STUDIES OF VARIATION IN INSECTS 205 



variation studies. The specific data are finally followed by the 

 general results, and the suggestions regarding the significance 

 of the data and their application to various problems, arranged 

 roughly according to certain particular phases or categories of 

 variation. 



Introduction. 



Statistical and ^lantitative Methods of the Study of Varia- 

 tion. — In the study of variation among certain insect species, 

 the results of which are embodied in this paper, the authors 

 have made constant use of the statistical and quantitative 

 methods devised and explained by Galton, Pearson, et al., and 

 in this paper the graphic (frequency polygons and curves) and 

 mathematical (standard deviation, coeflicient of variability, etc.) 

 expressions formulated and recommended by this school of bio- 

 metric workers are used. The writers believe in the marked 

 betterment and effectiveness of practically all variation study 

 when pursued from the point of view of the biometrician, and 

 they accept as a matter of course the formulae and methods re- 

 commended by Pearson, et al.^ for the mathematical expression 

 of the status of variation. 



But the danger referred to by the editors of Biometrika in 

 their introductory editorial (vol. i, 1901-1902, p. 5) is already 

 apparent in the pursuit of the new science of variation. " The 

 danger will no doubt arise," say the editors, " in this new 

 branch of science that — exactly as in some branches of physics 

 — mathematics may tend to diverge too widely from nature." 

 Biologists are rarely mathematicians, and only mathematicians 

 can understand the results and the worth, or even the purport, 

 of some of the recent biometric papers. 



From the writers' point of view the study of variation is a 

 phase of biology, and not of mathematics. Its basic data are 

 biological and not mathematical ; they lack, even at best, the 

 definitiveness and absoluteness of purely mathematical data, and 

 the superstructure of mathematical development and the expres- 

 sion of facts and principles based on these data, which char- 

 acterize the papers of the extremest biometricians, seem insecure 

 in their foundations. The methods which produce these expres- 

 sions seem over-refined, and carried to an extreme made unten- 



