280 THE KNTOMOLOGIST. 



Now only a few of the males can leave offspring. Let us say, 

 for the sake of simplicity, that only one male with a high power, 

 8, succeeds in pairing. The offspring of the union of that male 

 with a female of the ordinary power 9 will have a power of 8|^. 

 Now, among these offspring — say, 100 in number — any of the 

 powers from to 9 may occur in as many combinations as is pos- 

 sible without altering the average power 8|-. Of these offspring 

 only one again can pair, of which we will take, for the sake of argu- 

 ment, one with a power of 2. In the next generation, then, the 

 power will be reduced to (i^ x 2) + (^ x 9) = 5| ; so that the high 

 value of the previous generation will have been wasted, and to 

 no purpose. By this simple example it is shown how a con- 

 tinuous state of fluctuation would be preserved between the 

 various possible powers owing to the scarcity of females. 



In this way I believe that the two phenomena conspicuously 

 exhibited by the genus Erebia — namely, great variability and 

 scarcity of females compared to males — may be brought into 

 causal connection. I have neglected numerous factors, such as 

 reversion, continuous action of changed conditions, variability of 

 the female ; I have also treated the spots on the wings as definite 

 or particulate inheritable entities, which may well strike terror 

 into the heart of the entomologist ; but this has been done more 

 as illustrative of a process than as an actual statement of one. 



How far the principle here numerically illustrated may be a 

 general one, I neither know myself, nor have found stated in a 

 book ; but I hope to work some results out from Erebia material 

 in this essay. The principle itself may be enunciated broadly as 

 follows : that equality in the relative number of the sexes tends 

 towards th estability of a species, and that a preponderance of 

 one sex tends towards fluctuations of character, even though the 

 actual tendency to vary remains the same. 



In the case considered the female was not a variable quantity, 

 bat in other cases the variability of the female will have to be 

 taken into account, which will alter the problem somewhat, as 

 a mean value will have to be substituted for the constant 4|- in 

 our tables. This does not apply, however, to the particular 

 example under consideration, which has been taken to give 

 simple numerical expression to a rule which probably acts in 

 nature extremely complexly, and which will be considered in 

 different aspects later on. 



Explanation of Fig. I. — The percentages in columns 1 of Table I. 

 and 1 of Table II. are recorded on the graduated lower line. The 

 number of spots in columns 3 of Table I. and 6 of Table II. determine 

 the height of the vertical lines to be erected at the corresponding 

 grades on the lower line. The points of intersection of the vertical 

 and perpendicular lines are joined by a curve. To find the mean a 

 perpendicular is drawn from grade 50 to meet the curve, and from 



