CHAPTER XXIII.
THE USE OF HYPOTHESIS.
If the views upheld in this work be correct, all inductive investigation consists in the marriage of hypothesis and experiment. When facts are in our possession, we frame an hypothesis to explain their relations, and by the success of this explanation is the value of the hypothesis to be judged. In the invention and treatment of such hypotheses, we must avail ourselves of the whole body of science already accumulated, and when once we have obtained a probable hypothesis, we must not rest until we have verified it by comparison with new facts. We must endeavour by deductive reasoning to anticipate such phenomena, especially those of a singular and exceptional nature, as would happen if the hypothesis be true. Out of the infinite number of experiments which are possible, theory must lead us to select those critical ones which are suitable for confirming or negativing our anticipations.
This work of inductive investigation cannot be guided by any system of precise and infallible rules, like those of deductive reasoning. There is, in fact, nothing to which we can apply rules of method, because the laws of nature must be in our possession before we can treat them. If there were any rule of inductive method, it would direct us to make an exhaustive arrangement of facts in all possible orders. Given the specimens in a museum, we might arrive at the best classification by going systematically through all possible classifications, and, were we endowed with infinite time and patience, this would be an effective method. It is the method by which the first simple steps are taken in an incipient branch of science. Before the dignified name of science is applicable, some coincidences will force themselves upon the attention. Before there was a science of meteorology observant persons learned to associate clearness of the atmosphere with coming rain, and a colourless sunset with fine weather. Knowledge of this kind is called *empirical*, as seeming to come directly from experience; and there is a considerable portion of knowledge which bears this character.
We may be obliged to trust to the casual detection of coincidences in those branches of knowledge where we are deprived of the aid of any guiding notions; but a little reflection will show the utter insufficiency of haphazard experiment, when applied to investigations of a complicated nature. At the best, it will be the simple identity, or partial identity, of classes, as illustrated in pages 127 or 134, which can be thus detected. It was pointed out that, even when a law of nature involves only two circumstances, and there are one hundred distinct circumstances which may possibly be connected, there will be no less than 4,950 pairs of circumstances between which coincidence may exist. When a law involves three or more circumstances, the possible number of relations becomes vastly greater. When considering the subject of combinations and permutations, it became apparent that we could never cope with the possible variety of nature. An exhaustive examination of the possible metallic alloys, or chemical compounds, was found to be out of the question (p. 191).
It is on such considerations that we can explain the very small additions made to our knowledge by the alchemists. Many of them were men of the greatest acuteness, and their indefatigable labours were pursued through many centuries. A few things were discovered by them, but a true insight into nature, now enables chemists to discover more useful facts in a year than were yielded by the alchemists during many centuries. There can be no doubt that Newton was an alchemist, and that he often laboured night and day at alchemical experiments. But in trying to discover the secret by which gross metals might be rendered noble, his lofty powers of deductive investigation were wholly useless. Deprived of all guiding clues, his experiments were like those of all the alchemists, purely tentative and haphazard. While his hypothetical and deductive investigations have given us the true system of the Universe, and opened the way in almost all the great branches of natural philosophy, the whole results of his tentative experiments are comprehended in a few happy guesses, given in his celebrated “Queries.”
Even when we are engaged in apparently passive observation of a phenomenon, which we cannot modify experimentally, it is advantageous that our attention should be guided by theoretical anticipations. A phenomenon which seems simple is, in all probability, really complex, and unless the mind is actively engaged in looking for particular details, it is likely that the critical circumstances will be passed over. Bessel regretted that no distinct theory of the constitution of comets had guided his observations of Halley’s comet;[418] in attempting to verify or refute a hypothesis, not only would there be a chance of establishing a true theory, but if confuted, the confutation would involve a store of useful observations.
[418] Tyndall, *On Cometary Theory*, Philosophical Magazine, April 1869. 4th Series, vol. xxxvii. p. 243.
It would be an interesting work, but one which I cannot undertake, to trace out the gradual reaction which has taken place in recent times against the purely empirical or Baconian theory of induction. Francis Bacon, seeing the futility of the scholastic logic, which had long been predominant, asserted that the accumulation of facts and the orderly abstraction of axioms, or general laws from them, constituted the true method of induction. Even Bacon was not wholly unaware of the value of hypothetical anticipation. In one or two places he incidentally acknowledges it, as when he remarks that the subtlety of nature surpasses that of reason, adding that “axioms abstracted from particular facts in a careful and orderly manner, readily suggest and mark out new particulars.”
