Mb. HOPKINS, ON THE TRANSPORT OF ERRATIC BLOCKS. 



233 



19. It will be observed in the expressions above given that the lines denoted by a vary, in 

 every case, as v^, and consequently the weight of the mass in each case, which varies as a', varies as 

 v^. Therefore the moving force of a current estimated by the volume or weight of the mass of any 

 proposed form which it is just capable of moving, varies as the sixth power of the velocity. 

 This proposition may be easily proved independently of induction from particular cases. 

 Let a denote the length of any parameter in a proposed body of given form. Then, when « is 

 given, the force {F) of the current, estimated as above, varies as the surface of the body, varies as a'; 

 and when the surface is given, the force varies as «'. Therefore 



F oc a'«^ 

 and the moment of F to make the body roll 



cc a^v^ 



= Ca^v- (C = constant). 

 Also, the weight of the body x «', and its moment tending to keep the body at rest 



= C'a'. 

 Hence, when the body is on the point of moving, we must have 



Ca'v^ = C'a\ 



C , 

 .•. a = — ; V , 



c 



x v", 



and the weight oc o'* oc u° ; which proves the proposition. 



This result shews how excessively erroneous an opinion we might form of the transporting power 

 of rapid currents from that of the ordinary currents subjected to our observation. Thus if a stream 

 of 10 miles an hour would just move a block of a certain form of 5 tons weight, a current of 

 15 miles an hour would move a block of similar form of upwards of 55 tons; and a current of 20 

 miles an hour would, according to the same law, move a block of 320 tons. 



Again, according to the same law, a current of two miles an hour would move a pebble of 

 similar form of only a few ounces in weight. And here it should also be remarked, that minute 

 inequalities, or a want of perfect hardness in the bed of a current, which would produce little effect on 

 the motion of a large block, would entirely destroy that of a small pebble; so that the circumstance 

 of the transporting power of a stream of 2 or 3 miles an hour being inappreciable is perfectly 

 consistent with the enormous power of rapid currents. 



20. Let us now investigate the space through which a block might be conveyed by the current 

 attending a single wave of elevation. 



Let y be the velocity with which the wave is propagated. 



r, the greatest velocity of the current, or its velocity in the transverse section through the crest 

 or highest point of the wave, which will be very near the front of the wave, assuming it to have the 

 character of a lore, as will necessarily be the case if the elevation producing it be paroxismal. 



V the velocity of the current in any other section of the wave; 



«, the velocity of a current just sufficient to move the block. 



