Society, it seems to be supposed, has now assumed so highly developed a form, that what was accomplished in past times by the solitary exertions of a single great intellect, may now be gradually worked out by the united labours of an army of investigators. Just as the combination of well-organized power in a modern army entirely supersedes the single-handed bravery of the mediaeval knight, so we are to believe that the combination of intellectual labour has superseded the genius of an Archimedes, a Roger Bacon, or a Newton. So-called original research is now regarded almost as a recognised profession, adopted by hundreds of men, and communicated by a regular system of training. All that we need to secure great additions to our knowledge of nature is the erection of great laboratories, museums, and observatories, and the offering of sufficiently great pecuniary rewards to those who can invent new chemical compounds, or detect new species, or discover new comets. Doubtless this is not the real meaning of the eminent men who are now urging upon Government the elaborate endowment of physical research. They can only mean that the greater the pecuniary and material assistance given to men of science, the greater is the result which the available genius of the country may be expected to produce. Money and opportunities of study can no more produce genius than sunshine and moisture can generate living beings; the inexplicable germ is wanting in both cases. But, just as when the germ is present, the plant will grow more or less vigorously according to the circumstances in which it is placed, so it may be allowed that pecuniary assistance may favour the development of intellect. Public opinion however is not discriminating, and is likely to interpret the agitation for the endowment of science as meaning that science can be evolved from money or labour. p/> All such notions are, I believe, radically erroneous. In no branch of human affairs, neither in politics, war, literature, industry, nor science, is the influence of genius less considerable than it used to be. It is quite possible that the extension and organization of scientific study, assisted by the printing press and the accelerated means of communication, has increased the rapidity with which new discoveries are made known, and their details worked out by many heads and hands. A Darwin now no sooner propounds original ideas concerning the evolution of animated creatures, than those ideas are discussed and illustrated, and applied by other naturalists in every part of the civilized world. In former days his labours and discoveries would have been hidden for decades of years in scarce manuscripts, and generations would have passed away before his theory had enjoyed the same amount of criticism and corroboration as it has already received in fifteen years. But the general result is that the genius of Darwin is more valuable, not less valuable, than it would formerly have been. The advance of military science and the organization of enormous and well disciplined armies has not decreased the value of a skilful general; on the contrary, the rank and file are still more in need than they used to be of the guiding power of an ingenious and far-seeing intellect. The swift destruction of the French military power was not due alone to the perfection of the German army, nor to the genius of Moltke; it was due to the combination of a well-disciplined multitude, with a leader of the highest intellectual powers. So in every branch of human affairs the influence of the individual is not withering, but is growing with the extent of the material resources which are at his command.

Nature of Genius.

Turning to our own particular subject, it is a work of undiminished interest to reflect upon those qualities of mind which lead to great advances in natural knowledge. Nothing, indeed, is less amenable than genius to scientific analysis and explanation. Even precise definition is out of the question. Buffon said that 'genius is patience,' and certainly patience is one of its most constant and requisite components. But no one can suppose that patient labour alone will invariably lead to those conspicuous results which we attribute to genius. In every branch of science, literature, art, or industry, there are thousands of men and women who work with unceasing patience, and thereby ensure at least a moderate success; but it would be absurd to assent for a moment to crude notions of human equality, and to allow that equal amounts of intellectual labour yield equal results. A Newton may modestly and sincerely attribute his discoveries to industry and patient thought, and there is much reason to believe that genius is essentially unconscious and unable to account for its own peculiar powers. If genius, indeed, be that by which intellect diverges from what is common, it must necessarily be a phenomenon beyond the domain of the ordinary laws of nature. Nevertheless, it is always an interesting and instructive work to trace out, as far as possible, the characteristics of mind by which great discoveries have been achieved, and we shall find in the analysis much to illustrate the principles of scientific method.

Error of the Baconian Method.

Hundreds of investigators may be constantly engaged in experimental inquiry ; they may compile numberless notebooks full of scientific facts, and may frame endless tables full of numerical results; but if the views of the nature of induction here maintained be true they can never by such work alone rise to new and great discoveries. By an organized system of research they may work out deductively the detailed results of a previous discovery, but to arrive at a new principle of nature is another matter. Francis Bacon contributed to spread abroad the hurtful notion that to advance science we must begin by accumulating facts, and then draw from them, by a process of patient digestion, successive laws of higher and higher generality. In protesting against the false method of the scholastic logicians, he exaggerated a partially true philosophy, until it became almost as false as that which preceded it. His notion of scientific method was that of a kind of scientific bookkeeping. Facts were to be indiscriminately gathered from every source, and posted in a kind of ledger, from which would emerge in time a clear balance of truth. It is difficult to imagine a less likely way of arriving at great discoveries.

