64 ANALYSIS OF MILK. 



not fat, and lowered by the fat. This fact is not only true quali- 

 tatively, but also, as the following demonstration will show, 

 quantitatively. 



By our definition that specific gravity (S) is the weight (W) 

 of the unit volume (V), we get the equation — 



W 

 S=^ . . . . . (1) 



Let us suppose we have a mixture (having the specific gravity 

 S) of two substances, A and B, of differing specific gravities Sa 

 and Sb. 



Let us suppose that the respective weights are A and B, and 

 let A + B = 100. 



Then by (1) 



Volume of A = =-, volume of B = ,— , and volume of mixture = 15? 



Then 



S ^A S3 S^ Sg 



100 A(Sb-S^) 100 

 - + - 



S S^Sg Sg 



100100^^/83-8 



B ' 



S S^ \ s.s 





Now in the same way 



s=s.+BS( .;|— : 



^ \ 100 bj 



As both Sa and Sb are constants, we may write 



S = Sa + BS X Kb I „ ^ t^ ^ . 

 and S = Sb + AS X Ka i ^^ '"''^ ^^^ ^''"^^ constants . . (2) 



Now, as A + B = 100, A is the percentage by weight of this 

 substance ; and as 100 x S expresses the total number of grammes 

 in 100 c.c. of the mixture, AS is the number of grammes of this 

 substance in 100 c.c. 



From the equations above given we can deduce the law that 

 " if two substances of differing specific gravity be mixed, the 

 specific gravity of the mixture will be equal to the specific gravity 



