374 
4)? 
ro =p, (1 — =) (24) 
or 
dd 4}? 
pi =f VnV?p, (: -- =} : 
dt r 
The first of (21) is 
PA 3 4 4j4 7 p zl 
je re — — rhage — 4 # ETT Pe = ° ° . (25) 
Pp 1e Hist ‘ig 
If we multiply (25) by r and (22) by "9, and add, we find 
d 2 44° Ar ; 
—( ig? — ~]/=|38g’?4+ — }—... «. « (26) 
edt \ r ¢ J r 
The lefthand member put equal to zero gives, as in NEWTON's theory 
Lp — en == const. 
À 2 
The constant I call — ae Thus we have the approximation 
a, 
ee 
ee sn PY ee 
5, ay 
or 
— |] +77 {—|]=—k’m|———], 
dje dt Ee eis 
If this is introduced into the right-hand member of (26), this becomes 
d : rf ty 2024 Gas 
—{ g@? ——— | =| —— — — Jr, 
cdt r 7 ar” 
DRT LEN aes 102% 
p° rn Ee + = = — ae pen . . . . . . (28) 
lie a ar Ko 
from which 
The right-hand member is of the second order. If it is neglected 
(28) becomes the same as (27), i.e. the integral of living forces in 
NewronN’s theory. 
To find the orbit we must eliminate cdt from (24) and (25). 
This gives 
and if we introduce 
