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



be considered plastic, inasmuch as they yield to pressure ; so that, 

 after rupture, spaces become filled up, which would be left vacant 

 after the subsequent movements, if the material were rigid. ^ The 

 rationale of the mechanical action appears to be of the following kind. 



Let ACBD (Fig. 10) be the medial 

 section, parallel to the vertical sides of a Fig- 10. 



parallelepiped of unit thickness, within a 

 mass of rock ; and suppose this portion to ^ I ^ ^ 



be subjected to a horizontal stress in the 

 direction perpendicular to A C and £ B, 

 which may be either a pressure or a tension. 



As far as regards the disruption of this 

 mass, we need only take into account equal 

 stresses upon its opposite sides ; for, if the 

 opposite stresses are unequal, the excess of 

 the one over the other will tend only to 

 move the mass as a whole. Let then the 



horizontal stress at the place under consideration be P pounds upon 

 a square unit of vertical section. This assumption, that the pressure 

 varies as the area on which it acts, introduces the idea of plasticity. 

 If we then have regard to the vertical slice of unit thickness, of 

 which our parallelepiped forms part, the stresses upon A C and 

 B B will be each equal to P x ^ C, or P x ^ .5 sin 6*. 



The parallelepiped is also subjected to the stress, which arises from 

 the weight of the rock above it and the reaction of the bottom which 

 is supposed to be fixed ; and, upon a similar assumption as to its con- 

 stitution, PT being the pressure upon a square unit, the pressure ujDon 

 A D will be WxA B cos 0, which will act downwards upon A B, and 

 upwards upon BC. 



If now we resolve these two pairs of forces along the diagonal 

 A B, the force which tends to push the half A D B \n the direction 

 A B will be the sum or difference of the resolved parts according as 

 the horizontal stress is a tension or a pressure. Hence 



Force on ABB along AB=W x A B sm Q cosQ ;^ P x A B smQ cos e, 

 = \{f^±P) ABsm2e. 

 Let this be resisted by a statical force per unit area along AB, whose 

 measure is ju.. Then, so long as 1 ( W+P) sin 2$ is less than /n, no 

 motion can take place along A B. But, as soon as this is equal to, 

 or greater than, /j., motion may ensue, other controlling circumstances 

 being favourable. This force /t will arise from the constitution of 

 the material. If it is rigid, and continues rigid under the action of 

 the shearing stress until it separates along A B, then ^ is a coefficient 

 of adhesion. 



But if the material continues rigid until the shearing stress attains 

 a certain amount, and then begins to " flow " (as in M. Tresca's 



^ The writer offered some suggestions upon faulting in his Physics of the Earth's 

 Cnist (1881), which, although possibly applicable in some cases, he is now constrained 

 to admit are not generally satisfactory. The appearance of Mr. Teall's notice of a 

 faulted slate has led him to a review of the whole question. 



