428 Dr. F. G. Donnan on the Relative Bates of 



where x is a function of p . Equating these values and 

 integrating, we obtain for the time t, during which the 

 pressure in the reservoir sinks from pj to pj', the equation 



1 CP°'<l>+po<P 



ocp Q 



t = —^ H-U2Z. d Po . 



S/( 7 )VRT.J, « 



If now we measure the times ^ and t 2 for two different 

 gases, in the same apparatus, at the same temperature, and 

 between exactly the same limits of pressure, we obtain the 

 very simple formula 



h _ /fa) /(h 



h /(yOV p' 



■2 /fa) v p 2 

 Employing Parenty's elliptical formula, we obtain 



where 



h = <ftfa) h\ 



«r) = l -(^l) A - 



Suppose now that y l = 1*408 and y 2 = l'67. Then we 

 obtain 



y = 1-06 \/- (Hugoniot-Reynolds), 



^ = l-084-y ^ (Parentij). 

 These results indicate a marked deviation from the simple 

 "isothermal" formula T = \/ in cases where two gases 



are compared which possess very different values for y. It 

 accordingly becomes a matter of great interest to measure the 

 relative effusion-rates of two such gases as argon and oxygen, 

 which approximate very closely in their behaviour at moderate 

 temperatures and pressures to the ideal gas and yet possess 

 very different values of y. The theory indicates that argon 

 ought to effuse, when compared with oxygen, considerably 

 /'aster than would be calculated from the densities alone. 



Method of Measurement and Description of Apparatus. 



It will be seen that the theory sketched in the foregoing 

 section only leads to simple comparison-formulae for the case 

 of effusion in which the back-pressure is small in comparison 

 with the pressure in the gas-reservoir. The following expe- 



i 



