76 MOLECULAR MOTION AND ITS ENERGY 36 



done equally easily. For by Boyle's law, if p + dp and 

 p + dp represent the values of p and p when increased by 

 compression, the ratio 



p _ p + dp __ dp 



p p + dp dp 



is constant so long as the temperature remains unchanged. 

 We might therefore have written 



dp 



for the formula giving the speed of sound ; and herein the 

 increment dp of pressure and the corresponding increment 

 dp of density may be taken either as finite or as infinitely 

 small magnitudes. 



But the ratio of the pressure to the density remains con- 

 stant only so long as the temperature of the gas remains 

 unaltered. If, however, a gas is made to occupy a smaller 

 volume, not only do the pressure and density increase, but 

 also the temperature ; and if the gas expands, not only do 

 its pressure and density diminish, but its temperature falls 

 too. This rise and fall of temperature, when the volume 

 undergoes change, have both the effect of causing the 

 pressure to alter in greater measure than the density, and 

 therefore the ratio of dp to dp has in the actual case a 

 greater value than Boyle's law gives it when the tempera- 

 ture is not taken into account. Thus the formula must be 

 completed by a factor which is greater than 1, and, accord- 

 ing to the equations of the theory of heat, which have been 

 established by Laplace and others, this factor is the ratio 

 of the specific heat C at constant pressure to the specific 

 heat c at constant volume. Consequently we have 



C, p 3 c v 8 

 and the speed of sound itself is given by 



v = flvVC/Sc). 



That with this improved formula, also, the ratio of v to fl 

 is less than 1, I will show by taking atmospheric air as an 

 example. Putting for this substance 



C = 1-405 c, 



