230 VISCOSITY. [CHAP. ix. 



For a sphere of one-tenth this size, the value of V would be one 

 hundred times less. The viscosity of the air is therefore amply 

 sufficient to account for the apparent suspension of clouds, &c. 



185. If we suppose that there is a finite amount of slipping 

 at the surface of the sphere, the conditions (37) must be modified. 

 Regarding the sphere as in motion, and the fluid at rest at infinity, 

 the conditions to be satisfied when r = a are 



M = Fcos 0, and 2yu, [/] = 0(0 + Fsin 0), 

 where j3 is the coefficient of sliding friction. These give 

 *i . -tf , T _ ^\_ 



whence 



Substituting these values in (42), we obtain for the resistance 

 experienced by the sphere 



(46). 



When /3 = 00 this reduces to (43). Whatever the value of fi may 

 be, P always lies between 47r/-ia V and 67r/i,a V. 



