Das Princip der Erhaltung der Energie und seine Anwendung in der Naturlehre

Abstract

THOSE who are engaged in teaching applied mathematics cannot fail to appreciate the wide advantages arising from according greater prominence to the principle of conservation of energy than it obtained in the text-books of the last generation. Unfortunately, however, this principle, when stated in the restricted form in which it is most easily understood—viz. the mere assertion of constancy of the total energy, kinetic and potential, of a material system—is insufficient of itself to determine the actual motion of systems with more than one degree of freedom, and, moreover, cannot be applied to find the passive reactions arising from constraints. This particular point has been brought out forcibly in the recent controversy on “energetics” in which Boltzmann, Planck, Helm and others have taken part. Some further assumption or generalisation is necessary; either the principle of physical independence of force, or the extension of the principle of energy to virtual displacements (i.e. the principle of virtual work), or the hypothesis that the equation of energy holds good separately for every particle of a material system for the components of motion in every direction, or the assumption of the variational equation, or the principle of least action; all these alternatives are practically equivalent, and enable us to construct an energy theory of dynamics. Only quite recently Prof. Boltzmann, writing in Wiedemann's Annalen, suggested the possibility of building up the equations of motion, first of rigid bodies, and then of fluids and elastic solids, from the principle of energy aided by suitable subsidiary hypotheses; and the present volume is interesting as showing how this method works out when applied to a somewhat elementary text-book.

Das Princip der Erhaltung der Energie und seine Anwendung in der Naturlehre.

Von Hans Januschke. Pp. x + 456. Medium 8vo. (Leipzig: B. G. Teubner, 1897.)