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Yet, in fact, they revolve in the opposite direction. But why should we thus extend the inference? Perhaps we feel persuaded that there must be something common in the nature of all the planetary motions; nor can it be denied that such an idea is very natural; the only fault is, that the hypothesis is not comprehensive enough. Let us look at one other circumstance; the earth, Jupiter and Saturn have their satellites' orbits very nearly in the plane of the ecliptic. Suppose we were to affirm that those satellites, whose orbits are nearly in the plane of the ecliptic, have their motions from west to east, then our proposition would be completely verified; for the orbits of the satellites of Uranus differ from all the others in being almost perpendicular to the plane of the ecliptic. We should, therefore, now have a very fair ground of inductive inference in supposing some connexion between the inclination of the orbits and the direction of the motion. Again, there may possibly exist a relation of another kind; the peculiarities of this planet may form a connecting link, as it were, with other laws prevailing in a further series of planets beyond it; or if it be the last, in other systems beyond ours. From such instances as this we learn no disparagement to the uniformity of nature, though much caution in forming our conjectures as to its character; no distrust of the existence of order and arrangement, but only the necessity for a just ground of probability in tracing them.
(2.) We may adduce as another instance, the case which has been fully stated, and turned to such important purposes of argument, by Mr. Babbage*, derived from his own calculating engine. Considered here merely with reference to our present subject, it is perhaps one of the most remarkable illustrations which could be selected of the necessity of caution, and the most extended range of induction, before we can satisfactorily establish the absolute generality of any conclusion.
The case is briefly this: the machine being set in a particular manner, will go on producing the series of natural numbers, 1, 2, 3, 4, &c., and this may be carried to several thousands; from induction the observer might then infer that it would go on for as many thousands more. It in fact continues up to 100,000,000; the same induction would seem to render it next to certain that the series would be continued; it produces 100,000,001; but the next term, instead of being 100,000,002, will, in fact, be 100,010,002. Here we might infer analogy is entirely broken, and there is an end of all confidence in induction. But when the calculation is continued it is found that now a new but still perfectly regular law of a different kind begins to prevail. Again, at a further extremely remote period, this ceases, and another law commences; and these all connected by another rule; and so on without limit. The fault then was simply that our first induction was * Ninth Bridgwater Treatise, p. 36.
too limited; not that there was a failure in the real law.
(3.) To take another example:-Newton made observations on the rate at which hot bodies cool, and found a simple law to express how the rapidity changes as the time elapses. This was deduced by induction: but it did not extend beyond a certain range of temperature. Later observers went to higher temperatures, and found the law fail. Was this then any disparagement to the real existence of some analogy, or some determinate law? This question would receive but one answer from all who knew anything of physical reasoning; and that answer was speedily confirmed by the researches of Dulong and Petit, who established a more comprehensive law, applying accurately to all cases; and which, for lower temperatures, resolved itself into the simpler law before found by Newton.
(4.) Philosophers have been for the last century sedulously engaged in collecting observations on the direction, intensity, and variation of terrestrial magnetism. Various attempts have been made to frame some sort of theory to represent its laws, but none hitherto with more than very partial success. But are we, therefore, to infer that there really exists no fixed law, or regular cause of the phenomena? It is only a guiding principle of probability deduced by comparison with some corresponding class of effects, which is wanting. Now the later discoveries of electro-magnetism suggest the analogy
of a series of currents, and the idea of the globe as a vast electro-magnetic, or rather, perhaps, thermomagnetic, combination: which, again, is rendered extremely probable by the known metallic nature of its materials. Some theory of this kind is most likely to supply the clue which will ultimately conduct us to a systematic view of this curious subject.
(5.) To take one more instance: The extraordinary parallelism which subsists between the phenomena of light and sound has led to a theory for explaining the most perplexed and intricate results disclosed by optical experiments.
Two pipes, pitched a little out of unison, sounded together, produce, not a double sound, but beats, that is, alternations of sound and silence. Two streams of light, almost coinciding in direction, produce, not a double light, but stripes, that is, alternations of light and darkness.
Several distinguished philosophers had each proposed theories, which well explained some portion of the phenomena of physical optics. But it was not until the above analogy occurred to Dr. Young, that a general explanation was supplied, which he named the principle of interference. This doctrine, however, is only a branch and consequence of the more comprehensive theory of undulations, which, in the hands of Fresnel, Cauchy, and others, has now afforded the perfect explanation of nearly all the most complicated phenomena of light, which observation has presented.
There are, however, some phenomena which this theory does not perfectly account for. The absorption of certain of the primary rays, and not of others, by different transparent media, presents results of the most varied and apparently irregular kind. For á long time they were considered to defy all attempts at theoretical explanation. But even here a remarkably instructive instance of the value of philosophical analogy occurred. Sir J. Herschel brought arguments from such analogies alone, to bear on the question with the greatest effect; and by a striking reference to a parallel case in the doctrine of sound, (which is perfectly explained by the theory of vibrations of the air as the cause of sound,) he demonstrated, not that the undulatory theory explains the phenomena of absorption of light, but that those phenomena, however unexplained, constitute no valid objection against its truth. The paper*, independently of its physical interest, is well worthy of being studied by the intellectual philosopher. And, further, a very recent investigation by Baron Von Wrede, has at least shown that the analytical prosecution of the idea thus suggested gives a mathematical explanation of the general fact: though its precise laws have not yet been determined so as to afford data for any application of the test of numerical calculation†.
* London and Edinburgh Journal of Science, Dec. 1833.
+ Taylor's Foreign Scientific Memoirs, parts iii. and iv.