
EQUILIBRIUM OF ELASTIC SOLIDS. 101 
1. When the external and internal pressures are equal, or 4, =A. 
2. When the external pressure is to the internal pressure as the square of 
the interior diameter is to that of the exterior diameter, or when a,? & 
3. When the cylinder is solid, or when a,=0. 
4, When the solid becomes an indefinitely extended plate with a cylindric 
hole in it, or when a, becomes infinite. 
5. When pressure is applied only at the plane surfaces of the solid cylinder, 
and the cylindric surface is prevented from expanding by being inclosed in a 
— 
1 = 4," hy. 
strong case, or when oe =0. 
6. When pressure is applied to the cylindric surface, and the ends are re- 
tained at an invariable distance, or when a =0. 
1. When 4,=/,, the equations of compression become 
Oz 1 2 
= =o ¢ + 2h.) + 3m (o—h,) 
1 2 1 1 
= (gutsn) + 24 Ga-sn) 
3, (27.) 
1 1 
Poon” + 2 h,) + 3m ee) 
Dentin) | ) iY ec 
ae = Bm) +" Gatsa) 
When h,=h,=0, then 
Ox Or hy 
zor Be 
The compression of a cylindrical vessel exposed on all sides to the same hy- 
drostatic pressure is therefore independent of m, and it may be shewn that the 
same is true for a vessel of any shape. 
2. When a,? h, =a," ho, 
Oz 1 2 
Baths Tas) 
or 1 1 
~ 7, 9M (0) +3,,8 hy —o) ° > (28.) 
pera ial h, 
Sa in 
In this case, when o=0, the compressions are independent of p. 
3. In a solid cylinder, a,=0, 
ee 
: 0 0 : 
The expressions for = and == are the same as those in the first case, when 
h,=hy. 
