264 Chance, Causation, and Design. [CHAP. x. 



in the Case of a family of four, the numbers which had four male, three male 

 and one female, two male and two female, and so on. The lower line gives 

 the calculated results; i.e. the corresponding numbers which would have 

 been obtained had batches of M.s and F.s been drawn from a bag in which 

 they were mixed in the ratio assigned by the total observed numbers for 

 those families. 



The numbers for the larger families are as yet too small to be worth 

 giving, but they show the same tendency. It will be seen that in every case 

 the observed central values are less than the calculated; and that the 

 observed extreme values are much greater than the calculated. The results 

 seem to suggest (so far) that a family cannot be likened to a chance drawing 

 of the requisite number from one bag. A better analogy would be to suppose 

 two bags, one with M.s in excess and the other with F.s in less excess, and 

 that some persons draw from one and some from the other. But fuller 

 statistics are needed. 



It will be observed that the total excess of male births is large. This 

 may arise from undue omission of females ; but I have carefully confined 

 myself to the two or three last generations, in each pedigree, for greater 

 security, 



