48 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



mp being parallel to DC. Consequently, the distance of the physical 

 point p from the axis of the cone, will not be altered by the elevation ; 

 and since the same holds for every physical point in the circumference 

 of the horizontal circle whose radius is pn, there can be no tension at 

 any point of the physical line forming that circumference, in the di- 

 rection of its tangent at that point. This is consistent with_our as- 

 sumption of the equable extension of every part of the line A'C, which 

 will therefore be true*. Similarly, if we conceive the whole mass 

 AA'B'B to be formed by the superposition of similar conical sliells, 

 it is easily seen that the same result will hold for every horizontal 

 circle concentric about the axis of the cone. Hence it follows, that if 

 any vertical plane be drawn through the axis of the cone, there will be 

 no tension at any point of the mass in this plane in a direction per- 

 pendicular to it. The tension will be entirely in the plane, and parallel 

 to the slant side of the cone. 



If, then, a fissure which should pass through any proposed point 

 P, were formed according to the greatest tendency of the tensions of 

 the luibroken mass to form it, it would manifestly coincide with the 

 surface of an inverted cone, whose base would be the circle of which 

 the radius is pn, and whose axis would coincide with that of the 

 elevated cone. If j} should coincide with C, an orifice Avould be formed 

 along the axis C'C; and if we consider that the force will act, ac- 

 cording to our hypothesis, with the greatest intensity at C, it seems 

 highly probable that the first dislocation will usually take place along, 

 or very near to that axis. For the greater distinctness, suppose this 

 to be the case. 



47. The instant this has occurred, the conditions of the problem 

 will be entirely altered. The force at C maintaining every such line 

 as A'C and B'C in its state of tension, being now destroyed, the 



* Suppose a tension T to exist along the physical line forming the circumference of the 



T . 



circle whose radius is pn. This would produce a force — acting at p in the direction pn, 



the resolved part of which in the direction pC would increase the tension of A' p. In such 

 case the extension of A'C would be greatest at A', and our assumption of the uniform extension 

 of that line would not be true. 



