38 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



posed to vary continuously or discontinuously along any vertical line, 

 and, as explained in Art. 8, it may vary according to any continuous 

 law in any horizontal lamina of the mass. The same assumptions are 

 made respecting the continuous but rapid increase of the tensions, as in 

 Art. 12. 



I. If this mass be acted on by a single system of horizontal 

 parallel tensions, a fissure beginning at any point Avill be propagated 

 in a vertical plane perpendicular to the direction of the system. 

 (Art. 2). 



II. If the mass be subjected to any number of systems of parallel 

 tensions, the fissure will be propagated through any point in a direc- 

 tion perpendicular to the maximum resultant tension at that point, at 

 the instant the fissure reaches it, (Art. 12.) the horizontal direction 

 being determined by equation (2), (Art. 7). If the ratios of the ten- 

 sions at each point at the instant of propagation through it be the 

 same, the fissure will, in general, be formed in one vertical plane. 

 (Art. 14.) 



III. If there be only two systems of horizontal tensions, and these 

 be perpendicular to each other, the fissure will lie in one vertical 

 plane perpendicular to the direction of the system of the greatest in- 

 tensity, whatever be the ratio of the tensions at each point in the 

 two systems, provided the tension at each point always remain the 

 greatest in the same system. (Arts. 6, 14.) 



IV. Each fissure under the conditions assumed, will be propagated 

 with extreme velocity. (Art. 13.) 



V. The tendency of the tensions to propagate the fissure in one 

 particular direction rather than in any other, or the permanence of the 

 permanent direction of cleavage, depends on the rapidity with which 

 the magnitude of the resultant tension, estimated in a particular direc- 

 tion, decreases as that direction deviates from that of the maximum 

 resultant tension ; or generally, on the ratio which the maximum bears 

 to the minimum resultant tension, which is perpendicular to it. (Art. 18.) 



