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.1 Encke was quite justifed 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

1 Paris, Life of Davy, p. 274.

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.

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.

CHAPTER XXIV.

EMPIRICAL KNOWLEDGE, EXPLANATION, AND PREDICTION.

INDUCTIVE investigation, as we have seen, consists in the union of hypothesis and experiment, deductive reasoning being the link by which 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 which have not yet been brought into accordance with any hypothesis. Such facts constitute what is called Empirical Knowledge.

(2) Another extensive portion of our knowledge consists of 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 the third place comes the collection of facts, minor in number, but most important as regards their scientific interest, which have been anticipated by theory and afterwards verified by experiment.

(4) Lastly, there exists knowledge which is accepted solely on the ground of theory, and is incapable of experimental confirmation, at least with the instrumental means in our possession.

It is a work of much interest to compare and illustrate the relative extent and value of these four groups of knowledge. We shall observe that as a general rule a great branch of science originates in facts observed accidentally,

or without distinct consciousness of what is to be expected. As a science progresses, its power of foresight rapidly increases, until the mathematician in his library acquires the power of anticipating nature, and predicting what will happen in circumstances which the eye of man has never examined.

Empirical Knowledge.

By empirical knowledge we mean such as is derived directly from the examination of detached facts, and rests entirely on those facts, without corroboration from other branches of knowledge. It is contrasted with generalised and theoretical knowledge, which embraces many series of facts under a few comprehensive principles, so that each series serves to throw light upon each other series of facts. Just as, in the map of a half-explored country, we see detached bits of rivers, isolated mountains, and undefined plains, not connected into any complete plan, so a new branch of knowledge consists of groups of facts, each group standing apart, so as not to allow us to reason from one to another.

Before the time of Descartes, and Newton, and Huyghens, there was much empirical knowledge of the phenomena of light. The rainbow had always struck the attention of the most careless observers, and there was no difficulty in perceiving that its conditions of occurrence consisted in rays of the sun shining upon falling drops of rain. It was impossible to overlook the resemblance of the ordinary rainbow to the comparatively rare lunar rainbow, to the bow which appears upon the spray of a waterfall, or even upon beads of dew suspended on grass and spiders' webs. In all these cases the uniform conditions are rays of light and round drops of water. Roger Bacon had noticed these conditions, as well as the analogy of the rainbow colours to those produced by crystals.1 But the knowledge was empirical until Descartes and Newton showed how the phenomena were connected with facts concerning the refraction of light.

There can be no better instance of an empirical truth

1 Opus Majus. Edit. 1733. Cap. x. p. 460.