8

the specific gravities of the two bodies, is to the differencebetween the specific gravities of the compound and of theother.

For since (lG), M : M' :: cr — S' : S — a-

.\(M+M' = )P : M :: S - S' : a-S',

and P : M' :: S - S' : S-cr.

18. If the weights and specific gravities of two bodiesbe given ; to determine the specific gravity of the compoundformed by their mixture.

Let W and W' represent the weights, and -S' and S' thespecific gravities of the simples, and a that of the compound;then as in Art. 15, it may be shewn that

W W_ W+ W’

~S + S' ~ a ;

(FF+HO.ss'

and <r - WS’+W'S '

19 . Coe. 1 . If equal weights be mixed, a =

2SS 1S + S r

S-\- s'

but if equal magnitudes (15), cr = ---, being in the first

case an harmonic, in the second an arithmetic mean betweenS and S’.

20. Coe. 2. To determine the weights of each of thebodies in the mixture, the specific gravities of the simples,and the weight of the compound being known.

From (18), it appears that WS' .(S— cr) = IT'S.(cr — S');

.-. IT : IT' :: S . (a - S') : S'.(S-<r),and IT : W+W :: S.(a-S'): cr.(S-S'),also IT': IT+ W’ :: S'. (S - a) : cr . (S-S').

21. It has here been taken for granted, that the magni-tude of the compound is exactly equal to the sum of the