•552 



Scientific Proceedings, Royal Dublin Society. 



daily milk yields and fat percentages, because if the total fat varied directly 

 as the total milk, then the graph of the fat percentage would be a straight 

 line. No better result is obtained, therefore, from the total fat in a number 

 of random samples. 



It now remains to suggest some other method of determining the average 

 fat percentage in a cow's milk throughout a lactation period. The true fat 

 percentage for the period could be got with accuracy by sampling and testing 

 the milk every day ; but this is far too laborious. The problem is, therefore, 

 how is the milk to be sampled and tested in order, with the least labour, to 

 arrive at the average fat percentage with such approximate accuracy as the 

 case demands ? How shall sampling and testing be carried out so that the 

 approximate average shall differ from the true calculated average by, say, not 

 more than 10 per cent., i.e., that the approximate average for a cow with a 

 true calculated average of, say, 4 per cent, shall neither be above 4'4 per cent, 

 nor under 3'6 per cent. ? The average percentage of fat in the milk of cow 

 No. 97 over the whole period of observation is 3"86. It is obvious from a 

 glance at either the figures or the diagram that single samples taken at 

 random during the period might have given very erroneous results. A. 

 sample taken on July 3rd would give 2 - 37 per cent, of fat ; another on July 

 4th, 4 - 75 per cent.; another on July 16th, 5*16 per cent.; another on July 26th, 

 549 per cent. A number of random samples combined or a similar number 

 of samples at equal intervals would probably give a more satisfactory result. 



The averages of four samples taken at intervals of ten days are as 

 follows : — 



The averages of four samples taken at intervals of seven days are as 

 follows : — 



June 24 to July 15, 



„ 25 



„ 26 



.. 27 



,, 28 



„ 29 



,, 30 

 July 1 

 - „ 2 



July 



