26 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



Let P'P be the fissure. It is manifest that this force {j)) will produce 

 a tension on the mass contiguous to the extremity of the fissure, in 

 a direction Pp perpendicular to P'P, and must therefore tend to pro- 

 pagate the fissure along P'P produced. Hence it will follow that such 



a force cannot affect the permanent direction of cleavage as determined 

 by the tensions yj, ^, &c. alone. For, suppose PR the direction of 

 the maximum resultant {E) of these tensions, it is manifest that the 

 whole resultant tension (including that produced by p) immediately 

 beyond the extremity P of the fissure, must be in a direction PR 

 between Pp and PR; consequently, the direction of propagation from 

 P will deviate from P'PN, and approximate more nearly to perpen- 

 dicularity with PR', and therefore also with PR. For the same reason, 

 the direction of its further propagation will approximate still more nearly 

 to a line perpendicular to PR, till it coincide with it. The permanent 

 direction will therefore be the same as if the force p did not exist. 



If however p be large compared with R, it is manifest tliat the 

 angle pPR' wiU be very small, and that the tendency to resume the 

 permanent direction, when the fissure has been obliged by any partial 

 cause to deviate from it, will be much less than if p were relatively 

 smaller. 



21. If the lamina be subjected to no tension, and the fissure be 

 produced entirely by ^j, the tendency will be to propagate the fissure 

 in the direction in which it may originally be formed. Suppose AP^ 

 to be its original direction, but that from P, it follows a line P,P„ 



