A Theory of Natural Philosophy [antikvár]

INTRODUCTION^LTHOUGH the title to this work to a very large extent correctly describes the contents, yet the argument leans less towards the explanation of a theory than it does towards the logical exposition of the results that must follow from the acceptance of certain fundamental assumptions, more or less generally admitted by natural philosophers of the time. The most important of these assumptions is the doctrine of Continuity, as enunciated by Leibniz. This doctrine may be shortly stated in the words : " Everything takes place by degrees " ; or, in the phrase usually employed by Boscovich : " Nothing happens per saltum.^^ The second assumption is the axiom of Impenetrability ; that is to say, Boscovich admits as axiomatic that no two material points can occupy the same spatial, or local, point simultaneously. Clerk Maxwell has characterized this assumption as an unwarrantable concession to the vulgar opinion." He considered that this axiom is a prejudice, or prejudgment, founded on experience of bodies of sensible size. This opinion of Maxwell cannot however be accepted without dissection into two main heads. The criticism of the axiom itself would appear to carry greater weight against Boscovich than against other philosophers; but the assertion that it is a prejudice is hardly warranted. For, Boscovich, in accepting the truth of the axiom, has no experience on which to found his acceptance. His material points have absolutely no magnitude ; they are Euclidean points, " having no parts." There is, therefore, no reason for assuming, by a sort of induction (and Boscovich never makes an induction without expressing the reason why such induction can be made), that two material points cannot occupy the same local point simultaneously ; that is to say, there cannot have been a prejudice in favour of the acceptance of this axiom, derived from experience of bodies of sensible size; for, since the material points are non-extended, they do not occupy space, and cannot therefore exclude another point from occupying the same space. Perhaps, we should say the reason is not the same as that which makes it impossible for bodies of sensible size. The acceptance of the axiom by Boscovich is purely theoretical; in fact, it constitutes practically the whole of the theory of Boscovich. On the other hand, for this very reason, there are no readily apparent grounds for the acceptance of the axiom ; and no serious arguments can be adduced in its favour ; Boscovich's own line of argument, founded on the idea that infinite improbability comes to the same thing as impossibility, is given in Art. 361. Later, I will suggest the probable source from which Boscovich derived his idea of impenetrability as applying to points of matter, as distinct from impenetrability for bodies of sensible size.Boscovich's own idea of the merit of his work seems to have been chiefly that it met the requirements which, in the opinion of Newton, would constitute " a mighty advance in philosophy." These requirements were the derivation, from the phenomena of Nature, of two or three general principles; and the explanation of the manner in which the properties and actions of all corporeal things follow from these principles, even if the causes of those principles had not at the time been discovered." Boscovich claims in his preface to the first edition (Vienna, 1758) that he has gone far beyond these requirements; in that he has reduced all the principles of Newton to a single principlenamely, that given by his Law of Forces.The occasion that led to the writing of this work was a request, made by Father Scherffer, who eventually took charge of the first Vienna edition during the absence of Boscovich ; he suggested to Boscovich the investigation of the centre of oscillation. Boscovich applied to this investigation the principles which, as he himself states, " he lit upon so far back as the vear 1745." Of these principles he had already given some indication in the dissertations De Viribus vivis (published in 1745), De Lege Virium in Natura existentium (1755), and others. While engaged on the former dissertation, he investigated the production and destruction of velocity in the case of impulsive action, such as occurs in direct collision. In this, where it is to be noted that bodies of sensible size are under consideration, Boscovich was led to the study of the distortion and recovery of shape which occurs on impact; he came to the conclusion that, owing to this distortion and recovery of shape, there was produced by the impact a continuous retardation of the relative velocity during the whole time of impact, which was finite ; in other words, the Law of Continuity, as enunciated by