The greater the array of facts, the less is the probability that they will by any routine system of classification or research disclose the laws of nature they embody. Exhaustive classification in all possible orders is out of the question, because the possible orders are practically infinite in number. It is before the glance of the philosophic mind that facts must display their meaning, and fall into logical order. The natural philosopher must therefore have, in the first place, a mind of impressionable character, which is readily affected by the slightest exceptional phenomenon. His associating and identifying powers must be great, that is, a single strange fact must suggest to his mind whatever of like nature has previously come within his experience. His imagination must be active, and bring before his mind multitudes of relations in which the unexplained facts may possibly stand with regard to each other, or to more common facts. Sure and vigorous powers of deductive reasoning must then come into play, and enable him to infer what will happen under each supposed condition. Lastly, and above all, there must be the love of certainty leading him diligently and with perfect candour, to compare his speculations with the test of fact and experiment.

Freedom of Theorizing.

It would be a complete error to suppose that the great discoverer is one who seizes at once unerringly upon the truth, or has any special method of divining it. In all probability the errors of the great mind far exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must almost of necessity be many times as numerous as those which prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record may remain of more than the hundredth part. There is nothing intrinsically absurd except that which proves contrary to logic and experience. The truest theories involve suppositions which are most inconceivable, and no limit can really be placed to the freedom of framing hypotheses. Kepler is an extraordinary instance to this effect. No minor laws of nature are more firmly established than those which he detected concerning the orbits and motions of planetary masses, and on these empirical laws the theory of gravitation was founded. Did we not know by his own writings the multitude of errors into which he fell, we might have imagined that he had some special faculty of seizing on the truth. But, as is well known, lie was full of chimerical notions; his most favourite and long entertained theory was founded on a fanciful analogy between the planetary orbits and the regular solids. His celebrated laws were the outcome of a lifetime of speculation, for the most part vain and groundless. We know this with certainty, because he had a curious pleasure in dwelling upon erroneous and futile trains of reasoning, which most other persons carefully consign to oblivion. But Kepler's name was destined to immortality, on account of the patience with which he submitted his hypotheses to comparison with observation, the candour with which he acknowledged failure after failure, and the perseverance and ingenuity with which lie renewed his attack upon the riddles of nature.

Next after Kepler perhaps Faraday is the physical philosopher who has afforded us the most important materials for gaining an insight into the progress of discovery, by recording erroneous as well as successful speculations. The recorded notions; indeed, are probably at the most a tithe of the fancies which arose in his active brain. As Faraday himself said— 'The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator, have been crushed in silence and secresy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized.'

Nevertheless, in Faraday's researches published either in the Philosophical Transactions' or in minor papers, in his manuscript note-books, of in various other materials, fortunately made known in his interesting life by Dr. Bence Jones, we find invaluable lessons for the experimentalist. These writings are full of speculations which we must not judge by the light of subsequent discovery. It may even be said that Faraday sometimes committed to the printing press crude ideas which a cautious friend would have counselled him to keep back or suppress. There was occasionally even a wildness and vagueness in his notions, which in a less careful experimentalist might have been fatal to the attainment of truth. This is especially apparent in a curious paper concerning Ray-vibrations; but fortunately Faraday was fully aware of the shadowy character of his speculations, and expressed the feeling in words ,which must be quoted. 'I think it likely,' he says, 'that I have made many mistakes in the preceding pages, for even to myself my ideas on this point appear only as the shadow of a speculation, or as one of those impressions upon the mind, which are allowable for a time as guides to thought and research. He who labours in experimental inquiries knows how numerous these are, and how often their apparent fitness and beauty vanish before the progress and development of real natural truth.' If, then, the experimentalist has no royal road to the discovery of the truth, it is an interesting matter to consider by what logical procedure lie attains the truth.

