162 Testing Milk and Its Products. 



The weekly composite sample of the milk supplied by a 

 creamery patron from his herd of 21 cows tested 4.0 per cent, 

 fat. One day the farmer brought to the creamery a sample of 

 the morning's milk from each of his cows, and had them tested; 

 after adding the tests together and dividing the sum by 21, he 

 obtained an average figure of 5. 1 per cent, of fat. From this he 

 concluded that the average test of the milk from his cows ought 

 to be 5.1, instead of 4.0, and naturally asked for an explanation. 

 198. The first thing done was to show him that while 5.1 was 

 the correct average of the figures representing the tests of his 

 twenty-one cows, it was not a correct average test of the mixed 

 milk of all his cows, as he had not considered in calculating 

 this average, the quantities of milk yielded by each cow; the 

 following illustration was used: 



Cow No. 1, yield 25 Ibs. of milk, test 3.6 per cent.=0.9 Ibs. of butter fat. 



Cow No. 2, yield 6 Ibs. of milk, test 5.0 per cent. =0.3 Ibs. of butter fat. 



Total 31 ibs. 2)8.0 1.2 Ibs. 



4.3 per cent. 



The two cows gave 31 Ibs. of milk containing 1.2 Ibs. of fat; 

 the test of the mixed milk would therefore not be 4.3 per cent. 

 (^i 5 ^), but L2 g 1 100 =3.87 per cent. If the fat in the mixed 

 milk was calculated by the average figure 4.3 percent., 1.33 Ibs. 

 of fat would be obtained, i. e., 0.13 Ibs. more than the cows 

 produced. 



In order to further demonstrate the actual composition of 

 the mixed milk of the twenty-one cows, the milk of each cow 

 was weighed and tested at each of the two milkingsof one day. 

 The weights and tests showed that the cows produced the fol- 

 lowing total number of pounds of milk and of fat: 



Morning milking, 113.3 Ibs. of milk, containing 5. 17 Ibs. of fat. 



Night milking, 130.9 Ibs. of milk, containing 4.98 Ibs. of fat. 



The morning milk therefore contained 5 1 1 1 ^ X 3 100 =4.56 per 

 cent, of fat, and the night milk^|^=3.80 per cent, of fat. 



The sum of the morning and night milkings gave: milk, 

 244.2 Ibs., fat 10.15 Ibs. The mixed morning and night milk, 

 therefore, contained 10 '^ X 2 10 =4.1 per cent, of fat. This is the 



