m 



and Conduction, ami on the Propagation of Sound. 309 



value in 7 times the interval of time required by a mass of 

 air to cool to the same fraction of its original excess of 

 temperature. " There appear to be no data by which the 

 latter interval can be fixed with any approach to precision ; 

 but if we take it at one minute, the conclusion is that sound 

 would be propagated for (seven) minutes, or travel over about 

 (80) miles, without very serious loss from this cause 9> *. We 

 shall presently return to the consideration of the probable 

 value of q. 



Besides radiation there is also to be considered the influence 

 of conductivity in causing transfer of heat, and further there 

 are the effects of viscosity. The problems thus suggested 

 have been solved by Stokes and Kirchhofff. If the law of 

 propagation be 



u==e -m'x cos (nt—x/a), . . . . . (2) 

 then 



'=£{t^}' ^ 



in which the frequency of vibration is n/"27r, juJ is the kine- 

 matic viscosity, and v the thermometric conductivity. In 

 c.G.s. measure we may take /// = *14, v=\26, so that 



To take a particular case, let the frequency be 256 ; then 

 since a = 33200, we find for the time of propagation during 

 which the amplitude diminishes in the ratio of e : 1 , 



(m'a) =3560 seconds. 



Accordingly it is only very high sounds whose propaga- 

 tion can be appreciably influenced by viscosity and conduc- 

 tivity. 



If we combine the effects of radiation with those of viscosity 



and conduction, we have as the factor of attenuation 



i 



g— (m+m^x 



where m + m , = '14:(q/a) + '12 (n?/a?) (4) 



In actual observations of sound we must expect the 

 intensity to fall off in accordance with the law of inverse 

 squares of distances. A very little experience of moderately 

 distant sounds shows that in fact the intensity is in a high 

 degree uncertain. These discrepancies are attributable to 



* Proc. Roy. Inst., April 9, 1879. 



t Pogg. Ann. vol. cxxxiv. p. 177, 1868 ; Theory of Sound, 2nd ed., § 348. 



