312 Hydrostatics. 



Spirits, on the other hand, are lighter than the liquids with 

 which they are adulterated, so that, in each case, the specific 

 gravity becomes the test of purity. We have, hence, a curious 

 and important problem, namely, knowing the specific gravity of 

 the two ingredients that compose a compound, and the specific 

 gravity of the compound, to find the proportion of the ingredi- 

 ents. This proportion may be estimated by weight, as is usually 

 the case with respect to metals, or by measure, which is the com- 

 mon method where liquids are concerned. The weight of the in- 

 gredients being sought, we put x for that of the denser, and y for 

 that of the rarer or lighter, c representing that of the compound, 

 and S, S', S", denoting their specific gravities respectively. We 

 have x -f y = c ; also, on the supposition that the bulk of the 

 compound is equal to that of the constituent parts, the specific 

 gravity would be the same whether the compound were consid- 

 ered as one entire mass, or as composed of two distinct parts, and 

 the weight divided by t>he specific gravity in the one case would 

 be equal to the weight divided by the specific gravity in the 

 other, that is, 



To find #, we substitute in this equation the value of y deduced 

 from the first, namely, y = c #, which gives 



x c x c 

 ~S * S 77 " " S"' 



or 



x (S< S) c_ jSc _ _ (S 1 S") 



~~ r ~ ~ " ' ~ """" C ' 



(S' S") _ (S f S") S _ (S" S')S 

 ~S^ 7r ~ " (S' S) S" C '' (SS'}S" 



In like manner, we have 



_ (S . S") S' 

 - ( S S') S" 



