»(f 



Absorption of Gases in Vacuum-Tubes. 485 



Hence 



(*-*o)/B=(l-*)*(l+|)-l. ... (7) 



Using the second hypothesis, we put 



Y=mk(dp/dt) 2 , (8) 



m being once more some constant. Then we get 

 dp\ 2 _ (C-fo)f 

 P ' 



^ = -m^*(C-Zp)-i, .... (9) 



the negative ^ sign being used because the quantity dpjdt is 

 clearly negative. 

 Again put 



lp/G = x, (6) 



and we deduce 



dt m*CI !,-, N x 



_ = ___^ (1 _ A , ) - 1 .... (10) 



This cannot be integrated except by first expanding in a 

 power series in#, and then integrating each term separately. 

 Since x is always less than unity this is permissible. We 

 have 



m*Cf x / 1 "1.5 2 ' \ . '_ 



Hence 



a / t>/ s/1 1 ^' 1 • 5 «r 2 , \ 



A', B' being some constants. 



Again, if t is the time when the whole of the gas in the 

 tube has been absorbed, we get 



t = A, 

 and therefore 



B' V3 + 45 + 4.8 7 + "7 ' ' ^ 



The curves given by the equations (7) and (12) have been 



