TJlc Dissolution of an Isotropic Solid. 171 



at which the action takes place, and the quantity of water 

 holding the anhydride in solution, also on the chemical 

 nature of the solid to be dissolved. The number of vari- 

 ables in (24) may be diminished as follows. Suppose that 

 during the solution the same chemical compound is formed, 

 let <7o be the mass of the anhydride at the beginning, vi^ the 

 initial mass of the solid, vi the mass at time t. Then ing — in 

 will be the mass of the solid dissolved, and a^ — a will be the 

 mass of the anhydride which has entered into combination 

 with it, but by Dalton's law of combination the first of 

 these quantities will bear to the second a constant ratio 

 depending on the combining weights of the anhydride 

 and the substance to be dissolved, hence we have 



Wo - m = h{a,^ - a) 

 w^hen h denotes a constant. Hence : 



in + ha„ — m,„ 



h 

 Also if e denote the density of the solid ni = ev, and the 

 equation of chemical action becomes 



dv= - ns<^[ J- °- \dt. 



The form of the function f has, I think, not yet been 

 determined experimentally in a satisfactory manner ; subject 

 to previously mentioned conditions, I think it not unlikely 

 that the rate of dissolution will be found proportional to the 

 quantity of the anhydride remaining uncombined at any 

 instant. With this hypothesis the last equation may be 

 written in the form 



-^=-lsdt (25) 



Z' + r 



where r has been written for ~—Vo and / for ^. Wehave 



e h 



now three cases to consider depending upon the values of 



r. (i) Suppose that the quantity of acid is just sufficient 



to combine with the solid then r=0 ; (2) suppose that the 



