56 



which is defined as the excess of concentration of diffusible ions of 

 the jelly phase over that of the external solution — 



2x+e^2y + z. (3) 



Since [N~'] is greater in the jeUy than in the surrounding solution, 

 the negative ions of the coUoid compound will tend to diffuse outward 

 into the external solution, but this they cannot do without dragging 

 their coUoid cations with them. On the other hand, the cohesive 

 forces of tlie elastic jelly wiU resist this outward pull, the quantitative 

 measure of which is e, and according to Hooke's law — 



e=^GV (4) 



where C is a constant and V the increase in volume in cubic centi- 

 meters of one millimole of the coUoid. 



Now, since we have taken unit quantity of the substance G — 



[(?] + [(?ilf+]=l/(F+«) 

 or— 



[(?]=l/(F + a)-z • (5) 



where a is, not the initial volume of the colloid, but the free space 

 within the jelly before swelUng through which the ions may pass. 

 For our hypothetical substance, we may consider the limiting case 

 where the value of a is zero, in which case, from (1) and (5) we get — 



(l/F-z)2/=Zz (6) 



and from (2) and (3) — 



2 = e "1- 2 y/ey 

 or — 



z^CV + 2y/CVy (7) 



From (6) and (7)— 



V{K + y)(CV + 2^GVy) ~y=0 (8) 



where the only variables are V and y. Now we have only to know 

 the values for the two constants, K and C, to plot the curve for any 

 variable in terms of any other value. For example, by giving y a 

 definite value, we can calculate V from (8). Eaiowing y and V, we 

 can calculate z from (7) and with y and z, we can calculate x from (2), 

 while e is obtained directly from (4). 



If any values for K and C be substituted, the resulting relations 

 will be found to be of the same general nature as are obtained with 

 any proteins in acid solutions, but values of K and C for gelatin have 

 been determined. By means of the hydrogen electrode, Procter and 

 Wilson found the value K = 1-5 X 10 ~* for gelatin and HCl, while 

 their experimental value for C at 18° was 3 X 10~*. The whole 

 series of curves for these values of the gelatin constants has been 

 plotted, and appears in the Journal of the American Leather Chemists' 

 Association for 1918, pages 184 and 185, which should be consulted. 

 Procter's experimental determinations are included in the same figures, 

 and it wiU be seen that better agreement could not be obtained if the 

 curves were drawn from his data. 



Since, theoretically, the calculated curves should not coincide 

 absolutely with the experimental ones for gelatin and HCl, it is 

 interesting to note why no appreciable discrepancies were found. 



