418 L. V. HEILBRUNN 



THE METHOD 



In general the viscosity of a fluid may be determined in any 

 one of three ways. The usual method is to measure the rate 

 of flow of the fluid through a tube. One can also obtain a measure 

 of the viscosity by determining the rate at which solid substances 

 pass through the fluid, or one can measure viscosity by deter- 

 mining the force necessary to push solid materials through 

 the fluid. All three methods are used by physicists, but only 

 the second and third can be applied to the living cell. When 

 the protoplasm is not very viscous and contains large granules 

 of relatively high specific gravity, these granules may be seen 

 to move under the influence of gravity. The time of fall can 

 then be used as a measure of the viscosity of the protoplasm. 

 This method has been applied to some plant cells by Heilbronn 

 ('14). In animal cells generally the granules do not appear to 

 be affected by gravity, and a stronger force is necessary to move 

 them. Such a force can be obtained with the centrifuge, and 

 the centrifugal method of measuring viscosity is doubtless capable 

 of wide application. With the centrifuge both the second and 

 third methods of measuring viscosity can be used. One can 

 either determine the speed attained by protoplasmic granules 

 under the influence of a given centrifugal force or one can deter- 

 mine the amount of force necessary to produce a certain degree 

 of movement. To some extent both methods were used in 

 earlier work. 



At this point it might be w^ell to consider the theory of vis- 

 cosity measurements obtained by observing the movements 

 of solids through liquids. This method has been used compara- 

 tivfely rarely by physicists and chemists. Arndt ('07) used 

 it to determine the viscosity of fused salts. A general dis- 

 cussion of the subject with references to literature is given by 

 Ladenburg ('07). When fairly small particles are made to 

 move through viscous liquids, this movement is found to occur 

 at a uniform rate. For such a movement in the case of spheri- 

 cal particles, Stokes ('50) derived a formula often used by phys- 

 icists. In a suitable form it is: 



