444 Prof. J. Perry on Liquid Friction. 



got closer and closer to the side of the trough the torque did 

 increase, and hecame very large when the suspended cylinder 

 nearly touched the side of the trough. 



Again, it was observed that at our highest speeds the 

 amount of wetted surface did not perceptibly alter ; and we 

 are, we think, justified in assuming that the surface of the 

 liquid was always a plane surface. 



It is evident that the tractive forces on the suspended 

 cylinder are the same whether we assume the trough to 

 revolve steadily at © radians per second, the suspended 

 cylinder being at rest, or the suspended cylinder to revolve 

 steadily at © radians per second and the trough to remain at 

 rest. We shall therefore, for ease of calculation, always 

 assume the trough to be at rest and the suspended cylinder 

 to be revolving at © radians per second. Then the velocities 

 of its inner and outer surfaces are, in centimetres per second, 

 11-41 © and 11-63©. 



On any cylindric surface the tractive force per unit area 



being AM -j; — ) is j-f^ from (5) ; so that, whether for 



the outer or inner space, if K x is the radius of the suspended 

 moving cylindric surface, and R 2 the radius of the fixed 

 surface, the tractive moment per centim. of length is 



±47r© / *R 1 2 /(R 1 7R 2 2 _l). 



Taking actual sizes, this is 0'5 per cent, greater than the 

 value obtained by calculating the forces on the assumption 

 that the fluid moves in plane layers as in (2), b being the 

 actual thickness of fluid 1*02 centim., and V being the actual 

 velocity at the mean radius. We may, in fact, imagine the 

 speeds to be increased by 0*5 per cent., and make all calcu- 

 lations as to viscosity on the assumption of motion in plane 

 layers. 



The tractive torque per centimetre of length of cylinder is, 

 in our case, 19010/x©, or 1991 up if the angular velocity 

 is given as n turns per minute. If I is the wetted length 

 in centimetres, and A, is the virtual additional length repre- 

 senting the edge effect, the total torque is 1991?i/u(Z-j-A,). 

 The total observed motion of the pointer being D degrees, 

 and the torque per degree being a, the torque due to tractive 

 forces acting on the cylinder is 



aD = 1991 nfi(l + \) ; 

 and if this law is found to be true experimentally, then 



fjL = aD/{mi(l + \)n} (6) 



