( 572 ) 
be the mean motion, as determined by a, the mean anomaly at time 
t is given by 
t 
DE fn dt. 
0 
Further, let 2, “ and y be the direction-cosines of the velocity 
p with respect to: 1%. the radius vector of the perihelion, 2nd, a 
direction which is got by giving to that radius vector a rotation of 
90°, in the direction of the planet’s revolution, 3". the normal to the 
plane of the orbit, drawn towards the side whence the planet is 
seen to revolve in the same direction as the hands of a watch. 
na 
Put a=o—0, 5 = 0 and =0' (na is the velocity in a 
circular orbit of radius a). 
Then I find for the variations during one revolution 
Aa=0 
LEL 8: Pe 
emt (tefandS e°) oo e°) x99 a a 
27 1’ (L— 2) 
Aqg==; re 2) V [AOP cos 049 (05 dina +dtsino| 
AO hi rj Ò? sina + Ò(ed' — Pe vey et Ae 
yy (l—e2) s sin np 
+ u 0? cos 0) 
Veen | 
nóEsnts el ave ZE dek ee, kr, 
e 
eee 
i ee 
Va a 
ape cos ol 
[A 02 sin odd (ed'—g 0) cos 0] 
Ca mee Bt a pa 
4: 
A x' = 1 (A? — u?) 0? 
(le) ye) 
e° 
—2nudd' 
§ 10. I have worked out the case of the planet Mercury, taking 
276° and + 34° for the right ascension and declination of the apex 
of the Sun’s motion. I have got the following results : 
