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LII. Application of the Variations of Temperature in Air that 

 changes its Volume to account for the Velocity of Sound. By 

 J.lvoRY, Esq. M.A.F.R.S* 



THE formula for the velocity of sound investigated by 

 Newton, having finally overcome all objections, it still 

 remained to account for the remarkable discrepancy between 

 the theory and observation. Tlie difference, amounting to a 

 sixth of the whole quantity, could hardly be thrown entirely 

 upon incidental errors of the experiments. The author of 

 the Principia led the way in the conjectures that were ad- 

 vanced for reconciling the calculated velocity of sound with 

 the true velocity ; but as all these attempts have shared the 

 usual fate of hypotheses, and have lost all interest by the dis- 

 covery of the real cause, it would be supei-fluous to mention 

 them here. But it will be proper to observe, that the difficulty 

 was occasioned by no inaccuracy or neglect of Newton. It 

 arose from an inexact estimate of the air's elasticitj', which he 

 was unavoidably led to make from the state of natural science 

 in his time, and which the progress of knowledge has enabled 

 the philosophers of the present day to correct. When the ex- 

 act elasticity is substituted for the inaccurate quantity, the dis- 

 crepancy between theory and experiment disappears, without 

 any change being required in the demonstration. At the time 

 of the publication of the Principia, and long after that time, 

 what could possibly have led any one to surmise, that nearly 

 half as much heat enters into air when it dilates, and comes 

 out of it when it contracts, as must be applied from some ex- 

 traneous source, in order to produce the same change of vo- 

 lume? 



The fact, that air absorbs heat when it expands, and evolves 

 heat when it contracts, having been established by many ex- 

 periments ; and very notable effects being observed in some 

 cases of great and sudden condensation; Laplace, between 

 20 and 30 years ago, first suggested that this properly of air 

 was the cause of the perplexing difference between the velo- 

 city of sound as determined by theory and observation. In 

 the aerial undulations by which sound is conveyed to the ear, 

 every small portion of air is first condensed and then dilated; 

 and we may compare the elasticities on the two suppositions, 

 that die temperature of the agitated air remains the same as 

 in the quiescent state of equilibrium, and that it varies with 

 the changes of volume. The external compressive force be- 

 ing always the same, it is manifest that, whenever the bulk of 



* Communicated by the Author. 

 Ne-d) Scries. Vol. 1. No. 4. April 1827. 2 K the 



