54 



straint, the resultant pressure or tension on this plane will vary with 

 the angular position of the plane, and its direction will not, as in 

 fluid masses, be generally perpendicular to the plane. There are, 

 however, three angular positions in which the direction of the pres- 

 sure does coincide with a perpendicular to the plane. These are 

 called principal directions, and are at right angles to each other ; the 

 corresponding pressures are called principal pressures. In these par- 

 ticular positions of the plane there will be no tangential action upon 

 it ; but generally the whole pressure or tension may be resolved into 

 two parts, of which one is normal and the other tangential. In cer- 

 tain positions of the plane these forces assume their maximum or 

 minimum values. The normal action is a maximum, when a per- 

 pendicular to the plane coincides with one of the three principal 

 directions ; and a minimum, when it coincides with another, the 

 third of those directions, not corresponding either to a maximum or 

 minimum value. These conclusions have been established by Poisson, 

 Cauchy and others. In this paper the author has investigated the 

 positions of the small plane, when the tangential force upon it is a 

 maximum. There are two of these positions perpendicular to each 

 other, in each of which the plane passes through that principal di- 

 rection which does not correspond to either the maximum or mini- 

 mum value of the normal force, and bisects the corresponding right 

 angle between the other two principal directions — those of the maxi- 

 mum and minimum normal forces. Having established the relative 

 positions of the planes of greatest normal and of greatest tangential 

 action, the author proceeds to examine how far the evidence afforded 

 by the distorted forms of organic remains may justify the conclusion 

 that these forces have had an influence in determining the position 

 of the planes of cleavage in the rocks containing those remains. 



Conceive one stratified bed placed on another, and acted on by 

 forces tending to give the upper a small sliding motion along the 

 surface of the lower one. A considerable tangential force will be 

 called into action between the beds ; and if any object be placed 

 between them, its lower part will be pushed in one direction by the 

 action of the lower bed, while its upper part will be equally pushed 

 in the opposite direction by the action of the upper bed, and thus 

 the object will be twisted from its original form. For example, sup- 

 pose the object be an equilateral shell lying between the two beds, 

 with the plane of junction of the two valves parallel to the surfaces 

 of the beds, and suppose the median line of either valve to be per- 

 pendicular to the direction in which the one bed tends to move along 

 the other. The shell in its distorted form will no longer be equila- 

 teral ; one half of each shell will be crumpled into a smaller space, 

 while the other half will be extended into greater breadth ; so that 

 if there be longitudinal folds on the valve, those on the former half 

 will be pressed together, and those on the latter will be dilated into 

 greater breadth. An exactly similar effect will be produced on both 

 shells ; but the compressed half of one will be opposite to the dilated 

 half of the other. 



Again, suppose the beds to be acted on by forces tending to com- 



