737 
component and a component tangent to the circular orbit; in such 
a manner that these four directions will be all perpendicular to each 
other. Now, if the planet with the geodesical falling axes comes across 
some particular set of local axes, the axes of time, both the falling 
and the local, will coincide, and therefore the spaces of the falling 
and of the local axes too will be the same. Thus the position of 
the falling axes relative to the local ones can be stated and the 
positions before and after a revolution compared. 
The gravitational field of the sun is given by the form of the 
infinitesimal interval : 
B Saar 1s 
1 — afr 
In this field a circular motion is possible in the plane 6 = 3a, 
with “radius” A and with angular velocity 
dip/dt = w = Vark. 
—rd* —r* sint 6 dy’. 
Now, every where along the track define four vectors A“,,A*,,A%,,A%, 
as follows 
(0) (1) (2) (3) 
2R i “ 
Aa: a 0, 0, = ee 
2 R—8a R 2 R—3a 
Aa: 0: Vi—a/R, 0, 0, 
As: 0, 0, 1/R, 0, 
R 1 CMG ine 
As, : A si rel, 0, Pp LA ( aM, 
(R—a) (2 R—3a) R 2 R—3a 
It will be seen that these vectors are all of unit length and 
perpendicular to one another. They define the local axes. 
A set of these vectors in one particular point-instant can be taken 
as the starting vectors of the geodesic falling coordinates. To find 
the directions of the falling axes after a lapse of interval ds (com- 
ponents A“,ds) we need the values of CurisTorFEL’s symbols. These are, 
in coördinates ¢, 7, 0, p: 
01 
bos uw 
ON OR). 
00 — 11 — 22 33 
em ee SS | [=-(A-0), =~ (R-a) sin’ 0, 
1 Zot 1 2h (R—a) ( 1 1 
a fis Ë ve ai 1 
| Veet Re 
33 ; 23 cos @ bap ; 
= — sin 0 cos 0, | ==. The remaining symbols vanish. 
2 3 sin Ó 
