74 MOLECULAR MOTION AND ITS ENERGY 36 



the vibrations of sound. The latter motions spread from one 

 place to another, and the cause of this transmission is the 

 molecular motions which bring the particles that execute 

 the sound- vibrations into contact with others. From this 

 it follows that the velocity of propagation of sound cannot 

 depend on the nature of the sound-vibrations, but only on 

 the molecular motions. 



If we paid no regard to the variations in temperature 

 which a gas undergoes by condensation or rarefaction, it 

 would be easy to answer the question as to the speed with 

 which, on the basis of the assumptions of the kinetic theory, 

 a sound wave is propagated. If sound consists in alternate 

 rarefactions and condensations of the air, the speed of its 

 propagation cannot be different from the speed with which 

 /any inequality of the pressure that arises at any place 

 / would spread through air-filled space. 1 Now, according to 

 our theory the pressure arises from the to-and-fro motions 

 of the particles, and is exerted and carried on from one 

 layer to another by the same cause ; the velocity with 

 which a pressure- or sound-w r ave is propagated must there- 

 fore be just as great as that with which the particles of gas 

 move to and fro in the direction of propagation of the 

 wave. The value of the component of the molecular motion 

 in the given direction, and not the resultant velocity of the 

 particles, comes therefore into account in the calculation of 

 the velocity of sound ; and hence it follows at once that the 

 speed of propagation of sound in a gas must be smaller than 

 the mean speed of the molecular motion in this gas. This 

 theoretically deduced proposition is completely confirmed 

 by experiment ; for instance, in atmospheric air at C. the 

 speed of sound is about 332 metres per second, and is con- 

 sequently considerably less than the mean molecular speeds 

 G=485 and ft =447 (28). 



How much smaller the speed of sound is we may easily, 

 and with sufficient exactness, determine in the same way as 

 in 10 we calculated the pressure of a gas. 2 If the energy 



1 This conclusion has been experimentally confirmed by C alder oni, Wied. 

 Beibl. iii. p. 155. 



2 More mathematically strict calculations have been made by Stefan (Fogg. 



