188 The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 



dx ^ ° dy ^^'' dz 



P., = A^,,^ + A,.,-^^ + A,^, 



,p d^.p dt d^ 



dx^^'-dy^ -"-'dz 



^3=^„w^ + ^'W^ + ^4,v 



+ ^-"d^+^^-'dy + ^^'''d-z 



the values of Qi, Q2, Qs being deduced from these expressions by changing, 

 in the suffixed letters, a' into (i'; and those of i?i, i?2i ■??3, by changing a' into 7'. 

 Integrating by parts, and equating to zero the coefficients of??, hi/, 5^, under 

 the triple sign of integration, we find the equations of equilibrium to be 



dx dy dz ' 



eF-^ + ^+^ (L) 



dx dy dz ' ^ ' 



dRi dE., dR^ 

 dx dy dz 



The corresponding dynamical equations will be 



d'^\ dP, , dP, . dP^ 



d(-J dx dy dz ' 



df) ~ dx ^ dy'^ dz' ^ > 



y _ ^^ - ^ ^ ^ 



d<-/ d^r dy dz 



If now we suppose that no external forces act, and replace Pi , Pj , &c., by 

 their values (K), we shall have the three general equations of small oscillations 



