EXAMPLES OF FISSTJEING. 61 



In theory as in practice, only masses capable of considerable deformation 

 under the system of external stresses can be divided by a single clean cut. 



This conclusion seems to throw some light upon a general feature of 

 geological fractures. In the laboratory rocks are very brittle substances, 

 and every geologist has experienced a feeling of surprise that in natural 

 rock-exposures clean cuts in a single direction are so frequent. It now 

 appears that cuts of this description can occur only when the stresses are 

 such as to produce a considerable elastic or plastic deformation of the 

 mass. There is, of course, abundant other evidence that such stress 

 systems really accompany orogenic movements. 



Examples of inclined Pressure. — According to a famous theory developed 

 by Navier and Poisson the ideal isotropic solid is characterized by the 

 property that in a simple elongation of small amount the linear lateral 

 contraction is just one-fourth of the increment of length. Though must 

 elasticians refuse to acknowledge the theoretical basis of this conclusion 

 (viz, that the action between two molecules is reducible to a single force 

 acting between the centers of mass), there is no doubt that several sub- 

 stances, and especially glass, behave sensibly as this theory demands. 

 As some rocks are glasses, it is certainly legitimate to assume, for the 

 purpose of illustrating the theory of rupture developed above, that the 

 relation 1 / 4 holds true* 



Let a pressure Fact upon a slab of a rock fulfilling Poisson's ideal at 

 an angle of 30° and let the mass rest against a rigid support. Then if 

 U and Q are the horizontal and vertical components — 



U= — F cos 30° = — F \(^ ; Q=—F sin 30° = — C 



If also n is the modulus of rigidity, it is easy to show and is well known j 

 that — 



* Possible Test of Poisson's Hypothesis.— One of tin 1 obstacles attending the discussion of Pois.-.>n'-. 

 solid and the question whether or not the coefficients of rigidity and compressibility for isotropic 

 solids are independent consists in the fact that it is difficult to determine Young's modulus and 

 the modulus of rigidity for tin- same liody with sufficient accuracy to justify theoretical conclu- 

 sions. There seems to be a method of direct comparison which would test the question if the 

 experimental difficulties should not prove too great. If M is Young's modulus, 



/= — F sin <p j M and 6 = — F cos $ / n, 



If, then, a testing machine were so adapted as to produce a pressure at 45° to a stationary plane, 

 the deformation of a cube subjected to its action would give 6 ./and .1/ / n. If Poisson's hj pothesis 

 is verified, il//w = in I. 



t Compare Thomson and Tait. Nat. Phil., section G83. For Poisson's solid 3 ft = 5m. 



