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 and planets 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 lead 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 direction of the trade winds. All these are crucial facts in favour of the Copernican theory.

Davy's discovery of potassium and sodium in 1807 was a good instance of a crucial experiment; for it decisively confirmed Lavoisier's views, and at the same time negatived the ancient notions of phlogiston.

Descriptive Hypotheses.

There are some, or probably many, hypotheses which we may call descriptive hypotheses, and which serve for little else than to furnish convenient names. When a certain phenomenon is of an unusual and mysterious 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. Thus if we are to speak of what constitutes electricity, we must search for the nearest analogy, and as electricity is chiefly characterised by the rapidity and facility of its movements, the notion of a fluid of a very subtle character presented itself as most 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 grossly invalid. The analogy extends only to the rapidity of motion, and 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 would be even more absurd than to reinstate the Corpuscular theory of light. An infinitely closer analogy exists between electricity and light undulations, which are about equally rapid in propagation; and while we shall probably continue for a long time to talk of the electric fluid, there can be no doubt that this expression merely represents some phase of molecular motion, some wave of disturbance propagating itself at one time through material conductors, at another time through the ethereal basis of light. The invalidity of these fluid theories is moreover shown in the fact that they have not led to the invention. of a single new experiment. When we speak of heat as flowing from one body to another, we likewise use a descriptive hypothesis merely; for Lambert's theory of the fluid motion of heat is no better than the Corpuscular theory of light.

Among these merely descriptive hypotheses I should be inclined to place Newton's theory of Fits of Easy Reflection and Refraction. That theory has been since exploded by actual discordance with fact, but even when

really entertained it did not do more than describe what took place. It involved no deep analogy to any other phenomena of nature, for Newton could not point to any other substance which went through these extraordinary changes. We now know that the true analogy would have been the 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 had 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 always at freedom again to imagine the existence of a new agent or force, and 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, while they were unaware of its real character and place in chemistry. 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 entirely discrete things. We have no right, for instance, to confuse Encke's supposed resisting medium with the ethereal basis of light. The name protoplasm, now so familiarly used by physiologists, is doubtless legitimate so long as we do not mix up different sub

y Paris, 'Life of Davy,' p. 274.

stances 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 appear to me to be mere names for an unknown and inexplicable series of causes which out of apparently similar conditions produce the most diverse results.

Hardly to be distinguished from descriptive hypotheses are certain imaginary objects or conditions which we often frame for the more ready investigation or comprehension of a subject. The mathematician, in treating abstract questions of probability, finds it convenient, to represent the conditions to his own or other minds by a concrete analogy in the shape of a material ballot-box. The fundamental principle of the inverse method of probabilities upon which depends the whole of our reasoning in inductive investigations is proved by Poisson, who imagines a number of ballot-boxes, of which the contents are afterwards supposed to be mixed in one great box (vol. i. p. 280). Many other such devices are also used by mathematicians. When Newton investigated the nature of waves, he employed the pendulum as a convenient mode of representing the nature of the undulation. Centres of gravity, oscillation, &c., poles of the magnet, lines of force, are other imaginary existences solely employed to assist our thoughts (vol. i. p. 422). All such creations of the mind may be called Representative Hypotheses, and they are only permissible and useful so far as they embody analogies. Their further consideration properly belongs either to the subject of Analogy, or to that of language and representation, founded upon analogy.

CHAPTER XXIV.

EMPIRICAL KNOWLEDGE, EXPLANATION, AND

PREDICTION.

THE one great method of inductive investigation, as we have seen, consists in the union of hypothesis and experiment, deductive reasoning being the link by which the experimental results are made to confirm or confute the hypothesis. Now when we consider this relation between hypothesis and experiment, it is obvious that we may classify our knowledge under four heads.

(1) We may be acquainted with facts or phenomena which have come under our notice accidentally or without reference to any special hypothesis, and which have not been brought into accordance as yet with any hypothesis. Such facts constitute what is called Empirical Knowledge.

(2) Another very extensive portion of our knowledge consists of those facts which, having been first observed empirically, have afterwards been brought into accordance with other facts by an hypothesis concerning the general laws applying to them. This portion of our knowledge may be said to be explained, reasoned, or generalised.

(3) In a third place comes the collection of facts, minor in number, but most important as regards their scientific value and interest, which have been anticipated by theory and afterwards verified by experiment.