36 MAXWELL'S LAW 75 



of the motion of the molecules in a given direction is one- 

 third part of the whole energy, we might look on the 

 magnitude 



as the mean value of the component in a given direction, 

 G being, as before, the mean molecular speed ; for, as the 

 energy varies as the square of the velocity, the velocity 

 varies as the square root of the energy. We therefore find 

 for the velocity v of sound the formula 



v = 

 which shows that v is less than G ; we also have 



from which it appears that Maxwell's mean value O of 

 the molecular speed is also greater than that of sound. 

 If we put these formulae into the form 



we obtain Newton's 1 formula, with which the speed of 

 sound can be calculated from the pressure p and the corre- 

 sponding density p of the gas. 



But,_as Laplace 2 first saw, this formulae-needs.. a coxrec.- 

 tion. The oscillations constituting sound depend not so 

 much on the actual pressure and density of the gas as on 

 the changes which they simultaneously undergo in con- 

 sequence of the alternate condensations and rarefactions. 

 With more correctness, therefore, should we have expressed 

 G in terms of the variations which p and p undergo instead 

 of in terms of p and p themselves, and this could have been 



Ann. cxviii. 1863, p. 494), Eoiti (Mem. delV Accad. dei Lincei [3] i. 1876, pp. 

 39, 762; Nuovo Cimento [2] xvi. 1876; [3] i. 1877, p. 42), and Brusotti 

 (Ann. Sclent, del 1st. Tecnico di Pavia, 1874-5, p. 171) ; further by 

 Hoorweg (Arch. Neerl. xi. 1876, p. 131; Pogg. Beiblatter, i. 1877, p. 209), 

 Mees and H. A. Lorentz (Versl. en Med. K. Akad. Amst. xv. 1880), 

 Schlemiiller (Die Fortpflanzungsgeschw. in einem theor. Gase, bearb. auf 

 Grund d. dyn. Gastheorie, Prag 1894). S. T. Preston has given an elementary 

 explanation of the process in Phil. Mag. [5] iii. 1877, p. 441. 



1 Principia, ii. 8, prop. 49, probl. 11. 



2 Ann. Chim. Phys. [2] iii. 1816, p. 238 ; xx. 1822, p. 266 ; Mec. Gel. v. 



