[22] PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION 



For water the value of ft is a good deal smaller than for air, and the corresponding value of x 



smaller likewise, since it varies cceieris paribus as yV- Hence if a solid of revolution of 



large, or even moderately large, dimensions be suspended by a fine wire coinciding with the 



axis of revolution, and made to oscillate by the torsion of the wire, the effect of the fluid may 



be calculated with a very close degree of approximation by regarding each element of the 



surface of the solid as an element of an infinite plane oscillating with the same linear velocity. 



For example, let a circular disk of radius a be suspended horizontally by a fine wire 



attached to the centre, and made to oscillate. Let r be the radius vector of any element of 



the disk, measured from its centre, 6 the angle through which the disk has turned from its 



dB 

 mean position. Then in equation (13), we must put V = r — , whence 



dt 



_ . /V idQ i d?9\ 



The area of the annulus of the disk comprised between the radii r and r + dr is 4nrrdr, 

 both faces being taken, and if G be the whole moment of the force of the fluid on the disk, 



G = - 4tt / ^T^dr, whence 



P W 2 \dt n df) 



Let My 2 be the moment of inertia of the disk, and let «j be what n would become if the 

 fluid were removed, so that — n^My^O is the moment of the force of torsion. Then when the 

 fluid is present the equation of motion of the disk becomes 



(^^^V^I + ^Vyj^W^o, . . (14) 

 or, putting for shortness 



d?Q d9 



(i + ^)- + 2w /3- + ^ = o, 



which gives, neglecting /3 2 , 

 where 



e oe - npi sin (nt + a), (15) 



The observation of n and « l9 or else the observation of n and of the decrement of the arc 

 of oscillation, would enable us to determine /3, and thence //. The values of /3 determined in 

 these two different ways ought to agree. 



There would be no difficulty in obtaining a more exact solution, in which the decrement of 

 the arc of oscillation should be taken into account in calculating the motion of the fluid, but 

 I pass on to the problems, the solution of which forms the main object of this paper. 



