AND DIAGRAMS OF FORCES. 



199 



with similar equations for b and c. A sufficiently general solution of these 

 equations is given by putting 



(5). 



_LA 



O/yj fi ty 



4 Iv ' ' - 



The equations of longitudinal elasticity are of the form given in 693, 



(6), 



where k is the co-efficient of cubical elasticity, with similar equations for Q 

 and R. Substituting for P, a, ft and y in equation (6) their values from (3) 

 and (5), 



1 \ a 1 ?/ 2 ay dy* dz* aV dz~ / ' 

 If we put 



<PA cPB #C_ d^ <V_ <__.* 



0*35* dy dz* ' da? dy" dz" 



this equation becomes 



/ /* [ 4* YJ \ / A A I A 2 /-^ 1 A 2 fi^ ^^ I 7i I I /-) \ O.ii ^_ O/M ^^ ty Yl \ A l7l 



I A/ ^^ q'/t I I 1 ^i ^^ uA _/_^ ~y~ LA \_/ f IW ^T Q 't 1 / /-' ^~ It/ V ~~ ^ I tiA ^1 ((I/ I. 



We have also two other equations differing from this only in having .& 

 and (7 instead of .4 on the right hand side. Hence equating the three expres- 

 sions on the right hand side we find 



AM=A 2 J B = A 2 (7=Z) 2 , say, (8), 



and P+Q + R = ^ ^,~ 2 =6&| > .~ ~ (10). 



These equations are useful when we wish to determine the stress rather 

 than the strain in a body. For instance, if the co-efficients of elasticity, k 



