200 
[The introduction of w in (5) gives 
dv Zev 
de neee 
from which we immediately find 
(a4 
Dn 
ye 
a being a constant of integration. 
Differentiating this relation with respect to 7, we get 
Qax- dv 
or, v’ being equal to w, 
2a de 
= aes 
( ] —w")? 
,90°(4) changes into 
2 2 3 4a° 2 a JQa2z ae en 2 
ds = a dt a (1—a?)* daz (le) (dd En sin- o dg |E 
So we have now been led again to introduce another variable 
instead of 7, viz. wv. The form obtained leads us to introducing the 
variable € = 1 —a’. Then 
sf eee 4a° en GPa cet L 
ds’? = (1—s) dt — ea ds’ ——, (d0° + sm* 3 dp”). 
(l—s)s s 
Lastly we put 
a 
5 == 
7 
This # is not the same as occurs in (4). We obtain 
de == (: — =) di aie — (dv? ste sin pap). > ae 
7 ae re 
pe 
We have chosen the coordinates in a particular manner; it is 
now of course also very easy to introduce for 7 another variable, 
which is a function of 7. ') | 
3. From (7) we can immediately deduce some conclusions. The 
point (r, 0, p) lies at a distance 
a ce a ee cera r 
J =|— zer PE — + alog Ve —l + Van . (8) 
a r : a « 
1 
1) “After the communication to the Academy of my calculations, I discovered 
that also K. ScHwaArRzscHILD has calculated the field. Vid.: Sitzungsberichte der 
der Kén. Preuss. Akad. der Wiss. 1916, page 189. Equation (7) agrees with (14) 
there, if R is read instead of r. 
