8 THE ENTOMOLOGIST. 



effect on the constitution of their female offspring, for if so, a 

 mean would be established for the females intermediate between 

 9 and the various powers of the males. But this does not occur. 

 Hence we must suppose that the constant power of the females 

 is handed down independently of the males. But if this is so, 

 what reason is there for supposing that the constant power of 

 the females has any effect on the variable powers of the male 

 offspring ? The reason, I think, is given in the two terms con- 

 stant and variable. The constant power represents the power 

 that is typical of the species ; all reversionary processes tend 

 towards its re-establishment. It is consequently prepotent over 

 the variable powers, and in the females asserts itself entirely, 

 although the tendency of each female, being partly the product 

 of a variable male, should be to vary partly in accordance with 

 its male parent. In the males this variability is not entirely 

 effaced by the constant heritage from the female parent, but it 

 is largely affected by it, owing to the strength that naturally 

 belongs to a constant and typical factor. In other words, the 

 variable male heritage is not strong enough to influence the 

 female offspring, but the constant female heritage is strong 

 enough to influence the males. 



In cases (5) and (6) there is supposed to be no constant or 

 prepotent factor, so the mean (M) between the two sexes would 

 tend to establish itself if the numbers of the sexes were equal ; if 

 one sex or the other preponderates, a state of fluctuation would be 

 maintained. It will be well to follow this out a little more closely. 

 In cases (1) and (4) one of the sexes was supposed to be con- 

 stant with regard to the character under consideration : it was 

 shown for case (1), and so incidentally for case (4), that a state 

 of equilibrium or comparative constancy would be attained for 

 the variable sex if every individual paired, by means of a steady 

 march in the direction of the constant sex. It has also been 

 shown that if the sexes are quite unequal in number, this steady 

 march is very unlikely to occur. 



Now, in cases (5) and (6) there is no constant sex, ex hypo- 

 thesi, to which the other is to conform. How then would a state 

 of equilibrium be attained, supposing the sexes were equal in 

 numbers. Let us take an instance. 



The M of certain males of E. cassiope inhabiting a given area 

 is 4 ; that of the females inhabiting the same area is 5. If all 

 breed we may be certain, ignoring of course other factors and 

 exigencies, that the M of the next generation will be 4^. 

 Supposing that the range of variation is between 1 and 9, we 

 know that with the M at 4|- any of the values between 1 and 9 

 may occur. But if the M keeps at 4|, as it will do if proportional 

 numbers of each variety breed every generation, the number 4tk, 

 being the most probable value of any unknown measure in the 

 group — i.e. representing the mediocre condition — will tend to 



