CO G. F. BECKER — FINITE STRAIN JN RUCKS. 



depotentialization of energy per unit Length of crack, it is only necessary 

 to determine the value of #, which will give the last expression a maxi- 

 mum value. This problem lends at once to — 



2 tan (y -f- a)== tan #, 

 or — 



to = I cos (y + «), 



a result of very convenient simplicity. 



Thus far it has been assumed that only one set of fissures forms in tin- 

 slab. This case is of frequent occurrence in rocks, but it is not much 

 more frequent than the appearance of two sets of fissures forming large 

 angles to one another. Under conditions such that viscosity does not 

 essentially modify the results, there should be as great a tendency to 

 form fissures on the other set of planes of maximum tangential strain, 

 making an angle to — i> with o x, as on those planes discussed above. 



When two sets of fissures form at large angles to one another they must 

 seemingly develop simultaneously; for. if a single set of sheets were to 

 form first, and secondary fissures were to be produced by the grinding of 

 the sheets against one another, it is easy to see that the secondary fissures 

 would make but a small angle with the primary divisions, and there 

 would be more evidence of movement on the first fissures than on the 

 subsidiary cracks. These cracks would also not in general pass from one 

 primary sheet to the next. 



When the two sets of joints form simultaneously, each set must form 

 under similar conditions, and I can think of no reason to suppose that 

 they do not form independently. Hence the theory already developed 

 seems to apply also to the second set of fissures, the only change needful 

 being the substitution of to — v for m -f- '■>. 



The results derivable from this theory of division certainly accord with 

 some well known facts. Thus, if a tough mass is acted upon by a shear- 

 ing tool, it is a matter of daily experience that the mass undergoes a 

 single cut. For this case viscosity comes into play, and by the theory 

 only one set of fissures will he developed, cr = 0, to -{- v — and w I. 

 which means that only one fissure will intersect the mass. Again, it' one 

 attempts to cut a brittle substance like glass with a shearing engine, the 

 mass, according to experience, shatters instead of simply dividing. By 

 the theory as applied to this case the elastic deformation is extremely 

 small, neither set of planes of maximum tangential strain has a sensible 

 range, and to -J- v = 0, while to — v = 90°, nearly. Hence only a single 

 fissure will tend to form in the direction to -f >. but the mass will be 

 divided into scales of almost infinitesimal thickness in the direction 

 to — v. In other words, the theory substantially accounts for the facts. 



