ABSTRACT
The fundamental principles of Hertz’s theory are so simple and so admirable that it seems worth while to expound them briefly. His object, like that of most recent writers, is to construct a system in which there are only three fundamental concepts, space, time and mass. The elimination of a fourth concept, such as force or energy, though evidently demanded by theory, is difficult to carry out mathematically. Hertz seems, however, to have overcome the difficulty in a satisfactory manner. There are, in his system, three stages in the specification of a motion. In the first stage, only the relations of space and time are considered: this stage is purely kinematical. Matter appears here merely as a means of establishing, through the motion of a particle, a oneone correlation between a series of points and a series of instants. At this stage a collection of n particles has 3n coordinates, all so far independent: the motions which result when all are regarded as independent are all the thinkable motions of the system. But before coming to kinetics, Hertz introduces an intermediate stage. Without introducing time, there are in any free material
system direct relations between space and mass, which form the geometrical connections of the system. (These may introduce time in the sense of involving velocities, but they are independent of time in the sense that they are expressed at all times by the same equations, and that these do not contain the time explicitly.) Those among thinkable motions which satisfy the equations of connection are called possible motions. The connections among the parts of a system are assumed further to be continuous in a certain well-defined sense (p. 89). It then follows that they can be expressed by homogeneous linear differential equations of the first order among the coordinates. But now a further principle is needed to discriminate among possible motions, and here Hertz introduces his only law of motion, which is as follows:
“Every free system persists in its state of rest or of uniform motion in a straightest path.”
