indeed, their meaning would, in some cases, be involved in absurdity and contradiction.

Thus, then, the most important part of the process of induction consists in seizing upon the probable connecting relation by which we can extend what we observe in a few cases to all. In proportion to the justness of this assumption, and the correctness of our judgment in tracing and adopting it, will the induction be successful. The methods by which a facility in discovering such relations, and a readiness in forming such judgment, may be attained and improved, are precisely the objects principally to be kept in view by the philosophical student who would prepare himself for the work of interpreting the phenomena of the natural world. The analogies to be pursued must be those suggested from alreadyascertained laws and relations. This, in proportion to the extent of the inquirer's previous knowledge of such relations subsisting in other parts of nature, will be his means of guidance to a correct train of inference in that before him.

And he who has, even to a limited extent, been led to observe the connexion between one class of physical truths and another, will almost unconsciously acquire a tendency to perceive such relations among the facts continually presented to him. The truth of the remark to which we have been thus led is amply confirmed by the history of philosophical discovery.

In point of fact, discoveries, commonly termed

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inductive, have very seldom been really attained by the mere process of amassing collections of individual facts. It has been almost invariably the case that hypothesis has preceded observation; and that the discoverer has in truth only verified, by an appeal to experiment, the general theory which he had already imagined. The happy selection of such hypotheses is that which characterizes, and in fact constitutes, philosophical genius. And a just appreciation of the use of such imaginary provisional assumptions, eminently distinguishes the rational inquirer from the speculative visionary. The true philosopher neither discards hypothesis on the one hand, nor yields himself up to it on the other; but rates it at its proper value, and turns it to its legitimate use. He is always ready to reject an assumed theory the moment he finds it unsupported by fact: but if it be once duly substantiated, to adopt it, and be prepared to follow it out into all its legitimate consequences, however at variance with received notions-however contrary to established prejudices-however opposed to the prepossessions, the bigotry, the cherished delusions of mankind.

And the more extensive his acquaintance with nature, the more firmly is he impressed with the belief that some such relation must subsist in all cases, however limited a portion of it he may be able actually to trace. And it is by the exercise of an unusual skill in this way, that the greatest philosophers have been able to achieve their triumphs in

the reduction of facts under the dominion of general laws.

But important as these natural analogies are to the philosopher, they are yet of a nature which renders it difficult to make them generally appreciated: and, unless by actual and attentive study of physical science, it is difficult to convey an adequate conception of the irresistible claim to acceptance with which they present themselves to the mind of a person even moderately versed in such inquiries. Yet they are, in fact, no more than extensions of the very same elements of thought, which seem implanted in our nature; by which all our acquaintance with sensible objects is, in the first instance, acquired; and by which we are continually and unconsciously storing our minds with that knowledge which is so necessary for all the purposes of our existence; those natural persuasions upon which all uniform convictions, and all consistent conduct, is based;-and without which life would be a continued state of infancy.

Mathematical Laws.

Ir is not, perhaps, until we come to contemplate natural phenomena, exhibited in the form of numerical results, and find those data reducible to mathematical laws, that we fully appreciate the reality and exactness of that uniformity by which all nature works. The coincidence with such laws, is that

which, above all others, impresses us with the conviction of invariable order and uniformity pervading the material universe.

We find this, in the first instance, in the reduction of vast collections of observed numerical results, under simple mathematical formulas. But the more extended application of mathematical analysis powerfully augments the impression produced on our minds by the conspiring inductions, and corroborating generalizations, of purely physical investigations. From some one very simple, remote, and abstract datum, obtained from elementary physical facts, we often proceed by purely mathematical reasoning, perhaps through a long and intricate deduction, which at length brings us to the conclusion, that, under certain conditions, a particular kind of action ought to take place; and even the precise amount of its effects ought to be such as are given by a certain analytical expression. The results of observation exactly accord with these deductions; and even the minutest variations in the effects are exactly represented by calculation from the formula of theory.

We have occasionally singular exemplifications of the existence of recondite principles of analogy, in the coincidence of phenomena with the symbolical indications of mathematical analysis. A mathematical formula is found, which expresses the law of a certain class of phenomena. The analytical language of symbols admits, perhaps, of certain changes, or

embraces certain cases, not at all contemplated in the first numerical establishment of the law; but dependent purely upon abstract algebraical rules and transformations. These symbolical changes shall be found to have physical cases exactly corresponding to them.

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In the higher departments of physical optics, this has been most surprisingly exemplified. We need only cite the marvellous prediction of the conversion of plane into circular polarization of light, by two internal reflections in glass, made and verified by M. Fresnel, entirely upon the strength of certain mechanical and mathematical analogies. A conclusion," (as Professor Forbes justly remarks,) "which no general acuteness could have foreseen; and which was founded on the mere analogy of certain interpretations of imaginary expressions. The mere reasoner about phenomena could never have arrived at the result, the mere mathematician would have repudiated a deduction founded upon analogy alone*.”

Induction in Natural History.

THERE is, perhaps, no branch of science in which the use of analogy as subservient to the process of induction, is more conspicuously and instructively displayed than in comparative anatomy and physiology. Thus Cuvier† emphatically remarks that * On Polarization of Heat, Edinb. Trans. vol. xiii. + Leçons d'Anatomie Comparée.