,,the ,,romance ,,of ,,mathematics4 ,the ,romance of ,mathematics3 ,,being ,,the ,,original ,,researches ,,of ,a ,,lady ,,professor ,,of ,,girtham ,,college ,,in ,polemical ,science1 with some ,account of the ,social ,properties of a ,conic2 ,equations to ,brain ,waves2 ,social ,forces2 and the ,laws of ,political ,motion4 ,,by ,p4 ,,hampson1 ,m4,a41 ,,oriel ,,college1 ,,oxford4 ,,london3 ,,elliot ,,stock1 #fb1 ,,paternoster ,,row4 #ahhf4 ,,introduction4 ,the lectures1 essays1 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 ,college2 and as they contain some original thoughts and investigations1 they have been considered worthy of publication4 ,how they came into the possession of the present writer it is not his intention to disclose2 but inasmuch as they seemed to his unscientific mind to contain some important discoveries which might be useful to the world1 he determined to investigate thoroughly the contents of the mysterious desk1 and make the public acquainted with its profound treasures4 ,he found some documents which did not refer exactly to the subject of ',polemical ,mathematics2' but knowing the truth of the ,hindoo proverb1 ',the words of the wise are precious1 and never to be disregarded1' and feeling sure that this ,lady ,professor of ,girtham ,college was entitled to that appellation1 he ventured to include them in this volume1 and felt confident that in so doing he would be carrying out the intention of the ,authoress1 had she expressed any wishes on the subject4 ,in fact1 as he valued the interests of the ,state and his own peace of mind1 he dared not withhold any particle of that which he conceived would confer a lasting benefit on mankind4 ,internal evidence seems to show that the earlier portion of the ,,ms4 was written during the period when the authoress was still in statu pupillari2 but her learning was soon recognised by the ,collegiate ,authorities1 and she was speedily elected to a ,professorship4 ,her lectures were principally devoted to the abstruse subject of ,scientific ,politics1 and are worthy of the attention of all those whose high duty it is to regulate the affairs of the ,state4 ,the ,editor has been able to gather from the varied contents of the desk some details of the ,author's life1 which increase the interest which her words excite2 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 ,college4 ,,contents4 ,,paper ,,page ,i4 ,some ,remarks on ,female ,education3 ,cambridge ,man's ,powers of ,application4--,torturing ,ingenuity of ,examiners4--,slaying an ,enemy4--',concentration4'-- ',tangential ,action4'--',gravity' #a ,,ii4 ,lecture on the ,theory of ,brain ,waves and the ,transmigration and ,potentiality of ,mental ,forces #ae ,,iii4 ,the ,social ,properties of a ,conic ,section1 and the ,theory of ,polemical ,mathematics3 ',circle4'--',parabola4'--',ellipse4' ',eccentricity of ,curves' #be ,,iv4 ,the ,social ,properties of a ,conic ,section 7continued73 ',ellipse4'--,most favoured ,state4--,alarming ,result of ,suppression of ,house of ,lords4--,analogies of ,nature4-- ,directrix4--,contact of ,curves and ,states4--',hyperbola4'-- ,problems4--,radical ,axis and ,patriotism4--,extension of ,franchise to ,women4--,correspondence #ci ,v4 ,social ,forces1 with some ,account of ,polemical ,kinematics3 ,the ,use of ,imagination in ,scientific ,discovery4--,kinetic and ,potential ,energy4--,social ,statics and ,dynamics4--,attractive ,forces4--,cohesion4--,formation of ,states4--,inertia4--,dr4 ,tyndall on ,social ,forces #ga ,,vi4 ,social ,forces 7continued73 ,polemical ,statics and ,dynamics3 ',personal ,equation4'--,public ,opinion1 how calculated4-- ,impulsive ,forces4--,friction4--,progress #hi ,,vii4 ,laws of ,political ,motion3 ,m4 ,auguste ,comte on ,political ,science4--,first ,law of ,motion4--,the ,biology of ,politics4--,stages of ,growth and ,decay of ,states4--,doctrine of ,nationality4--,doctrine of ,independence4--,law of ,morality4--,ignorance of ,electors and ,selfishness of ,statesmen opposed to ,action of ,law4--,final ',reign of ,law' #aja ,,viii4 ,the ,principle of ,polemical ,cohesion3 ,centralization4--,co-operation of ,states4--,marriage4--,trade ,unions4--,international ,law #aae ,extracts from the ,diary of the ,lady ,professor #abe ,conclusion #abi ,,paper ,i4 ,,some ,,remarks ,,of ,a ,,girtham ,,girl ,,on ,,female ,,education4 ,this essay upon ,female ,education was evidently written when the future ,professor of ,girtham ,college was still in the lowlier condition of studentship1 before she attained that eminence for which her talents so justly entitled her4 ,its unfinished condition tends to show that it was probably evolved during moments of relaxation from severer studies1 without any idea of subsequent publication4 ,oh1 why should ,i be doomed to the degradation of bearing such a foolish appellation6 ,a ,girtham ,girl6 ,i suppose we have to thank that fiend of invention who is responsible for most of the titular foibles and follies of mankind--artful ,alliteration4 ,the two ,g's1 people imagine1 run so well together2 and it is wonderful that they do not append some other delectable title1 such as ',the ,gushing ,girl of ,girtham1' or ',the ,glaring ,girl of ,glittering ,girtham4' ,o ,alliteration6 ,alliteration6 what crimes have been wrought in thy name6 ,little dost thou think of the mischief thou hast done1 flooding the world with meaningless titles and absurd phrases4 ,how canst thou talk of ',lyrics of ,loneliness1' ',soliloquies of ,song1' ',pearls of the ,peerage'8 ,why dost thou stay thine hand8 ,we long for thee to enrich the world with ',dreams of a ,dotard1' the ',dog ,doctor's ,daughters1' and other kindred works4 ,exercise thine art on these works of transcendent merit1 but cease to style thy humble1 but rebellious1 servant a ,girtham ,girl6 ,but what's in a name8 ,let the world's tongue wag4 ,i am a student1 a hard-working1 book-devouring1 never-wearied student1 who burns her midnight oil1 and drinks the strong bohea1 to keep her awake during the long hours of toil1 like any ,oxford or ,cambridge undergraduate4 ,i often wonder whether these mighty warriors in the lists--the class lists1 ,i mean--really work half so hard as we poor unfortunate ',girls of ,girtham4' ,now that ,i am writing in strict confidence1 so that not even the walls can hear the scratchings of my pen1 or understand the meaning of all this scribbling1 ,i beg to state that ,i have my serious doubts upon the subject2 and when last ,i attended a soiree of the ,anthropological ,society1 sounds issued forth from the windows of the snug college rooms1 which could not be taken as evidences of profound and undisturbed study4 ,sometimes ,i glance at the examination papers set for these hard-working students1 in order that they may attain the glorious degree of ,b4,a41 and astonish their sisters1 cousins1 and aunts by the display of these magic letters and all-resplendent hood4 ,and again ,i say in strict confidence that if this same glorious hood does not adorn the back of each individual son of ,alma ,mater1 he ought to be ashamed of himself1 and not to fail to assume a certain less dignified1 but expressive1 three-lettered qualification4 ,but before those ,tripos ,papers ,i bow my head in humble adoration4 ,they sometimes take my breath away even to read the terrible excruciating things1 which seem to turn one's brain round and round1 and contort the muscles of one's face1 and stop the pulsation of one's heart1 when one tries to grasp the horrid things4 ,here is a fair example of the ingenuity of the hard-hearted examiners1 who resemble the inquisitors presiding over the tortures of the rack1 and giving the hateful machine just one turn more by way of bestowing a parting benediction on their miserable victims3 ',a uniform rod' 7it is a marvellous act of mercy that the examiner invented it uniform2 it is strange that its thickness did not vary in some complicated manner1 and become a veritable birch-rod67 'of length #b;c1 rests in stable equilibrium' 7stable6 another act of leniency671 'with its lower end at the vertex of a cycloid whose plane is vertical' 7why not incline it at an angle of #cj degrees87 'and vertex downwards1 and passes through a small1 smooth1 fixed ring situated in the axis at a distance b from the vertex4 ,show that if the equilibrium be slightly disturbed1 the rod will perform small oscillations with its lower end on the arc of the cycloid in the time --------------------- ac#b #c7;b - c7#b #dpi ------------------- 1 #c;g7b#b - #d;ac7 where #b;a is the length of the axis of the cycloid4' ,a sweet pretty problem1 truly6 ,and there are hundreds of the same kind--birch-rods for every back6 ,how the examiner must have rejoiced when he invented this diabolical rod1 with its equilibrium1 its oscillations1 its cycloid1 and other tormenting accessories4 ,and yet1 ,i suppose1 before my days of studentship are over1 ,i shall be called upon to attack some such impregnable fortresses of mathematics1 when ,i hope to be declared equal to some twentieth wrangler1 if ,i escape the misfortune of sharing a portion of the 'wooden spoon4' ,ah1 you male sycophants6 ,you would prevent us from competing with you2 you would separate yourselves on your island of knowledge1 and sink the punt which would bear us over to your privileged shore4 ,of all the twaddle--forgive me1 male sycophants6--that the world has ever heard1 ,i think the greatest is that which you have talked about female education4 ,and the best of it is1 you are so anxious about our welfare2 you are so afraid that we should injure our health by overmuch mental exertion2 you profess to think that our brains are not calculated to stand the strain of continued mental exercise2 you think that competition is not good for the female mind2 that we are too competitive by nature--too ambitious6 ,yes1 we are so ambitious that we would enter the lists with those who are asked in ,public ,examinations to find the simple interest on #a1jjj pounds for #e years at #f-a_/d per cent42 so ambitious that we would compete with those who are requested to disclose the first aorist middle of ,greek3 tupto4 ,oh1 think of the mental strain involved in such questions6 ,how it must ruin your health to find out how many times a wheel of radius #f feet will turn round between ,york and ,london1 a distance of #bjj miles6 ,it is quite wonderful how your brains1 my dear male sycophants1 can stand such fearful demands upon your intelligence and industry6 ,but you are so kind to us1 so afraid of our health6 ,really1 we are much obliged to you4 ,if you married one of us1 or became our guardian1 or left us a legacy1 we should then recognise your interest in us1 and be very grateful to you for your good advice4 ,but as matters stand1 we are quite capable of taking care of ourselves4 ,we will promise not to work too hard1 if you will promise not to weary us with your paternal jurisdiction4 ,but1 male sycophants1 ,i want a word with you4 ,why do you object to our taking degrees1 or going in for examinations in order to qualify ourselves for our duties in life8 ,you need not speak out loud if you would rather not4 ,are you not just a little afraid that we might eclipse you8 ,and it is not pleasant to be beaten by a woman1 is it8 ,and then you profess to think that we ought to be all housewives and cooks1 and knitters of stockings1 and sewers-on of our husbands' buttons2 but what if we have no husbands1 no buttons to sew8 ,and is it not a little selfish1 my dear male sycophant1 to wish to keep us all to yourself8 to attend upon the wants of the lords of creation1 who often distinguish themselves so much in the domain of science8 ,now1 look me straight in the face 7no shirking1 sir674 ,is it not jealousy--green-eyed1 false-tongued jealousy--which saps your generous instincts1 and makes you talk rubbish and nonsense about strains1 and brains1 and ambition1 and the like8 ,and if that is not hypocritical1 ,i do not know what is4 ,well1 good-day to you1 male sycophant6 ,i really have not time to indulge myself in scolding you any more4 ,you are a good creature1 no doubt2 and when you have shown us what you can do1 and can estimate the capacity of the female brain1 and take a common-sense view of things1 we will recognise your privilege to speak2 and when ,i am the presiding genius of ,girtham ,college1 ,i will grant you the use of our hall for the purpose of lecturing to us on ',women's ,rights1' or1 as you may prefer to entitle your discourse1 ',men's ,wrongs4' 99 99 99 99 99 ,oh1 this is shameful6 ,i really am very sorry4 ,here have ,i been wasting a good half-hour in dreaming1 and slaying an imaginary enemy with envenomed words and frequent dabs of ink4 ,if ,i cannot concentrate my mind more on these mathematical researches1 ,i fear a dreadful 'plough' will harrow my feelings at the end of my sojourn in these halls of learning4 ,concentration6 ,how many of our words and ideas and thoughts are derived from that primal fount of all arts and sciences--mathematics6 ,here is one which owes its origin to the mathematically trained mind of some early philological professor1 who had learnt to apply his scientific knowledge to the enrichment of his native tongue4 ,he quoted to himself the words of the ,roman poet3 ',ego cur1 acquirere pauca ,si possum1 invideor1 cum lingua ,catonis et ,enni ,sermonem patrium ditaverit1 et nova rerum ,nomina protulerit8 ,licuit1 semperque licebit4' ,his mind conceived endless figures of circles and ellipses scattered promiscuously over the page1 defying the attempts of the student to reduce them to order4 ,what must he do before he can apply his formulae and equations1 determine their areas1 or describe their eccentric motion8 ,he must reduce them to a common centre1 and then he can proceed to calculate the abstruse problems in connection with the figures described4 ,they may be the complex motions of double-star orbits1 or the results of the impact of various projectiles on the tranquil surface of a pool4 ,it matters not--the principle is the same2 he must concentrate1 and reduce to a common centre4 ,this is the great defect of those who have no accurate mathematical knowledge2 they cannot concentrate their minds with the same degree of intensity upon the work which lies before them4 ,their thoughts fly off at a tangent1 as mine do very often2 but then ,i have not been classed yet in the ,tripos2 and1 ,o male poetical sycophant1 you may be right after all when you say3 ',o woman6 in our hours of ease ,uncertain1 coy and hard to please1 ,as variable as the noon-day shade4' ,yes1 as variable as the most variable quantities x1 y1 z4 ,i1 a student of ,girtham ,college1 blush to own that my thoughts very often fly off at a tangent4 ',fly off at a tangent6' ,all hail to thee1 most noble mathematical phrase6 ,here is another fine mathematical expression1 plainly exemplifying the action of centrifugal force4 ,the faster the wheel turns1 the greater is the velocity of the discarded particles which fly off along the line1 perpendicular to the radius of the circle4 ,the world travels very fast now2 the increased velocity of the transit of earthly bodies1 the rate at which they live1 the multiplicity of engagements1 etc41 have made the social world revolve so fast that the speed would have startled the torpid life of the last century4 ,and what is the result8 ,men's thoughts fly off at a tangent2 they are unable to concentrate their minds on any given subject2 they are content with hasty generalisms1 with short magazine articles on important subjects1 which really require large volumes and patient study to elucidate them fully4 ,what we want to do is to increase the attractive force1 in order to prevent this tangential motion--to increase the force of gravity4 ',well1' says the young lady who loves to revel in the ',ghastly ,secret of the ,moated ,dungeon1' or the ',mysteries of ,footlight ,fancy1' 'you are grave enough4 ,pray don't increase your gravity6' ,thank you1 