Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 13 



SECTION I. 



1. The simplest form of tlie mass in which we have to consider 

 the formation of fissures, is obviously that of a thin lamina. The in- 

 vestigations therefore of this section will be applied directly to this 

 case, from which the results applicable to a mass of three dimensions 

 are immediately deducible. It will appear that its cohesive power may 

 vary according to any continuous law. 



§. Lamina subjected to one System of Tensions. 



2. Suppose the lamina acted on by external forces, which shall 

 place it in a state of tension, such that the direction of the tension at 

 every point shall be parallel to a given line CD*. Let AJi be any 



proposed line in the lamina ; P any point in this line. Also assume 

 F to be the tension at P, estimated by the force which the tension at 

 that point would produce, if it acted uniformly on a line of which the 

 length should be unity, and which should be perpendicular to CD. the 

 common direction of the forces of tension. Then if we take Pp a small 

 and given element of the line AB, and draw P^ parallel to CD, and 

 pm perpendicular to P^, the force of tension on Pp in the direction 

 PQ will be measured by P .pm, or F.Pp.%\x\\\/ {BPQ, = \\i)\ or the 



* The reference will always be made to the figure in the same page, unless stated to 

 the contrary. 



