2 6 PHYSICS OF STREAMING 



float, heavy particles ascending slightly less rapidly than the upward 

 stream, but descending more rapidly in the downward stream. With 

 particles of lesser density (oil globules, &c.) the reverse is the case. 

 Suppose that the true velocity of the stream is V mm. per min., and 

 the velocity of slip of a denser particle U mm. per min. Then, if the 

 particle has an apparent velocity of 2-83 mm. per min. in the ascending, 

 and 3-14 in the descending stream : 



F+^7=3-i4; V-U= 2-83 

 .-. V 2-98 and U = 0-15 mm. per min. 



Neither the density of the plasma, nor that of the floating particles, 

 can be calculated with sufficient accuracy to enable the viscosity of the 

 protoplasm to be deduced from the velocity of slip of denser or lighter 

 particles. The differences of velocity are by no means always as pro- 

 nounced as the above, but they suffice to indicate that the viscosity of 

 the streaming endoplasm cannot be very great since its density and that 

 of the denser floating particles only differ to a slight extent. Moreover, 

 the above facts point strongly to the conclusion that the visible floating 

 particles are passively carried by the streaming plasma, and neither propel 

 themselves nor it. 



SECTION 10. The Energy expended in a Streaming Cell. 



The problem in the case of a large cell of Nitella may be stated in the 

 following simplified form. A cylinder AB with rounded ends is bounded 

 externally by a thin homogeneous membrane 0-05 mm. thick (Fig. 5, p. 28). 

 Within this is a very viscous non-moving layer EF, and internally to 

 the latter is a less viscous layer FG streaming steadily round the cell 

 parallel to its long axis, the motion being reversed in the opposite halves 

 of the cell. Centrally is water containing inorganic salts, and frequently 

 sugar, &c., in solution. The outer layers of water also move in the same 

 direction as the living layers they touch, but more slowly, and with a 

 velocity which rapidly decreases to nil towards the centre of the cell. 

 The following are the dimensions : AB = 20 mm. ; CD = i mm. ; EF = 

 005 mm. ; FG = o-i mm. ; GH = 0-6 mm. The motion is most rapid 

 (3 mm. per minute) just to the outside of the median point of FG, thence 

 decreasing rapidly externally and less rapidly internally. 



The volume of the streaming plasma is 6 cubic mm. approximately, 

 and its average velocity is slightly over 2 mm. per minute. The volume 

 of the cell-sap is 5 cubic mm., and its average velocity i mm. per minute. 



The endoplasm takes eight minutes to complete a rotation. 



Hence in one minute | cubic mm. of the plasma and T 5 ^ cubic mm. 

 of the cell-sap pass a section across the cell. 



If we suppose the streaming endoplasm to correspond to egg-albumin 

 containing 90 per cent, of water, its viscosity will be approximately 0-075 



