QQg PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



= J!!^P^d6f(a-R+e) I +(8«^TR-8a2)(« + R)(2R-0) 



-(2R-0)< } 



= ^P^d d/\a-R + 0) I 8 a R (a + R) (2 R- 0) 



-4(«^ + 3«R + R2)(2R-0)'' + 4(a + R)(2R-0)'-(2R-ay } 



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

 have we, whole force of attraction 



= _::_. |8aR(« + R)-^/(^ + a) 



-8(a^ + 3aR + R0 ~^f{z + «.) 



+ 24 (fl + R) ^f{z + a) - 24 J^/(. + «) } . 

 Now, if /(s + a) = s + a, or the force varies as the distance 



rf-y(g+«) _ g^ gg- 



rf;^-2 """273"''" 1.2 



rf-^/(g + a) _ g' g^^ 



rfs-' ~ 2.3.4 "^ 2.3 



rfs-* 2.3.4.5 2.3.4 



d^f{z + a) _ g" «^' 



rfl=^ "2.3.4.5.6 2.3.4.5 

 and i = 2R, a = a— R, 



hence we get -whole attraction 



= JL_|8aR(« + R)(^ + («-R)2R'^ 



-8(rt' + 3rtR + R-)(-|-R' + «-R. ^R') 

 + 24(a + R) ( ji R' + <i:-R ~ R') 



_^ (o^ + 3 « R + R=) (2 « R=- R*) 



.16 ^„R' - 1 R^) (« + R)-^ aR' + gR»} 



