and Conduction, and on the Propagation of Sound. 311 



occur in a finite time. There appears to be nothing in the 

 behaviour of gases, as revealed to us by experiment, which 

 forbids the supposition of a delay capable of influencing the 

 propagation of sound. 



Returning now to the question of the radiating power of air, 

 we may establish a sort of superior limit by an argument based 

 upon the theory of exchanges, itself firmly established by the 

 researches of B. Stewart. Consider a spherical mass of radius 

 r, slightly and uniformly heated. Whatever may be the 

 radiation proceeding from a unit of surface, it must be less 

 than the radiation from an ideal black surface under the same 

 conditions. Let us, however, suppose that the radiation is the 

 same in both cases and inquire what would then be the rate 

 of cooling. According to Bottomley* the emissivity of a 

 blackened surface moderately heated is '0001. This is the 

 amount of heat reckoned in water-gram-degree units emitted 

 in one second from a square centimetre of surface heated 1° C. 

 If the excess of temperature be 0, the whole emission is 



0x47n' 2 x-OOOl. 



On the other hand, the capacity for heat is 



7r>> 3 x-0013x-24, 



the first factor being the volume, the second the density^ and 

 the third the specific heat of air referred as usual to water. 

 Thus for the rate of cooling, 



dd -0003 1 

 Jdt = ""•0013x«24xr = ~ r ^ nea * l 7> 

 whence 0=0 Qe -V r , (5) 



O being the initial value of 6. The time in seconds of cooling 

 in the ratio of e : 1 is thus represented numerically by r 

 expressed in centims. 



When r is very great, the suppositions on which (5) is 

 calculated will be approximately correct, and that equation 

 will then represent the actual law of cooling of the sphere of 

 air, supposed to be maintained uniform by mixing if neces- 

 sary. But ordinary experience, and more especially the 

 observations of Tyndall upon the diathermancy of air, would 

 lead us to suppose that this condition of things would not be 

 approached until r reached 1000 or perhaps 10,000 centims. 

 For values of r comparable with the half wave-length of 

 ordinary sounds, e.g. 30 centim., it would seem that the real 

 time of cooling must be a large multiple of that given by (5) . 

 * Everett, C.G.S, Units, 1891, p. 134. 



