134 TIME 



dimensional formulae in which the fundamental dimensions 

 are fused into a single magnitude endowed with different 

 material properties. For example, he expresses the unit of 

 volume by L^, seeing that the measurement of a volume is 

 obtained by multiplying three lengths one by the other. For 

 the unit, these lengths are equal and give LxLxL=L^. 



He likewise expresses the unit of velocity by — or LT^^, since 



velocity is length divided by time. Acceleration, which is 

 the quotient of velocity by time becomes LT". But with the 

 same symbols he can write the formulae of very complex 

 units such as that of quantity of electricity: V^M-T~^ of 

 potential difference: L'M'^T-^- of magnetic moment L^M^T-^ 

 or simply that of work or of moment of force: L^MT^^. 

 Absolute notions, such as that of energy, are naturally beyond 

 the scope of these definitions. Thus, the physicist, accustomed 

 as he is to juggling with various dimensions, escapes the tempta- 

 tion of comparing them to each other except to bring them back 

 to conventional units. For instance, he will say that a 

 magnitude 'has the dimensions of a velocity'. This is a steno- 

 graphic expression which simply means that time enters into 

 the formula as a denominator. If he speaks of 'the dimensions 

 of an acceleration' it means that time is to be found as a 

 denominator but at the power 2. 



Though everybody is aware of the fact that in order to 

 measure time one must resort to the displacement of an object 

 in space, we will develop this subject a little further. If we 

 perceived only two dimensions instead of three, it would be 

 almost impossible to assure oneself that time flows uniformly. 

 Indeed, let us suppose that a distant mobile body travels along 

 a path in the plane of our vision. Let us suppose, for example, 

 that we are examining the movement of a body on the earth 

 from a great height, say from the moon. If this body — a marble, 

 for instance — covers equal distances m equal times, we cannot 

 infer that its movement is uniform, for by definition, we have 

 no means of knowing if the ground on which the marble 



