Films and the Foaming of Solutions. 631 



expression for the extension of the film 



8r|i 



oc 



As an example of the practical application of this formula, 

 we will take the case of an aqueous solution of valeric acid 

 of concentration '0048 grm. per c.c. From Traube's * 

 surface-tension measurements we obtain the value 



-|- T =2200 dyneCm - 2 . 

 Oc grm. 



Milner's formula gives 



r=*4xio-«£*%, 



cm. 2 ' 



so that tiSt ft _ lA-sj 



— r^-= 9*7x10 5 dyne. 

 oc 



Hence if h and t are expressed in cm. wo have 



A7i=A 2 * 2 xl'3xl0 6 cm. 



If we assume the comparatively large values /i=l cm. and 

 t = 10~ 4 cm. we have 



Hence a film 1 cm. high and 1000 /jl/jl thick would stretch 

 only about one-eightieth of its height under its own weight. 



We see that the elasticity of a film of a solution is deter- 

 mined by the magnitude of the product of the surface excess 

 and the rate of decrease of the surface tension with increasing 

 concentration. This quantity may therefore be regarded as a 

 measure of the foaming power of a solution. If the quantity 

 were evaluated for a number of solutions, we should expect 

 those solutions, for which the value was relatively high, to 

 possess the property of forming a durable foam. At present 

 I am investigating the relation between this quantity (or the 

 corresponding quantity in the more general theory) and the 

 foaming power of solutions. 



In the case of solutions of the type we are considering, 

 the value of —T'^T/'dc increases at first with increasing con- 

 centration, and then diminishes as the concentration is further 

 increased. This is in agreement with the experimental fact 



* Lieh. Ann. vol. cclxv. p. 30 (1891). 

 2T2 



