510 VISCOSITY. 



Hence a = / 1 2 a / +/,&' + l* c ' t 



the last two relations being written down from symmetry. We 

 notice that 



a-f b + c = a' + b'+c' ..................... (2), 



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

 Again 

 dw dv f d d d 



+ V 1 dx' +n2 ch/ + HS dfJ ^ HlU/ + m ^ 

 and this, with the two corresponding formula, gives 



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 

 P\, P<2, P* respectively. In the figure of Art. 2 let ABC now 

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

 meeting the axes of 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 BG will then be ^A, / 2 A, Z 3 A. Resolving parallel 

 to x the forces acting on the tetrahedron, we find 



p xx A =p l l l & . /! +p 2 l 2 A . It +jp s t A . 4 ; 



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). 



