The principles of science

by William Stanley Jevons

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.

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.

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.”

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.