58 
REl'OBT— 1847» 
generation of the elastic vapour, so llint the action of the force should not 
assume the character of an explosion. The portion of the solid crust acted 
on may, as a simplification of the problem, be first considered of unilorm 
thickness and of uniform density. 
Under these conditions the crust, when acted on by a sufficient fluid pr«- 
sure beneath, would first be elevated through a certain space without dU- 
location, since it would possff7.8 sumo degree of extensibility. Let us conccjre 
if elevated into that position in which It should be just im Ihc point of dis¬ 
location, so that by the smallest additional elevation fissures would begin to 
be formed. The boundary of the elevated district would then be stricllf 
defined by the line beyond which the crust had sulfcrcd no sensible disturb* 
anee, and which may be regarded as identical with tl>e supeifieial line which 
would mark the boundary of the internal lake. Under these circumstaoces 
the ease presents to us a determinate mechanical pit»blem. The princi^ 
points which offer themsedvos for de-lcrmination are those connected with 
the tension to which the mass would becotn* subjected by its idcvsHon. 
With respect to this tension then) are certain general propositions which 
would hold independently of the j)nrticular conditions of the prublem, and 
of which it is important to have n distinct conception, both in the present 
problem and in one which will present in^elf lo us in the followiBg section. 
To explain these ])ropositIon8, as far ns may be neccKuiry for our immediate 
purpose, conceive n plane of indefinitely stuall given area (<) to have its mid* 
die point coincident with any proposed point (P) in the interior of a solid 
mass having some dogix'c of oxtciiieibility, and in a state of constraint, like 
that, for instance, of our elcvateil muss. The purLie.lcs in contact with each 
other, but on opposite sides of this small geometrical plane, will act on each 
other, and the resulting force between them may be represented byps. 
The force.am! the angle which its direction makes witli a perpendicular 
to the plane will vary with the angular position of the plane; hut there wc 
always three positions of the plane in which the direction of the. force and 
the perpendicular to the plane will coincide. The three corresponding 
directions of the perpendicular are called pritunpaf direction, and the three 
corresponding values of/? are princijtal tcii 8 io 7 is ox presswrts. These 
, ----—v,..vv....«..o through w—, 
in the case of the elevated but still unbroken crust abovc-nientioni’d, two of 
the principal directions, one of which would be the direcUim of msxinium 
tension, would bo approximately parallel to the surface and the tliird 
pendicular to it. 
21. Formation of Fissures —In considering the formation of fissurf*’ 
which are here termed the primury phtejumienn of cUnHition, we must direct 
our atUmtion to that state of the uplilled mass in which it U just on thcpoiiti 
oj dtsUicnlwn, which would bo the case at the instant when the maximuiu 
tension «Jt somo imint (P.) just became equal to the cohesive power at that 
point. If the tension were then Incn^ased by any indefinitely small quaDtiiy* 
the cohesion would be. overcome, mid a fissure would begin to be formed: 
and It 18 sufficinifly manifest that a plane perpendicular to the direction ol 
n^v !•*' be a tangent plane to the fissure, or what w? 
rnSim at that point. Thus, if the direction of 
maxininm tension at hi,,. 
