272 
MR. LUBBOCK’S RESEARCHES 
3 m i a ' Jj ^_ e a_ ^ e a y 3 \ J ^ + 1 1 = 
2 /x a, 3 1 2 2 1 2 J 1 1 — m J 
2 [x. 
[1 — 3 r 0 } — 1 + ^4 3 = 0 
*■ J /x a 3 
2 -c 
(2 -2«. - c)»{r, - I- r,} - r, + |-?l ^ { 2 _ 2 w _ c 
(2 - 2 « + c)* { r 4 - |. ri } - r, - A ^ ^ J o 
+ 1 y = o 
+ 1 
}= 
} = ° 
„ 3 m. a 3 n 
m 2 — r . r ■' — = U 
2 /x a, 3 
(2-3m)«r„_r,-^3*{_|_ + ,} =0 
(!-«)'r,- f ,+ |-5A{jA_ + l}=» 
4c*{(l-3r 0 )r,-A+ 3r 0 }-r s + i^ =0 
f 3 1 15 m, a 3 f 5 
( 2 - 2 »- 2 c)*{r,- T r s )-r,- T _'_{ J _ 
( 2 - 2 »+ 2 c)*{r lo -_r 1 |-r 10 - Y -!- s | 
2 — 2 , 
2 m — 2 c 
2 + 2c 
2 — 2 m + 2c 
+ 1 } =0 
+ l} = 0 
(c + mr-{r I 1 -|r s }-r I1 + f + , }=° 
c + i}=o 
( 2 - ra + c)={r, J -|-r I }-r 15 + A’5l^{, 2 + ' 
jx «, 3 L 2 — m + c 
+ 1 
H 
(c - m) 2 | r 14 — r 5 j - r I4 + A JL j — — + 1 j = 0 
L 2 J 2 ju, a ( 3 L c — m J 
s„ f 3 1 9 m, a 3 J 
(2-i»-c)<*|r„- — r,j -r ls - _ - jr{j 
2 — c 
2 — m — c 
}- 
+ 1^ = 0 
* The letter r does not strictly denote the same quantity as in the notation of M. Damoiseau, or in 
that of the Mathematical Tracts, p. 33. 
