44 
MR. LUBBOCK’S RESEARCHES 
, 3 (3 a 2 -a/) 7 , , 3.3 a* 
+ 2.4 a/ 5 > 4 + 2.4.2a/ 5 ’ 5 
3 5 
Changing b 3 into 2r an d ^5 into “ y we have 
3.3 a 7 3.3 a ; 5.3.3 a 2 7 5.3 (3 a/ — a 2 ) a a, A 
~ 2T4T4 V 5 ’ 2 47274 V ° 5 ' 4 67274 . 2 V 7,1 ~ 6T2T4 V 7 ’ 2 
, 5.3 .7 a- h 5.3 (3 a 2 — a/) a a, A 5.3.3 a 2 A 
+ 6.2.4 a/ 7,3 6 .2.4 a/ 7,4 6.2.4.2 a/ 7,5 
3.3 a j 3.3a , 5.3.3 a 2 
° 5.2 ~ 7 0 755577 ° 5 * 4 “ 
2.4.4 a/ 4.2.4 a/ 
, 5 .3 . 3 (a 2 + a/) aa ( , 
°7,i ~ + 0 a 75 & 7,S 
6.2.4.2a/ 6.2.4 
,5.3a 2 ; , 5.3.7 a 2 A , 5.3 (a 2 + a/) a a ; A 
5/2 a/ 07,2 + « o '7 ~ 3 °7,s + °7. 
6.2.4a/ 
6.2.4 a/ 
5.3 a A 5.3.3 a 2 A 
~ O T 4 7,4 “ 6 . 2 . 4 . 2 a/ 7,5 
3.3 a 7 3.3 a A 5 .3 a / (a 2 + a/) A a A a t 1 
“ ~ 2T4T4 7/ 5)2 ~ 47274 V- M “ 474 a/ l a/ ° 7 * 2 ” 7/ ° 7 ' 1 ' ^ &7 ’ 3 / 
,5.3a 3 , , 5.3 a / (a 2 + a/) A a , a ; 1 
+ 672 «7 1 ”‘ + 670 V- 1 — ^ ^ 4 m - 37 I 
5.3.3a 2 / 7 . \ 5 a 2 / 7 , A 1 5.3 a 3 , 
- 270 VC 7 ’ 1- 7,3 J + 2X4^l’- 3 " 7 ’ s ) 0<* 7 * 4 
3.3 a ; 3.3 a 7 5.3 a j , 3 . 3 a A 
“ 074 H/ 5 ' 2 4.2.4 a/ 5 ’ 4 4.4 a/ 5 * 2 + 6 a/ 5 ' 3 
5.3 a, 2.3.3 a , 4 a ; 
+ 6.2.4 a/ 5,4 4.4 a / 2 5,2 + 4.4 a/ 5,4 
_ 75 a, ,3a 2 , , _9 _£l 
32 a/ 5,2 + 2 a/ 65,3 + 32 a/- 5,4 
Operating in the same way on all the terms in R multiplied by the squares 
of the eccentricities, we obtain finally the quantity 
, ^ J{a 2 e 2 + a/e/} 5 jLjLsin 2 ii-/ b, . , 4- b, . , , \ 
+ 2 | 32 5,* 16 a/ 2 1 5 > l ~ 1 5,i+l/ 
- ^ { ib S,i-l - ib S,i+ 1 } } C0S * ‘ 
,^[{2i+7}a t , { 8 i + 1 3 } a 2 { 18 i + 15} a 4- . , . 1 ^ , . 0 
+ 2 | 84 V *«- 1 + 32 V 64 -,%+lp ! cos(..l + 2x) 
