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 
