ON WAVES. 323 



p k are equal, and a given volume of water has effectively descendecl from 

 PGw into Kkp, and g^ and gc, being the centres of gravity; the quantity 

 of power developed is measured by the descent of the weight of water through 

 a height ^, g^, or through half the depth of the generating reservoir, and is 

 of course capable of generating in any equal mass of fluid a velocity equal 

 to that which is acquired by falling through a space equal to one-half the 

 depth, reckoned from the top of the generating column to the bottom of the 

 channel. 



Imperfect Genesis of the Wave. — The wave may be said to have imperfect 

 genesis, as far as the purposes of accurate experiment are concerned, when it 

 is accompanied by other wave pheenomena Avhich interfere with it. The pre- 

 cautions necessary to perfect genesis appear to be these, that the volume of 

 water should not widely differ from the volume of the wave it is proposed to 

 generate, and that the height of the water should not greatly differ from that 

 of the wave ; and even these precautions are scarcely sufficient for the gene- 

 ration of a perfect solitary Avave in a case where it is extremely high. The 

 reason is obvious. 



Residuary Positive Wave. — In a case of genesis Avhere the precautions 

 mentioned above are not observed, the following phaenomenon is exhibited. 

 If, as in the case fig. 6, the volume of the generating fluid considerably exceed 

 (in consequence of the length of tlie generating reservoir) the length of the 

 wave of a height equal to that of the fluid, the wave will assume its usual 

 form W notwithstanding, and will pass forward with its usual volume and 

 height ; it will free itself from the redundant matter lo by whicli it is accom- 

 panied, leaving it behind, and this residuary wave, Wo, will follow after it, only 

 with a less velocity, so that although the tAvo waves Avere at first united in the 

 compound wave, they afterwards separate, as at Wo to, and are more and more 

 apart the further they travel. 



Disintegration of large Wave Classes. — Thus also by increasing the length 

 of the generating column, there may be generated any number of residuary 

 waves, and it is a result of no little importance, to just conceptions of the 

 nature of the wave of the first order, that it be not regarded as an arbitrary 

 phaenomenon deriving all its characters from the conditions in which it was 

 at first generated, but that it is a phaenomenon sui generis, assuming to itself 

 that form and those dimensions under which alone it continues to exist as a 

 wave. The existence of a moving heap of water of any arbitrary shape or 

 magnitude is not sufficient to entitle it to the designation of a wave of the first 

 order. If such a heap be by any means forced into existence, it will rapidly 

 fall to pieces and become disintegrated and resolved into a series of different 

 waves, which do not move forward in company with each other, but move on 

 separately, each Avith a velocity of its own, and each of course continuing to 

 depart from the other. Thus a large compound heap or wave becomes re- 

 solved into the principal and residuary Avaves by a species of spontaneous 

 analysis. 



Residuary Negative Waves. — There is a method of genesis the reverse of 

 the last, Avhich also produces residuary waves, but they are thus far the reverse 

 of the last in form, as they have the appearance of cavities propagated along 

 the surface of the still water in the channel, and they move more slowly than 

 the positive wave : Ave may give them the appellation of residuary negative 

 waves. When the elevation of the fluid in the reservoir is great in proportion 

 to its breadth (reckoned as amplitude), the descending column of genesis com- 

 municates motion to a greater number of particles of water than its own, but 

 with a less velocity ; these go to form a Avavc which is larger in volume than 

 the column of genesis, and therefore contribute to the volume of the wave 



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