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 a 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 calculationt.

* London and Edinburgh Journal of Science, Dec. 1833.
+ Taylor's Foreign Scientific Memoirs, parts iii. and iv.

Rejection of Principles foreign to Analogy.

Of this, however, we may be most certainly convinced, that although, in any particular instance, we may fail in tracing out the real connexion of natural causes by this or that assumed analogy, which may in itself appear very conformable to probability, we shall assuredly never succeed by adopting any hypothesis which is independent of natural analogies, or foreign to them; we shall never arrive at any satisfactory explanation of nature, or any real philosophical truth, by having recourse to other principles ALIEN from those of induction. Nature must always be her own interpreter.

If we adopt hypotheses for example built upon metaphysical or moral considerations, we may be certain they will never conduct us to physical truth. Whatever may be their merits in themselves, and when directed to their proper purposes, they are totally misapplied in physical subjects: or rather, it must be from an entire misapprehension of the nature and objects of physical researches, that we shall ever be induced to connect them with such speculations.

Example: Theories of Cosmogony.

In the earlier stages of geological science it was in a singular degree abandoned, as it were, to groundless

hypotheses, often framed in utter defiance of all principles of analogy. But a more just and rational method has since begun to prevail; a method which (whatever difference of opinion may exist on some points of detail) must be recognised by all philosophic inquirers, as sound in its principle, viz., that of reasoning cautiously on the facts, from the known to the unknown, by the guidance of rationally adopted analogies. Speculations, which, in accordance with some formerly received views, once passed current for sound geology, were really such as altogether to discredit the uniformity of natural causes. But the more closely we adhere to sober and legitimate induction, the more will every discovery indicate the unbroken uniformity of plan, which has prevailed through the immeasurable periods of past stages of organized life. "If," says Mr. Lyell, "instead of inverting the natural order of inquiry, we cautiously proceed in our investigations, from the known to the unknown, and begin by studying the most modern periods of the earth's history, attempting afterwards to decipher the monuments of more ancient changes, we can never so far lose sight of analogy as to suspect that we have arrived at a new system, governed by different physical laws."

The necessity of proceeding on such principles, to the utter rejection of all gratuitous suppositions, or cherished prejudices, is now becoming more generally acknowledged: the grand conclusions deduced are * Geology, vol. i. p. 160.