Page:Eddington A. Space Time and Gravitation. 1920.djvu/158

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142
MOMENTUM AND ENERGY
[CH.

It was formerly supposed that the mass of a particle was a number attached to the particle, expressing an intrinsic property, which remained unaltered in all its vicissitudes. If is this number, and the velocity of the particle, the momentum is ; and it is through this relation, coupled with the law of conservation of momentum that the mass was defined. Let us take for example two particles of masses and , moving in the same straight line. In the space-time diagram for an observer the velocity of the first particle will be represented by a direction (Fig. 19). The first particle moves through

a space in unit time, so that is equal to its velocity referred to the observer . Prolonging the line to meet the second time-partition, is equal to the velocity multiplied by the mass 2; thus the horizontal distance represents the momentum. Similarly, starting from and drawing in the direction of the velocity of , prolonged through three time-partitions, the horizontal progress from represents the momentum of the second particle. The length then represents the total momentum of the system of two particles.

Suppose that some change of their velocities occurs, not involving any transference of momentum from outside, e.g. a collision. Since the total momentum is unaltered, a similar