Prof. Challis on the Theory of the Velocity of Sound.. 93 



its pressure (p) varies as the density (p) under all circumstances, 

 whether of rest or of motion. If p and p be given correspond- 

 ing values of the pressure and the density, we shall always have, 



according to these hypotheses, p= — .p. Also the velocity of 



P°. 



propagation, determined by the investigation just referred to, is 



k\/ — , k being a certain numerical constant, the same for all 



v Po . 

 perfect fluids. Hence if experiments be made for ascertaining 



the velocity of sound in different fluids in such a manner that p 

 is the same for all, the different velocities should vary inversely 

 as the square root of p . That condition was satisfied in the 

 above-mentioned experiments of Dulong, which are contained in 

 vol. xli. of the Annates de Chimie et de Physique. The results 

 given in p. 150 for seven gases, show that the velocities conform 

 to the above law in the instances of atmospheric air, oxygen, 

 hydrogen, and oxide of carbon ; but that the velocities deduced 

 according to the law from that in atmospheric air for carbonic 

 acid, oxide of nitrogen, and olefiant gas exceed the experimental 

 values by 8 m, l, 7 m '6 } and 22 m, 2 respectively. The physical reason 

 for these differences I now proceed to investigate. 



The following explanation is based on physical principles 

 which I have frequently enunciated in this Magazine, conjoined 

 with certain experimental results recently obtained by Professor 

 Tyndall. I suppose an elastic fluid to consist of inert spherical 

 atoms of constant magnitude, each of which, by means of the 

 reflexion of setherial undulations from its surface, becomes a centre 

 of repulsive force, the undulations being of necessity such that 

 by their dynamical action they keep the atoms asunder. The 

 aggregate effect of this action of heat-undulations is to produce a 

 pressure of the fluid proportional to its density, as I have endea- 

 voured to show by the solution of Problem II. at the end of the 

 " Theory of Molecular Forces " contained in the Philosophical 

 Magazine for February 1860. Now if any portion of the fluid 

 be compressed within a smaller space, and the repulsive force 

 from each atom (which for brevity I shall call its specific heat) 

 be supposed to remain the same as before the compression, the 

 increase of pressure of the fluid will be entirely due to the greater 

 proximity of the atoms to each other, the atomic repulsion in- 

 creasing with the diminution of distance. If the two states of 

 compression be separated by a considerable interval of time, 

 there is no difficulty in admitting that the specific heat of each 

 atom is the same in both, because its amount is determined by 

 the general temperature of surrounding substances. But would 

 the case be the same during the rapid changes of density which 

 occur in the vibrations of the fluid ? The answer to this ques- 