Nevertheless Bacon’s method, as far as we can gather the meaning of the main portions of his writings, would correspond to the process of empirically collecting facts and exhaustively classifying them, to which I alluded. The value of this method may be estimated historically by the fact that it has not been followed by any of the great masters of science. Whether we look to Galileo, who preceded Bacon, to Gilbert, his contemporary, or to Newton and Descartes, Leibnitz and Huyghens, his successors, we find that discovery was achieved by the opposite method to that advocated by Bacon. Throughout Newton’s works, as I shall show, we find deductive reasoning wholly predominant, and experiments are employed, as they should be, to confirm or refute hypothetical anticipations of nature. In my “Elementary Lessons in Logic” (p. 258), I stated my belief that there was no kind of reference to Bacon in Newton’s works. I have since found that Newton does once or twice employ the expression *experimentum crucis* in his “Opticks,” but this is the only expression, so far as I am aware, which could indicate on the part of Newton direct or indirect acquaintance with Bacon’s writings.[419]
[419] See *Philosophical Transactions*, abridged by Lowthorp. 4th edit. vol. i. p. 130. I find that opinions similar to those in the text have been briefly expressed by De Morgan in his remarkable preface to *From Matter to Spirit*, by C.D., pp. xxi. xxii.
Other great physicists of the same age were equally prone to the use of hypotheses rather than the blind accumulation of facts in the Baconian manner. Hooke emphatically asserts in his posthumous work on Philosophical Method, that the first requisite of the Natural Philosopher is readiness at guessing the solution of phenomena and making queries. “He ought to be very well skilled in those several kinds of philosophy already known, to understand their several hypotheses, suppositions, collections, observations, &c., their various ways of ratiocinations and proceedings, the several failings and defects, both in their way of raising and in their way of managing their several theories: for by this means the mind will be somewhat more ready at guessing at the solution of many phenomena almost at first sight, and thereby be much more prompt at making queries, and at tracing the subtlety of Nature, and in discovering and searching into the true reason of things.”
We find Horrocks, again, than whom no one was more filled with the scientific spirit, telling us how he tried theory after theory in order to discover one which was in accordance with the motions of Mars.[420] Huyghens, who possessed one of the most perfect philosophical intellects, followed the deductive process combined with continual appeal to experiment, with a skill closely analogous to that of Newton. As to Descartes and Leibnitz, they fell into excess in the use of hypothesis, since they sometimes adopted hypothetical reasoning to the exclusion of experimental verification. Throughout the eighteenth century science was supposed to be advancing by the pursuance of the Baconian method, but in reality hypothetical investigation was the main instrument of progress. It is only in the present century that physicists began to recognise this truth. So much opprobrium had been attached by Bacon to the use of hypotheses, that we find Young speaking of them in an apologetic tone. “The practice of advancing general principles and applying them to particular instances is so far from being fatal to truth in all sciences, that when those principles are advanced on sufficient grounds, it constitutes the essence of true philosophy;”[421] and he quotes cases in which Davy trusted to his theories rather than his experiments.
[420] Horrocks, *Opera Posthuma* (1673), p. 276.
[421] Young’s *Works*, vol. i. p. 593.
Herschel, who was both a practical physicist and an abstract logician, entertained the deepest respect for Bacon, and made the “Novum Organum” as far as possible the basis of his own admirable *Discourse on the Study of Natural Philosophy*. Yet we find him in Chapter VII. recognising the part which the formation and verification of theories takes in the higher and more general investigations of physical science. J. S. Mill carried on the reaction by describing the Deductive Method in which ratiocination, that is deductive reasoning, is employed for the discovery of new opportunities of testing and verifying an hypothesis. Nevertheless throughout the other parts of his system he inveighed against the value of the deductive process, and even asserted that empirical inference from particulars to particulars is the true type of reasoning. The irony of fate will probably decide that the most original and valuable part of Mill’s System of Logic is irreconcilable with those views of the syllogism and of the nature of inference which occupy the main part of the treatise, and are said to have effected a revolution in logical science. Mill would have been saved from much confusion of thought had he not failed to observe that the inverse use of deduction constitutes induction. In later years Professor Huxley has strongly insisted upon the value of hypothesis. When he advocates the use of “working hypotheses” he means no doubt that any hypothesis is better that none, and that we cannot avoid being guided in our observations by some hypothesis or other. Professor Tyndall’s views as to the use of the Imagination in the pursuit of Science put the same truth in another light.
