6 10 W77T. E. Kellicott 



plants a similar relation has been found between variability and 

 correlation. (See ^._^., Weldon's ('oi) recalculation of MacLeod's 

 data in Ficaria.) On the other hand, we have seen also that in all 

 the data available in internal characters the higher variability 

 is associated with the lower correlation. As a specific instance 

 may be mentioned some of the figures given by Greenwood ('04). 

 In her study of the human viscera she found that the normal con- 

 dition is one of low variability and high correlation as contrasted 

 with a relation of high variability and low correlation among those 

 diseased or in "general poor health." Pearson ('02b) in one of 

 his Mathematical Contributions to the study of evolution demon- 

 strates by a purely mathematical method that natural selection must 

 determine the amount of correlation, that indeed, it is probably 

 the chief factor in the production of correlation throughout the 

 constitution of the organism even though it may operate occasion- 

 ally upon single characters. This certainly agrees with the bio- 

 logically determined facts. He farther establishes mathematically 

 the general principle that "intensity of selection connotes a lessen- 

 ing of correlation," that a condition of lower variability must be 

 associated with lower correlation. For example supposing the 

 correlation between the lengths of tibia and femur to be .70, if 

 selection reduces the variability of the tibia by 50 per cent the 

 correlation will then be but .44 — a reduction of 37 per cent. The 

 correlation between organs related only indirectly would be simi- 

 larly reduced though not to quite the same extent. 



Pearson does not make it sufficiently plain that this relation 

 would hold only for the same pairs of characters before and atcer 

 a period of selection. It is evident that, speaking in general terms, 

 a condition of higher variability is frequently associated with a 

 higher correlation, and that also a lower variability is associated 

 with a lower correlation. But that this is not a necessary relation 

 is clear when we compare the internal and external characters on 

 this basis. That the relation mentioned by Pearson is not a neces- 

 sary one is again evidenced by Greenwood's data. The following 

 table summarizing some of these data shows that the variability 

 of the weights of the viscera is higher but the correlation at the 

 same time lower in a general hospital population than in a popula- 



