96 Prof. Challis on the Theory oj 



cluced by suddenly increasing and suddenly diminishing the 

 number of atoms in a given space, and which takes place as well 

 in olefiant gas as in atmospheric air. Thus, although both kinds 

 of radiation are brought into play in sudden changes of density 

 of olefiant gas, the rate of propagation may not be thereby sen- 

 sibly altered, because all the reasons above adduced for conclu- 

 ding that the latter radiation produces but little alteration are 

 applicable to the former. So far as they have effect, they in- 

 crease the velocity of propagation by augmenting the gradations 

 of temperature and elasticity. There remains, then, only the 

 above-mentioned effect of the imperfect elasticity of the gas in 

 vibration, to which may reasonably be ascribed such excesses of 

 the theoretical above the observed velocities as those in the 

 instances of carbonic acid, oxide of nitrogen, and olefiant gas, 

 which were adduced towards the beginning of this communi- 

 cation. 



The foregoing explanation, which rests entirely on the new 

 principles of theoretical physics which I have proposed in various 

 previous articles, is one among many explanations of physical 

 phenomena which I have given on the same principles, and adds 

 to the cumulative evidence of the truth of the fundamental 

 hypotheses. 



With respect to Prof. Le Conte's paper " On Laplace's Cor- 

 rection of the Theoretical Velocity of Sound," I beg in the first 

 place to remark that any decision respecting the validity of that 

 correction necessarily involves a full consideration of the mathe- 

 matical reasoning by which the theoretical velocity was obtained, 

 because the correction implies a previous mathematical determi- 

 nation. Now the mathematical investigation of the motion of 

 fluids was left by Lagrange in a very imperfect state ; and no 

 important addition was made by Laplace. The theoretical velo- 

 city which they accepted has therefore no right to be considered 

 final. By an extension of the principles on which the mathema- 

 tical reasoning is based, I first succeeded in showing that the 

 velocity of propagation is greater than that which had been gene- 

 rally adopted, and subsequently found for air a numerical value 

 closely agreeing with the observed velocity of sound. This result, 

 being obtained by reasoning from admitted premises, ought cer- 

 tainly to be capable of disproof if it is not true. I will also 

 concede that the mathematical reasoning will be proved to be 

 untrue, if the development of heat and cold by the sudden con- 

 densation and rarefaction of the air in vibration be, as Prof.' 

 Le Conte contends, a vera causa, accounting for an increment of 

 velocity equal to one-sixth of the observed value. But this is a 

 point of much difficulty, on which I find that French writers 

 speak with a degree of caution that has not been generally imi- 



