Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 21 



greatest tendency to form it, i. e. it will be nearly perpendicular to the 

 direction of that resultant. 



12. Let us now suppose P, to designate a point in the lamina, 

 at which a fissure shall begin, and P, another point through whicii it 

 shall be subsequently propagated; and let n„ n,, denote tlie cohesive 

 powers of the lamina at those points respectively, n, being the least. 

 It has been already stated, (Introd. p. 11.) that in the case to which 

 these investigations are to be applied, tiie intensity of the elevatory 

 force, and therefore, of the tensions produced by them, will be assumed 

 to increase continuously from the commencement of the action of this 

 force, to the formation of the fissures; we shall here also make an 

 additional assumption, viz., that this intensity shall increase rapidly, so 

 that a very small time shall elapse between the commencement of the 

 elevatory action, and the instant when the fissures shall begin to be 

 formed*. The tensions therefore to which our lamina is subjected, will 

 be assumed to increase in the same manner. Let Ri denote the intensity 

 of their resultant at the time t; then if t, be the time when the fissure 

 begins at P„ /?,, must be equal to the cohesive power at P, = n,. When 

 the fissure is thus begun to be formed, the partial system of tensions 

 described in Art. 9„ will be superimposed about its extremities. Let 

 <1>, denote its intensity at the time t, and at any proposed point. As 

 the fissure in its progressive formation approaches P„ this force will 

 be superimposed on the lamina there, in addition to the force Rt jjre- 

 viously acting' there, so that if t,, be the time when the fissure is first 

 formed at P, we must have at P„ the resultant of R, , and of <i>, = n,. 

 Now, if during the time t,-t^, R, increases from R,„ or ri„ so that R^ 

 nearly = n,, a>,„, must be small at P„ and therefore can have but little 

 influence on the direction of the fissure through that point, whatever 

 be the direction of that tension, or the intensity it might acquire if 

 the cohesive power at P, were sufficient to prevent the propagation of 

 the fissure beyond that point (Art. 11.) In such case therefore the direction 

 of the fissure will be at least very approximately determined by equa- 

 tion (2), p. 18, in which the values of m do not include the tension <1>, 



• This assumption is not absolutely necessary for the truth of the approximation we 

 have to establisli or for the proof of it. It renders however the approximation more ac 

 curate, and the proof much more simple. 



