106 On the Theory of mixed Gases. 



plane MKNV y : now the fluxion of the space PMKNV 

 is expressed by y into the fluxion of x ; moreover the quan- 

 tities of matter in two soHds are in the complicate ratios of 

 their magnitudes and densities, or in that of the densities 

 only, if their magnitudes be equal ; therefore the fluxion of 

 W is to that of iv as D is to d, because the fluxionary mag- 

 nitude is common both to W and to ; but T) is to d a.s p 

 to q, a constant ratio; consequently fluxion of W is to fluxion 

 of It' as /; is to q] therefore Whas to w the same given ratio; 

 tliat is, the matter in A is to the matter in B as p is 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 pro- 

 duct of D, Y, .r, and the fluxion of x, from a well known 

 theorem in mechanics ; for the same reason r into the fluxion 

 of iv is equal to ti\e product of d, y, x, and fluxion x ; hence 

 R into fluxion of W is to r into fluxion of w as D is to d; 

 but D is to d as fluxion of W is to fluxion iv ; therefore R 

 and r are equal : consequently the centres of A and B coin- 

 cide, and the point of their coincidence is also the centre 

 of the system C, Thus it appears, that when the compo- 

 nent gases of a fluid mixture possess separate equilibria, their 

 densities are every where in a given ratio, and they have a 

 common 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. 



It is necessary to observe in this stage of the inquiry, that 

 though we admit the particles of A and B to be inelastic in 

 relation to each other, the concession must be strictly con- 

 fined to the particles themselves ; for the gases which are 

 composed of them are elastic bodies; they therefore receive 

 and couup.unicate motion according to the laws which are 

 peculiar to bodies of this description. The foregoing pro.- 

 perties of a fluid mixture, which has been supposed to be 

 duly adjusted, are now to be used in the examination of the 

 fundamental proposition of the new theory intended to ex- 

 plain the constitution of the atmogpherei According to this 

 proposition, if two gases come into contact the particles of 



which 



