346 REPORT — 1844. 



Let us study the manner in which wave motion is originally communicated 

 to and through each of these elementary columns of fluid. 



For this purpose it may be well to recur to the original mode of wave ge- 

 nesis (Plate XL VII. fig. 5.). A vertical generating plane P is inserted in the 

 fluid, and forms one of the vertical boundaries of one of the elementary water 



columns. ^^ ^^ ^^ ^^^ f^ ^g ^^J &c. A moving force is applied 



to P, and the plane communicates to the water column n that pressure ; now 

 this water column is bounded on its anterior surface by a similar vertical plane 

 (of water particles) ^ in a state of rest, and the effect of this pressure is two- 

 fold, to raise the water column above the level to the height due to the velo- 

 city of P, and to diminish the breadth of the column in proportion to the in- 

 crease of length. Such is the immediate effiect of pressure on the plane P. 



Let us now consider the second (water) plane o ; it has now behind it a co- 

 lumn of water pressing it forward with a velocity due to its height above the 

 level of repose : it is therefore pressed forward, a, tergo, just as the plane 

 P originally was pressed forward, only its moving force is measured by the 



pressure of the column q with a given height above the plane of repose. In 

 all respects the water column n is now in the condition which in the pre- 

 vious moment wc found the column n. Let us now return to n which is 



ap ap 



pressed by the plane P with a pressure not only equal to that which raised it 

 to its former height, but with an accelerating force which raises it still higher, 

 and communicates to it a velocity due to that greater height, and also dimi- 

 nishes its breadth in proportion to the increment in height. This new height 



in the column ■, is a new increment of pressure on the vertical water plane 



oj which in its turn presses the water column n in the same manner, with a 



pressure due to the new height of the water column n, raises its height to that 

 due to this pressure, and gives it a corresponding velocity. The third water 

 column J is now in similar circumstances to those of its predecessor ^ at 



the preceding instant of time, and is pressed by the plane with a force due 



to the height of ^ , and the plane now moves forward, raises the height of 



cd 



^, and diminishes proportionally its breadth. The same process continues 



during the acceleration of the original plane P until it ceases to be further 

 accelerated, and now the whole anterior half of the wave has been generated, 



and the column n is moving with the velocity due to its elevation above the 



level, or the height due to the crest of the wave, having passed successively 

 through each of the successive conditions of the colunuis before it. The 

 force acting on P, a ttryo, is now to be diminished ; the pi'essure back upon 



