='\/!- 



the Velocity of Sound. 283 



this relation, o- being the maximum condensation corresponding 

 toy=l. As there are no other quantities concerned in this 

 relation, and as h and I are the only linear quantities, this 



equation is equivalent to j =%(<'■). And we have above 



7 

 Hence 



'^\/-=x(°")- 



But it has already been shown that k is independent of cr. 

 Hence x{'^) is a constant, and k is the same for all vibrations. 



We have thus been led, by reasoning exclusively on hydro- 

 dynamical principles, to the following conclusion. The velo- 

 city of transmission of a vibration in a medium, for which the 

 relation between the pressure and the density is given by the 

 equ ation p = a^p^ is not simply a, but a greater quantity 

 a \^l-\-ki which is the same for vibrations of different magni- 

 tudes. 



To ascertain the numerical value of Ar, it would be necessary 



in a particular instance to obtain by experiment the ratio j. 



The application of the foregoing result is not confined to 

 particular cases of disturbance. For according to the mathe- 

 matical theory above given, the state of the fluid, whatever it 

 may be, is, at every instant, and therefore at the instant of dis- 

 turbance, composed of vibrations in fluid filaments unlimited 

 in number, and unlimited as to the directions of their propa- 

 gation. In all these filaments the velocity of propagation is the 

 same. 



I cannot avoid adverting here to a difficulty which has long 

 presented itself to me, with respect to the explanation usually 

 given of the excess of the velocity of sound above the value a. 

 Admitting that a sudden condensation by developing heat 

 produces a higher degree of temperature, and therefore of 

 elastic force, than would exist in the same state of density 

 without such development, does it not thence follow, that a sud- 

 den rarefaction, by absorbing heat, produces a lower tempe- 

 rature and a Jess elastic force than would exist in the same 

 state of density without such absorption ? But the observed 

 mcrease of velocity of propagation requires an increase of ela- 

 stic force, as well where the fluid is rarefied as where it is con- 

 densed. May it not be that the developed heat (whether 

 positive or negative) is carried off too quickly by radiation to 



