Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 29 



extremity, become evanescent; but since the line is extended, thougli 

 not by a force at its extremity P, it must at every other point be 

 subjected to a certain tension, and our object will be to compare this 

 tension at any point Q with that acting in the direction EQF at 

 the same point, with the view of ascertaining within what limits 

 another fissure might be foi^med subsequently to the formation of AB, 

 and parallel to it between the lines AU and BV. Such a fissure could 

 not be formed through Q, by the tensions to which we are supposing 

 the lamina subjected, if the tension in the direction EQF at that 

 point should be greater than that in the direction PS, since the fissure 

 must necessarily be formed perpendicular to the greater of these ten-' 

 sions (Art. 6). 



24. In the first place, let us suppose a physical line of indefinitely 

 small width to be attached at its extremities to the fixed points A, B, 

 and then conceive parallel forces to act on each element of this line, 



with the same or different intensities at different points, and in direc- 

 tions perpendicular to AB. The line will thus be made to assume a 

 curvilinear form, and if the extensibility be small, as we shall suppose 

 it to be, the curvature will be small, so that if AQ = s, and a; be the 

 original length of AQ, x and s may be considered as very approximately 

 equal. Let t denote the tension at Q, p the radius of curvature, and 

 <p the intensity of the force at that point, cp being any function 

 of X. Then the force on the element ^s, will be ^ . Sa-, and the nor- 

 mal force produced by the tension t, will = - estimated by the effect 



p 



it would produce, if it acted uniformly on a unit of the line, so that 



the normal force acting on the element ^s, will = - . ^*, or — ^x very 



p p 



