138 TIME 



Before passing on to the measurement of time let us come 

 back for an instant to the notion of the deformed — curved — 

 space-time continuum. It is impossible to have a clear picture 

 of this if one considers the three-dimensional space. But a 

 sufficiently close if not absolutely rigorous analogy can be 

 drawn from the idea of a two-dimensional space which we 

 used to show the necessity of the third dimension in the 

 measurement of time. Indeed, time is measured by means 

 of the movement of a mobile body in space. It cannot be 

 measured without displacement. The reader may remember 

 that in the example of a scenic railway mentioned above, 

 we came to the conclusion that the observer in the moon, 

 ignoring the existence of the third dimension which would 

 alone enable him to ascertain that the wagon ascends and 

 descends, could only conceive the acceleration and slowing up 

 observed as being due to variations in the actual velocity of 

 the moving body. On the other hand, if the rate of the 

 moving body was variable as a function of the slope, so that 

 the distance travelled in projection was always the same in 

 equal times, the observer would have the impression of a 

 uniform velocity. Thus, curvatures in a path contained in 

 the plane of observation, in a two-dimensional space, would 

 entail gross errors in the determination of the fourth dimension, 

 time. And reciprocally, fluctuations in speed, the cause of 

 which are unknown, would entail errors in the estimation of 

 the distance travelled; that is to say, of space. I repeat once 

 more that this is only an analogy, but it seems to me that this 

 rough comparison enables one to grasp how the deformations 

 of space can affect the measurement of time and how the 

 deformations or variations of velocity, which are the only 

 magnitude at our disposal for measuring time, affect space. 



If I have insisted at length on this point, it is because we 

 shall soon see that there is perhaps another means of 

 measuring our time which escapes the causes of error just 

 enumerated. 



