442 PHAGOCYTOSIS OF SOLID PARTICLES. I 



kept for nearly a year at room temperature, without sterilizing, and 

 there has always been an abundant supply of uniform particles in 

 each when shaken up and allowed to settle. Uniform suspensions 

 cannot be kept, however, without the addition of acacia or some 

 other protective colloid to prevent agglutination. 



Chances of Collision. 



If a suspension of cells of diameter C and velocity (under the influ- 

 ence of gravity) Vc, and of particles of diameter P and velocity 

 Vp, is allowed to settle in a test-tube, the chances of colHsion, R, 

 between them will be proportional to the velocity of the particle 

 relative to the leucocyte and to the square of the sum of their diam- 

 eters or 



R = {Vp - Vc) (C + PY (1) 



The last factor is derived by a consideration of Fig. 1. If an infinitely 

 small particle is settling down, its chance of hitting a single cell C 

 is proportional to the cross-sectional area of C or ttO. If, however, 

 the particle has a finite diameter P, its center may miss the edge of 



P . . 



the cell by a distance — and still collide. The effective cross-sectional 



area of C as a target for a particle is thus increased to ■k{C -}- P)^. 

 The chance that P will hit C is, therefore, proportional to (C -1- Py} 

 In these experiments, however, the suspensions were not allowed 

 to settle out in stationary test-tubes as the formula could no longer 

 be applied to cells and particles which were resting on the bottom. 

 Instead, the test-tubes holding 1 to 2 cc. of the mixture were placed 

 horizontally on a drum revolving slowly about a horizontal axis. 

 It can be shown, however, that the same formula applies to this case. 

 Consider first a case where there is no air bubble in the tube. Each 

 cell and particle in the mixture is settling at a constant rate in a 

 uniformly rotating medium, and at the end of one revolution will 

 have returned exactly to the original position in the tube, having 



' The writer is indebted to Dr. E. K. Carver, National Research Fellow in Chem- 

 istry, of the Wolcott Gibbs Memorial Laboratory of Harvard University, for 

 assistance with this formula. 



