300 On the Theory of Mixed Gase<r, 



equal to the sums of/? and q united to their in- 

 crements respectively ; let these sums be called 

 € and/; then ^ is to/as /) is to q, bv compo- 

 sition of proportion : in like manner we find 

 the density of A at Y to be to that of B at the 

 same point as e is tof; i. e. as /; is to q-, thence 

 it follows, that the fiuxionary mcrements of the 

 two densities have universally the given ratio 

 of /? to q ; consequently the contemporary 

 fluents, or the densities themselves have the 

 same given ratio : now what has been proved 

 of die two gases A and B may be extended to 

 any other number ; viz. the ratios of their den- 

 sities, on the same horizontal plane will be 

 given. 



The ratio of A B, &c. being found to be 

 constant, we can proceed to investigate the 

 proportions of the quantities of matter con- 

 tained in these fluids. Let D and d be the 

 densities of A and B, in the plane MKNV -, 

 also let W and w be the quantities of matter of 

 each kind, contained in the variable space 

 PMKNV ; call PV x, and the area of the 

 plane MKNV y : now the fluxion of the 

 space PMKNV is expressed by y into the 

 fluxion of X ; moreover the quantities of matter 

 in two solids are in the complicate ratios of 

 their magnitudes and densities or in that of the 

 densities only, if their magnitudes be equal ; 



