of the Surface Layers of Liquids. 263 



If we take values of cr as abscissae and values of r as 

 ordinates, the cycle is represented by the elementary rect- 

 angle PQRS of area 0V0Y, described in an anti-clockwise 



Fig. 2. 



s , 



R 





3 



p 



1 



Q 



direction (see fig. 2) . Hence the system does an amount of 

 work 6V§t against the force controlling the surface *. The 

 force controlling the volume must therefore do an equal 

 amount of work on the system. Suppose now that we take 



Fijr. 3. 



S' R' 



values of v as abscissse and values of p as ordinates. The 

 cycle will be represented by a parallelogram P'Q'E/S' (see 

 fig. 3) with two sides (P'Q' and B/S x ) parallel to the v axis, 



* A certain force will be necessary to counteract the effect of the 

 difference in the hydrostatic pressure on the two sides of the vertical 

 portion of the plate P. Since the work done by this force in any dis- 

 placement is equal to the product of the total weight of the components 

 and the increase in the height of their centre of gravity, the work done 

 in a cycle will be zero, so that this force may be left out of account in 

 considering a cycle of operations. 



