﻿Vol. 64.] QUANTITATIVE METHODS TO THE STUDY OP ROCKS. 175 



in proportion as the particles are smaller. Thus, if the thickness 

 be the same for 0*1 as for 0*001 inch in diameter, 1 calculate 

 that the relative effect would be 450 times as great in the latter 

 case. This must have a most important influence in modifying 

 the deposition of coarse and fine-grained material ; and it seems to 

 me that all the facts that I have described are of fundamental 

 importance in studying stratified rocks, and well deserve a much 

 more complete investigation. 



Thus, for example, the above-described facts show that the 

 different amount of sinking of the small pebble causes the frictioil 

 to be 57 per cent, more in the case of very fine sand than in that of 

 coarse. On the contrary, a current of water would have much less 

 power, since only half its surface would be exposed. It would thus 

 be almost impossible for a small pebble to occur in fine sand, since 

 a current much less than sufficient to drift along the pebble would 

 wash away the sand ; whereas, in the case of the coarse Millstone- 

 Grit sand, the pebble would be washed along much more easily, 

 and the sand washed away with much more difficulty, so that it is 

 easy to understand why pebbles are so common in such rocks as 

 the Millstone Grit, and absent in the finer-grained sandstones of 

 the Coal-Measures. The common occurrence of, as it were, a bed 

 of small pebbles at the lower part of many beds of drifted sand is 

 also easily explained, since on arriving at the top of the slope 

 at the angle of rest of the coarse sand, the great majority of the 

 pebbles would roll down to the bottom and only a few stick higher 

 up in the sand. In a similar manner, these facts would probably 

 explain many other details of structure which have attracted little 

 attention. 



Possible Explanation of the Angles of Rest of 

 Different Sands. 



As will be shown in the sequel, when sand is deposited and well 

 shaken, the grains arrange themselves on an average so that the 

 percentage of interspaces is the same as that deduced theoretically 

 for such an arrangement as would give rise to depressions bounded 

 by a mean slope of 30°, up which a grain would have to be raised ta 

 be carried away. If a general surface of such a kind were inclined 

 at an angle of 30°, the above-mentioned small slope would be level : 

 therefore the grain would not require any lifting, and the only 

 force to be overcome to let it go free would be that required to start 

 motion and overcome friction. Taking all the facts into considera- 

 tion, it appears to me that the most probable supposition is that, 

 when the slope is such that the grain slips off and slides down, the 

 force of gravitation acting at that angle is just in excess of that 

 which kept it in position, and that this force varies as the sine of 

 the angle of the slope. Part of this is balanced by the conditions, 

 and the rest by friction. If these suppositions are correct, it follows 

 that the variation in the angle of rest for different kinds of sand 



Q.J. G. S. No. 254. n 



