[71]PAPER V.

[58]‘I would serve my King,Serve him with all my fortune here at home,And serve him with my person in the wars;Watch for him, fight for him, bleed for him, die for him,As every true-born subject ought.’This, most noble professors, is the language of true patriotic loyalty. Let the monarch be loved and loving, let the laws be just and equal, happy will be the people, prosperous the realm. There are those who counsel different things, and preach sedition and the breaking-up of laws; but those who advocate such doctrines lack that judicial mathematical training which we, students and professors of Girtham College, have acquired. If polemical mathematics, the science of the future, should become more widely studied; if its results were disseminated far and wide; above all, if the proper position which women ought to occupy in the counsels of the nation were assigned to them, we should hear less of these wild schemes and foolish theories, and the influence of women would tend greatly to[59]promote the stability and security of the State.Why, let me ask, should woman be excluded from that position which is so justly hers? from those duties which she can discharge so faithfully? It has been said that if we wish to know the political and moral condition of a State, we must ask what rank women hold in it. We are told that women have more strength in their looks than men have in their laws. Why, then, do men debar her from those fields of occupation wherein she may labour for the nation’s good, and use her influence, which they acknowledge to be great, in those callings wherein she may most easily benefit the State, and the country she so ardently loves?At some future time I hope to speak more fully on this subject; and in concluding this lecture, I will remark that English politics need a leavening influence which will counteract the evil tendencies and corrupt theories which, in spite of our advantageous social system, at present[60]exist; and this leavening influence will be best produced by the admission of those into the counsels of the nation who are acknowledged to have a benign and healthy influence—the women of England. Let women have their proper share in the government of the country, and I have no fear lest we shall preserve our elliptical constitution, and all the advantages which we at present enjoy.[Editorial Note.]—In the bundle of papers which contained the foregoing lectures, some letters of great interest were found, which show that the fame of the learned Lady Professor of Girtham College had already gone abroad, and attracted the attention of the leading statesmen of the day. It is to be regretted that the answers to these letters are not forthcoming, as it might be proved from them that the science of polemical mathematics has already influenced the minds of our legislators in their conduct[61]of affairs at home and abroad. The following letter is of unique interest, and may be taken as evidence of the favourable impression which this new science has made on the mind of one of our greatest thinkers and statesmen:Downing Street,May, 18—My dear Lady Professor,—The report of the amazing results of your scientific researches has reached me, and I congratulate you most heartily on the originality and acumen which you have displayed in your investigations. A new light has dawned upon our country. Instead of groping in the darkness of political warfare, ensnared by party ties and jealousies, the statesmen of the future will be able to calculate and determine the correct course with mathematical precision and perfect accuracy. No one can dispute the truth of a proposition in Euclid, or the genuineness of Newton’s laws; and if your method enables men to[62]calculate and determine the correct political course of action, to solve political problems as easily as exponential equations, why—then adieu to the bickerings of party, the querulous complaints of the Opposition! Nay, joy to the Ministry! There will be no Opposition! Our statesmen will be able to guide the great ship of the State by means of charts which know no error; and they will resemble an association of savants met together to determine the exact moment of the transit of Venus, or to examine the degree of density of a comet’s tail.This condition of Parliamentary procedure is much to be desired; you have shown how such an ideal state of things may be obtained. In the name of the Government I thank you for your endeavours on behalf of your country’s welfare, and look forward to a further development of your admirably conceived system. As in the domain of ordinary science there are complex questions which defy the acumen of the philosopher;[63]so in polemical science there may be questions which present the same difficulties and complications. But as the first are daily yielding before the persevering attacks of the mathematician, so I doubt not polemical science will soon overcome the various problems which may arise.But it is mainly on my own account that I venture to address you. I desire to consult you with regard to certain matters—political complications—which have recently occupied the attention of Her Majesty’s Ministers. By the help of your new science, can you aid us in our deliberations? Of course, I am writing to you instrict confidence, and beg that you will keep this communication profoundly secret. I fear that would be a hard task for many of your sex, who do not possess your knowledge and powers of mind; but I have great confidence in your discretion.These are the problems which are presented to us for solution:[64]1. Some members of the Cabinet are secretly in favour of Protection, and the country is rather stirred by the question. Can you, from your knowledge of the contact of curves and nations, help us to determine what course we ought to take with regard to Spain, for example? Are the principles of Adam Smith mathematically correct?2. I observe that England is represented mathematically by an ellipse. Are we right in assuming that Ireland is a portion of that ellipse? Or, on the other hand, in our chart of nations, must we describe that troublesome country as a rotating parabola, or complex figure, altogether outside our more favoured State?3. Do you consider, from your minute observation of our social system, that the form of our elliptical government is gradually undergoing a change, and that a revolutionary parabolic tendency is observable in the action of individual particles?4. Is it not possible that the differences[65]in the policy of the various nations of Europe; the difficulties which beset the carrying out of international law; the jealousies, quarrels, and rivalries of States might disappear, if the same form of government (i.e., elliptical) were adopted in each?If you will kindly favour Her Majesty’s Ministers with your opinion on these questions, they will owe you a debt of gratitude, which they, as representatives of the nation, will do their utmost to repay.With every good wish for your further success in the regions of polemical science,I beg to remain,My dear Lady Professor,Your faithful servant,4[Editorial Note.]—The next letter is not of quite the same pleasing nature as the foregoing, and shows that it is[66]impossible to please everyone, even if that happy consummation were desirable. This letter was evidently called forth by some remarks which the learned Lady Professor had made in her third lecture with reference to eccentricity in dress. Our readers will recollect that the professor pointed out that an extravagant ‘bloomer’ costume—half male, half female—was no more a sign of genius than æsthetic dresses, always betokened the artist.5This latter statement evidently gave great offence to the members of a society which called itself the ‘Æsthetic and Dress Improvement Association,’ and the following letter is the result of one of their solemn conclaves:Oscar Villa, South Kensington,June, 18—.The Secretary of the Æsthetic and Dress Improvement Association presents his compliments to the Lady Professor of Girtham College, and begs to contradict emphatically her statements with regard[67]to a subject upon which she is evidently in entire and lamentable ignorance, and to protest against her aspersions upon the artistic studies of this and kindred societies. He begs to state that true æsthetes arenoteccentric (they leave that to lady professors and her Philistine followers); that to dress becomingly is one of the principal objects of life, and that true greatness is achieved as much by the study of the art of dress as by any other noble pursuit or graceful accomplishment. Are not Horatio Postlethwaite, Leonara Saffronia Gillan, Vandyke Smithson entitled to greatness? And yet their laurels have been won solely by the art of dress. Perhaps the lady professor has never read ‘Sartor Resartus’! In conclusion, he would ask the Lady Professor to refrain from casting obloquy upon the work of the Association which he has the honour to represent; to prevail upon her pupils to abandon the unfeminine attire which some of them have assumed, contrary to the first principles of art; to array themselves in flowing robes of sage-green and[68]other choice colours (patterns enclosed), and to study art, instead of absurd mathematics, which no one can understand, and do no one any good.(Approved by the Committee of the Æsthetic and Dress Improvement Association.)June, 18—.[Editorial Note.]—The next letter, written by a pupil of the Lady Professor, requires no explanation, and speaks for itself.Jesus College, Cambridge,March, 18—.My dear Tutor,You will be glad to hear that after superhuman exertions I have at last succeeded in passing my Little-go, and I am eternally grateful to you for all you have done for me. I should never have got through if it had not been for you. All the coaches in Cambridge would never have managed it, but you drove me through in a canter. And why? I never could make up my mind to work for them;[69]but when I coached with you, you made me like it. I almost revelled in the Binomial when you wrote it out for me; and then I could not help listening to you; and you looked so grieved when I would not learn, and made me feel such a brute; so somehow or other you drove some mathematics into my head, and I pulled through. By-the-bye, I think you must have tried the ‘brain wave’ dodge with the examiners, as five out of the six propositions in Euclid, which you told me to get up specially, were set! I wish I could read people’s thoughts; can you read mine? If I were a Don, or a Fellow, or something, I would advise the University to have some lady professors like you to teach the men, instead of some of these sleepy old tutors. It would be a great improvement, and I am sure we should get through a great deal more work.They have given me a place in the Jesus Eight, which I shall take now that I am released from your professorial ban, and have time for rowing. But I don’t half like giving up mathematics. You see, I[70]have grown fond of the study. Do you think you could make a wrangler of me? At any rate, I should like to come to your lectures again. May I?Your Grateful Pupil.* * *4It is to be regretted that this letter has evidently fallen into the hands of some autograph collector, who has ruthlessly cut off the signature; but the reader will easily determine, after careful perusal of the document, from whose pen it emanated.5Cf. page36.