510 VISCOSITY. [CHAP, xi 



Hence a = l*a + LrV + l*c 9 



(1), 



the last two relations being written down from symmetry. We 

 notice that 



a + & + c = a + & + c ..................... (2), 



an invariant, as it should be, by Art. 7. 

 Again 

 dw dv / d d d 



/ d \ , , 



= r &&amp;gt; + *? + m - d?) (n M + &quot; + w 



and this, with the two corresponding formula?, gives 

 f= m^af + m^nj) + 



; (3). 



liO, + LmM + 



283. From the symmetry of the circumstances it is plain 

 that the stresses exerted at P across the planes y z, z x , x y must 

 be wholly perpendicular to these planes. Let us denote them by 

 PI, P-2, P* respectively. In the figure of Art. 2 let ABC now 

 represent a plane drawn perpendicular to cc, infinitely close to P, 

 meeting the axes of # , y , z in A, B, C, respectively ; and let A 

 denote the area ABC. The areas of the remaining faces of the 

 tetrahedron PA BC will then be ^A, / 2 A, 3 A. Resolving parallel 

 to os the forces acting on the tetrahedron, we find 



paa-A =p 1 l l A . h +p 2 l 2 A . 4 +p. A l s & . 1 3 ; 



the external impressed forces and the resistances to acceleration 

 being omitted for the same reason as before. Hence, and by 

 similar reasoning, 



We notice that 



(2). 



