ME. EOBEET MALLET ON VOLCANIC ENEEGY. 
179 
therefore, for the entire equatorial annulus or section of the shell, 
T 0 = 25 rEx-?xP, 
or 
T 0 =7rE 2 xP ; 
but as P is the weight of the cubic unit of the shell, W, the weight of the hemispherical 
shell, is 
hence 
W=2tR 2 xP; 
that is to say, the mutual pressure by gravitation (under the condition of shell and 
nucleus) of two hemispheric shells taken in an equatorial plane is equal to one half the 
weight of one hemisphere. 
91. Signor Belli enters into several subordinate discussions as to the probable modifi- 
cations of resistance to crushing that may arise in rigid materials when exposed to great 
compression in all directions, and whether the tendency to Crushing will be increased or 
diminished by the simultaneous action of two orthogonal pressures. These refinements 
are not required for our purpose, as we may conclude that no modification of condition 
of application can enable a rigid solid to remain coherent under pressures several 
hundred times greater than will crush between two opposite surfaces a cube of the same 
material. 
92. The cube in this case is exposed to pressures on two faces, and is free to yield in 
four directions at right angles to the pressure and opposite to each other respectively ; 
but a cube such as the unit-cube of our shell, exposed to pressures simultaneously on 
four of its faces, is only free to yield in two directions parallel to each other and at 
right angles to the pressures. Direct experiments on this point have not, to the writer’s 
knowledge, ever been made ; but certain facts well known to engineers appear to warrant 
the conclusion that rigid bodies, such as cast or wrought iron, steel, or bronze, are 
weakened (i. e. the tendency to become broken up is increased) by the simultaneous 
application of orthogonal pressures or tensions. 
93. Thus, for example, the metal of the interior of a discharged cannon is exposed at 
any point at once to compression radially to the bore and to two orthogonal tensions, 
longitudinal and circumferential, and it is known that the resistance of the material 
thus is less per unit of section than of the same exposed to tension or compression in a 
single direction only. 
94. Another question may arise. If the earth’s solid shell be of very considerable 
thickness (as it almost certainly is), and if we conceive a cubic unit of it at a large 
depth exposed necessarily to pressures upon all its sides, how is the cube to suffer such 
deformation as shall admit of crushing at alll 
O 
MDCCCLXXIIJ. 2 B 
