Bertrand on Electricity

Abstract

THIS book contains lectures on electricity given by M. Bertrand at the Collège de France. In his preface the author states that he has confined himself to the mathematical principles of the subject; but this hardly expresses the limitation he has imposed upon himself, for a great many results which English students of electricity are accustomed to find in text-books on this subject are omitted from this work. A brief description of the contents of the book will suffice to show this. The first chapter contains an investigation of the attractions of spheres and spherical surfaces when the law of attraction is inversely as the square of the distance; the second and third are devoted to the properties of the potential; the fourth contains an investigation of the conditions under which the method of lines of force can be used; the fifth, which has the comprehensive title “Électricité Statique,” contains a short discussion of the electrical distribution on two spheres which mutually influence each other, the reciprocal theorems, and a discussion of the properties of the Leyden jar so far as they can be discussed without introducing the idea of specific inductive capacity; the sixth chapter contains some remarks upon magnets; the seventh treats of Ohm's law, and contains Kirchhoff's equations for the distribution of currents amongst a network of conductors, without, however, any applications even to such an important case as that of Wheatstone's bridge; the eighth, ninth, and tenth chapters contain, respectively, investigations of the magnetic forces produced by linear currents, the laws according to which such currents act on each other, and simple applications of these laws; the eleventh chapter contains some account of the induction of currents, and, amongst other things, some well-founded reasons for not deducing the laws of induction from the principle of the conservation of energy alone, but no hint is given of the possibility of regarding a system of currents as a dynamical system, though the introduction of this idea by Maxwell has thrown new light over the whole subject and enabled many of the properties of currents to be recognized at once as those belonging to any dynamical systems; the twelfth chapter contains some account of the application of the results of the previous chapters to dynamo-electric machines; and the thirteenth and last chapter discusses units.

Leçons sur la Théorie Mathématique de L'Électricité professées au Collège de France.

Par J. Bertrand. (Paris: Gauthier-Villars.)