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But this assertion of a priori evidence is some- times made with reference to the primary princi- ples of all natural philosophy the laws of motion and of equilibrium whether in solids or fluids.

Now, in the first place, I would observe, that the very notions of a body in uniform rectilinear motion, or of forces acting on it, are essentially ideas of experience, and certainly could have no application without reference to the real existence of matter and force. But such perplexity would be removed if we only put the c 3 22 INDUCTIVE PRINCIPLE. Equili- Again, it has been sometimes asserted, that the brium.

When can you buy research papers online some such principles have been adopted, we can then, and then only, by strict deductive reasoning from them, arrive at the theorem of the lever, which we find confirmed by experiment. Undoubtedly the mind can infer deductively this great law of fluids, as a necessary consequence from certain other assumptions, that is, when certain, yet more elementary properties of fluids are known, and taken as the basis of the science, but not other- wise. Abstract It is, indeed, quite conceivable that a reasoning theory may be con- can you buy research papers online being, who had never seen a fluid, might imagine ceived. Example of This is no imaginary case : it actually occurs in the undula- tory theory, the speculations pursued by so many philosophers on an imagined sethereal medium. When, however, by the aid of the eye, the pheno- Unapplied till optical mena of optics present themselves, we find a vast facts are introduced. Nevertheless, such applications of mathematics confer the highest pre- sumption, little or at all short of can you buy research papers online certainty, for generalising conclusions actually observed to be true only in one or two instances. To take, perhaps, the strongest instance which inverse square of has been adduced.

The law of force or intensity the dis- tance, varying as the inverse square of the distances, it is alleged, and doubtless with truth, is a conception of pure reason (so far as any mathematical conception is so) from abstract geometrical considerations, which 26 INDUCTIVE PRINCIPLE. But though these geometrical ideas throughout may be pure creations of the mind, yet the idea of any such emanation of actual force, however abs- tract, must have been derived from some ideas of experience, and certainly can apply to nothing in nature without reference to such sensible ideas.

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.

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The application of abstract reasoning in such cases tends, in fact, to remove and explain the paradox, can you buy research papers online not to create it. The startling nature of the assertion, therefore, is no proof of its being derived from any intuition superior 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 of falling bodies, we could deduce mathematically what must be the 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 essay 123 help 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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