18 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



or %^ ^^ a — 1 = ; 



.-. cot-1^-2 .-^- — ■ „,j cot.x^- =0 (2). 



The same remarks will apply to this equation as to equation (1). 



Hence, then, when the directions of the different tensions tt> 

 which a lamina is subjected, and the ratios of their intensities, are 

 known, this equation will determine that position of the line AJB 

 passing through any proposed point P, in the direction of which there 

 is the maximum or minimum tendency to cause a fissure to beghi at 

 that point. If /3 be less than a right angle, it is manifest by inspec- 

 tion that the negative root will correspond to the former, and the 

 positive root to the latter case. 



8. The actual direction in which the fissure will begin to be formed 

 at P, may, however, be different from that in which the tensions have 

 the greatest tendency to form it; for if there be any particular line 

 through that point, along which the cohesive power of the lamina is 

 less than in any other, the fissure may begin to be formed in that 

 direction, though it may not coincide with that of the maximum re- 

 sultant tension. If however the cohesive power at the proposed point 

 be equal in every direction, /. e. if it vary continuously in passing from 

 one point to another, and not suddenly as at a line of less resistance, 

 the direction in which the fissure wQl begin to be formed, will coin- 

 cide with that of the maximum resultant tension determined by equa- 

 tion (2). This observation respecting the constitution of the mass to 

 which the investigations of the previous articles are applicable, is im- 

 portant. T/ie cohesive power may vary according to any continuous law, 

 as was before stated. (Introd. p. 11). 



Direction in which the Fissure will be continued. — Partial System of 

 Tensions imposed on the Lamina about the extremities of the Fissure. — 

 Direction of the Fissure not affected by it in the case proposed. 



9. In the preceding investigations the tensions have not been con- 

 sidered necessarily sufficient to produce a fissure. Let us now suppose 



