56 



G. F. BECKER — STRUCTURE OF THE SIERRA NEVADA. 



that only a thrust acting at an angle of 45° to the fissures along that diagonal 

 of the prism which strikes north-northeast to south-southwest would bring 

 about the phenomena to be accounted for. 



This I will proceed to show by a demonstration to be found in a somewhat 

 modified form in treatises on elasticity, but which has not hitherto, to my 

 knowledge, appeared in geological literature. 



Analysis of a Thrust. — Suppose a cubical portion of the mass of granite of 

 the Sierra, oriented as in figure 2a, to be subjected to a uniformly distributed 

 pressure acting from the south-southwest, this pressure being opposed to a 

 resistance in the opposite direction. Let the uniformly distributed pressure 

 be represented by a single force P. This force P may be considered as 



FiGUKE 2— Cube subjected to Thrust. 



divided into three equal parts, and one may also assume that other forces 

 are applied to the cube, provided that these other forces exactly balance one 

 another. Thus a normal traction P/3 may be applied to each of the lateral 

 faces of the cube, provided that a lateral pressure P/3 is also applied to 

 each of these faces. Such a system of forces is shown in figure 2b, and is 

 exactly equivalent to the seemingly simpler system shown in figure 2a. 



When the distortions of an elastic mass are small, the forces which pro- 

 duce them may be regarded as applied in any succession which is convenient. 

 This is called " the principle of superposition of small stresses," which is 

 applicable whenever the displacements produced are so small that all powers 

 of these displacements higher than the first are so minute as to be negligi- 

 ble. It is on-ly with such distortions that the mathematical theory of elas- 

 ticity deals, as it is at present developed.^ 



*The theory of elasticity deals with such strains as occur iu bridges, buildings, and machinery, 

 not with defornnations like those to be observed in masses of rubber or jelly. Suppose that an iron 

 girder lOU feet long sags under a load to the extent of l-20th of a foot ; then the square of this flex- 

 ure is l-4,000,000th part of its length, which is inappreciably small relatively to the size of the mass. 



