Mr. S. T. Preston on an Acoustic Thermometer. 59 



vibrate in resonance with the tube possessing a certain length. 

 Then it will be seen at once that changing the temperature 

 of the object where the tube is placed will alter this state of 

 affairs. Another fork of different vibrating period must now 

 be selected in order to resound with the tube. Of course 

 there are certain relations between the vibrating period and 

 the temperature, and it is to illustrate the extreme simplicity 

 of these relations under the kinetic theory of gases that is 

 one point in the present paper. 



Maxwell showed, in his celebrated paper, " On the Dyna- 

 mical Evidence of the Molecular Constitution of Bodies," 

 published in i Nature,' March 4, 1875, that it was demon- 

 strable matliematically that " the pressure of a gas cannot be 

 explained by assuming repulsive forces between the particles. 

 It must therefore depend, in whole or in part, on the motion 

 of the particles''' (Maxwell's paper, p. 358). 



Hence it appears so far clear, as we may say, that we must 

 have recourse to a dynamical theory in order to explain one 

 of the simplest and most fundamental properties of a gas. 



A confidence in the dynamical theory led me (Phil. Mag. 

 June 1877) to suggest its application to illustrate the me- 

 chanism of the propagation of sound in gases ; and the very 

 simple relation showed itself, viz. that the velocity of propa- 

 gation of sound could only depend on the velocity (normal) 

 of the molecules of gas themselves, and on nothing else ; in 

 fact, that the sound-wave moved independently of the density 

 and pressure of the gas. Indeed, according to the kinetic 

 theory, the molecules of the gas have of course no distant 

 action on each other, and can therefore only influence each 

 other by impact (so that the velocity of the normal motion of 

 the molecules of the gas alone comes into play in propagating 

 the wave). 



Now this applies very simply, as will be apparent at once, 

 to our proposed acoustic thermometer. For it is this normal 

 motion of the molecules of the gas (in the tube) , the energy 

 of which motion we call the " temperature,"" which is the sole 

 factor in determining the velocity of sound, of which the 

 tuning-fork (we employ with the tube) is the mechanical in- 

 dicator. The velocity of sound being as the velocity of the 

 gaseous molecules, and velocity of the molecules being as the 

 square root of their energy, then, since the temperature is 

 the energy, the velocity of sound in a gas is proportional to 

 the square root of the temperature, as we see. 



If we have a tuning-fork whose vibrating period is me- 

 chanically adjustable, it is easy to perceive, then, from the 

 above, that the temperature (in the tube) is inversely propor- 



