ON THE MATHEMATICAL THEORY OP FLUIDS. 248 



the subject before us. M. Dulong takes foi' demonstrated that 

 the square of the quotient of the real velocity of sound in any- 

 elastic fluid whatever, divided by the velocity calculated accord- 

 ing to the formula of Newton, is equal to the ratio of the speci- 

 fic heat for a constant pressure to the specific heat for a constant 

 volume. His object is to find this ratio for different elastic fluids, 

 which, it is plain, may be inferred, according to this theoi'em, 

 from the real velocity with which sound is propagated in them. 

 It is not possible to obtain these velocities for any other elastic 

 fluid than atmospheric air, excepting by indirect means. M. 

 Dulong avails himself of a method which had been previously em- 

 ployed by various experimenters, but not with complete success, 

 as was evident from the discordant results they obtained. The 

 method consists in determining the velocity of propagation from 

 the musical note rendered by a given cylindrical tube, and from 

 the measured distance between two consecutive nodal sections 

 or positions of minimum vibration, which interval he calls the 

 length of a concameration. The pitch of the note gives the 

 number of vibrations in a given time, and consequently the time 

 of propagation over the measured interval, and therefore the ve- 

 locity of the sound. By pursuing a process different from any 

 that had been adopted before, M. Dulong is enabled to give 

 great precision to this method. He first operates on atmo- 

 spheric air, with the view of ascertaining the accuracy which the 

 method admits of. By various trials, each more exact than the 

 preceding, he obtains results, all of which fall short in a small 

 degree of the velocity obtained by direct observation, and ac- 

 cordingly comes to the conclusion that the relation indicated by 

 theory between the velocity of sound in free air, and the length, 

 such as it can be observed, of the concameration s that are formed 

 in a flute-tube, is not verified exactly. He hints at some experi- 

 ments proper for making evident the cause of this discordance, 

 but I am not aware that any such have been published. 



As this method fails in giving exactly the ratio of the specific 

 heats of atmospheric air, M. Dulong adopts a ratio (viz. 1'421) 

 which he says " is the mean of a great number of direct obser- 

 vations made in free air by different observers." I mention this 

 particularly, as it seems to have been supposed* that Dulong 



" M. Poisson's excellent Treatise on Mechanics is a work so extensively used 

 that it is desirable to point out any error that may have inadvertently crept 

 into it. I do not therefore scruple to advert to an inaccuracy in p. 716, torn. ii. 

 (2nd ed.), where the author asserts that the ratio 1"421 is deduced from obser- 

 vation of the sound produced by air inclosed in a tube, and endeavours to ac- 

 count for the excess of this value above another derived from the propagation of 

 sound in free air, by the different radiation of heat in the two circumstances. 

 This is contradicted by the assertion quoted above from Dulong's Memoir. 



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