735 
will be considered moving slowly relative to the falling axes and 
that the square of their velocities will be negligible compared with 
the square of the velocity of light, which, in our coordinates, is 
nearly unity. 
The equations of motion are 
| Pet y {iil dede 
dats: 18 a\ de ds” 
With the above assumption we may put dz°/ds = 1, and we need 
only consider combinations where 7 or j or both of them are 0. 
In the CrrrsrorreL symbols the differential coefficients of g' are not 
known beyond the first powers of the coordinates; therefore the 
reciprocals g may be taken to be 1, —1, —1, —1, and 0. This 
makes 
5 tod 
= a 
Calculating we find: 
00 
| | == TT = Roaor zr, 
| a 
ij 
a 
and 
+ PS (R'28,0r + Rer,0g EE R'ga,or Tei BR groe) 27, 
08 
ps 
= — & Raor 27 — & & (R'px,70 + Par,go + Rope) zt. 
The bracket vanishes by symmetry of the R's,,.0, thus 
0 
| ai =P Rau, or Zr 
a 
Finally the equations of motion for free particles become: 
d* z% 
dz,’ 
Here we can put 
daf 
=d Loe, or ME == = Rea, or pA 
dz 
0 
Pe, R'23,0r ZR 2w,, 
= R’310- SS 20, 
= R'12,or = 2, 
This brings the last term into the form 
— 2[w.v]. 
Interpreting the equation of motion we note that the first term 
in the right hand member accounts for the forces causing the tidal 
effects. The second member has the form of a Cortomisian force, 
but the peculiarity is that the rotation vector w figuring in it, is a 
linear function of the coordinates and thus on opposite sides of the 
planet has the opposite direction. It is conveniently called the 
compound tidal force. It might come into play when we consider 
the motions of a satellite. 
