DERIVATION OP FORMULA. 67 



The equation (5) may be written 



^'^ ^=aT + (6-a)F (6) 



In expressing the specific gravity of milk it is usual to do so 

 in lactometer degrees, which are the specific gravity multiplied 

 by 1,000 minus 1,000. 



Thus if the specific gravity be 1032, the lactometer degrees 

 are 1-032 X 1,000 — 1,000 = 32. 



Let us express lactometer degrees by the symbol G. 



Then G = 1,000 S, and, substituting this in (6), we get 



j--™ = 10a T + 10 {h - a) F. 



The specific gravity was expressed as 1 + S for ease in calcu 

 lation ; it is better, however, to substitute the symbol D in the 

 formula, which then stands as 



jy-= IIW T + IK (b - a) V 



^-.o.^^-(V)^ 



(7) 



As, by the definition above, a = and b = — ; — , we could 



•' 11 f 



calculate a formula, did we know the specific gravities of soUds 



not fat and fat, but we do not know both of these. Fleishmann 



has determined the specific ijiavity of the fat of milk to be 



\'y C 

 0'9307 at ,7^„-p', but it is impossible to determine the specific 



gravity of solids not fat in solution. ^Moreover, Fleischmaun's 

 determination of the specific gravity was made on fat in the 

 solid state, and it is possible that in milk it may have a dift'erent 

 specific gravity. 



By transforming equation (7) into the form 



" 10« " TD I a )^ T 



G 

 and making a large number of determinations of =;=;, T, and F 



in different milks, we can form each pair of results into simul- 

 taneous equations and solve them. In this way we can get 

 a large number of values for a and h, and, from the mean of 

 these, we can calculate the specific gravities of fat and soUds not 

 fat respectively. This method is not wholly free from objection. 



