Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 273 
the greatest tendency to cause a fissure to begin at any proposed 
point. ‘To give all requisite generality to the investigation, 
let us suppose there to be any number of these tensions, and 
let F, f,,,f:, &c. denote their respective intensities at any pro- 
posed point, 8,, 8, &c. the angles which their directions 
make with that of F; 
b= A, hog = = es 
ze cos2B = p, cos 26, + p.cos2 6, +, &c. 
v the angle which the required direction makes with that of 
F; we shall have for the determination of ¥, 
1+ pcos 26 
' =psin 2 B 
This equation will determine the direction in which the ten- 
sions have the greatest tendency to cause a fissure to begin at 
any assigned point, but when its formation has begun, it is ob- 
vious that the state of tension in its immediate vicinity must 
be altered, and that the tensions thus modified may not have 
a tendency to continue the fissure in the same direction as that 
in which it was the tendency of the original tensions to make 
it begin. I have shown, however, that with our hypothesis 
as to the mode of action of the elevatory force (see p. 234) the 
above equation will be very approximately applicable to the 
action of these modified as well as to that of the original ten- 
sions. 
The actual direction in which the fissure will be formed 
will not in all cases depend solely upon this tendency of the 
tensions, but partly also on the constitution of the elevated 
mass. If, however, its cohesive power be perfectly uniform, 
it is manifest that this direction will be determined by the ten- 
sions alone, or will coincide with that given by the above 
equation. It will appear also that this is equally true in cer- 
tain other cases; when it is not so, the effect of any peculiar 
constitution of the elevated mass must be investigated. I shall 
now proceed with these points. 
Let us still confine our attention to a simple lamina of uni- 
form thickness. Its cohesive power at any proposed point 
may be estimated in exactly the same manner as the intensity 
of the tension at that point. Let the point of the lamina be 
designated by P, and draw through it, in any direction in the 
plane of the lamina, a straight line whose length is unity. 
Then conceive two equal and opposite forces (f/f) acting 
cot?» + cot P—1 = 0.* 
* See Memoir, p. 18. + Memoir, pp. 20, 21. t Memoir, p. 13. 
Third Series. Vol. 8. No. 47. April 1836. 2F 
