1087 



one system of' coordinates of the above incnfioned properties there 

 exists an infinite quantity of such systenns of coordinates, and our 

 formulae hold for all these systems. Not alone the directions of the 

 X^-, X,-, A'j-axes can be chosen in an infinite number of ways, 

 but we are still free to chose the method of measurement for 

 the length ot the radius vector in space. Without destroying the 

 validity of our formulae we may thus pass from a system of coor- 

 dinates iPi, X,, x\, x\ to an other one a;\ x\ xj x^ with the same time 

 coordinate, but for which 



where r' = l'^,^''l'' -)- ^'V + '^V is a function of r (comp. Droste, Het 

 zwaartekrachtsveld p. 16). For such a transformation of coordinates 

 u, p, 10 change of course. If therefore we have to calculate u, p, lo 

 (which according to (25) determine all ^//v's) we must first fix the 

 system of coordinates. This may e. g. be chosen in this way that 

 everywhere p = 1 (corresponding to v =^ r of Droste). If then still 

 the unit of time is chosen so that the universal constant c has the 

 value 1 the system of coordinates is determined except as to the 

 directions of the three axes in space, which for spherical symmetry 

 are of no importance. For the thus specially fixed system of coor- 

 dinates we have outside the body (see Droste, Het zwaartekrachts- 

 veld, p. 18) 



10^=^=1-"^ , p = l {r>Ry. . . . (46) 



M r 



where « is a constant. . 



That these formulae are right can easily be verified from the 

 formulae (38); they are also found more directly from more general 

 formulae which will be deduced in a following paper. The 

 constant a must of course be connected with the mass of the body. 

 Formula (45) gives for this relation, c being equal to 1, 



4jr a 

 m = Ez= (46a) 



In this special system of coordinates we have according to the 

 formulae (25) outside the body ^) 



V/^ =1 (466) 



Inside the body however this value of ^ — g need not hold. If 



^) This is seen most clearly by considering a point on one of the axes of 

 coordinates. We then find first [/ g = u w p"^. 



