1893.J 



On the Densities of the Principal Gases. 



149 



Note A. 



On the Establishment of Equilibrium of Pressure in Two Vessels con- 

 nected by a Constricted Channel. 



It may be worth while to give explicitly the theory of this process, 

 supposing that the difference of pressures is small throughout, and 

 that the capacity of the channel may bo neglected. If v u p x denote 

 the volume and pressure of the gas in the first vessel at time t ; v 2 , p 2 

 the corresponding quantities for the second vessel, we have 



v x dp^dt+.c (pi— p 2 ) = 0, 

 v 2 dp 2 jdt + c (pz—pO = 0, 



where c is a constant which we may regard as the conductivity of the 

 channel. In these equations inertia is neglected, only resistances of 

 a viscous nature being regarded, as amply suffices for the practical 

 problem. From the above we may at once deduce 



^=£l) + (JL + _<L) (j , i _ j32) = 0; 



at \Vi v 2 ] 

 showing that (^1—^2) varies as e - ^, where 



c , e 1 

 3 = — + — = -, 



#1 V 2 T 



if t be the time in which the difference of pressures is reduced in 

 the ratio of e : 1. 



Let us now apply this result (a) to the case where the globe of 

 volume Vi communicates with the atmosphere, (b) to the case where 

 the globe is connected with a manometer of relatively small volume v 2 . 

 For (a) we have — 



i/t = chi, 



and for (b) l/r = cjv 2 ; 



so that t/t = v 1 /v 2 . 



For such a manometer as is described in the text, the ratio v x /v 2 is 

 at least as high as 30 ; and in this proportion is diminished the time 

 required for the establishment of equilibrium up to any standard of 

 perfection that may be fixed upon. 



