442 Prof. J. Perry on Liquid Friction. 



rotation. G may be raised or lowered relatively to the trough. 

 The outer radius of G is IT 63 centim., the inner being 1P41 

 centim. The whole apparatus is supported on a stand, with 

 three adjustable feet. We exhibit also some photographs of 

 the apparatus in position, showing how it was driven. 



The trough contains the liquid whose viscosity is to be 

 measured : when it rotates, G tends to rotate ; and when for 

 any constant speed G is in equilibrium, the twist in the steel 

 wire measures the torque due to the tractive forces with which 

 the liquid acts upon G at its inner and outer surfaces. The 

 twist was measured by the angular motion of a pointer clamped 

 on the wire at a distance of 59 centim. from the fixed end. 



To test the accuracy of our assumption that the fluid 

 behaved as if between parallel plane surfaces, let us consider 

 the actual motion in which the stream-lines are circles. 

 Consider the motion of a stream-tube of section 8r8x, 

 on being measured axially and r radially. The tangential 



force on unit cylindric surface of radius r is /jlI-j -I, if 



v is the velocity. The moment due to all such forces on 

 the inner surface of our ring is 



2irr 



fdv 



7--Y 



\dr r) 





The moment tending to increase the velocity of the ring due 

 to forces on the cylindric parts of it is therefore 



* \dr 2 ^ rdr r V ' ' 

 also, due to the plane faces we have the moment 



27r/j,r 2 —- 2 8r .8%. 



Equating the sum of these to the rate of increase of the 

 moment of momentum of the ring, we have 



dr 2 + rdr r 2 + dx 2 " u dt ' ' ' ' {6) 



as the equation of motion in co-axial circular stream-lines. 

 Now the discontinuity at the edge, and also the nearness of 



the bottom of the trough, cause the term -?-§ to be important; 



but the solution seems to be very difficult. Maxwell satisfied 

 himself (Collected Papers, vol. ii. pp. 16-18) that the dis- 

 continuity at the edge of a vibrating disk could be allowed 