It ought to be pointed out that Neil in his *Art of Reasoning*, a popular but able exposition of the principles of Logic, published in 1853, fully recognises in Chapter XI. the value and position of hypothesis in the discovery of truth. He endeavours to show, too (p. 109), that Francis Bacon did not object to the use of hypothesis.
The true course of inductive procedure is that which has yielded all the more lofty results of science. It consists in *Anticipating Nature*, in the sense of forming hypotheses as to the laws which are probably in operation; and then observing whether the combinations of phenomena are such as would follow from the laws supposed. The investigator begins with facts and ends with them. He uses facts to suggest probable hypotheses; deducing other facts which would happen if a particular hypothesis is true, he proceeds to test the truth of his notion by fresh observations. If any result prove different from what he expects, it leads him to modify or to abandon his hypothesis; but every new fact may give some new suggestion as to the laws in action. Even if the result in any case agrees with his anticipations, he does not regard it as finally confirmatory of his theory, but proceeds to test the truth of the theory by new deductions and new trials.
In such a process the investigator is assisted by the whole body of science previously accumulated. He may employ analogy, as I shall point out, to guide him in the choice of hypotheses. The manifold connections between one science and another give him clues to the kind of laws to be expected, and out of the infinite number of possible hypotheses he selects those which are, as far as can be foreseen at the moment, most probable. Each experiment, therefore, which he performs is that most likely to throw light upon his subject, and even if it frustrate his first views, it tends to put him in possession of the correct clue.
*Requisites of a good Hypothesis.*
There is little difficulty in pointing out to what condition an hypothesis must conform in order to be accepted as probable and valid. That condition, as I conceive, is the single one of enabling us to infer the existence of phenomena which occur in our experience. *Agreement with fact is the sole and sufficient test of a true hypothesis.*
Hobbes has named two conditions which he considers requisite in an hypothesis, namely (1) That it should be conceivable and not absurd; (2) That it should allow of phenomena being necessarily inferred. Boyle, in noticing Hobbes’ views, proposed to add a third condition, to the effect that the hypothesis should not be inconsistent with any other truth on phenomenon of nature.[422] I think that of these three conditions, the first cannot be accepted, unless by *inconceivable* and *absurd* we mean self-contradictory or inconsistent with the laws of thought and nature. I shall have to point out that some satisfactory theories involve suppositions which are wholly *inconceivable* in a certain sense of the word, because the mind cannot sufficiently extend its ideas to frame a notion of the actions supposed to take place. That the force of gravity should act instantaneously between the most distant parts of the planetary system, or that a ray of violet light should consist of about 700 billions of vibrations in a second, are statements of an inconceivable and absurd character in one sense; but they are so far from being opposed to fact that we cannot on any other suppositions account for phenomena observed. But if an hypothesis involve self-contradiction, or is inconsistent with known laws of nature, it is self-condemned. We cannot even apply deductive reasoning to a self-contradictory notion; and being opposed to the most general and certain laws known to us, the primary laws of thought, it thereby conspicuously fails to agree with facts. Since nature, again, is never self-contradictory, we cannot at the same time accept two theories which lead to contradictory results. If the one agrees with nature, the other cannot. Hence if there be a law which we believe with high probability to be verified by observation, we must not frame an hypothesis in conflict with it, otherwise the hypothesis will necessarily be in disagreement with observation. Since no law or hypothesis is proved, indeed, with absolute certainty, there is always a chance, however slight, that the new hypothesis may displace the old one; but the greater the probability which we assign to that old hypothesis, the greater must be the evidence required in favour of the new and conflicting one.
[422] Boyle’s *Physical Examen*, p. 84.
I assert, then, that there is but one test of a good hypothesis, namely, *its conformity with observed facts*; but this condition may be said to involve three constituent conditions, nearly equivalent to those suggested by Hobbes and Boyle, namely:--
(1) That it allow of the application of deductive reasoning and the inference of consequences capable of comparison with the results of observation.
(2) That it do not conflict with any laws of nature, or of mind, which we hold to be true.
(3) That the consequences inferred do agree with facts of observation.
