E fusion of Argon , Helium, and some other Gases. 445 



is positive. Consider next the region where the efflux is 

 independent of the back-pressure. 

 From the equation 



y-l\po pj loW y / 



we obtain 



where the laws of the ideal gas are assumed, and £ = k. To 



obtain the value of p at the vena contracta, it is necessary to 

 differentiate with respect to p and equate to zero. This leads 

 to the equation in p : — 



^[^ :(7+ l)^] + KOB^p=^-.i]-0 s 



This equation is unfortunately not directly solvable; but its 

 actual solution is unnecessary for the present purpose. The 

 value of p given by it when substituted in the right-hand 

 member of the preceding equation gives qp at the vena 

 contracta, and this multiplied by the sectional area S' of the 

 jet at that point gives the mass-efflux. From the above it is 

 clear that in this case too the sign of the correction-term 



depends on K and the expression (— ) — 1 . As before, 



we find that this expression is positive, since — f >. 1, where 



p' ', p' denote the pressure and density at the vena contracta. 

 The final result may be stated as follows: — "A gas will effuse 

 more rapidly or more slowly than an ideal gas of equal density 

 according as K is positive or negative." 



Now Joule and Thomson found K to be positive for all 

 gases, with the exception perhaps of hydrogen. For hydrogen 

 K was very small and its sign rather uncertain. Accordingly 

 most gases will effuse in some degree faster than the usual 

 theory of efflux would indicate. Now helium * is even more 

 " perfect " than hydrogen. It is therefore just possible that 

 for helium K is negative, in which case helium would effuse 

 somewhat more slowly than the ordinary theory would indicate. 



How far these effects would compensate each other, and in 

 particular what the relative importance of the correction-term 

 is, I have not yet investigated, but hope to do so in a subsequent 

 communication. 



* This has been shown by Professor Ramsay and Dr. Travers in a set 

 of experiments (not yet published) on the compressibility of helium, 