gentle critic4 ,i will1 in turn1 ask you one favour4 ,leave for once the ',mysteries of ,footlight ,fancy2' seek to know no more 'ghastly secrets1' and increase your gravity--your mental weight2 and hence your attraction in the eyes of all who are worth attracting will be marvellously increased1 by understanding a little about ,newton's law of universal gravitation1 and don't fly off at a tangent4 99 99 99 99 99 ,at the end of this portion of the ,,ms4 the editor of these papers discovered a photograph which1 from subsequent inquiry1 proved to be that of the accomplished authoress of the above reflections4 ,the face is one of considerable beauty1 with eyes as clear1 steadfast1 and open as the day4 ,there is a degree of firmness about the mouth1 but it is a sweet and pretty one notwithstanding2 and a smile1 half scornful1 half playful1 can be detected lurking about the corners of the lips1 which do not seem altogether fitted for pronouncing hard mathematical terms and abstruse scientific problems4 ,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 examination4 ,the said enamoured youth had evidently placed it there for the sake of its inspiring qualities2 and it was said that all his hopes of gaining the hand of the fair original depended upon his passing that same examination4 ,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-paper2 and he narrowly escaped expulsion from the ,senate-house on the charge of 'cribbing4' ,certainly he took a mean advantage of his fellow-sufferers1 if this were the identical photograph1 for it portrays a most inspiring face4 ,forgive us1 lenient reader2 one moment6 ,there--thank you--we have done4 ,and now we will proceed to disclose the researches and original problems which the ,,ms4 contains4 ,evidently the collegiate authorities were not slow in recognising the talents of the assiduous student1 and elected her without much delay to a ,professorship of ,girtham4 ,in this capacity the learned lady delivered several lectures1 of which the second ,,ms4 contains the first of the series4 ,,paper ,,ii4 ,,lecture ,,on ,,the ,,theory ,,of ,,brain ,,waves ,,and ,,the ,,transmigration ,,and ,,potentiality ,,of ,,mental ,,forces4 ,professors and ,students of the ,university of ,girtham1 my ,lords1 ,ladies1 and ,gentlemen1--,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 knowledge2 and though you may be inclined at first to pronounce them as somewhat hastily conceived hypotheses1 ,i hope to be able to demonstrate the actual truth of the propositions which ,i shall now endeavour to enunciate4 ,it is with some feelings of diffidence that ,i stand before so august an assembly as the present2 and if ,i were not actually convinced of the accuracy of my calculations1 ,i should never have presumed to appear before you in the character of a lecturer4 ,but ',magna est veritas1 et praevalebit4' ,i cast aside maiden timidity2 ,i clothe myself in the professorial robe which you have bestowed upon me1 and sacrifice my own feelings on the altar of ,truth4 ,i have been engaged1 as you are doubtless aware1 for some years in the pursuit of mathematical research1 exploring the mines of science1 which have of late been worked very persistently1 but often1 like the black diamond mines1 at a loss4 ,concurrently with these researches1 ,i have speculated on the great social problems which perplex the minds of men1 both individually and collectively4 ,and ,i have come to the conclusion that the same laws hold good in both spheres of work2 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 man4 ,take1 for example1 the ,force of public opinion4 ,of what is it composed8 ,it is the ,resultant of all the forces which act upon that which is generally designated the ',social ,system4' ,public opinion is a compromise between the many elements which make up human society2 and compromise is a purely mechanical affair1 based on the principle of the ,parallelogram of ,forces4 ,sometimes disturbing forces exert their influence upon the action of ,public ,opinion1 causing the system to swerve from its original course1 and precipitating society into a course of conduct inconsistent with its former behaviour2 and it is the duty of the ,governing ,body to eliminate as far as possible such disturbing forces1 in order that society may pursue the even tenor of its way4 ,professors1 we have one great problem to solve2 and all questions social1 political1 scientific1 or otherwise1 are only fragments of that great problem4 ,all truths are but different aspects of different applications of one and the same truth2 and although they may appear opposed1 they are not really so2 and resemble lines which run in various directions1 but lovingly meet in one centre4 ,now1 let us take for our consideration the secret influence which men exert upon each other1 apart from that produced by the power of speech 7although that would come under the same general law74 ,as mathematicians1 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 calculation4 ,we know that the rays of light travel in waves1 and the equation representing the waves is a #bpi y --- sin ------ 7vt - r71 r lambda where y is the disturbance of the ether1 a the initial amplitude1 r the distance from the starting-point1 lambda the wave-length1 and v the velocity of light4 ,sound and heat likewise have much the same form of equation4 ,now1 ,i maintain that the waves of thought are governed by the same laws1 and can be determined by an equation of the same form4 ,you are aware that in all these equations a certain quantity denoted by lambda appears1 and varies for the different media through which the sound1 or light1 or heat passes1 and which must be determined by experiment ,now1 in my equation for brain waves1 the same quantity lambda appears which must be determined by the same method--by experiment4 ,but how is this to be done8 ,after mature deliberation and much careful thought1 ,i have discovered the method for finding lambda4 ,this method is mesmerism4 ,we find the ratio of brain to brain--the relative strength which one bears to another2 and then by an application of our formula we can actually determine the wave of thought1 and read the minds of our fellow-creatures4 ,an unbounded field for reflection and speculation is here suggested4 ,like all great discoveries1 the elements of the problem have unconsciously been utilized by many who are unable to account for their method of procedure4 ,for example1 thought-readers1 mesmerists1 and the like1 have unconsciously been working on this principle1 although lack of mathematical training has prevented them from fully mastering the details of the problem4 ,hence in popular minds a kind of mystery has hung about the actions of such people1 and excited the curiosity of mankind4 ,the development of this theory of brain waves may be of great practical utility to the world4 ,it shows that great care ought to be exercised in the domain of thought1 as well as that of speech4 ,for example3 ,a man has made a startling discovery1 from which he expects to receive considerable worldly advantage4 ,he would be careful not to disclose his discovery in speech to his acquaintances until his plans are sufficiently matured1 lest they should impart it to the world1 patent his device1 and reap the reward4 ,but while he is endeavouring to talk carelessly about it1 the wave of thought may be travelling from brain to brain1 suggesting the existence of the discovery2 and if the conditions are favourable1 and lambda sufficiently small1 it is possible that the idea itself may be conveyed4 ,of course the more complicated the discovery1 the less likely would the wave convey the conception4 ,or suppose that one of the learned professorial body of our sister university should conceive an attachment for a lady-student of ,girtham ,college 7of course a very improbable supposition671 and the infatuated savant became somewhat jealous of another learned lecturer of the same college 7another improbability671 the fact of his jealousy would be imparted to the latter by a wave of thought1 and might cause considerable confusion in the serene course of love or science4 ,the fact of the existence of the wave is indisputable4 ,what do all the stories of impressions and double-sight teach us8 ,how could the intelligence of the death of ,professor ,steele have been conveyed to his friend and fellow-student1 ,professor ,tait--the one at ,cambridge1 the other at ,edinburgh--were it not for the existence of some wave1 which1 like that of electricity1 wings its rapid flight unobserved by human eyes8 ,are all the records of the ,psychical ,society only myths and legends bred of superstitious fancy8 ,it were hard to suppose so4 ,but if1 gentlemen1 and ladies especially1 you wish to keep your secret discoveries to yourselves1 watch over your thoughts as well as your words2 for my researches prove1 and the universal experience of mankind corroborates the fact1 that some portion of your inmost thoughts and secret desires are understood by your neighbours 7especially when lambda is small672 that they travel along the waves which ,i have attempted to indicate2 and if you would desire to extend your influence in the world1 probe the secret instincts of mankind1 and prevent yourself from being deceived and wronged--study the art and science of ,brain ,waves4 99 99 99 99 99 ,the following verses of rather doubtful merit were found in connection with the previous ,,ms4 ,they were evidently written by a different hand2 but inasmuch as they were deemed worthy of preservation by the learned owner of the sealed desk1 we venture to publish them4 ,they are closely connected with the previous lecture1 and were evidently composed by an admirer of the fair lecturer who did not share her love for scientific research4 ,wavelet1#a wing thy airy flight2 ,let thine amplitude be great2 ,tell her all my thoughts to-night1 ,how ,i long to know my fate4 ,all the fields of ,mathematics ,i have roamed at her decree2 ,from ,binomial and ,quadratics1 ,to the strange hyperbole4#b ,i have soared through ,differential1 ,deeply drunk of ,finite ,boole2#c ,though its breath is pestilential1 ,reeking of the hateful ,school4 ,i have tried to shape a ,conic1 ,vainly read the ,calculus2 ,but my feebleness is chronic1 ,morbus ,mathematicus4 ,all my curves are cardioidal2 ,i confuse my x and ys1 ,which they say is suicidal2 ,and my tutor vainly sighs4 ,wavelet1 tell her how ,i love her1 ,as she mounts her learned throne2 ,and that love ,i hope may cover ,all the failings which ,i own4 ,wavelet1 cry to her for pity2 ,bid her end this bitter woe2 ,i might do something 'in the city1' ,but never pass my ,little-go4 #a ,we presume this is addressed to an imaginary brain wave4 #b ,we observe here the dash of an indignant pen1 and a substituted for e4 ,but now the rhyme is spoiled4 ,gentle ,muse1 thou art sacrificed by the stern hand of ,mathematical ,truth6 #c ,query3 ,does the writer refer to the learned treatise on ,finite ,differences by ,professor ,boole8 ,,paper ,,iii4 ,,lecture ,,on ,,the ,,social ,,properties ,,of ,a ,,conic ,,section1 ,,and ,,the ,,theory ,,of ,,polemical ,,mathematics4 ,most ,learned ,professors and ,students of this ,university1--,from the interest manifested in my first lecture1 ,i conclude that my method of investigation has not proved altogether unsatisfactory to you1 and ,i hope ere long to produce certain investigations which will probably startle you1 and revolutionize the current thought of the age4 ,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 matters4 ,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 postulate1 and to explain on scientific principles the various convulsions which sometimes agitate the social and political world4 ,indeed1 by this method we shall be able to prophesy the future of states and nations1 having given certain functions and peculiarities appertaining to them1 just as easily as we can foretell the exact day and hour of an eclipse of the moon or sun4 ,in order to do this1 we must first determine the social properties of a conic section4 ,for the benefit of the unlearned and ignorant1 ,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 angle1 which remains fixed4 ,the fixed side is called the axis of the cone4 ,conic sections are obtained by cutting the cone by planes4 ,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 cone1 the section described on the surface of the cone is a parabola2 if the former angle be greater than the latter1 the curve will be an ellipse2 and if less1 the section will be a hyperbola4 ,but the simplest conic section is1 of course1 a circle1 which is formed by a plane at right angles to the axis of the cone2 and the simplest circle is that formed by a plane passing through the apex of the cone4 ,all this is simple mathematics2 and let beginners consult more elementary treatises than this one to satisfy themselves on these points4 ,but if they will assume these things to be true1 they will know quite enough for our present purpose4 ,the simplest conic section of all has been proved to be a point4 ,now1 this represents the simplest and original form of society1 a single family4 ',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 lord4 ,marriage is the rudiment of all social life1 from which all others spring1 out of which all others are developed4 ,around the parents' knees soon cluster a group of children1 and in their relation to each other we discern the earliest forms of law and discipline--the bonds by which society is held together4 ,when the children grow up1 separate households are formed2 and then the multiplication of families1 the congregating of men together for purposes of security and mutual advantages in division of labour2 and thus is gradually formed a state1 which is only the development of the family--the king representing the parent1 and ruling on the same principle4 ,mathematically speaking1 our plane no longer passes through the apex4 ,the point represented the single family2 but keeping the plane horizontal1 we move it along the axis1 the sections will become circles1 which represent mathematically the next simplest form of society1 where the centre is the seat of government1 which is connected with each individual member of the social circle by equal radii4 ,the social property of a circle is that of a monarchical government in its purest and simplest form4 ,the larger the circle becomes 7i4e41 the further you move the plane from the apex71 the greater the distance between the individual and the monarch4 ,therefore1 the more independent the monarchy becomes1 and the less influence do individuals possess over the ruling power4 ,hence1 we may infer that as years roll on1 the government will become more despotic2 but the stability of the country diminished1 and probably some individual particle1 when sufficiently withdrawn from the attraction of the central head1 will begin to revolve on its own account1 and spontaneously generate a government of its own4 ,we may1 therefore1 conclude from mathematical reasoning that an unlimited monarchy1 though advantageous for small states1 is not a safe form of government for a large or populous country1 inasmuch as the people do not derive much benefit from the sovereign2 the mutual attraction1 which ought to exist in a flourishing state between the ruler and the ruled1 is weakened2 and the isolation of the monarch tends to make him still more despotic4 ,as a practical example of the truth of the foregoing statement1 ,i may mention the present condition of ,russia1 which shows that the result of an unlimited monarchy1 in a large and unwieldy social circle1 is such as we should have reasonably expected from mathematical investigations4 ,invariably1 under the circumstances which ,i have described1 the country will become disorganized2 the sovereign will cease to have any power over the people1 and the country will become a chaos1 without order1 influence1 or power4 ,when the centre of a conic section