[71]PAPER V.A LECTURE UPON SOCIAL FORCES, WITH SOME ACCOUNT OF POLEMICAL KINEMATICS.Most noble Professors and Students of Girtham College,—Since last ‘I wandered ’twixt the pole and heavenly hinges, ’mongst encentricals, centres, concentricks, circles, and epicycles,’ like the great Albumazar, and found them full of life and wisdom for the guidance of our States and laws, I have turned my attention to the Applied Mathematics, in order to determine what other truths this shaft may yield.The strength of all sciences, according to Bacon, consists in their harmony; and it is truly marvellous how perfect this harmony is, if our ears are tuned aright to hear it. We have observed how the[72]beautiful and regular laws of curves and cones correspond to the social laws of States and nations, guiding them as if by word of counsel, admonishing them on what principle they ought to regulate their governments and inter-relations. We have seen that the laws which govern thought and light and sound are almost identical, and that harmony pervades not merely the ordinary sciences, but extends her benign influence over these newly discovered fields of scientific research, which I claim to have discovered.All this may appear at first sight surprising; but the real philosopher, who knows that all kinds of truth are intimately connected, will receive such revelations of science with satisfaction rather than astonishment; for this new science, which has opened itself out before me, is only an extension of other well-known laws and discoveries which have come down to us from the remote past.If my investigations should appear to you, most noble professors, somewhat novel and imaginary, remember the maxim of[73]the sage, that in the infancy of science there is no speculation which does not merit careful examination; and the most remote and fanciful explanations of facts have often been found the true ones. Perhaps some ‘self-opinionated particle’ (I speak mathematically) may have been inclined to laugh at our theories and discoveries, as the wise fools of the day laughed at Kepler and his laws; but time has changed the world’s laughter into praise, and a century hence our discoveries may rank among the achievements of modern science. As Cicero says, ‘Time obliterates the fictions of opinions, but confirms the decisions of nature.’I have not shunned, most noble professors, to enlist Imagination under the banner of Geometry; for I am fully persuaded that it is a powerful organ of knowledge, and is as much needed by the mathematician as by the poet or novelist. It is, I fear, often banished with too much haste from the fields of intellectual research by those who take upon themselves to give laws to philosophy. We need[74]imagination to form an hypothesis; and without hypotheses science would soon become a lifeless and barren study, a horse-in-the-mill affair ever strolling round and round, unconscious of the grinding corn. In my previous investigations my imagination pictured the symmetry of curves and States; the hypothesis followed that the laws which regulated them were identical, and you have observed how the supposition was confirmed by our subsequent calculations.In this lecture I propose to examine some of the forces which exist in our social system, and shall endeavour to estimate them by methods of mathematical procedure and analogical reasoning. We will begin with the old definition of Force asthat which puts matter into motion, or which stops, or changes, a motion once commenced. When a mass is in motion, it has a capacity for doing work, which is calledEnergy; and when this energy is caused by the motion of a body it is called Kinetic Energy (in mathematical languageKE = ½ MV²).[75]Another form of kinetic energy is called Potential Energy, which is in reality the capacity of a body for doing workowing to its position. For example we may take an ordinary eight-day clock. When the weights are wound up, they have a certain amount of potential energy stored up, which will counteract the friction of the wheels and the resistance of the air on the pendulum. Or, again, we have the example of a water-wheel: first the water in the reservoir, being higher than the wheel, has an amount of potential energy. This is converted into kinetic energy in striking against the paddles, and after this we have potential energy again produced by the action of the fly-wheel.By the principle of conservation of energy, if we consider the whole universe, not our planet alone (for its heat and energy are continually diminished to some slight degree), we find thatno energy is lost.Force is recognised as acting in two ways: inStatics, so as to compel rest, or to prevent change of motion; and inKinetics, so as to produce or to change[76]motion; and the whole science which investigates the action of force is calledDynamics.All this is of course pure mathematics, and I have made these elementary observations for the benefit of my younger hearers, the students of this University. My grave and reverend seniors will pardon, I am sure, the repetition of facts well known to them for the sake of those who are less informed than themselves.Now before I proceed further, I will endeavour to point out that these elementary truths of physical science hold good in our social system. Each individual is a mass, acted on by numerous forces, capable of ‘doing work,’ which work can be measured and his velocity calculated. Some individuals have a vastpotential energy; that is to say, from their position and station in the social system, they have a power which is capable of producing work which a less exalted individual has not. Like the weights in an eight-day clock, or the water in a reservoir, they have a capacity for doing work, owing to[77]the position to which they have been raised. How vast the influence of a Primate or a Premier, a General or a King! And yet their power is chiefly potential energy, arising from the position they occupy, not from the individuals themselves. Schiller has described this in poetical language, which, strange to say, is mathematically correct:‘Yes, there’s a patent of nobilityAbove the meanness of our common state;With what theydothe vulgar natures buyTheir titles; and with what theyare, thegreat.’Other forces may have raised these men to their exalted positions; but their influence is due to their height, their potential energy. Placed on a lower level, they would cease to have that power. How calm the dignity of this potential rank! The water in the reservoir is scarcely ruffled or disturbed, as if unconscious of its power; when it has lost its force it rushes along with a sullen murmur and a roar, howling and hissing and boiling in endless torture, until—‘It gains a safer bed, and steals at lastAlong the mazes of the quiet vale.’[78]So the vulgar crowd rushes on, with plenty of kinetic force, making noise enough and looking very busy; while those who seem to sleep in calm forgetfulness, exercise their potential energy, and do the real work of turning the great engine of the State.There are attractive and repulsive forces (more commonly the latter, the cynic will say) in our social system, but each individual is the centre of various forces acting upon him. In nature all matter possesses the force of gravity, and whatever the size of two particles may be, they mutually attract each other. The earth attracts the moon; the moon attracts the earth. A stone thrown up into the air exercises an infinitesimal force upon the earth; so in the social system every individual, however small and insignificant he may be, exercises some attractive force upon his neighbour. There is no one in the world who does not exercise some influence for good or for evil upon his fellows.The force ofcohesionis manifest in society as in nature, that force, I mean,[79]which resists the separation of a body’s particles. Different bodies possess different powers of cohesion,e.g., the cohesion of chalk is far less than that of flint embedded in it; even the same body possesses different powers of cohesion in different directions,e.g., it is easier to split wood in the direction of the fibres than perpendicular to them. If by our old principle of continuity we change the words ‘bodies’ into ‘States’ or ‘individuals,’ we shall see that the same laws hold good in social science as in natural philosophy.These are a few analogous laws which I have taken almost at random; but it must strike the most casual listener to my remarks that it is wondrous strange that men, regarded as social beings, should possess the same qualities, and be governed by the same laws, as the rest ofmatter. As Bishop Butler says, ‘the force of analogy consists in the frequency of the supposed analogous facts, and the real resemblance of the things compared.’ It appeals to the reasoning faculty, and may form a solid argument. Hence, if we can prove the[80]similarity of various laws and conditions, we may not be wrong in assuming by analogy the identity of those laws and conditions.I have stated my case in this manner in order to convince the gainsayers, if any such there be, and to banish any doubts or questionings which may have arisen in your minds. I will now proceed with some further investigations, full of the most profound interest and importance.Doubtless many of the lady-students present are in the habit of welcoming peaceful evening in with a potent draught of ‘the cup which cheers but not inebriates;’ and as men are great flatterers (for imitation is the greatest flattery), I believe the male portion of my audience have been known to follow that excellent example. Some perhaps are in the habit of burning the midnight oil, and keep their eyes open by means of this fruit of the hermit’s pious zeal, endowed by high omnipotence with the power of hindering sleep;6but that practice I do[81]not advise, as that delicate portion of our system, the nerves, especially of women, often becomes injured by such stimulating doses. However, you will have observed (if you do not follow the modern pernicious fashion of taking tea without sugar) that numerous bubbles are formed upon the surface of the liquid. After a few moments these unite into one central mass of bubbles by the force of mutual attraction.It appears from considerations which are detailed in works on physical astronomy, that two particles of matter placed at any sensible distance apart attract each other with a force directly proportional to the product of their masses, and inversely proportional to the square of their distance.Now, suppose that we have a number of circular masses situated upon a plane[82]surface, they will attract each other with a force which may be determined with exactitude; and the greater the masses the greater the force. We will now apply this to polemical science. The agricultural settlement is the first stage in the civilization and formation of a State. How did this arise? First, a single family immigrated to some uncultivated parts of the country, perhaps accompanied by others, who formed a little colony. Other settlements were made in other parts of the land; and thus the country became overspread with these detached and separate communities. An eminent writer declares that these settlements can be traced in the beginnings of every race which has made progress; that they were characteristic of those races in Greece and Italy, in Asia and Africa, which grew into the opulent and famous cities in which so much in the early history of civilization was developed. The colonies of England have been formed in the same way, just as in olden time England itself was occupied when the Roman power ceased.[83]These settlements correspond to the circular masses situated on the plane surface; they were quite separate from each other, each having its own laws, its own headman or ruler, its own assembly or parish council. But as time elapsed, the force of mutual attraction set in; by degrees these separate settlements were drawn together by force which increased in proportion as the settlements increased; until at last one united kingdom was formed under one king, governed by uniform laws and regulations. The bubbles have blended, the circles have come together, and one large circle or other curve is the result. This may be called theLaw of Social Attraction. In accordance with the results of one of my previous lectures, I have taken the circle as representing the simplest form of government, which figure, in the case of the elementary settlements, must have been small.Many of you, most noble professors, are doubtless accustomed to make experiments with the microscope. I will[84]suggest a simple one, which illustrates very forcibly what I am endeavouring to show you. Take some particles of copper, and scatter them at intervals over the surface of an object-glass, and pour some sulphuric acid upon the glass. Now, what is the result? A beautiful network of apparently golden texture spreads itself gradually over the whole area of the glass. Steadily it pursues its way, and the result is beautiful to behold. The minute particles of copper were the original settlements scattered over the land; the sulphuric acid the civilizing agent; and the final picture of a united civilized homogeneous nation is well represented by the progressive and finally glorious network of gold. This example is of course outside our present subject, but it serves as a beautiful illustration.As an instance of the attractive force exercised by small communities upon each other, I may mention the united kingdom of Germany, which is composed of numerous small States and nations, which have been drawn together by the power of[85]mutual attraction. Until recently they were each self-contained, separate constitutions, with their own kings and forms of government; but the attracting force, assisted by forces from without, has proved too much for them, and the great and powerful united kingdom of Germany is the result.But why, you may ask, have not the people in Hindustan united in the same way? There the agricultural settlements remain as they did ages ago; separate petty chieftains rule under the all-governing power of England. Why have they not united?To this objection I reply that there is in social science, as in Nature, avis inertia; that is to say, there is a tendency in matter to remain at rest if