122 L. V. HEILBRUNN 



the viscosity. Thus Heilbrunn (1928) studied the rate of return of 

 granules centrifuged to one-half of a sea urchin egg cell. These 

 granules return to their original position by virtue of their Brownian 

 movement. According to the Einstein equation for Brownian move- 

 ment: 



Z)/ = {R/N)iTt/3Tr,a) 



in which Dx is the distance traveled by the granule in any given plane, 

 R is the gas constant in c.g.s. units, T the absolute temperature, t the 

 time, 7] the viscosity, a the radius and N the Avogadro number. 



In order to use the Einstein equation it is not necessary to know 

 the specific gravity either of the granules or the fluid through which 

 they move. 



The Einstein equation was also used by Baas-Becking, Sande 

 Bakhuyzen, and HoteUing (22) in their study of Brownian movement 

 of particles in the protoplasm just under the cell wall in the alga 

 Spirogyra. Using a magnification of 2100 X, they made numerous 

 records of the movement of individual particles. Such records are 

 very hard to obtain. "The position of a certain particle was re- 

 corded on coordinate paper every 15 seconds. At this high magnifica- 

 tion the procedure is strenuous ; 180 seconds being the physical limit 

 of observation. Moreover, the particle often disappears behind other 

 structures." It might be thought that it would be simpler and more 

 accurate to use motion picture records, but Baas-Becking, Sande 

 Bakhuyzen, and Hotelling state that such records would necessitate 

 the use of very thin preparations and that the Einstein equation does 

 not hold for such thin films. 



As a matter of fact, the movements observed by Baas-Becking, 

 Sande Bakhuyzen, and Hotelling were in thin films. The protoplasm 

 under the cell wall in the Spirogyra cell is a very thin layer bounded 

 by two concentric cylindrical surfaces. The particles observed by 

 Baas-Becking, Sande Bakhuyzen, and Hotelling were only 0.4 fi 

 in diameter and their movement was rapid. Obviously, they must 

 have collided frequently with the limiting surfaces of the thin layer 

 of protoplasm in which they were enclosed. Such collisions would 

 tend to restrict the amplitude of the movements and they would 

 tend to make the speed of movement variable and frequently less 

 than it would have been had no limiting surface been present. Ac- 

 cordingly, it is not surprising that highly variable values for the ab- 

 solute viscosity were found by Baas-Becking, Sande Bakhuyzen, and 