moves along the axis of the curve to infinity1 banished by the mutual consent of the individual particles which compose the curve1 or the nation1 a figure is formed1 called a parabola4 ,this is the curve which the most erratic bodies in the universe describe in space1 as they rush along at a speed inconceivable to human minds1 and are supposed to produce all kinds of mischief and injury to the worlds whose courses they wend their way among4 ,this curve1 then1 represents the position which the nation assumes when the constituted monarchy1 the centre of the system1 has been banished to infinity4 ,a revolution has occurred2 the monarch has been dethroned2 and it is not hard to see that the same erratic course which the comet pursues in its flight1 is observable with respect to the social system which is represented by a parabola4 ,we observe with eager scrutiny the wanderings of these erratic comets4 ,they appear suddenly with their vapoury tails2 sometimes they shine upon us with their soft1 silvery light1 brilliant as another moon2 sometimes they stand afar off in the distant skies1 and deign not to approach our steady-going earth1 which pursues its regular course day by day1 and year by year4 ,then1 after a few days' coy inspection of our planet from different points of view1 they fly to other remote parts of the universe1 and do not condescend to show themselves again for a hundred years or so4 ,such is the erratic conduct of a heavenly body whose course is regulated by a parabolic curve4 ,we may look for similar eccentric behaviour on the part of a community1 nation1 or state1 whose centre is at infinity1 whose constitution has been violently disturbed1 and whose monarchy is situated in the far-off regions of unlimited space4 ,the erratic course of ,republican rule is proverbial4 ,there is no stability1 no regularity4 ,to-day we may observe its brilliancy1 which seems to laugh at and eclipse the sombre shining of more steady and enduring worlds2 but ere to-morrow's moon has risen1 it may have vanished into the regions of eternal night1 and we look for its bright shining light in the councils of the nations1 but it has ceased to shed its rays1 and we are disappointed4 ,sometimes it is asked1 with fear and trembling3 ',what would be the effect if our earth were to come in contact with the tail of a comet8 ,should we be destroyed by the collision1 and our ponderous world cease to be8' ,but we are assured that no such disastrous results would follow4 ,we have already passed through the tails of many comets1 but we have not discovered any inconvenient change in our ordinary mode of procedure4 ,it is probable that the comet's tail is composed of no solid substance4 ,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 government4 ,a shower of meteoric stones1 like passing fireworks1 might take place2 but beyond that nothing would occur to excite the fear1 or arouse the energies of the more favoured nation4 ,as an example of the weakness of a ,republican ,state ,i may mention ,france4 ,there we see an industrious race of people1 endowed with many natural gifts and graces1 a country rich and productive2 and yet1 owing to the unsettled nature of its government1 all these natural advantages are neutralized2 its course amongst the nations is erratic in the extreme1 a spectacle of feeble administration2 and it would offer no more resistance to a colliding ,power than the empty vacuum of a comet's tail4 ,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 curve4 ,we will now turn from this picture of insecurity and unrest to another figure which possesses most advantageous social properties4 ,i refer to the ellipse4 ,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 cone1 greater than the angle between the axis and the generating line4 ,now1 this is a curve which possesses most attractive properties4 ,it is the curve which the earth and other planetary orbs describe around the centre of the solar system1 as if nature intended that we should take this figure as a guide in choosing the most advantageous social system4 ,it possesses a centre1 ,c1 in view of all the particles which compose the curve1 and connected with them by close ties4 ,it has two foci1 ,s and ,s'1 fixed points1 by the aid of which we may trace the curve4 ,in the interpretation of this figure1 the centre of the curve represents the throne of monarchy4 ,there is no tendency here to revolutionize the ,state1 to banish the ruling power1 and institute a ,republican form of government2 but inasmuch as we saw the weakness of an absolute monarchy in large and populous ,states1 as represented by the circle1 the wisdom of an elliptical social system has ordained that there shall be two foci1 or houses of representatives of the people1 who shall assist in regulating the progress of the nation4 ,here we have a limited monarchy2 the throne is supported by the representatives of the people2 and the nearer these foci of the nation are to the centre 7i4e41 in mathematical language1 the less the eccentricity of the curve71 the more perfect the system becomes--the greater the happiness of the community4 ,in cases where the eccentricity becomes very great1 the beauty of the curve is destroyed1 and ultimately the ellipse is merged into one straight line4 ,most learned ,professors1 here we have a terrible warning of the awful result of too much eccentricity4 ,whether we regard the life of the nation or of the individual1 let all bear in mind this alarming fact1 that eccentricity of thought1 habit1 or behaviour may result1 as in the case of this unfortunate ellipse1 which once presented such fair and promising proportions to the student's admiring gaze1 in the 'sinister effacement of a man1' or the gradual absorption of a ,state into an uninteresting thing 'which lies evenly between its extreme points4' ,the great examples of ,bacon1 of ,milton1 of ,newton1 of ,locke1 and of others1 happen to be directly opposed to the popular inference that eccentricity and thoughtlessness of conduct are the necessary accompaniments of talent1 and the sure indications of genius4 ,i am indebted to ,lacon for that reflection4 ,you may point to ,byron1 or ,savage1 or ,rousseau1 and say1 ',were not these eccentric people talented8' ',certainly1' ,i answer2 'but would they not have been better and greater men if they had been less eccentric--if they had restrained their caprice1 and controlled their passions8' ,do not imagine1 my young students of this university1 that by being eccentric you will therefore become great men and women of genius4 ,the world will not give you credit for being brilliant because you affect the extravagances which sometimes accompany genius4 ,some of you ladies1 ,i perceive1 have adopted a peculiar form of dress1 half male1 half female2 or1 to be more correct1 three-fourths male1 and one-fourth female4 ,do not imagine that you will thus attain to the highest honours in this university by your eccentricity1 unless your talents are hid beneath your short-cut hair1 and brains are working hard under your college head-gear4 ,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 ,academicians4 ,it is apparent that many aspirers to fame and talent are eager to exhibit their eccentricities to the gaze of the world1 in order that they may persuade the multitude that they possess the genius of which eccentricity is falsely supposed to be the outward sign4 ,i may remark in passing that the eccentricity of a parabolic curve is always unity4 ,what does this prove8 ,you will remember that a ,republican ,state is represented by a parabola4 ,therefore1 however such a nation may strive to alter its condition1 and secure a settled form of government1 its eccentricity will always remain the same4 ,it will always be erratic1 peculiar1 unsettled2 and this conclusion substantiates our previous proposition with regard to the condition of a social system represented by a parabola4 ,with regard to other advantages afforded by an elliptical social system1 we will defer the consideration of this important subject until my next lecture4 ,,paper ,,iv4 ,,the ,,social ,,properties ,,of ,a ,,conic ,,section1 ,,and ,,the ,,theory ,,of ,,polemical ,,mathematics--7continued74 ,most learned ,professors and ,students of this ,university1--,you have already gathered from my preceding lecture my method of procedure in the investigation of the corresponding properties of curves and ,states4 ,you have perceived that we have here the elements of a new science1 which may be extended indefinitely1 and applied to the various departments of self-government and ,state control4 ,this new science of polemical mathematics is in itself an extension of the principle of continuity1 for the discovery of which ,poncelet is so justly renowned4 ,we can prove by geometry that the properties of one figure may be derived from those of another which corresponds to it2 and the new science teaches us that if we can represent1 by projection or otherwise1 a society of particles or individuals on a plane surface1 the properties of the ,state so represented are analogous to the properties of the curve with which it corresponds4 ,it is only possible for me to touch upon the elements of the science in these lectures1 but ,i hope to arouse an interest in these somewhat unusual complications and curious problems1 that you may hereafter make further discoveries in this unexplored region of knowledge1 and that the world may reap the benefit of your labours and abstruse studies4 ,i have already1 in my previous lecture1 touched upon the social properties of the parabola1 and examined the constitution of erratic curves and eccentric nations4 ,it is my intention to-day to speak of similar problems which arise with reference to elliptical ,states4 ,but1 first1 let me answer an objection which may have occurred to your minds4 ,am ,i wrong in my calculations in attributing too much to the power and usefulness of forms of government8 ,does the well-being and happiness of a nation depend on the government1 or upon the individuals who compose the nation8 ,most assuredly1 ,i assert1 they rest upon the former4 ,men love their country when the good of every particular man is comprehended in the public prosperity2 they undertake hazard and labour for the government when it is justly administered4 ,when the welfare of every citizen is the care of the ruling power1 men do not spare their persons or their purses for the sake of their country and the support of their sovereign4 ,but where selfish aims are manifest in ,court or ,parliament1 the people care not for ,state officials who are indifferent to their country's weal2 they become selfish too2 ,liberty hides her head1 and shakes off the dust of her feet ere she leaves that doomed land1 and the stability1 welfare1 and prosperity of that country cease4 ,i might refer you to many a stained page of national history in order to prove this4 ,compare the closing chapters of the life of the ,roman empire with the record of the brave deeds of its ancient warriors and valorous statesmen4 ,grecian preeminence and virtue died when liberty expired4 ,i agree with ,sidney when he writes that it is absurd to impute this to the change of times2 for time changes nothing1 and nothing was changed in those times but the government1 and that changed all things4 ,these are his words3 ',as a man begets a man1 and a beast a beast1 that society of men which constitutes a government upon the foundation of justice1 virtue1 and the common good1 will always have men to promote those ends2 and that which intends the advancement of one man's desires and vanity will abound in those that will foment them4' ,i may not1 therefore1 be altogether wrong in attributing the prosperity and well-being of a nation to the form of government which it possesses4 ,we will now proceed to the consideration of the social advantages which an elliptical ,state affords4 ,this is the form of government and social position which we1 as a nation1 at present enjoy2 and from mathematical considerations ,i am of opinion that it is the best1 and hope that no change will ever be made in our constitution4 ,you may remember that ,i have previously stated that an ellipse has a centre and two foci1 in view of all the particles which compose the curve1 and connected with them by close ties4 ,the centre1 in the projected figure1 represents the monarchy1 which is limited2 and the government is carried on by the aid of the two houses of representatives of the people1 depicted in the projection by the two foci4 ,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 constant4 ,no particle is left out in the cold2 no one does not possess the advantages of a social government4 ,though his distance may be far from the ,upper ,house1 he has the advantage of nearness to the ,lower1 and vice versa4 ,the sum of the distances is constant4 ,the extinction of one focus1 the ,house of ,lords1 for example1 would create a complete disorganization of the whole system3 the other focus would set up a powerful magnetic attraction1 and a curious bulb-shaped curve would be evolved1 very different from the beautiful symmetrical form which the original figure presented to the eye4 ,the centre of the system would be disturbed2 and it is probable that ere long it would disappear along the axis and be vanished to infinity4 ,thus the curve would become a parabola4 ,this is the alarming result of the extinction of one focus4 ,abolish the ,house of ,lords1 and you will soon find that the ,throne will be disturbed2 the ,state will become disorganized2 the nation will become confused by the magnetic force of the ,lower ,house1 uncounteracted by any other attraction2 and very soon a complete revolution of the whole system will set in3 the monarch will be dethroned1 and a ,republican form of government1 with all the eccentricities of a parabolic course1 will take the place of a more orderly and settled constitution4 ,this is a plain deduction from our mathematical investigations2 and it behoves all our statesmen1 our philosophers and great men1 our fellow-citizens and the humblest artisans in our manufacturing towns1 to weigh well this alarming result of the abolition of that ,house which has been threatened with destruction2 and to ascertain for themselves the truths upon which my proposition and reasoning rest4 ,i have already observed that the fact that the earth's orbit and that of other planets are in the form of ellipses2 that the curvature of the earth is nearly the same1 ought to guide us in choosing this particular curve as a model of the projection of a complete and most advantageous social system4 ,the circle described on the major axis of an ellipse1 is called the auxiliary circle1 and affords much assistance in the investigation of the properties of an ellipse4 ,as we have already shown1 the circle represents the simplest form of monarchical government4 ,hence1 if we compare the form of government represented by an ellipse 7i4e41 such as we now enjoy7 with that of a system where the king is the only governing power1 we may obtain great assistance in solving complicated political problems4 ,in all conics there is a straight line called the 'directrix1' which represents in social or polemical science the laws of the nation1 and plays a prominent part in the mutual relations of the individual particles4 ,for instance1 in the case of the parabola1 the distance of any particle from the directrix is equal to its distance from the focus4 ,from this we may conclude that if an individual deviates at all from the path which the laws 7or1 directrix7 indicate1 if he does not show true respect to the decrees of the focal government1 and preserve the true position between them1 directly he is found deviating from his course1 he is quickly banished to a less enlightened sphere4 ,in an ellipse there is less likelihood of his straying away from the course which the directrix points out1 on account of the two-fold guidance which he receives from