the Propagation of Sound. 449 



or pressure), the velocity of sound will remain unaltered so 

 long as the velocity of the molecules remains unaltered. 



Thus, if the density of a gas (or air) be changed by forcing 

 fresh air into the same space, the velocity of sound will remain 

 unaltered, simply because the velocity of the molecules remains 

 unaltered. The old theory would assume that the velocity of 

 sound has remained unaltered in this case because increased 

 density (or increased number of air-molecules) has a power of 

 diminishing the velocity of the sound-wave, while, on the other 

 hand, the increased pressure of the air against the sides of the 

 vessel (considered to represent increased " elasticity ") has a 

 power of increasing the velocity of the wave, and that the two 

 actions counteract each other, and therefore the velocity of 

 the wave has remained unaltered. Contrast this with the 

 simple and realizable explanation of the kinetic theory, viz. 

 that the velocity of the wave has remained unaltered simply 

 because the velocity of the molecules which propagate it has 

 remained unaltered. 



13. Clausius has demonstrated that, for a gas to fulfil 

 Mariotte and Gray-Lussac's laws : — 



(1) " The space actually filled by the molecules of the gas 

 must be infinitesimal in comparison with the whole space occu- 

 pied by the gas itself." 



(2) " That those portions of the path of a molecule through- 

 out which the molecular forces are of influence in sensibly 

 altering the motion of the molecule either in direction or velo- 

 city must be of vanishing value compared with those portions 

 of the path throughout which such forces may be considered 

 as inactive." 



V Since, therefore, the portion of a molecule's path through 

 which it is acted on by other molecules of the gas is vanish- 

 ingly small compared with the range of its path throughout 

 which it is not so acted on, there is therefore practically no 

 distance action between the molecules of a gas, which accord- 

 ingly can only influence each other by direct impact. The 

 only way, therefore, one molecule of a gas can influence ano- 

 ther is by moving up to it and striking against it. The only 

 way, therefore, a wave or small impulse can be propagated from 

 molecule to molecule through a gas is by the molecule pos- 

 sessing the impulse moving up to and striking against another 

 molecule ; and therefore the velocity of propagation of such 

 wave or impulse must depend solely and entirely upon the 

 velocity with which the molecule moves ; or the sole conceiv- 

 able cause regulating the velocity of an impulse propagated 

 from molecule to molecule is the velocity of the molecule itself 

 or the velocity with which the molecule traverses its free path. v - 

 Phil, Mag. S. 5. Vol. 3. No. 20. June 1877. 2 G 



