234 



TRANSPORTING POWER OF WATER. 



But when the current is just able to move the rock, we 

 have 



P oc W. (3) 



Therefore, from (1), (2), and (3), 

 d? a v 3 x d? ; 

 /. d a y 2 , 



which in (1) gives P oc v 8 x v*, 

 or P <x v 6 . (4) 



That is, the transporting power of a current varies 

 as the sixth power of the velocity, 



This may also be shown geometrically as follows : Let a 

 represent a cubic inch of stone, which a current of given 

 velocity will just move, and let b be a cube 

 of stone 64 times as large. Now if the 

 velocity of the current be doubled, the 

 force against each square inch of b will be 

 four times as great as that against a ; but 

 the surface of b opposed to the current is 

 sixteen times as great as that of a, and the 

 pressure would be increased sixteen times 

 from this cause ; therefore the whole press- 

 ure against b from these two causes would 

 be 4 x 16 = 64 times as great as against a. 

 But the weight also of b is 64 times as great as that of a ; 

 therefore the current would be just able to move it. 



We have seen (Art. 124) that a current 3 feet per second, 

 or about two miles an hour, will move pebbles an inch in 

 diameter, or about three ounces in weight. It follows from 

 the above law that a current of ten miles an hour will bear 

 fragments of H tons, and a torrent of 20 miles an hour will 

 curry fragments of 100 tons in weight* 



Fig. 65 



Le Conte'a Geology, p. 18, 