If I have taken a correct view of logical method, there is really no such thing as a distinct process of induction. The probability is infinitely small that a collection of complicated facts will fall into an arrangement capable of exhibiting directly the laws obeyed by them. The mathematician might as well expect to integrate his functions by a ballot-box, as the experimentalist to draw deep truths from haphazard trials. All induction is but the inverse application of deduction, and it is by the inexplicable mental action of a gifted mind that a multitude of heterogeneous facts are caused to range themselves in luminous order as the results of some uniformly acting law. So different, indeed, are the qualities of mind required in different branches of science that it would be absurd to attempt to give an exhaustive description of the character of mind which leads to discovery. The labours of Newton could not have been accomplished except by a mind of the utmost mathematical genius ; Faraday, on the other hand, has made the most extensive and undoubted additions to human knowledge without ever passing beyond common arithmetic. I do not remember meeting in Faraday's writings with a single algebraic formula or mathematical problem of any complexity. Professor Clerk Maxwell, indeed, in the preface to his new Treatise on Electricity, has strongly recommended the reading of Faraday's researches by all students of science, and has given his opinion that though Faraday seldom or never employed mathematical formulae, his methods and conceptions were not the less mathematical in their nature. I have myself protested against the prevailing confusion between a mathematical and an exact science, yet I certainly think that Faraday's experiments were for the most part purely qualitative, and that his mathematical ideas were of a rudimentary character. It is true that he could not possibly investigate such a subject as magne-crystallic action without involving himself in geometrical relations of considerable complexity. I nevertheless think that he was deficient in purely mathematical deductive power, that power which is so exclusively developed by the modern system of mathematical training at Cambridge. Faraday, for instance, was perfectly acquainted with the forms of his celebrated lines of force, but I am not aware that he ever entered into the subject of the algebraic nature of those curves, and I feel sure that he could not have explained their form as depending on the resultant attraction of all the magnetic particles acting according to general mathematical laws. There are even occasional indications that he did not understand some of the simpler mathematical doctrines of modern physical science. Although he so clearly foresaw the establishment of the unity of the physical forces, and laboured so hard with his own hands to connect gravity with the other forces, it is very doubtful whether he understood the fundamental doctrine of the conservation of energy as applied to gravitation. Thus, while Faraday was probably equal to Newton in experimental skill and deductive power as regards the invention of simple qualitative experiments, he was contrasted to him in mathematical power. These two instances are sufficient to show that minds of widely different conformation may meet with suitable regions of research. Nevertheless, there are certain common traits which we may discover in all the highest scientific minds.

The Newtonian Method, the True Organum.

Laplace was of opinion that the 'Principia' and the 'Opticks' of Newton furnished the best models then available of the delicate art of experimental and theoretical investigation. In these, as he says, we meet with the most happy illustrations of the way in which, from a series of inductions, we may rise to the causes of phenomena, and thence descend again to all the resulting details.

The popular notion concerning Newton's discoveries is that in early life, while driven into the country by the Great Plague, a falling apple accidentally suggested to him the existence of gravitation, and that, availing himself of this hint, he was led to the discovery of the law of gravitation, the explanation of which constitutes the Principia: It is difficult to imagine a more ludicrous and inadequate picture of Newton's labours and position. No originality, or at least priority, could be or was claimed by Newton as regards the discovery of the celebrated law of the inverse square, so closely associated with his name. In a well-known Scholium^* he acknowledges that Sir Christopher Wren, Dr. Hooke, and Dr. Halley, had severally observed the accordance of Kepler's third law of motion of the planets with the principle of the inverse square.

Newton's work was really that of developing the methods of deductive reasoning and experimental verification, by which alone great hypotheses can be brought to the touch-stone of fact. Archimedes was the greatest of ancient philosophers, for he showed how mathematical theory could be wedded to physical experiments; and his works are the first true Organum. Newton is the modern Archimedes, and the 'Principia ' forms the true Novum Organum of scientific method. The laws which he actually established are great, but his example of the manner of establishing them is greater still. There is hardly a progressive branch of physical and mathematical science, excepting perhaps chemistry and electricity, which has not been developed from the germs of true scientific procedure which he disclosed in the 'Principia' or the 'Opticks.' Overcome by the success of his theory of universal gravitation, we are apt to forget that in his theory of sound he originated the mathematical investigation of waves and the mutual action of particles; that in his Corpuscular theory of light, however mistaken, he first ventured to apply mathematical considerations to molecular attractions and repulsions; that in his prismatic experiments he showed how far experimental verification could be pushed ; that in his examination of the coloured rings named after him, he accomplished the most remarkable instance of minute measurement yet known, a mere practical application of which by M. Fizeau was recently deemed worthy of a medal by the Royal Society. We only learn by degrees how complete was his scientific insight; a few words in his third law of motion display his acquaintance with the fundamental principles of modern thermodynamics and the conservation of energy, while manuscripts long overlooked prove that in his inquiries concerning atmospheric refraction he had overcome the main difficulties of applying theory to one of the most complex of physical problems.

