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. 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 Cuviert emphatically remarks that * On Polarization of Heat, Edinb. Trans. vol. xiii. + Leçons d'Anatomie Comparée.

a naturalist, in his researches, happening to find only a hoof, directly and certainly infers that it was associated with grinding teeth, having flat surfaces, a long alimentary canal, a large stomach, or several; and many other similar characteristics. Yet such conclusions are of a nature strictly inductive. Again, the system of the organs of motion is universally found to be so adjusted, that a variation in the form of one bone is invariably accompanied by variations more or less in all the others. Thus in any new case which may present itself, from a single bone the skilful naturalist will often be able to infer the form of the whole skeleton. On what docs the legitimacy of such inferences depend: on what ground of confidence can such reasoning be pursued, but on the assurance of those unfailing principles of analogy which unquestionably pervade the entire range of organized nature, and thus supply the main ground of stability to these inductive conclusions.

That whenever a new plant or animal is discovered, we should never come to any thing anomalous or at variance with systematic order; but that, even in those instances which are apparently the most unlike any previously known, the skilful naturalist should always succeed in assigning to the production in question its precise place in the scale and order of organized beings, and that all fresh discoveries should but fill up blanks in the scheme, is the strongest proof of the existence of some prin

ciple of the most recondite uniformity throughout all the modifications of organized structures. In fact, to elucidate and develope such principles of uniformity and analogy, has been the very object of the labours of the most eminent naturalists; and the best proof of the actual prevalence and admirable unity of those principles is found in the increasing simplicity to which the arrangement of natural classes has been reduced.

Thus the researches of Cuvier reduce the laws of animated existence to only four principal "types," or general schemes of organization, founded on the presence or absence of vertebræ, after which (as he observes,) all animals appear to have been modelled; and of which the subordinate divisions are only comparatively slight modifications, founded on the developement or addition of certain parts, which produce no essential change in the original plan: viz., 1. The Vertebrata, with bony skeletons; 2. The Mollusca, soft, with shells; 3. The Articulata, jointed or ringed; 4. The Radiata, or zoophytes.

Within the limits of each of these four classes, Cuvier traced a precise set of analogies among all their various subdivisions; so that for every member or organ in one species, there was to be found invariably some member or organ in all the others, holding exactly the same place in relation to the general structure and nature of the animal; and thus between the two extreme instances which fall under any one class, though there might exist the

utmost possible dissimilarity in every respect, yet there was found the closest analogy; in every creature of that class could be pointed out by the skilful comparative anatomist, an exact correspondence in the nature and office of every part relative to the nature of the animal, though bearing not the slightest resemblance. When, however, these great classes themselves were compared together, such analogy seemed to be no further traceable. Each elass seemed to include a distinct plan of organization, possessing an unity within itself, but not apparently related to that of the other classes. But these views have been pushed further; another school of physiologists, among whom Geoffrey St. Hilaire stands most conspicuous, have contended that even these breaks between the four classes may be filled up, and new principles of analogy developed and traced out, by which these apparently distinct plans of organization may be shown to have a common system of relation; and thus throughout all classes, a principle of still more recondite connexion be perceived.

This principle carried out to its full extent, has been named the "unity of plan or of composition," or the " theory of analogues," and the particular views of structure by which it is upheld, have been designated as the " equilibrization of organs," or

other similar names.

While, however, the main principle of the reality of some such system of primitive types is universally recognised by naturalists,

yet considerable difference of opinion prevails as to the details of its application, and as to the extent to which it may be followed out. And the question which has thus arisen has occasioned considerable controversy between the partisans of the two rival schools; principally, perhaps, in consequence of its being mixed up with other topics, with which it has at least no necessary connexion; and to which we shall recur in another place. With reference to our present purpose, it will be sufficient to remark simply, that the question between these theories, or rather the question whether the extension given to the great principle of uniformity by the second of them, is true, must be decided merely by physiological evidence: it is purely a question of fact, and must be investigated by careful examination and enlightened comparison of facts and analogies, without any reference to the speculative topics with which it has been mixed up; a distinction which, however plain, seems to have been too much overlooked.

But however this question may be determined, our chief consideration should be to observe, either way, how beautiful an extension of the great principles of natural order and harmonious arrangement. is opened to our view. And it is the increasing assurance of this which is continually strengthening the foundation of all our inductive reasonings; of all consistent and profitable search into the laws of the material creation.