A SPHERE IN A VISCOUS LIQUID 63 



Therefore 



. 2o> (sin Xa A/) 



x = "a'XS' 1 (\a) * 



nnd 



2w e - V ( 8 in \*i -Xa) S (Xr) 



- 



whence the velocity of the liquid, which is equal to rsin 6, can be found. 



When the angular velocity is variable, the value of the retarding couple, and the 

 equation of motion of the sphere, can be obtained by a process analogous to that 

 employed in 11. 



[March 10th, 1888. Since this paper was read, a paper has been published in the 

 ' Quarterly Journal of Mathematics,'* by Mr. WHITEHEAD, in which he attempts to 

 develope a method of obtaining approximate solutions of problems relating to the 

 motion of a viscous liquid, when the terms involving the squares and products of the 

 velocities are retained ; and he applies his method (see p. 90) to obtain expressions 

 for the components in the plane passing through the axis of rotation, of the velocity 

 of a viscous liquid, which surrounds a sphere which is rotating about a fixed diameter, 

 when the motion has become steady. It will be observed, however, that the expressions 

 for these components contain the coefficient of viscosity as a factor in the denominator, 

 and therefore become infinite when the liquid is frictionless. It would therefore 

 appear that tho method of approximation adopted is inapplicable to the problem 

 considered.] 



Vol. 23. p. 78. 



