733 
This is, to the second approximation, the equation for the geodesic 
starting from the point-instant #*, + 5“ with initial direction para- 
meters 
bm 
ke 
Ab, Am Ll 4 = Qs mn Ab, A AM, TT, 
a 
and where z’ is the interval measured along the arc. We notice 
that these parameters are the components of the wntt vector Aon 
translated geodesically from the origin of time along the timetrack, 
with an accuracy up to the second approximation. As a geodesic 
translation does not alter the mutual angles of the translated vectors, 
it follows that the axes of space and time remain perpendicular. 
In the same way it may be shown that every spatial radius, that 
Penne z,—r, 20 As, 20 As, 28) 4,s, with 2,7-- 4,7 1,71, 
is a geodesic, s being the interval along the are from the origin. 
The potentials g' in geodesical falling coordinates. 
We shall calculate the new values g';; by means of the trans- 
formation formula 
Jij = & Pai Pbj Jabs 
where 
Pa = Òvafdzt. 
In calculating the pa; the symmetry of Qs in the suffixes 5 
and m is of great use. [t enables us to arrange terms in a practical 
way. We get 
bm ek 
Pao = As, we >| Ab, A”; gue 4 D3; Qa anh Ab, Al; fj zi zl == 
a 
Ie 5 Ss OF ain Ab; (An; An, oe A”; Am) zi 2d, 
and for any u F0, we get 
bm rae 
Pap. === Ay Pr =| Ab, Am; zt eed 4 = Q%5 mn Ab, Ami A"; zt 2J EE 
a 
=f S065 mn Ab (Ars Artemia er 
— 14 FS Q% mn Abs (Arte A", — Ate Ami) 2° 27, 
In the second lines of both formulae we shall replace Q‚n by 
4 Renn. This is permitted because the bracket forms are skew- 
symmetrical in the suffices m and n. 
In the first lines we find exactly the components of the vectors 
A“; shifted geodesically from the origin to the point-instant denoted 
by 2%. Thus, as far as these parts of pq are concerned, the trans- 
formation formula 2 pa po; Jos gives 1, —1 or O for 2=j=0, 
I=j=u, or 147 respectively. We get 
