by the Red Corpuscles of the Blood. 



065 



in the surface-tension, that under these conditions the surface 

 observed is a surface of minimum surface energy. 



I have subjected this idea to mathematical analysis, and 

 by applying the methods of the Calculus of Variations, have 

 obtained a differential equation connecting the curvature 

 with the variable surface-tension. On making a fairly 

 reasonable assumption about the manner in which the surface- 

 tension of a film alters with its thickness, I find that the 

 form assumed by these red corpuscles and lecithin emulsion 

 particles is physically possible, in the sense that this surface 

 is one having less surface-energy than any surface obtained 

 from it by a small deformation consistent with constant 

 volume. 



Let the accompanying drawing represent a meridional 

 section of the corpuscle — dumbbell-shaped, as mentioned 

 above. Choose as axes of coordinates the long diameter and 

 short diameter of the " dumbbell," so that OX is perpen- 

 dicular to the plane of the disk edge, and the body is a 

 surface of revolution about OY as axis. 



Then an elementary "zonal " area = 2ttj& . ds where ds is 

 an element of length of the curve. 



Also an elementary " zonal " volume^ 2trxy dx 



where 



dx 



= 2ttx//x ds, 



Now let T be the surface-tension or surface-energy per 

 unit area of interface between the drop and the surrounding 

 liquid, so that the whole surface-energy is 



4:77 



J> 



T . ds. 



Now in accordance with the assumption made above, we 

 shall consider T as a function of y, which will become a 

 constant at a sufficient thickness, i. e. as one approaches the 

 " dumbbell" ends of the curve. 



Phil. Mag. S. 6. Vol. 28. No. 167. Nov. 1914. 2 X 



