058 



THE AMERICAN NATURALIST [Vol. XLIX 



micrometer screw, on the basis of the equation for similar 

 triangles ; 



1,460 mm. : 1,000 mm.= 160 mm.— x mm. : x mm. 

 where 160 represented the total length of the dividers, 

 and x or 65.04 mm. the point of adjustment. Having 

 checked the adjustment, it only became necessary to note 

 the size of a given zygospore with the longer legs of the 

 instrument, then by applying the shorter legs to a milli- 

 meter scale, to read the result. The various constants 

 were then computed on the basis of the work of Pearson 

 and of Elderton by means of a Brunsviga calculating ma- 

 chine. I am indebted to Dr. H. H. Mitchell of the Uni- 

 versity of Illinois for checking the mathematical data. 



II. Consideration of Eesults. 

 The direct results obtained by the statistical methods 

 employed are here presented. These furnish the basis 

 for the general discussion and conclusions which follow. 

 The problems of biology relating to evolution need the 

 application of statistical methods to studies in genetics. 

 In no other way will it be possible to clearly demonstrate 

 the relative efficiency of the different types of variation- 

 fluctuation, amphimutation, cumulation, etc. — in originat- 

 ing and maintaining the diverse forms of life that exist. 

 Similarly the importance or unimportance of small varia- 

 tions in animal and plant breeding may only thus be ex- 

 plained. The refinements of curve fitting are by no 

 means necessary, nevertheless values are thus exhibited 

 which are presentable in no other way. 



1. Comparative Variability in Length of Zygospores 

 In the frequency distribution for lengths of the two 

 groups of zygospores (Table I) the class range adopted 

 was two microns as compared with a range of one micron 

 in the distribution of diameters. The more extended as 

 well as the more irregular distribution of lengths of the 

 lateral zygospores when compared with the scalariform 



