We are now in a position to understand the advantage of Einstein’s definition. First, he states that the electromagnetic experiments have established the relativity of velocity. This in turn entails the maintenance of form of all natural laws—in particular, Maxwell’s laws of electromagnetics. Hence it follows that there must exist a critical invariant velocity that is given by the constant c which enters into Maxwell’s equations. Inasmuch as Maxwell had proved that and the velocity of light in vacuo were one and the same, the invariant velocity is defined by this velocity of light. Thus, with Einstein’s definition, we know that the world-structure demands the existence of a finite invariant velocity, and not of an infinite one, as was believed by classical science. And, in addition, we know that this velocity is given by Maxwell’s celebrated constant , a constant whose value had been determined with accuracy long before the advent of the relativity theory. In other words, Einstein defines the unknown in terms of the known, not in terms of the ambiguous. To return to our illustration of the needle in the haystack, not only has Einstein given us the assurance that the needle is there, but he also tells us exactly where to look for it. For this reason his definition, in contradistinction to Dr. Whitehead’s, satisfies the requirements demanded by physical science. In these pages we have discussed Whitehead’s definition at some length because it illustrates the danger there is in confusing mathematics and physics. Thus, whereas in mathematics we may postulate anything we please (with certain reservations) and then proceed to reach our conclusions deductively, in physics this procedure is impossible. We must take our cue from experiment and formulate our premises accordingly. The result is that whereas in mathematics we are concerned with formal possibilities, in physics we are limited to an analysis of actual facts. And in every case the transition from the possibilities of mathematics to the actualities of physics necessitates the introduction of physical measurements. In this connection it is most important to understand the difference between a physical and a mathematical definition. Take a number like n in mathematics. We can define it as the ratio of the length of a circumference to its diameter in Euclidean geometry. Without performing physical measurements, we can deduce from this definition, by purely mathematical means, the precise value of to any order of approximation we please. Thus the definition does not lead to ambiguity, hence is a valid one. On the other hand, try to give a physical definition by some similar method—say, the definition of the “gram” or of the “dyne.” The purely logical type of definition breaks down, and we are compelled to resort to physical determinations. Accordingly, we define the gram as the mass of a cubic centimetre of distilled water under specified conditions of temperature and pressure.