176 
ME. BOBEET MALLET ON VOLCANIC ENEEG-Y. 
on the second supposition P=T and 
dV f E 
= — W and T= J W dr. 
If § (a function of r) be the density, g being the force of gravity at the surface, then 
gravity at the depth r is 
F 9 ] 0 ^ dr 0 ^ dr 
1 r i T'r 
wi er 2dr C §rdr 
md 
W=- 
.f; 
pb 
jo V 
Hr \ 
Hr g y 
Thus, for example, let g be constant as to depth, then 
W =Mr- 
Upon our first supposition 
and upon the second 
T 
E 
111 the first case T = ^gH at the surface of the globe, decreases with increasing depth, 
and becomes zero at the centre. In the second case T=0 at the surface and equals 
at the centre. 
For the above expressions I am indebted to Professor Stokes, Sec. R.S.] 
86. Mathematical considerations only would thus indicate that in a thick terrestrial 
crust, assumed rigid and composed of dome-shaped laminae of superposed rock all of 
equal density and cohesion, the horizontal thrusts tending to produce crushing will be a 
maximum at the superior surface and a minimum at the inferior surface ; but that if 
composed of loose discontinuous material, or of any material such, in relation to the 
vast volume of the crust and to the immense forces engaged, that it can transmit interior 
pressures in all directions, as a quasi liquid or plastic body, the maximum deforming 
thrusts will be greatest at the inferior surface and nothing at the superior surface. 
87. So far mathematical investigation serves us ; but it throws but little further light 
upon the question that most interests us here — namely, at what fraction of the entire 
depth of such a thick terrestrial crust will be found the couche of maximum vulcanicity, 
that is to say, of greatest work in crushing or deformation. This depends not only 
on the depth at which T is a maximum, but on that at which the couche of maximum 
resistance to T is to be found ; and this latter depends upon the nature of the materials 
at all depths, as well as upon their state as forming the shell of a globe such as ours. 
Viewed upon the great scale, our earth’s crust is neither quite rigid and dome-like nor 
