﻿Vol. 64.] QUANTITATIVE MBTHvODS TO THE STUDY OF ROCKS. 187 



unable to wash sand any farther, the sand being therefore thrown 

 down at the angle of rest, forming a bed the thickness of which 

 corresponds to the increased depth. I^umerous examples of this 

 structure, on a small scale, may be seen on sandy roads after 

 rain. The thickness of the bed {t) does not bear a constant 

 relation to the depth of the water, either before or after depo- 

 sition. It may be abnormally small, when the reduction in the 

 velocity of the current merely causes the sand to be thrown down 

 at a less angle than the normal angle of rest, owing to the 

 current sweeping down the face of the slope, and causing the 

 stratula to be S-shaped, curved at the top and bottom. On the 

 contrary, the increase in depth may be indefinitely great, so as 

 to give rise to a thick bed at the true angle of rest, perhaps 

 modified at the bottom by a talus due to the giving way of the 

 deposit, caused by breaking waves or other disturbances. Between 

 these two extremes is what may be called a normally thick bed, 

 where the increase in depth and the diminution of the current are 

 just sufficient to allow of the sand accumulating at the true angle 

 of rest, in a bed the thickness of which bears a definite relation to 

 the depth of the water and the character of the sand, so that the 

 depth may be determined. 



Judging from the Millstone Grit near Sheffield, when the thick- 

 ness of the bed (t) and the angle of the stratula (a) are abnormally 



small, -. — = -: — , and therefore in each case we may calculate 

 sm a sin a *' 



the value t. Considering the independent evidence of great variation 



in depth, this yields reasonable conclusions, and assists in giving 



the true value of t. 



In studying particular rocks, allowance must be made for the 

 contraction which has occurred since deposition. What should be 

 learned in each case is the smallest thickness of the beds when the 

 angle of rest is just true. This may vary considerably in different 

 parts of the same rock, since the depth has often been reduced by 

 as much as 20 feet by one continuous drift, over a flat bottom of 

 considerable area, leaving the water so much more shallow. In 

 varying currents in shallow water, there is often much confusion 

 and much that may be called false bedding, from which little 

 can be learned by calculation. 



Having then determined, in a more or less satisfactory manner, 

 the normal thickness in one or more particular cases, the question 

 remains, what was the actual depth of the water before and after 

 deposition? Experiments are wanted on a fairly-large scale, with 

 plenty of water under complete control, in order to ascertain the 

 general facts. In the absence of these, it is necessary to fall back 

 on what I learned in another manner. I found that sand of the 

 average diameter of a hundredth of an inch is drifted along with a 

 current of 1 foot per second, and, if it arrives where the depth is 

 twice as deep, so that the velocity is reduced to 6 inches per second, 

 it is thrown down and accumulated at the true angle of rest. Both 

 these limits are doubtless subject to variation, according to circum- 