unmoved by any external agency, and also of persisting to move, after it has once been set in motion. Thevisinertiaof some bodies is greater than that of others, and depends upon their weight and density. Now it so happens that the moralvis inertiaof the Hindustani is very great, hence their[86]tendency to amalgamation is small. They remain in the state in which they happen to be.On the other hand the inertia of Englishmen is small, of Englishwomen smaller, and therefore their power of combining is greater. Here let me observe that the quality of inertia is one which ought to be removed as far as possible from each social system. Inertia was regarded as a capital crime by the Egyptians. Solon ordained that inert persons should be put to death, and not contaminate the community. As savages bury living men, so does inertia practise the same barbarous custom upon States and individuals. Observe the putrid state of inert water, the clear and sparkling beauty of the moving stream, bearing away by the force of its own motion aught that might contaminate it. Men more often resemble the stagnant water than the rivulet. A healthy social state enforces labour by natural laws, and banishes inertia as much as possible from the system. If the principles of some noisy English[87]politicians were fully carried out, and all things made ‘free,’ inertia would be increased, and listless indolence pervade the masses of our countrymen. I may say that inertia is not entirely unknown in our sister University of Cambridge.The existence of social forces is supported by the testimony of Dr. Tyndall, who plainly recognises their power, though he does not attempt to expound their origin. ‘Thoughtful minds are driven to seek, in the interaction of social forces, the genesis and development of man’s moral nature. If they succeed in their search—and I think they are sure to succeed—social duty would be raised to a higher level of significance, and the deepening sense of social duty would, it is to be hoped, lessen, if not obliterate, the strife and heart-burnings which now beset and disguise our social life.’ I accept with gratification Dr. Tyndall’s conclusions: to determine, examine, trace, calculate these social forces which exercise such a powerful influence on our characters, our lives, our customs, which produce the[88]greatness of the State, or drag it down with irresistible strength from its pinnacle of glory to an abyss of degradation; to estimate such forces is the great and noble object of our lectures and researches in this University. Prosecute, most noble professors, your studies in this direction with all the energy of your enlightened intellects, and there is yet hope that this new science, which I have endeavoured to sketch out, however feebly, may be the means of saving our beloved nation from degradation and ruin, and raising her to a higher level of glory and honour. I hope to continue the subject of social forces in my next lecture.6A Chinese legend relates that a pious hermit, who in his watchings and prayers had often been overtaken by sleep, so that his eyelids closed, in holy wrath against the weakness of the flesh, cut them off, and threw them on the ground. But a god caused a tea-shrub to spring out of them, the leaves of which exhibit the form of an eyelid bordered with lashes, and possess the gift of hindering sleep.—Dr.Ure.[89]PAPER VI.ON SOCIAL FORCES (continued)—POLEMICAL STATICS AND DYNAMICS.Most Noble Professors and Students of Girtham,—We have embarked upon a stormy sea of speculation, on a voyage of grand discovery, and the dangerous waves of adverse criticism, and the deceptive under-current of prejudice, often make the steersman’s lot by no means an enviable one. But our vessel is sound and perfectly equipped, and therefore I do not fear to guide her across the great unknown.It may have occurred to you that the problems which present themselves for solution in social science are far more difficult and complicated than those which arise in ordinary mathematics. That is undoubtedly the case; but this extra degree of difficulty is due to the fact that[90]we make no assumptions; we take the things as they really are, not as they are assumed to be. In physical science, if we take into consideration the resistance of the air, the curvature of the earth, the rigid connection which exists between particles in the same body, and a host of other things which are often conveniently neglected in elementary works, how complicated the various problems become! So we must not be surprised at some of the difficulties which occur in social science, as nothing is neglected; the whole problem is before us, and having solved it we need not make allowances for any falsely assumeddata.It is possible that other professors of this science may come to slightly different conclusions to those which I have arrived at. That is only to be expected, because their original observations may have slightly varied. But in physical science allowances are made for different observers. In astronomy, for example, we find the value of the ‘Personal Equation.’ One observer on looking through the telescope[91]may take the meridian of a star rather differently from another watcher of the heavenly bodies, and thepersonal equationis used to make allowances for this quickness, or slowness, of observation. So in social science there must be a personal equation too, and our object ought to be, in the ordinary affairs of life as well as in the higher duties of scientific action, to make our personal equation as small as possible. But until the old proverb, ‘Quot homines, tot sententiæ,’ has ceased to have any meaning, there will be abundant need of this most useful aid to accuracy.The close connection which exists between social forces and material forces is plainly shown by the doctrine of the conservation of energy. ‘This doctrine,’ says Dr. Tyndall, ‘recognises in the material universe a constant sum of power made up of items among which the most Protean fluctuations are incessantly going on. It is as if the body of nature were alive, the thrill and interchange of its energies resembling those of an organism. The[92]parts of the stupendous whole shift and change, augment and diminish, appear and disappear; while the total of which they are the parts remains quantitatively immutable,plusaccompaniesminus, gain accompanies loss, no item varying in the slightest degree without an absolutely equal change of some other item in the opposite direction.’ So do the forces in the social world ebb and flow, rise and fall, carrying on the same universal law which regulates the energy of material force.I will now proceed to enumerate some of those forces which exercise such a powerful influence on society.First, let us take the force ofPublic Opinion, which seems to exercise a relentless sway over the minds and manners of men. This is a very subtle and secret force, which is most difficult to trace, and resembles electricity in the science of physics. We cannot see it, but are only able to judge of its power by its results. Its point of application is not in the individual, but in the collection of individuals[93]who make up the social system; and it is, in reality, the resultant of, or the compromise between, the various elementary forces which make up human society. Yes, compromise is a purely mechanical affair, based on the principle of the parallelogram of forces; and as public opinion is the result of a compromise, we may calculate its force. For example: ‘It is required to know the state of public opinion in the matter of politics, when the results of a General Election show that the Conservatives are to the Liberals as10 : 9.’Let OC be the direction of the Conservative force.Let OL be that of the Liberal.Then bydataOC : OL :: 10 : 9.Diagram: parallelogram with leading diagonalComplete the parallelogram, and join OP.[94]Then OP represents the force of public opinion in magnitude and direction.N.B.—The direction of OL is determined by the amount of deviation of the policy of the Liberals from that of the Conservatives.As in physical, so in social science, impulsive forces sometimes act, and effectually disturb our system and our calculations. Public opinion is very liable to the action of disturbing forces. Panic is an impulsive force, which defies the power of the most learned professors of social science to determine its magnitude and direction. Some strange unforeseen catastrophe—the fascination caused by a brilliant and unscrupulous orator, a cruel wrong, a blind revenge for real or imaginary injustice—will sometimes rouse one element of passion latent in the vast body of public opinion; so that it breaks with all that hitherto restrained and balanced it, and precipitates society into a course of conduct inconsistent with its former behaviour, and bloodshed, revolution, the breaking-up of laws, are the terrible results of panic or revengeful passion.[95]Society is, as it were, split up by the terrible action of such impulsive forces, just as wood is split up by the repeated blows of the hatchet. It is, therefore, the duty of statesmen to increase the power or force of cohesion, to strengthen the fibres of the State, so that the force of such impulsive blows may not be felt, nor disturb the continuity of the framework of the State. If such measures had been adopted in the neighbouring country of France, much misery might have been avoided, and the terrible revolutions which have so frequently convulsed her social system entirely prevented.Frictionis another disturbing element in our calculations, and although it may be made a useful servant, it is a bad master in mathematics, as in polemics. Without the aid of friction, progress would be impossible. For example: Take the case of a man with perfectly smooth skates on perfectly hard, smooth ice; he would be unable to reach the land unless he had provided himself with some stones, by throwing which he would just be able to[96]get to his destination by a backward motion. The engine would be unable to proceed on its iron road if it were not for friction. The same is true in polemical science: the government of the country would not be able to be carried on under our present conditions if it were not forparty friction. But suppose it increased indefinitely, party friction becomes partyobstruction; and the engine of the State would no longer proceed smoothly and evenly along its appointed course at the rate of sixty miles an hour, but would resemble an old-fashioned coach, up to its axle-trees in mud, its motion altogether stopped by the action of party friction.We have seen that forces have two ways of acting: that of compelling rest and that of producing motion. In statics forces act so as to prevent any change of motion, or disturb the body’s original position. In kinetics, on the contrary, the power is recognised as acting so as to produce or change a body’s motion. Now, in polemical science we have these two ways of considering the action of[97]forces. There is thestaticalorconservativeforce, which compels rest, which seeks security, stability, and peace, and is not ardently devoted to change. It reduces the system to equilibrium. There are, of course, two kinds of equilibrium—stableandunstable—according as the social and political system is in a healthy or unhealthy state. If a body is in stable equilibrium, and any slight motion takes place, the body will return immediately to its former position; but if in unstable, it will decline further and further away from its original position, and be entirely upset. So a healthy and sound conservative equilibrium is not disturbed by outside forces, and the State will resume its former position of stability and rest when the opposing force is withdrawn. But an unhealthy and insecure conservatism is as easily disturbed as an egg balanced on its narrow end.The kinetics of society, that is to say the Radical way of estimating force, is the party of motion, generally supposed to be the ‘party of progress.’ It has[98]therefore many attractions in the eyes of those who delight in motion, speed, and rushing about. To run at full speed, to feel the keen air upon one’s face, to experience the delightful sensation of freedom of will, and limb, are joys which cannot be denied. Such exercise is beneficial to the system, bodily or political. Motion is the life of all things; it is characteristic of nature; it adores nature; because it is an emblem and characteristic of life. The ceaseless rolling of the ocean waves, the swaying of the trees, the bending of the flowers, the waving of the corn, all these fill us with pleasure; whereas a flat uninteresting plain, unrelieved by the motion of terrestrial objects, is depressing to the spirit. So there is much to be said in favour of motion, and Carlyle has defined progress as ‘living movement.’ And men love this ‘living movement,’ and take up the Laureate’s cry:‘Forward, forward, let us range,Let the great world spin for ever down the ringingGrooves of change.’But, after all, there is a danger in this[99]everlasting motion. We cannot tell whither this progress may lead. It may be along a safe sure road; but perchance a precipice may open out before us; and rejoicing in the acceleration of our velocity, with eyes intent upon some distant heights of glory and ambition, we may not discover our danger until it is too late to stop, and a terrible plunge into an unknown abyss of turmoil and tumultuous waves is the alarming result of an unguarded policy of unrestrained ‘progress.’ I recall to my mind the quaint words of Holmes which aptly illustrate my contention.‘If the wild filly, “Progress”, thou would’st ride,Have young companions ever at thy side;But wouldst thou stride the staunch old mare, “Success,”Go with thine elders, though they please thee less.’Progress and success do not always go together hand in hand; and while motion is essential to life, it is not always safe to urge a country forward at too great a speed; and security and stability are quite as important to the nation’s life as actual progress.There are other impulsive forces which[100]act occasionally in the sphere of politics, and which baffle all our calculations, and exclude scientific considerations of the polemical problems which arise.Ambitionis such an impulsive force, and when the rulers of the people are actuated by it, and struggle for money, place, and power, politics is degraded from its position as a science, and it becomes impossible to estimate the result of forces so generated.In my next lecture I propose to treat the important subject of the Laws which govern States and Governments, and which regulate, generate, and control the social forces which we have seen at work in the body politic.[101]PAPER VII.LAWS OF POLITICAL MOTION.Sincethe last time I had the honour of addressing you on polemical matters, I have met with a passage in the writings of M. Auguste Comte which afforded me much pleasure. It seemed to be the one word for which I had been waiting, and confirmed many of my own impressions and speculations. He lays down two propositions: first, that the constructive politics of the future must be based on the history of the past; and second, that political science is a composite study, and presupposes the complete apprehension of every branch of science, beginning with the physical, such as astronomy, and ending with the moral, such as ethics and sociology. M. Comte evidently does not regard as a vain dream and imaginative[102]speculation the theory that it will be possible for statesmen to calculate a policy, and to determine a course of action by purely scientific considerations. May I entertain the hope that in this university, where all branches of physical science have found a home, and are studied by most able and learned professors, the science of politics may be pursued under most favourable circumstances? I trust that each professor will bring before me the results of their deliberations, and contribute to the growth of this particular science for which our university has already become deservedly famous.My present lecture is devoted to the important consideration ofLaw. At first sight it may appear to you that the wills and passions of mankind are so diverse and unknowable, that it would be absurd to suppose that they can be calculated, or rendered amenable to any law. But Professor Amos has pointed out that in proportion as we examine history, and compare the actions present and past of different[103]nations and states, the more uniform does human nature appear; the more calculable the actions, sentiments, and emotions of large masses of people. As we have already stated, the difficulties of the study are not likely to deter the professors of Girtham College from the pursuit of any particular branch of science.A prioriwe might suppose from analogy that these polemical laws existed, as there is no department of nature which is not governed by law. It is an essential feature in nature, and also in government. What is political economy but the study of certain laws of nature? These were first discovered by Adam Smith, and have since been traced and estimated by such men as Ricardo, the two Mills, Professor Cairnes, Jevons, and many others. Moreover, our physical constitutions are governed by laws, which physicians have determined, and which it is perilous to resist. Our moral constitution is also governed by laws, which evidently exist, although it is difficult to find them out. But the nation is only an assemblage of[104]individuals; and since individuals are so governed, it is only natural to suppose that the nation, composed of individuals, is so constituted and controlled. And not only is that true, but we shall see that polemical laws are as permanent and universal, as invariable and irreversible, as the laws of nature which regulate the courses of the heavenly bodies, and raise the tides, or depress the sandstone hills.We may notice first the preponderant impulse observable in a nation’s life in favour of supporting existing facts and institutions; and every reformer has discovered the difficulty and danger of changing or opposing the customs and habits of the people. As a wheel will travel most smoothly along a well-worn groove, whereby friction is diminished, so there is a natural national tendency always to run along those paths with which the habits and customs of the people have made them familiar. This law is nothing else than Newton’s first law of motion, which is quite as applicable to human masses as to lifeless matter. The[105]tendency of matter to remain at rest, if unmoved by any external agency, and of persisting to move after it has once been set in motion, is a conservative tendency; and is as true in political science as in any other.The special branch of our science, which we may call theBiology of Politics, shows how absolute is the domain of law in polemical matters. The law of human life is that men are born, grow, become strong and vigorous, and then decay and die. This is the law of life, to which we must all yield an enforced obedience. This same law is observed to be at work in the heavenly bodies; and astronomy shows us that planets are born, flourish, and at length die, just as our human bodies do. The moon is, as you may have observed, a dead planet, such as our earth may be some day. The same growth and decay are also manifest in national life. First, there is the birth of the nation, which sometimes lies a long time in a dormant state, and then wakes up to life and energy. China and Russia[106]are examples of dormant States, just waking from a long sleep of childishness and ignorance. The next stage is the strong an healthy period of its existence, which England is at present enjoying; and then, after various stages of gradual decline, we come to the senile period of national life, when every energy and faculty, every national feeling and power of invention, are completely exhausted. As an example of this depressing condition, we may mention Turkey and several of the effete States of South America. Sometimes, when life is nearly extinct in the human body, physicians have made use of the power of galvanism, in order to revive the dying energies. This process of galvanizing a State into life was tried by Lord Palmerston and others on the worn-out frame of Turkey. But such attempts can only meet with partial and transitory success; and where the loss of national power and faculty betokens the senile period of the nation’s existence, it is vain to attempt to restore its former life and energy. The study of the biology[107]of politics presents many interesting and important details in this special branch of knowledge; and I commend this part of our subject to the special attention of the professor of physiology. The law of development is observable in nations as in nature. Recent scientific discoveries have tended to take away all ideas ofchancein the workings of nature, and have substitutedlawinstead of it. It would be unscientific and incorrect to speak of the world being formed by the ‘fortuitous concourse of atoms.’ So we cannot speak of a State being generated in this manner. Laws—economical, geographical, natural—preside over the formation of States and nations, and produce their further development.The laws of political motion occupy the same prominent place in our new science as Newton’s laws do in ordinary dynamics. These are very important in calculating the positions which various States will occupy in the future. First, we have thedoctrine of nationality, which prevented the progress of Austria into[108]Italy, and of the Bourbons in Naples, and produced the amalgamation of the small German States in the great empire of Germany. The second law of political motion is the doctrine of theindependenceof all true States, and the equality of all States to each other. This had its growth in feudalism; and all the chief wars of modern times have been the result of the efforts of nature to establish this law of independence. The doctrine of intervention is a modification of the preceding law, and is applicable when the law of necessity demands its use, such as the restoration of order after protracted anarchy, the abolition of slave trade, etc. The third law is thelaw of morality. Just as for each man there exists arightand awrong; just asdutyandconscienceare certain elements in his daily motion, which dictate his course of action, although he may chose to neglect them; so a nation is bound by the same moral laws which govern the individual; and a nation errs if it transgresses them. Christianity is the agent which has[109]produced so powerful an influence in making men obey the dictates of conscience and walk in the path of duty; and I read with thankfulness the conclusion of Mr. Amos, that Christianity has triumphed quite as much in moralizing secular politics as it has in the sphere of individual life.These are some of the principal laws of motion which I have observed at work in various States and nations. Inasmuch as political science embraces, in addition to the physical sciences, all those branches which are contained in ethics, economics, jurisprudence, sociology and others, the laws of each are generally applicable to the whole grand subject of which my lectures treat. Other general laws may be deduced, and have been enumerated in my previous lectures, from the social properties of curves and conics; and when our researches are complete we may hope to produce a code of laws for the guidance of our statesmen which maybe of immense use in determining[110]the policies of the future. Already there is strong evidence that the affairs of this country are being conducted on sound scientific principles, rather than by any species of guess-work or haphazard contrivances. The use of history is recognised as extremely important in determining a future line of conduct; and statesmen are in the habit of endeavouring to find from their study of the past what is the logical sequence of events. Just as mathematicians endeavour to determine the law of a series of figures, and having found the law, can write down the next, and the next,ad infinitum; so scientific politicians may be able soon to establish the various laws of a series of events, and calculate their course of actions. That there is considerable progress in this direction is manifest by the value which they place upon statistics, and their continued use of this important information.There are a few great evils in our present system which are strongly opposed to any scientific methods in politics; and in the interests of the country as well as those of[111]science they ought to be removed. One great evil is the want of political and scientific knowledge on the part of the electors, who are in the habit of choosing their representatives on personal grounds, or party considerations, rather than on sound principles of political science. All this is opposed to any idea of law. Owing to the ignorance of the electors they fall an easy prey to adventurers and unprincipled politicians, who make all kinds of specious promises, tempt them with all manner of baits, and make self-interest instead of the welfare of the State the principle of voting. Selfishness is the ruin of social life and intercourse, the destroyer of all happiness, peace, and mutual trust in family life or in society. It is the root of most of the faults, vices, and crimes in the individual; and who can tell the endless disasters which will befall the State, where selfishness is the chief motive-power of the electors and the elected? A selfish statesman, one who goes into Parliament to gain his own ends and forward his own personal interests, is a disgrace to society—

