196 THE ANALYSIS OF MILK PRODUCTS. 



which would distil, when one-third of one-third is collected, 



are : 



For butyric acid, 0'325 



For pro pionic acid, . . . . .0-163 

 For acetic acid, 0-063 



Thus, a mixture of butyric and propionic acids in equal pro- 

 portions should yield approximately a 2 : 1 mixture in the dis- 

 tillate, while a mixture of butyric and acetic in equal proportions 

 would yield a 5 : 1 mixture. It is even possible to deduce the 

 relative proportions of a mixture of the three acids. 



Methods of Calculation. If two acids only are present, the 

 equation for calculating the results is aA -f- 0B = R. 



a = Fraction of acid (A) from Table XXXIV. 

 & = (B) 



R = actually distilled. 



A = (A) present. 



B= (B) 



p JL 



This simplifies to A = =- and nine values are obtained of 



a 



the ratio of the nine distillations (B = 1 A). If three acids are 

 present, the equation becomes aA -}- &B -f- pP = R, which sim- 

 plifies to B -f P^ = -=- , which gives nine simultaneous 



b -a b a 



equations to be solved ; and the problem is how to obtain mean 

 values for P and B (and also for A, which is 1 P B) with the 

 least labour and greatest accuracy. 



The tables below give the difference between each pair of acids 

 for each 10 c.c. distilled out of 100 c.c., together with difference 

 factors for calculating small differences in volume. These may 



be used for calculating the values of \ and = -. 



a b a 



To facilitate calculation still more a table of the values of ~ 



a 



has also been calculated. The values of ^-- - and -=- are 



then tabulated. 



JY\ _,^ ft T? , /y 



The values of %- and -= for 90 c.c. are subtracted from 



b a b a 



those for 10 c.c. (1) ; those for 80 c.c. subtracted from those for 

 20 c.c. (2) ; those for 70 c.c. from those for 30 c.c. (3) ; those 

 for 60 c.c. from those for 40 c.c. (4). Then the values for 

 50 c.c. are subtracted successively from those for 40, .30, and - 

 20, and the sum of these three last called (5). The sum of 



2(1) + 3(2) + 2(3) -f- (4) + f(5) for =-^ - divided by the similar 



