Mass of Air confined by Walls at Constant Temperature, 315 



radiation or conduction, it compresses the remaining parts, 

 and these in their turn become heated in accordance with the 

 laws of gases. To take account of this effect a special 

 investigation is necessary. 



But although the fixity of the boundary does not suffice to 

 prevent local expansions and contractions and consequent 

 motions of the gas, we may nevertheless neglect the inertia of 

 these motions since they are very slow in comparison with 

 the free oscillations of the mass regarded as a resonator. 

 Accordingly the pressure, although variable with time, may 

 be treated as uniform at any one moment throughout the mass. 



In the usual notation *, if .9 be the condensation and 6 the 

 excess of temperature, the pressure p is given by 



p = kp(l + s + aO). . (1) 



The effect of a small sudden condensation s is to produce an 

 elevation of temperature, which may be denoted by /3s. Let 

 rfQ be the quantity of heat entering the element of volume in 

 the time dt, measured by the rise of temperature which it 

 would produce, if there were no " condensation/' Then 



d0 - R ds j. d $ i'9\ 



-Jt-Pd; + it* {Z) 



and, if the passage of dQ be the result of radiation and con- 

 duction, we have 



§-**-&. .... • (3) 



In (3) v represents the " thermometric conductivity h found 

 by dividing the conductivity by the thermal capacity of the 

 gas (per unit volume), at constant volume. Its value for air 

 at 0° and atmospheric pressure may be taken to be *26 

 cm 2 ./sec. Also q represents the radiation, supposed to depend 

 only upon the excess of temperature of the gas over that of 

 the enclosure. 



If</Q=0, 0^/38, and in (1) 



p=A/){l + (l + ^}; 

 so that 



i + «£=y, (4) 



where y is the well-known ratio of specific heats, whose value 

 for air and several other gases is very nearly 1*41. 

 In general from (2) and (3) 



i+4***'-* • • • • •?> 



* 



'Theory of Sound,' §247. 



