VARIATION IN BEES. 73 



was done only in the case of our figures concerning the ratios 

 between the veins M 2 and m where a careful examination showed 

 us that these ratios did not vary according to lots but from the 

 criticism it might be inferred that we had committed this "grave 

 error " throughout the work. Just how Mr. Lutz could know, 

 since the ratios for the individual wings were not published, that 

 we had "jumbled together" some measurements in an unjusti- 

 fiable manner is still a mystery but I am convinced that his Criti- 

 cism is unjust, having carefully examined the ratios with this very 

 criticism in mind at the time of the preparation of our paper. 



At the close of his article our critic says : " It is also probably 

 unnecessary to remark that, even if it turns out that the greater 

 variability of the drones can be established, their proof of their 

 theory to account for this difference seem rather unsatisfactory." 

 I think it is shown, by us and by Mr. Lutz, that the drones do 

 vary the more and our theory of the cause, based as it is on care- 

 ful investigations of the habits of the bee, must be controverted 

 by more observations of an equally careful nature. Too often 

 students of variation work on forms, concerning the habits of 

 which they know nothing, and conclusions are reached which 

 would be modified if causes were looked for in the habits, but I 

 feel free to state that we are not open to that criticism. 



By omitting the parts of our paper in which we explain our 

 stand regarding the variability being " due to chance," Mr. Lutz 

 would make out that we do not know that all chance is in ac- 

 cord with some mathematical formula. On this point we stated : 

 " It may be argued that variation according to chance is but a 

 way of stating our ignorance of the true law, but if there is a law 

 for this variation it is certainly very obscure, and the working 

 out of this law would require an extremely large number of 

 measurements taken from individuals each one with its life his- 

 tory known," and again : " While it is probable that even this 

 chance is according to fixed law, the fact remains that in any 

 event this law is beyond a possibility of formulation from any 

 observations except those extending over far more individuals 

 than those here used." If as we believe the particular size varia- 

 tion of any individual bee depends on the size of the cell in which 

 it grows, then the formulation of this law of variation must be 



