Mr Taylor, Experiments ivith Rotating Fluids 327 



verified that after a time the sheets may become so thin and closely 

 wound round one another that it is only possible to see that the 

 colouring matter is not uniformly diffused through the hquid by 

 placing one eye directly over the rotating basin. The sheets then 

 suddenly reveal themselves as they pass vertically under the eye, 

 and disappear as soon as they get into a part of the basin which 

 is not exactly under the eye. 



2. Motion of a sphere in a rotating fluid. 



The steady motion of a sphere in a rotating fluid along the axis 

 of rotation is discussed mathematically. The velocity of the flmd 

 at any point is expressed by means of Stokes' stream function. 

 So far as the present writer is aware the Stokes' stream function 

 has hitherto only been used in problems where the motion is 

 symmetrical about an axis and is confined to axial planes. It is 

 equally apphcable however to cases in which only the first of these 

 conditions holds, and it is used in the present instance. The ex- 

 pression obtained which represents the stream hues when the whole 

 system is given a uniform vertical velocity so as to bring the sphere 

 to rest is 



^=/sin'^^, 



, ( , sin(z + e)) 



where f=z^ + Vfi^ + S/x^ + 9 j cos (z + e) ^ 1 



and z = kr, k = 2n/y, /x = ka, tan (/^ + e) - 3^/(3 - /x'-). 



Q. is the angular velocity of rotation of the fluid. 



V is the velocity of the sphere along the axis. 



r, e are the polar coordinates of a point referred to the centre 

 of the sphere as origin, and a is the radius of the sphere. 



The components of velocity of the fluid at any point are found 

 from this expression by the formulae 



u=- -If cos dlf\ y = ^ ^ sin 6, iv = kf sin d/r. 



In this expression the axes of reference are not rotating. It is 

 found that although the solution allows slip to take place at the 

 surface of the sphere, the actual solution obtained involves no shp. 

 This is a point of considerable importance because it is the assump- 

 tion that there is a shp at the surface of solids which vitiates all 

 the ordinary hydrodynamical theories of the motion of fluids. 

 The stream hues due to the motion of a sphere along the axis 

 of a rotating fluid may therefore be expected to be more hke 

 the theoretical stream lines than they are in the case when the 

 fluid is not rotating. This is found to be the case. 



