﻿Vol. 64.] QUANTITATITE METHODS TO THE STUDY OF ROCKS. 179 



Millstone Grit. 



For some miles north and south on the west side of Sheffield, 

 the Millstone Grit contains many excellent examples of charac- 

 teristic drift-bedding. At one time, it was puzzling to find that the 

 mean angle of the inclined beds in a quarry at Bell Hag, where the 

 sand-grains measure on an average -01 inch in diameter, is only 

 about 25°, since the angle of rest for such sand is 34°. However, 

 on further study it was found that this reduction in the angle agrees 

 with what would be the effect of the alterations that have taken 

 place in the rock. Pebbles of felspar are common, and on close 

 examination it was seen that what was originally felspar-sand has 

 been decomposed, and the resulting clay forced into the interspaces 

 between the grains of quartz. In the case of such sand when 

 recently deposited and not shaken, the interspaces amount to about 

 46 per cent., whereas they are now only 15 per cent., thus showing 

 a contraction of 36 per cent, of the original volume. The tangent 

 of the original angle is -674, and therefore that of the altered rock 

 should be 64 per cent, of this, which nearly agrees with the tangent 

 of 25°, as seen in the rock. Hence, both the change in the angle 

 and that in the amount of interspaces agree in showing that the 

 thickness of the rock is about two-thirds of the original. As 

 indicated by the angle of rest, the average contraction for all the 

 above-described rocks is from 100 to 59, which is a very con- 

 siderable change. 



Drifting on a Horizontal Surface. 



According to Du Buat ('Traite d'Hydraulique'), the velocity of a 

 current near the bottom is about half the mean velocity of the whole 

 depth. Possibly, however, that of the water in contact with the 

 sand is still less. My experiments and observations showed that, in 

 shallow water, the mean velocity of the current just able to wash up 

 sand measuring about a hundredth of an inch in diameter is about 

 •4 foot per second. Before being moved, the surface would be very 

 similar to that of sand inclined at the angle of rest, and it seems 

 probable that, as in that case, the force necessary to lift the sand 

 out of the depressions against gravity and overcome friction, so as 

 to move it forward, must be nearly as the sine of the angle of 

 rest, which in this case is -59. The final velocity of such sand is 

 •106 foot per second, so that the calculated velocity of a current 

 just able to move the sand would be -59 X '106 ='063 feet per 

 second, which is not quite a sixth of the observed mean velocity, 

 or about a third of that near the bottom according to Du Buat. 

 This lower velocity is, however, that in actual contact with the 

 sand, which must certainly be considerably less than higher up. 

 On the whole, considering all the circumstances, we may conclude 

 provisionally that the velocity in contact with the sand is about 

 a sixth of the mean velocity, although this might not be correct 

 in the case of deep water. 



