124 L. V. HEILBRUNN 



movement of a particle during ten passages. If the number of pas- 

 sages for a given time interval is known, the viscosity can be com- 

 puted from the following formula, due originally to Fiirth: 



R Tt 



^ — — ^ 



N STraPn 



In which rj is the viscosity, R the gas constant, N the Avogadro num- 

 ber, T the absolute temperature, t the time interval for the total num- 

 ber of passages, n, and I the distance traveled for a given passage. 



Pekarek tested the method for distilled water and found excellent 

 agreement with the known value for the viscosity. In using the 

 method, certain conditions must be fulfilled. The cells examined 

 must be intact and healthy. In the protoplasm studied, there should 

 be no directed movement, such as occurs in protoplasmic streaming 

 or in the so-called "Glitschbewegung" found in the cells of certain 

 algae. The Brownian movement should be random; this necessi- 

 tates making a sufficient number of observations. Inasmuch as the 

 Fiirth formula depends on the Einstein formula for Brownian move- 

 ment, and this in turn depends on Stokes' law, the limitations of 

 Stokes' law should be noted. The fluid through which the granules 

 move should be homogeneous, that is to say, the diameter of the par- 

 ticles should be large in comparison with the mean free path of the 

 fluid molecules. This condition is easily satisfied. Then, too, the 

 particles should be spherical. They should not change size during the 

 course of a determination. The presence of a limiting surface or wall 

 in the vicinity of the moving particles introduces complications; 

 hence it is w^ise to study particles in relatively large masses of proto- 

 plasm. Finally, the number of particles should not be too great, 

 for if the particles are crowded their movement is retarded. 



In view of these various difficulties, it is not a very simple matter 

 to find material suitable for study. Pekarek determined the vis- 

 cosity of the cell sap in the vacuoles of various plants. Such meas- 

 urement was relatively easy by his method. In his studies of actual 

 protoplasm, Pekarek determined the viscosity of the protoplasm of 

 an amoeba that did not contain too great a concentration of granules 

 and was not actively moving. He also studied the protoplasm of the 

 rhizoids of the alga Cham. For Anioeha protoplasm, he obtained a 

 value of 5 centipoises, which is exactly the same as that previously 

 found by Heilbrunn (35) using the centrifuge method. For Chara 

 protoplasm, Pekarek also found the same value. 



