94 MR. C. J. HARGREAVE ON THE CALCULATION OF ATTRACTIONS, 



2nd. Let n = 4, and the term is 



. 1 



or 



f^ — 



3rd. Let /? = 6, and we get 



+ a7 ^ a ( - g ^'2 + ^'4 (4 g2 - A) ) + a8 (p' « !!|l! _|_ ^\'6 p a' c? a' - a7 F a £ ^'2 



which is 



4 

 r 



47r^ 



20. In these three terras write a for a, s^ for s, and Aj for A, and add them to the 

 other value of V, and apply the equations 



7^"«'2 na'da'= \f^^ a'4 d ix a'^ ^' d) +^" a'3 & a! d{(p d) =\ aU^ ip' a -^ a^ k(^ a 

 - 2j*J d'^xd"^ ,d(pd -J'J <pd d{d'^ M) = ^a4g2 (p' a + aS a (p a - 2 a3g2 ^ a 



+ 2^' 9 a' ^ (a'3 g'2) - fj <p d d {d^ A'), 



and similar equations for the other integrals, and the value of V for an internal point 

 becomes 



r ,4'1i-T^+kl'"-^')}),,^i /.. <«'4i-.'+|(2.--Ao}) 



y. ^« — a:j ^ ''«' + 3-Jo ^ " — s;? ~ ''" 



+ 9l^'- 7^+35) V^y« ^«' ^^^ dd + ;jj^ <pd \^, ^' ddj I 



= 47r^|M'a-M'a + ^Ma + y(^2_l) (r2N'a - r2N' a + ^ Na) 



+ |(^^-y^2 + A)(^p^_^Pa+^Pa)}, 

 where the functions M, N, P, &c. are substituted for the corresponding integrals. 



