44 Arrangement and Formation of the Series. [CHAP. II. 



5 ft. 9 in.; for Belgians about 5 ft. 7 in.; for the French about 

 5 ft. 4 in. It need hardly be added that these measures are 

 those of adult-males. 



15. It may fairly be asked here what would have 

 been the consequence, had we, instead of keeping the English 

 and the French apart, mixed the results of our measurements 

 of them all together ? The question is an important one, as it 

 will oblige us to understand more clearly what we mean by 

 homogeneous classes. The answer that would usually be 

 given to it, though substantially correct, is somewhat too de 

 cisive and summary. It would be said that we are here 

 mixing distinctly heterogeneous elements, and that in con 

 sequence the resultant law of error will be by no means of 

 the simple character previously exhibited. So far as such an 

 answer is to be admitted its grounds are easy to appreciate. 

 In accordance with the usual law of error the divergences 

 from the mean grow continuously less numerous as they 

 increase in amount. Now, if we mix up the French and 

 English heights, what will follow ? Beginning from the 

 English mean of 5 feet 9 inches, the heights will at first fol 

 low almost entirely the law determined by these English 

 conditions, for at this point the English data are very nume 

 rous, and the French by comparison very few. But, as we 

 begin to approach the French mean, the numbers will cease 

 to show that continual diminution which they should show, 

 according to the English scale of arrangement, for here the 

 French data are in turn very numerous, and the English by 

 comparison few. The result of such a combination of hetero- 



of the mean height, nor does he afford accurate data on any large 



always give precisely the same mea- scale. The statistics given a few 



sure. Practically, none but soldiers pages further on are probably far 



being measured in any great num- more trustworthy, 

 bers, the English stature did not 



