the Radiation of Heat on the Propagation of Sound. 315 



the temperatui'e of the heated air over that of the surrounding 

 air, we should have, supposing to be siifficiently small to allow 

 us to adopt Newton^ s law of cooling, r. r/ p in 



vto'/l rir 



ft'om which it follows that the excess of temperature would be 

 diminished during the time t in the ratio of e'l' to 1 . It would 

 follow from the numerical value of q above given, that, even in 

 so short a time as the hundredth part of a second, the tempera- 

 ture would be reduced in the ratio of about 3514 millions to 1. 

 Such rapidity of cooling as this is utterly contrary to observation. 

 Put a poker into the fire, and when it is hot look along it, and an 

 ascending stream of heated air will be rendered visible by the 

 distortion which it produces in objects seen through it, in con- 

 sequence of the diminution of refractive power accompanying 

 the rarefaction produced by heat. But were the rate of cooling 

 anything like what has just been determined, no such stream 

 could exist. Yet we have seen that the observed fact, that sound 

 is propagated to a distance, obliges us to suppose that the rate 

 of cooling is either immensely greater or immensely less than 

 con-esponds to ^ = 2198. It is needless now to say which alter- 

 native we must choose. Accordingly, no doubt whatever exists 

 as to the correctness of Laplace's explanation of the excess of thCj 

 observed velocity of sound over that calculated by Newton. ,j(( 

 Now that it has been decided which of the two ratios n : q ana 

 q:n we must regard as extremely small, we may simplify the 

 formula (13.) by retaining only the first power of the ratio in 

 question, and we shall thus be the more readily enabled to see 

 in what direction we must look for the first fahit indications of 

 the efiect of radiation. Retaining only the first power of q, and 

 putting w = V/A, /i = 27rX,~', where V= -/(AK), the velocity of 

 propagation, we get from (11.), (12.) and (13.), ''^^ 



iOil Jaji ■ _, qx "i; =: s* baeoqqna f>8Ba 9flJ 



i-i, s=Ke~^^~^ AMfiQ^^{^t-x). . . (19.) 



Hence it is to a diminution of intensity, rather than to an alteration 

 of velocity corresponding to an alteration of pitch, that we are 

 to look for the effect of radiation. Now that the objection raised 

 against Laplace's cxjilanation of the velocity of sound has been 

 answered, we may take 1'4'14 for the value of k, this being the 

 mean of the values quoted by Poiason in art. 664, which were 

 deduced from the velocity of sound, and are probably nearer the 

 truth than the somewhat smaller values determined by a different 

 process. Putting K=l'4]4, V = 1]00, taking the square of the 



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