i6 PHYSICS OF STREAMING 



SECTION 6. The Influence of the Viscosity of the Protoplasm and 



Cell-sap. 



The viscosities of the protoplasm and of the cell-sap are factors of the 

 utmost importance in dealing with protoplasmic movements in plant-cells, 

 although little or no attention has hitherto been paid to them. The 

 importance of this purely physical property is sufficiently indicated by 

 the fact that the viscosity of water at 30 C. is one-half what it is at o C., 

 while that of glycerine containing a little water is one-fifth at 20 C. of 

 what it is at 3C. This decrease of viscosity with rise of temperature is 

 a general phenomenon, and seems almost sufficient to explain the accele- 

 ration of streaming produced by moderate rises of temperature, although, 

 as we shall see subsequently, the causation of the increased velocity is not 

 quite so simple as this. 



The viscosity of a solution increases as it is concentrated. Thus 

 a 5 per cent, solution of sucrose has nearly the same viscosity at o C. 

 (TJ = 0-02048) as a 40 per cent, solution at 50 C. (rj = 0-0241), and has 

 the same viscosity as a 40 per cent, solution at 58 C. 1 It is, however, 

 always possible that the constitution of the protoplasm and its percentage 

 of water may alter as the temperature rises or falls, but within a certain 

 range (o C. to 40 C.) we are probably justified in assuming that it retains the 

 same average composition during short exposures. 



In a rotating cell the question of friction between the surfaces in 

 contact need not be considered, for the friction of a fluid against a smooth 

 surface is independent of the material of the latter if it is wetted by the 

 fluid. The fact that water and solutions of glycerine ' can pass through 

 the vacuolar membrane to the cell-sap and also outwardly, proves that the 

 cell-sap wets the vacuolar membrane. A liquid flows through a uniform 

 capillary tube in the form of parallel concentric sliding lamellae. Hence 

 when rotation occurs in a plant-cell the vacuolar membrane carries with it 

 the layer of cell-sap immediately touching it. The next layer, however, 

 slips slightly to an extent determined by the viscosity of the cell-sap, the 

 next stilt more, until a little distance inwards the motion is practically 

 extinguished. An increase in the viscosity of the cell-sap, or in the 

 velocity of streaming, will bring more of the cell-sap into motion, and 

 hence will increase the retarding effect of the latter upon the streaming 

 endoplasm. A rise of temperature increases the velocity of streaming but 

 decreases the viscosity of the cell-sap, the influence of the former being 

 greater than that of the latter upon the bulk and average velocity of 

 rotating cell-sap. Thus at low temperatures when streaming is slow, it 

 is usually difficult to distinguish any translatory movement in the cell-sap 



1 R. Hosting, Phil. Mag., 1900, pp. 274-86. 



