28 Mr. H. C. Sorby on Slaty Cleavage, 



According to these principles, if we suppose that in a mass of 

 rock there were 600 particles having their longer axes lying iu 

 the space included within 5° on each side of positions inclined at 

 0°, 10°, 20^, &c. to the line of pressure, so that they were uni- 

 formly distributed, as is nearly the case in thick-bedded, un- 

 cleaved rocks, then, after compression so that the ratio was 1 : 6, 

 their distribution would be changed, as shown in the following 

 Table :— 



90 600 3324 



It will thus be seen that the effect is to produce a great dimi- 

 nution in the quantity that are inclined in the direction of the 

 pressure, and a great increase in those nearly perpendicular to 

 it, and thus to cause a very great preponderance nearly in the 

 plane perpendicular to the pressure. In fact, as will be seen, 

 in a space of 10°, there, we have thirty-three times as many 

 as in an equal one in the line of pressure ; and if very small 

 spaces were taken, since the ratio between the arc and tan- 

 gent of a very small angle is one of equality, in the exact direc- 

 tion of the pressure, the number of particles whose axes lay in 

 that line would be spread over six times the space, whilst per- 

 pendicular to it they would be condensed into one-sixth, and 

 hence the relative amounts in those two positions would be as 

 1^ ; 6^ = 1 : 36. If, then, the amount of the unsymmetrical frag- 

 ments was very great compared with the rest of the rock, and if their 

 strength was such that to break them was very much more diffi- 

 cult than to split along them without breaking them, the resist- 

 ance to fracture in the two directions would be as 1 : 36 j or in 

 other words, the facility of cleavage in the plane perpendicular 

 to the pressure would be far greater than in one inclined at any 

 considerable angle to it. Of course for other changes of dimen- 

 sions the same results would apply. For instance, if it was 1 : 3, 

 the relative strength would be 1 : 9, and similarly for other values. 



In order to confirm these results by experiment, as mentioned 



