DERIVATIOX OF FORMULA. 



65 



of one of the substances plus the number of grammes of the other 

 per 100 CO. of the mixture multiplied by a constant factor." 



Regarding milk as a mixture of fat and a solution of solids 

 not fat in water, we can say that the specific gravity of a milk 

 is equal to the specific gravity of the solution of solids not fat 

 plus the number of grammes of fat per 100 c.c. multiplied by 

 a constant. 



In the solution of solids not fat we have in 100 c.c. of it x 

 grammes of solids not fat ; let us assume that their density is y. 



Then x grammes will occupy a volume - Let the specific gravity 



of the solution be S. The 100 c.c. weigh 100 S grammes, and 

 the water in this weighs 100 S — x grammes ; it also measures 



loo c.c. Now, as the specific gravity of water is 1, 



100 S - a; = 100 - "^ 



y 



100 S = 100 + a: - - 



S = 1 + 



.y 1 



"" I'JU y 



(3) 



Now, 



1007 



is a constant, provided that y remains constant. 



Putting the equation into words we find " tliat the specific gra\ it y 

 of a solution of solids not fat is equal to 1 pi 11.^ the number ni 

 grammes of solids not fat in 100 c.c. multiplied by a constant." 

 It is known, however, that the specific gravity of sul)stanro> in 

 solution is not quite constant, but varies slightly with dilution. 



The following figures will show that in milk the law just enu- 

 merated holds good within the limits of experimental error. .\ 

 poor skim milk was diluted with water, and the total solids and 

 specific gravity at 15-1)!)'' estimated : — 



SpociflL- Gravity. 



1 ■o:».".44 

 1 i):i:u:i 

 1-03170 

 1 0-20.'>0 

 1 -0^829 

 1 02439 



-00.3688 

 0-003093 

 0-00:«94 

 0-0036S4 

 0-003t)90 

 00036S8 



From the laws expressed by equations (i) and (3) we see that 

 the specific gravity of an aqueous liquid containing a substance 

 in solution or in admixture can be expressed equally as a. direct 



