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. 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 inconceiv able 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

1 Boyle's Physical Examen, p. 84

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.

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 Inuch 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.

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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