It follows from the ambiguity of simultaneity between distant events that we cannot speak unambiguously of "the distance between two bodies at a given time." If the two bodies are in relative motion, a "given time" will be different for the two bodies and different again for other reference-bodies. It follows that such a conception cannot enter into the correct statement of a physical law. On this ground alone, we can conclude that the Newtonian form of the law of gravitation cannot be quite right. Fortunately, Einstein has supplied the necessary correction. [Pg 53] It will be observed that, as a consequence of the Lorentz transformation, the mass of a body will not be the same when it is in motion relatively to the reference-body as when it is at rest relatively to it. The mass of a body is inversely proportional to the acceleration produced in it by a given force, and two reference-bodies in uniform relative motion will give different results for the acceleration of a third body. This is obvious as a consequence of the FitzGerald contraction. The increase of mass with rapid motion was known experimentally before the special theory of relativity had explained it; it is very marked for velocities such as those attained by -particles (electrons) emitted by radio-active bodies, since these velocities may be as great as 99 per cent, of the velocity of light. This change of mass, like the FitzGerald contraction, seemed strange and anomalous until the special theory of relativity explained it. One more point is important as showing how easily what seems axiomatic may be false: it concerns the composition of velocities. Suppose three bodies moving uniformly in the same direction: the velocity of the second relatively to the first is , that of the third relatively to the second is . What is the velocity of the third relatively to the first? One would have thought it must be , but in fact it is: It will be seen that this ; if or , it is , otherwise it is less than . This is an illustration of the way in which the velocity of light plays the part of infinity in relation to material motions.