SPACING OF FISSURES. 



50 



by the movement of particles in the direction of the pressure, irrespective 

 of the movements which they execute in other directions. 



The rupturing of the slab into sheets may be regarded as a change in 

 its physical properties such as is contemplated above. 



f\f 



a. 



b 



Figure 9. 

 Cut a shows'the same mass as figure 8, the sheets now being rotated through a small angle S by 

 the pressure acting in the direction <j>. Cut 6 represents the corner c' of one sheet on an enlarged 

 scale, together with the original position of this corner at c. 



The line c' r is the distance measured in the direction of the force 

 through which the point c has moved in passing from c to c', so that c' r 

 is proportional to the depotentialization of energy. The angle of rotation 

 being small and arbitrary, say, <J, the angle cc' i = # and — 



(•r) = («0 



cos # 

 sin <p 



Then, too, (cc) = (oc) 8 = 18 js'm &, so that the relief of pressure varies 

 with the line — 



(c'r) = 



18_ 

 sin <p 



cot #. 



The relief of pressure per unit length of crack therefore varies with- 



w 



, i >. 4 I 2 8 , . f 1 tan(y + ut)} < 



Cc r) = — — cos 4- «0 i 1 — — -, — - - cot >> 



sin <p ( tan * 3 



and to find the distribution of fissures which will ensure the greatest 