*Possibility of Deductive Reasoning.*
As the truth of an hypothesis is to be proved by its conformity with fact, the first condition is that we be able to apply methods of deductive reasoning, and learn what should happen according to such an hypothesis. Even if we could imagine an object acting according to laws hitherto wholly unknown it would be useless to do so, because we could never decide whether it existed or not. We can only infer what would happen under supposed conditions by applying the knowledge of nature we possess to those conditions. Hence, as Boscovich truly said, we are to understand by hypotheses “not fictions altogether arbitrary, but suppositions conformable to experience or analogy.” It follows that every hypothesis worthy of consideration must suggest some likeness, analogy, or common law, acting in two or more things. If, in order to explain certain facts, *a*, *a′*, *a″*, &c., we invent a cause A, then we must in some degree appeal to experience as to the mode in which A will act. As the laws of nature are not known to the mind intuitively, we must point out some other cause, B, which supplies the requisite notions, and all we do is to invent a fourth term to an analogy. As B is to its effects *b*, *b′*, *b″*, &c., so is A to its effects *a*, *a′*, *a″*, &c. When we attempt to explain the passage of light and heat radiations through space unoccupied by matter, we imagine the existence of the so-called *ether*. But if this ether were wholly different from anything else known to us, we should in vain try to reason about it. We must apply to it at least the laws of motion, that is we must so far liken it to matter. And as, when applying those laws to the elastic medium air, we are able to infer the phenomena of sound, so by arguing in a similar manner concerning ether we are able to infer the existence of light phenomena corresponding to what do occur. All that we do is to take an elastic substance, increase its elasticity immensely, and denude it of gravity and some other properties of matter, but we must retain sufficient likeness to matter to allow of deductive calculations.
The force of gravity is in some respects an incomprehensible existence, but in other respects entirely conformable to experience. We observe that the force is proportional to mass, and that it acts in entire independence of other matter which may be present or intervening. The law of the decrease of intensity, as the square of the distance increases, is observed to hold true of light, sound, and other influences emanating from a point, and spreading uniformly through space. The law is doubtless connected with the properties of space, and is so far in agreement with our necessary ideas.
It may be said, however, that no hypothesis can be so much as framed in the mind unless it be more or less conformable to experience. As the material of our ideas is derived from sensation we cannot figure to ourselves any agent, but as endowed with some of the properties of matter. All that the mind can do in the creation of new existences is to alter combinations, or the intensity of sensuous properties. The phenomenon of motion is familiar to sight and touch, and different degrees of rapidity are also familiar; we can pass beyond the limits of sense, and imagine the existence of rapid motion, such as our senses could not observe. We know what is elasticity, and we can therefore in a way figure to ourselves elasticity a thousand or a million times greater than any which is sensuously known to us. The waves of the ocean are many times higher than our own bodies; other waves, are many times less; continue the proportion, and we ultimately arrive at waves as small as those of light. Thus it is that the powers of mind enable us from a sensuous basis to reason concerning agents and phenomena different in an unlimited degree. If no hypothesis then can be absolutely opposed to sense, accordance with experience must always be a question of degree.
In order that an hypothesis may allow of satisfactory comparison with experience, it must possess definiteness and in many cases mathematical exactness allowing of the precise calculation of results. We must be able to ascertain whether it does or does not agree with facts. The theory of vortices is an instance to the contrary, for it did not present any mode of calculating the exact relations between the distances and periods of the planets and satellites; it could not, therefore, undergo that rigorous testing to which Newton scrupulously submitted his theory of gravity before its promulgation. Vagueness and incapability of precise proof or disproof often enable a false theory to live; but with those who love truth, vagueness should excite suspicion. The upholders of the ancient doctrine of Nature’s abhorrence of a vacuum, had been unable to anticipate the important fact that water would not rise more than 33 feet in a common suction pump. Nor when the fact was pointed out could they explain it, except by introducing a special alteration of the theory to the effect that Nature’s abhorrence of a vacuum was limited to 33 feet.
*Consistency with the Laws of Nature.*
In the second place an hypothesis must not be contradictory to what we believe to be true concerning Nature. It must not involve self-inconsistency which is opposed to the highest and simplest laws, namely, those of Logic. Neither ought it to be irreconcilable with the simple laws of motion, of gravity, of the conservation of energy, nor any parts of physical science which we consider to be established beyond reasonable doubt. Not that we are absolutely forbidden to entertain such an hypothesis, but if we do so we must be prepared to disprove some of the best demonstrated truths in the possession of mankind. The fact that conflict exists means that the consequences of the theory are not verified if previous discoveries are correct, and we must therefore show that previous discoveries are incorrect before we can verify our theory.
An hypothesis will be exceedingly improbable, not to say absurd, if it supposes a substance to act in a manner unknown in other cases; for it then fails to be verified in our knowledge of that substance. Several physicists, especially Euler and Grove, have supposed that we might dispense with an ethereal basis of light, and infer from the interstellar passage of rays that there was a kind of rare gas occupying space. But if so, that gas must be excessively rare, as we may infer from the apparent absence of an atmosphere around the moon, and from other facts known to us concerning gases and the atmosphere; yet it must possess an elastic force at least a billion times as great as atmospheric air at the earth’s surface, in order to account for the extreme rapidity of light rays. Such an hypothesis then is inconsistent with our knowledge concerning gases.
