94 MR JAMES CLERK MAXWELL ON THE 
The quantity p is the coefficient of cubical elasticity, and m that of linear 
elasticity. 
By solving these equations, the values of the pressures P,, P,, P,, and the 
compressions oe a8. = may be found. 
P,=(u— 3m) (Se oP ia) +m oe 
0) a 6 B. “OY op 
(cat B a + m B 


P,=(u—3m) 6) 

Py=(u— 4m) (244 oe — om 
nee Ga" 5a) (P,+P,+P,) + =P, 
Bia (Plea el 
aaa So) BERD ise 
Oy 1 
Y =(5573 a) ae +P) +5 m By 
From these values of the pressures in the axes a, 8, y, may be obtained the 
equations for the axes 2, y, 2, by resolution of pressures and compressions.* 



















For p=eP, +P, +P, 
and g=aaP, + 66P, + ccP, 
ym) (1024 ddy dd ‘) 4 moot 
Rie 3 dx dy dz ax 
1d2a ht doz dé " 
p.=(u—gm) (G24 Tae +2) +mShrr. (8, 
P.= (4-3) (= oe (ie so mone 
=" (aby oo 
n=9 dz i: = 
m (doz doz 
Pat (eee) 0.) 
_m (dd« ddy 
a= (a ee ) 
doz i af 1 
da = am) it P2+Ps) += Py 
ay Gea) (Pit+P2+ Ps) + = Po . (10.) 
ni 
ddz_ 1 alt 1 
woe Raye 3m (P1 7 Pat Ps) a m Ps 

* See the Memoir of Lamé and Clapeyron, and note A. 
