ME. EOBEET MALLET ON VOLCANIC ENEEGY. 
175 
proportionate to whatever value we take for E, a cubic mile of rock in any portion 
of the self-sustaining shell is exposed to a horizontal thrust upon each of its vertical 
faces =~ times its own weight. 
That on our previous data will be 2000 times its own weight ; but on the same 
data the crushing load for granite or porphyry being about 2000 tons per square foot, 
and the weight of the material 178 lbs. per cube foot, the modulus of cohesion, or 
the length of the column in feet of the material that shall crush by its own weight, is 
*r 4 -=25169 feet=4T95 miles of G000 feet. But the height of the column of the 
same material representing the horizontal thrust is 2000 miles, or nearly 480 times the 
height of the crushing column. 
In fact while the materials of the hardest and most coherent rock are crushed at 14 
tons per square inch, the crushing force is here upwards of GOOO tons per square inch, 
if the equilibrated shell be, as assumed, wholly unsupported. It follows, therefore, that 
if of its total weight from attraction by the nucleus were supported by the latter, or 
that it were only free to descend by of the total gravitation, the materials of the shell 
must still crush. 
85. If the thickness of such a terrestrial shell be considerable (as supposed by Mr. 
Hopkins), the question arises at what depth from the outer surface will the couclie of 
maximum tangential pressure be found. 
[Let T and P be the horizontal thrust and the pressure, T as well as P being now 
referred to a unit of surface, and W the weight of a unit of volume, estimated at the 
depth at which it is situated, not as brought up to the surface of the globe, the equation 
for vertical forces in a sectorial element is 
2pTrdr+Pp 2 =( V r 2 dr, 
«/r c/r 
E being the radius of the globe, and r the radius vector from the centre drawn through 
the unit volume ; whence 
2Tp-^fi'=Wf 2 , 
dr 
the condition of equilibrium between T and P. 
Two extreme suppositions as to th e physical state of the globe (or its sectorial element) 
present themselves: — 1st, that it consists of successive thin dome-like couches super- 
posed, each rigid and self-supporting, so as to transmit no pressure to those below ; or, 
2nd, that no dome-like support exists, but that each couche transmits pressure to those 
beneath, as in the case of a liquid. 
On the first supposition 
P=0 and T=4Wr ; 
