SPECIFIC GRAVITY AND PERCENTAGE OF SOLIDS. 33 



three factors is the same for all kinds of milk, and whether it holds 

 universally true and is practically useful, and can be stated in a 

 definite form. If these three factors be respectively denoted by 

 the letters s, /, and t, the ascertained specific gravity of the milk-fat 

 by the letter <r, and the unknown specific gravity of the " solids not 

 fat" by the letter n, the value of s will be easily found by the 



following formula: 



,,x _ lOOxnxo- 



V ~ 



n x <r(100 - 



If n were like a- a constant quantity, equation (1) would give the 

 desired universally applicable ratio. Whether n is constant or not 

 can be easily discovered. It is only necessary to ascertain the values 

 of s, t, and / accurately, for a large number of different milk samples, 

 in order to calculate the corresponding value of the letters in 

 equation (1). 



(2)n = _ xcr(*-/) 



100 x <r - s x <r(100 -t)-sxf 



If the above formula be worked out, the surprising result is 

 obtained that n is found to have always approximately the same 

 value. The author has obtained for a large number of determinations 

 in the North of Germany an average value for n of 1 '600734. 



From this it may be proved that the specific gravity of the 

 " solids not fat " is approximately a constant number, and that it is 

 possible, therefore, to write down equations for each of the above- 

 mentioned three factors, provided the other two are known. 



If in equation (1) we take the value of 1/6 for n, and the known 

 value '93 for <r, the following formulae are obtained: 



(4) /= -833 xt- 2-22 x 



and 



1000 



s 

 100 xs- 100 



(5) = 



1000 -3-75(t- 1-2 x/) 



The value of n is not, strictly speaking, constant, but is only approxi- 

 mately so. It varies within very narrow limits. In countries in which 

 the average composition of cows' milk materially differs from that found 

 in Germany, or in parts of Germany where the conditions are exceptional, 

 the average value for n may possibly vary to a small extent, but only so 

 far as to permit of the above equations (3) (4) and (5) always yielding 



( M 175 ) C 



