60 MK. A. B. BASSET ON THE MOTION OF 



which determines the value of the angular velocity as far as v*. 



1 2. HELMHOLTZ and PIOTROWSKI discovered from their experiments that in the case 

 of many liquids slipping takes place at the surface of the solid ; when this happens, 

 the surface condition is 



........ (58) 



where ft is the coefficient of sliding friction. Putting k = vpft~ l , we obtain from 



(43A) 



d M A f f3F() . 2F()1 / 



*L"* V *].* + *} exp - (~ 



1 /7T f fF() . _,,, J rf / 3 



2* V 5 Jo { + F (a) i s exp - r a 



3F 3F 



provided F(0) = F'(0) =0, and F()e- a ' and F()e ' are zero when a = oo 

 Equation (58) will be satisfied if 



/3 



the solution of which is 



F = - 



where p and 5 are the roots of the equation 



The roots of (59) will be real if a > k, that is, if a > vp/fi. Now, if there is no 

 slipping, /3 will be infinite, and therefore, when there is comparatively little slipping, 

 ft will be large, and this relation will be satisfied unless a is small or v is large ; on 

 the other hand, if there were no friction between the surface of the sphere and the 

 liquid, ft would be zero, but it seems improbable that any liquid exists which possesses 

 the property of viscosity with regard to the internal motion of its particles, and which 

 at the same time is incapable of exerting any action in the nature of friction against 

 any surfaces with which it is in contact. If therefore ft were zero, v would probably 



