92 ANALYSIS OF MILK. 



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

 precipitate ; 



then a; = 4«i x i^-- . ... (1) 



8771- X 



200 -w 

 100 X 200 



Now 



xy ^ • (100-^;)(200-i>) 



4(a.-3/) ,/ , 100 „ 200 \ 



\ 100 -V 200 -D/ 



8»i- X 100 X 200 



"4(4m X (200 -«) x 100 -2ni x (100 -i;) x 200) 

 Sni- I 100 X 200 



4(4?j! X 100 X 200 - 2m x 100 x 200 - 4m x lOOu + 2m x 200i;) 

 = „ — - m. 



The volume may be calculated thus : — From (1) we see that 



im X 100 



or 



which may be similarly deduced from (2). 



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 and 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 Ewell'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. 



