444 PHAGOCYTOSIS OF SOLID PARTICLES. I 



of the arrow. Its radius equals — ^. Then the cells of velocity 



2r 



Vc which will collide with the particle at B, C, and D after one- 

 quarter, one-half, and three-quarters of a revolution, respectively, 

 must have been originally located at the points b, c, and d. But all these 



points lie on a circle (Fig. 2) whose radius is — — — , and whose 



lir 2t 



circumference is therefore, Vp — Vc. Obviously the chance of 

 collision depends upon the length of the line upon which colliding 

 cells may lie. 



In some of the following experiments, however, these ideal conditions 

 were not quite reahzed, especially at the beginning before the theory 

 of the chances of colHsion had been thoroughly worked out. Instead, 

 an air bubble was allowed to be present and in many cases traveled 

 from one end of the tube to the other as it revolved, owing to the fact 

 that the tube was not quite horizontal. As the bubble passes along 

 the tube it leaves behind it Kttle eddies. These may be seen in a thick 

 suspension of quartz as layers of unequal concentration of particles 

 caused by the pihng up of particles in the eddies by centrifugal force. 

 It was observed that counts of the number of particles from small 

 amounts of samples (5 c.mm.), removed immediately after stirring, 

 showed greater variations than from samples taken when these 

 inequahties in concentration had disappeared. It is probable that 

 both particles and cells are acted upon by centrifugal force when 

 stirred up, and move, therefore, with exactly the same relative veloci- 

 ties as when setthng under the force of gravity alone. However the 

 mixture is stirred, there would be no collisions if all particles and cells 

 had exactly the same velocities, for they would merely be carried 

 along by the current. Any collisions, then, must be due to differences 

 in velocities. 



In the smallest of these particles brownian motion was just per- 

 ceptible. Even if the particles were so small, however, as to have no 

 velocity under gravity and therefore very active brownian motion, 

 this fact would not affect the calculation of the chances of collision 

 with a cell which is literally "sweeping up" the particles with a velocity 



^ n is taken equal to 1. 



