Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 277 
the case in which there are two tensions only, and these ten- 
sions at right angles to each other. The direction of the fis- 
sures will then be always perpendicular to that of the greater 
tension. If therefore the directions of this tension at different 
points be parallel to each other, the fissure will be rectilinear, 
whatever be the ratio of the two tensions. The case of a 
single tension is a particular case of the above, when the 
smaller tension vanishes. If there be two tensions making an 
acute angle with each other, the direction of the fissure will 
be within the exterior or obtuse angle between the directions 
. . . 5 . 
of the tensions; and if one tension be considerably greater 
than the other, or if the angle between their directions do not 
deviate materially from a right angle, the fissure will lie much 
nearer to the direction of the smaller tension* than to that of 
the greater. 
III. Having thus explained how a single fissure may be 
formed, and its direction determined, let us consider the for- 
mation of a number of similar fissures all following the same 
law, and not remote from each other, thus forming a system 
of fissures. In the greater number of cases in which such sy- 
stems have been recognised the lines of dislocation have been 
approximately rectilinear and parallel. It will suffice, there- 
fore, to take this case, which will be somewhat the most simple 
to explain. 
In the first place I have considered in my memoir, how far 
it would be possible that the fissures of a system should be 
formed consecutively. For this purpose I have examined the 
modification which would be produced in the tension of the 
mass by the existence of a rectilinear fissure extending for any 
assigned distance, assuming, for the greater simplicity, the 
mass to be acted on by one system of tensions perpendicular 
to the fissure ; and it appears that if we draw a line perpendi- 
cular to the fissure and meeting it at a point P, not too near 
its extremities, the tension at any proposed point of this line 
and in its direction (or perpendicular to the fissure) will be 
less than that which will be caused by the existence of the 
fissure, in a direction parallel to itself, provided the distance 
of the proposed point from the fissure be less than the radius 
of curvature at P of the curve formed by the intersection of 
the vertical side of the fissure with a horizontal planet. Now 
it has been before stated that when there are two tensions at 
any point in directions perpendicular to each other, if they 
produce a fissure it must be perpendicular to the greater of 
* Considerably nearer to it than the resultant of two forces respectively 
equal in intensity to the two tensions, and in the same directions. 
+ Memoir, p. 33. 