After all, it is only by examining the way in which he effected discoveries, that we can rightly appreciate his greatness. The 'Principia' treats not of gravity so much as of forces in general, and the methods of reasoning about them. He investigates not one hypothesis only, but mechanical hypotheses in general. Nothing so much strikes the reader of the work as the exhaustiveness of his treatment, and the almost infinite power of his insight. If he treats of central forces, it is not any one law of force which he discusses, but many, or almost all imaginable cases, the laws and results of each of which he sketches out in a few pregnant words. If his subject is a resisting medium, it is not air or water alone, nor any one resisting medium, but resisting media in general. We have a good example of his method in the Scholium to the twenty-second proposition of the second book, in which he runs rapidly over many possible suppositions as to the laws of the compressing forces which might conceivably act in aan atmosphere of gas, a consequence being drawn from each case, and that one hypothesis ultimately selected which yields results agreeing with experiments upon the pressure and density of the terrestrial atmosphere.

Newton said that he did not frame hypotheses, but, in reality, the greater part of the 'Principia' is purely hypothetical, endless varieties of causes and laws being imagined which have no counterpart in nature. The most grotesque hypotheses of Kepler or Descartes were not more imaginary. But Newton's comprehension of logical method was perfect; no hypothesis was entertained unless it was definite in conditions, and admitted of unquestionable deductive reasoning; and the value of each hypothesis was entirely decided by the comparison of its consequences with facts. I do not entertain a doubt that the general course of his procedure is identical with that view of the nature of induction, as the inverse application of deduction, which I have advocated throughout these volumes. Francis Bacon held that science should be founded on experience, but he wholly mistook the true mode of using experience, and in attempting to apply his method he ludicrously failed. Newton did not less found his method on experience, but he seized the true method of treating it, and applied it with a power and success never since equalled. It is wholly a mistake to say that modern science is the result of the Baconian philosophy; it is the Newtonian philosophy and the Newtonian method which have led to all the great triumphs of physical science, and I repeat that the 'Principia' forms the true 'Novum Organum.'

In bringing his theories to a decisive experimental verification, Newton showed, as a general rule, an exquisite skill and ingenuity. In his hands a few simple pieces of apparatus were made to give results involving an unsuspected depth of meaning. His most beautiful experimental inquiry was that by which he proved the differing refrangibility of rays of light. To suppose that he originally discovered the power of a prism to break up a beam of white light would be a great mistake,. for he speaks of procuring a glass prism to try the celebrated phenomena of colours. But we certainly owe to him the theory that white light is a mixture of rays differing in refrangibility, and that lights which differ in colour, differ also in refrangibility. Other persons might have conceived this theory; in fact, any person regarding refraction as a quantitative effect, must see that different parts of the spectrum have suffered different amounts of refraction. But the power of Newton is shown in the tenacity with which he followed his theory into every consequence, and tested each result by a simple but conclusive experiment. He first shows that different coloured spots are displaced by different amounts when viewed through a prism, and that their images come to a focus at different distances from the Tense, as they should do, if the refrangibility differed. After excluding by various experiments a variety of indifferent circumstances, lie 'fixes leis attention upon the question whether the rays are merely shattered, disturbed, and spread out in a chance manner, as Grimaldi supposed, or whether there is a constant, relation between the colour and the refrangibility. If Grimaldi was right, it might be expected that any part of the spectrum taken separately, and subjected to a second refraction, would suffer a new breaking up, and produce some new spectrum. Newton inferred from his own theory that a particular ray of the spectrum would have a constant refrangibility, so that a second prism would merely bend it more or less, but not further disperse it in any considerable degree. By simply cutting off most of the rays of the spectrum by a screen, and allowing the remaining narrow ray to fall on a second prism, he proved the truth of this conclusion; and then slowly turning the first prism, so as to vary the colour of the ray falling on the second one, he found that the spot of light formed by the twice-refracted ray travelled up and down, a palpable proof that the amount of refrangibility varied with the colour. For his further satisfaction, he sometimes refracted the light a third or fourth time, and he found that it might be refracted upwards or downwards or sideways, and yet for each coloured light there was a definite amount of refraction through each prism. He completes the proof by showing that the separated rays may again be gathered together into white light by an inverted prism. So that no number of refractions alters the character of the light. The conclusion thus obtained serves to explain the confusion arising in the use of a common lease; with homogeneous light he shows that there is one distinct focus, with mixed light an infinite number of foci, which prevent a clear view from being obtained at any one point.

What astonishes the reader of the 'Opticks' is the persistence with which Newton follows out the consequences of a preconceived theory, and tests the one notion by a wonderful variety of simple comparisons with fact. It is certainly the theory which leads him to the experiments, and most of these could hardly be devised by accident. The fertility with which he invents new combinations, and foresees the results, subsequently verified, produces an invincible conviction in the reader that he has possession of the truth. Newton actually remarks that it was by mathematically determining all kinds of phenomena of colours which could be produced by refraction that he had 'invented' almost all the experiments in the book, and he promises that others who shall 'argue truly,' and try the experiments with care, will not be disappointed in the results.

