30 PHYSICS OF STREAMING 



take 100 years for the escape of i cubic mm. of the cell-contents through 

 3,000 threads of T V p. diameter. Hence it is safe to conclude that 

 no streaming movements in mass take place through the interprotoplasmic 

 connexions of neighbouring cells, these structures serving for the con- 

 veyance of physical and chemical impulses (stimuli), and the transference 

 of solid materials taking place almost entirely by the diffusion of liquids 

 through the cell-wall. In the case of the short broad pores of sieve-plates, 

 however, comparatively small differences of pressure would suffice to 

 induce slow movements in mass through the pores. Thus in the series 

 of 2,000 sieve-plates, each with sieve-pores of 2 p diameter and 10 ^ length, 

 included in 50 cms. of the cribral system of Cucurbita, a pressure of about 

 half an atmosphere would be needed to produce a movement in mass 

 of the more watery contents through the tubes at an average rate of 

 5 mm. per minute, so long as the pores remained unblocked. This 

 corresponds with the slow exudation which takes place when the tubes 

 are first opened. 



For the above reasons it is hardly probable that any perceptible 

 streaming movements occur in Bacteria, in spite of the remarkably active 

 transformations of energy of which these organisms are capable. 



In the case of protoplasmic threads crossing the vacuole within a 

 cell, the conditions are very different, for the flow does not take place 

 in rigid tubes with fixed walls. The plasmatic membrane moves with 

 the stream, and hence only the friction against the cell-sap, which is of 

 low viscosity, need be considered. In a cell exhibiting circulation, the 

 total resistance to flow will be somewhat greater than in one in which 

 the protoplasm rotates around a single central vacuole. Hence arises 

 in part at least the increase in the average velocity when circulation 

 changes into rotation. 



Calculation of work done from coefficient of friction. 



The coefficient of friction between a smooth metal plate and water 

 is at room- temperature 0-23 Ib. per sq. foot at a velocity of ten feet per 

 second. If the cell-wall (or ectoplasm) is considered as a flat smooth 

 plate moving through a liquid having ten times the viscosity of water, 

 it is possible to calculate the drag upon it, and hence the relative 

 magnitude of the force inducing movement. 



A cell 2 cm. long and of o-i cm. internal diameter has an external 

 surface of 0*659 sc l' cm - (2 TT r /+ 2 TT r 2 ). But the friction between the liquid 

 in question and a smooth plate would be equal to V of a dyne per sq. 

 cm. at a velocity of 2 mm. per minute, that is, -08 dyne per 0-659 s q- cm. 



But the volume of the moving plasma is 6 cubic mm., and the mass 

 of it moving is 0-072 gram approximately. Hence per gram of plasma 

 a force of i-i dynes is required. 