the two foci4 ,the following curious problem may be noticed4 ,if a parabola roll on another parabola1 their vertices coinciding1 the focus of the first traces out the directrix of the second4 ,here we come to the consideration of the international relationship of ,states4 ,two nations have the same form of government 7in this example this form is ,republican72 their policies coincide3 we may conclude from this proposition that the course which the government of one nation will pursue1 will be that which is prescribed by the laws of the other4 ,the subject of the contact of curves presents many interesting problems with reference to ,polemical ,science1 and may be extended indefinitely4 ,it is well known that there are different orders of contact1 which are designated as the first1 second1 or third order4 ,this last order may be termed the 'marriage of curves1' cemented by the osculating circle1 or 'wedding-ring2' and when two nations have contact of the third order1 they have formed a very close alliance1 and by calculation we can obtain the radius of curvature1 or size of the wedding-ring1 by means of which they may be united4 ,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 law4 ,alas6 too many ,states refuse this friendly contact1 and1 consequently1 cut each other1 instead of blending in sweet accord4 ,their peace is at best an armed neutrality2 and if they have contact of only the first or second order1 we can prove mathematically that they are sure to intersect in some other point or points2 and divergence of policy and disturbed relations are the results4 ,contact of the third1 or highest1 order is the only safe position for two allied1 or contiguous1 ,states4 ,with your permission ,i will add a few words to those ,i have already uttered with regard to the directrix4 ,as necessary as the directrix is to the curve1 so are the corresponding laws to the ,state4 ,i will prove this fact by a few examples4 ,english people have laws1 and know how to obey them2 therefore their numbers increase2 they thrive and are prosperous4 ,a friendly critic of another nation has said that the reason why ,englishmen rule the world1 is because they know how to obey4 ,on the other hand1 the gipsies have no laws2 hence they become fewer and less powerful4 ,what is the condition of all tribes and nations which are not governed by laws8 ,they invariably remain poor and miserable4 ,they are in want of a directrix2 and if we could supplement the gift with foci and centre1 they would soon emerge from their savage condition1 and become more civilized4 ,i have omitted to mention the hyperbolic form of government4 ,the curve formed by the intersection of the surface of a cone with a plane will be a hyperbola1 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 axis4 ,it is manifest that the plane will thus intersect the higher cone1 and produce the figure which is known to mathematicians as the hyperbola4 ,we may hence deduce the following property of the corresponding hyperbolic ,state4 ,we take cognizance of that higher cone with which the mundane affairs of the lower cone are closely connected4 ,as an example of this system we may mention the vast temporal rule and power of the ,papal ,throne1 which formerly exercised such marvellous sway over the nations of ,europe4 ,by an appeal to a ,higher ,authority than that of earthly kings and potentates was this rule exercised2 but its hyperbolic form is fast passing away1 and degenerating into that of a circle with indefinitely small radius4 ,we shall not1 therefore1 discuss the complex polemical problems which a hyperbolic ,state suggests4 ,i will now mention a few problems which are easily capable of proof1 and deduce from them the necessary conclusions which must follow when we apply our newly discovered principles of polemical science4 #a4 ',if from any point in a straight line a pair of tangents be drawn to an ellipse1 the chords of contact will pass through a fixed point4' ,i will not trouble you with the proof of this proposition1 as it is evident to all mathematicians1 and can easily be demonstrated4 ,but mark well the deductions1 when we interpret this mathematical language in correct polemical terms4 ,a ,state1 through various convulsions of its own1 has merged into a condition represented by a straight line1 having lost its symmetry1 its beauty1 its curvilinear proportion4 ,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 government1 and other blessings which accompany elliptical jurisdiction and laws4 ,two tangents are drawn to an ellipse4 ,no matter where the individual may be in the unhappy envious straight line1 the result of his reflection will be the same4 ,sympathetic chords are drawn1 joining the points of contact of the tangents with the curve2 they all pass through a fixed point4 ,all these conclusions of the various individuals on the straight line will be the same4 ,all are of opinion that the elliptical form is the best2 and they mourn in secret over the sad events which have occurred in their own national life1 their eccentricity1 their lawlessness1 when they see the advantages which their more staid and sober-minded neighbours so freely enjoy4 #b4 ,the normal at any point of an ellipse bisects the angle between the focal distances of that point4 ,the normal is the perpendicular from the point on the major axis2 it is the line of thought directed by the observance of just laws and rules4 ,hence this proposition shows that the individual citizen1 when guided by sound judgment1 regards with equal favour and entire approval the existence of both foci1 or ,houses of ,legislature4 ,he considers that both are necessary to his comfort1 and the right regulation of the ,state's welfare4 ,he cares not for the abnormal condition of those who talk as if the existence of either ,house were unnecessary to his country's weal1 and bestows a pitying glance on those wandering lights1 or disturbed erratic governments1 which do not possess the advantages which from experience he has learned to love and to respect4 ,no matter what his condition may be1 the same opinions are held by all classes1 all ranks and degrees2 and if a self-opinionated particle think otherwise1 he ought to be transferred to a less enlightened sphere1 and migrate to a parabolic state1 or uninteresting straight line4 ,and when he has changed his location1 he will look back on his old home and old surroundings with longing eyes and an aching heart1 thinking of the blessings he has lost by his own rash act4 ,this can be proved mathematically4 ,he looks for an ideal state of society1 leaps after the shadow his fancy has depicted2 and when he finds himself outside his former state1 he looks back with longing eyes at the once-scorned focus4 ,what is the focus of a perpendicular on the tangent of an ellipse from any external point8 ,can it not be proved to be a circle8 ,that is to say1 he will be more conservative than ever4 ,he would like to return to a primitive form of government4 ,farewell to his wild schemes and revolutionary measures6 ,farewell to his disestablishments1 abolitions1 and suppressions6 ,the throne and government have new attractions in his eyes2 loyalty1 a new feeling1 asserts its benign influence2 and if he could return to his former position1 his normal conduct would be straighter than ever1 for by sad experience he has learned the value of those things which he once despised4 ,but we need not depend upon one proof alone4 ,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 distance4' #c4 ,the same opinions are often held by individuals in quite different walks and classes of life4 ,let these individuals be represented by points on an ellipse4 ,join these1 and we have a system of parallel chords4 ,draw a straight line through the middle points of these chords1 and lo6 it will always pass through the centre4 ,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 laws4 ,i will conclude this lecture with a few remarks on the nature and properties of the radical axis4 ,this name was first given1 ,i believe1 by ,m4 ,gaultier1 of ,tours1 and for a full account of its nature ,i refer you to the ,journal de l',ecole ,polytechnique1 xvi41 #ahac4 ,the radical axis of two circles is the line perpendicular to the line joining the centres1 from any point of which the tangents to the circles are equal4 ,let us suppose that one circle becomes a point1 and that this point is situated on the circumference of the first circle4 ,what is the result8 ,the radical axis becomes the tangent to the circle4 ,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 monarch4 ,therefore we may conclude that the radical axis indicates a tendency of particles1 or individuals1 to fly off at a tangent1 at right angles to the connecting-link between the individual and the king4 ,when any motion takes place1 this is evident1 and this tendency is called centrifugal force4 ,sad is it for the ,state when this force is called into play1 and the radical axis is a standing menace to the stability of ,states and nations4 ,the only way to counteract its baneful1 disturbing influence is to increase the attraction of the monarch on the individual1 which nullifies the former force1 and prevents further mischief4 ,this is the method which nature itself adopts in the motions of the planetary worlds2 the attraction of the sun prevents any disturbance which might be caused in the course of the planets by the action of centrifugal force1 and nature suggests this plan for our adoption4 ,increase the attraction of the ,throne2 rigidly connect each individual by the strong chords of affection1 advantage and utility with the ruling power2 and then1 though the radical axis may be there1 it will cease to indicate any motion along it1 it will not prevail over the counteracting influence of loyalty1 and the stability of the social system and the happiness of the individuals will be the results4 ',i would serve my ,king1 ,serve him with all my fortune here at home1 ,and serve him with my person in the wars2 ,watch for him1 fight for him1 bleed for him1 die for him1 ,as every true-born subject ought4' ,this1 most noble professors1 is the language of true patriotic loyalty4 ,let the monarch be loved and loving1 let the laws be just and equal1 happy will be the people1 prosperous the realm4 ,there are those who counsel different things1 and preach sedition and the breaking-up of laws2 but those who advocate such doctrines lack that judicial mathematical training which we1 students and professors of ,girtham ,college1 have acquired4 ,if polemical mathematics1 the science of the future1 should become more widely studied2 if its results were disseminated far and wide2 above all1 if the proper position which women ought to occupy in the counsels of the nation were assigned to them1 we should hear less of these wild schemes and foolish theories1 and the influence of women would tend greatly to promote the stability and security of the ,state4 ,why1 let me ask1 should woman be excluded from that position which is so justly hers8 from those duties which she can discharge so faithfully8 ,it has been said that if we wish to know the political and moral condition of a ,state1 we must ask what rank women hold in it4 ,we are told that women have more strength in their looks than men have in their laws4 ,why1 then1 do men debar her from those fields of occupation wherein she may labour for the nation's good1 and use her influence1 which they acknowledge to be great1 in those callings wherein she may most easily benefit the ,state1 and the country she so ardently loves8 ,at some future time ,i hope to speak more fully on this subject2 and in concluding this lecture1 ,i will remark that ,english politics need a leavening influence which will counteract the evil tendencies and corrupt theories which1 in spite of our advantageous social system1 at present exist2 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 ,england4 ,let women have their proper share in the government of the country1 and ,i have no fear lest we shall preserve our elliptical constitution1 and all the advantages which we at present enjoy4 99 99 99 99 99 ,editorial ,note4--,in the bundle of papers which contained the foregoing lectures1 some letters of great interest were found1 which show that the fame of the learned ,lady ,professor of ,girtham ,college had already gone abroad1 and attracted the attention of the leading statesmen of the day4 ,it is to be regretted that the answers to these letters are not forthcoming1 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 abroad4 ,the following letter is of unique interest1 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 statesmen3 ,downing ,street1 ,may1 #ah-- ,my dear ,lady ,professor1--,the report of the amazing results of your scientific researches has reached me1 and ,i congratulate you most heartily on the originality and acumen which you have displayed in your investigations4 ,a new light has dawned upon our country4 ,instead of groping in the darkness of political warfare1 ensnared by party ties and jealousies1 the statesmen of the future will be able to calculate and determine the correct course with mathematical precision and perfect accuracy4 ,no one can dispute the truth of a proposition in ,euclid1 or the genuineness of ,newton's laws2 and if your method enables men to calculate and determine the correct political course of action1 to solve political problems as easily as exponential equations1 why--then adieu to the bickerings of party1 the querulous complaints of the ,opposition6 ,nay1 joy to the ,ministry6 ,there will be no ,opposition6 ,our statesmen will be able to guide the great ship of the ,state by means of charts which know no error2 and they will resemble an association of savants met together to determine the exact moment of the transit of ,venus1 or to examine the degree of density of a comet's tail4 ,this condition of ,parliamentary procedure is much to be desired2 you have shown how such an ideal state of things may be obtained4 ,in the name of the ,government ,i thank you for your endeavours on behalf of your country's welfare1 and look forward to a further development of your admirably conceived system4 ,as in the domain of ordinary science there are complex questions which defy the acumen of the philosopher2 so in polemical science there may be questions which present the same difficulties and complications4 ,but as the first are daily yielding before the persevering attacks of the mathematician1 so ,i doubt not polemical science will soon overcome the various problems which may arise4 ,but it is mainly on my own account that ,i venture to address you4 ,i desire to consult you with regard to certain matters--political complications--which have recently occupied the attention of ,her ,majesty's ,ministers4 ,by the help of your new science1 can you aid us in our deliberations8 ,of course1 ,i am writing to you in strict confidence1 and beg that you will keep this communication profoundly secret4 ,i fear that would be a hard task for many of your sex1 who do not possess your knowledge and powers of mind2 but ,i have great confidence in your discretion4 ,these are the problems which are presented to us for solution3 #a4 ,some members of the ,cabinet are secretly in favour of ,protection1 and the country is rather stirred by the question4 ,can you1 from your knowledge of the contact of curves and nations1 help us to determine what course we ought to take with regard to ,spain1 for example8 ,are the principles of ,adam ,smith mathematically correct8 #b4 ,i observe that ,england is represented mathematically by an ellipse4 ,are we right in assuming that ,ireland is a portion of that ellipse8 ,or1 on the other hand1 in our chart of nations1 must we describe that troublesome country as a rotating parabola1 or complex figure1 altogether outside our more favoured ,state8 #c4 ,do you consider1 from your minute observation of our social system1 that the form of