172 Dr. J. BOTTOMLEY on 



mass of the solid, is greater than that required to saturate the 

 acid, then r is negative ; (3) suppose that the mass of the 

 solid is less than that required to saturate the acid, then r 

 is positive. The expressions obtained by integrating (25) 

 will be different in each case. If we suppose r negative 

 and integrate (25) in its present form we obtain the equation 



which may also be expressed in the form 



when a denotes the mass of the unneutralised anhydride 

 at any time ; this would make the time required to saturate 

 the acid infinite, if the mass of the solid be just sufficient 

 to combine with the acid, or if it be greater than the 

 mass required to saturate the acid ; this would seem 

 contrary to experience, but practically the acid might be 

 considered to be neutralised in a finite time, for the quantity 

 remaining unneutralised might be too small to be detected. 

 For example, suppose the area of the surface exposed to 

 the acid to be constant so that we may write 

 a = a^e-^'' ; 



if the quantity of acid neutralised in one hour be nine- 

 tenths of the initial quantity, after the lapse of ten hours 



the quantity of free acid would be only of 



I 0000000000 



the initial quantity. 



In a former part of the paper it was pointed out that 

 from an isotropic solid there would be removed in the 

 small element of time dt, a shell having everywhere the 

 same normal thickness dc, also that the volume remaining 

 undissolved at time / would be some function of c ; hence for 

 dv we may write -sdc, and (25) may be written in the 

 form 



M^r 



