yv 
S= — du—rd— ur, 
¢ ? 
ry) 0 Pres of 
Ds) Se ee ta he pe Va Ole ea eee eee ee 
0 
N 
RA EN 
W == + 3u 20 Jg. 
o 20 
In these formulae 7 and 9 are the coordinates of the moon in 
its orbit, and z is the coordinate perpendicular to the ecliptic. 
Further u is the ratio ”/,,, of the masses of the sun and the earth 
and » is the. mean motion of the sun divided by the velocity of 
light, »—”'/,. It appears that the second terms in S and W are 
exactly cancelled by the correction to the ordinary perturbing force, 
- which was mentioned above, and need thus not be computed. The 
other terms give a secular motion of the perigee and the node, both 
of the same amount, viz.: 
dels A 
u OREN TER Ee Ile 
De | © 
dw db 
‘The motion in one century is 
+ 1.91. 
Beyond these motions of the perigee and the node there are no 
new secular terms in the motion of the moon. 
5. Comparison with the observations. 
The observed values have been taken from Nrwcoms'). I have, 
however, reduced them to the value 5024".90 of the precessional 
constant (for 1850-0). To the theoretical values as given by Newcoms 
I have added the motions of the perihelia which have been found 
above. We then find, for one century 
edw Observed Theory Difference 
Mercury +118"00+0"40 +118"58+0"16 — 0'58 + 0'43 
Venus Sata aca) et 103 de hp ORT Se | he, 
Earth + 1946+ 12 + 1945+ 05 + 001+ ‘13 
Mars +14944+ 35 +114893+ 04 +0494 ‘35 
sint ds, 
Mercury — 92084045 — 925024016 +4047 + 0-48 
Venus kde 419) -~.106:00,42) 42, 9 +05 7 
Mars ety ote) 20). 72:63 209 SOE EAA 
1) Astronomical constants, page 109. 
