﻿176 DE. H. C. SORBT OX THE APPLICATION OF [May I908, 



depends mainly on these latter retarding conditions. Assuming 

 that the sine of the angle of rest is a measure of all the forces just 

 balanced, we may calculate as follows. For grains of -05 inch in 

 diameter the sine is '755, and for "01 it is 'oSS. Hence for each 

 •01 above '01 the value of the sine increases about -042. Sub- 

 tracting this from '588 we get '546, which is the sine of 33-6°, or 

 closely that of the angle of rest for grains '003 in diameter. The 

 excess over 30° may be due to the force necessary to start movement, 

 or to the somewhat different arrangement of the surface-grains from 

 that assumed. These facts seem to show that the above-named 

 resistance is of little value where the grains are small, but increases 

 nearly as the diameter of larger grains. At all events, these suppo- 

 sitions explain the variations in the angle of rest sufficiently well 

 for the purposes of this paper. 



Relation between the Angle of Rest and the 

 Velocity of a Current. 



I trust that it will not be thought that I am making mountains 

 of molehills, when I discuss in detail the properties of grains of 

 sand ; but it must be borne in mind that the very existence of some 

 mountains must have depended on the properties of their constituent 

 grains. As described above, the most probable angle of the slope 

 of the minute depressions on the surface of sand is about 30°, up 

 which a grain would have to be lifted before it would be washed 

 along by a current. In addition to this, there would be friction to 

 be overcome, so that the effective angle may be about 33°. 



It seems to me, therefore, that these conditions are so closely the 

 same as in the case of the angle of rest, that the sine of this angle 

 may be looked upon provisionally as a measure of the resistance that 

 must be overcome by a current just able to drift along the sand. At 

 all events, this seems to give satisfactory results, when we compare 

 one variety of sand with another. 



lY. The Efeects of CuEEEiirTs. 



Velocity of Current Able to Start or Maintain Drifting. 



As in the case of the friction of one surface on another, there is 

 a difiPerence between the current necessary to start the motion of 

 sand and that which is necessary to maintain it. This is well seen 

 in the case of the angle of rest — since the angle at which sand slips 

 down after having been at rest, and that at which moving sand is 

 brought to rest, differ materially. Very important results depend 

 on this property. We may, I think, provisionally calculate the 

 velocities of current required to start and maintain the drifting of 

 different varieties of sand from these angles, as measured in each 

 case. It is, however, important to bear in mind that drifting on a 

 rippled surface is not the same as on one without ripples. 



