are we to think of the force of gravity, which appears to reach the sun in an instant-so short that no calculations have yet been able to detect any interval at all? In fact there seems some reason to suppose that gravity is felt instantaneously throughout the immeasurable regions of

space.

The undulatory hypothesis of light presents features equally extraordinary and inconceivable. That light does consist of minute but excessively rapid vibrations of something occupying space, is almost certain, because of the great harmony which this hypothesis introduces into the exceedingly various and complicated phenomena of light, and the explanation which it affords of the analogy of light to sound. It is difficult indeed to imagine that anything can oscillate so rapidly as to strike the retina of the eye 831,479,000,000,000 in one second, as must be the case with violet light according to this hypothesis. But this is nothing to the difficulty of imagining space to be filled with solid ether of extreme rigidity and elasticity, but which nevertheless offers no appreciable resistance to the passage through it of ordinary matter, and does not itself possess any gravity*. It has been asserted indeed that the retardation in the return of comets is due to friction against this ether, and Mr Balfour Stewart believes he has produced heat by friction of a metallic disc against the ether in a vacuum. Should these assertions prove to be true we have new facts in harmony with the theory of light, which would thereby become less hypothetical than before.

There is no difficulty now in perceiving the part which hypothesis plays in the deductive method of scientific investigation considered in the last lesson. The preliminary induction is replaced more or less completely by

* See Sir John Herschel's Familiar Lectures, p. 315, &c.

imagining the existence of agents which we think adequate to produce the known effects in question. If it is our object to explain the causes of ebbing and flowing wells, which occur in many parts of the world, we cannot possibly proceed by first exploring the interior of the earth, until we can discover the source of a spring, and observe its circumstances. We are obliged to imagine cavities and channels of various forms, until we conceive such an apparatus as will, in accordance with known laws of hydrostatics, occasion the irregular flowing of water in the way observed. If we can show that cavities of a particular form will produce that effect, and can think of no other mode in which it could be produced, the hypothesis becomes established as almost a certain fact.

It is the same with any great hypothesis like that of the theory of light. We have no means of directly observing and measuring the qualities of the ether which is the medium of light. All we know about this ether at present is derived from the observed phenomena of light. Hence we are driven to invent something and endow it with qualities from which we may calculate, according to some of the principles of mechanics, the effect to be expected ; and finding that these effects may be made to harmonize with those actually observed, we depend upon this coincidence to prove the existence of the ether. The truth of a hypothesis thus altogether depends upon subsequent verification and accordance with observed facts. Το invent hypotheses which cannot thus be verified, or to invent them and then neglect the verification, leads to no result at all, or to fallacy. But when the verification is careful and complete no reproach can be brought against the employment of hypothesis. It becomes, perhaps, as certain as any other mode of investigation, and is at any rate indispensable. There was, in fact, little truth or reason in Newton's celebrated protest against the use of

hypothesis-"Hypotheses non fingo." The fact is that as his theory of gravitation rested upon the greatest and most successful of hypotheses, so his views of the material nature of light and the causes of its peculiar phenomena involved a false hypothesis, which has long since been completely disproved.

The word theory has constantly been used in the last few lessons, and deserves some examination. It comes from the Greek Oeopía, meaning contemplation, reflection or spéculation; but this gives us little clue to its modern use. In reality the word is highly ambiguous, being sometimes used as equivalent to hypothesis, at other times as equivalent to general law or truth. When people form theories concerning comets, the sun, the cause of earthquakes, &c., they imagine a great many things which may or may not exist; such theories are really complicated hypotheses, and should be so called. In this sense there are two theories of electricity, one of which supposes the existence of a single fluid which accumulates in some places and has then a tendency to discharge itself towards places where there is a deficiency, just as water always tends to find its level; the other supposes the existence of two fluids which are commonly united, but when separated tend to rush back into union again. These so-called theories are really hypotheses, because we have no independent evidence of the existence of any fluid, and it is now almost certain that there is no such thing. The atomic theory, again, is really a hypothesis suggested by Dalton to explain the remarkable laws which he detected in the proportions of chemical elements which combine together. It is a valid hypothesis in so far as it does really explain the fixedness of the quantities which combine; but it is purely hypothetical as regards the shapes, properties or absolute magnitudes of the atoms, because we have no facts which it can har

monise in these respects, and no apparent means of gaining them.

In another and more proper sense theory is opposed to practice, just as the general is opposed to the particular. The theory of gravitation means all the more general laws of motion and attraction on which Newton founded his system of the Universe. We may know what those laws are without being able to determine the place of a planet or make any practical use of them; the particular results must be calculated out by skilful astronomers before navigators, travellers or others can make practical use of them in the determination of the latitude or longitude. When we speak of the mathematical theory of sound, the lunar theory, the theory of the tides, the word is employed without any special reference to hypothesis, and is merely equivalent to general knowledge or science, implying the possession of a complete series of general and accurate laws, but in no way distinguishing them from accurate knowledge in general. When a word is really used in an equivocal manner like theory, it is not desirable to attempt to give it an accurate definition which would be imaginary and artificial.

The word fact is used very often in this as in most books, and demands a few remarks. It is derived from factum, the past participle of facere, to do, and would thus mean something which is done, an act, or deed; but the meaning is evidently greatly extended by analogy. We usually oppose to each other fact and theory, but just as theory seems to have two ambiguous meanings, so I believe that fact is ambiguous. Sometimes it means what is certain and known by the evidence of the senses, as opposed to what is known only probably by hypothesis and inference; at other times it is contrasted to a general law, and is equivalent to a particular instance or case. A law of great generality may often be as certain and true,

especially in mathematics, as the particular facts coming under it, so that the contrast must in this case be that between the general and particular. We often use the word too in common life, as merely equivalent to truth; thus we might say, "It is a fact that the primary laws of thought are the foundation of reasoning." In short, as theory means ambiguously what is hypothetical, general, abstract or uncertain, so fact is equally ambiguous, and means confusedly what is intuitively known, particular, concrete or certain.

Mill's System of Logic, Book III. Chapters 12, 13 and 14, Of Explanation, and Hypothesis.

LESSON XXXII.

CLASSIFICATION, AND ABSTRACTION.

IN an earlier Lesson, upon the subject of the Predicables, we considered the doctrine of classification as it was treated by logicians many centuries ago. The progress of science, however, during the last two centuries has caused great attention to be given to the true principles on which we can arrange a great multitude of diverse objects in order, and we have to consider what are the characteristics of a natural and perfect system of classification.

It may be said, indeed, that the subject we are treating is coextensive with the science of logic. All thought, all reasoning, so far as it deals with general names or general notions, may be said to consist in classification. Every common or general name is the name of a class, and every name of a class is a common name. "Metal" is the name