3O D. B. CASTEEL AND E. F. PHILLIPS. 



the true test of the relative variability far more than is the range 

 of variation. 



So far we have discussed the range of variability in each case, 

 but a far more important test of the comparative variability is the 

 relative centralization of individuals about the average point in 

 the table. If, for example, the drones showed exactly the same 

 range as did the workers, the fact that in every one of the tables 

 the workers show a greater number of individuals with the average 

 dimensions, together with a rapidly decreasing number in each 

 direction, while the drones show a more nearly equal number of 

 individuals over several dimensions on each side of the average 

 point, would lead one to conclude that the drones show far more 

 variability than do the workers. It is not necessary to go over 

 all the tables to point out this fact, but even a hurried examina- 



FIG. 3. 



tion will show the facts as above stated. If, for example, the 

 tables were put in the form of curves of variation the workers 

 would show a longer and narrower curve in every case than the 

 drones, and were these curves expressed in the form of mathe- 

 matical formulae the fact would be brought out still more strongly 

 that the males in this case show more variation than do the 

 abortive females. 



It may be well here to offer some explanation as to why curves 

 were not used in this work, since that is the usual method for 

 work on variation. It was not the purpose of this investigation 

 to work out the law of variation for the two sexes, but merely to 

 show which sex did vary to the greater extent. This purpose 

 has been fulfilled and is shown in the tables. In order to get a 

 true curve of comparative variability it would be necessary to 



