TJie Dissolution of an Isotropic Solid. i8i 



from this equation the calculated numbers in column C of 

 the last table have been derived ; the value of the constant 

 employed is 0'00045, and has been obtained from the 

 observation that 50 cc. of gas were evolved in 82 seconds. 

 In several cases there is a fair agreement between the 

 observed and the calculated time ; in the latter stages of 

 the dissolution, the observed intervals increase more rapidly 

 than the calculated intervals ; the reason may probably be 

 the one previously suggested, that there was not sufficient 

 disturbance of the solvent to render it homogeneous. The 

 observed rapid diminution of evolution of the gas towards 

 the end of the operation would also harmonise well with 

 the theory which I have advanced, which would require for 

 perfect solution an infinite time. In none of their experi- 

 ments have the authors given the observed time of the 

 complete dissolution of the sphere ; they only carried their 

 observations as far as the evolution of 1,000 cc. of gas. 



The authors in their paper give the following equation 

 to denote the velocity of solution, 



V = KSo( A - C)IAi 

 In this equation V denotes the velocity of the solution, S^ 

 the initial surface of the sphere, A the initial concentration 

 of the acid employed, and C the portion of the acid con- 

 sumed in the operation, K denotes a constant. 



This formula does not appear to me to be adapted to their 

 own results. They have estimated the velocity as follows : 

 they collected the gas in a graduated vessel, and the time 

 required for the evolution of each successive 50 cc. of gas 

 was noted ; this number divided by the interval of time 

 they take as the velocity ; but this will not be a correct 

 expression for the velocity at any given instant, it will be 

 the mean velocity during the interval, and will only be 

 suitable when the velocity varies slowly. If k be the 

 volume of hydrogen evolved at time /, the proper expres- 

 sion for the velocity will be -!• Let H denote the volume 



