On tht Theory of Mixeil 6ase.f. SOI 



therefore the fluxion of W is to that of to as 

 D is Xo d ; because the fluxionary magnitude 

 is common both to W and w ; but D is to ^as 

 p to <7, a constant ratio ; consequently fluxion 

 of W is to fluxion of to as p\s\.oq ; therefore 

 W has to IV the same given ratio ; that is, the 

 matter in A is to the matter in B as pis to q. 

 In the next place let R and r be the distances 

 of the centres of gravity of A and B, from the 

 point P, taken in the line PI : then R into the 

 fluxion of W is equal to the product of D, Y, r, 

 and the fluxion of .r, from a well known 

 theorem in mechanics ; for the same reason r 

 into the fluxion of w is equal to the product of 



. rf, ?y, .r and fluxion .r ; hence R into fluxion of 

 W is to r into fluxion olw ; as D is to d ; but 

 D is to r/, as fluxion of W is to fluxion w ; 

 therefore R and r are equal : consequently the 

 centres of gravity of A and B coincide, and 



# the point of their coincidence is also the centre 

 of the system C. Thus it appears, that when 

 the component gases of a fluid mixture possess 

 separate equilibria, their densities are every 

 where in a given ratio ; and they have a com- 

 mon centre of gravity : the converse of which 

 is equally true ; viz. if their densities be not 

 every where in a given ratio, and if they have 

 not a common centre of gravity, they do not 

 possess separate equilibria. 