The philosophic method of Huyghens was almost exactly the same as that of Newton, and Huyghens' investigation of the laws of double refraction furnishes almost equally beautiful instances of theory guiding experiment. Double refraction was first discovered by accident, so far as we know, and was described by Erasmus Bartholinus in 1669. The phenomenon then appeared to be entirely exceptional, and the laws governing the two separate paths of the refracted rays were so unapparent and complicated, that even Newton altogether misunderstood the phenomenon, and it was only at the latter end of the last century that scientific men generally began to comprehend its laws.

Nevertheless, Huyghens had, with rare genius, arrived at the true theory as early as 1678. He regarded light as an undulatory motion of some medium, and in his 'Traité de la Lumière;' he pointed out that, in ordinary refraction, the velocity of propagation of the wave is equal in all directions, so that the front of an advancing wave is spherical, and reaches equal distances in equal times. But in crystals, as he supposed, the medium would be of unequal elasticity in different directions, so that a disturbance would reach unequal distances in equal times, and the wave produced would have a spheroidal form. Huyghens was not satisfied with an unverified theory. He calculated what might be expected to happen when a crystal of calc-spar was cut in various directions, and he says, 'I have examined in detail the properties of the extraordinary refraction of this crystal, to see if each phenomenon which is deduced from theory would agree with what is really observed. And this being so, it is no slight proof of the truth of our suppositions and principles; but what I am going to add here confirms them still more wonderfully; that is, the different modes of cutting this crystal, in which the surfaces produced give rise to refraction exactly such as they ought to be, and as I had foreseen them, according to the preceding theory.'

The supremacy of Newton's mistaken corpuscular doctrine of light caused the theories and experiments of Huyghens to be disregarded for more than a century; but it is not easy to imagine a more beautiful or successful application of the true method of inductive investigation, theory guiding experiment, and yet wholly relying on experiment for confirmation.

Candour and Courage of the Philosophic Mind.

Perfect readiness to reject a theory inconsistent with fact is, then, a primary requisite of the philosophical mind. But it would be a mistake to suppose that this candour has anything akin to fickleness; on the contrary, readiness to reject a false theory may be combined with a peculiar pertinacity and courage in maintaining an hypothesis as long as its falsity is not actually apparent. There must, indeed, be no prejudice or bias distorting the mind, and causing it to under-estimate or pass over the unwelcome results of experiment. There must be that scrupulous honesty and flexibility of mind, which assigns an adequate value to all evidence; indeed the more a man loves his theory, the more scrupulous should be his attention to its faults. Nothing is more common in life than to meet with some theorist, who, by long cogitation over a single theory, has allowed it to mould his mind, and render him incapable of receiving anything but as a contribution to the truth of his one theory. A narrow and intense course of thought may sometimes lead to great results, but the adoption of a wrong theory at the outset is in such a mind irretrievable. The man of one idea has but a single chance of truth. The fertile discoverer, on the contrary, chooses between many theories, and is never wedded to any one, unless impartial and repeated comparison has convinced him of its validity. He does not choose and then compare; but he compares time after time, and then chooses.

Having once deliberately chosen, the philosopher may rightly entertain his theory with the strongest love and fidelity. He will neglect no objection; for he may chance at any time to meet a fatal one; but he will bear in mind the inconsiderable powers of the human mind compared with the tasks it has to undertake. He will see that no theory can at first be reconciled with all possible objections, simply because there may be many interfering causes, or the very consequences of the theory may have a complexity which prolonged investigation by successive generations of men may not exhaust. If then, a theory exhibit a number of very striking coincidences with fact, it must not be thrown aside until at least one conclusive discordance is proved, regard being had to possible error in establishing that discordance. In science and philosophy something must be risked. He who quails at the least difficulty will never establish a new truth, and it was not unphilosophic in Leslie to remark concerning his own experimental investigations into the nature of heat - 'In the course of investigation, I have found myself compelled to relinquish some preconceived notions; but I have not abandoned them hastily, nor, till after a warm and obstinate defence, I was driven from every post.'

Faraday's life, again, furnishes most interesting illustrations of this tenacity of the philosophical mind. Though so candid in rejecting some of his theories, there were others to which he clung through everything. One of his most favourite notions was finally realised in a brilliant discovery; another remains in doubt to the present day.

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