230 
MR. LUBBOCK’S RESEARCHES 
+ 
re 2 f i a 2 , __ ( 1 + 2 i) a 3 , 
(i(n-re,)+2re)i(n-re,) W ^ * a? S,i 
+ ^>3,i+i} £C0S (*(»*- n,t) +»<-,«) 
+ 
3 (i (re — n ( ) + re} 2 ! 
n a , 
— o 
l,i 
+ 
2(i (re — nj) + 2 re) i (re — re,) (re — re,) — re) n ^ a > 
+ phi j> e cos (i(nt — njt ) +nt — 
2 in 3 f _ 3 a s 
(i (re — re,) + « ( ) (i (« — «,)+« + re ,) (i (re — ?i,) — re + n,) *■ 4a ‘ 
'Ai- 1 + 2a/s,i 
+ 4^ *s,£H-l } e / cos (‘ ( w * “ w /0 + M ~ 
+ 
n 2 / 3 (1 + i ) a^_ 
("i (re — re,) + « + re,) (i (re — re,) — re + re,) L 4 a 
za , 
,, 2 3,i— 1 3,8 
(1 -i 
- fc S,i+l } e l C0S ( i ( re 1 - »i0 + »J* “ 
£ being any whole number positive or negative, but excepting the arguments, 
0, n t — zs, njt — zr r 
re 3 
. - » J 
r 
n 
re 1 
(re - re ; ) (i (re - n^) + re) (i (re - re^) - re) 
1 
s 
1 
J3 
L 2 ( 
[i (» - »<) “ «) 
) 2 ( 
(re — « ( ) + «)•* 
re 1 
m 
2 (i{n — nj) — re) n ~ n ‘ 2 (i(n — nj) + re) 
Resolving the other fractions in the same manner, 
iL = — b , • cos i(nt — n,t) 
r (re — re,) 2 a, J >* v " 
« b + J2Lj_. . + ^—b ,, . , 1 1 cos i (re t — n.t) 
2 (i(n-n,) + n) *■ a i ' a t s ’* 2 a / 2 3,1-1 2 a, 2 3,8+1/ 
2 (i+l )re_f jL bo .+l£ b....\ecM(i(Ht-nfl+nt- V \ 
^ {*(*_„,) + „} l 4 a, 2 3 ,.-l 2 ^ 33 , 8 ^ 4 ^ 3 , 8 + 1 / ^ W 1 - ^ 
+ 2{i (re — nj) + 2re} { 1 + { 4a ] 2 &3 ,t— 1 + yja} is »* ~ 4a] 2 * 3 ,i-+i } ~ 4^ 6 3,i- 1 
, (1 + 2 i) a 3 3 ia 2 , 1 . A . . \ 
+ —^- 1 - 3 ,i- 4^**3, i+ij® 0 * v <m ^ + " / 
