190 THEORY OF COLLOIDAL BEHAVIOR 



J. A. and W. H. Wilson 1 developed Procter's line of reasoning 

 further and derived the following formula by purely mathe- 

 matical reasoning from the assumption that gelatin combines 

 chemically with hydrochloric acid to form a highly ionizable 

 gelatin chloride: 



V(K + y)(CV + 2VCY y ) - y = 



where V is the increase in volume in cubic centimeters of one 

 milliequivalent weight of gelatin, C is the constant corresponding 

 to the modulus of elasticity of the gelatin, and K is a constant 

 defined by the equation 



[gelatin] [H+] = ^[gelatin ion] 



Given the constants, it is obviously possible to calculate all the 

 variables of the equilibrium. 



Procter and Wilson found the value K = 0.00015 by means 

 of the hydrogen electrode on gelatin solutions and the value C 

 = 0.0003 at 18C. from experiments on the swelling of gelatin 

 jellies. From Procter's data on gelatin, Wilson 2 calculated 768 

 as its equivalent weight. Using these constants, Wilson and 

 Wilson calculated the variables V, y, and z for comparison with 

 the data obtained experimentally by Procter. The calculated 

 and observed results are shown in Table XXXVIII and it will 

 be seen that the agreement is absolute, within the limits of 

 Procter's experimental error. This is shown even more strik- 

 ingly when the values are plotted. Procter and Wilson regard 

 this as establishing their theory quantitatively. 



The relation of V to e is governed by Hooke's law, ut tensio 

 sic vis, and since e represents a pressure equal in all directions, 

 the result is a pull upon the jelly equal in each dimension. The 

 quantitative expression is 



e = CV 



where the constant C is determined by the bulk modulus of the 

 gelatin. 



1 WILSON, J. A., and WILSON, W. H., J. Am. Chem. Soc., vol. 40, p. 886, 

 1918. 



2 WILSON, J. A., J. Am. Leather Chem. Assn., vol. 12, p. 108, 1917. 



