9 6 D O C . 9 1 R E L A T I V I T Y & E Q U A T I O N S O F M O T I O N ourselves to the investigation of quantities of first and second order, whereby (= 1 or = 0, depending on whether or ) is considered to be a quantity of zero th order. The are the electromagnetic potentials, i.e., . If one substitutes (5) into (1) and (4), the result for every order (i.e., for every power of the constant ) is a system of differential equations. We are interested only in systems that correspond to the first and second order. In order to obtain them in a clear-cut form, we first take note of the fact that for quantities of second order, we find exactly: , [16] which can be replaced to the same approximation by , where denotes the Christoffel symbol formed from the , and is that formed from the . Taking all this into account, (2) becomes , (2a) where the indices to the lower right of the square brackets indicate ordinary differ- entiation re. and . An essential point is that in this expression, the occur only linearly. Furthermore, with the precision at which we are aiming, we can write the in the form . (3a) One can see from (2a) that the linear operator  i i  = i    i  i  x   i i x  –   = [p. 237]   i g  i   g  – –    i   2 i  +        = = – i   2 – g  i  i  +         g i   g i R i  i   i   –      2  x  g  i  i  +        + =  x  g  i  i  +      + i    i       – –          x  x  g i T i T i  2 4 –1 i   2+  i     =