280 PHYSICAL PROPERTIES 



The relation between the time of stirring and the quantity 

 of casein dissolved does not obey either of the above cited equa- 

 tions; it does not appear to obey any of the ordinary chemical 

 reaction or solution velocity formulae. The rate at which the 

 velocity of solution falls off; the negative acceleration of the 

 process; is far too great to permit of representation by either 

 of the formulas (i) and (ii). Nor is any better agreement ob- 

 tained if we insert, for the value of a in these equations, the 

 actual number of grams of casein present in the mixture, or if, 

 allowing for the diminution in the surface of the casein exposed 

 to the action of the solvent, as solution proceeds, we endeavor 

 to apply the relation 



^ = K(A - X) {B - X), (iii)* 



where A is the number of grams of casein which the amount of 

 alkali present in the solvent is capable of holding in solution, 

 B is the number of grams of casein actually present in the mix- 

 ture, X is the amount of casein dissolved at any given moment 

 and X is a constant. The relation between the time of stirring 

 and the amount of casein dissolved, however, does obey, very 



accurately, the relation 



X = Kt"", (iv) 



where x is the amount dissolved after time t, and K and m are 

 constants which vary with the nature and concentration of the 

 alkali solution employed as solvent and with the total mass of 

 casein present in the mixture. 

 The following tables enumerate illustrative results. f The 



supernatant fluid very nearly clear. It must be recollected, however, that 

 when periods of time of the order of a year are concerned no protein solution 

 can be regarded as being in equilibrium. Even in absolutely neutral solutions 

 the H+and OH' ions of the water lead to a measure of " autohydrolysis " (Cf. 

 Chap. XVI) and the above solution was distinctly acid (Cf. Chaps. V and IX). 

 Hydrolysis of caseinates of the bases leads to the formation of paranucleins 

 which are insoluble in neutral and faintly acid solutions, and to substances 

 which bind bases and therefore tend to abstract them from the casein (Cf. 

 Chap. XVI) and consequently, when the total amount of base present is so 

 very little more than enough to hold the casein in solution, to indirectly pre- 

 cipitate the casein itself. 



* In its integrated form: log . ,„ _ — r = Kt. 



t For additional experimental results the reader is referred to my original 

 communication (86). 



