136 TIME 



is clear, that of a deformed continuum is less so. And yet the 

 general theory of Relativity explains gravitation by a deforma- 

 tion of the continuum. The existence of a 'force' which acts 

 in inverse ratio to the square root of the distance and deflects 

 the normally rectilinear course of bodies in space, is admitted 

 in the classical theory of Nev^ton. But the theory of Relativity 

 does not accept mysterious 'unknowable' forces.^ The 

 formulae which define its continuum, based, it is true, on a 

 certain number of undemonstrated postulates, must explain 

 everything. From the relativistic point of view, the criticism 

 of Newton's theory can be summarily expressed in the follow- 

 ing fashion. This theory is based on a hypothetical motion 

 never observed by any one: the straight-line motion, arbitrarily 

 named natural motion. To explain all natural motions we 

 have to bring into play unknown forces the existence of which 

 can only be proved by the hypothesis from which we started 

 and which cannot be verified. In all evidence we are facing 

 a petitio principii. A straight line exists as a geometrical 

 concept, but motion in a straight line does not exist as an 

 objective reality, or at any rate it has never been observed. 

 What I mean is, that if we trace a straight line on paper with 

 a ruler, we have before our eyes a picture which concretes 

 our concept of a straight line, providing that all its points are 

 simultaneously perceived by the eye. But the course of the 

 pencil which has traced this line is far from having been a 

 straight line in the universe. Our hand participated in the 

 complex movements of the earth around its axis, of the earth 

 around the sun, and of the entire solar system in space. The 

 trajectory, as seen by an observer in Sirius, would have been 

 very complicated indeed. It was only in relation to ourselves 

 that it was in a straight line. Thus, when Newton says 



^ We can easily imagine in a one-dimensional space (straight line) 

 the apparition of a force as a simple consequence of a curve (second 

 dimension). For example, the 'centrifugal force' which throws the 

 passengers of an automobile towards the exterior as soon as it aban- 

 dons a straight line to take a curve (P. Martignan). The single 

 presence of matter deforms the space-time continuum and the force 

 of gravitation is the result. We will take up again this question of 

 deformations a little farther on. 