[58]‘I would serve my King,Serve him with all my fortune here at home,And serve him with my person in the wars;Watch for him, fight for him, bleed for him, die for him,As every true-born subject ought.’

[58]‘I would serve my King,

Serve him with all my fortune here at home,

And serve him with my person in the wars;

Watch for him, fight for him, bleed for him, die for him,

As every true-born subject ought.’

This, most noble professors, is the language of true patriotic loyalty. Let the monarch be loved and loving, let the laws be just and equal, happy will be the people, prosperous the realm. There are those who counsel different things, and preach sedition and the breaking-up of laws; but those who advocate such doctrines lack that judicial mathematical training which we, students and professors of Girtham College, have acquired. If polemical mathematics, the science of the future, should become more widely studied; if its results were disseminated far and wide; above all, if the proper position which women ought to occupy in the counsels of the nation were assigned to them, we should hear less of these wild schemes and foolish theories, and the influence of women would tend greatly to[59]promote the stability and security of the State.

Why, let me ask, should woman be excluded from that position which is so justly hers? from those duties which she can discharge so faithfully? It has been said that if we wish to know the political and moral condition of a State, we must ask what rank women hold in it. We are told that women have more strength in their looks than men have in their laws. Why, then, do men debar her from those fields of occupation wherein she may labour for the nation’s good, and use her influence, which they acknowledge to be great, in those callings wherein she may most easily benefit the State, and the country she so ardently loves?

At some future time I hope to speak more fully on this subject; and in concluding this lecture, I will remark that English politics need a leavening influence which will counteract the evil tendencies and corrupt theories which, in spite of our advantageous social system, at present[60]exist; and this leavening influence will be best produced by the admission of those into the counsels of the nation who are acknowledged to have a benign and healthy influence—the women of England. Let women have their proper share in the government of the country, and I have no fear lest we shall preserve our elliptical constitution, and all the advantages which we at present enjoy.

[Editorial Note.]—In the bundle of papers which contained the foregoing lectures, some letters of great interest were found, which show that the fame of the learned Lady Professor of Girtham College had already gone abroad, and attracted the attention of the leading statesmen of the day. It is to be regretted that the answers to these letters are not forthcoming, as it might be proved from them that the science of polemical mathematics has already influenced the minds of our legislators in their conduct[61]of affairs at home and abroad. The following letter is of unique interest, and may be taken as evidence of the favourable impression which this new science has made on the mind of one of our greatest thinkers and statesmen:

Downing Street,

May, 18—

My dear Lady Professor,—The report of the amazing results of your scientific researches has reached me, and I congratulate you most heartily on the originality and acumen which you have displayed in your investigations. A new light has dawned upon our country. Instead of groping in the darkness of political warfare, ensnared by party ties and jealousies, the statesmen of the future will be able to calculate and determine the correct course with mathematical precision and perfect accuracy. No one can dispute the truth of a proposition in Euclid, or the genuineness of Newton’s laws; and if your method enables men to[62]calculate and determine the correct political course of action, to solve political problems as easily as exponential equations, why—then adieu to the bickerings of party, the querulous complaints of the Opposition! Nay, joy to the Ministry! There will be no Opposition! Our statesmen will be able to guide the great ship of the State by means of charts which know no error; and they will resemble an association of savants met together to determine the exact moment of the transit of Venus, or to examine the degree of density of a comet’s tail.

This condition of Parliamentary procedure is much to be desired; you have shown how such an ideal state of things may be obtained. In the name of the Government I thank you for your endeavours on behalf of your country’s welfare, and look forward to a further development of your admirably conceived system. As in the domain of ordinary science there are complex questions which defy the acumen of the philosopher;[63]so in polemical science there may be questions which present the same difficulties and complications. But as the first are daily yielding before the persevering attacks of the mathematician, so I doubt not polemical science will soon overcome the various problems which may arise.

But it is mainly on my own account that I venture to address you. I desire to consult you with regard to certain matters—political complications—which have recently occupied the attention of Her Majesty’s Ministers. By the help of your new science, can you aid us in our deliberations? Of course, I am writing to you instrict confidence, and beg that you will keep this communication profoundly secret. I fear that would be a hard task for many of your sex, who do not possess your knowledge and powers of mind; but I have great confidence in your discretion.

These are the problems which are presented to us for solution:

[64]1. Some members of the Cabinet are secretly in favour of Protection, and the country is rather stirred by the question. Can you, from your knowledge of the contact of curves and nations, help us to determine what course we ought to take with regard to Spain, for example? Are the principles of Adam Smith mathematically correct?

2. I observe that England is represented mathematically by an ellipse. Are we right in assuming that Ireland is a portion of that ellipse? Or, on the other hand, in our chart of nations, must we describe that troublesome country as a rotating parabola, or complex figure, altogether outside our more favoured State?

3. Do you consider, from your minute observation of our social system, that the form of our elliptical government is gradually undergoing a change, and that a revolutionary parabolic tendency is observable in the action of individual particles?

4. Is it not possible that the differences[65]in the policy of the various nations of Europe; the difficulties which beset the carrying out of international law; the jealousies, quarrels, and rivalries of States might disappear, if the same form of government (i.e., elliptical) were adopted in each?

If you will kindly favour Her Majesty’s Ministers with your opinion on these questions, they will owe you a debt of gratitude, which they, as representatives of the nation, will do their utmost to repay.

With every good wish for your further success in the regions of polemical science,

I beg to remain,

My dear Lady Professor,

Your faithful servant,

4

[Editorial Note.]—The next letter is not of quite the same pleasing nature as the foregoing, and shows that it is[66]impossible to please everyone, even if that happy consummation were desirable. This letter was evidently called forth by some remarks which the learned Lady Professor had made in her third lecture with reference to eccentricity in dress. Our readers will recollect that the professor pointed out that an extravagant ‘bloomer’ costume—half male, half female—was no more a sign of genius than æsthetic dresses, always betokened the artist.5This latter statement evidently gave great offence to the members of a society which called itself the ‘Æsthetic and Dress Improvement Association,’ and the following letter is the result of one of their solemn conclaves:

Oscar Villa, South Kensington,

June, 18—.

The Secretary of the Æsthetic and Dress Improvement Association presents his compliments to the Lady Professor of Girtham College, and begs to contradict emphatically her statements with regard[67]to a subject upon which she is evidently in entire and lamentable ignorance, and to protest against her aspersions upon the artistic studies of this and kindred societies. He begs to state that true æsthetes arenoteccentric (they leave that to lady professors and her Philistine followers); that to dress becomingly is one of the principal objects of life, and that true greatness is achieved as much by the study of the art of dress as by any other noble pursuit or graceful accomplishment. Are not Horatio Postlethwaite, Leonara Saffronia Gillan, Vandyke Smithson entitled to greatness? And yet their laurels have been won solely by the art of dress. Perhaps the lady professor has never read ‘Sartor Resartus’! In conclusion, he would ask the Lady Professor to refrain from casting obloquy upon the work of the Association which he has the honour to represent; to prevail upon her pupils to abandon the unfeminine attire which some of them have assumed, contrary to the first principles of art; to array themselves in flowing robes of sage-green and[68]other choice colours (patterns enclosed), and to study art, instead of absurd mathematics, which no one can understand, and do no one any good.

(Approved by the Committee of the Æsthetic and Dress Improvement Association.)

June, 18—.

[Editorial Note.]—The next letter, written by a pupil of the Lady Professor, requires no explanation, and speaks for itself.

Jesus College, Cambridge,

March, 18—.

My dear Tutor,

You will be glad to hear that after superhuman exertions I have at last succeeded in passing my Little-go, and I am eternally grateful to you for all you have done for me. I should never have got through if it had not been for you. All the coaches in Cambridge would never have managed it, but you drove me through in a canter. And why? I never could make up my mind to work for them;[69]but when I coached with you, you made me like it. I almost revelled in the Binomial when you wrote it out for me; and then I could not help listening to you; and you looked so grieved when I would not learn, and made me feel such a brute; so somehow or other you drove some mathematics into my head, and I pulled through. By-the-bye, I think you must have tried the ‘brain wave’ dodge with the examiners, as five out of the six propositions in Euclid, which you told me to get up specially, were set! I wish I could read people’s thoughts; can you read mine? If I were a Don, or a Fellow, or something, I would advise the University to have some lady professors like you to teach the men, instead of some of these sleepy old tutors. It would be a great improvement, and I am sure we should get through a great deal more work.

They have given me a place in the Jesus Eight, which I shall take now that I am released from your professorial ban, and have time for rowing. But I don’t half like giving up mathematics. You see, I[70]have grown fond of the study. Do you think you could make a wrangler of me? At any rate, I should like to come to your lectures again. May I?

Your Grateful Pupil.

* * *

4It is to be regretted that this letter has evidently fallen into the hands of some autograph collector, who has ruthlessly cut off the signature; but the reader will easily determine, after careful perusal of the document, from whose pen it emanated.5Cf. page36.

4It is to be regretted that this letter has evidently fallen into the hands of some autograph collector, who has ruthlessly cut off the signature; but the reader will easily determine, after careful perusal of the document, from whose pen it emanated.

5Cf. page36.

Most noble Professors and Students of Girtham College,—Since last ‘I wandered ’twixt the pole and heavenly hinges, ’mongst encentricals, centres, concentricks, circles, and epicycles,’ like the great Albumazar, and found them full of life and wisdom for the guidance of our States and laws, I have turned my attention to the Applied Mathematics, in order to determine what other truths this shaft may yield.

The strength of all sciences, according to Bacon, consists in their harmony; and it is truly marvellous how perfect this harmony is, if our ears are tuned aright to hear it. We have observed how the[72]beautiful and regular laws of curves and cones correspond to the social laws of States and nations, guiding them as if by word of counsel, admonishing them on what principle they ought to regulate their governments and inter-relations. We have seen that the laws which govern thought and light and sound are almost identical, and that harmony pervades not merely the ordinary sciences, but extends her benign influence over these newly discovered fields of scientific research, which I claim to have discovered.

All this may appear at first sight surprising; but the real philosopher, who knows that all kinds of truth are intimately connected, will receive such revelations of science with satisfaction rather than astonishment; for this new science, which has opened itself out before me, is only an extension of other well-known laws and discoveries which have come down to us from the remote past.

