36 Dr. Schroder van der Kolk on the Velocity of Sound. 



city than such as were made by means of less intense waves of 



air, and hence for different intensities we should find different 



c 

 values for - , and the accurate determination of the mechanical 



c » 

 equivalent of heat would be impossible. Experimentally this has 



not been made out; experiments upon this point have never been 

 instituted ; for the observation that a melody can be recognized 

 equally well near or at a considerable distance only proves that 

 the effect m question is very slight, since in the first place the 

 distance, and secondly the difference of intensity of the various 

 tones, can never be very great. 



Accordingly, if I venture in the following pages to calculate 

 the amount of this effect with greater exactitude, I must at once 

 state that I by no means undertake to give a complete theory of 

 sound. It may be true that the theory of elasticity leads to dif- 

 ferent fundamental formulae ; but just as, in experimental inves- 

 tigations which yield only approximate values of the magnitude 

 under examination, the influence of one factor may often be ac- 

 curately ascertained by means of comparative experiments, so I 

 believe that the influence of intensity as calculated below would 

 be found to be the same, even if the fundamental formulae for 

 the propagation of a wave-motion in air were differently developed. 



Theoretical Development. 

 We have in general, for the velocity of propagation of longitu- 

 dinal waves, the formula s = a / -, where s is the velocity, ethe 



force with which the molecules attract each other when the dis- 

 tance between has been doubled, and d the density of the medium. 

 Hence if a particle is displaced in the direction of two molecules 

 by the amount 8, the force tending to bring it back is =eS. 



In the case of air, e = H/3, and d= -> if H denotes the height 



of the barometer, g the constant force of gravity, and /3 and b 

 the specific gravities of mercury and air respectively, and the 



above formula consequently becomes s= \/- • 



This formula then would express the velocity of waves of air 

 if it were not for the development of heat by the condensation in 

 the crest of the wave, and the absorption of heat in the trough 

 of the wave ; in the first case the elasticity, or the height of the 

 column by whose pressure it is measured, is increased, and in 

 the second case it is diminished ; both ways, therefore, the dif- 

 ference of pressure, which is the cause of the advance of the wave, 

 is increased. 



