44 
MR. LUBBOCK’S RESEARCHES 
i ° (3 a ~ a r) i i 3.3a- , 
'2.4 a/ 5,4 + 2.4.2a/ 5 ' 5 
3 . 5 
Changing’ b 3 into- b 5 , and b 5 into — -g- b~, we have 
3.3 a ^ _ 3.3 a ^ 5.3.3 a 2 , 5.3 (3 a/ — a 2 ) a a t ^ 
~ 2.4.4 a/ 5,2 4.2.4 a/ 5,4 6.2.4.2 a/ 7,1 6.2.4 ^ 7 
a/ 
, 5.3.7 a 2 t 5.3 (3 a 2 —a/)aa (A 5.3.3 a 2 A 
+ 074 V 7,3 6 .2.4 a/ 7 * 4 6.2.4.2 a/ 7,5 
3.3 a, 3.3a ^ _ 5.3.3 a 2 , 5.3.3 (a 2 + a/) aa ; , 
— 944 / y 2 5 > 2 4 9 4 « 3 5,4 fi 9 4 9 /» 3 ° 7 > 1 d O A „ 3 ° 7 > 2 
2.4.4a/ 4.2.4a 
6.2.4.2a/ 6.2.4 
,5.3a 2 / ,5.3.7a 2 , 5.3 (a 2 + a, 2 ) as, , 
+ 672 7? 5 «> + 67274 V + 67274-/- 4 
5.3 a j 5.3.3 a 2 ^ 
672 a/ 7,4 “ 6.2.4.2 a/ 7,5 
3.3 a A 3.3 a ; 5.3 a J (a 2 + a/) 7i a h a A } 
2.4.4a/ 5,2 4,2.4 b/ 3,4 474 a/ I a/ 7,2 a } 67,1 ~ ~a, 67,3 J 
,5.3a 3 , , 5.3 a / (a 2 + a/) 7 a , a 7 \ 
+ 672 if ^ ■ 4 670 V l ~if 5 ’.‘ - ^ *» - i, l "} 
5.3.3 0"-;, , 1 . 5 o»/, , 1 5.3 o> , 
"!X4vr' ,_V r 27474 vt M ’•’/ Ov 7 ' 4 
3.3 a 
2.4.4a/ 
3.3 a 
fA 4 ~ 
5.3 a 
^ 5,2 + 
3.3 a 
4.2.4 a/ 4.4a/' 3,s ' 6 a/ 
^ 5,3 
5.3 a, 2.3.3a, 4 a, 
+ - — °5,4 2—r- rs °5,2 + 777 7s s ' 4 
6.2.4 a/ 
4.4 a/ 3,4 ' 4.4 a/ 
/ 0 a , .3 a- 7 | 9 a , 
“ “ 32 ^/ 5 ’ 2 + "2 a/ 5,3 + 32 a/ 3,4 
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/} A 7 L sin 2 A / , +b _ \ 
+ 2 i -32- 5,1 16 a/ 2 l 5 ’ 1_1 5 > l + 1 / 
- ,4 if (e! + { ' b 5,i -1 - f 4 5,i+l } } ® S f ‘ 
{iii+n « 4 . . . 4 . { 8 i + 13} «• J_, _ {I8i+ 15? ai si+ 1 } e . cos(it + 2 „ ) 
, j i - " 1 ' ) , {8i + 13 } a 2 /, {18 i + 15 ^} 
+ Z 1 64 T 2 5,i-1 32 7i 5,i 64 
