00 FORMULAE FOR CALCULATIONS. 



as, unless there is a considerable difference between the figures 

 actually determined, the figures from which a and 6 are calcu- 

 lated are so small as to be affected greatly by experimental 

 error ; while, if the difference be large (as in the case of analyses 

 of cream and skim milk), it is found that the experimental error 

 is also increased. For this reason, and also for the reason that 

 the specific gravity of fat and solids not fat are themselves liable 

 to slight variations, it is necessary to deduce the formula from 

 a great many determinations, which means much labour in 

 calculating. 



In order to ascertain the specific gravities of fat and solids 

 not fat in milk, the author has calculated their value from over 

 200 analyses made by the most exact methods at his command, 

 and finds the following figures : 



Specific gravity of fat, . . . .0-93 

 solids not fat, . . . 1-616 



Leonard has calculated by the method of least squares from 

 a large series of results the factors 0-931 and 1-613, which are 

 practically identical with the above. 



It is seen that the author's figure, as \vell as Leonard's, calcu- 

 lated from actual analyses, agrees with Fleischmann's determina- 

 tion of the specific gravity of fat. 



As the specific gravity of milk does not vary much, it will not 



c* c* 



make an appreciable error if, instead of -=r, the expression 



JJ 1 *Uo 20 



be used ; this form of calculation is much easier. 



The idea of deducing a relation between specific gravity, fat, 

 and total solids appears to have arisen with Behrend and Morgen, 

 who published a table. Shortly afterwards Clauznitzer and 

 Mayer, and Hehner published formulae, but as they were founded 

 on inaccurate data, they are now abandoned. 



Fleischmann and Morgen next published a formula in which the 

 specific gravity of fat was assumed to be 0-94 ; this was corrected 

 by Fleischmann after his determination of the specific gravity of 

 fat as 0-93. His formula is 



T = 0-2665~+ 1-2F. 



Hehner and the author deduced the formula 

 T = 0-254 G-f 1-164F.* 



This is in the less scientifically correct, but more convenient 

 form ; as it was found that milk differing appreciably in specific 



* In the original paper a slight correction for skim milks was included 

 in the formula ; this has now been abandoned. 