our elliptical government is gradually undergoing a change1 and that a revolutionary parabolic tendency is observable in the action of individual particles8 #d4 ,is it not possible that the differences in the policy of the various nations of ,europe2 the difficulties which beset the carrying out of international law2 the jealousies1 quarrels1 and rivalries of ,states might disappear1 if the same form of government 7i4e41 elliptical7 were adopted in each8 ,if you will kindly favour ,her ,majesty's ,ministers with your opinion on these questions1 they will owe you a debt of gratitude1 which they1 as representatives of the nation1 will do their utmost to repay4 ,with every good wish for your further success in the regions of polemical science1 ,i beg to remain1 ,my dear ,lady ,professor1 ,your faithful servant1 ---------------------- #d ---------------------- ,editorial ,note4--,the next letter is not of quite the same pleasing nature as the foregoing1 and shows that it is impossible to please everyone1 even if that happy consummation were desirable4 ,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 dress4 ,our readers will recollect that the professor pointed out that an extravagant 'bloomer' costume--half male1 half female--was no more a sign of genius than aesthetic dresses1 always betokened the artist4#e ,this latter statement evidently gave great offence to the members of a society which called itself the ',aesthetic and ,dress ,improvement ,association1' and the following letter is the result of one of their solemn conclaves3 ,oscar ,villa1 ,south ,kensington1 ,june1 #ah--4 ,the ,secretary of the ,aesthetic and ,dress ,improvement ,association presents his compliments to the ,lady ,professor of ,girtham ,college1 and begs to contradict emphatically her statements with regard to a subject upon which she is evidently in entire and lamentable ignorance1 and to protest against her aspersions upon the artistic studies of this and kindred societies4 ,he begs to state that true aesthetes are not eccentric 7they leave that to lady professors and her ,philistine followers72 that to dress becomingly is one of the principal objects of life1 and that true greatness is achieved as much by the study of the art of dress as by any other noble pursuit or graceful accomplishment4 ,are not ,horatio ,postlethwaite1 ,leonara ,saffronia ,gillan1 ,vandyke ,smithson entitled to greatness8 ,and yet their laurels have been won solely by the art of dress4 ,perhaps the lady professor has never read ',sartor ,resartus'6 ,in conclusion1 he would ask the ,lady ,professor to refrain from casting obloquy upon the work of the ,association which he has the honour to represent2 to prevail upon her pupils to abandon the unfeminine attire which some of them have assumed1 contrary to the first principles of art2 to array themselves in flowing robes of sage-green and other choice colours 7patterns enclosed71 and to study art1 instead of absurd mathematics1 which no one can understand1 and do no one any good4 7,approved by the ,committee of the ,aesthetic and ,dress ,improvement ,association47 ,june1 #ah--4 ,editorial ,note4--,the next letter1 written by a pupil of the ,lady ,professor1 requires no explanation1 and speaks for itself4 ,jesus ,college1 ,cambridge1 ,march1 #ah--4 ,my dear ,tutor1 ,you will be glad to hear that after superhuman exertions ,i have at last succeeded in passing my ,little-go1 and ,i am eternally grateful to you for all you have done for me4 ,i should never have got through if it had not been for you4 ,all the coaches in ,cambridge would never have managed it1 but you drove me through in a canter4 ,and why8 ,i never could make up my mind to work for them2 but when ,i coached with you1 you made me like it4 ,i almost revelled in the ,binomial when you wrote it out for me2 and then ,i could not help listening to you2 and you looked so grieved when ,i would not learn1 and made me feel such a brute2 so somehow or other you drove some mathematics into my head1 and ,i pulled through4 ,by-the-bye1 ,i think you must have tried the 'brain wave' dodge with the examiners1 as five out of the six propositions in ,euclid1 which you told me to get up specially1 were set6 ,i wish ,i could read people's thoughts2 can you read mine8 ,if ,i were a ,don1 or a ,fellow1 or something1 ,i would advise the ,university to have some lady professors like you to teach the men1 instead of some of these sleepy old tutors4 ,it would be a great improvement1 and ,i am sure we should get through a great deal more work4 ,they have given me a place in the ,jesus ,eight1 which ,i shall take now that ,i am released from your professorial ban1 and have time for rowing4 ,but ,i don't half like giving up mathematics4 ,you see1 ,i have grown fond of the study4 ,do you think you could make a wrangler of me8 ,at any rate1 ,i should like to come to your lectures again4 ,may ,i8 ,your ,grateful ,pupil4 99 99 99 #d ,it is to be regretted that this letter has evidently fallen into the hands of some autograph collector1 who has ruthlessly cut off the signature2 but the reader will easily determine1 after careful perusal of the document1 from whose pen it emanated4 #e ,cf4 page #cf4 ,,paper ,v4 ,a ,,lecture ,,upon ,,social ,,forces1 ,,with ,,some ,,account ,,of ,,polemical ,,kinematics4 ,most noble ,professors and ,students of ,girtham ,college1--,since last ',i wandered 'twixt the pole and heavenly hinges1 'mongst encentricals1 centres1 concentricks1 circles1 and epicycles1' like the great ,albumazar1 and found them full of life and wisdom for the guidance of our ,states and laws1 ,i have turned my attention to the ,applied ,mathematics1 in order to determine what other truths this shaft may yield4 ,the strength of all sciences1 according to ,bacon1 consists in their harmony2 and it is truly marvellous how perfect this harmony is1 if our ears are tuned aright to hear it4 ,we have observed how the beautiful and regular laws of curves and cones correspond to the social laws of ,states and nations1 guiding them as if by word of counsel1 admonishing them on what principle they ought to regulate their governments and inter-relations4 ,we have seen that the laws which govern thought and light and sound are almost identical1 and that harmony pervades not merely the ordinary sciences1 but extends her benign influence over these newly discovered fields of scientific research1 which ,i claim to have discovered4 ,all this may appear at first sight surprising2 but the real philosopher1 who knows that all kinds of truth are intimately connected1 will receive such revelations of science with satisfaction rather than astonishment2 for this new science1 which has opened itself out before me1 is only an extension of other well-known laws and discoveries which have come down to us from the remote past4 ,if my investigations should appear to you1 most noble professors1 somewhat novel and imaginary1 remember the maxim of the sage1 that in the infancy of science there is no speculation which does not merit careful examination2 and the most remote and fanciful explanations of facts have often been found the true ones4 ,perhaps some 'self-opinionated particle' 7,i speak mathematically7 may have been inclined to laugh at our theories and discoveries1 as the wise fools of the day laughed at ,kepler and his laws2 but time has changed the world's laughter into praise1 and a century hence our discoveries may rank among the achievements of modern science4 ,as ,cicero says1 ',time obliterates the fictions of opinions1 but confirms the decisions of nature4' ,i have not shunned1 most noble professors1 to enlist ,imagination under the banner of ,geometry2 for ,i am fully persuaded that it is a powerful organ of knowledge1 and is as much needed by the mathematician as by the poet or novelist4 ,it is1 ,i fear1 often banished with too much haste from the fields of intellectual research by those who take upon themselves to give laws to philosophy4 ,we need imagination to form an hypothesis2 and without hypotheses science would soon become a lifeless and barren study1 a horse-in-the-mill affair ever strolling round and round1 unconscious of the grinding corn4 ,in my previous investigations my imagination pictured the symmetry of curves and ,states2 the hypothesis followed that the laws which regulated them were identical1 and you have observed how the supposition was confirmed by our subsequent calculations4 ,in this lecture ,i propose to examine some of the forces which exist in our social system1 and shall endeavour to estimate them by methods of mathematical procedure and analogical reasoning4 ,we will begin with the old definition of ,force as that which puts matter into motion1 or which stops1 or changes1 a motion once commenced4 ,when a mass is in motion1 it has a capacity for doing work1 which is called ,energy2 and when this energy is caused by the motion of a body it is called ,kinetic ,energy 7in mathematical language ,,ke #a_/b ,,mv#b74 ,another form of kinetic energy is called ,potential ,energy1 which is in reality the capacity of a body for doing work owing to its position4 ,for example we may take an ordinary eight-day clock4 ,when the weights are wound up1 they have a certain amount of potential energy stored up1 which will counteract the friction of the wheels and the resistance of the air on the pendulum4 ,or1 again1 we have the example of a water-wheel3 first the water in the reservoir1 being higher than the wheel1 has an amount of potential energy4 ,this is converted into kinetic energy in striking against the paddles1 and after this we have potential energy again produced by the action of the fly-wheel4 ,by the principle of conservation of energy1 if we consider the whole universe1 not our planet alone 7for its heat and energy are continually diminished to some slight degree71 we find that no energy is lost4 ,force is recognised as acting in two ways3 in ,statics1 so as to compel rest1 or to prevent change of motion2 and in ,kinetics1 so as to produce or to change motion2 and the whole science which investigates the action of force is called ,dynamics4 ,all this is of course pure mathematics1 and ,i have made these elementary observations for the benefit of my younger hearers1 the students of this ,university4 ,my grave and reverend seniors will pardon1 ,i am sure1 the repetition of facts well known to them for the sake of those who are less informed than themselves4 ,now before ,i proceed further1 ,i will endeavour to point out that these elementary truths of physical science hold good in our social system4 ,each individual is a mass1 acted on by numerous forces1 capable of 'doing work1' which work can be measured and his velocity calculated4 ,some individuals have a vast potential energy2 that is to say1 from their position and station in the social system1 they have a power which is capable of producing work which a less exalted individual has not4 ,like the weights in an eight-day clock1 or the water in a reservoir1 they have a capacity for doing work1 owing to the position to which they have been raised4 ,how vast the influence of a ,primate or a ,premier1 a ,general or a ,king6 ,and yet their power is chiefly potential energy1 arising from the position they occupy1 not from the individuals themselves4 ,schiller has described this in poetical language1 which1 strange to say1 is mathematically correct3 ',yes1 there's a patent of nobility ,above the meanness of our common state2 ,with what they do the vulgar natures buy ,their titles2 and with what they are1 the great4' ,other forces may have raised these men to their exalted positions2 but their influence is due to their height1 their potential energy4 ,placed on a lower level1 they would cease to have that power4 ,how calm the dignity of this potential rank6 ,the water in the reservoir is scarcely ruffled or disturbed1 as if unconscious of its power2 when it has lost its force it rushes along with a sullen murmur and a roar1 howling and hissing and boiling in endless torture1 until-- ',it gains a safer bed1 and steals at last ,along the mazes of the quiet vale4' ,so the vulgar crowd rushes on1 with plenty of kinetic force1 making noise enough and looking very busy2 while those who seem to sleep in calm forgetfulness1 exercise their potential energy1 and do the real work of turning the great engine of the ,state4 ,there are attractive and repulsive forces 7more commonly the latter1 the cynic will say7 in our social system1 but each individual is the centre of various forces acting upon him4 ,in nature all matter possesses the force of gravity1 and whatever the size of two particles may be1 they mutually attract each other4 ,the earth attracts the moon2 the moon attracts the earth4 ,a stone thrown up into the air exercises an infinitesimal force upon the earth2 so in the social system every individual1 however small and insignificant he may be1 exercises some attractive force upon his neighbour4 ,there is no one in the world who does not exercise some influence for good or for evil upon his fellows4 ,the force of cohesion is manifest in society as in nature1 that force1 ,i mean1 which resists the separation of a body's particles4 ,different bodies possess different powers of cohesion1 e4g41 the cohesion of chalk is far less than that of flint embedded in it2 even the same body possesses different powers of cohesion in different directions1 e4g41 it is easier to split wood in the direction of the fibres than perpendicular to them4 ,if by our old principle of continuity we change the words 'bodies' into ',states' or 'individuals1' we shall see that the same laws hold good in social science as in natural philosophy4 ,these are a few analogous laws which ,i have taken almost at random2 but it must strike the most casual listener to my remarks that it is wondrous strange that men1 regarded as social beings1 should possess the same qualities1 and be governed by the same laws1 as the rest of matter4 ,as ,bishop ,butler says1 'the force of analogy consists in the frequency of the supposed analogous facts1 and the real resemblance of the things compared4' ,it appeals to the reasoning faculty1 and may form a solid argument4 ,hence1 if we can prove the similarity of various laws and conditions1 we may not be wrong in assuming by analogy the identity of those laws and conditions4 ,i have stated my case in this manner in order to convince the gainsayers1 if any such there be1 and to banish any doubts or questionings which may have arisen in your minds4 ,i will now proceed with some further investigations1 full of the most profound interest and importance4 ,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 inebriates2' and as men are great flatterers 7for imitation is the greatest flattery71 ,i believe the male portion of my audience have been known to follow that excellent example4 ,some perhaps are in the habit of burning the midnight oil1 and keep their eyes open by means of this fruit of the hermit's pious zeal1 endowed by high omnipotence with the power of hindering sleep2#f but that practice ,i do not advise1 as that delicate portion of our system1 the nerves1 especially of women1 often becomes injured by such stimulating doses4 ,however1 you will have observed 7if you do not follow the modern pernicious fashion of taking tea without sugar7 that numerous bubbles are formed upon the surface of the liquid4 ,after a few moments these unite into one central mass of bubbles by the force of mutual attraction4 ,it appears from considerations which are detailed in works on physical astronomy1 that two particles of matter placed at any sensible distance apart attract each other with a force directly proportional to the product of their masses1 and inversely proportional to the square of their distance4 ,now1 suppose that we have a number of circular masses situated upon a plane surface1 they will attract each other with a force which may be determined with exactitude2 and the greater the