The Dissolution of an Isotropic Solid. 169 



from (19) we have 



d-a d-A 

 dydx~dYdX 

 integrating we obtain 



changing the variables from x, y to X, Y b}' means of (20) 

 the last equation becomes 



n^A-cJ J .ecv( -^ + — - j^V^X +.-_/ J sec,. 



fdcosa dcosft dcosa dcosl3\ 



[-dx -^Y~—dT^T'r^'^^- 



It will be possible to assign to c such values that the co- 

 efficients of c and c" in this equation do not contain c. If 

 we denote these coefficients by P and O, multiply both 

 sides by dc and integrate, and denote by V the volume of 

 the shell, bounded by the primitive and the instantaneous 

 surfaces we shall get the following equation 



V = Ar-^P-^^-Q (23) 



a result which will be frequentl}' useful in the theory of 

 solution. 



II. Tlie subject considered chemically. 



In the foregoing investigation, dissolution has been con- 

 sidered as a geometrical question, there yet remains to 

 consider the matter as a chemical problem. 



The rate of diminution of a solid depends on a variety 

 of circumstances. If the acid be very dilute, the action is 

 slow, and if concentrated, in some cases the action may be 

 slow also, as in the case of strong sulphuric acid and zinc. 

 Solution requires not onl)' the presence of an agent capable 

 of forming a soluble compound with the solid, but also the 

 presence of some menstruum which continually removes 

 the product so formed. If the solution be heated, there is 

 usually an acceleration of action ; hence, if there be an evo- 



