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



at the angle 45° ; and the requisite value of TF" -1- P would be 

 given by the relation 



*(7r+P) =(,. 



Hence, if other conditions permitted sepai'ation, and faulting, it 

 would always be ready to occur at the angle 45°. 



But there are two other conditions to be satisfied. 



The first of these is that there must be room for the mass to move. 

 This, as we have assumed in our preliminary considerations, will 

 result either from cracks being opened by the contraction, or from 

 there being a tendency set up to open them. Their formation may 

 be thus explained. 



The stress normal to A B, tending to produce separation by 

 cracking, is, 



P X A B siii2 e— W y. A B cos"- 0. 



And K being, as before, the coefficient of cohesion, we must have, 

 in order that the rock may be pulled asunder, 

 F sin^ e — TF cos^ 9 = k. 



Suppose, as before, that P increases gradually until this con- 

 dition is satisfied. It will be so when 6 = 90° and P —. k. 



We shall then have a vertical joint formed, or tending to be 

 formed, according as the material is not or is ductile. And another 



will be similarly formed at a distance from this one of — • 



We may thus get a system of equidistant vertical joints. 



As soon as the rock is I'eady to separate, the contractile force will 

 begin to draw the blocks together as in Fig. (7). Being held ex- 

 tended at the bottom by the force X, a horizontal shearing force will 

 be generated tending to cut up the blocks along horizontal planes. 

 This force will be the excess of the contractile force over the exten- 

 sile stress at any height. The contractile force may be regarded as 

 constant, but the extensile stress will diminish with the diminishing 

 friction as the cover diminishes. Hence their difierence, which is 

 the force tending to draw the rock together horizontally, continally 

 increases upwards, and at every interval at which this difference 

 becomes large enough to produce rupture, a horizontal joint will be 

 produced. 



If, however, the substance is of such a ductile nature, that the 

 weight makes the friction too great for separation before a viscous 

 shearing is set up, we may have a kind of horizontal laminated 

 cleavage induced, such as occurs in some coals. 



The contractile force of which we have just spoken is not a com- 

 pressing force of the character which we have attributed to P. It 

 acts upon the parallelepiped almost entirely in one direction ; for the 

 difference of intensity on the two faces may be neglected. 



We have then now no compressing force left to consider except W. 

 Consequently the shearing force along AB will have become ^ W 

 sin 2 ; and, in order that separation may take place, we must have 



1 Ws[n2 = fi. 

 There is no doubt that in the case of solid rocks /lo will be a very large 



