BADIAT10N   OF  HEAT  ON  THE   PROPAGATION  OF  SOUND.     153
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 corresponds to $=2198. It is needless now to say which alternative we must choose. Accordingly, no doubt whatever exists as to the correctness of Laplace's explanation of the excess of the observed velocity of sound over that calculated by Newton.
Now that it has been decided which of the two ratios n : q and 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 faint indications of the effect of radiation. Retaining only the first power of q, and putting n=V/jt,, _yc6 = 27rAT^1, where V=*/(kK), the velocity of propagation, we get from (11), (12) and (18),
(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 explanation of the velocity of sound has been answered, we may take 1'414 for the value of k, this being the mean of the values <|uotcd by Poisson in art. 664, which were deduced from the velocity of sound, arid are probably nearer the truth than the somewhat smaller values determined by a different process. Putting K= 1*414, V=1100, taking the square of the coefficient as a measure of the intensity, and putting N : 1 for the ratio in which the intensity is diminished while the sound travels, without divergence, over a length x, we get
Iog_10#=0-00(mr%a; .................. (20),
the units of time and space to which q and x are respectively referred being a second and a foot.
From the account of M. .Biot's experiments given by Sir John Hersehel in art. 24 of his Treatise on Sound*, it would seem that the diminution of intensity which we can by any possibility refer to radiation must be very small, especially when we remember
*  Mitcyc.loiHvdia Mc.h'opoHtuna, art. Sound.