4215 Dr. : F. Gv Donnan on the Relative Bates of 



/ 2 • V y - 



however, ^i<( r) 7-1 ^ then the theory leads to the 



formula 



Mass-efflux = S' (—^ 2<N V^, 



where p = density of quiescent gas in reservoir. 



Hugoniot's recalculations of Hirn's results show that S', 

 the area of the vena contracta, must be taken as a function of 

 the pressure, unless the orifice in the thin plate be provided 

 with a conical or conico-cylindrical nozzle. In the following 

 experiments S' is therefore taken as a function of the pressure; 

 but it is assumed that this function does not vary with the 

 nature of the gas which is effusing. 



In the paper referred to above Parenty has succeeded in 

 representing Hirn's results by means of the empirical formula 



\/^[ PQ -^-^0 {P0 ~ Pl) ^ 



Y =»/2a.mS\/^- 



where S = area of orifice, 



m= a coefficient varying with the nature of the orifice 



or nozzle, 

 2a= a constant varying with the nature of the gas, 

 V = volume-efflux. 

 If we imagine V plotted against p x as the latter decreases 

 from Pi=Po to P\ = (p 9 remaining constant),, it will be- 



observed that V becomes a maximum for 1 - = — , and 



Po m 

 that the maximum value is given by 



v Po 



This value is independent of p x . Parenty regards the efflux 



as "regulating itself" when pi falls to the value ( 1 \p , 



and becoming constant and equal to the above value. The 

 critical value oip 1 on the adiabatic theory is given by 



p \y-\-u 



In Parenty's formula the critical value of pi corresponds to 



\ p Q s m 



