ftS On the Velocity of Sound. 



where g is the velocity which a heavy body acquires by falling 

 during one second, P the barometric pressure *, D the density 

 of air, compared with that of mercury at 32° Fahrenheit, as 

 unit, and k the ratio between the quantity of heat which would 

 raise the temperature of a mass of air one degree, if free to ex- 

 pand under the same atmospheric pressure, and what would 

 raise it one degree, if confined in a close inextensible vessel. A 

 mean of four experiments of MM. Gay Lussac and Welter 

 gave this ratio as 1.3748 to 1 ; but many experiments of my 

 own make it as 4 to 3. The former requires the particles of 

 air to repel each other, with forces inversely as the 2.1244 powers 

 of their distances, — a most improbable law, to be sure, having 

 no known parallel in nature ; whereas the latter implies, that the 

 repulsion varies inversely as the square of the distance ; which, 

 indeed, is the only law known, and most likely the only one 

 which exists. For these reasons, I have little hesitation in a- 

 dopting the ratio of 4 to 3, as the true value of Tc. 



An expression for D may be obtained in terms of P, g^ and 

 ty the Fahrenheit temperature, thus : The density of dry air 

 varies, as P for pressure, as g for gravity, and inversely, as 

 448'' + ty for temperature, according to the experiments of Mr 

 Dalton, M. Gay Lussac, &c. ; but the additional expansive 

 force of moisture^ makes the density vary for pressure not ex- 

 actly as P, but as P — fy*; because, according to M. Gay Lus- 

 sac, the density of aqueous vapour, is to that of dry air, in like 

 circumstances, as 5 to 8. Wherefore, combining these together, 

 the density varies, as 



448-|-2f 



Let D' be the density of dry air at the freezing point, and un- 

 der a pressure of 30 inches, at some place where the intensity 

 of gravity is g', then 



• The place which P occupies here has led several into the mistake of sup- 

 posing that Newton, Laplace, and other theorists, made the velocity of sound 

 vary as the square root of the barometric pressure, when the temperature is 

 the same. It should be recollected, that D involves P ; but, as we shall pre- 

 sently see, it likewise involves ^r; and therefore, this formula is independent 

 of the latitude, or height above the sea. 



4 



