274 Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 
uniformly along this line perpendicular to it, and in the plane 
of the lamina, on the contiguous particles situated respec- 
tively on opposite sides of the line, thus tending to form 
a fissure along it. The cohesive power opposes this tendency, 
and if it be uniform along the line just mentioned it will be 
measured by that value of f which is just sufficient to over- 
come it. Ifthe cohesive power along this line be variable, f 
will manifestly not be a measure of it with reference to the 
single point P. In such case we must conceive the cohesive 
power to be equal (for the unit of length) at every point of 
the line to that at P, and then that value of (which we may 
designate by 11) which would, under such circumstances, just 
overcome the cohesive power, may be taken as a measure of 
it at the point P, when estimated in the direction perpendicu- 
lar to the above line through that point. 
In the first place let us suppose the value of II the same for 
every direction of this line; then is it manifest that the direc- 
tion in which a fissure may be formed immediately at the 
point P cannot be determined in any degree by the cohesive 
power, since its value is the same for every direction through 
P. The same conclusion will clearly apply to every point 
where the value of II is independent of angular direction, and 
equally so whether 17 be the same or different for different 
points, 7.e. whether the cohesive power be uniform or vari- 
able, so long as its variation depends solely on the position of . 
the point P; or, in mathematical Janguage, the above con- 
clusion will hold whenever I is a function only of the co- 
ordinates of P. In such case then, the fissure will be formed 
through P in that direction in which the tensions there have 
the greatest tendency to form it, and our equation will be as 
strictly applicable for the determination of this direction as if 
the lamina were perfectly homogeneous. We shall be able 
shortly to extend still further the conditions under which this 
equation will be similarly applicable. 
It is easy to extend the above reasoning from a lamina to 
the general elevated mass. 
If, however, the value of I be different for different angu- 
lar positions of our line of a unit of length through P, (as, 
for instance, when a laminated or jointed structure prevails 
in the mass, or any accidental line of less resistance passes 
through the proposed point,) it is manifest that the direction 
of the fissure there will depend on the tensions and this vari- 
able value of IJ conjointly, and the equation above given will 
no longer suffice generally for its determination. ‘The case of 
Jaminated or jointed masses I professedly exclude from these 
investigations, since their lines of dislocation will’ necessarily 
