FERTILITY AND HATCHING OF EGGS. II3 



but hatched very well. The last column of the table is inserted 

 for the purpose of showing that the differences in these individ- 

 ual records are not to be attributed to differences in incubation. 

 The figures in this column show the number of different indi- 

 vidual machines in which the eggs of particular birds were set 

 at different times during the hatching season. Thus, the 45 

 eggs of bird No. 375 during the whole season were set in 7 

 different incubators. 



While Table I shows by illustrative cases that fertility and 

 hatching quality of eggs are essentially different things it does 

 not tell anything about what is the average relationship between 

 these two phenomena or characteristics when large numbers of 

 birds are taken into account. Granting that fertility does not 

 necessarily denote superior hatching quality there still remains 

 the question : what in general, or on the average, is the relation 

 between the fertility of a hen's eggs on the one hand and their 

 hatching quality on the other hand ? On the average will hens 

 or flocks of hens showing relatively high fertility of eggs also 

 show relatively high hatches from the fertile eggs? In order 

 to answer this question it is necessary to determine numerically 

 and exactly the average relation or, as it is technically called, 

 the correlation between these characters fertility and hatching 

 quality of eggs. The nature of the problem here must be 

 clearly grasped if what follows is to be intelligible. The first 

 thought which comes to the reader of the questions just pro- 

 pounded is that the proportion of fertile eggs hatched will 

 depend altogether on how they are incubated and that the 

 answer to be given to the question will be determined by this 

 obvious fact. 



It is quite true that the methods and vicissitudes of incuba- 

 tion determine what proportion of fertile eggs shall hatch, but 

 this has nothing to do with the answer to the question. Sup- 

 pose the eggs of 50 hens to be taken for incubation. It is abso- 

 lutely certain that whatever the method of incubation — whether 

 it be such as to lead to good or poor average hatches- — the fer- 

 tile eggs of some individual hens among the 50 will produce 

 more chickens than will the fertile eggs of other individual 

 hens. Our problem is to learn whether, on the average, these 

 hens which show relatively high hatches also show relatively 

 high fertility of eggs. With this problem the method of incu- 



