479]
FUNCTION IN THE LUNAR AND PLANETARY THEORIES.
519
and for the purpose of reference form as it were an Index to his result as follows :
Reciprocal of Distance = as follows :
Terms of order zero : terms of orders 2, 4, 6, having the same arguments.
A' - ©'
L’-11'
L - ©
z- n
(iy ( 1 . . 20) . .
cos
i
0
— i
0
(21)* a e) (K> (21 ..30) ..
33
i
+ 1
— i
-1
CO
CO
He*
CO
33
i
+ 2
— i
- 2
(35 )«(*«)» (*«')* ( 35 •• 35) ..
33
i
+ 3
— i
- 3
(36)*(i«)V (36 ..39) ..
5?
i
0
-i + 2
- 2
(40) ¿ e) e') f (40 ..43) ..
3 3
i
- 1
-i + 2
- 1
(44)* (J e'frf (44 ..47) ..
3)
i
- 2
— i + 2
0
(«»‘(M'diV (48 ..48) ..
33
i
+ 1
-i + 2
- 3
(49)* (| e) (| e') 3 rf (49 ..49)
3?
i
- 3
- i + 2
+ 1
Terms of the first order : terms of orders 3, 5, 7, having the
same arguments.
L' - ©'
L'-W
Z - ©
z - n
( 50) £ \e ( 50 . . 69)
cos
i
0
— ¿
+1
(70y ( 70 .. 89) ..
33
i
+ 1
— ¿
0
(90 )«(*« )■(*«') (90 •• 99) ..
3)
i
+ 1
— ¿
- 2
(100)*(Je) (ief (100 .. 109) ..
3?
i
+ 2
— ¿
- 1
<U0)*(è«)*(èO’ (no •• ns) ••
33
i
+ 2
— i
- 3
(1147(16 f^e'f (114 .. 117) ..
33
i
+ 3
— ¿
- 2
(H8)‘(Je) 4 (J«') s (118 .. 118) ..
33
i
+ 3
— i
- 4
(1197(*«>»(i0 4 (119 •• 119) ••
33
i
+ 4
— i
- 3
(1207(1 e)rf (120 .. 129)
33
i
0
-i+ 2
- 1
(1307(1 e') if (130 .. 139)
33
i
- 1
— -i + 2
0
(1407 (|e ) 3 rf (140 .. 143)
33
i
0
- i + 2
- 3
(144)* (¡j e ) 2 (¿ d) rf (144 .. 147) ..
33
i
+1
-¿+2
- 2
(148)‘ft e ) ! (Je')f (148 .. 151) ..
33
i
- 1
-¿+2
- 2
(1527 (i«) e'frf (152 .. 155) ..
33
i
- 2
- i + 2
- 1
(1567 h (i e') 2 ^ 2 (156 .. 159)
33
i
- 2
-¿ + 2
+ 1
(160 7(|e')V (160 .. 163)
33
i
- 3
- ¿ + 2
0
(1647 (¿ e ) 4 (2 e ) rf (164 .. 164)
33
i
+ 1
- ¿ + 2
- 4
(1657(ie) 3 (£e')V (165 .. 165)
33
i
+ 2
- ¿ + 2
- 3
(166)* (J e ) 2 (| e'y rf (166 .. 166)
33
i
- 3
+ 2
+ 2
(167)<(ie) (Je')- 1 ^ (107 .. 167) ..
33
i
- 4
- i + 2
+ 1
(1687 (|e)V (168 .. 168)
33
i
0
- ¿ + 2
- 3
(169)* (1 e ) 2 (è e ') rf (169 .. 169)
33
i
- 1
— i + 4
- 2
(170)*(J«) (MV (170 .. 170) ..
33
i
- 2
— % + 4:
- 1
(1717(K)V (171 .. 171)
33
i
- 3
- i + 4
0
