Mass of Air confined by Walls at Constant Temperature. 317 



Thus if <£) denote the initial value of 6 as a function of 

 x, y, z, and O its mean value, the complete solution may be 

 written 



0=0 o «-8'+(0-0 o )<r-«'/v ] 



k . . . (14) 



s = « a (@_0 o ) £? -^/y J 



giving 



* + «0=a@ o <r-8< (15) 



It is on (15) that the variable part of the pressure depends. 



When the conductivity v is finite, the solutions are less 

 simple and involve the form of the vessel in which the gas is 

 contained. As a first example we may take the case of gas 

 bounded by two parallel planes perpendicular to x, the 

 temperature and condensation being even functions of x 

 measured from the mid-plane. In this case \J" 2 = a n ldx 2 , and 

 we get 



= C-f- Acosma?, -s/« = D + Acosw^, . . (16) 



S + a0 = «C-aD = H (17) 



By (9), (17) 



C-M!, D=i!LpM v . . . (18^ 



hy — q a [liy — q) 



There remain two conditions to be satisfied. The first is 

 simply that = when x = + «, 2a being the distance between 

 the walls. This gives 



C + Acos?na = (19) 



The remaining condition is given by the consideration that 

 the mean value of s, proportional to \sdx, must vanish. 



Accordingly 



ma.D+ sin ma. A = (20) 



From (18), (19), (20) we have as the equation for the 

 admissible values of m, 



tan ma ctfiq — vm 2 



ma a(3{q + vm i y 



reducing for the case of evanescent q to 

 tan ma 1 



ma aj3 



The general solution may be expressed in the series 



Phil. Mag. S. 5. Yol. 47. No 286. March 1899. 



(21) 



(22) 



(23) 



