156 THE ESTIMATION OF SUGARS. 



Calling the reading of the solution obtained from 100 c.c. x, 

 and that obtained from 200 c.c. y, the true percentage of milk. 



sugar is -.-. - - . 

 4{x - y) 



The double dilution does away with any correction for the 

 volume of the precipitated fat and protein. The rationale of 

 the process lies in the fact that, while the percentage of milk- 

 sugar and the volume of the precipitate are constant, the total 

 volume varies. 



Let m be the percentage of milk-sugar, and v the volume of 

 precipitate ; 



(2) 



And 400m = x( 100 - v) = y (200 - c) 



e = 100* -200,, 



Now, from (1), substituting the value for v, 

 x = 400m _400w(a;-y) . 



100 - 100x n^ 00 ^ 

 " 



then 



x-y 



or 



4 (x-y) 



This method not only allows of an estimation of milk-sugar 

 to be made in milk without correction of any kind, but enables 

 the volume of the precipitate of fat ard protein to be calculated. 

 The author, in conjunction with Boseley, has shown that the 

 experimental error of Wiley and Ewell's method is, however, 

 very appreciable ; and, though correct in principle, it is not so 

 accurate in practice as originally claimed. 



It is not necessary to adhere strictly to the volumes given ; 

 by a modification of the formulae the percentage can be cal- 

 culated from any two dilutions, but the greatest ' delicacy of 

 Wiley and Swell's method i.e., the point at which the influence 

 of unavoidable errors in reading is least is obtained when the 

 volume of water added to the more dilute solution is equal to 

 the volume of the milk taken, less that of the fat and precipitated 

 protein. 



Vieth Method. Vieth, when using the small Mitscherlich 

 half-shadow polariscope made by Schmidt and Hsensch, prefers 

 adding the stronger mercuric nitrate solution, described above, 



