92 PROCEEDINGS OF THE AMERICAN ACADEMY. 



This being granted, we can express quantitatively the degree of varia- 

 tion in the glands by determining the average deviation in the number of 

 glands of any set of legs from the mean number of that set. Thus in 

 the right leg of the female the mean number of glands is approximately 

 3.5. Since there is no individual with 3,5 glands on the leg, every in- 

 dividual shows in the number of its leg glands a departure of at least 

 0.5 from the mean. Adding together the departures of every individual 

 and dividing by the total number of individuals (2,000) we get the mean 



departure, which is known to mathematicians as the mean error, and is 



■S3, 



indicated by the formula , in which 2x indicates the sum of the 



n 



individual departures, a:, and 71 the total number of individuals. Pro- 

 ceeding in this way, the average departure, as an Index of Variability, 

 was determined to be as follows for each set of legs : — 



Average departure of J^ R 1.41089 



« " " J^ L 1.41083 



« « " 9 R 1.36457 



" " " 9 L 1.38766 



These determinations indicate that the variability of the right and the 

 left legs, of the male is exactly the same to four places of decimals ; that 

 the variability of the right leg of the female is slightly less than that of 

 the left lecf, and that the male shows a greater variability than the female 

 in the ratio of about 1.411 : 1.376, or 1.025 : 1.000. In other words, 

 the male is 2.5% more variable than the female. 



As we have seen, the variabilities of the right and of the left sides of 

 the male are practically equal. In the female, the left side is more va- 

 riable. Disregarding sex, we find the variability of the left side is to 

 that of the right as 1.3993 : 1.3877, or as 1.0084 : 1. That is to say, 

 the glands are 0.8% more variable on the left side than on the right. 



Let us now compare the relative variability of symmetrical legs with 

 that of the two sexes. "We find the variability to be greater between the 

 same leg (say the right) in opposite sexes, than between symmetrical legs. 

 The relation may be expressed by the ratio 1.025 : 1.0084, or 1.016 : 1. 

 These numbers indicate a closer morphogenetic kinship between the two 

 legs of a symmetrical pair than between the corresponding leg in differ- 

 ent sexes. 



We may now briefly indicate the method of constructing the proba- 

 bility curve in the diagram. The abscissas represent the numbers of 

 glands from to 10 on a leg, and the ordinates the corresponding number 