Provided that there be no clear and absolute conflict with known laws of nature, there is no hypothesis so improbable or apparently inconceivable that it may not be rendered probable, or even approximately certain, by a sufficient number of concordances. In fact the two best founded and most successful theories in physical science involve the most absurd suppositions. Gravity is a force which appears to act between bodies through vacuous space; it is in positive contradiction to the old dictum that nothing can act but through some medium. It is even more puzzling that the force acts in perfect indifference to intervening obstacles. Light in spite of its extreme velocity shows much respect to matter, for it is almost instantaneously stopped by opaque substances, and to a considerable extent absorbed and deflected by transparent ones. But to gravity all media are, as it were, absolutely transparent, nay non-existent; and two particles at opposite points of the earth affect each other exactly as if the globe were not between. The action is, so far as we can observe, instantaneous, so that every particle of the universe is at every moment in separate cognisance, as it were, of the relative position of every other particle throughout the universe at that same moment of time. Compared with such incomprehensible conditions, the theory of vortices deals with commonplace realities. Newton’s celebrated saying *hypotheses non fingo*, bears the appearance of irony; and it was not without apparent grounds that Leibnitz and the continental philosophers charged Newton with re-introducing occult powers and qualities.
The undulatory theory of light presents almost equal difficulties of conception. We are asked by physical philosophers to give up our prepossessions, and to believe that interstellar space which seems empty is not empty at all, but filled with *something* immensely more solid and elastic than steel. As Young himself remarked,[423] “the luminiferous ether, pervading all space, and penetrating almost all substances, is not only highly elastic, but absolutely solid!!!” Herschel calculated the force which may be supposed, according to the undulatory theory of light, to be constantly exerted at each point in space, and finds it to be 1,148,000,000,000 times the elastic force of ordinary air at the earth’s surface, so that the pressure of ether per square inch must be about seventeen billions of pounds.[424] Yet we live and move without appreciable resistance through this medium, immensely harder and more elastic than adamant. All our ordinary notions must be laid aside in contemplating such an hypothesis; yet it is no more than the observed phenomena of light and heat force us to accept. We cannot deny even the strange suggestion of Young, that there may be independent worlds, some possibly existing in different parts of space, but others perhaps pervading each other unseen and unknown in the same space.[425] For if we are bound to admit the conception of this adamantine firmament, it is equally easy to admit a plurality of such. We see, then, that mere difficulties of conception must not discredit a theory which otherwise agrees with facts, and we must only reject hypotheses which are inconceivable in the sense of breaking distinctly the primary laws of thought and nature.
[423] Young’s *Works*, vol. i. p. 415.
[424] *Familiar Lectures on Scientific Subjects*, p. 282.
[425] Young’s *Works*, vol. i. p. 417.
*Conformity with Facts.*
Before we accept a new hypothesis it must be shown to agree not only with the previously known laws of nature, but also with the particular facts which it is framed to explain. Assuming that these facts are properly established, it must agree with all of them. A single absolute conflict between fact and hypothesis, is fatal to the hypothesis; *falsa in uno, falsa in omnibus*.
Seldom, indeed, shall we have a theory free from difficulties and apparent inconsistency with facts. Though one real inconsistency would overturn the most plausible theory, yet there is usually some probability that the fact may be misinterpreted, or that some supposed law of nature, on which we are relying, may not be true. It may be expected, moreover, that a good hypothesis, besides agreeing with facts already noticed, will furnish us with distinct credentials by enabling us to anticipate deductively series of facts which are not already connected and accounted for by any equally probable hypothesis. We cannot lay down any precise rule as to the number of accordances which can establish the truth of an hypothesis, because the accordances will vary much in value. While, on the one hand, no finite number of accordances will give entire certainty, the probability of the hypothesis will increase very rapidly with the number of accordances. Almost every problem in science thus takes the form of a balance of probabilities. It is only when difficulty after difficulty has been successfully explained away, and decisive *experimenta crucis* have, time after time, resulted in favour of our theory, that we can venture to assert the falsity of all objections.
