The Eev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 1 85 



F- yip cos a ^- + cos /3 -r- + cos 7 -r I 

 \ ax "^ dy dz) 



+ i?,(cosa|>cos^g + cos7g) (D) 



+ Cp(cOSa| + COS^| + COSv|). 



Let a', j3', 7' be the angles which the direction of this force makes with tlie 

 axes, and X, Y, Z its components. Then 



X=i^cosa' = p cosa' 1 yl (cos a -p- + cos/3 -7^ + C0S7 — 1 

 \ \ dx "^ dy dz) 



T, I dn ^ dn d>i\ 



+ £ COS a ^ + cos /3 -=-^ + cos 7 -^ 1 



\ dx '^ dy dzj 



+ c(cosa| + cos|3| + cos7|)|; (E) 



r = F cos ^ = p COS ^' j A /'cos a ^ + &c^ + &c. j ; 



Z = i^ cos 7' = p cos 7' Lfl f cos a ^ + (i-C. j + &C. | . 



We have next to consider the effect which this force tends to produce ; and 

 on this point the assumption here made is, that the forces developed by the displace- 

 ments of the several particles tend to change their relative positions only. Hence 

 it is evident, that tlie moments of the forces X, Y, Z will be 



Xo (!'-§), n(,/-r,), Zo{^'-0, 

 respectively, or 



pA cos a — — 1- cos B —r- + cos 7 -y- , 

 \ dx dy ' dz ) 



■,;r / don „ din dtrA 



pZ I cos a -~ 

 \ dx 



^ diK dit' 



+ cos 8 —^ + cos 7 — 

 dy dz 



