14 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



tendency of the forces of tension to separate the particles which are 

 contiguous, but on opposite sides of the geometrical line Pp, by causing 

 them to move parallel to CD, will be measured by 



pm ■ F sin ^|/, 



= ^x.Fsm^ (if AP = X). 



The tendency to separate the particles at P, by causing them to move 

 in a direction making an angle 9 with CD or PQ, will be estimated by 



^x .cos 9. sin \|/ . F. 



This is greatest when = 0, and ^ = ^ . as of course it ought to be, 

 AB being then perpendicular to CD. 



&. Lamina acted on by two or more Systems of Tensions — Direction in 

 which their tendency to produce a fissure is greatest. 



3. Let us next suppose a second system of parallel tensions super- 

 imposed on the former, their common direction making an angle /3 with 

 that of the first system. Let PQ, PQ, in the following figure, be the 

 directions of the tensions acting on the element Sx, of the line A£ at 



P, and therefore QPQ' = fi ; and let the intensities of these tensions 

 (estimated as in Art. 2.) be represented by F and /. Then if QPB 

 = \ff, and therefore QPB = 4' — ^, we shall have the forces Sx.F. 

 sin >//, and ^x .J" . sin (^ — fi) acting on the element ^x; and to find 



