XL. 0/t the Soiution of the Problem of Sound transmitted through 

 Liquids. By Professor FotteBj A.M.* 



THE' propagation of sound tlirougli liquids^ it is Wdlkhcikn^ 

 does not follow the same law as tlie propagation through 

 the air ; for on the old method of treating the problem of soimd, 

 it was found that the velocity of transmission in air was given 

 one-sixth part too small by the theory^ whilst the velocity of 

 sound through water was that which was given by theoiy^^as 

 nearly as could be expected; the compressibility of water being 

 slightly different in the results of the experiments and reductions 

 as given by Canton, ffirsted, and CoUadon and Sturm. The 

 explanation which has been given is this ; — so little heat is de- 

 veloped in the compression of liquids, that there wasncit reqtiii'eJd 

 the same correction as for gases. ' '''' ■'' '-'^^^"i '^' '"^'^ ^'■'''" 



The true cause of the difference itftKe^aW of th^ 'Jirqia^aiiS^tf 

 of sound must be sought in the different constitutions of the 

 fluids. The repulsive force between the atoms of gases, from the 

 caloric which belongs to each, does not exist in liquids ; but, oto 

 the other hand, there is the attraction of aggregation. We sfefe 

 this attraction to be veiy considerable in water-, by allowing the 

 water in a fine-pointed glass tube held vertically to escape iit 

 idi'ops. Then, again, the law of elasticity is essentially different, 

 fihe density being proportional to the pressure by Eoyle's law 

 for gases at a constant temperature ; whereas liquids possess a 

 definite density when the pressure is zero, and are veiy slightly 

 compressed under the ordinary pressure of the atmospher'e. The 

 1-elative distance of the centres of the atoms is also great in gases 

 Compared with liquids. These considerations assure us that the 

 equalization of density in every direction must be exceedingly 

 rkpid in gases compared with what it is in liquids ; and the ve- 

 locity of sound being more than four tunes greater in water than 

 in air, we may readily believe that the equalization of density in 

 eveiy direction which accom])ariies the transmission of a! wave of 

 sound in air, does not exist in the ti'ansmission of such a wave in 

 a liquid.- '---■■ ■"■ ''''"- "■ .->^>f'^"p-3&r,or> no^^n.^.1 -nn oriK 



From the foregoing considerations, we mii^Viif^ifi^ry' ^aki^^^'He 

 compression and dilatation attendant oil the ])asi^agc 7)f sound 

 through a liquid to be only in the direction of the wave motion. 



Let Vq be a given volume of liquid, which 'bcc(mK's 



V, under a unit of pressure, aiid ''■''' '' ' " 



V under a pressure (y>) on a nhW(ii\iVc^J '^ ' 



Then by Canlon's hnv we have ''■''' f^ 



* Communicated by the Author. 



