85 
first place, the viscosity or internal friction of the air must cause a dimin- 
ution of the vibrational energy and the production of heat. Again, in 
each condensed part of a sound wave heat is produced by the condensa- 
_ tion; this causes a rise of temperature and an immediate tendency for 
radiation of heat and conduction of heat to take place. Similarly a fall 
of temperature takes place in the rarefied part of the wave with a similar 
tendency to radiation and conduction. Now, the greater the extent of this 
radiation and conduction, the less will be the amount of vibrational 
energy handed on and consequently the less the intensity of the sound. 
In addition to spherical spreading, viscosity, conduction and radiation, 
two other sources of diminution of intensity might be mentioned, namely, 
atmospheric refraction and lack of atmospheric homogeneity; but these 
two latter influences are only occasional or local, while the former are 
invariable and universal. 
Several eminent physicists have given theoretical discussions of the 
effects of viscosity, radiation or conduction separately or of two of them 
simultaneously. Thus Stokes, in 1845, studied the effect of viscosity and 
deduced numerical results, and in 1851 he found a formula for the effect 
of radiation, but calculation from this result is still impossible because 
of our total ignorance of the rate of radiation of a gas. Rayleigh has 
applied Stokes’ method to estimate the effect of conduction. These in- 
vestigations referred to plain waves only. Kirchoff, in 1868, discussed 
the effect of conduction and viscosity together on plane waves, and indi- 
cated the result for spherical waves also. Brunhes has recently examined 
the effect of conduction on plane waves, obtaining a result in accord with 
those of Kirchoff and Rayleigh. 
In order to deduce any intelligible results from the observations, I 
have made it necessary to either assume or establish a law of diminution 
of intensity in spherical waves, taking account of viscosity, radiation, con- 
duction and spherical spreading simultaneously. As considerable doubt 
might attach to a general formula framed by the superposing the formule 
already obtained for the separate effects enumerated, it seemed advisable 
to undertake a new theoretical investigation for spherical waves affected 
by viscosity, radiation and conduction. (This discussion is here omitted, 
but will be printed in full elsewhere.) The conclusion which we arrive at 
is that the intensity varies as 
— uy 
e “mr 
9 
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