28 
MR. LUBBOCK’S RESEARCHES 
a 2 d- . 6 lj0 _ a 
da 2 
a i 
a 2 
d 2 .6, 
A- a 
da 2 
a t 
a 2 
d 2 .6, 
,2_ « 
da 2 
a i 
a 2 
d 2 .6, 
,3_ O 
da 2 
«/ 
a 2 
d 2 . b ] 
,4_ O 
da 2 a t 
{y~ t b3 '°~\ h3 A 
i^; 63 ’ 2 + 2 b3 ’ 3 
3 + &s, 8 -26 3>4 } 
{ 2 ^- b ^ + ^ b ^~T b3 ’ s 
} 
} 
The value of R given p. 349 of the former part of this paper is susceptible 
of much simplification. The first term of R for instance 
/ hs . 3 (« 2 e- + a? e , 2 ) aa^ ( . o ± (e°- + <y) \ 
a, + 2.2 a* ^ + 2a ( 3 \ sm ~ 2 + 2 ) bl ’ 1 
- 2 ~ . 4 a , 5 ( 2 e " + 5 a / 2 ( e °‘ + e / 2 ) + 2 a / 4 e / 2 ) 6 s,o + ^ (« 2 e2 + «, 2 e / 2 ) « «; 
1.3.3 a 2 a 2 , o 1 
+ 2.4 - .2 a,® ( e2 + e / a )^. g } 
/ ®1., 
= Wi. < 
' l a / 
b i,o , 3(a 2 e 2 + a ( 2 e^) aa k ( i k , e°~ + e 
+ 
2.2a, 3 
a a y / 
■° + 2a7 v 
sm 2 ^- + 
3 . 2 (a 2 + a, 2 ) (a 2 e 2 + a, 2 e, 2 ) 3 .3 a 2 a 2 
o s . n — s— j— rs- (e- + e,*) 6 
+ 
2 . 4 a, 2 i 
3 . 2 (a 2 e 2 + a, 2 e, 2 ) ja 
2.4 a, 3 a ; 
5,0 2.4 a ( ® 
3,0 
fe 5.l + <2.4. ; 2 n. V ( e2 + e /°') 6 s.s } 
3.3 a 2 a, 2 
2.4.2 a® 
and since 
, (« 2 + «/ 2 ) , « , 
fc 3 ,o = Ti & 6 .o — — 6 S , i See p. 26 
“/ u / 
3 a 
t3, ‘ “ a , {^ 5, ° * 6i ’ 2 } 
this term reduces itself to 
{ “ ~£ t + 2^7 3 ( Sin ' J 2 + 2 ) 6 ®-» ~ 274 V" (e °‘ + e ' 2) h' } 
=” , 4-f + 2 i vv s,n 2 — r-)M 
