REMARKS, &C.
It will hardly be doubted by any one who attentively considers the method explained in the Novum Organum, which we have now attempted to sketch, that it contains a most comprehensive and rigorous plan of inductive investigation. A question, however, may occur, how far has this method,been really carried into practice by those who have made the great discoveries in natural philosophy, and who have raised physical science to its pre sent height in the scale of human knowledge ? Is the whole method necessary, or have not circumstances occurred, which have rendered experimental investigation easier in prac tice than it appears to be in theory ? To answer these questions completely, would re quire more discussion than is consistent with the limits of this Dissertation ; I shall, there , fore, attempt no more than to point out the principles on which such an answer may be founded.
In a very extensive department of physical science, it cannot be doubted that investi gation has been carried on, not perhaps more easily, but with a less frequent appeal to ex perience, than the rules of the Novum Organum would seem to require. In all the phy sical inquiries where mathematical reasoning has been employed, after a few principles have been established by experience, a vast multitude of truths, equally certain with the princi ples themselves, have been deduced from them by the mere application of geometry and algebra.
In mechanics, for example, after the laws of motion were discovered, which was done by experiment, the rest of the science, to a great extent, was carried on by reasoning from those laws, in the same manner that the geometer makes his discoveries by reasoning on the definitions, by help of a few axioms, or self-evident propositions. The only difference is, that, in the one case, the definitions and axioms are supplied solely from the mind it self, while, in the other, all the definitions and axioms, which are not those of pure geome try, are furnished by Bacon certainly was not fully aware of the advantages that were thus to accrue to the physical `sciences. He was not ignorant, that the introduction of mathematiCal reasoning into those sciences is not only possible, but that, under certain conditions, it may be at tended with the greatest advantage. He knew also in what manner this application had been abused by the Platonists, who had attempted, by means of geometry, to establish the first principles of physics, or had used them, in a.viomatis constituendis, which is ex actly the province belonging exclusively to experience. At the same time, he pointed
out, with great precision, the place which the mathematics may legitimately occupy, as serving to measure and compare the objects of physical inquiry. He did not, however, perceive beforehand, nor was it possible that he should, the vast extent to which the ap plication of that science was capable of being carried. In the book, De Augmentis, he has • made many excellent remarks on this subject, full of the sagacity which penetrated so far into futurity, but, nevertheless, could only perceive a small part of the scene which the genius of Newton was afterwards to unfold.
Hence, the route which leads to many of the richest and most fertile fields of science, is not precisely that which Bacon pointed out ; it is safer and easier, so that the voyager finds he can trust to his chart and compass alone, without constantly looking out, or hav ing the sounding-line perpetually in his hand.
Another remark I must make on Bacon's method is, that it •does not give sufficient im portance to the instantice radii, or those which furnish us with accurate measures of phy sical quantities. The experiments of this class are introduced as only subservient to prac tice ; they are, however, of infinite value in the theoretical part • of induction, or for as certaining the causes and essences of the things inquired into. We have an instance of this in the discovery of that important truth in physical astronomy, that the moon is re tained in her orbit by the force of gravity, or the same which, at the earth's surface, makes a stone fall to the ground. ' This proposition, however it might have been suspected to be true, could never have been demonstrated but by such observations and experiments as assigned accurate geometrical measures to the quantities compared. The semidiameter of the earth ; the velocity of falling bodies at the earth's surface ; the distance of the moon, and her velocity in her orbit ;—all these four ,elements must be determined with great precision, and afterwards compared together by certain theorems deduced from the laws of motion, before the relation between the, force which retains the moon in her orbit, and that which draws a stone to the ground, could possibly be discovered. The discovery also, when made, carried with it the evidence of demonstration, so that here, as in many other cases, the instantie radii are of the utmost importance in the theoretical part of physics.