276 Prof. Challis's Theoretical Determination of 



logous to those of colour. Such is the origin of the curious 

 phsenomena of chemical and calorific transmission and dif- 

 fusion which I had the honour to submit, many years ago, to 

 the Academy*. 



In conclusion, I cannot but express my admiration how the 

 discovery of a series of facts, which seemed contrary to the 

 theory of the identity of light and heat, has become now the 

 fundamental basis of that theory. Who would not have 

 thought at first sight, that the radiations of heat were of a 

 nature altogether different from light, on seeing them trans- 

 mitted in such different proportions through substances endued 

 with the greatest transparency ; traversing other bodies, 

 strongly coloured, in an immediate and instantaneous manner, 

 and this in greater abundance than through some media per- 

 fectly limpid; and going in a single rectilinear path through 

 a plate of completely opake glass ? Yet, nevertheless, these 

 singular properties are the necessary consequences of the 

 transparency and coloration of bodies for heat combined with 

 different periods of the £Elhereal undulations. No one could 

 have ever maintained the identity of light and heat until there 

 had first been proved coloration of the one and the other of 

 these agents, and the quality that every ray of dark heat pos- 

 sesses of propagating itself and being refracted in a solid body. 



XL. Theoretical Determination of the Velocity of Sound. By 

 the Rev. J. Challis, M.A., F.R.A.S., Pliwiian Professor of 

 Astronomy and Experimental Philosophy in the University 

 of Cambridge^. 



THE following mathematical investigation of the velocity 

 of sound differs from any hitherto adopted, and conducts 

 to a new result. 



Let a-(l +5) be the pressure at any point xyz of the air, at 

 any time ^, s being a small numerical quantity, the powers 

 of which above the first are neglected ; and let ?<, v, iso be the 

 resolved jiarts of the velocity at the same point and at the same 

 time, in the directions of the axes of co-ordinates. Then re- 

 taining only the first powers of u^ v, w, we have, as is known, 



„ ds du ^ ^ ds dv ^ ^ ds dw 



''''d-x + di=''>'''di} + dt=^'"''rz + ii=''' . 



and 



ds du dv dw ^ . . 



• Sitting of Nov. 16, 1811, and Feb. 1, 1843. 

 "t" Coiuinuiiicated by the Author. 