If my investigations should appear to you, most noble professors, somewhat novel and imaginary, remember the maxim of[73]the sage, that in the infancy of science there is no speculation which does not merit careful examination; and the most remote and fanciful explanations of facts have often been found the true ones. Perhaps some ‘self-opinionated particle’ (I speak mathematically) may have been inclined to laugh at our theories and discoveries, as the wise fools of the day laughed at Kepler and his laws; but time has changed the world’s laughter into praise, and a century hence our discoveries may rank among the achievements of modern science. As Cicero says, ‘Time obliterates the fictions of opinions, but confirms the decisions of nature.’

I have not shunned, most noble professors, to enlist Imagination under the banner of Geometry; for I am fully persuaded that it is a powerful organ of knowledge, and is as much needed by the mathematician as by the poet or novelist. It is, I fear, often banished with too much haste from the fields of intellectual research by those who take upon themselves to give laws to philosophy. We need[74]imagination to form an hypothesis; and without hypotheses science would soon become a lifeless and barren study, a horse-in-the-mill affair ever strolling round and round, unconscious of the grinding corn. In my previous investigations my imagination pictured the symmetry of curves and States; the hypothesis followed that the laws which regulated them were identical, and you have observed how the supposition was confirmed by our subsequent calculations.

In this lecture I propose to examine some of the forces which exist in our social system, and shall endeavour to estimate them by methods of mathematical procedure and analogical reasoning. We will begin with the old definition of Force asthat which puts matter into motion, or which stops, or changes, a motion once commenced. When a mass is in motion, it has a capacity for doing work, which is calledEnergy; and when this energy is caused by the motion of a body it is called Kinetic Energy (in mathematical languageKE = ½ MV²).[75]Another form of kinetic energy is called Potential Energy, which is in reality the capacity of a body for doing workowing to its position. For example we may take an ordinary eight-day clock. When the weights are wound up, they have a certain amount of potential energy stored up, which will counteract the friction of the wheels and the resistance of the air on the pendulum. Or, again, we have the example of a water-wheel: first the water in the reservoir, being higher than the wheel, has an amount of potential energy. This is converted into kinetic energy in striking against the paddles, and after this we have potential energy again produced by the action of the fly-wheel.

By the principle of conservation of energy, if we consider the whole universe, not our planet alone (for its heat and energy are continually diminished to some slight degree), we find thatno energy is lost.

Force is recognised as acting in two ways: inStatics, so as to compel rest, or to prevent change of motion; and inKinetics, so as to produce or to change[76]motion; and the whole science which investigates the action of force is calledDynamics.

All this is of course pure mathematics, and I have made these elementary observations for the benefit of my younger hearers, the students of this University. My grave and reverend seniors will pardon, I am sure, the repetition of facts well known to them for the sake of those who are less informed than themselves.

Now before I proceed further, I will endeavour to point out that these elementary truths of physical science hold good in our social system. Each individual is a mass, acted on by numerous forces, capable of ‘doing work,’ which work can be measured and his velocity calculated. Some individuals have a vastpotential energy; that is to say, from their position and station in the social system, they have a power which is capable of producing work which a less exalted individual has not. Like the weights in an eight-day clock, or the water in a reservoir, they have a capacity for doing work, owing to[77]the position to which they have been raised. How vast the influence of a Primate or a Premier, a General or a King! And yet their power is chiefly potential energy, arising from the position they occupy, not from the individuals themselves. Schiller has described this in poetical language, which, strange to say, is mathematically correct:

‘Yes, there’s a patent of nobilityAbove the meanness of our common state;With what theydothe vulgar natures buyTheir titles; and with what theyare, thegreat.’

‘Yes, there’s a patent of nobility

Above the meanness of our common state;

With what theydothe vulgar natures buy

Their titles; and with what theyare, thegreat.’

Other forces may have raised these men to their exalted positions; but their influence is due to their height, their potential energy. Placed on a lower level, they would cease to have that power. How calm the dignity of this potential rank! The water in the reservoir is scarcely ruffled or disturbed, as if unconscious of its power; when it has lost its force it rushes along with a sullen murmur and a roar, howling and hissing and boiling in endless torture, until—

‘It gains a safer bed, and steals at lastAlong the mazes of the quiet vale.’

‘It gains a safer bed, and steals at last

Along the mazes of the quiet vale.’

[78]So the vulgar crowd rushes on, with plenty of kinetic force, making noise enough and looking very busy; while those who seem to sleep in calm forgetfulness, exercise their potential energy, and do the real work of turning the great engine of the State.

There are attractive and repulsive forces (more commonly the latter, the cynic will say) in our social system, but each individual is the centre of various forces acting upon him. In nature all matter possesses the force of gravity, and whatever the size of two particles may be, they mutually attract each other. The earth attracts the moon; the moon attracts the earth. A stone thrown up into the air exercises an infinitesimal force upon the earth; so in the social system every individual, however small and insignificant he may be, exercises some attractive force upon his neighbour. There is no one in the world who does not exercise some influence for good or for evil upon his fellows.

The force ofcohesionis manifest in society as in nature, that force, I mean,[79]which resists the separation of a body’s particles. Different bodies possess different powers of cohesion,e.g., the cohesion of chalk is far less than that of flint embedded in it; even the same body possesses different powers of cohesion in different directions,e.g., it is easier to split wood in the direction of the fibres than perpendicular to them. If by our old principle of continuity we change the words ‘bodies’ into ‘States’ or ‘individuals,’ we shall see that the same laws hold good in social science as in natural philosophy.

These are a few analogous laws which I have taken almost at random; but it must strike the most casual listener to my remarks that it is wondrous strange that men, regarded as social beings, should possess the same qualities, and be governed by the same laws, as the rest ofmatter. As Bishop Butler says, ‘the force of analogy consists in the frequency of the supposed analogous facts, and the real resemblance of the things compared.’ It appeals to the reasoning faculty, and may form a solid argument. Hence, if we can prove the[80]similarity of various laws and conditions, we may not be wrong in assuming by analogy the identity of those laws and conditions.

I have stated my case in this manner in order to convince the gainsayers, if any such there be, and to banish any doubts or questionings which may have arisen in your minds. I will now proceed with some further investigations, full of the most profound interest and importance.

Doubtless many of the lady-students present are in the habit of welcoming peaceful evening in with a potent draught of ‘the cup which cheers but not inebriates;’ and as men are great flatterers (for imitation is the greatest flattery), I believe the male portion of my audience have been known to follow that excellent example. Some perhaps are in the habit of burning the midnight oil, and keep their eyes open by means of this fruit of the hermit’s pious zeal, endowed by high omnipotence with the power of hindering sleep;6but that practice I do[81]not advise, as that delicate portion of our system, the nerves, especially of women, often becomes injured by such stimulating doses. However, you will have observed (if you do not follow the modern pernicious fashion of taking tea without sugar) that numerous bubbles are formed upon the surface of the liquid. After a few moments these unite into one central mass of bubbles by the force of mutual attraction.

It appears from considerations which are detailed in works on physical astronomy, that two particles of matter placed at any sensible distance apart attract each other with a force directly proportional to the product of their masses, and inversely proportional to the square of their distance.

Now, suppose that we have a number of circular masses situated upon a plane[82]surface, they will attract each other with a force which may be determined with exactitude; and the greater the masses the greater the force. We will now apply this to polemical science. The agricultural settlement is the first stage in the civilization and formation of a State. How did this arise? First, a single family immigrated to some uncultivated parts of the country, perhaps accompanied by others, who formed a little colony. Other settlements were made in other parts of the land; and thus the country became overspread with these detached and separate communities. An eminent writer declares that these settlements can be traced in the beginnings of every race which has made progress; that they were characteristic of those races in Greece and Italy, in Asia and Africa, which grew into the opulent and famous cities in which so much in the early history of civilization was developed. The colonies of England have been formed in the same way, just as in olden time England itself was occupied when the Roman power ceased.

[83]These settlements correspond to the circular masses situated on the plane surface; they were quite separate from each other, each having its own laws, its own headman or ruler, its own assembly or parish council. But as time elapsed, the force of mutual attraction set in; by degrees these separate settlements were drawn together by force which increased in proportion as the settlements increased; until at last one united kingdom was formed under one king, governed by uniform laws and regulations. The bubbles have blended, the circles have come together, and one large circle or other curve is the result. This may be called theLaw of Social Attraction. In accordance with the results of one of my previous lectures, I have taken the circle as representing the simplest form of government, which figure, in the case of the elementary settlements, must have been small.

Many of you, most noble professors, are doubtless accustomed to make experiments with the microscope. I will[84]suggest a simple one, which illustrates very forcibly what I am endeavouring to show you. Take some particles of copper, and scatter them at intervals over the surface of an object-glass, and pour some sulphuric acid upon the glass. Now, what is the result? A beautiful network of apparently golden texture spreads itself gradually over the whole area of the glass. Steadily it pursues its way, and the result is beautiful to behold. The minute particles of copper were the original settlements scattered over the land; the sulphuric acid the civilizing agent; and the final picture of a united civilized homogeneous nation is well represented by the progressive and finally glorious network of gold. This example is of course outside our present subject, but it serves as a beautiful illustration.

As an instance of the attractive force exercised by small communities upon each other, I may mention the united kingdom of Germany, which is composed of numerous small States and nations, which have been drawn together by the power of[85]mutual attraction. Until recently they were each self-contained, separate constitutions, with their own kings and forms of government; but the attracting force, assisted by forces from without, has proved too much for them, and the great and powerful united kingdom of Germany is the result.

But why, you may ask, have not the people in Hindustan united in the same way? There the agricultural settlements remain as they did ages ago; separate petty chieftains rule under the all-governing power of England. Why have they not united?

To this objection I reply that there is in social science, as in Nature, avis inertia; that is to say, there is a tendency in matter to remain at rest if unmoved by any external agency, and also of persisting to move, after it has once been set in motion. Thevisinertiaof some bodies is greater than that of others, and depends upon their weight and density. Now it so happens that the moralvis inertiaof the Hindustani is very great, hence their[86]tendency to amalgamation is small. They remain in the state in which they happen to be.

