310 Lord Rayleigh on the Cooling of Air by Radiation 



atmospheric refraction and reflexion, and they are sometimes 

 very surprising. But the question remains whether in a 

 uniform condition of the atmosphere the attenuation is sensibly 

 more rapid than can be accounted for by the law of inverse 

 squares. Some interesting experiments towards the elucida- 

 tion of this matter have been published by Mr. Wilmer Duff *, 

 who compared the distances of audibility of sounds proceeding 

 respectively from two and from eight similar whistles. On an 

 average the eight whistles were audible only about one-fourth 

 further than a pair of whistles ; whereas, if the sphericity of 

 the waves had been the only cause of attenuation, the dis- 

 tances would have been as 2 to 1. Mr. Duff considers that in 

 the circumstances of his experiments there was little oppor- 

 tunity for atmospheric irregularities, and he attributes the 

 greater part of the falling off to radiation. Calculating from 

 (1) he deduces a radiating power such that a mass of air at 

 any given excess of temperature above its surroundings will 

 (if its volume remain constant) fall by radiation to one-half 

 of that excess in about one-twelfth of a second. 



In this paper I propose to discuss further the question of the 

 radiating power of air, and I shall contend that on various 

 grounds it is necessary to restrict it to a value hundreds 

 of twines smaller than that above mentioned. On this view 

 Mr. Duff's results remain unexplained. For myself I should 

 still be disposed to attribute them to atmospheric refraction. 

 If further experiment should establish a rate of attenuation of 

 the order in question as applicable in uniform air, it will I 

 think be necessary to look for a cause not hitherto taken into 

 account. We might imagine a delay in the equalization of 

 the different sorts of energy in a gas undergoing compression, 

 not wholly insensible in comparison with the time of vibra- 

 tion of the sound. If in the dynamical theory we assimilate 

 the molecules of a gas to hard smooth bodies which are nearly 

 but not absolutely spherical, and trace the effect of a rapid 

 compression, we see that at the first moment the increment 

 of energy is wholly translational and thus produces a maxi- 

 mum effect in opposing the. compression. A little later a due 

 proportion of the excess of energy will have passed into, 

 rotational forms which do not influence the pressure, and this 

 will accordingly fall off. Any effect of the kind must give 

 rise to dissipation, and the amount of it will increase with the 

 time required for the transformations, i. e. in the above men- 

 tioned illustration with the degree of approximation to the 

 spherical form. In the case of absolute spheres no transforma- 

 tion of translatory into rotatory energy, or vice versa, would 

 * Phys. Keview, vol. vi. p. 129,.189B. 



