256] VELOCITY OF SOUND. 467 



from one element to another has hardly set in before its direction 

 is reversed, so that practically each element behaves as if it 

 neither gained nor lost heat. 



On this view we have, in place of (1), the adiabatic law 



where, as explained in books on Thermodynamics, 7 is the ratio of 

 the two specific heats of the gas. This makes 



K = ypo .............................. ..... (6), 



and therefore c = (WO/PO)* ........................... (7). 



If we put 7=1*410*, the former result is to be multiplied by 

 1-187, whence 



c = 332 metres per second, 



which agrees very closely with the best direct determinations. 



The confidence felt by physicists in the soundness of Laplace s view is so 

 complete that it is now usual to apply the formula (7) in the inverse manner, 

 and to infer the values of y for various gases and vapours from observation 

 of wave-velocities in them. 



In strictness, a similar distinction should be made between the adiaba 

 tic and isothermal coefficients of elasticity of a liquid or a solid, but 

 practically the difference is unimportant. Thus in the case of water the 

 ratio of the two volume-elasticities is calculated to be l 0012f. 



The effects of thermal radiation and conduction on air-waves have been 

 studied theoretically by Stokes J and Lord Rayleigh. When the oscillations 

 are too rapid for equalization of temperature, but not so rapid as to exclude 

 communication of heat between adjacent elements, the waves diminish in 

 amplitude as they advance, owing to the dissipation of energy which 

 takes place in the thermal processes. 



According to the law of Charles and Gay Lussac 

 p /po oc 1 + -00366 0, 



where 6 is the temperature Centigrade. Hence the velocity of 

 sound will vary as the square root of the absolute temperature. 

 For several of the more permanent gases, which have sensibly the 

 same value of 7, the formula (7) shews that the velocity varies 



* The value found by direct experiment. 

 t Everett, Units and Physical Constants. 



J &quot; An Examination of the possible effect of the Radiation of Heat on the Pro 

 pagation of Sound,&quot; Phil. Mag., April, 1851. 

 Theory of Sound, Art. 247. 



302 



