320 THE AMERICAN NATURALIST [Vol.LVI 



The observed regression line is shown in Fig. 3. 

 Here the regression appears at once to be substanti- 

 ally linear, and is proved to be by the analytical con- 

 stants, which are as follows: 



r=- .057 + .020, 

 V = .120 + .020, 

 ^ = .011 + .004. 

 The criterion ^ is less than 3 times its probable error 

 and cannot be regarded as significant. 



IV 



Putting all the data together, we have here indispu- 

 table evidence that the density of population is a signifi- 

 cant factor in influencing the duration of life (or death- 

 rate) in DrosopJiila. The correlation ratio v is certainly 

 significant in the case of all three stocks. Its lower value 

 in the case of the Quintuple stock is almost certainly due 

 to the fact that in the Quintuple experience there is not 

 a sufficiently extensive representation of densities. If 

 the other two tables were to be cut off at the density 

 array where the Quintuple is, they also would show a 

 much lower association between the two variables. So, 

 then, the general portion of Farr's Law which affirms 

 that death-rate is some function of density of popula- 

 tion receives experimental confirmation in a widely dif- 

 ferent form of life. 



When one comes, however, to the precise fonn dis- 

 covered by Farr (35) and confirmed by Brownlee (36, 

 37), the case is not so clear. We do hot care to enter 

 upon any detailed discussion of the point now, because 

 we do not care to draw any conclusions as to the true 

 form of the skew regressions observed till we have some 

 additional experimental results in hand. Provisionally, 

 however, it may be said that the indications are that in 

 Drosophila something like the following relations hold: 

 (a) the lowest density is not the optimum; (b) the mean 

 duration of life tends to increase with increasing density 

 up to a certain point which is optimum; (c) after the 



