NOTES 99 



Substituting sin 6 cos <f> for cos ty and the value found for 



E, and integrating over the hemisphere from = o to 6 = 



and from < = o to < = 2?r we get the tangential stress 



ff R C * 6 sin B cos <#/ 1 + - sin (9 cos </> \ r 2 sin 



FIG. 42. 



(3) Force on a sphere radius a moving with velocity 

 9. 



Let A (fig. 42) be the end of the diameter along which 

 the sphere is moving. A point P making if/ with A has 

 velocity v cos if/ along the normal at P and velocity v 

 sin if/ along the tangent at P which passes through AB. 



The normal velocity gives a force along BA, 



cos 2 i]/ . 20? sin 



for the term -' disappears on integration. 



3 



