VISCOSITY CHANGES DURING MITOSIS 419 



V = 



9/x 



in which V is the velocity of movement, g the gravity constant, 

 a the specific gravity of the particle, p the specific gravity of 

 the liquid, a the radius of the particle, and ^u the viscosity of 

 the liquid. 



In the mathematical derivation of Stokes' formula various 

 assumptions are made. Arnold ('11) has considered the signifi- 

 cance of all these assumptions. He has shown that for small 

 particles dropping through viscous liquids, Stokes' law holds. 

 When the particles drop through comparatively narrow tubes 

 of the liquid, then a correction must be made for the effect .of 

 the walls of the tube. For comparative tests of viscosity in which 

 the same tube is used throughout, this correction disappears. 



Stokes' law applies to the action of gravity. In order to make 

 it apply to centrifugal force, one must insert a factor c for the 

 centrifugal force in terms of gravity. The formula then becomes : 



2cg(a - p)a^ 

 9m 



Centrifugal force may be many times gravity. It might be 

 thought that with such a powerful force, the velocity of the 

 particles might become so great that Stokes' law would no longer 

 hold. In the present experiments no such high velocity was 

 ever attained. The speed of the granules ranged approximately 

 from 0.0002 to 0.0018 cm. per second. This is a very low rate 

 of speed. 



We are reasonably safe, therefore, in assuming that Stokes' 

 law can be applied to the movement of cytoplasmic granules 

 under the influence of centrifugal force. With a given centrifu- 

 gal force, the speed with which the granules move is accord- 

 ingly inversely proportional to the viscosity of the fluid through 

 which they move, the cytoplasm. But this speed also depends 

 on two other factors, the radius of the particle, and the difference 

 in specific gravity between the particle and the fluid of the cyto- 

 plasm. If the simple formula is to be used to measure viscosity 



