278 Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 
these tensions, and therefore, in the present case, perpendi- 
cular to the former fissure. Consequently, since the radius 
of curvature above mentioned will, if the fissure be of con- 
siderable length, be very large at every point, it will be im- 
possible for a second fissure to be formed parallel to the first 
and not very remote from it, by the general tensions to which 
the mass is supposed to be subjected *. 
We may conceive, however, any number of parallel fissures 
in the case we are considering to be formed simultaneously. 
Acotctgtt aes Bute ae 
a ey 
Thus suppose two parallel fissures, AP, A'P’, produced by 
tensions acting perpendicularly to their directions, to begin 
simultaneously at A and A’, and also to arrive at P, P’ at the 
same instant, P P! being perpendicular to A P and A’ P". 
There will manifestly be no reason why they should not in 
such case be continued simultaneously from P, P’, just as they 
began at the same instant at A and A’. If, however, the re- 
laxation produced by the opening of A P be communicated 
through the distance P P! instantaneouslyt, it is clear that as 
soon as A P should have advanced in its progressive forma- 
tion by the smallest quantity further than the other fissure, 
the formation of this latter would be instantly arrested. Un- 
der such circumstances, then, the possibility of the simulta- 
neous formation of two or more fissures would be rather a 
mathematical than a physical possibility. The fact is, how- 
ever, that the relaxation produced by the one fissure is not 
communicated instantaneously to the distance of the other. 
Time will be necessary for this purpose, and this removes the 
difficulty of conceiving this mode of formation, since it is no 
longer necessary that the velocities of propagation of the two 
fissures should be mathematically equal. For, suppose one 
fissure to have reached P when the other has reached Q’, 
* If there were another system of tensions perpendicular to the first, 
this conclusion weuld be true for still greater distances from the existing 
fissure. We may remark that these two cases of tensions would seem to be 
the only ones in which systems of rectilinear parallel fissures near each other 
could in any way be produced. See Memoir, p. 36. 
+ This would be the case if the mass were absolutely inextensible. 
