175177.] GENERAL EQUATIONS. 217 



or a=l?a + W + 7,V. ^ 



Similarly b = m&amp;gt; + mfb + w 3 Y, &amp;gt; ................. ; (3). 



c = Wi V + ?i 2 2 6 + n 8 V. J 



We notice that 



a + b + c = a + l + c ..................... (4), 



an invariant, as it should be. See Art. 8. Again 



+s-(^ 



* i + 7?2 + &quot;* a?) ( x + m * v + m ^ 



or = w^a m 2 w 2 3 . 



Similarly g = nj l a +nJJ&amp;gt; + w 8 ?.c , &amp;gt; ................ (5). 



177. From the symmetry of the circumstances it is plain 

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

 wholly perpendicular to these planes. Let us denote them by 

 Pi&amp;gt; P*&amp;gt; P*&amp;gt; respectively. In the figure of Art.- 3 let ABC be a 

 plane drawn perpendicular to x, infinitely close to P, meeting the 

 axes of x, y, z in A, B, C, respectively ; and let A denote the 

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

 PABC will then be ^A, / 2 A, ? 3 A. Resolving parallel to x the 

 forces actin on the tetrahedron we find 



the external impressed forces and the resistances to acceleration 

 being omitted for the same reason as in Art. 3. Hence 



from which we write down, by symmetry, 



=Pi m i* + P* m ** + P* m 3*&amp;gt; | 



+^3 ?? 3 2 - 



We notice that 



so that 2) denotes the average pressure about the point P. 



