THE VARIATION, RACES AND MIGRATIONS OF THE MACKEREL. 253 



preceded by a retardation in the relative rate of growth, as compared 

 with that of females of the same size. It is improbable that any 

 considerable percentage of males actually stop growing at 11, 12, or 13 

 inches, so that, taking the normal number of females for every 100 males 

 to be 117, as explained in the preceding section, we must explain 

 the relative excess of males below 14 inches as due to retarded growth 

 of the males in excess ; but the increasing relative deficiency of 

 males above 14 inches in length must be due to a large extent to 

 actual arrest of growth, since the normal proportion of males to 

 females is never realized in groups of fish measuring more than 

 14 inches in length. 



The minute economy which prevails among species under natural 

 conditions of existence is clearly revealed by the facts established 

 in the preceding paragraphs ; for it is obvious that, ceteris paribus, 

 the equivalent growth of males and females would lead to an 

 increasing superfluity of the male reproductive elements, owing to 

 the great difference in size between an ovum and a spermatozoon. 



It remains to add that the average size of 423 males recorded in 

 the tables is 12-988 inches; that of the 495 females, 13145 inches. 

 Consequently, if the average size of the males be taken as 100, that 

 of the females becomes 101. The difference between the size of 

 mahcre males and females is probably a little greater than this, but 

 the subject of maturity in the mackerel is reserved for a later report. 



§ 4, Secondary Sexual Characters. Apart from size, I have been 

 unable to discover any evidence whatever of the existence of secondary 

 sexual peculiarities in the mackerel. My investigations of this point 

 will be found under the special sections dealing with the shape of the 

 Transverse Bars (p. 261), the Dorso-lateral Intermediate Spots (p. 263), 

 and the First Dorsal Fin (p. 267). With the exception already 

 mentioned, I can therefore repeat the remark of Smitt that " all the 

 statements as to an external difference of sex in the mackerel which 

 have been made up to the present have proved untrustworthy on closer 

 examination" {Scandinavian Fishes, I. 1892, p. 112). 



VI. Number of Transverse Bars. 



§ 1. The Entire Series. The frequency of the variations in the entire 

 number of transverse bars in the various local samples and in certain 

 chosen combinations of these is set out in Table B. (p. 290). 



The extreme range of variation is from 23 to 33, i.e., 11 bars. 



The modal (i.e., most frequent) number is almost invariably 27, there 

 being only three exceptions to this rule among 21 samples, viz., Scilly, 

 June 9th, (50 fish), Kinsale, July 1st (100 fish), and Brandon, April 



K 2 



