144 ANALYSIS OF MILK. 



For the calculation of the results the following formulae are 

 used : — 



1— ?/ = (l— a:)'-' for butyric acid, or log {l—y) = 2-l log (1— a;) ; 

 l—y = ll—x)^'^' for propionic acid, or log (1— j/) = l-18 log (1— x) ; 



and 1— 2/ = (l— .r)* for acetic acid, or 3 log (l—y) = 2 log (1— a:). 



y = quantity of acid distilled ; total quantity = 1. 

 X = volume of liquid distilled ; total quantity = 1. 



For each fraction calculate the proportion of each of the 

 acids which would "distil, and calculate the ratios of butyric to 

 acetic, and butyric to propionic acid, which correspond to the 

 proportion actually distilled. The ratios from first and last 

 fractions are liable to be slightly erroneous, the first because a 

 small amount of a very volatile acid, as carbonic, would appear 

 in this fraction, and the last because experimental error is greatly 

 magnified ; but usually the other six ratios are practically 

 constant for either butyric and acetic acids, or butyric and 

 propionic acids. 



The distillation of the third of a third is undertaken in order 

 to decide definitely the composition of the mixture. From the 

 formulae above, the proportions which would distil, when one- 

 third of one-third is collected, are : — 



For butyric acid, 0-3285 



For propionic acid, ..... 0-1445 

 For acetic acid, ..... 0'061 



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. 



An example, where the acids present are acetic and butyric, 

 is given in Table XV. 



The quantity distilled in J of J was 0"193. 



The figure calculated for a mixture of 0"495 molecule of butyric 

 to 0'505 molecule of acetic was 0"192. 



The ratio of butyric acid in the second distillate should be 

 0-83. 



Corrections for Solids not Fat in Sour Mills. — When it is desired 

 to ascertain from the analysis of a sour milk the original com- 

 position of the sample, the following constituents should be 

 determined ; fat and solids not fat by the maceration method, 

 alcohol, ammonia, acidity, and aldehyde figure of the milk, volatile 

 acidity by the Government Laboratory method, and aldehyde 

 figure of the neutralised solution obtained in this method. If 

 the volatile acidity is high, the proportions of butyric, propionic. 



