Effusion of Argon, Helium, and some other Gases. £21 



Hence, to make both theories agree in the critical value of/?!, 

 we have 



-4-fcfr) 



y_ 



According to Pareniy, therefore, we have, for the volume- 

 efflux in the region where p ± < the critical value, the formula 



^=-s[i-(^ 1 )-]v/' 







If we put 



v+i 



(^l>-V=/(7), 



we can also write, using the adiabatic theory 



dt ^ /w vET' 



It remains now to consider the application of these results 

 to the conditions under which the following experiments were 

 carried out. The first remark to make is that p was not kept 

 constant, but decreased considerably during the course of an 

 experiment. If, however, we neglect acceleration-terms we 

 may consider the equations as giving the instantaneous efflux 

 at any moment, and integrate between the limits of pressure 

 corresponding to any actual experiment. Secondly, the 

 dimensions of the apparatus were so chosen that the back- 

 pressure p l in the receiver (which was initially vacuous) never 

 attained its critical value, which is about one-half of p . 

 Accordingly we have to apply either the equation 



Mass-efflux = #S( — y \ 2{7 ~ iy y/yp po (Hugoniot-Reynolds) , 

 or the equation 

 Mass-efflux = «iSN — (— —. V -i ^/2g?np p (Parenty). 



The progress of the effusion was determined by means of a 

 closed mercury barometer-gauge attached to the reservoir out 

 of which the gas was effusing ; so that the volume of the gas- 

 reservoir was not constant, but a function of the pressure p 

 of the gas in the reservoir at any moment. Call this $(/? ). 

 Accordingly the mass-efflux is given by 



