"the ex-post-facto obviousness of discoveries, is a delusion to which we are liable with regard to many of the most important discoveries.”

The validity of a Law of Nature thus discovered, as it were, by a happy casualty, is regarded as sufficiently established by comparison with but very few of the observed data from which it was educed. Thus, Dalton's magnificent generalization, coextensive with all matter, and now verified by almost countless analyses, that chemical elements combine only in definite, reciprocal, and multiple proportions, was first suggested to him during his examination of only two compounds; "and was asserted generally," says Dr. Whewell, "on the strength of a few facts, being, as it were, irresistibly recommended by the clearness and simplicity which the notion possessed." What is the ground of this bold anticipation of the universality of a Law as yet verified only by a very few examples, when, in the case of a General Fact, as already shown, a very extensive Induction may still leave us in doubt whether the supposed truth may not be contradicted by the next instance that arises? In general terms, the answer is obvious. Simple uniformities, such as are comprehended in a General Fact, may be merely accidental; to recur to an instance already cited, all ruminating animals now known divide the hoof; but as the number of such animals is not very great, this simple coincidence of two properties may be as casual as the experience of an individual observer who has never happened to see a squint-eyed person that had not also brown hair. But complex uniformities, such as are marshalled into the symmetrical series called Laws of Nature, and thus expressed in one formula, cannot be regarded as accidental. As the number of individual facts comprehended in one of these series is very great, it is incredible that mere chance should throw even a portion of them into symmetrical groups, bearing a constant ratio to

each other. Hence, if we can detect but a portion, even a fragment, of such a series, we feel assured that it will prove to be continuous, that the Law will not change, that the uniformity will be carried out to the end. Only the action of a permanent and unvarying Cause, it is assumed, could so harmonize results. Nay, so strong is our assurance of the universality of the principle thus discovered, though it seems as yet very imperfectly verified, that, when an anomalous or inconformable instance actually arises, we seek at once for the means of eliminating it, or explaining it away, instead of allowing it to wrest the inchoate discovery out of our grasp and send us to the work of research again. We class the exception immediately among those apparent exceptions which really confirm the rule; -just as we now see that the rising of a balloon in the atmosphere does not contradict, but actually verifies, the Law of gravita

tion.

We come, then, to the conception of a physical Cause, as indicating the third or highest stage in the generalizations of science, and therefore as bearing the same relation to a Law of Nature, that such a Law bears to a General Fact. As thus understood, a Cause is simply a higher Law, under which several inferior Laws are subsumed; it appears as the original principle, of which these lower Laws are the derivatives by immediate and necessary consequence. Thus, the theory of gravitation, or the doctrine that every body attracts every other body with a force which is directly as its mass and inversely as the square of its distance, is the statement of a universal principle, under which not only Kepler's Laws of the planetary motions, but the Laws of falling bodies, of the equilibrium of fluids, &c., are subsumed in this sense; that if we take for granted the existence of the force or physical Cause, termed Gravity, which this theory assumes, then these inferior Laws may all be deduced from it by Demonstrative Reasoning. That

such Deduction is possible, is the only proof we have that such a force or Cause exists. The hypothetical force, for it is nothing more, represents the inferior Laws that are subsumed under it, merely because it is an expression of them in a single formula. It may well happen that two or more such formulas may be devised, differing essentially from each other, yet answering equally well all the conditions of the case, as the given Laws may logically be deduced from either of them. For instance: all, or the greater part, of the Laws of vision and light may be explained with equal precision and accuracy either on the doctrine of emission, or on the undulatory theory. Two such hypotheses correspond to two very dissimilar engines, which different mechanics might invent, in order to cause the hands of a clock to make the required movements over the dial-plate, or the little balls in an orrery to counterfeit the motions of the solar system. It is no more necessary to suppose that such an attractive force as Gravity, or such a luminiferous ether as the undulatory theory treats of, actually exists, than it is to believe that a set of wheels and pinions, like that which moves an orrery, really produces the motion of the planets. All that the theory does for us is to represent the phenomena correctly; no one who understands the subject supposes that the hypothetical force or Cause, which is merely a convenient supposition for the theorist, actually produces those phenomena.

It is evident that such Causes as we are now speaking of are merely the highest generalizations of Physical Science, and that the invention of them for they are rather invented than discovered affords not the slightest additional evidence of the universality of those Laws of Nature which they represent, or which are subsumed under them. The proof, indeed, proceeds in the opposite direction; the only evidence we have that the right Cause has been assigned is, that it correctly represents the Laws which are

placed under it. When it is demonstrated that the Law may be deduced from such a Cause, the real course of the argument is, from the admitted validity of the Conclusion. to infer the soundness of the Premise. Gravity does not cause heavy bodies to fall to the ground, nor does it bind the planets to their orbits; but Gravity is rightly considered as a "physical Cause," in the technical sense of that phrase, because its hypothetical existence enables us correctly to represent in a single formula the phenomena of falling bodies and of the planetary motions.

The higher generalizations, then, depend exclusively, for proof of their correctness, on the validity of those which are next below them. When the proper Law of Nature is provisionally assumed, certain consequences can be demonstrated to follow which agree with the General Facts that were previously established on Inductive evidence; when the proper physical Cause is assumed, we can logically make certain Deductions from it which harmonize with the Laws of Nature which this Cause was invented to express. Neither the Law nor the Cause brings any additional evidence of its own, but both alike depend for proof, in the last analysis, on the validity of the Induction by simple enumeration by which we first collected their common basis, the General Facts. The process of verifying both consists in enlarging the Induction, but not in altering its character; both the Law and the Cause being assumed to be universally true, we make further Deductions from them, and still find these to coincide with the observed Facts. In other words, we first reason Inductively from some to all, and then, assuming provisionally that the principle holds true of all, we reason from it Deductively to other some, and find that these also are confirmed by observation, so that they reflect evidence upon the Law or the Cause of which they are the logical consequences. Turn the matter as we may, Induction by simple enumeration is

still the basis of the whole procedure, and the discovery or invention of Laws of Nature, or physical Causes, only supplies names and formulas of expression for the successive steps of generalization, as we form one after another the proper hierarchy of Concepts.

We can now see more plainly than before the correctness of the doctrine already advanced, that the strong and unhesitating belief which we accord to any well-established Law of Nature, and which we indicate by saying that an event happening under it takes place by a physical necessity, is not due to the strength of the Induction through which the Law was discovered, but to our absolute a priori conviction of the fixedness of the relation which connects every effect with its efficient Cause. The Law is discovered by Induction; but it is proved by a different process, -- by bringing it under a necessary a priori conception of the human mind, that of Efficient Cause, and thereby subjecting it to the principle of Causality, that every event must have a Cause, and must be proportional to that Cause.

In speaking of the use which is sometimes made of Inductive reasoning in pure mathematics, as in the case of Newton's discovery of the Binomial Theorem, Mr. Mill maintains that the process of thought in such cases is not an Induction properly so called, but is governed by certain "a priori considerations (which might be exhibited in the form of demonstration), that the mode of formation of the subsequent terms, each from that which preceded it, must be similar to the formation of the terms which have been already calculated." But it was certainly Inductive in this respect, that the observed regular formation of the first few terms of the series originally led Newton to anticipate that all the other terms must be formed in the same manner, and to act upon this anticipation, use the Theorem for a long time,

that is, confidently to without giving himself

the trouble to work out a demonstration of it. Undoubt