masses the greater the force4 ,we will now apply this to polemical science4 ,the agricultural settlement is the first stage in the civilization and formation of a ,state4 ,how did this arise8 ,first1 a single family immigrated to some uncultivated parts of the country1 perhaps accompanied by others1 who formed a little colony4 ,other settlements were made in other parts of the land2 and thus the country became overspread with these detached and separate communities4 ,an eminent writer declares that these settlements can be traced in the beginnings of every race which has made progress2 that they were characteristic of those races in ,greece and ,italy1 in ,asia and ,africa1 which grew into the opulent and famous cities in which so much in the early history of civilization was developed4 ,the colonies of ,england have been formed in the same way1 just as in olden time ,england itself was occupied when the ,roman power ceased4 ,these settlements correspond to the circular masses situated on the plane surface2 they were quite separate from each other1 each having its own laws1 its own headman or ruler1 its own assembly or parish council4 ,but as time elapsed1 the force of mutual attraction set in2 by degrees these separate settlements were drawn together by force which increased in proportion as the settlements increased2 until at last one united kingdom was formed under one king1 governed by uniform laws and regulations4 ,the bubbles have blended1 the circles have come together1 and one large circle or other curve is the result4 ,this may be called the ,law of ,social ,attraction4 ,in accordance with the results of one of my previous lectures1 ,i have taken the circle as representing the simplest form of government1 which figure1 in the case of the elementary settlements1 must have been small4 ,many of you1 most noble professors1 are doubtless accustomed to make experiments with the microscope4 ,i will suggest a simple one1 which illustrates very forcibly what ,i am endeavouring to show you4 ,take some particles of copper1 and scatter them at intervals over the surface of an object-glass1 and pour some sulphuric acid upon the glass4 ,now1 what is the result8 ,a beautiful network of apparently golden texture spreads itself gradually over the whole area of the glass4 ,steadily it pursues its way1 and the result is beautiful to behold4 ,the minute particles of copper were the original settlements scattered over the land2 the sulphuric acid the civilizing agent2 and the final picture of a united civilized homogeneous nation is well represented by the progressive and finally glorious network of gold4 ,this example is of course outside our present subject1 but it serves as a beautiful illustration4 ,as an instance of the attractive force exercised by small communities upon each other1 ,i may mention the united kingdom of ,germany1 which is composed of numerous small ,states and nations1 which have been drawn together by the power of mutual attraction4 ,until recently they were each self-contained1 separate constitutions1 with their own kings and forms of government2 but the attracting force1 assisted by forces from without1 has proved too much for them1 and the great and powerful united kingdom of ,germany is the result4 ,but why1 you may ask1 have not the people in ,hindustan united in the same way8 ,there the agricultural settlements remain as they did ages ago2 separate petty chieftains rule under the all-governing power of ,england4 ,why have they not united8 ,to this objection ,i reply that there is in social science1 as in ,nature1 a vis inertia2 that is to say1 there is a tendency in matter to remain at rest if unmoved by any external agency1 and also of persisting to move1 after it has once been set in motion4 ,the vis inertia of some bodies is greater than that of others1 and depends upon their weight and density4 ,now it so happens that the moral vis inertia of the ,hindustani is very great1 hence their tendency to amalgamation is small4 ,they remain in the state in which they happen to be4 ,on the other hand the inertia of ,englishmen is small1 of ,englishwomen smaller1 and therefore their power of combining is greater4 ,here let me observe that the quality of inertia is one which ought to be removed as far as possible from each social system4 ,inertia was regarded as a capital crime by the ,egyptians4 ,solon ordained that inert persons should be put to death1 and not contaminate the community4 ,as savages bury living men1 so does inertia practise the same barbarous custom upon ,states and individuals4 ,observe the putrid state of inert water1 the clear and sparkling beauty of the moving stream1 bearing away by the force of its own motion aught that might contaminate it4 ,men more often resemble the stagnant water than the rivulet4 ,a healthy social state enforces labour by natural laws1 and banishes inertia as much as possible from the system4 ,if the principles of some noisy ,english politicians were fully carried out1 and all things made 'free1' inertia would be increased1 and listless indolence pervade the masses of our countrymen4 ,i may say that inertia is not entirely unknown in our sister ,university of ,cambridge4 ,the existence of social forces is supported by the testimony of ,dr4 ,tyndall1 who plainly recognises their power1 though he does not attempt to expound their origin4 ',thoughtful minds are driven to seek1 in the interaction of social forces1 the genesis and development of man's moral nature4 ,if they succeed in their search--and ,i think they are sure to succeed--social duty would be raised to a higher level of significance1 and the deepening sense of social duty would1 it is to be hoped1 lessen1 if not obliterate1 the strife and heart-burnings which now beset and disguise our social life4' ,i accept with gratification ,dr4 ,tyndall's conclusions3 to determine1 examine1 trace1 calculate these social forces which exercise such a powerful influence on our characters1 our lives1 our customs1 which produce the greatness of the ,state1 or drag it down with irresistible strength from its pinnacle of glory to an abyss of degradation2 to estimate such forces is the great and noble object of our lectures and researches in this ,university4 ,prosecute1 most noble professors1 your studies in this direction with all the energy of your enlightened intellects1 and there is yet hope that this new science1 which ,i have endeavoured to sketch out1 however feebly1 may be the means of saving our beloved nation from degradation and ruin1 and raising her to a higher level of glory and honour4 ,i hope to continue the subject of social forces in my next lecture4 #f ,a ,chinese legend relates that a pious hermit1 who in his watchings and prayers had often been overtaken by sleep1 so that his eyelids closed1 in holy wrath against the weakness of the flesh1 cut them off1 and threw them on the ground4 ,but a god caused a tea-shrub to spring out of them1 the leaves of which exhibit the form of an eyelid bordered with lashes1 and possess the gift of hindering sleep4--,dr4 ,ure4 ,,paper ,,vi4 ,,on ,,social ,,forces 7continued7--,,polemical ,,statics ,,and ,,dynamics4 ,most ,noble ,professors and ,students of ,girtham1--,we have embarked upon a stormy sea of speculation1 on a voyage of grand discovery1 and the dangerous waves of adverse criticism1 and the deceptive under-current of prejudice1 often make the steersman's lot by no means an enviable one4 ,but our vessel is sound and perfectly equipped1 and therefore ,i do not fear to guide her across the great unknown4 ,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 mathematics4 ,that is undoubtedly the case2 but this extra degree of difficulty is due to the fact that we make no assumptions2 we take the things as they really are1 not as they are assumed to be4 ,in physical science1 if we take into consideration the resistance of the air1 the curvature of the earth1 the rigid connection which exists between particles in the same body1 and a host of other things which are often conveniently neglected in elementary works1 how complicated the various problems become6 ,so we must not be surprised at some of the difficulties which occur in social science1 as nothing is neglected2 the whole problem is before us1 and having solved it we need not make allowances for any falsely assumed data4 ,it is possible that other professors of this science may come to slightly different conclusions to those which ,i have arrived at4 ,that is only to be expected1 because their original observations may have slightly varied4 ,but in physical science allowances are made for different observers4 ,in astronomy1 for example1 we find the value of the ',personal ,equation4' ,one observer on looking through the telescope may take the meridian of a star rather differently from another watcher of the heavenly bodies1 and the personal equation is used to make allowances for this quickness1 or slowness1 of observation4 ,so in social science there must be a personal equation too1 and our object ought to be1 in the ordinary affairs of life as well as in the higher duties of scientific action1 to make our personal equation as small as possible4 ,but until the old proverb1 ',quot homines1 tot sententiae1' has ceased to have any meaning1 there will be abundant need of this most useful aid to accuracy4 ,the close connection which exists between social forces and material forces is plainly shown by the doctrine of the conservation of energy4 ',this doctrine1' says ,dr4 ,tyndall1 'recognises in the material universe a constant sum of power made up of items among which the most ,protean fluctuations are incessantly going on4 ,it is as if the body of nature were alive1 the thrill and interchange of its energies resembling those of an organism4 ,the parts of the stupendous whole shift and change1 augment and diminish1 appear and disappear2 while the total of which they are the parts remains quantitatively immutable1 plus accompanies minus1 gain accompanies loss1 no item varying in the slightest degree without an absolutely equal change of some other item in the opposite direction4' ,so do the forces in the social world ebb and flow1 rise and fall1 carrying on the same universal law which regulates the energy of material force4 ,i will now proceed to enumerate some of those forces which exercise such a powerful influence on society4 ,first1 let us take the force of ,public ,opinion1 which seems to exercise a relentless sway over the minds and manners of men4 ,this is a very subtle and secret force1 which is most difficult to trace1 and resembles electricity in the science of physics4 ,we cannot see it1 but are only able to judge of its power by its results4 ,its point of application is not in the individual1 but in the collection of individuals who make up the social system2 and it is1 in reality1 the resultant of1 or the compromise between1 the various elementary forces which make up human society4 ,yes1 compromise is a purely mechanical affair1 based on the principle of the parallelogram of forces2 and as public opinion is the result of a compromise1 we may calculate its force4 ,for example3 ',it is required to know the state of public opinion in the matter of politics1 when the results of a ,general ,election show that the ,conservatives are to the ,liberals as #aj 3 #i4' ,let ,,oc be the direction of the ,conservative force4 ,let ,,ol be that of the ,liberal4 ,then by data ,,oc 3 ,,ol 33 #aj 3 #i4 ,illustration ,complete the parallelogram1 and join ,,op4 ,then ,,op represents the force of public opinion in magnitude and direction4 ,n4,b4--,the direction of ,,ol is determined by the amount of deviation of the policy of the ,liberals from that of the ,conservatives4 ,as in physical1 so in social science1 impulsive forces sometimes act1 and effectually disturb our system and our calculations4 ,public opinion is very liable to the action of disturbing forces4 ,panic is an impulsive force1 which defies the power of the most learned professors of social science to determine its magnitude and direction4 ,some strange unforeseen catastrophe--the fascination caused by a brilliant and unscrupulous orator1 a cruel wrong1 a blind revenge for real or imaginary injustice--will sometimes rouse one element of passion latent in the vast body of public opinion2 so that it breaks with all that hitherto restrained and balanced it1 and precipitates society into a course of conduct inconsistent with its former behaviour1 and bloodshed1 revolution1 the breaking-up of laws1 are the terrible results of panic or revengeful passion4 ,society is1 as it were1 split up by the terrible action of such impulsive forces1 just as wood is split up by the repeated blows of the hatchet4 ,it is1 therefore1 the duty of statesmen to increase the power or force of cohesion1 to strengthen the fibres of the ,state1 so that the force of such impulsive blows may not be felt1 nor disturb the continuity of the framework of the ,state4 ,if such measures had been adopted in the neighbouring country of ,france1 much misery might have been avoided1 and the terrible revolutions which have so frequently convulsed her social system entirely prevented4 ,friction is another disturbing element in our calculations1 and although it may be made a useful servant1 it is a bad master in mathematics1 as in polemics4 ,without the aid of friction1 progress would be impossible4 ,for example3 ,take the case of a man with perfectly smooth skates on perfectly hard1 smooth ice2 he would be unable to reach the land unless he had provided himself with some stones1 by throwing which he would just be able to get to his destination by a backward motion4 ,the engine would be unable to proceed on its iron road if it were not for friction4 ,the same is true in polemical science3 the government of the country would not be able to be carried on under our present conditions if it were not for party friction4 ,but suppose it increased indefinitely1 party friction becomes party obstruction2 and the engine of the ,state would no longer proceed smoothly and evenly along its appointed course at the rate of sixty miles an hour1 but would resemble an old-fashioned coach1 up to its axle-trees in mud1 its motion altogether stopped by the action of party friction4 ,we have seen that forces have two ways of acting3 that of compelling rest and that of producing motion4 ,in statics forces act so as to prevent any change of motion1 or disturb the body's original position4 ,in kinetics1 on the contrary1 the power is recognised as acting so as to produce or change a body's motion4 ,now1 in polemical science we have these two ways of considering the action of forces4 ,there is the statical or conservative force1 which compels rest1 which seeks security1 stability1 and peace1 and is not ardently devoted to change4 ,it reduces the system to equilibrium4 ,there are1 of course1 two kinds of equilibrium--stable and unstable--according as the social and political system is in a healthy or unhealthy state4 ,if a body is in stable equilibrium1 and any slight motion takes place1 the body will return immediately to its former position2 but if in unstable1 it will decline further and further away from its original position1 and be entirely upset4 ,so a healthy and sound conservative equilibrium is not disturbed by outside forces1 and the ,state will resume its former position of stability and rest when the opposing force is withdrawn4 ,but an unhealthy and insecure conservatism is as easily disturbed as an egg balanced on its narrow end4 ,the kinetics of society1 that is to say the ,radical way of estimating force1 is the party of motion1 generally supposed to be the 'party of progress4' ,it has therefore many attractions in the eyes of those who delight in motion1 speed1 and rushing about4 ,to run at full speed1 to feel the keen air upon one's face1 to experience the delightful sensation of freedom of will1 and limb1 are joys which cannot be denied4 ,such