166 The Rev. S. Haucuton on the Equilibrium and 
eae al pe ay &n : 
(Weg + Liana in “bast Gee ae dady +B, aah Tris) indy 
oe xe 
Gr ‘ay ye wie is “ie ; 2( Bz ean “dyds zt %s d. i) eae 
e PE DE Me : 
WG 1% Gat % de Tat 2( Bag: ttgade |! daw Tay) Jeni 
OF ae Snee 
We §(S(egs+ i eae Loot (nas an ily +y,-> ELLE + 7 at:)) a¢dadydz 
VE ae we Gite 
= (SS(1e 55 dz? + ay, rag B, Tt? (wag: + SAS +a 1 am ian)) é¢dadydz 
= dy dy dyn I ay dn dy eee 
§W(ug dat “ag t Pipa th? (x ‘dedz +? dedy T + Fr) )eedodyd 
Hence, finally, equation (12) becomes 
SMS e(xbé + vn + zig )dadydz = A — SS (P,eé + Q,oy + R,E¢)dadydz, (19) 
where e denotes the density, A the sum of the nine double integrals, which 
belong exclusively to the limits, and P,, Q,, R, the coefficients of &é, oy, &¢, in the 
triple integrals, which give the indefinite equations of equilibrium and motion. 
The equations of equilibrium and motion of solid bodies deduced from (19), are 
the following : 
H = 25 =, mers Oo. SS Sm (20) 
an 
oas dy a? 
n= x+p, eon = 49, cSaath, (21) 
These are the most general equations of equilibrium and motion, and P,, Q,, R, are 
expressed in their most general form, without making any supposition as to the 
arrangement of the molecules of the body. 
In order to express the conditions at the limits produced by A, it will be 
convenient to make use of the following transformation of the equation (19). 
Let 
dy 
a(®) Ete +oM Oey au bev baw 
