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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.
It 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 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.
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 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 does 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 principle 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