364 Mr Greeiihill, Integrals expressed by [Mar. 8, 



Again, a>b> c, 



r^ dx _ 2 / /a-b Ib-c 



^ ^ Ja\/<ix-a.x-b.x-c)~ ^{a-c) ^^^ ^^ vV x^ ' \/ a^c 



if oo> x> a. 



r* dx 2 / fx-c /6-c\ 



(16) 



(17) 



6 /sj— {x — a.x — b.x — c) 



2 . ( I'b-c /a-b\ 



a > io J. 

 For example 



Jx V(a' + >-. fc'+X. c^ + X) 



2 / / c^ + X /a'-6^ 



2 „2 y > 



an integral occurring in the theories of Attraction, Electricity, 

 Magnetism, &c. 



(18) ' ^"^ 



\J\x — a.x — b.\{x — 'mf-\-n^'^ 



- — arrcnf ^^^"^^-^^^-^ ) A 

 -Ja^^'^'''ta(^-6)+^(x-a)' ^j' 



where a^ = (m — a)^ + r^, 



^''={m-bf + n\ 



2al3 



