94 
MR. C. J. HARGREAVE ON THE CALCULATION OF ATTRACTIONS, 
2nd. Let n = 4, and the term is 
T (^ 2 ~ t) 1 d ( jJ 0*' 2 ~t) { P a ' d a ' "+ ° b $ a ( " 2 ^ + ( jJi ( 3 j2 ~ A )) 
+ a 6 <2>' a — j- a' 4 F a' da! — a 5 Fas y/ 2 J* 0 a ' 4 IT a' </ a' j- , 
or 
y8 |a 5 ?ffl (- -1- + ^ (3 s 2 - A)) + a 6 ?' a^s 2 + a' 4 F a! d a' 
- §- 5 a^a. s +§- 5 /\'*na'da’j. 
3rd. Let rc = 6, and we get 
^fr 0" 4 - t ^ + s) A) d t*' A - fv 2 + I) { X” <, " i ? «' 
+ a 7 ipfl^-£ jw,' 2 + |X 4 (4 s 2 — A)) a s p’ a — |- a' 6 F a' d a' — a 7 F as pJ 2 
+ f o a a' e Ila' da' j, 
which is 
^(f* 4 - y + §Q { P ay ( 4 £ 2 - A) + a 8 p' a ^ s 2 - 
a 7 F a + j/ a' 6 n ah/a' j . 
20. In these three terms write a for a, s x for s, and A 1 for A, and add them to the 
other value of V, and apply the equations 
J ^ a' 2 Yla' da' = \ a' 4 d {x a' 2 <p' a!) + a' 3 0 a' d (p a') = ~ a 4 s 2 p' a + a 3 A p a 
— 2/1 a! 3 x a ,s • d p a' — J' p a' d (a' 3 A') = a4 s 2 p' a + a 3 A p a — 2 a 3 s 2 p a 
+ ‘iC‘ pa' d (a' 3 s' 2 ) -fj pa! d (a' 3 A'), 
and similar equations for the other integrals, and the value of V for an internal point 
becomes 
= 4 7T | M' a — M' a + ~ M a -f ~ (jjJ 2 — {f 1 N'a-r 2 N'a + ^Na) 
+ y (^-|^ 2 + |)(r«Pa-r»Pa+ipa) ), 
where the functions M, N, P, &c. are substituted for the corresponding integrals. 
