256 
MR. LUBBOCK’S RESEARCHES 
— e s e ; cos (3 x — z) — ^e 2 e ; 3 cos (2a? + 2 z) — —e^e^os (2x —2 z) 
16 
[44] 
[47] 
[50] 
— ee, 3 cos (a? + 3 z)— -^-ee/cos (a? — 3z) + '-L e 4 cos4z 
10 10 1 o 
[53] [56] [59] 
— * 
Terms in R multiplied by — -^-cos 4 — 
{i + t (e2 + e ' 2) + i e2fi ' 2 } { 1 + 5 e ' 2 + ^- 5 } 
[ 0 ] 
+ {_ 1 + ^ 4 e 4 ( 4 e / 2 + ! 35 e/ 
8 2 
+ 
+ 
{ { 4 <eS + ^ +S (e< + e ’ t)+ 1 «*«,*} { ■ + 5 «,*+ Jf-V } 
+ {M)4 
{- 1+ l- 
, f 3 . 13 „ 15 0 15 „ 15 9 45 ,1 /0 , . 
+ { -~2 + T6 e + 4 e ‘ ” T e ‘ - T e> + T e ‘ / ecos (2 1 - x) 
[3] 
+ { J ~ rl e °" “ J e * + T C/2 + T e/2 ~T e/2 } ecos ( 2 1 + *) 
[4] 
+ | - 1 + ^ e- - 5 c ( - + - + - e 2 + — e r + — e/ 2 - — e r - 5 e r j ^ cos 2 
[5] 
f 1 19 „ 5 o , 5 9i 5 0.5 25 4 25 9 
4- < — — — e, 2 e 2 + — e. 2 + — e, 2 4 e 2 — — e, 2 
^ \ 2 16' 4 2 ( ~ 4 ~ 4 8 8 ' 
• cos 2 £ 
[I] 
3 e, 2 -5e;-4- e ( 2 4- ~ e, 2 } 
e cos x 
[ 2 ] 
+ 
y e / 2 } e /Cos ( 2 «-*) 
[ 6 ] 
* This multiplication of r 2 r ( 2 cos (X' — X,) 2 by r, 5 may be effected at once by means of Table II. 
