Motion of Solid and Fluid Bodies. 165 
I shall now proceed to determine the differential equations of equilibrium and 
motion arising from (12), which is the general equation applicable to all solid 
bodies, and common to them and fluids. 
Substituting for v, its value (11), we obtain, by the calculus of variations, 
Wividedyde = SE pata “i +™M = ar au +av+a sw )tdyde 
ar Wer a i +Ag os nit Zi 4 au +av+ nw )enrdyde 
4 (5 (uF 1s Lng + yu +uMv+ aw eedyde 
d 
vot woe tN + Bu + Biv + Bw )ondeds 
~ 
( 
+\V(aoe HAG tgs + Le + ay + Baw Jide 
v 
+f eee +B, ? te ae + p,u + av + NW ded 
( 
+WV(ck+u e+e tH +1 +0 )idady 
( 
( 
dé dy dé 
eet Peay Hae + 0 + Mv + aw )éédady 
+{f 3 +B, ath “pw + vv + B.w endedy 
Pe PE PE 
r NC ae te aa 2( 4 \dydz * “dadz * os Tay) ded 
ay ay ay Th ay ad ay dy 
. (M(« “Sax + Bs ae ss Tg, dz 2(a ‘dadz wy Pid + Bs d Inks) )eetedyde 
Nef tae (ail nif +a fh) 
