376 THEORETICAL RESPONSE OF CELLS TO CONTACT 



/, ^ !/ 8(^^ + ») ^ li s {gTc - gTp~+~ap) 

 J An- 2m 1 4cTp - 2gTc + 2gTp 



With this equation, knowing w and n, we can calculate h in terms of 

 the original radius of the cell and from h, in turn, we can calculate by 

 equation (4) the radius of the base of the cell, a. 



Another formula for the equilibrium is given by Tait from consid- 

 erations of the contact angle in Fig. 2. 



gTp = gTc + cTp cos A (8) 



gTp — gTc = cTp cos A 



— m = M cos A (9) 



P 



^gTp /A gTc ^ 



G m = gTc - gTp 



Fig. 2. Diagram of the equilibrium of surface tension forces at the angle of 

 contact, A, between a hypothetical cell, C, suspended in plasma, P, and a glass 

 slide, G. Arrows indicate direction of pull only. 



By simple geometry and trigonometry it may be shown that 



cos^ = ^-^ (10) 



Substituting the value of h from equation (7) in (10) and reducing, we 



have cos A = which is the same as equation (9) , and proves that 



n 



the same equilibrium results either from considerations of the contact 



angle or considerations of the surface energy. 



Now Tait's argument is incomplete because in using equation 



(9) he assumes that ^ = 0, i.e., that the cell spreads to infinity, whence 



cos A = 1 and m -\- n = or, in his terminology, a cell will spread to 



infinity^ when 



^ The cell is, of course, assumed to be a mathmatical sphere without structure. 

 Even a pure liquid could not spread out in a layer less than one molecule thick. 



