168 The Rev. S. Haucuron on the Equilibrium and 
If w represent the element of the bounding surface, and (A, , v) the angles 
made by the normal with axes of coordinates, and (2, ®, ¥) the particular forces 
acting at the limits of the solid; the equation of condition to be satisfied by the 
limits will be 
§§( 20é + boy + ¥EC)w = A; 
but we have 
A= {§(Ncosd + ycosu + cosy) wee + [§ (acosu + 4cosy + Jcosr) wey 
+§(cosv + cosr + dcosn) woe 
because 
dydz=weosA, dadz=wcosu, dady = wcosr, 
therefore 
= = ncosA + Jcosu + w2cosy 
= acosu + dcosy + JcosA (25) 
¥ = )cosy + »cosA + 5cosu 
will be the equations of condition to be satisfied at the limiting surface. If the 
limits be fixed, then we shall have A =0, without any equation of condition; 
and if the surface be perfectly free, we shall have 
ncosA + Jcosu + acosy = 0 
acosu + d5cosy + dcosA = 0 
jycosy + »wcosA+ 5cosu = 0 
I shall now proceed to the laws of propagation and transmission of waves in 
an elastic erystalline solid, no external forces acting ; and afterwards consider some 
more particular cases of the theory, which will tend to throw light on the general 
method used in this Paper. 
The differential equations of motion to be integrated are : 
his hts ZENS Gees igs PE We in) 
“de — de FN pa Me Tae 2( 1 “dydz er * dadz nag “3 di vdy 
S ul dy he EN ad? ay a ay dy .) 
Tits dp t eae 2(a dade * ™ dedy +? dydz 
ne LP oe na nes ae a .) 
+ gga TBs apy Ye +2(075 1 3 ds dydz PM ede 