The sole real test of an hypothesis is its accordance with fact. Descartes’ celebrated system of vortices is exploded, not because it was intrinsically absurd and inconceivable, but because it could not give results in accordance with the actual motions of the heavenly bodies. The difficulties of conception involved in the apparatus of vortices, are child’s play compared with those of gravitation and the undulatory theory already described. Vortices are on the whole plausible suppositions; for planets and satellites bear at first sight much resemblance to objects carried round in whirlpools, an analogy which doubtless suggested the theory. The failure was in the first and third requisites; for, as already remarked, the theory did not allow of precise calculation of planetary motions, and was thus incapable of rigorous verification. But so far as we can institute a comparison, facts are entirely against the vortices. Newton did not ridicule the theory as absurd, but showed[426] that it was “pressed with many difficulties.” He carefully pointed out that the Cartesian theory was inconsistent with the laws of Kepler, and would represent the planets as moving more rapidly at their aphelia than at their perihelia.[427] The rotatory motion of the sun and planets on their own axes is in striking conflict with the revolutions of the satellites carried round them; and comets, the most flimsy of bodies, calmly pursue their courses in elliptic paths, irrespective of the vortices which they pass through. We may now also point to the interlacing orbits of the minor planets as a new and insuperable difficulty in the way of the Cartesian ideas.
[426] *Principia*, bk. iii. Prop. 43. General Scholium.
[427] Ibid. bk. ii. Sect. ix. Prop. 53.
Newton, though he established the best of theories, was also capable of proposing one of the worst; and if we want an instance of a theory decisively contradicted by facts, we have only to turn to his views concerning the origin of natural colours. Having analysed, with incomparable skill, the origin of the colours of thin plates, he suggests that the colours of all bodies are determined in like manner by the size of their ultimate particles. A thin plate of a definite thickness will reflect a definite colour; hence, if broken up into fragments it will form a powder of the same colour. But, if this be a sufficient explanation of coloured substances, then every coloured fluid ought to reflect the complementary colour of that which it transmits. Colourless transparency arises, according to Newton, from particles being too minute to reflect light; but if so, every black substance should be transparent. Newton himself so acutely felt this last difficulty as to suggest that true blackness is due to some internal refraction of the rays to and fro, and an ultimate stifling of them, which he did not attempt to explain further. Unless some other process comes into operation, neither refraction nor reflection, however often repeated, will destroy the energy of light. The theory therefore gives no account, as Brewster shows, of 24 parts out of 25 of the light which falls upon a black coal, and the remaining part which is reflected from the lustrous surface is equally inconsistent with the theory, because fine coal-dust is almost entirely devoid of reflective power.[428] It is now generally believed that the colours of natural bodies are due to the unequal absorption of rays of light of different refrangibility.
[428] Brewster’s *Life of Newton*, 1st edit. chap. vii.
*Experimentum Crucis.*
As we deduce more and more conclusions from a theory, and find them verified by trial, the probability of the theory increases in a rapid manner; but we never escape the risk of error altogether. Absolute certainty is beyond the powers of inductive investigation, and the most plausible supposition may ultimately be proved false. Such is the groundwork of similarity in nature, that two very different conditions may often give closely similar results. We sometimes find ourselves therefore in possession of two or more hypotheses which both agree with so many experimental facts as to have great appearance of truth. Under such circumstances we have need of some new experiment, which shall give results agreeing with one hypothesis but not with the other.
Any such experiment which decides between two rival theories may be called an *Experimentum Crucis*, an Experiment of the Finger Post. Whenever the mind stands, as it were, at cross-roads and knows not which way to select, it needs some decisive guide, and Bacon therefore assigned great importance and authority to instances which serve in this capacity. The name given by Bacon has become familiar; it is almost the only one of Bacon’s figurative expressions which has passed into common use. Even Newton, as I have mentioned (p. 507), used the name.
I do not think, indeed, that the common use of the word at all agrees with that intended by Bacon. Herschel says that “we make an experiment of the crucial kind when we form combinations, and put in action causes from which some particular one shall be deliberately excluded, and some other purposely admitted.”[429] This, however, seems to be the description of any special experiment not made at haphazard. Pascal’s experiment of causing a barometer to be carried to the top of the Puy-de-Dôme has often been considered as a perfect *experimentum crucis*, if not the first distinct one on record;[430] but if so, we must dignify the doctrine of Nature’s abhorrence of a vacuum with the position of a rival theory. A crucial experiment must not simply confirm one theory, but must negative another; it must decide a mind which is in equilibrium, as Bacon says,[431] between two equally plausible views. “When in search of any nature, the understanding comes to an equilibrium, as it were, or stands suspended as to which of two or more natures the cause of nature inquired after should be attributed or assigned, by reason of the frequent and common occurrence of several natures, then these Crucial Instances show the true and inviolable association of one of these natures to the nature sought, and the uncertain and separable alliance of the other, whereby the question is decided, the former nature admitted for the cause, and the other rejected. These instances, therefore, afford great light, and have a kind of overruling authority, so that the course of interpretation will sometimes terminate in them, or be finished by them.”
