Prof. J. Perry on Liquid Friction. 443 



for as a virtual increase in the radius of his disk, and the 

 assumption that the behaviour of his fluid was the same as if 

 his disk were part of an infinite disk. The correction not 

 being readily obtained for a disk, he assumed it to be the 

 same as for the straight edge of an infinite plane surface. We 

 are certainly not less correct in taking the same correction 

 for the edge of our cylinder *. Following Maxwell, there- 

 fore, we assumed that when our cylinder G was immersed 

 to the depth AB or I in the fluid it w r as really a portion of 

 length l+X of an infinite cylinder of the same diameter. We 



d 2 v 

 therefore neglect -=-5 in (3), and we use 



d 2 v 1 dv v _ p dv , . . 



dr 2 r dr r 2 ~~~ p dt' ' ' ' ^ ' 



When the motion is steady, that is when dv/dl=0, the 

 solution is 



v = Ar+B/?- (5) 



If v—v 1 when r=Bi, and v = when R=R 2 , then 



We must now distinguish between the space outside the 

 suspended cylinder and the space inside it. The radii of the 

 inner and outer surfaces of the suspended cylinder are 11*41 

 and 11-63 centim., and the inner and outer radii of the trough 

 are 10*39 and 12*65 centim. 



Our cylindric surfaces were not perfectly true, although 

 great care was taken to make them so ; and the radii given 

 are only average dimensions. But, inasmuch as slightly 

 tilting the apparatus or otherwise putting the axis of the 

 suspended cylinder out of coincidence with the axis of the 

 trough made only small differences in the observations, we 

 did not think that such inaccuracies of workmanship or mea- 

 surement as existed could affect our results. 



Even when the tilting of the apparatus was quite evident 

 to the eye, the tractive torque was found to be only slightly 

 increased by the tilting. Of course, as the suspended cylinder 



* It is to be remarked that Maxwell assumed, generally, that there was 

 no radial motion of his fluid. Now there must have been radial motion, 

 his disks resembling centrifugal fans in their action, creating a variable 

 flow always outwards between his fixed and moving disks ; and the 

 energy wasted in producing this flow is neglected by him. We do not 

 know the amount of this error, and he may have satisfied himself as to its 

 insignificance. Prof. Maurice FitzGerald in criticizing this proof has 

 pointed out the fact that on James Thomson's theory of river bends there 

 must exist a radial motion of an interesting kind in our apparatus. 



