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Equal areas Again : to take what is almost an equally striking proved abs-.

It is undeniably a pure result of reason that a me- taphysical point revolving about another metaphysical point by virtue of an impulse conspiring with a cen- tripetal force tending to that point, varying according to any law whatsoever, must describe areas propor- tional to the times. Where- ever these forces exist in nature, we reason deduc- tively to the conclusion of a description of equal areas, and we find it confirmed by observation. Any new All truths paradoxes truth, even a mere matter of observation, is a paradox to prepos- in popular estimation, if it contradict a received pre- judice. The application of abstract reasoning in such cases tends, in fact, to remove and explain the paradox, not to create it. The startling nature of the assertion, therefore, is no proof of its being derived from any intuition superior help with papers to sense.

Deductive The question between the inductive and the de- proof only from physi- ductive process is merely a question of degree : in cal princi- ples more some cases the abstract part of the process may be or less re- mote, longer, and its origin more remote from material facts in others less so. Theory of matical theories, we might discover experimentally pendulum. But, again: if we knew in the first instance, by experimental trial, the law help with papers of falling bodies, we could deduce mathematically what must be the help with papers law of the pendulum, that is, it is a necessary consequence in reason from a simpler mechanical truth, provided that reason be first furnished with that simpler truth. But even, still further : if we investigated, on pure theory, the effects of a constant force, we should deduce the same law for bodies moving from a state of rest under its influence, and this would apply directly to the deduction of the laws of a body 30 INDUCTIVE PRINCIPLE. But the real application of such reasoning essen- tially involves the actual existence in nature of such a force as that of gravity, which can only be derived from observation. Many would have been the hypotheses of peculiar magnetic, electric, or other causes, for the observed deviation.

Yet more astonishingly paradoxical are the effects Paradoxes of the gy- exhibited by means of the gyroscope, which seem to roscope. To mention one only : a wheel loaded round its circumference, in rapid rotation at one end of a horizontal axis, having the other end merely resting on a pivot, is supported on that pivot alone against gravity, the whole at the same time revolving round the pivot.

Scarcely less remarkable is the application of this i instrument by M. If, however, he set out with a mathematical know- ledge of the principle of the " composition of rotatory motion," and proceeded deductively, the explanation is easy, and its relation to a number of other im- portant cases readily manifest. Yet the application of this mathematical theory requires the idea of a material body in rotation, inclined The ancients, notwithstanding all their refined plane. But it was not until Stevin reasoned, not upon any abstruse axioms, but on simple mechanical considerations, that the demon- stration was discovered. A highly instructive instance of the application Discovery of magneto- of an abstract principle to physical discovery may be electricity, found in the way in which Faraday reasoned to the discovery of magneto-electricity, which I cannot de- scribe better or more briefly than in the words of Mr.

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Hence originates the science of magneto-electricity, the true converse of electro-magnetism. Yet these and the like instances are not at all ESSAY I. Thus a simple analysis of the actual train of argu- conclusion, ment tends to dispel the mystification and confu- No really sion which have sometimes arisen on the subject proof o7 of abstract reasoning applied to physical subjects, truth. Necessary A confusion of ideas is sometimes introduced by truths only necessary the use of the term " necessary" dependence or conse- quences. Speculative The subject here discussed, is beautifully illus- ideas of (Ersted. But these cases are, after all, not precisely in point to the original question, since here the starting-point was obviously previous inductive knowledge. These distinctions are important to the funda- Accordance of reason mental analysis of our reasonings on which we ad- and nature. CErsted has well remarked that it is a common error to imagine matter something constant and invariable. But the permanence and invariability of nature are not found in its individual parts, which are all undergoing perpetual changes. The invari- able, he argues, is found only in the abstract nature of things : " nothing is invariable in nature but laws which may be called the thoughts of nature.

In short, nature is to me the revelation of an endless living and acting reason. Tendency ALL branches of inductive science continually tend of sciences towards more and more towards a grand unity of principle. We perceive this to a partial and limited extent in every lesser advance of discovery : in proportion as new facts accumulate and become embarrassing from their multiplicity, sooner or later some happy advance in generalisation is always found to help with papers occur by which they are simplified and reduced to some ESSAY I. In the science of the ancients (exact as it was in progress of some limited departments, each within itself) all eneralisa - tion and branches were isolated and disconnected : and all Uf? All the first great modern advances were directed First ad- vances.

The peculiar character of high generalisation which results out of an ap- parently immensely complicated mass of small de- tails, is perhaps one of the most striking features of this wonderful series of investigations. It is impossible here to do more than select one or two instances. Magnetism Few generalisations of a more striking character and dia- magnetism. Action of But in this union of relation between magnetic magnetism on light. What could be a more singular and striking identification of properties in cases apparently the most remote from each other than the production of rotatory polarisation in light passing through quartz and some other substances, and in passing through ESSAY I.

Or to go back to an earlier discovery : Grand indeed was the conception of the principle Definite electrolysis. Equally important, though apparently remote from either of the last was the principle of definite proportions in atomic combinations disclosed by Dalton.

These two comprehensive generalisations, each equally wonderful in itself, yet seemingly uncon- nected, it was reserved for the penetrating genius of Faraday to place in intimate connection and to unite in a still higher bond of generality.

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