On the other hand the inertia of Englishmen is small, of Englishwomen smaller, and therefore their power of combining is greater. Here let me observe that the quality of inertia is one which ought to be removed as far as possible from each social system. Inertia was regarded as a capital crime by the Egyptians. Solon ordained that inert persons should be put to death, and not contaminate the community. As savages bury living men, so does inertia practise the same barbarous custom upon States and individuals. Observe the putrid state of inert water, the clear and sparkling beauty of the moving stream, bearing away by the force of its own motion aught that might contaminate it. Men more often resemble the stagnant water than the rivulet. A healthy social state enforces labour by natural laws, and banishes inertia as much as possible from the system. If the principles of some noisy English[87]politicians were fully carried out, and all things made ‘free,’ inertia would be increased, and listless indolence pervade the masses of our countrymen. I may say that inertia is not entirely unknown in our sister University of Cambridge.

The existence of social forces is supported by the testimony of Dr. Tyndall, who plainly recognises their power, though he does not attempt to expound their origin. ‘Thoughtful minds are driven to seek, in the interaction of social forces, the genesis and development of man’s moral nature. If they succeed in their search—and I think they are sure to succeed—social duty would be raised to a higher level of significance, and the deepening sense of social duty would, it is to be hoped, lessen, if not obliterate, the strife and heart-burnings which now beset and disguise our social life.’ I accept with gratification Dr. Tyndall’s conclusions: to determine, examine, trace, calculate these social forces which exercise such a powerful influence on our characters, our lives, our customs, which produce the[88]greatness of the State, or drag it down with irresistible strength from its pinnacle of glory to an abyss of degradation; to estimate such forces is the great and noble object of our lectures and researches in this University. Prosecute, most noble professors, your studies in this direction with all the energy of your enlightened intellects, and there is yet hope that this new science, which I have endeavoured to sketch out, however feebly, may be the means of saving our beloved nation from degradation and ruin, and raising her to a higher level of glory and honour. I hope to continue the subject of social forces in my next lecture.

6A Chinese legend relates that a pious hermit, who in his watchings and prayers had often been overtaken by sleep, so that his eyelids closed, in holy wrath against the weakness of the flesh, cut them off, and threw them on the ground. But a god caused a tea-shrub to spring out of them, the leaves of which exhibit the form of an eyelid bordered with lashes, and possess the gift of hindering sleep.—Dr.Ure.

6A Chinese legend relates that a pious hermit, who in his watchings and prayers had often been overtaken by sleep, so that his eyelids closed, in holy wrath against the weakness of the flesh, cut them off, and threw them on the ground. But a god caused a tea-shrub to spring out of them, the leaves of which exhibit the form of an eyelid bordered with lashes, and possess the gift of hindering sleep.—Dr.Ure.

Most Noble Professors and Students of Girtham,—We have embarked upon a stormy sea of speculation, on a voyage of grand discovery, and the dangerous waves of adverse criticism, and the deceptive under-current of prejudice, often make the steersman’s lot by no means an enviable one. But our vessel is sound and perfectly equipped, and therefore I do not fear to guide her across the great unknown.

It may have occurred to you that the problems which present themselves for solution in social science are far more difficult and complicated than those which arise in ordinary mathematics. That is undoubtedly the case; but this extra degree of difficulty is due to the fact that[90]we make no assumptions; we take the things as they really are, not as they are assumed to be. In physical science, if we take into consideration the resistance of the air, the curvature of the earth, the rigid connection which exists between particles in the same body, and a host of other things which are often conveniently neglected in elementary works, how complicated the various problems become! So we must not be surprised at some of the difficulties which occur in social science, as nothing is neglected; the whole problem is before us, and having solved it we need not make allowances for any falsely assumeddata.

It is possible that other professors of this science may come to slightly different conclusions to those which I have arrived at. That is only to be expected, because their original observations may have slightly varied. But in physical science allowances are made for different observers. In astronomy, for example, we find the value of the ‘Personal Equation.’ One observer on looking through the telescope[91]may take the meridian of a star rather differently from another watcher of the heavenly bodies, and thepersonal equationis used to make allowances for this quickness, or slowness, of observation. So in social science there must be a personal equation too, and our object ought to be, in the ordinary affairs of life as well as in the higher duties of scientific action, to make our personal equation as small as possible. But until the old proverb, ‘Quot homines, tot sententiæ,’ has ceased to have any meaning, there will be abundant need of this most useful aid to accuracy.

The close connection which exists between social forces and material forces is plainly shown by the doctrine of the conservation of energy. ‘This doctrine,’ says Dr. Tyndall, ‘recognises in the material universe a constant sum of power made up of items among which the most Protean fluctuations are incessantly going on. It is as if the body of nature were alive, the thrill and interchange of its energies resembling those of an organism. The[92]parts of the stupendous whole shift and change, augment and diminish, appear and disappear; while the total of which they are the parts remains quantitatively immutable,plusaccompaniesminus, gain accompanies loss, no item varying in the slightest degree without an absolutely equal change of some other item in the opposite direction.’ So do the forces in the social world ebb and flow, rise and fall, carrying on the same universal law which regulates the energy of material force.

I will now proceed to enumerate some of those forces which exercise such a powerful influence on society.

First, let us take the force ofPublic Opinion, which seems to exercise a relentless sway over the minds and manners of men. This is a very subtle and secret force, which is most difficult to trace, and resembles electricity in the science of physics. We cannot see it, but are only able to judge of its power by its results. Its point of application is not in the individual, but in the collection of individuals[93]who make up the social system; and it is, in reality, the resultant of, or the compromise between, the various elementary forces which make up human society. Yes, compromise is a purely mechanical affair, based on the principle of the parallelogram of forces; and as public opinion is the result of a compromise, we may calculate its force. For example: ‘It is required to know the state of public opinion in the matter of politics, when the results of a General Election show that the Conservatives are to the Liberals as10 : 9.’

Let OC be the direction of the Conservative force.

Let OL be that of the Liberal.

Then bydataOC : OL :: 10 : 9.

Diagram: parallelogram with leading diagonal

Complete the parallelogram, and join OP.

[94]Then OP represents the force of public opinion in magnitude and direction.

N.B.—The direction of OL is determined by the amount of deviation of the policy of the Liberals from that of the Conservatives.

As in physical, so in social science, impulsive forces sometimes act, and effectually disturb our system and our calculations. Public opinion is very liable to the action of disturbing forces. Panic is an impulsive force, which defies the power of the most learned professors of social science to determine its magnitude and direction. Some strange unforeseen catastrophe—the fascination caused by a brilliant and unscrupulous orator, a cruel wrong, a blind revenge for real or imaginary injustice—will sometimes rouse one element of passion latent in the vast body of public opinion; so that it breaks with all that hitherto restrained and balanced it, and precipitates society into a course of conduct inconsistent with its former behaviour, and bloodshed, revolution, the breaking-up of laws, are the terrible results of panic or revengeful passion.

[95]Society is, as it were, split up by the terrible action of such impulsive forces, just as wood is split up by the repeated blows of the hatchet. It is, therefore, the duty of statesmen to increase the power or force of cohesion, to strengthen the fibres of the State, so that the force of such impulsive blows may not be felt, nor disturb the continuity of the framework of the State. If such measures had been adopted in the neighbouring country of France, much misery might have been avoided, and the terrible revolutions which have so frequently convulsed her social system entirely prevented.

Frictionis another disturbing element in our calculations, and although it may be made a useful servant, it is a bad master in mathematics, as in polemics. Without the aid of friction, progress would be impossible. For example: Take the case of a man with perfectly smooth skates on perfectly hard, smooth ice; he would be unable to reach the land unless he had provided himself with some stones, by throwing which he would just be able to[96]get to his destination by a backward motion. The engine would be unable to proceed on its iron road if it were not for friction. The same is true in polemical science: the government of the country would not be able to be carried on under our present conditions if it were not forparty friction. But suppose it increased indefinitely, party friction becomes partyobstruction; and the engine of the State would no longer proceed smoothly and evenly along its appointed course at the rate of sixty miles an hour, but would resemble an old-fashioned coach, up to its axle-trees in mud, its motion altogether stopped by the action of party friction.

We have seen that forces have two ways of acting: that of compelling rest and that of producing motion. In statics forces act so as to prevent any change of motion, or disturb the body’s original position. In kinetics, on the contrary, the power is recognised as acting so as to produce or change a body’s motion. Now, in polemical science we have these two ways of considering the action of[97]forces. There is thestaticalorconservativeforce, which compels rest, which seeks security, stability, and peace, and is not ardently devoted to change. It reduces the system to equilibrium. There are, of course, two kinds of equilibrium—stableandunstable—according as the social and political system is in a healthy or unhealthy state. If a body is in stable equilibrium, and any slight motion takes place, the body will return immediately to its former position; but if in unstable, it will decline further and further away from its original position, and be entirely upset. So a healthy and sound conservative equilibrium is not disturbed by outside forces, and the State will resume its former position of stability and rest when the opposing force is withdrawn. But an unhealthy and insecure conservatism is as easily disturbed as an egg balanced on its narrow end.

The kinetics of society, that is to say the Radical way of estimating force, is the party of motion, generally supposed to be the ‘party of progress.’ It has[98]therefore many attractions in the eyes of those who delight in motion, speed, and rushing about. To run at full speed, to feel the keen air upon one’s face, to experience the delightful sensation of freedom of will, and limb, are joys which cannot be denied. Such exercise is beneficial to the system, bodily or political. Motion is the life of all things; it is characteristic of nature; it adores nature; because it is an emblem and characteristic of life. The ceaseless rolling of the ocean waves, the swaying of the trees, the bending of the flowers, the waving of the corn, all these fill us with pleasure; whereas a flat uninteresting plain, unrelieved by the motion of terrestrial objects, is depressing to the spirit. So there is much to be said in favour of motion, and Carlyle has defined progress as ‘living movement.’ And men love this ‘living movement,’ and take up the Laureate’s cry:

‘Forward, forward, let us range,Let the great world spin for ever down the ringingGrooves of change.’

