428 Henry Echvard Crampton. 



the advantage in favor of the surviving or more successful group 

 of pupae should appear more clearly where the co-efficients of 

 correlation are used than where the comparison with the eliminated 

 group is based upon the types and variabilities of the individual 

 characters concerned. Such is, indeed, the case. While the 

 former group is not invariably the superior in correlation, there 

 is a smaller proportion of negative cases than where the individual 

 characters are taken singly; so that definite confirmation is found 

 for the conclusion reached at first entirely by inference. 



III. 



It now becomes the task to develop the principle of "the corre- 

 lative basis for selection" so as to cover the wider range, over 

 which, I believe, it extends. And I may state at the outset that 

 statistical results have already been obtained proving in part that 

 the wider range is indeed covered, though in the nature of the case, 

 as will appear, complete mathematical demonstration is impos- 

 sible. 



So far, the general condition of correlation, which it is contended 

 serves as the basis for elimination, has been regarded as deter- 

 mined by the whole series of internal or organismal characters 

 taken together. We may next attempt to bring the series of en- 

 vironmental conditions or influences into the case by taking as an 

 illustration the correlation between a single internal character as 

 representing the whole series of internal characters and a single 

 external character as a representative of that series. The first 

 is " length of pupal period" m days, and the second is the '^time of 

 the year." Neither of these varieties is simple, it is true. The time 

 of emergence will depend upon a number of things, upon the time 

 of pupation, upon the weight of the whole organism, which, it is 

 found, is indeed correlated with the t3^pe character; while in the 

 second place the time of emergence is dependent also upon the time 

 of the year, as increase of temperature hastens metamorphosis. 

 But the point is rather, that when a given series of pupae is kept 

 under natural conditions of temperature, their times of emergence, 

 even when they are members of a single family, will form a curve 

 of error, like that of structural character such as antenna length, 

 weight, etc. Likewise, the time of the year reckoned as so many 

 days from an arbitrary date such as January first, will form a 



