Tlic Dissolution of an Isotropic Solid. 



i6i 



Next consider a right cylinder of which the section is 

 the ellipse 



Also let us suppose that the action of the solvent is confined 

 to the curved surface, then x, y being co-ordinates of a point 

 on the instantaneous curve situated on the same normal as 

 the point X, Y we have the following relationship 



Y-y fi'^X 



X-.x «-'Y-^ 

 whence 



^~a%x-X) + d-'X 

 substituting this value of Y in the equation to the ellipse 

 and the equation 



we obtain 



X"{a''x - X{a'^ - b"") Y + a^b'^X^ - d^{a-x - X(«2 - //-) }^ = 

 (X - x)\ay- + {a\x - X{a' - b^) Y] - c^a^-x - X{a^ - F-) }- = 

 expanding these equations in powers of X, we may for 

 brevity write the results as follows 



PX*-QX« + RX- + SX-T = (14) 



UX*-VX3 + WX--YX + Z = (15) 



the coefficients of the different powers of X having the 

 following values : 



Y = \]^{a^-b^f 

 Q = 2a'^x{a^-b') 



R = ayP + «*^2 _ ^2(^2 _ /,2)2 



S^2xa\a^-b') 

 T = a'x^ 



Y = 2x{a'"-b^){2a^~-b') 



W - a'i^.^ +/) + 4«2^^(fl2 _ b^) + («2 _ //2)2(^2 _ ^2) 



Y = 2{a'x{x^ +y-) + a-x{a^ - b''){x- - c-)} 



Since P = U, if we subtract (14) from (15), we obtain 



X\Q - V) + X'^W - R) - X(Y + S) + Z + T = (17) 



L 



(16) 