[429] *Discourse on the Study of Natural Philosophy*, p. 151.
[430] Ibid. p. 229.
[431] *Novum Organum*, bk. ii. Aphorism 36.
The long-continued strife between the Corpuscular and Undulatory theories of light forms the best possible illustration of an Experimentum Crucis. It is remarkable in how plausible a manner both these theories agreed with the ordinary laws of geometrical optics, relating to reflection and refraction. According to the first law of motion a moving particle proceeds in a perfectly straight line, when undisturbed by extraneous forces. If the particle being perfectly elastic, strike a perfectly elastic plane, it will bound off in such a path that the angles of incidence and reflection will be equal. Now a ray of light proceeds in a straight line, or appears to do so, until it meets a reflecting body, when its path is altered in a manner exactly similar to that of the elastic particle. Here is a remarkable correspondence which probably suggested to Newton’s mind the hypothesis that light consists of minute elastic particles moving with excessive rapidity in straight lines. The correspondence was found to extend also to the law of simple refraction; for if particles of light be supposed capable of attracting matter, and being attracted by it at insensibly small distances, then a ray of light, falling on the surface of a transparent medium, will suffer an increase in its velocity perpendicular to the surface, and the law of sines is the consequence. This remarkable explanation of the law of refraction had doubtless a very strong effect in leading Newton to entertain the corpuscular theory, and he appears to have thought that the analogy between the propagation of rays of light and the motion of bodies was perfectly exact, whatever might be the actual nature of light.[432] It is highly remarkable, again, that Newton was able to give by his corpuscular theory, a plausible explanation of the inflection of light as discovered by Grimaldi. The theory would indeed have been a very probable one could Newton’s own law of gravity have applied; but this was out of the question, because the particles of light, in order that they may move in straight lines, must be devoid of any influence upon each other.
[432] *Principia*, bk. i. Sect. xiv. Prop. 96. Scholium. *Opticks*, Prop. vi. 3rd edit. p. 70.
The Huyghenian or Undulatory theory of light was also able to explain the same phenomena, but with one remarkable difference. If the undulatory theory be true, light must move more slowly in a dense refracting medium than in a rarer one; but the Newtonian theory assumed that the attraction of the dense medium caused the particles of light to move more rapidly than in the rare medium. On this point, then, there was complete discrepancy between the theories, and observation was required to show which theory was to be preferred. Now by simply cutting a uniform plate of glass into two pieces, and slightly inclining one piece so as to increase the length of the path of a ray passing through it, experimenters were able to show that light does move more slowly in glass than in air.[433] More recently Fizeau and Foucault independently measured the velocity of light in air and in water, and found that the velocity is greater in air.[434]
[433] Airy’s *Mathematical Tracts*, 3rd edit. pp. 286–288.
[434] Jamin, *Cours de Physique*, vol. iii. p. 372.
There are a number of other points at which experience decides against Newton, and in favour of Huyghens and Young. Laplace pointed out that the attraction supposed to exist between matter and the corpuscular particles of light would cause the velocity of light to vary with the size of the emitting body, so that if a star were 250 times as great in diameter as our sun, its attraction would prevent the emanation of light altogether.[435] But experience shows that the velocity of light is uniform, and independent of the magnitude of the emitting body, as it should be according to the undulatory theory. Lastly, Newton’s explanation of diffraction or inflection fringes of colours was only *plausible*, and not true; for Fresnel ascertained that the dimensions of the fringes are not what they would be according to Newton’s theory.
[435] Young’s *Lectures on Natural Philosophy* (1845), vol. i. p. 361.
Although the Science of Light presents us with the most beautiful examples of crucial experiments and observations, instances are not wanting in other branches of science. Copernicus asserted, in opposition to the ancient Ptolemaic theory, that the earth moved round the sun, and he predicted that if ever the sense of sight could be rendered sufficiently acute and powerful, we should see phases in Mercury and Venus. Galileo with his telescope was able, in 1610 to verify the prediction as regards Venus, and subsequent observations of Mercury led to a like conclusion. The discovery of the aberration of light added a new proof, still further strengthened by the more recent determination of the parallax of fixed stars. Hooke proposed to prove the existence of the earth’s diurnal motion by observing the deviation of a falling body, an experiment successfully accomplished by Benzenberg; and Foucault’s pendulum has since furnished an additional indication of the same motion, which is indeed also apparent in the trade winds. All these are crucial facts in favour of the Copernican theory.
