your confidence. You spend
+hours and hours in this room all by yourself, writing away, and never
+say a word to me about the subject of your literary work. There was a
+time when things were different, and you were not so slow in availing
+yourself of my help, and asking my advice.'
+
+We murmured something about taking up the pen which had been laid aside
+by a far abler hand, and our deep gratitude for past assistance in our
+work, which could never be forgotten.
+
+'And do you think that I cannot help you now?' our visitor replied, in a
+very injured tone of voice. 'Is the old power dead, because it has not
+recently been used? Ernest, I think you very ungrateful not to confide
+in me. Come, tell me what you are writing.'
+
+A suggestion about the proverbial curiosity of women rose to our lips,
+but died away without utterance. In the meantime, her eyes wandered over
+our study-table strewed with papers, and lighted upon the well-worn
+desk.
+
+'Why, Ernest, where did you find this? My dear old desk, which has been
+lost ever so long! I do believe you have been ransacking its contents!
+Why did you not tell me that you had found it? What are you doing with
+my papers, sir?'
+
+The mischief was out! We tried to explain that the world ought not to be
+deprived of that which would benefit mankind; that the peace and
+prosperity of the country might be sacrificed if it were deprived of
+these discoveries of science, which were calculated to secure such
+beneficial results.
+
+At length we gained our point, and obtained the full sanction of the
+late Lady Professor of Girtham College to publish her papers. Thus her
+obedient pupil is enabled to repay his late instructress for all her
+kindness to him, and in some measure to compensate the scientific and
+political world for the loss of one of its most original investigators
+in the regions of polemical studies, which, not without a struggle, she
+resigned when she deigned to become his wife.
+
+
+THE END.
+
+
+
+
+_Elliot Stock, Paternoster Row, London._
+
+
+
+
+
+End of Project Gutenberg's The Romance of Mathematics, by P. Hampson
+
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