THE STATISTICAL STUDY OF VARIATION 35 



From Fig. 15 it is evident that as n becomes larger the straight lines of 

 the polygon more closely approximate the normal curve. 



The normal curve is perfectly symmetrical because it represents the 

 distribution of an indefinitely large number of items and it assumes all 

 causes to be of equal strength or value. It is assumed that certain 

 biological frequency polygons should simulate this curve for these reasons. 

 It is probable that the environment of any organism is made up of a 

 large number of factors each of which may vary around a mean independ- 



Fio. 15. Polygons representing expansion of the binomials (a + b) 5 and (a + b) 10 as 

 compared with the normal curve. 



ently of the others. Now if a frequency polygon is to be made regarding 

 a character of a population composed of individuals alike in zygotic 

 constitution, such as a field of potatoes of the same variety, the differences 

 found in the development of any character are due wholly to these en- 

 vironmental factors. Hence it is likely that the mean of the distribution 

 is made up of observations on individuals upon which an equal number 

 of favorable and unfavorable forces have acted and the deviates are those 

 upon which a greater or less number of favorable or unfavorable forces 

 have acted. But in sexually reproduced allogamous species the in- 

 dividuals are not alike in zygotic constitution. Moreover, the causes 

 Affecting a given character may have an unequal mass effect according to 

 ecological conditions. Either of these factors may cause a high degree of 

 asymmetry in a polygon of variation. Graphs in which the mode is 

 rather far removed from the mean are called skew polygons or curves. 