*Descriptive Hypotheses.*
There are hypotheses which we may call *descriptive hypotheses*, and which serve for little else than to furnish convenient names. When a phenomenon is of an unusual kind, we cannot even speak of it without using some analogy. Every word implies some resemblance between the thing to which it is applied, and some other thing, which fixes the meaning of the word. If we are to speak of what constitutes electricity, we must search for the nearest analogy, and as electricity is characterised by the rapidity and facility of its movements, the notion of a fluid of a very subtle character presents itself as appropriate. There is the single-fluid and the double-fluid theory of electricity, and a great deal of discussion has been uselessly spent upon them. The fact is, that if these theories be understood as more than convenient modes of describing the phenomena, they are altogether invalid. The analogy extends only to the rapidity of motion, or rather the fact that a phenomenon occurs successively at different points of the body. The so-called electric fluid adds nothing to the weight of the conductor, and to suppose that it really consists of particles of matter is even more absurd than to reinstate the corpuscular theory of light. A far closer analogy exists between electricity and light undulations, which are about equally rapid in propagation. We shall probably continue for a long time to talk of the *electric fluid*, but there can be no doubt that this expression represents merely a phase of molecular motion, a wave of disturbance. The invalidity of these fluid theories is shown moreover in the fact that they have not led to the invention of a single new experiment.
Among these merely descriptive hypotheses I should place Newton’s theory of Fits of Easy Reflection and Refraction. That theory did not do more than describe what took place. It involved no analogy to other phenomena of nature, for Newton could not point to any other substance which went through these extraordinary fits. We now know that the true analogy would have been waves of sound, of which Newton had acquired in other respects so complete a comprehension. But though the notion of interference of waves had distinctly occurred to Hooke, Newton failed to see how the periodic phenomena of light could be connected with the periodic character of waves. His hypothesis fell because it was out of analogy with everything else in nature, and it therefore did not allow him, as in other cases, to descend by mathematical deduction to consequences which could be verified or refuted.
We are at freedom to imagine the existence of a new agent, and to give it an appropriate name, provided there are phenomena incapable of explanation from known causes. We may speak of *vital force* as occasioning life, provided that we do not take it to be more than a name for an undefined something giving rise to inexplicable facts, just as the French chemists called Iodine the Substance X, so long as they were unaware of its real character and place in chemistry.[436] Encke was quite justified in speaking of the *resisting medium* in space so long as the retardation of his comet could not be otherwise accounted for. But such hypotheses will do much harm whenever they divert us from attempts to reconcile the facts with known laws, or when they lead us to mix up discrete things. Because we speak of vital force we must not assume that it is a really existing physical force like electricity; we do not know what it is. We have no right to confuse Encke’s supposed resisting medium with the basis of light without distinct evidence of identity. The name protoplasm, now so familiarly used by physiologists, is doubtless legitimate so long as we do not mix up different substances under it, or imagine that the name gives us any knowledge of the obscure origin of life. To name a substance protoplasm no more explains the infinite variety of forms of life which spring out of the substance, than does the *vital force* which may be supposed to reside in the protoplasm. Both expressions are mere names for an inexplicable series of causes which out of apparently similar conditions produce the most diverse results.
[436] Paris, *Life of Davy*, p. 274.
Hardly to be distinguished from descriptive hypotheses are certain imaginary objects which we frame for the ready comprehension of a subject. The mathematician, in treating abstract questions of probability, finds it convenient to represent the conditions by a concrete hypothesis in the shape of a ballot-box. Poisson proved the principle of the inverse method of probabilities by imagining a number of ballot-boxes to have their contents mixed in one great ballot-box (p. 244). Many such devices are used by mathematicians. The Ptolemaic theory of *cycles* and *epi-cycles* was no grotesque and useless work of the imagination, but a perfectly valid mode of analysing the motions of the heavenly bodies; in reality it is used by mathematicians at the present day. Newton employed the pendulum as a means of representing the nature of an undulation. Centres of gravity, oscillation, &c., poles of the magnet, lines of force, are other imaginary existences employed to assist our thoughts (p. 364). Such devices may be called *Representative Hypotheses*, and they are only permissible so far as they embody analogies. Their further consideration belongs either to the subject of Analogy, or to that of language and representation, founded upon analogy.