gQg PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



= -^P^def{a-'R+d) { +(8a^rTR-8a2)(« + R)(2R-0) 



-(2R-ey ] 



= ^n^dd/(a-'R + e) {8aR(a + R)(2R-^) 



-4(fl2 + 3«R + R^)(2R-^)2 + 4(« + R)(2R-^)3-(2R-0y } 



To exemplify our formula, let us suppose it applied to this proposition ; then 

 have we, whole force of attraction 



-8(a^ + 3aR + R0 -^« /(« + «) 



d-^ „, ... d 



+ 24(a + R) ^/(. + «)-24^/(^ + a) } . 

 Now, if /(2f 4- a) = ^ + a, or the force varies as the distance 



d~^f{z-\-a) _ z^ az' 



77^^ ~'¥73"'^T72 



d-'^f{z + a) _ z^ a, 



dz-"" 2.3.4 2.3 



d-^f{z + a) _ ^ 



+ 



dz-^ 2.3.4.5 2.3.4 



d-^f{z + a) _ z"" az' 



dz-" 2.3.4.5.6 2.3.4.5 



and ^ = 2R, a = «-R, 



hence we get \^'hole attraction 



= Jl_/8aR(a + R)(i^ + (a-R)2R^) 

 -8(a= + 3aR + R0(|-R' + ^^^. I^R') 

 + 24(« + R) (^R^ + 7^^ . -| R^) 



= ^|l6aR(« + R) (flR^-^) 



_^ (a^ + 3 a R + R^ (2 a W-B,') 

 o 



+ 16(«R^--|-R^)(a + R)-f «R^ + f|R'^} 



