740 
PROFESSOR CAYLEY ON PREPOTENTIALS. 
Also 
and hence 
2q + ldV r * _ 
-V *=J„ <BmI 
10+ri 
2q+l 
2 , 
t 
e de 
□ V 
=f 4- 
Je+>i L 
2m 
l ■ 1 + (2g+ 
tf+A 2 ’*' t 
t +/ 2 
+m(m- 1) I- . 4{^ . . . +^+£}t] 
+4mJ «-©(' ? - 4—5 ^_i 
/<W\ 3 
0 ^(G«) ••• + (^c) +(*)) 
— j m 0 
cm rf g fl 2g + l 
da* ’ ’ ' ' dc*' de*' e del’ 
105. Writing I', T' for the first derived coefficients of I, T in regard to t, we have 
T t “ i 
“(*+/*)* ' * * *** (t + h*)^ 2 2 ’ 
and the integral is therefore 
~ 2\t+p”’^t+h^ t )■- 
£ dt[2ml m - 1 T+m(m-l) I”- 2 . 4I'T ) . 
=r dt( 4m I m ~ 1 T' + 4m(m — 1 ) I w_2 1'T), 
= 1 ^4m^( Iro - 1T ); 
= — 4m J m - 1 0. 
d 
Hence, writing (J’ B 0 )' instead of ^ (J Wi ©), we have 
□ V — — 4m J m - X 0 
. T / a dd c dQ e dQ\ 
+4roJ 0 («+,+/ s s5---+9+v^s+jt' < *; 
viz. this is 
-(J m ©)' 
— J m 0 D0; 
□ V=— 4mJ ra - 1 0 
J o 
-4(J»0)'i 
+ 4J "®I4 
