28 



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



The working out of these ratios brought to light another point 

 which explains this greater range in the values of x in the propor- 

 tion. It was found that a certain inverse ratio exists between the 

 lengths of ;;/ and M 2 so that the area of the cell istM 2 bounded 

 distally and posteriorly by these veins remains more nearly con- 

 stant for wings of the same area than do the bounding veins. 

 This does not mean that the area of the cell istM 2 does not vary, 

 for a little calculation shows that it does vary considerably. The 

 ratios of the wings for each length of M were gathered together 

 and an average taken of the ratios in each case, with the result 

 that we found a relatively constantly decreasing ratio with the 

 increase in the length of M 2 . The range of these ratios for drones 

 was from 1.80 to 2.57, omitting again the one abnormal wing 

 mentioned above, and for workers from 1.77 to 2.21, a difference 

 in this case of .33 in the ranges of the two sexes. This would 

 indicate seventy-five per cent, more range of variation for the 

 drones than for the workers and this difference is directly corre- 

 lated with the great difference in the size of M 2 found to exist. 



TABLE VI. 



RATIOS FOR LENGTHS OF VEIN M . 



HOOKS ON THE HIND WING. 



The number of hamuli or hooks on the hind wing which are 

 used to fasten the two wings together during flight were used as a 

 means of testing the variability of this wing. The examination of 

 1,000 wings has shown that this is not the most variable feature of 

 this wing, but that far more variation occurs in the breadth of the 

 wing and in the angles of the veins which form the cross sup- 

 ports. As the area of the hind wing increases the increase takes 

 place principally by a widening of the wing although by no 

 means entirely by that method. The drones especially show 



