VARIATION IN BEES. 2IQ 



Passing over the grave error of lumping the different series of 

 ratios (p. 27) because they seemed to be alike, when really their 

 only claim to homogeneity is that they are of the same sex and 

 all bees- - Italians, hybrids, " peculiar strains," ct <?/., from cen- 

 tral Ohio to eastern Pennsylvania being jumbled together let 

 us take up the first table (vein R) as we have done the last. We 

 find that the standard deviation of lot I. of the workers is 1.5637- 

 0.1055, and for lot V. of the drones--" from the same hive " 

 is 2.25 17 d= o.i 5 19. There is here a difference of 0.6880. The 

 probable error of this difference is d= o. 1 849. The standard 

 deviation of lot I. of drones is 2.4023 d= 0.1620 and that of lot 

 III., of the same sex, also from the same hive is, 2.9598 =t 0.1412. 

 The difference here is 0.5575 ^ 0.2149. This is due to the ex- 

 tremely small size of the series measured. Since the formula 

 for the probable error of the standard deviation is 0.6745 

 (stand. dev./i/27z), we see how rapidly an increase of " n ''' 

 the number of individuals measured --decreases the error of the 

 result. But it is manifest that the differences between the two 

 sexes, as shown by these data are of no significance ; for, far 

 within the probable error of our work, we get as great a differ- 

 ence between two lots of drones (one lot being twice as large as 

 either of the two considered in the comparison of the different 

 sexes) as we get between the two sexes. 



I have not taken the time to go over the rest of Messrs. Cas- 

 teel and Phillip's work ; but, having reached the above results 

 with the first and the last tables will leave them to go over 

 the intervening ones. It is also probably unnecessary to remark 

 that, even if it turns out that the greater variability of the drones 

 can be established, their proofs of their theory to account for 

 this difference seem rather unsatisfactory. 



HULL ZOOLOGICAL LABORATORY, 

 UNIVERSITY OF CHICAGO. 



