On the Theory of mixed Gases. 105 



disposition of the heterogeneous particles be first established; 

 so that the former requisite of the theory is entirely dependent 

 on the latter. After having acquired a distinct idea of a 

 fluid mixture, composed of gases possessing separate equili- 

 bria, we come in the next place to investigate the mechani- 

 cal properties of such a compound ; in the prosecution of 

 which inquiry the comparative densities of the constituent 

 lluids nmst be first determined in a horizontal plane, the 

 situation of which is given in the common space. 



Let the figure PMINKV (Plate I. fig. 2.*) represent this 

 space, in w hich M VN K is the given plane. Now since every 

 point of this plane may be supposed to be at an equal distance 

 from the earth's centre, the density of every homogeneous gas 

 supported bv it will be the same in all parts of it. Let the con- 

 stituent fluids be denominated A and B ; also let C denote the 

 compound ; moreover let the densities of A and B, at P, ho. p 

 and q; let PX and XY be two equal evanescent parts of 

 the line PV. Now, seeing the pressure acting upon an 

 clastic fluid is as the density of it, the fluxionary increments 

 of p and q are as these quantities ; but the densities of A 

 and B, in the point X, are equal to the sums of p and q united 

 to their incfements respectively : let these sums be called e 

 and f; then e is to y as p is to q, by composition of pro- 

 portion : in like manner we find the density of A at Y to 

 be to that of B at the same point as e is to J'\ i. e. as p is 

 to q ; thence it follows, that the fluxionary increments of 

 the two densities have universally the given ratio oi p to q ; 

 coi>sequently the contemporary fluents, or the densities them- 

 selves, have the same given ratio : now what has been proved 

 of the two gases A and B may be extended to any other 

 number, viz. the ratios of their densities on the same hori- 

 zontal plane will be given. 



The ratio of A, B, &cc. being found to be constant, we 

 can proceed to investigate the proportions of the quantities 

 of matter contained in these fluids. Let D and d be the 

 densities of A and B in the plane M KN V ; also let W and 

 tv be the quantities of niatter of each kind contained in the 

 variable space PMKNV; call PV x, and the area of the 



• Given in our 'ast numhe.-. 



plane 



