﻿Shape of small Drops of Liquid. 191 



calculates that the shape of particle for which the value of 

 the integral 



TiS, 



$ 



taken over the surface S of the particle, is a minimum. 



The fallacy of the above method lies in the assumption 

 that the above integral represents the u surface-energy." At 

 the beginning of his mathematical treatment of the subject, 

 Mr. Rice writes: "Now let T be the surface-tension or surface- 

 energy per unit area of the interface " — a sentence in which 

 the fundamental error is tacitly introduced. This identifi- 

 cation of surface-tension with surface-energy per unit area is 

 allowable only so long as the surface-tension is constant. 

 The surface-tension is the rate of increase of the free energy 

 with the area of the surface. If the area S of a film is 

 increased by external forces from Sj to S 2 the work done is 



I TtfS, 



which is equal to the change of free energy of the film. 

 If the film is so thick that T is independent of S, the above 

 expression becomes 



1(8,-8,). 



Hence in this case the variation of the quantity TS is equal 

 to the variation of the free energy, so that T mav be called 

 the " surface-energy per unit area of surface "*. When the 

 film is so thin that T is a function of the thickness (i. e. of the 

 area), it is as incorrect to call the surface-tension the " surface- 

 energy per unit area of surface " as to call the pressure of a 

 gas the " negative volume-energy per unit volume," or the 

 tension of a spring the " elastic energy per unit extension/' 



The fact that a blood corpuscle is not spherical simply 

 shows that it cannot be regarded as a drop of liquid sus- 

 pended in another liquid. The occurrence of factors modifying 

 simple surface-tension effects is quite common even outside 

 the sphere of biology. A familiar instance is the formation 

 of a soap layer at the interface between an alkaline solution 

 and a vegetable or animal oil. This makes possible the 

 formation of long thin cylinders of solution in the oil, which 

 do not break up into drops till exceedingly thin — a process 

 impossible in ordinary cases. 



Yours faithfully. 



The University, Leeds. S 4 SHORTER 



26th Nov. 1914. 



* Or more precisely u fr 



