[ 1« ] 
X. On the Thermally exeited Vibrations of an Atmosphere. 
By C. V. Burton, D.Scr 
IN Lord Rayleigh's paper " On the Vibrations o£ an Atmo- 
sphere," f the free vibrations of a gaseous mass in certain 
ideal circumstances are investigated. In the present note an 
attempt is made to carry the investigation a step further by 
considering the vibrations which in like circumstances arise 
from fluctuating thermal conditions ; the problem presented 
in each case being the determination of the pressure as a 
function of time and coordinates when the thermal conditions 
are specified. 
Equations of a gas subject to small fluctuations of thermal 
state, but otherwise at rest. 
It will be convenient to prefix the symbol 8 to indicate the 
disturbances of the various quantities involved, as arising 
from the given small thermal fluctuations. Thus 
p is the density at any point when there is no disturbance ; 
p + &p the density when disturbances are present ; 
T, T + 8T the undisturbed and disturbed (absolute) tem- 
perature at any point ; 
p, p + 8p pressure ; 
u, v } w are the velocity-components at any point in the 
disturbed condition, and vanish when disturbances are 
absent ; 
R as usual stands for p/pT, and is an absolute constant. 
Thus RT —pip = (velocity of sound) 2 when Boyle's law is 
applicable „ , . . 
= cr suppose (I) 
The equation of continuity is 
3* ~3i + ~ ~3.y 3l - U -W 
where "dfdt is time-differentiation at a point fixed in space. 
That is, to a first order, 
a$> 3^0 B(££) a^> = _ _ 
Ot dd' oy 02 v J 
* Coniniimicated by tlie Author. 
t ' Collected Papers/ vol. iii. p. 335 ; Phil. Mag. vol. xxix. 1890, 
pp. L73-180. 
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