382 REPORT— 1844. 



Section IV. — Waves of the Fourth Order. 



TJie Corpuscular Wave. 



The Sound Wave of Water. 



This order of wave I have denominated the corpuscular wave, because the 

 motions by which it is propagated are so minute as to escape altogether direct 

 observation, and it is only by mathematical a priori investigation and indi- 

 rect deductions from phsenomena, that we come to recognise its existence as 

 a true physical wave. The motions by which it is propagated are so minute, 

 that it is only by supposing a change in the form of the molecules of the liquid, 

 or of their density, if conceived to be in contact, or an instantaneous and 

 infinitesimal change in the minute distances of the molecules from each other, 

 that the existence of such a wave can be conceived to be possible. 



I have not examined this wave by any experiments of my own, and indeed 

 I find that labour to be perfectly unnecessary, for there has been kindly 

 transmitted to me by M. Colladon, a communication of his to the Academy 

 of Sciences, which has been printed in the fifth volume of the ' Memoires des 

 Savans Etrangeres,' in which there is given in great detail, an account of a 

 complete and most satisfactory determination of tlie elements of this question. 



Newton's approximate determination of the velocity of sound in the at- 

 mosphere was followed by that of Dr. Young and M. Laplace, who effected 

 a similar approximation for water and other liquids, and finally the complete 

 solution was satisfactorily given by M. Poisson, the velocity being determined 

 both for solids and liquids by the formula 



VDe' 



where D is the density of the substance, k the length of a given column, and 

 £ the small diminution of length caused by a given pressui-e P. 



For tlie determination of the velocity of the sound wave in water, MM. 

 Colladon and Sturm undertook a series of experiments on the compression 

 of liquids, conducted with very ingenious apparatus, and observed and dis- 

 cussed with much accuracy ; by this means they obtained values for the 

 quantities P, k and s, from which the velocity of sound should be theoretically 

 determined. 



They obtained for the water of the lake of Geneva the following quan- 

 tities : — 



Assuming D=l, A =1,000,000, 



they found £=48'66, 



and P=(0'"-76).^.m=(0'"-76).(9-8088).(13,544), 



whence c= 1437*8 metres, 



being the theoretical velocity per second of the sound wave in water. 



A very elegant apparatus was next employed for the direct determination 

 by experiment of the truth of this result. Two stations were taken on the 

 lake of Geneva, the mean depth of water lying between them being about se- 

 venty fathoms, and the distance between tlie stations was carefully determined 

 to be 13,487 metres, or 14,833 yards, about eight miles and a half, lying be- 

 tween the towns Rolle and Thonon. At one end of this station a large bell 

 was suspended at a depth of five or six fathoms below the surface of the 

 water, and struck by mechanism so contrived, as at the instant of striking to 

 explode a small quantity of gunpowder, and so indicate (during a dark night) 



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