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diff --git a/26481.txt b/26481.txt new file mode 100644 index 0000000..0ad70d2 --- /dev/null +++ b/26481.txt @@ -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. 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