22 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



but only the values F, y„ ,/!, &e. of the general tensions, at the 

 instant when the fissure is propagated through the proposed point*. 



13. Under the circumstances here supposed, the fissure will be pro- 

 pagated from P, to Po, nearly in tlie time t^^ — t,, during which ^i increases 

 from n, to ris. Consequently, if the difference between these latter 

 quantities be not great, t. e. if the cohesive power do not vary rapidly ; 

 or if Rt (heretofore assumed to be the same at the same time at difiTerent 

 points of the lamina) increase with rapidity, it follows that the velocity 

 of propagation will be extremely great, becoming infinite, when the 

 cohesive power, and the tension R, are accurately uniform throughout 

 the lamina. 



If Ri be not uniform, it is easy to see that reasoning similar to the 

 above will hold equally true, with respect to the progressive formation 

 of any fissure. 



14. The fissure will be propagated in a straight line, if the values 

 of y. in equation (2) remain the same, /. e. if the ratios of the tensions 

 at different points be the same at the instant the fissure is propagated 

 through them. If these ratios be different for different points, the 

 fissure will generally be curvilinear; there is, however, an important 

 exception to this rule, when there are only two systems of tension, of 

 which the directions are perpendicular to each other ; for in this case 

 it appears by Art. 6, that the direction of the fissure will always be 

 perpendicular to that of the greater of these two tensions. 



Effect of Lines of Less Resistance on the Direction of a Fissure. 

 Permanent Direction of Cleavage. 



1.5. In the preceding articles, we have supposed the cohesive power 

 of the lamina to vary according to some continuous law. Let us now 



* When the cohesive power of the lamina is not sufficient to prevent the propagation 

 of the fissure, the problem presented to us is no longer a statical one. In the case above 

 considered, a small portion only of the extraneous forces producing the tension <I>, is 

 effective in causing an additional tension of the lamina before the formation of the fissure. 

 The greater part is effective in communicating motion to those parts of the mass, the re- 

 ceding of which from each other causes the opening of the fissure. On the contrary, when 

 the formation of the fissure is arrested, the whole of these forces is effective in producing 

 this partial system of tensions. 