exercise is beneficial to the system1 bodily or political4 ,motion is the life of all things2 it is characteristic of nature2 it adores nature2 because it is an emblem and characteristic of life4 ,the ceaseless rolling of the ocean waves1 the swaying of the trees1 the bending of the flowers1 the waving of the corn1 all these fill us with pleasure2 whereas a flat uninteresting plain1 unrelieved by the motion of terrestrial objects1 is depressing to the spirit4 ,so there is much to be said in favour of motion1 and ,carlyle has defined progress as 'living movement4' ,and men love this 'living movement1' and take up the ,laureate's cry3 ',forward1 forward1 let us range1 ,let the great world spin for ever down the ringing ,grooves of change4' ,but1 after all1 there is a danger in this everlasting motion4 ,we cannot tell whither this progress may lead4 ,it may be along a safe sure road2 but perchance a precipice may open out before us2 and rejoicing in the acceleration of our velocity1 with eyes intent upon some distant heights of glory and ambition1 we may not discover our danger until it is too late to stop1 and a terrible plunge into an unknown abyss of turmoil and tumultuous waves is the alarming result of an unguarded policy of unrestrained 'progress4' ,i recall to my mind the quaint words of ,holmes which aptly illustrate my contention4 ',if the wild filly1 ,progress1 thou would'st ride1 ,have young companions ever at thy side2 ,but wouldst thou stride the staunch old mare1 ,success1 ,go with thine elders1 though they please thee less4' ,progress and success do not always go together hand in hand2 and while motion is essential to life1 it is not always safe to urge a country forward at too great a speed2 and security and stability are quite as important to the nation's life as actual progress4 ,there are other impulsive forces which act occasionally in the sphere of politics1 and which baffle all our calculations1 and exclude scientific considerations of the polemical problems which arise4 ,ambition is such an impulsive force1 and when the rulers of the people are actuated by it1 and struggle for money1 place1 and power1 politics is degraded from its position as a science1 and it becomes impossible to estimate the result of forces so generated4 ,in my next lecture ,i propose to treat the important subject of the ,laws which govern ,states and ,governments1 and which regulate1 generate1 and control the social forces which we have seen at work in the body politic4 ,,paper ,,vii4 ,,laws ,,of ,,political ,,motion4 ,since the last time ,i had the honour of addressing you on polemical matters1 ,i have met with a passage in the writings of ,m4 ,auguste ,comte which afforded me much pleasure4 ,it seemed to be the one word for which ,i had been waiting1 and confirmed many of my own impressions and speculations4 ,he lays down two propositions3 first1 that the constructive politics of the future must be based on the history of the past2 and second1 that political science is a composite study1 and presupposes the complete apprehension of every branch of science1 beginning with the physical1 such as astronomy1 and ending with the moral1 such as ethics and sociology4 ,m4 ,comte evidently does not regard as a vain dream and imaginative speculation the theory that it will be possible for statesmen to calculate a policy1 and to determine a course of action by purely scientific considerations4 ,may ,i entertain the hope that in this university1 where all branches of physical science have found a home1 and are studied by most able and learned professors1 the science of politics may be pursued under most favourable circumstances8 ,i trust that each professor will bring before me the results of their deliberations1 and contribute to the growth of this particular science for which our university has already become deservedly famous4 ,my present lecture is devoted to the important consideration of ,law4 ,at first sight it may appear to you that the wills and passions of mankind are so diverse and unknowable1 that it would be absurd to suppose that they can be calculated1 or rendered amenable to any law4 ,but ,professor ,amos has pointed out that in proportion as we examine history1 and compare the actions present and past of different nations and states1 the more uniform does human nature appear2 the more calculable the actions1 sentiments1 and emotions of large masses of people4 ,as we have already stated1 the difficulties of the study are not likely to deter the professors of ,girtham ,college from the pursuit of any particular branch of science4 ,a priori we might suppose from analogy that these polemical laws existed1 as there is no department of nature which is not governed by law4 ,it is an essential feature in nature1 and also in government4 ,what is political economy but the study of certain laws of nature8 ,these were first discovered by ,adam ,smith1 and have since been traced and estimated by such men as ,ricardo1 the two ,mills1 ,professor ,cairnes1 ,jevons1 and many others4 ,moreover1 our physical constitutions are governed by laws1 which physicians have determined1 and which it is perilous to resist4 ,our moral constitution is also governed by laws1 which evidently exist1 although it is difficult to find them out4 ,but the nation is only an assemblage of individuals2 and since individuals are so governed1 it is only natural to suppose that the nation1 composed of individuals1 is so constituted and controlled4 ,and not only is that true1 but we shall see that polemical laws are as permanent and universal1 as invariable and irreversible1 as the laws of nature which regulate the courses of the heavenly bodies1 and raise the tides1 or depress the sandstone hills4 ,we may notice first the preponderant impulse observable in a nation's life in favour of supporting existing facts and institutions2 and every reformer has discovered the difficulty and danger of changing or opposing the customs and habits of the people4 ,as a wheel will travel most smoothly along a well-worn groove1 whereby friction is diminished1 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 familiar4 ,this law is nothing else than ,newton's first law of motion1 which is quite as applicable to human masses as to lifeless matter4 ,the tendency of matter to remain at rest1 if unmoved by any external agency1 and of persisting to move after it has once been set in motion1 is a conservative tendency2 and is as true in political science as in any other4 ,the special branch of our science1 which we may call the ,biology of ,politics1 shows how absolute is the domain of law in polemical matters4 ,the law of human life is that men are born1 grow1 become strong and vigorous1 and then decay and die4 ,this is the law of life1 to which we must all yield an enforced obedience4 ,this same law is observed to be at work in the heavenly bodies2 and astronomy shows us that planets are born1 flourish1 and at length die1 just as our human bodies do4 ,the moon is1 as you may have observed1 a dead planet1 such as our earth may be some day4 ,the same growth and decay are also manifest in national life4 ,first1 there is the birth of the nation1 which sometimes lies a long time in a dormant state1 and then wakes up to life and energy4 ,china and ,russia are examples of dormant ,states1 just waking from a long sleep of childishness and ignorance4 ,the next stage is the strong an healthy period of its existence1 which ,england is at present enjoying2 and then1 after various stages of gradual decline1 we come to the senile period of national life1 when every energy and faculty1 every national feeling and power of invention1 are completely exhausted4 ,as an example of this depressing condition1 we may mention ,turkey and several of the effete ,states of ,south ,america4 ,sometimes1 when life is nearly extinct in the human body1 physicians have made use of the power of galvanism1 in order to revive the dying energies4 ,this process of galvanizing a ,state into life was tried by ,lord ,palmerston and others on the worn-out frame of ,turkey4 ,but such attempts can only meet with partial and transitory success2 and where the loss of national power and faculty betokens the senile period of the nation's existence1 it is vain to attempt to restore its former life and energy4 ,the study of the biology of politics presents many interesting and important details in this special branch of knowledge2 and ,i commend this part of our subject to the special attention of the professor of physiology4 ,the law of development is observable in nations as in nature4 ,recent scientific discoveries have tended to take away all ideas of chance in the workings of nature1 and have substituted law instead of it4 ,it would be unscientific and incorrect to speak of the world being formed by the 'fortuitous concourse of atoms4' ,so we cannot speak of a ,state being generated in this manner4 ,laws--economical1 geographical1 natural--preside over the formation of ,states and nations1 and produce their further development4 ,the laws of political motion occupy the same prominent place in our new science as ,newton's laws do in ordinary dynamics4 ,these are very important in calculating the positions which various ,states will occupy in the future4 ,first1 we have the doctrine of nationality1 which prevented the progress of ,austria into ,italy1 and of the ,bourbons in ,naples1 and produced the amalgamation of the small ,german ,states in the great empire of ,germany4 ,the second law of political motion is the doctrine of the independence of all true ,states1 and the equality of all ,states to each other4 ,this had its growth in feudalism2 and all the chief wars of modern times have been the result of the efforts of nature to establish this law of independence4 ,the doctrine of intervention is a modification of the preceding law1 and is applicable when the law of necessity demands its use1 such as the restoration of order after protracted anarchy1 the abolition of slave trade1 etc4 ,the third law is the law of morality4 ,just as for each man there exists a right and a wrong2 just as duty and conscience are certain elements in his daily motion1 which dictate his course of action1 although he may chose to neglect them2 so a nation is bound by the same moral laws which govern the individual2 and a nation errs if it transgresses them4 ,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 duty2 and ,i read with thankfulness the conclusion of ,mr4 ,amos1 that ,christianity has triumphed quite as much in moralizing secular politics as it has in the sphere of individual life4 99 99 99 99 99 ,these are some of the principal laws of motion which ,i have observed at work in various ,states and nations4 ,inasmuch as political science embraces1 in addition to the physical sciences1 all those branches which are contained in ethics1 economics1 jurisprudence1 sociology and others1 the laws of each are generally applicable to the whole grand subject of which my lectures treat4 ,other general laws may be deduced1 and have been enumerated in my previous lectures1 from the social properties of curves and conics2 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 future4 ,already there is strong evidence that the affairs of this country are being conducted on sound scientific principles1 rather than by any species of guess-work or haphazard contrivances4 ,the use of history is recognised as extremely important in determining a future line of conduct2 and statesmen are in the habit of endeavouring to find from their study of the past what is the logical sequence of events4 ,just as mathematicians endeavour to determine the law of a series of figures1 and having found the law1 can write down the next1 and the next1 ad infinitum2 so scientific politicians may be able soon to establish the various laws of a series of events1 and calculate their course of actions4 ,that there is considerable progress in this direction is manifest by the value which they place upon statistics1 and their continued use of this important information4 ,there are a few great evils in our present system which are strongly opposed to any scientific methods in politics2 and in the interests of the country as well as those of science they ought to be removed4 ,one great evil is the want of political and scientific knowledge on the part of the electors1 who are in the habit of choosing their representatives on personal grounds1 or party considerations1 rather than on sound principles of political science4 ,all this is opposed to any idea of law4 ,owing to the ignorance of the electors they fall an easy prey to adventurers and unprincipled politicians1 who make all kinds of specious promises1 tempt them with all manner of baits1 and make self-interest instead of the welfare of the ,state the principle of voting4 ,selfishness is the ruin of social life and intercourse1 the destroyer of all happiness1 peace1 and mutual trust in family life or in society4 ,it is the root of most of the faults1 vices1 and crimes in the individual2 and who can tell the endless disasters which will befall the ,state1 where selfishness is the chief motive-power of the electors and the elected8 ,a selfish statesman1 one who goes into ,parliament to gain his own ends and forward his own personal interests1 is a disgrace to society-- ',feeling himself1 his own low self1 the whole1 ,when he by sacred sympathy might make ,the whole one self4 ,self1 that no alien knows6 ,self1 far diffused as fancy's wing can travel6 ,self1 spreading still1 oblivious of its own1 ,yet all of all possessing6' ,i have said that the ignorance of the electorate makes them an easy prey to such men2 and until they have learnt to detect the false from the true1 until they become acquainted with the elements of political science1 and have been taught that their own selfish interests are not the highest aims of social government1 it is vain to hope for a reasonable method of regulating the affairs of the nation1 based upon logical laws and scientific principles4 ,and how is this work of educating the electors to be accomplished8 ,not1 ,i maintain1 by furious speeches and rhetorical displays2 not by bribery1 baits and banter2 but by patient1 never-ceasing labour1 by lectures on history and science1 by individual instruction1 is the great work to be accomplished upon which the security and stability of the country depend4 ,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 people1 and its benign influence extend from the throne of the monarch and the council-chamber of his ministers to the hearth of the cottager4 ,politicians will rule by law2 policies be calculated by laws2 people vote by law2 and then methinks ,i see in my mind 7to use the words of the blind old poet7 a noble and puissant nation rousing herself like a strong man after sleep1 and shaking her invincible locks2 methinks ,i see her as an eagle1 renewing her mighty youth1 and kindling her undazzled eyes at the full mid-day beam2 purging and unsealing her long-abused sight at the fountain itself of heavenly radiance2 while the whole noise of timorous and flocking birds flutter about amazed at what she means4 ,such is the glorious vision of the ',reign of ,law4' ,let it be the business of every ,englishman and ,englishwoman to arrange the framework of our social and political system1 that law may have an uninterrupted sway2 then shall we be a united1 prosperous1 and contented people1 and the reign of lawless agitators1 bribery-mongers1 and counterfeit statesmen will have passed away into the oblivion and obscurity of a more suitable but less favoured region4 ,,paper ,,viii4 ,,on ,,the ,,principle ,,of ,,polemical ,,cohesion4 ,in my previous lectures ,i have had occasion to mention the principle of cohesion2 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 it4 ,this is a large and comprehensive subject1 and embraces such principles as the ,centralization of ,states2 the ,co-operation of ,states2 ,monogamic ,marriage2 ,unions2 ,free ,trade1 and many others equally important4 ,we have already noticed that cohesion is a well-known property of matter2 that its influence is not confined to the regions of physical sciences2 and that it is the manifest duty of all governments to increase the force of cohesion4 ,various methods have been tried to accomplish this purpose4 ,the principle of ,feudalism was one of the earliest attempts to produce the cohesion of the nation2 and1 in an elementary condition of society1 it was partly successful4 ,the theories of ',divine ,right' and ',social ,contract' were other methods which have been adopted2 and the unity of the ,christian ,church has been the great means of producing the cohesion of the ,state in olden times2 and its aid may be again required for the same beneficent object in future complications and social disruptions4 ,but it is always advantageous in scientific pursuits to go back to first principles2 and we will adopt that method in our present investigations4 ,the social unit is the family2 the multiplication of families makes the tribe2 the multiplication of tribes makes the ,state2 and1 therefore1 we shall not be far wrong if we consider the family tie as the first principle of political cohesion4 ,i am in agreement with several learned thinkers upon this subject when ,i say that marriage is a most important political factor2 and as marriage cannot take place without women1 it is evident that women play a very important part in promoting the cohesion of the ,state4 ,this prominent position was duly assigned to women by one of our greatest political philosophers1 ,m4 ,auguste ,comte1 who strongly opposed the fatal fallacy of ancient political systems1 which greatly overestimated the powers of men1 and depreciated those of women4 ,if the superiority of bodily strength be the sole cause of greatness in political and intellectual pursuits1 then1 most noble lords of creation1 we yield to you the palm--you are our masters in this respect4 ,but if1 on the other hand1 it can be shown that physical strength is not a requisite for great achievements in these occupations2 if the powers of endurance1 elasticity1 adaptability1 nervous energy1 and patience are quite as needful as mere animal strength2 then we women are quite as capable1 and indeed more capable than men1 for achieving political greatness4 ,in the 'good old days1' when the law of might was right1 and the strongest arm was the most powerful machinery in the government of the country1 women were compelled naturally to occupy a less prominent position in the conduct of the affairs of the nation2 and for centuries they have been degraded by a dominating tradition1 and supposed incapable of performing duties for which they were mentally well suited4 ,but those militant days are past4 ,animal strength and brute force are no longer needed in the councils of the nation2 and the time has arrived when women should cease to be oppressed by the disparaging1 illogical deductions of former generations1 and when their assistance ought to be invoked in the great work of promoting the nation's welfare4 ,i have stated that marriage is an important political factor2 and1 therefore1 women have always occupied a primary1 though obscure1 part in political affairs4 ,the cohesion of the ,state has been produced by the secret influence of family life4 ,but it may be asked1 ,what kind of marriage is most conducive to national cohesion8 ,this question has been carefully and conclusively answered by a learned scientific writer1 who shows that polygamic marriage never exists in an advanced state1 as instanced by the history of ,judaism and ,mohammedanism2 that a strict form of monogamic marriage is essential to political greatness and true progress in civilization4 ,the cohesion of the ,state is destroyed by polygamy1 and by any system which relaxes the binding nature of the marriage tie4 ',domestic disorganization is a sure augury of political disruption4' ,cohesion1 the essential property of all rightly constituted nations1 is often in danger of being lost when the ,state is geographically very large1 or when local interests have greater power than the attractive force of the central government4 ,to obviate this evil1 the method of centralization has been adopted with satisfactory results1 as in the case of the ,united ,states of ,america1 and ,germany4 ,by this means the local authorities are brought into close relationship with the central head1 and the centrifugal influences of independent interests and customs are counteracted by the force of central attraction4 ,centralization increases the importance of the whole body1 and1 like the pendulum of a clock1 regulates the movements of the whole ,state4 ,in some cases it tends to make the government despotic1 when the local governments are entirely under the control of the central2 and every enactment1 and scheme1 and plan checked and supervised by the chief officers of the ,state4 ,such was the system adopted in ,france by ,napoleon ,,iii4 ,but cohesion without the enforcement of a hard and rigid connection1 a general supervision without severe tyrannical jurisdiction1 are the best methods of securing the unity of composite ,states4 ,but the force of cohesion is evidently at work in the nation apart from centralization4 ,men who have a community of interests unite together for the purposes of strength and mutual assistance4 ,they combine for the sake of securing means of support in sickness1 and form benefit societies1 such as the ,order of ,oddfellows or ,foresters4 ,this force of cohesion has produced trade unions1 and similar institutions which exist for the purpose of protecting a common interest1 and giving expression to the concurrent opinions of the members4 ,these have their legitimate use in every civilized ,state1 in spite of some of the disadvantages which follow in their train4 ,there are1 of course1 opposed interests in every community3 attractive forces1 which produce trade unions1 guilds1 corporations1 companies1 and the like2 and repulsive forces1 which result from the opposed interests of employers and employed1 landlords and tenants1 and similar pairs of different classes in the community4 ,as time goes on1 and the ,state advances with it1 these forces will gain in strength2 the cohesion of classes will become greater2 association will grow as naturally as the bubbles form on the surface of our evening beverage4 ,it is a law of nature1 and therefore cannot be resisted4 ,but the repulsive forces will be no less strong1 and to calculate the resultant of these contending interests will be the problem for practical statesmen to solve4 ,the force of cohesion is also evidently at work1 not only in individual ,states1 but also amongst the nations of ,europe1 and of the world4 ,that is to say1 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 cohesion4 ,international law is based on the principle of cohesion1 and every day it is gaining power and favour in the eyes of our leading statesmen4 ,the doctrine of ,free ,trade1 which1 if universally adopted1 would be of the greatest service to mankind1 results from a desire for co-operation2 and whatever evils may result from one-sided ,free ,trade in this country at the present time1 there can be no doubt that ultimately the complete system will be adopted4 ,sad is the fate of a nation when the force of cohesion is weakened4 ,the first revolution in ,france is a proof of this assertion2 there was no cohesion1 no common faith1 or loyalty to the throne and ,government2 and indeed the ,government1 which was rotten to the core1 was hardly likely to awake any feelings of loyalty and respect2 and therefore the social disruption which followed was only a natural sequence of events1 and was prophesied with the accuracy with which an astronomer can foretell an eclipse4 ,but that is not all2 when the cohesion of the ,state is destroyed1 it takes a long time to restore the action of the force2 and1 as in the case of ,france1 further disruption is sure to take place4 ,in this lecture ,i have already enumerated some of the ways in which this force acts2 there are doubtless others which will suggest themselves to you4 ,but ,i contend that the prosperity of the ,state1 and the peace of the world1 depend upon cohesion4 ,let this be your work1 most noble professors1 to promote the action of this helpful and life-giving force4 ,promote1 as far as in you lies1 the sacred union of family life4 ,encourage the generous feelings of true loyalty and patriotism amongst the people of this realm of ,england2 counsel our statesmen with regard to the primary necessity of national cohesion1 and the advantages of international co-operation2 and your work will be blessed2 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 prosperity2 and your memory will live in the hearts of your grateful countrymen4 ,editorial ,note4--,we regret to state that the various ,,mss4 in the sealed desk are nearly exhausted1 and are therefore compelled to present the series of lectures on polemical studies in an incomplete form4 ,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 occupations4 ,we append a few extracts3 ,extracts from the ,author's ,diary4 ,june #crd4--,arnold called again to-day--the fifth time during the last fortnight6 ,his attention is rather overpowering1 and wastes much of my valuable time4 ,he says he hates science--the heathen6--and wants me to lecture in classics4 ,he affirms that mathematics are dry and hard--too hard for women1 and tend to make them unsympathetic and critically severe4 ,i am afraid ,i was rather severe with him4 ,but really he is very trying1 and always seems to talk like a ,greek chorus in the most profound platitudes4 ,arnold is a classical tutor at ,clare ,college4 ,my old pupil is getting on famously4 ,poor fellow6 he seems quite oppressed with his work4 ,but he is making great progress1 and sticks to his books like--a student of ,girtham ,college6 ,june #dth4--,lectured on the ,scientific ,basis of ,blackstone's ,commentaries2 afterwards received pupils until #a p4m4 ,really ,blanch ,s---- is more tiresome than ever4 ,it appears that she has taken up with a young undergraduate of ,king's1 and there is no prospect of any improvement in her work unless this nonsense is terminated4 ,how foolish some of my sex are1 in spite of their improved opportunities6 ,i blush for them6 ,arnold has sent me a copy of ,robert ,browning's ',belaustion1' in order to make me like classics1 and give up science4 ,misguided young man6 ,he has written some tolerable verses on the fly-leaf2 but ,i have no intention of playing ,belaustion to his 'entranced youth4' ,these are his verses3 ',my lady dear1 if ,i may call you so1 ,for you are dearer than all else beside1 ,i know the love you bear to golden verse1 ,to golden thoughts enshrined in classic lore1 ,to all that's beautiful2 so here ,i send ,some echoes of the songs of ancient days1 ,attuned and chanted by an ,english bard1 ,who fires one's old love for the rolling lines ,of youthful ,hellas2 may your cultured ear ,receive1 and gladly welcome his sweet song4 ,and while we revel in the poet's dream1 ,and hear his actors speak1 we'll play our parts4 ,you1 sweet ,belaustion on the temple-steps1 ,taking your captors captive by your voice2 ,and ,i1 the youth who1 more entranced than all1 ,was bound by fetters that he would not loose2 ,and so we'll play our part4 ,what say you1 dear8' ,june #fth4--,have just seen our new ,professor of ,physics1 ,amelia ,cordial1 who is an excellent woman1 and well suited for the high office which she holds4 ,she has told me of the foolish conduct of ,lady ,mary1 who is evidently of opinion that the professorial mantle ought to have fallen on her shoulders4 ,really1 this jealousy in the ranks of the learned is most disgraceful2 and the bickerings which arise from disappointed ambition1 the envyings and silly quarrels1 are the weak places in our female collegiate system4 ,such good news6 ,the wrangler list is just out1 and my hard-working pupil is bracketed twelfth6 ,this is really delightful1 and abundantly repays us for all our hard toil4 ,but really ,i have not found working with him distasteful2 he is such an excellent pupil1 so painstaking and eager1 that ,i have quite looked forward to his coming1 and found him much more interesting than some of these foolish maidens4 ,but ,i almost dread seeing him4 ,he will be so elated and overpoweringly grateful1 whereas ,i ought to be grateful to him for all his work for me2 for ,i am sure he would never have gone in for the ,tripos if ,i had not persuaded him4 ,well1 ,i wonder why he does not come to tell me of his triumph4 ,june #gth4--,it has come6 and ,i half expected it4 ,my eager pupil writes with all the energy and love of his noble nature to ask me to be his wife6 ,he says that is all he cares for1 and only values his ,honours as a step to a higher honour and dignity1 that of gaining my love and being my husband4 ,all this is very nice to read2 but a terribly difficult problem is placed before me for solution4 ,i do indeed love this dear1 good fellow--no one could help doing so1 ,i am sure2 but do ,i not love science more8 ,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 cares4 ,all married women are excluded4 ,if ,i say ',yes1' ,i must resign my high position1 leave this beloved college1 give no more lectures to entranced audiences4 ,in the interests of science1 ought ,i to refuse1 and sacrifice my heart's affections for the cause of mathematics8 ,but if ,i say ',no1' ,i must give up--him2 sacrifice his happiness too1 and blight his life4 ,was ever anyone so perplexed8 ,science1 aid thine obedient servant6 ,may ,i not determine this vital question by thine all-pervading light8444 99 99 99 99 99 ,editorial ,note4--,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 study1 and ere we could secrete our ,,ms4 the door was opened1 and a well-known voice exclaimed3 ',i do not know why you should have become so studious lately1 ,ernest1 and why you should refuse to take me into your confidence4 ,you spend hours and hours in this room all by yourself1 writing away1 and never say a word to me about the subject of your literary work4 ,there was a time when things were different1 and you were not so slow in availing yourself of my help1 and asking my advice4' ,we murmured something about taking up the pen which had been laid aside by a far abler hand1 and our deep gratitude for past assistance in our work1 which could never be forgotten4 ',and do you think that ,i cannot help you now8' our visitor replied1 in a very injured tone of voice4 ',is the old power dead1 because it has not recently been used8 ,ernest1 ,i think you very ungrateful not to confide in me4 ,come1 tell me what you are writing4' ,a suggestion about the proverbial curiosity of women rose to our lips1 but died away without utterance4 ,in the meantime1 her eyes wandered over our study-table strewed with papers1 and lighted upon the well-worn desk4 ',why1 ,ernest1 where did you find this8 ,my dear old desk1 which has been lost ever so long6 ,i do believe you have been ransacking its contents6 ,why did you not tell me that you had found it8 ,what are you doing with my papers1 sir8' ,the mischief was out6 ,we tried to explain that the world ought not to be deprived of that which would benefit mankind2 that the peace and prosperity of the country might be sacrificed if it were deprived of these discoveries of science1 which were calculated to secure such beneficial results4 ,at length we gained our point1 and obtained the full sanction of the late ,lady ,professor of ,girtham ,college to publish her papers4 ,thus her obedient pupil is enabled to repay his late instructress for all her kindness to him1 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 studies1 which1 not without a struggle1 she resigned when she deigned to become his wife4 ,,the ,,end4 ,elliot ,stock1 ,paternoster ,row1 ,london4