302 THE TREND OF THE RACE 



bution of a normal population, and, supposing all members of it 

 to be liable to some disease in equal proportions, obtain from it 

 the distribution of the sibships of the affected by order of birth 

 which is to be expected on the assumption made. We shall find 

 that the distribution of the sibships is by necessity so different 

 as to account for practically the whole difference found by Pear- 

 son." 



Here we have differences of opinion among statistical experts 

 regarding a purely mathematical problem, quite apart from any 

 biological or social factors which may possibly be involved in it. 

 Dublin and Langham have arrived at precisely the same theoret- 

 ical distribution of 381 tuberculous patients as Greenwood and 

 Yule found. The statistics show that there is still a preponder- 

 ance of first born among the tuberculous, but it is so much less 

 than that estimated by Pearson that the authors do not consider 

 it especially significant. 



Pearson has replied to Greenwood and Yule and his argument 

 would affect the criticisms of Dublin and Langham also claiming 

 that their method, when applied to the kind of material which is 

 investigated leads to incorrect results. We shall not attempt to 

 enter upon a discussion of the details of the mathematical ques- 

 tions which are the subject of controversy. There is occasionally 

 a surplus of first born over the expectation as estimated by the 

 methods of Greenwood and Yule as is the case with tuberculosis, 

 criminality and insanity. Characteristics found to occur fre- 

 quently in small families will naturally be found in a relatively 

 large percentage of first born offspring. As Pearson remarks, 

 "Certain types of parental degeneracy seem incapable of pro- 

 ducing more than one or two children at most, and the children 

 of such parents are themselves feeble. But, if any small families 

 are thus selected, we shall increase the number of early-borns in 

 the diseased population, for such small families have no late- 

 borns." 



It may very well happen that the first-borns may be relatively 

 abundant in a diseased or defective stock, although they may not 

 be relatively less frequent among the sibships of the affected stock 



