MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 633 



beside be very laborious, as the series do not begin to converge until after 

 the sixth or seventh term. The difficulty of the series expansion might, 

 however, be obviated by the employment of tables that have been com- 

 puted for the definite integral. 



We have employed a method in which a previous independent deter- 

 mination of the diffusion constants was not necessary. Before passing 

 to the solution we shall call attention to an important and easy deduction 

 from equation (9). In order for H to be a constant the lower limits of 



integration 



x — x 



and 



2 a y/'t 2 by} 



should be constant for all rings in a given tube with given initial values 



x 



of Uq and V , and since a and b are constants — = should be a constant. 



Vt 



That is, for example, if we plunge a tube containing potassium chromate 

 in gelatine into a solution of silver nitrate and observe with a catheto- 

 meter the distance from the bottom of the tube at which each thin disc of 

 precipitate appears, and note, at the same time, the number of seconds that 

 have elapsed since plunging in the tube, the distance divided by the square 

 root of the time is a constant for all the discs in this tube, and for all tubes 

 with the same initial concentrations of the reacting substances. The 

 sample set of results given in Table II and all the tables, IV to XXIV 

 (pp. 643-648), show with what consistency this conclusion is verified. 



III. Determination op the Diffusion Constant and the 



Metastable Limit. 



x 

 This constancy of — -_ for any one set of observations under given 



Vt 



conditions does not show, when taken alone, that there is a constant 

 metastable solubility product H, but does show that, for a given concen- 

 tration of one of the ions, there is a definite concentration of the other 

 ion that will cause precipitation. 



In order to examine into the Constancy of H, the product of ionic con- 

 centrations as defined by equation (9), we shall need to employ the data 

 furnished by different initial concentrations of the reacting substances, as 

 collected in Table III, p. 635. 



Every two sets of initial concentrations, together with the correspond- 



x 

 ing values of — = , will give the data for calculating the diffusion constant 



Vt 



