Accordingly Einstein was compelled so to modify the classical laws of mechanics as to ensure their invariance to the Lorentz-Einstein transformations. This modification was then found to entail the relativity of mass. By this we mean that the mass of a given body could no longer be regarded as an invariant, independent of the body’s relative motion. On the contrary, it was now found to increase with the relative velocity of the body, becoming infinite when the velocity of light was reached. In the same way the relativity of force was [Pg 157] established, and classical Newtonian mechanics, with its invariance of mass and force, was proved to be incorrect, and acceptable only as a first approximation for slow velocities. It also followed that no material body could ever move with a speed greater than or even equal to the speed of light, since it would require a force of infinite magnitude to give it this critical velocity. A number of paradoxes associated with the theory are due to the critic’s initial assumption that the observer is moving with the speed of light. But all these paradoxes may be dismissed at the outset, since no observer could ever move with such a speed. When the mathematical expression of the mass of a body in relative motion was considered, it was found to be decomposable into several parts. First of all we had the mass of the body as at rest (this was the mass which classical science assumed to be invariant, i.e., independent of the body’s motion). To this was added the vis viva, or energy of motion of the body with respect to the observer, as well as a number of other terms depending on the relative velocity. These last terms were, however, of very minor importance unless the relative motion of the body was considerable. Thus the mass of a body in relative motion was increased over its mass at rest by its energy of motion or vis viva, so that the distinction between mass and energy became obscured. Since part of the mass of the body when in motion was due to its vis viva, it appeared probable that the entire mass of the body, whether at rest or in motion, was due to its energy of one kind or another. Now matter even at rest was known to contain energy, as exhibited by radioactive phenomena and by the thermal effects produced by chemical combinations. So it was natural to assume that the mass of the body at rest was due to its contained or bound energy, which would be released were the body to disintegrate into nothingness. The formula connecting this energy of constitution of the body with its mass was obtained from the mathematical expression of the mass, and it was found that in C.G.S. units the contained energy was equal to the mass multiplied by the square of the velocity of light. From this formula it is easy to realise the tremendous liberation of energy and the dire consequences that would result from the complete disintegration of even a small parcel of matter.