2 



THE EQUATIONS OF MOTION. 



[CHAP. i. 



at length ceases altogether ; and it is found that during this pro 

 cess the portions of fluid which are further from the axis lag 

 behind those which are nearer, and have their motion more 

 rapidly checked. These phenomena point to the existence of 

 mutual actions between contiguous elements which are partly 

 tangential to the common surface. For if the mutual action were 

 everywhere wholly normal, it is obvious that the moment of 

 momentum, about the axis of the vessel, of any portion of fluid 

 bounded by a surface of revolution about this axis, would be 

 constant. We infer, moreover, that these tangential stresses are 

 not called into play so long as the fluid moves as a solid body, but 

 only whilst a change of shape of some portion of the mass is 

 going on, and that their tendency is to oppose this change of 

 shape. 



3. It is usual, however, in the first instance, to neglect the 

 tangential stresses altogether. Their effect is in many practical 

 cases small, but, independently of this, it is convenient to divide the 

 not inconsiderable difficulties of our subject by investigating first 

 the effects of purely normal stress. The further consideration 

 of the laws of tangential stress is accordingly deferred till 

 Chapter ix. 



If the stress exerted across any small plane area situated at a 

 point P of the fluid be wholly normal, its intensity (per unit area) 

 is the same for all aspects of the plane. The following proof of 



this theorem is given here for purposes of reference. Through P 

 draw three straight lines PA, PB, PC mutually at right angles, 

 and let a plane whose direction-cosines relatively to these lines 

 are I, m t n, passing infinitely close to P, meet them in A, B, C. 



