252 THE VARIATIOX, RACES AND MEGRATIONS OF THE MACKEREL. 



be noticed that the males are relatively more numerous among the 

 small lish than among the large ; or, in other words, that the numerical 

 ratio of males to females becomes more and more reduced as the size 

 of the fish under consideration increases. This fact is expressed by 

 the figures on the last horizontal line, which gives the number of 

 females of each size corresponding to a constant number of males, 

 taken as 100. It will be seen that, except for a slight irregularity 

 in the columns representing 12 and lo inches, the relative number 

 of females becomes considerably increased as the size enlarges. 



As, however, the extreme sizes, both small and large, are represented 

 by relatively small numbers of fish, whether male or female, a more 

 reliable result will be obtained by dividing the fish into a smaller 

 number of size-groups. Thus, in two-inch groups, the proportion of 

 females to every 100 males becomes — 



10-11 inches . . .103 



12-13 „ . . . . 108 



14-15 ., . . . . 128 



16-17 „ . . . . 289 



thus revealing an increase in the preponderance of females at every 

 successive grade. The increase is not quite regular, being slight from 

 10 to 13 inches, then rapid at 14 and 15 inches, and very highly 

 marked above 15 inches. 



Two explanations of this increasing preponderance of females with 

 increasing size suggest themselves : — 



1. The males may be subject to a more rapid death-rate than 

 the females ; or 



2. The growth of the males may be arrested at an earlier stage 

 than that of the females. 



As the true proportion of the sexes of the mackerel at the time 

 of hatching or in ovo cannot be ascertained with our present know- 

 ledge, it is difficult to test the former alternative, which is a priori 

 improbable, owing to the absence of any known differences between 

 male and female mackerel as regards habits of life or structure of 

 the body. So far as the physiological wear and tear of reproduction 

 goes, this probably affects the female more severely than the male. 



The second alternative is the more probable one, since sexual 

 dimorphism in regard to size is a very common phenomenon, and in 

 fishes the female frequently exceeds the male in length. Still the 

 cessation of growth in the males does not take place uniformly at any 

 one stage, since the extreme limit (17 inches) attained by the females 

 in my samples is also attained by the males. The exact stage of 

 cessation is clearly subject to considerable variation, and is probably 



