LEE BARKER WALTON 10 J 



the apparent dimensions were completed, the length of the 

 lines X and y were measured with proportional dividers 

 (Keuffel and Esser No. 441 special) adjusted at the ratio 

 1,460 to 1,000, thus giving a reading in tenths of microns. 

 Accurate adjustment was made possible by means of a 

 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 

 machine. I am indebted to Dr. H. H. Mitchell of the 

 University of Illinois for checking the mathematical data. 



II. Consideration of Results 



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 orig- 

 inating and maintaining the diverse forms of life that 

 exist. Similarly the importance or unimportance of small 

 variations in animal and plant breeding may only thus be 

 explained. 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 LengtJj of Zygospores 



In the frequency distribution for lengths of the two 

 groups of zygospores the class range adopted was two 

 microns as compared with a range of one micron in the 



