1917] 



on Soap Bubbles of Long Duration 



199 



Effect on the Gas Tra^jj^sference Rate of the 

 Composition of the Soap Solution. 



The internal excess pressure P, in a bubble of constant composi- 

 tion, and therefore of constant surface tension T, enclosed in a vessel 

 sealed off from the atmosphere, varies inversely as the diameter D, 

 according to the law F = 4T/D. 



Hence if the rate of gas transference varies directly as the internal 



excess pressure, it will consequently vary inversely as the diameter. 



Now, in Fig. 6, taking the oriirin^at the point where the bubble 



vanishes, and measuring x (time) horizontally to the right in days, 



and y (diameter) vertically downwards in cms, we found tliat the gas 



- 1 . . d y ^ d y k 



transrerence was measured at any time x m - ^ \ hence - -^— = - 



^ ^ dx dx y 



where ^ is a constant, the graph o^ ^- to - is a straight line, and 



dx y 



the curve of contraction is the i^arabola y'^ 



Do^ 



h X, where D„ is 



O 05 lO 15 -20 -25 -30 



Fig. 10. — Gas Transference through Bubbles. 



Rates plotted with reciprocals of diameters. (1) Black H bubble of constant 



composition. (2) Golden H bubble of increasing dilution. 



the initial diameter— a result usually found to be the case. The 



121 



X. 



equation of the particular curve in Fig. 6 is y- = 121 



But, when a bubble partly composed of glycerine is exposed to 

 water vapour and thereby progressively diluted, then the surface 

 tension will increase ; and' the internal pressure will rise at a greater 

 rate than would be due to diminution of diameter alone. The graph 

 of the rates of gas transference, plotted with the reciprocals of the 

 corresponding diameters, would no longer be a straight line. The 

 next figure (Fig. 10) shows the graphs obtained in the case of (1) bubble 



