. Theory of the relativity of motion . l, having a mass of mgrams, and the observer B on system Sf is also provided with a similarsphere. The two spheres are made so that they are exactly alikewhen both are at rest; thus Bs sphere, since it is at rest with respectto him, looks to him just the same as the other sphere does to A>As the two systems pass each other (fig. 9) each of these clever experi-menters rolls his sphere towards the other system with a velocity ofu cm. per second, so that they will just collide and rebound in a lineperpendicular to the direction of motion. Now, from the fi
. Theory of the relativity of motion . l, having a mass of mgrams, and the observer B on system Sf is also provided with a similarsphere. The two spheres are made so that they are exactly alikewhen both are at rest; thus Bs sphere, since it is at rest with respectto him, looks to him just the same as the other sphere does to A>As the two systems pass each other (fig. 9) each of these clever experi-menters rolls his sphere towards the other system with a velocity ofu cm. per second, so that they will just collide and rebound in a lineperpendicular to the direction of motion. Now, from the first postu-late of relativity, system S appears to B just the same as system Sappears to A, and 5s ball appears to him to go through the sameevolutions that A finds for his ball. A finds that his ball on collision 38 Chapter Three. undergoes the algebraic change of velocity 2u, B finds the same changein velocity 2u for his ball. B reports this fact to A, and A knowingthat .Bs measurements of length agree with his own in this transverse. Fig. direction, but that his clock gives time intervals that are shorter than his own in the ratio 1, calculates that the change in veloc- ity of 5s ball must be 2u \ 1 4 From the principle of the conservation of momentum, however,A knows that the change in momentum of 5s ball must be the sameas that of his own and hence can write the equation maU = TYlbU V- ,2 where ma is the mass of As ball and mb is the mass of Bs ball. Solv-ing we have m0 mb I V2 In other words, Bb ball, which had the same mass m,a as As when Some Elementary Deductions. 39 mboth were at rest, is found to have the larger mass _ — when placed in a system that is moving with the velocity V.* The theory of relativity thus leads to the general expression m0m ^ for the mass of a body moving with the velocity u and having themass m0 when at rest. Since we have very few velocities comparable with that of light / y?it is obvious that the quantity a/1 seldom differs much from unity,
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