VISCOSITY. [CHAP. ix. 



Again, resolving parallel to y we find 



whence we write down, by symmetry, 



The truth of the relations (1) follows from (8) by symmetry. 

 The student should notice the analogy of (3) and (5) with (6) 

 and (8) respectively. 



If in the same figure (Art. 3) we suppose PA, PB, PG to be 

 drawn parallel to x, y, z, respectively, and ABC to be any plane 

 near P whose direction-cosines are Z, m, n, we find, in exactly the 

 same manner, for the components of the stress exerted across 

 this plane, the values 



respectively. 



178. Nowp^pypi differ from p by quantities depending 

 on the motion of distortion/which are therefore functions of a , b ,c 

 only ; and if a , & , c be small we may suppose these functions to 

 be linear. We write therefore 



i = -p 



where X, /* are constants, this being plainly the most general as 

 sumption consistent with the above suppositions, and with sym 

 metry. Substituting these values of p lt p^, p s in (6) and (8), and 

 making use of (3) and (5), we find 



p xx = -p + \(a + b + c)+2^a, &c., &c., 

 P=tyf&amp;gt; &c.,&c. 



But from the definition (7) of p we must have 



3X + 2ya = 0, 



whence, finally, introducing the values of a, b, c, &c. from Art. 38, 

 we have 



