86 FORMULAE FOE CALCULATIONS. 



From the laws expressed by equations (2) 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 

 multiple of the number of grammes per 100 c.c. ; for if we suppose 

 that the substance A is water, S# will equal 1, and equation (2) 

 can then be written 



S = 1 + BS x K H . 



which is practically equation (3). 



In order to deduce a formula expressing the relation between 

 specific gravity and percentage by weight of fat and solids not 

 fat, let us call the specific gravity (for convenience) 1 -f- S, the 

 percentage by weight of fat F, and of solids not fat N. 



Then the number of grammes of fat per 100 c.c. will be 

 F X (1 + S) and of solids not fat N X (1 -f S). 



The weight of the water in 100 c.c. is then 



100 X (1 + S) - N x (1 + S) - F x (1 + S) grammes ; 

 and its volume 100 x (1 + S) - N x (1 + S) - F x (1 + S) c.c. 



The volume of fat and solids not fat in 100 c.c. is therefore 

 100 - [100 x (1 + S) - N x (1 -f S) - F x (1 + S)] c.c. 



which equals 



N x (1 + S) + F x (1 + S) - 100 S ..... (4) 



Let us assume that the specific gravity of fat is / and of solids 

 not fat n. 



T? \/ (1 I Q\ 



Then the volume of fat in 100 c.c. is - -- and of solids 



. tt. N X (1 + S) ., , 

 not fat - - ; therefore 



or 



or 100 S = N x (1 + S) - -f F x (1 + S) 



Now, as n and / are constant, we may write for (- - ), a ; 

 /f 1\ \ n / 



and for 



Then the equation stands 



. ...... (5) 



It is usual, however, to estimate total solids (T) and fat in 

 an analysis. 



T = N + F, and, therefore, N = T - F. 



