92 MR JAMES CLERK MAXWELL ON THE 
62, and differentiating with respect to 2, y, and 2, in each equation, we obtain the 







equations — 
le a be a? ae eel oe? 
ae os 2 oe 6,2 fa 2 (1). 
ee i he fy ‘2 18429 ¢,” 
a ee te oP, 4 oY a6 +06 
a » uly Aa “Pa3, + —¢,¢, — 6 6, 
ROE OE I = oP PEL Pe 
oe az, era! “Bat, +2%o,c,- 6, | a 
use eae a, a, + “2 b, by + - c,¢, + 08, 
a z oe ae °2 5,0 hac, — 06, 
Equations of the equilibrium of an element of the solid. 
Equations of 
compression. 
The forces which may act on a particle of the solid are :— 
1. Three attractions in the direction of the axes, represented by X, Y. Z. 
2. Six pressures on the six faces. 
3. Two tangential actions on each face. 
Let the six faces of the small parallelopiped be denoted by 2,, %,, 2, 25 Yys 
and z,, then the forces acting on 2, are :— 
1. A normal pressure p, acting in the direction of x on the area dy d z. 
2. A tangential force 7, acting in the direction of 7 on the same area. 
3. A tangential force y,' acting in the direction of z on the same area, and so 
on for the other five faces, thus :— 
Forces which act in the direction of the axes of 


x y z 
On the face x, | —p,dydz —9q,dydz —q,'\dydz 
1 ; ad q,} 
at, | (p+ fi da)dyde (3+ Ot a2) dydz (qo + “2 dx)dydz 
Y, —q,idzdx —p,dzdx —g,dzd% 
dq,} 
Sar Fa aed 




d 9 
(Py + dy (yazan 

(q+ haydzda 