‘Forward, forward, let us range,

Let the great world spin for ever down the ringing

Grooves of change.’

But, after all, there is a danger in this[99]everlasting motion. We cannot tell whither this progress may lead. It may be along a safe sure road; but perchance a precipice may open out before us; and rejoicing in the acceleration of our velocity, with eyes intent upon some distant heights of glory and ambition, we may not discover our danger until it is too late to stop, and a terrible plunge into an unknown abyss of turmoil and tumultuous waves is the alarming result of an unguarded policy of unrestrained ‘progress.’ I recall to my mind the quaint words of Holmes which aptly illustrate my contention.

‘If the wild filly, “Progress”, thou would’st ride,Have young companions ever at thy side;But wouldst thou stride the staunch old mare, “Success,”Go with thine elders, though they please thee less.’

‘If the wild filly, “Progress”, thou would’st ride,

Have young companions ever at thy side;

But wouldst thou stride the staunch old mare, “Success,”

Go with thine elders, though they please thee less.’

Progress and success do not always go together hand in hand; and while motion is essential to life, it is not always safe to urge a country forward at too great a speed; and security and stability are quite as important to the nation’s life as actual progress.

There are other impulsive forces which[100]act occasionally in the sphere of politics, and which baffle all our calculations, and exclude scientific considerations of the polemical problems which arise.Ambitionis such an impulsive force, and when the rulers of the people are actuated by it, and struggle for money, place, and power, politics is degraded from its position as a science, and it becomes impossible to estimate the result of forces so generated.

In my next lecture I propose to treat the important subject of the Laws which govern States and Governments, and which regulate, generate, and control the social forces which we have seen at work in the body politic.

Sincethe last time I had the honour of addressing you on polemical matters, I have met with a passage in the writings of M. Auguste Comte which afforded me much pleasure. It seemed to be the one word for which I had been waiting, and confirmed many of my own impressions and speculations. He lays down two propositions: first, that the constructive politics of the future must be based on the history of the past; and second, that political science is a composite study, and presupposes the complete apprehension of every branch of science, beginning with the physical, such as astronomy, and ending with the moral, such as ethics and sociology. M. Comte evidently does not regard as a vain dream and imaginative[102]speculation the theory that it will be possible for statesmen to calculate a policy, and to determine a course of action by purely scientific considerations. May I entertain the hope that in this university, where all branches of physical science have found a home, and are studied by most able and learned professors, the science of politics may be pursued under most favourable circumstances? I trust that each professor will bring before me the results of their deliberations, and contribute to the growth of this particular science for which our university has already become deservedly famous.

My present lecture is devoted to the important consideration ofLaw. At first sight it may appear to you that the wills and passions of mankind are so diverse and unknowable, that it would be absurd to suppose that they can be calculated, or rendered amenable to any law. But Professor Amos has pointed out that in proportion as we examine history, and compare the actions present and past of different[103]nations and states, the more uniform does human nature appear; the more calculable the actions, sentiments, and emotions of large masses of people. As we have already stated, the difficulties of the study are not likely to deter the professors of Girtham College from the pursuit of any particular branch of science.

A prioriwe might suppose from analogy that these polemical laws existed, as there is no department of nature which is not governed by law. It is an essential feature in nature, and also in government. What is political economy but the study of certain laws of nature? These were first discovered by Adam Smith, and have since been traced and estimated by such men as Ricardo, the two Mills, Professor Cairnes, Jevons, and many others. Moreover, our physical constitutions are governed by laws, which physicians have determined, and which it is perilous to resist. Our moral constitution is also governed by laws, which evidently exist, although it is difficult to find them out. But the nation is only an assemblage of[104]individuals; and since individuals are so governed, it is only natural to suppose that the nation, composed of individuals, is so constituted and controlled. And not only is that true, but we shall see that polemical laws are as permanent and universal, as invariable and irreversible, as the laws of nature which regulate the courses of the heavenly bodies, and raise the tides, or depress the sandstone hills.

We may notice first the preponderant impulse observable in a nation’s life in favour of supporting existing facts and institutions; and every reformer has discovered the difficulty and danger of changing or opposing the customs and habits of the people. As a wheel will travel most smoothly along a well-worn groove, whereby friction is diminished, so there is a natural national tendency always to run along those paths with which the habits and customs of the people have made them familiar. This law is nothing else than Newton’s first law of motion, which is quite as applicable to human masses as to lifeless matter. The[105]tendency of matter to remain at rest, if unmoved by any external agency, and of persisting to move after it has once been set in motion, is a conservative tendency; and is as true in political science as in any other.

The special branch of our science, which we may call theBiology of Politics, shows how absolute is the domain of law in polemical matters. The law of human life is that men are born, grow, become strong and vigorous, and then decay and die. This is the law of life, to which we must all yield an enforced obedience. This same law is observed to be at work in the heavenly bodies; and astronomy shows us that planets are born, flourish, and at length die, just as our human bodies do. The moon is, as you may have observed, a dead planet, such as our earth may be some day. The same growth and decay are also manifest in national life. First, there is the birth of the nation, which sometimes lies a long time in a dormant state, and then wakes up to life and energy. China and Russia[106]are examples of dormant States, just waking from a long sleep of childishness and ignorance. The next stage is the strong an healthy period of its existence, which England is at present enjoying; and then, after various stages of gradual decline, we come to the senile period of national life, when every energy and faculty, every national feeling and power of invention, are completely exhausted. As an example of this depressing condition, we may mention Turkey and several of the effete States of South America. Sometimes, when life is nearly extinct in the human body, physicians have made use of the power of galvanism, in order to revive the dying energies. This process of galvanizing a State into life was tried by Lord Palmerston and others on the worn-out frame of Turkey. But such attempts can only meet with partial and transitory success; and where the loss of national power and faculty betokens the senile period of the nation’s existence, it is vain to attempt to restore its former life and energy. The study of the biology[107]of politics presents many interesting and important details in this special branch of knowledge; and I commend this part of our subject to the special attention of the professor of physiology. The law of development is observable in nations as in nature. Recent scientific discoveries have tended to take away all ideas ofchancein the workings of nature, and have substitutedlawinstead of it. It would be unscientific and incorrect to speak of the world being formed by the ‘fortuitous concourse of atoms.’ So we cannot speak of a State being generated in this manner. Laws—economical, geographical, natural—preside over the formation of States and nations, and produce their further development.

The laws of political motion occupy the same prominent place in our new science as Newton’s laws do in ordinary dynamics. These are very important in calculating the positions which various States will occupy in the future. First, we have thedoctrine of nationality, which prevented the progress of Austria into[108]Italy, and of the Bourbons in Naples, and produced the amalgamation of the small German States in the great empire of Germany. The second law of political motion is the doctrine of theindependenceof all true States, and the equality of all States to each other. This had its growth in feudalism; and all the chief wars of modern times have been the result of the efforts of nature to establish this law of independence. The doctrine of intervention is a modification of the preceding law, and is applicable when the law of necessity demands its use, such as the restoration of order after protracted anarchy, the abolition of slave trade, etc. The third law is thelaw of morality. Just as for each man there exists arightand awrong; just asdutyandconscienceare certain elements in his daily motion, which dictate his course of action, although he may chose to neglect them; so a nation is bound by the same moral laws which govern the individual; and a nation errs if it transgresses them. Christianity is the agent which has[109]produced so powerful an influence in making men obey the dictates of conscience and walk in the path of duty; and I read with thankfulness the conclusion of Mr. Amos, that Christianity has triumphed quite as much in moralizing secular politics as it has in the sphere of individual life.

These are some of the principal laws of motion which I have observed at work in various States and nations. Inasmuch as political science embraces, in addition to the physical sciences, all those branches which are contained in ethics, economics, jurisprudence, sociology and others, the laws of each are generally applicable to the whole grand subject of which my lectures treat. Other general laws may be deduced, and have been enumerated in my previous lectures, from the social properties of curves and conics; and when our researches are complete we may hope to produce a code of laws for the guidance of our statesmen which maybe of immense use in determining[110]the policies of the future. Already there is strong evidence that the affairs of this country are being conducted on sound scientific principles, rather than by any species of guess-work or haphazard contrivances. The use of history is recognised as extremely important in determining a future line of conduct; and statesmen are in the habit of endeavouring to find from their study of the past what is the logical sequence of events. Just as mathematicians endeavour to determine the law of a series of figures, and having found the law, can write down the next, and the next,ad infinitum; so scientific politicians may be able soon to establish the various laws of a series of events, and calculate their course of actions. That there is considerable progress in this direction is manifest by the value which they place upon statistics, and their continued use of this important information.

There are a few great evils in our present system which are strongly opposed to any scientific methods in politics; and in the interests of the country as well as those of[111]science they ought to be removed. One great evil is the want of political and scientific knowledge on the part of the electors, who are in the habit of choosing their representatives on personal grounds, or party considerations, rather than on sound principles of political science. All this is opposed to any idea of law. Owing to the ignorance of the electors they fall an easy prey to adventurers and unprincipled politicians, who make all kinds of specious promises, tempt them with all manner of baits, and make self-interest instead of the welfare of the State the principle of voting. Selfishness is the ruin of social life and intercourse, the destroyer of all happiness, peace, and mutual trust in family life or in society. It is the root of most of the faults, vices, and crimes in the individual; and who can tell the endless disasters which will befall the State, where selfishness is the chief motive-power of the electors and the elected? A selfish statesman, one who goes into Parliament to gain his own ends and forward his own personal interests, is a disgrace to society—

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