1 CYTOPLASM 167 



Viscosity measurements can be performed by examining the Brownian 

 movement of granule inclusions (Pekarek, 1930) or by observing the 

 speed of a heavy particle falling through the cytoplasm by its own 

 weight, or by centrifugal force (Heilbronn, 1914; Heilbrunn, 1930). 

 The intensity of Brownian movement is given by 



X2 RT I 



t N ^Ttrrj 



where X^ represents the mean square of the displacement of a granule 

 with radius r during time t, Ris the gas constant, T the absolute tempera- 

 ture, and N is Loschmitt's number. It is seen that the viscosity r} of 

 the medium is inversely proportional to the intensity of Brownian 

 movement. 



For the movement of a particle through a Uquid (Fig. 1 12a, p. 192), 

 Stokes' law 



2ng (d — d'y 



T] = 



9v 



holds good. Here v is the velocity of the moving spherical particle, 

 (d — d') the difference in density between cytoplasm and observed 

 particle, g the acceleration due to gravity, and n the number of times 

 which the applied centrifugal force is stronger than gravity. 



With these methods it is found (Table XXII, p. 1 69) that the sap 

 in the vacuole of plant cells is often only about twice as viscous as 

 water (Frey, 1926c). For the cytoplasm, however, relative viscosities 

 of six in Amoeba (Pekarek, 1930), twenty-four in parenchyma cells 

 of the Viciafaba seedling (Heilbronn, 19 14) or thirty in erythrocytes 

 of man (Ponder, 1934) are found. Such values are more reliable if 

 derived from Brownian movement than if determined by Stokes' law, 

 since the latter requires a uniform velocity v of the faUing particles 

 which is not often realized in cytoplasm. 



Once again these measurements do not establish the existence of 

 structural viscosity in cytoplasm. To solve this question it is necessary 

 to carry out viscosity measurements with different pressure gradients. 

 Since protoplasm cannot be made to flow through a narrow tube like 

 a liquid, Pfeiffer (1936) sucks naked protoplasts (so-called gymno- 

 plasts from the decomposing fruit pulp of Pbysalis, Solanum or Juni- 

 perus, of Allium epidermic cells, etc.) through a capillary under a given 



