453 
The last equation shows that 0 is the same quantity as the 
quantity named so before and occurring in (6) and (8). 
7 
Substituting (10) in (7) and (8) and returning to the quantities 
Jij themselves, we find 
.{ Ògu 0 gia 0°38 
sn ( nn |= 2% 20e , … … (AI) 
ay Oar Ae, Owjiot | 
and 
: 5 tg ney DEL = ws LN 
A(g,,— 3x72") =x(0 +3p+oP)—x’ 08 Hoer HALE dt (12) 
1) n Orde; dt 
5. We now proceed to the solution of (11) and (12). From (6) 
it follows that 
= odS 4 
den er ER Sl es ee anelas 
where 7 means the distance from dS to the point where 3 is to 
be calculated. (11) is satisfied by 
5 owjdS 
Ji4 —= 2x | E ; ° . . . . . . (14) 
from which we get 
O° gis 023 
POET 
and consequently (12) becomes 
A (9,, —4 #8’) =z (0 + 3p + oP) — #038 + 2x0 =a)" + x 
Putting now 
: o(L#/)dS 
(J) 
*ordS 
A= “| —-——— , Bef ee ads La) 
Anr 4a 
we have 
AS eo ea AB SS ad 
(1 
and so 
ioe eB. 8 
Alg, — 5% + 2A+ 4 as =x(o + 3p + of) — #0}. 
- fp s s s 
We now consider the case of a number of separate bodies ; more 
in particular we consider an astronomical system. In each body p 
and P may then be considered to be only dependent of the field of the 
first order, produced by tbe body itself, and consequently do not 
change. The term — z’03 can be divided into as many terms as 
there are bodies, in such a way that say in the first body 
“ — “ > 
5a 20 _ TTT xO md Ba 
a 
