20 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



contiguous to those points, consisting of that superimposed as above 

 described, as well as of that impressed generally on the lamina; ami 

 consequently, if we conceive the latter of these tensions, (and therefore 

 also the former) to increase till the resultant tension is sufficient to 

 overcome the cohesive power at A or B, the fissure will not necessarily 

 be continued in the same direction, as if its continuation were inde- 

 pendent of the partial system superimposed about its extremities. 



It will be observed, however, that in the case just considered, in 

 which the forces are not producing motion in the mass, the whole force 

 exerted by gG, and kK, and similar lines is effective in producing 

 the superimposed system of tension about the extremity of the fissure. 

 We shall shew however, that such is not generally the case during 

 the propagation of the fissure, if propagated in the manner we shall sup- 

 pose it to be, and that consequently this force will have no material 

 effect on the direction in which the fissure will be continued, and which 

 will therefore be very approximately determined by equation (2). 



11. For this purpose, let us suppose in the first place, any systems 

 of tensions impressed on the lamina, of which the resultant tension (i?) 

 shall be less than the cohesive power (11), at any proposed point P\ 

 and let us then conceive subsequently superimposed on these another 

 system of which the direction is different to that of R, and of which 

 the intensity <l> shall increase continuously with the time f, till the re- 

 sultant of R and O shall be equal to n, so that a fissure shall then begin 

 to be formed at P. Its direction will evidently depend on R, and 

 the value (<!>,), which <t> shall have acquired at the instant the fissure 

 conimences. If R differ but little from n, <I>, will be generally small*, 

 and cannot (however the forces producing <1> may subsequently act 

 on the lamina), produce any material influence on the direction of 

 the fissure, which will therefore, in such case, nearly coincide with 

 the direction in which the tensions whose resultant is R may, have the 



* If the direction of <t> coincided with that of i?, the fissure would manifestly begin to 

 be formed when i? + <I>, should = FT, or <t>| = n-fi, which by hypothesis is small. If the angle 

 between the directions of R and <^ be not too near a right angle, it is equally manifest that 

 <I>, must be small. In the actual case considered in the text, this angle obviously cannot be 

 very considerable. 



