1 14 Proceedings. 



p and q being constants to be determined by the initial 

 length of the edges. Substituting these values in (1), (2), 

 (3), we get 



V = xhnn + x 2 (pn + qm) + xpq 

 d~V = — 2dx(3x 2 mn + 2x(pn + qm) + 2 ) l) 

 S = 2 [x"-{m + n + mn) + x(p{i + n) + q(i + m)) + pq}. 



If such a solid were subject to the same conditions of 

 dissolution as were assumed in the paper referred to, the 

 differential equation would assume the form, 



(■zx 2 mn + 2x(pn + qm) +pq)dx ,, „. . . . . 



-^ ^7-^ -~ — - AL — = - l\xHm + n + mn) + x(p(i + n) 



armn + x-\jpn + qm) + xpq + r l ' ' vs 



+ 2(i +m)) +pq}dt. 



When the arithmetical values of the letters p, q, m, n are 

 assigned this expression may be integrated, and the dimen- 

 sions of the parallelopiped at any time determined. The 

 above expression will be simplified if certain relations co- 

 exist among the constants ; for example, if we have the 

 relations 



p q 



— = -> imn = m + n 



m n 



the equation takes the form 



dx 



hit. 



x 3 mn + x 2 (pn + qm) + xpq + r 



Also we may have the relation p = Q, q = ; in this case 

 the parallelopiped at any instant will be similar to its initial 

 form, a condition which would probably hold in the dissolu- 

 tion of some crystalline forms ; in this case the equation 

 assumes the much simplified form 

 2,dx 



x mn + r 



= - l(m + 71 + mn)dt. 



From this expression for the velocity, the other circum- 

 stances of dissolution would admit of easy determination 

 by integration. In the previous paper, page 166 {Mem. and 



