Rev. 0. Fisher — On Faulting, Jointing and Cleavage. 273 



The tangential pressure anywhere across KS will be horizontal, 

 but not quite so the tangential pressure across any other ordinate 

 where it meets the successive curves. But the total resolved part 

 of all the tangential pressures must be everywhere nearly equal to 

 that supported at ilf iV'and L H, and consequently the same every- 

 where, so that we may take the value of P just found as fairly 

 representing the horizontal pressure at any point of the curve that 

 we have drawn through P. 



o 



To find the compressing force W we observe that the acceleration 



on KP is g—^. And that on PS is g-{-^- 



S 



And these 



must be equal whence we obtain 







w = f^^ s = f s 



KS h 







\\Jl-\ f\Y^r^r\ • 







vvnence -~- — .7 . 





= d suppose. 

 Unless S is nearly equal to loh, i.e. unless the column is supported 

 from below, this will be always small, because r is much greater 

 than X ; S will therefore be always small while the settlement is 

 going on. 



We can now see why the conditions supposed will in general 

 produce cleavage and not faulting. For if we take a parallelepiped 

 within the mass as in the previous Parts of this paper, we know 

 that faulting; cannot be induced unless 



= -P-^. J / P-T7 \^_ W 

 < YVF - ^ ^ 2uP ) P 



If we substitute 1 — ^ for — — and neglect the higher powers of 

 B, we shall find that this condition is equivalent to 

 cot ^ = J/ (1 + (1 + i^') d). 

 A fortiori cot 6 must be greater than v. 



This implies that the relation between the pressures which is the 

 consequence of the supposed conformation of the tract necessitates 

 as a condition for faulting that the co-hade, or inclination to the 

 vertical, of the surface of shearing shall be greater than the angle of 

 repose for the particular kind of rock affected, a condition which is 

 not compatible with a steep hade such as we have seen will occur in 

 the neighbourhood of the crest of the ridge. Therefore we cannot 

 have faulting there, but only viscous shearing, without separation of 

 tlie rock along the surfaces of shear. 



The distance between two surfaces of shear near enough together 

 to be regarded as parallel must of course be measured along their 

 common normal. If they encounter a layer of harder rock which does 

 not shear so easily, any two surfaces of uniform velocit}' must recede 

 from one another in crossing it. This will necessitate a change in 



DECADE III. — VOL. I. — NO. YI. 18 



