630 Mr. S. A. Shorter on the Elasticity of L\ 



value, because the amount of solute drawn from the interior 

 of the film will be large enough to cause a diminution of 

 concentration sufficient to increase appreciably the surface 

 tension. 



The magnitude of this elastic effect is easily calculated. 

 Suppose that a film of thickness t is held in a rectangular 

 framework of length h and breadth 6, and suppose that one 

 of the sides (which is supposed to be movable) is moved so 

 that the length of the film is increased to h + Ah. This 

 causes an increase 2b Ah in the area of the film, and if we 

 neglect the effect of the variation of the surface excess with 

 the concentration * the amount of solute drawn from the 

 interior of the film, to form the new surface excess, is 

 2Tb Ah. The consequent change of concentration is given 

 byt 



2TAh 



Ac— — — ^ . 



ht ' 



and the change of surface tension by 



Let us consider the stretching effect produced by gravity 

 when the film is placed with its length vertical, and the 

 movable side (which is supposed to be weighted to support 

 the initial tension of the film) downward. To support the 

 weight of the film, the highest parts of the film must be 

 extended so that the tension is increased by an amount 

 \pght (where p is the density of the solution) . The tension 

 in the lowest parts of the film will be unaltered. Hence we 

 may regard the stretching produced as equal to that which 

 would be produced by an increase of half the weight of the 

 film in the force acting on the movable side, i. e. we must 

 write 



Ar=ip 9 kt 

 in the preceding equation. We thus get the following 



* This amounts to neglecting- fiTc in comparison with t, which is 

 allowable, except in the case of extremely dilute solutions. 



t In the more general theory, applicable to solutions of any degree of 

 concentration, it is necessary to take into account the amount of solvent 

 expelled from the surface layers, 



