Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 25 



since the resultant tension is a maximum in the direction PR and 

 a mmn^um in that perpendicular to PR. (Art. 5). Consequently', the 

 greater the ratio which the former of these resultants bears to the 

 atter, tl.e more rapidly will R; decrease while RPR increases, and 

 the smaller W.11 be the angle EPR, within which the above condition 

 win be satisfied, and the narrower therefore will the angular limits 

 mthm which a line of less resistance must be situated, in order thaJ 

 It may cause a fissure proceeding in any assigned direction to deviate 

 from Its course. A line through P perpendicular to PR, may be 

 termed a permanent line of cleavage. If the ratios '^, •^, &c. be the 



TZ T.r7 ''t*, °' the lamina, all such lines will bf straight lines 

 Art. 14) and parallel to each other. A fissure will always have a tendency 

 to resume this direction, when made by any partial cause to deviate 

 from It, and will resume it {taking our assumptions respecting the im- 

 pressed tensions, (Art. 12)} almost immediately after the cessation of 

 such cause. It will be well to examine this tendency in a few parti 

 cular cases. It may be considered as measuring ■ what may be termed 

 the permanence of the fissure's general direction. 



19. Let there be two systems of tensions, the directions of which 

 are perpendicular to each other, and of which the intensities are F 

 and /respectively, at any proposed point, when they become sufficient 

 to form the fissure there. The greatest of these {F) will be the max 

 imum, and / the minimum resultant tension, (Art. 6), and therefore 

 the less / IS, the greater will be the permanence of the permanent 

 direction, perpendicular to that of F. If /= F, there will be no 

 permanence m any particular direction. We have already seen (Art 6) 

 that there is, m fact, no greater tendency in this case to form a fissure 

 m one direction than another. 



20. Again, let us suppose in addition to the systems of tensions 

 of which the intensities are /, /, &e., and which have determinate 

 directions, a force acting within the fissure perpendicularly to its direc 

 tion and with equal intensity on its opposite sides, exactly as a fluid 

 would act when forcibly injected into a fissure formed in a solid mass 

 Vol. VI. Paet I. n 



