The Fourth Order Perturbations. 
185 
The above yield — 
iy P^>°- 0-351701 
ly P3 ' = l-160576?i 
2, p-v = 1.542166 
L P''^ = l-569966?i 
L P°^- 1-169637 
If these figures are coropared with de Haerdtl's {Bull. Astr., ix., p. 215) 
a grave discordance will be found in the last, but de Haerdtl's figures can 
be reproduced if, in his formula, we replace b2hf, which is correct, by 
520^^3)^ which is erroneous. 
We also have — 
L riL^ = 5-90244-10 (Sampson) 
L 111^= 5-65360-10 (Sampson) 
Le, = 7-18070-10 (de Sitter)- 
Le, = 7-87017-10 (de Sitter) 
L n, = 1-7017203 
L ^ 1-3338724 
a;3 =+0°-0069513 
=+0°-0018975 
from which we get — 
L 9^ii—ip"- 5-08047 
L 21 ^^^-^^^^0'^ = 5-20683 
1+w; 
i. (77^,-37^3— Oa>,— 40.3) -8-23104-10 
L (77^4— 3/^3— Iw^—Su^g) =8-34394-10 
L (772,— 3^3— 20.4— 20.3) = 8-43346-10 
L (7w,— 37^3— 3d>,— ld>3) = 8-50765-10 
L {ln—^n—^u}~OQ^) = 8-57099-10 
With these numbers we have finally : — 
Argument. 
S(7V 
—3^3 — Ow,- 
-4^3) 
+ 0"-00 
-0"-01 
S(7Z,- 
— 3/3 — l(jt»,- 
-3^3) 
-0-09 
+ 0-12 
S(7V 
3/3 2tL),- 
-2-3) 
+ 0-72 
-0-96 
8(7/4- 
— 3L — 3w,- 
-1-3) 
-2-67 
+ 3-57 
S(7/,- 
-3/3—40;,- 
-00.3) 
+ 3-88 
-5-19 
It should be remembered that the mean values of e^ and e,, and the 
mean values of the motions of the apsides have been employed, so that 
the perturbations shown are mean values. Thus as e^ is variable to the 
* See Kon. Akad. v. WetenHcliappen te Amsterdam, April 24, 1908. 
