240 KELLOGG AND BELL 



some measure the advantage or disadvantage of variations in the 

 number of these hooks, with the variation in these hooks in the 

 case of individuals which have not been exposed to the strenuous 

 life outside the hive, /. e.^ which have certainly not been selected 

 on a basis of variation in these hooks, we find that in all meas- 

 ures of this variation, namely, in extreme range, in the mean, 

 and the mode, the standard deviation (index of variability) and 

 in the ratio (coefficient of variation) derived from the mean and 

 the deviation, practical identity obtains in the case of both drones 

 and workers. That is, the statistical study of the variation in 

 this character shows no evidence of a selection by Nature among 

 exposed individuals on a basis of variations in this character. 



Comparing the variation in hooks in drones (males) and 

 workers (females) we find practical correspondence in degree of 

 this variation. In the range, mean and mode, to be sure, the 

 workers show lesser figures but this is obviously simply due to 

 the smaller size of the wings of the workers, and the standard 

 deviation and coefficient of variation show that in relative degree 

 or ratio, the variation is nearly equal in the sexes, the drones 

 showing a slightly higher variability coefficient in both the ex- 

 posed lots of individuals and the non-exposed lots. 



This comparison also indicates the slight preponderance of 

 variation in this character among the parthenogenetically pro- 

 duced individuals (which are the males) as contrasted with the 

 individuals (workers) of bisexual parentage. Thus we have a 

 definitely ascertained case, where, in the same species, indi- 

 viduals of bisexual parentage (results of amphimixis) show no 

 greater, indeed show less variation than individuals partheno- 

 genetically produced. 



Cori'clations^ Bilateral^ Metemcric, and Othcrzi'i'sc^ in the 

 Variations of the Wings. — In examining the variation in char- 

 acter of venation, linear dimension of vein-parts and number of 

 costal hooks on hind wings in the honey bee, to determine the 

 correlation conditions in these variations, we have limited our 

 work by not undertaking to determine mathematical expres- 

 sions for these conditions as would be possible by the biometric 

 methods of Pearson, et al.; we present nerely certain direct 

 statements of comparison. 



