Mk. HOPKINS, ON THE TRANSPORT OF ERRATIC BLOCKS. 



221 



SECTION I. 



Transporting Currents. 



1. These currents may be divided into River Ctirrents, Tidal Currents, Ocean Currents, 

 and Elevation Currents. By the latter, I mean those currents which would be produced by the 

 more or less sudden elevations of determinate portions of that part of the surface of the earth 

 which is covered with water. They are the only currents among those above mentioned of which 

 it will here be necessary for me to speak. Currents of this kind are always accompanied by a 

 corresponding temporary elevation of the surface of the water, constituting a wave. We are 

 indebted to Mr. Russell for all the experimental knowledge we possess of the nature and properties 

 of this wave, of the laws of its motion, and of the current which attends it. He has denominated 

 it the great wave of translation. The details of his experiments will be found in the Proceedings 

 of the British Associatioti. It will only be necessary for me here to state his general results. 



2. Suppose a long canal to be filled with water, and, for the greater simplicity, let it be sup- 

 posed to be of uniform width and depth. There are various ways in which a wave of translation 

 might be produced in this canal. One of the simplest, and most appropriate for our immediate 

 object, would be the sudden elevation of a determinate portion of the bottom of the canal, which 

 portion, for distinctness, may be conceived to be about its middle point, and of small extent as 

 compared with the length of the canal. Two waves will thus be sent off in opposite directions. 

 Each wave will move with uniform velocity, preserving very approximately the same form. Its 

 length will depend, in great measure, on that of the portion of the bottom elevated to produce the 

 wave. Each particle of water begins to move when the front of the wave reaches the vertical 

 transverse section in which the particle is situated, and continues in motion till the wave has passed 

 over it, when it is again left at rest. Its motion therefore is not oscillatory, but one of translation 

 in the direction of the wave's motion. Mr. Russell has established experimentally the following 

 law of this motion : 



(1) Every particle in the same vertical transverse sectio?i of the canal has the same motion. 

 He has also established the following law respecting the propagation of the wave : 



(2) The velocity with which the wave is propagated is equal to that due to half the height of 

 the crest or highest point of the wave above the bottom of the canal*. 



3. From these laws we easily deduce the expression for the velocity of each particle, i.e. for the 

 velocity of the current which accompanies the wave. Let LPN represent the position of a 

 longitudinal section of the wave, at the time t, and VPN" at the time t + Zt, AB being the bottom 



Pi 



of tlie channel, and CFD the level of the general surface of the water. Let P, be the crest of 

 the wave, QP, = /(,; /» any other point on the surface of the wave at time t, P' the corresponding 



• It thould be stated tli.it the cxpcrimenlH and observalionii by 

 which tliese laws were catutilished, were made on canals not many 

 feci in depth. There appeun, however, to be no reasonable doubt 



that the same laws hold, at least approximately, tor much greater 

 depth, as I have assumed them to do in the application of these 

 iovcBtigations to the transport of erratic blocks. 



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