1860.] On the Translation of Waves of Water. 269 



to move directly upwards. At C. it will be carried forwards with the 

 wave: — At D. it will h ave no horizontal motion, but will be carried 

 downwards to the same extent it was moved upwards at B. and at E., 

 it will be again carried backwards : — at which point the whole wave 

 having passed, it will hold the same actual position which it did at 

 A., the vertical and horizontal displacements having exactly balanced 

 each other. * It is scarcely needful to remark that there is no sudden 

 alteration from the horizontal to the vertical motions, and vice versa, 

 but that at each intermedíate position the motion is a compound one, 

 forming a gradual curve : — these fixed points having been only 

 selected for convenient illustration. All the partióles below the 

 surface pursue the same course as those above them ; i. e. — all those 

 below the crest of the wave move forwards ; and all those below the 

 hollow move backwards, but where the water is deep the motion 

 low down becomes imperceptible, and where it is shaliow it is practi- 

 cally the same as at the surface. 



12. The motion of a wave therefore, being simply the translation 

 of a shape, is unaffected by any current which may be running in the 

 stream on which it is generated. According to the direction of its 

 original Ímpetus it may travel with a current, at right angles to it, or 

 even directly against it ; and either up hill or down hill ; without its 

 speed or rate of transit being materially affected thereby. I say 

 materially, for a current does, to a certain extent, modify the condi- 

 tions of a wave, and I have reason therefore to think that it may 

 also aífect its speed, but that this eífect, if there be any, is very slight, 

 may be easily demonstrated. 



The Hooghly, like all other rivers, must be considered as a stream of 

 fresh water running towards the sea, into which is poured, once every 

 twelve hours, a large wave. As the crest of this wave is approaching 

 or passing a given spot within the river, the particles of -which it is 

 temporarily composed are flowing upwards, or it is technically termed 

 flood tide. It is evident that the upward speed of the particles is 

 checked by the constant resistance of the river stream, and that in 

 like manner when the crest of the wave has passed, and the parti- 

 cles receding in the hollow, they are aided in their backward course, 

 by the velocity of the river stream. 



13. The river stream is therefore a constant — plus to the ebb, 

 and minus to the flood. 



