5 1 6 Hydrostatics. 



to find the specific gravity of a compound, by means of that of 

 each of the ingredients ; and the rule which has generally been 

 given, is to take the arithmetical mean of the specific gravities 

 of the ingredients. 



It will be observed that, the greater the weight of a body, 

 other things being the same, the greater the specific gravity ; also 

 that the less the bulk, other things being the same, the greater 

 the specific gravity ; that is, the specific gravity of one body is 

 to that of another, as the weight of the first divided by its bulk, 

 is to the weight of the second divided by its bulk, and hence the 

 mean specific gravity of the two will be found by dividing the 

 sum of the weights by the sum of the bulks. Thus, 



from which we obtain, 



b =^, and &' = ^- ; 



j >V 



also, 



7, _l- A/ w J_ w ' W& +&' S 



+ ' 6 ~"S + ^ 5S 



Hence, calling M the mean specific gravity sought, from the 

 equation M = , j~ , above sho 

 reasoning, we obtain, by substitution, 



equation M = , j~ , above shown to be true, by general 



M w S 1 a.' S = 



i , 



S-+ ' S 



Let gold, for example, of a specific gravity 19,36, be alloyed 

 in equal weights with copper of a specific gravity 8,87, we shall 

 have 



. (1 + 1) 19,36 8,87 _ 2 X 171,7232 

 ~~8^7 -f- 19,36 28,23 " 



whereas the arithmetical mean is 



