﻿182' DE, H. C. SOEBT ON THE APPLICATIOlf OF [May I908, 



is taking place from above ; and it is necessary to enter somewhat 

 fully into detail, in order to show the data from which conclusions 

 may be drawn. 



It is convenient, in the first place, to consider the case when no 

 deposit is being formed from the superjacent water, material being 

 merely drifted along the bottom. Also, for the sake of simplicity, 

 we may assume that the sand consists of grains having an average 

 diameter of about a hundredth of an inch, and that the length of 

 the ripples is about 3^ inches, which I find is a common size in 

 many rocks. 1 shall also consider only their length and height, 

 since the third dimension may be looked upon as uniform and as 

 having no influence on the ratios under discussion. 



Ey very carefully studying some excellent ripples on the shore 

 at Ryde and Sandown, I found that, although their average length 

 varied from 1*3 to 12 inches, their shape was almost identical, the 

 exposed side being inclined at about 18° and the sheltered at about 

 30°. Hence, for ripples 3| inches long, the height would be '72 

 inch, which corresponds to what is seen in older rocks. However, 

 for a reason which I do not fully understand, some ripples 3| 

 inches long are only about '36 inch high, ai]d the slopes are in- 

 clined at 9^ and 19°. Those formed in my experiments at Wood- 

 bourne seem to have been of this character, and I found that with 

 a current of about 1 foot per second they advanced 3 inches per 

 minute. So far as I can judge, their length was about 4 inches, 

 which would give a minute and a third as the time in which they 

 would advance their own length, which I call their period. It 

 seems very probable that this period would be nearly the same for 

 ripples varying considerably in length, since the exposed surface 

 from which the sand is washed up would vary directly as the length 

 of the ripples, and we may, therefore, assume that the period of 

 ripples 3| inches long would be 1*33 minute. The question then 

 is, what would be the period for those that are -72 inch high? 

 The amount of material to be drifted forward in their period 

 would be J^=2, and there is no reason to believe that it would 

 be drifted along more quickly. On the contrary, it would have 

 to be washed up a slope of 18° instead of 9°; and, adding the 

 angle of rest when such sand gives way for the efiect of the small 

 depression, the extra inclination is 54° instead of 45° and the extra 



force required ^-!"^ ^j° = 1*14. Hence, probably the period for 

 sinG tO 



ripples -72 inch high would be l-33x2x 1*14 = 3 minutes; but 



this must be looked upon as merely an approximation, which needs 



confirmation by experiment on a larger scale. It must also be 



remembered that all my calculations refer to sand of medium 



coarseness, with grains about a hundredth of an inch in diameter. 



The tables given in this paper supply the data for calculating the 



results for coarser or finer sand. 



