452 On the Mode of the Propagation of Sound. 



now referred to increased " elasticity " of the air (represented 

 by the increased pressure of the confined air upon the sides of 

 the vessel). This increased pressure upon the sides of the 

 vessel, however, is only due to the increased velocity of the air- 

 molecules which impinge against the sides of the vessel, and 

 whose velocity has been augmented by the application of 

 heat (and whose motion represents the "heat"). The in- 

 creased pressure of the heated air may serve as a convenient 

 means for estimating the augmentation of molecular velocity, 

 upon which the augmented velocity of propagation of the 

 sound-wave depends. Thus it may be a convenient rule that 

 the velocity of sound in heated (confined) air (of unchanged 

 density) is proportional to the square root of the " elasticity" 

 of the air (as measured by the pressure), the reason of this 

 being that the velocity of the molecules of air (which deter- 

 mines the velocity of the propagation of the wave) is itself pro- 

 portional to the square root of the pressure. The augmented 

 pressure of heated confined air is evidently not itself the cause 

 of the increased velocity of propagation of the wave ; but the 

 augmented pressure (" elasticity ") is the effect attendant on 

 the increased velocity of the molecules of air, which increased 

 velocity is itself the cause of the augmented velocity of propa- 

 gation of the wave. 

 ^v 19- The result of these considerations may therefore be 

 summarized as follows : — 



That the velocity of propagation of a wave (such as a wave 

 of sound) in a gas is solely determined by, and proportional tO) 

 the velocity of the molecules of the gas ; that this velocity of pro- 

 pagation of the wave is not affected by density, pressure, or by 

 the specific gravity of a gas, or by any thing else excepting the 

 velocity of its molecules. 



20. This, it may be observed, is a condition following inevi- 

 tably on the acceptance of the kinetic theory ; and surely the 

 very simplicity of this relation as affording a definite physical 

 conception of the condition determining the velocity of sound, 

 and as giving an insight into its mode of propagation, would 

 be by itself sufficient to recommend it over the old system. 

 If any thing I have written should serve to divert the atten- 

 tion of others more competent than myself to this interesting 

 subject, the purpose of this paper will have been served. ^ 



PS. (1). It is proper for me to add that this paper is not 

 wholly original, but the perusal of a paper by Mr. J. J. 

 Waterston in the i Philosophical Magazine ' (Jan. 1859, Sup. 

 to vol. xvi.) formed the starting-point of the present paper. 

 The method of illustrating the propagation of a wave by 

 means of a line of spheres is due to Mr. Waterston ; but the 



