116 Mr W. Hopkins on the Internal Pressure 



pal directions, and are at right angles to each other ; the cor- 

 responding pressures are called principal pressures. In these 

 particular 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 certain positions of the plane, these 

 forces assume their maximum or minimum values. The nor- 

 mal action is a maximum, when a perpendicular 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 mini- 

 mum 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 tan- 

 gential 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 direction which does not 

 correspond to either the maximum or minimum value of the 

 normal force, and bisects the corresponding right angle be- 

 tween 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 or- 

 ganic 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 tangen- 

 tial 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 direc- 

 tion by the action of the upper bed, and thus the object will 

 be twisted from its original form. For example, suppose 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 



