AN EXPLANATION OF THE APPENDED TABLES. 329 



Table IV A. and IV B. serve for the calculation of total solids (t) 

 when the specific gravity (s) at 15 C. and the percentage of fat (/) 

 are known. Both tables are based on the following formula: 



In the above formula (ri) equals the specific gravity of the solids 

 not fat at 15 C. This amount, as has already been pointed out, 

 is very nearly constant. It may be worth while to calculate its 

 value in those districts in which the above formula will be used. 

 This can be done by the following formula: 



in which (s 1 ) is the specific gravity of the butter -fat at 15 C. 

 compared with water at a similar temperature. 



If 1-600734 be taken for the value of (ri), as stated in formula 

 (1), the following will be the result. Substituting for the figures 

 10()xs-100 = d: 



(3) *=1. 



and from this we obtain the following: 



*=. 833 x <- 2-22 x-^, 



and 



100C 



1000-3-75 (t-l-2xf) 



If, for example, it had been calculated that (s) = 1*0321 and 

 (/) = 3*456 per cent, from Table IV A. for 1-2 x/= 4*147 per cent, and 



from Table IV B. 2*665 x^ = 8*288 per cent; therefore (Q = 12*435 

 per cent. 



Both tables can be used for the calculation of (/), if (s) and (t) 

 are given, for from equation (3) it follows that 



If, therefore, (t) equals 12*435 and (s) 1*0321 from Table IVB., its 

 value would be 2*665x^ = 8*288. If we take this number from 



12*435, the figure 4*147 is found, a number which, by division with 

 1'2, gives the percentage of fat at 3*456 per cent. 



