SWELLING 293 



(70) (71) (72), Wo. Ostwald (64) (65), Chiari (16), Ehrenberg 

 (23), Procter (74) (75) (76) (77) (78), and Lenk (50). 



Hofmeister found that the swelHng of gelatin plates proceeds, 

 at first rapidly and then more slowly, until it attains a maximum 

 which is a function of the thickness and weight of the plate. 

 After the attainment of this maximum the superficial layers of 

 the plate tend to go into solution, especially if the water be acid 

 or alkaline, and the plate, in consequence loses weight. Desig- 

 nating by the sjonbol W the weight of water which unit weight 

 of the gelatin absorbs from water or a watery solution in t 

 minutes, Hofmeister found that the empirical equation: 



w = pIi i — \ (v) 



^h) 



applies with tolerable accuracy, P being the maximum amount 

 of water which unit weight of the gelatin plate will imbibe (the 

 swelling-maximum), c a constant and d the thickness in milli- 

 meters of the plate at its maximal degree of swelling. This 

 leads to the conclusion that the initial velocity of swelling is 

 proportional to the amount of swelling which the plate is able 

 to undergo and that it therefore decreases regularly as the degree 

 of swelling approaches more and more nearly the maximum. 



Pauli assumed that each particle of the gelatin takes up water 

 from every neighboring, more fully swollen particle at a velocity 

 proportional to the difference between their water contents. This 

 leads to the equation: 



„ 1 , M-Q , .. 



where Q is the quantity of water taken up by unit weight of 

 gelatin in time t, M is the maximum degree of swelling which 

 the gelatin attains, Qi is the quantity of water taken up by unit 

 weight of gelatin in time ti and i^ is a constant which varies 

 inversely with the thickness of the plate. 



Hofmeister's formula leads to the conclusion that the velocity 

 of swelling is at every instant proportional to the square of the 

 swelling which the plate has yet to undergo, Pauli's to the con- 

 clusion that the velocity of swelling is at every instant propor- 

 tional to the first power of the same quantity (termed by Pauli 

 the "swelling deficit")- Both formulae lead to the conclusion 



