COMPARATIVE VARIABILITY IN THE HONEY BEE. 



RATIO BETWEEN M, AND ;;/. 



Z 



To get this ratio the length of the vein m was divided by the 

 length of the vein M 2 and the division carried to two decimal 

 points giving a ratio in the form M^.in: : i : x. To get the com- 

 parative variability of the two sexes the individuals were tabulated 

 according to the values of x and in this tabulation the values of 

 x to two decimal points were used, but owing to the length of 

 such a table we have combined these values and give them ac- 

 cording to x carried to one decimal point. This is advisable also 

 for another reason ; owing to the relative smallness of the num- 

 bers in the first part of the proportion certain columns remained 

 empty since, for example, no combination of figures between 32 

 and 57 and between 63 and 1 15 can give a ratio of i : 1.99. In 

 order then to get a series of numbers which represents what is 

 no doubt more nearly the true scale of ratios, the first table has 

 been reduced to a table with x carried to but one decimal point. 

 In tabulating these ratios the individuals were not grouped ac- 

 cording to lots as in the other cases since we found practically 

 little difference between the lots in any one sex. The average 

 ratio for drones is 1 : 2.06 and for workers i : 2.08 so that no ac- 

 count need here be taken of the difference in averages since it is 

 so slight. The range of the values of x for workers is from 1.70 

 to 2.34 or .64 ; that for drones from 1.68 to 2.90, or, omitting one 

 wing with a very abnormal ratio, from 1.68 to 2.57 or .89 show- 

 ing .25 greater range in drones than in workers. It might also 

 be said, since our long table cannot be used here, that this 

 greater range is not caused by a few abnormal cases but that the 

 variations are shown by a gradually decreasing number of indi- 

 viduals in each value of x in both drones and workers, barring, 

 of course, certain values of x which as above mentioned are im- 

 possible with the figures worked upon. 



TABLE V. 



RATIO BETWEEN M AND m. 



