﻿Vol. 64.] aUAJ^TITATIVE METHODS TO THE STUDY OF EOCKS. 221 



at all angles, but in the plane of cleavage were inclined on an 

 average at 27° to the horizontal. In the quarries in N"ant 

 Ffrancon and at Llanberis, the data, being intermediate, are not 

 good for calculation. 



Although having much in common with concretions, the spots were 

 due to the deoxidization of the peroxide of iron. They are really 

 ellipsoids ; but, since the calculations require the ratios of the axes 

 in particular planes, we need not consider the third dimension. 



In studying the rocks in situ, it was easy to see that the axis of 

 the original spots was longest in the plane of stratification ; and 

 the question to be first considered is, what was the exact ratio of 

 the axes ? It was assumed, in the first place, that in the plane 

 perpendicular to the cleavage, when the rock was compressed, the 

 sectional area of the spot remained the same ; so that, for example, 

 if the axis in the line of the pressure was reduced to one-half, that 

 at right-angles was increased to double. If then the longest axis of 

 the spot was inclined at all angles to the cleavage, the maximum 

 value of the ratio between the longest and the shortest axis must be 

 when the stratification was nearly in the plane of cleavage, and the 

 smallest ratio when it was nearly perpendicular to the cleavage. It 

 can thus be easily shown that the ratio of the shortest axis of the 

 original spot, compared with its longest, was the square root of the 

 smallest ratio after cleavage was developed, divided by the largest. 

 In the quarry at Bethesda, perpendicular to the cleavage, the smallest 



ratio is 1 : 4 and the largest 1 : 10. Hence we have a/ 1-= -632, 



that is the axes of the original spots were 63:100:100. In the 

 quarry at Penrhyn the extreme ratios are 1:4-78 and 1:11*96, 



which give \/i^^. = -632, or the same as Bethesda. However, 

 the probability is, that in both cases the result is somewhat too 

 large. Combining the measurements made at both quarries, and 

 taking the means of the maxima and minima, we get 3*66 and 



10*37; and therefore ^y ^^ = '597. Consequently, I conclude 

 that the axes of the original spots were about 60 : 100 : 100. In the 

 quarry at Bethesda, in the plane of cleavage we get y^^l|^=*645, 



whereas at Penrhyn we have -y/^?J=*836. These last two results 



agree with what would be expected from the manner in which the 

 axes of the original spots were inclined to the cleavage. At all 

 events, it seems reasonable in further calculations to adopt the 

 conclusion that, before cleavage was developed, the axes of the 

 spots were about 60:100:100. 



The next thing to consider is, what change was produced by the 

 compression of the rocks. For the quarry at Bethesda, the mean 

 ratios of all my observations are, in the plane of cleavage 1:2-01, 

 and perpendicular to the cleavage 1 : 7*10 ; and for the quarry at 

 Penrhyn, 1:1*60 and 1:6*99. The great discrepancy between the 

 results in the plane of cleavage is mainly due to the fact, that at 



