vo 
hand | 
bho 
while in EiNsreiN’s system it is 
do 
tn et salle oee 
edt 
Here do is a line-element in the three-dimensional space (w,, «,, #,) 
and V is the angle between this element and the radius-veetor. The 
curvature of rays of light of course is the same in both systems. 
2. The equations of motion. 
The world-line of a material point is a geodetic line of which the 
differential equations are 
dx; (ae pal de, de, kan 
md md 
dat ean rig on \ ds ds 
(2; -95.G = sd wah) 
Here ds is the element of the world-line, which is given by 
de = > 5 Inq day, de. 
pq 
All sums are to be taken from 1 to 4. 
If now we take re, ==ct we find easily 
dz; E ) ( )( : > a ae ot 3 
fs sl? i i - ] ai | ze ( “\ 7 
edt” eed el PI zr I 3 
The points indicate differentials „with respect to cf, so that Hi 
\P 9 
ia) 
order of accuracy we have, for rectangular coordinates : 
pr pil il 
Ue a He; Ep dw en En rary | 
The brackets | are easily found from the gv. To the required 
(15) 
Ü r 7 
and for polar coordinates 
Las)” a 22)’ A 83) A 
= = = | = Cos uy — - ay | | ee 
| 1 | r 1 r 1 r | 
2d. PSone ) 22 | 
=== ae =— en = sin W cos WP , (19) 
2 5 r 
| 
ae | wa 22 JE \ 14 ' 22 | 
== tan wd , B Berten tp ==: 
2 8 1 \ ? r* (4 r° 
ry Ô : Se Vx 
Those not mentioned are zero. If now we put: 2? = — m, (where 
: ¢ 
m is the same as i’ of the preceding article), then the. equations 
of motion become, for rectangular coordinates : 
