314 THE AMERICAN NATURALIST [Vol.LVI 



bottle, but a little thought will show that this would be 

 an erroneous procedure when one is dealing with dura- 

 tion of life as the second variable, because mean density 

 bears a direct and implicit functional relation to mean 

 duration of life of the flies in the bottle. We shall be on 

 a clearer footing to take initial density as the variable. 

 Since the cubical content of the bottles is constant 

 throughout, there is no necessity of reckoning density 

 per c.c. The number of flies per bottle can be taken as 

 the measure of density, and a good deal of useless com- 

 putation saved. 



We are indebted to Dr. John Eice Miner for aid in the 

 computations. 



Ill 



Table I presents the data for the correlation of dura- 

 tion of life with density of population for the wild type 

 flies. The material is in the usual form of a correlation 

 table. 



An examination of this surface suggests at once that 

 the regression is probably non-linear. Owing to the 

 manner in which the material was obtained (by compila- 

 tion of the control series of a number of different experi- 

 ments) it results that the different arrays have rather 

 highly different total frequencies. The number of flies 

 per bottle was in no way artificially selected or prede- 

 temiined in this material. Instead it was determined 

 solely by the aggregate fertility of the mating bottles 

 furnishing the material for each particular experiment. 

 As has been explained in the first of these Studies (Pearl 

 and Parker (27)), the routine procedure in our experi- 

 ments is to put into one bottle for duration of life test 

 all the flies emerging as imagoes at the same time (i.e., 

 usually on the same day). It therefore would result that 

 if the hatch was particularly good on some day, there 

 might be as many as 90 flies in the duration of life bottle 

 initially. On the other hand, there might be only 2 flies, 

 because only that number emerged on that particular 

 day. 



Even in spite of the differences in the frequencies of 



