864 THE MECHANISM OF PHAGOCYTOSIS 



mutual contact, then the three forces of surface tension acting on the line of mutual 

 contact must be capable of representation both in magnitude and in direction by the 

 three sides of a triangle (the Neumann triangle). When one phase is solid, there is a 

 simplification in that only those components of the forces of surface tension which 

 pull in the plane of the solid surface need be considered. The formula for this condi- 

 tion may be derived simply from the equilibrium diagramed in Figure i in which one 

 fluid phase, called conveniently the "cell," is represented as in an equilibrium position 

 between a fluid phase and a solid phase, cafled conveniently the "particle." The 

 interface between the particle and the fluid is represented as flat and infinite, i.e., the 

 particle is infinite in size. At equilibrium the forces of surface tension which pull the 

 point of contact to the left may be considered as equal to those which pull it to the 

 right. Thus 



Tpf=Tpc+ cos A Tcf , 

 Tpf-Tpc 



cos A = ■ 



Tcf 



Fig. 



Since it is difficult to conceive of a force of surface tension on a solid surface 

 actuaUy pulling the point of contact, this formula is by no means obviously true. The 



same formula may be derived, how- 

 r ever, from the more general proposi- 



tion that the free surface energy must 

 be at a minimum at the point of 

 equilibrium.^ Harkins and Feldman^ 

 have also preferred the thermody- 

 namic approach for the derivation of 

 their spreading coefficient. There is 

 some theoretical justification, therefore, for a thermodynamic proof of this equation. 

 Granted the equation, of course, the rest follows simply. 



Three general classes of equilibrium are possible according to this equation: 



1. If Tpf=or>Tpc-{-Tcf: Cos A is then= or >i and p will be completely in- 

 gested by c, or c will spread to infinity on p. This will be the position at which the pf 

 interface with its high surface tension disappears altogether. 



2. li Tcp = or >Tpf-\- Tcf: Cos ^ is then = or < — i, and there will be no contact 

 between p and c, the values of A being unreal. This will be the position of minimum 

 free energy because the cp interface with its high surface tension is absent. When this 

 is true the force of attraction between the cell and the particle is o or negative (re- 

 pulsion). Ponder^ inadvertently states that when cos A = — i the cell would be inside 

 the particle. The correct condition for this equilibrium is that Tcf—or>Tpf-\-Tcp, 

 in which case cos yl, according to the formula, must be somewhere between i and — i. 

 As Tcf increases cos A approaches o and A approaches 90°. Whenever Tcf is greater 

 than Tpf the particle may be thought of as "trying" to ingest the cell. The rigidity 



' Fenn, W. O.: op. cil., 4, 373. 1922. 



^ Harkins, \V. D., and Feldman, A.: J. Am. Chem. Soc, 44, 2665. 1922. 



•5 Ponder, E.: J. General Physiol., 9, 827. 1925-26. 



I 



