W. 0. FENN 86s 



of the particle prevents this, but the cell nevertheless proceeds partially to ingest the 

 particle because by so doing the cf interface is reduced to a minimum. 



3. If neither (i) nor (2) is true, the particle will be partially ingested by the cell 

 or the cell will be partially spread out on the particle. Cos A will be between + 1 and 

 — I, and A will be between o and 180°, 



These three conditions cover all the possibilities. According to the formula, it is not 

 possible for the cell to be inside the particle, and of course it is not possible practically. 

 Such a condition is, however, possible to conceive, and, with certain surface tension 

 values (particularly when TcJ is large), this would be a truer equilibrium than that 

 actually assumed, because the total free surface energy would be less. 



Earlier writers on the mechanism of phagocytosis (Rhumbler,' Tait^) have con- 

 sidered only the first and second conditions above, neglecting, as I have pointed out,^ 

 the possibility that partial ingestion or partial spreading should occur. Ponder,^ while 

 recognizing clearly this possibility, nevertheless doubts whether partial spreading does 

 in fact occur, and states that it does not occur with pure liquids. This is hardly cor- 

 rect, however, for even oils which do not spread on water nevertheless have a definite 

 contact angle against water. Thus the contact angle between water and paraffin is 

 100° not i8o°.5 Likewise, many cases are known where solids accumulate at an inter- 

 face between two liquids, showing that the contact angle must be somewhere between 

 0° and 180° (Reinders,^ Hofmann,'' Fenn*). Where air is one phase, in fact, the diffi- 

 cult condition to find exemplified is where the contact angle is 180°. 



Since the formula for the equilibrium can be developed entirely from considera- 

 tions of the free energy of the interfaces, ' it is obvious that it must include all forces 

 which could affect the equilibrium. Electrical forces, therefore, may be regarded as 

 affecting the spreading of cells and phagocytosis by virtue of their effect upon surface 

 tension, surface tension being merely the free energy of a unit area of the interface. 

 Where there is a large electrical attraction between two phases the surface tension 

 of the interface is low, etc. 



Much can nevertheless be learned from an accurate analysis, both experimental 

 and theoretical, of the electrical forces between cells and particles, for the charges in 

 such bodies can be measured experimentally. Ponder'" has begun the theoretical 

 analysis of these forces. The particle is surrounded by an electrical double layer and 

 as a whole is electrically neutral. There is, therefore, no repulsion between equally 

 charged particles so long as the distance between them is large compared to the dis- 

 tance between the two layers of the double layer (Michaelis)." When the distance be- 



' Rhumbler, L.: Arch.f. Enlwcklngsmechn. d. Organ., 7, 279. 1898. 



^ Tait, J.: Quart. J. Exper. Physiol., 12, i. 1918-20. 



3 Fenn, W. O.: op. ciL, 4, 373. 1922. ^ Ponder, E.: loc. cit. 



s Adam, N. K., and Jessop, G.: /. Chem. Soc, 127, 1863. 1925. 



^ Reinders, W. : Kolloid-Ztschr., 13, 235. 1913. 



7 Hofmann, F. B.: Ztschr. phys. Clicmie, 83, 385. 1913. 



*Fenn, W. O.: op. cit., 3, 575. 1921. 



'Fenn, W. O.: ibid., 4, 373. 1922. '"Ponder, E.: loc. cit. 



" Michaelis, L.: chapter in Bogue, R. H.: Colloid Chemislry, Vol. I, chap, ix, p. 251. 1924. 



