THE VARIATION, RACES AND MIGRATIONS OF THE MACKEREL. 239 



the number of finrays in the first dorsal fin to vary between 10 and 

 14, the value 12 will 'prolahly occur with greatest frequency. But 

 other possibilities occur; and while 12 might be constantly the 

 most frequent value in samples of one local group of fish, it is quite 

 conceivable that 13 might be constantly the most frequent value 

 in samples of another group ; in which case, if the two groups were 

 examined under similar conditions of sex, size, preservation, and so 

 forth, we should be prepared to regard the two groups as racially 

 distinct, the one indispensable condition being that the frequency of 

 the particular variation shall have been determined in all instances 

 upon a sufficient number of specimens. 



It is, however, impossible to assign any one number beforehand as 

 universally sufficient. The minimum sufficient number may be re- 

 garded as that which yields results approximately coinciding with those 

 derived from an infinitely large number, i.e., the percentages of 

 frequency derived from it must bear some close degree of correspon- 

 dence with the percentages derived from a much larger number. I 

 have taken 100 as the minimum number of mackerel from which it is 

 possible to derive a fairly reliable statement concerning the relative 

 frequency of the variations exhibited by any one of the chosen 

 characters. But the number of specimens requisite to yield a reliable 

 statement of the frequency of variations of any organ bears a relation 

 to the variability of the organ. If an organ varies slightly, the number 

 of specimens must be increased. It is certain, for example, that 100 

 is an inadequate number for determining the normal frequency of the 

 variations in the number of the dorsal finlets in the mackerel of British 

 seas (see table H, p. 295); for, among 100 fish from Ramsgate, not a 

 single specimen possessed less than 5 finlets, and 5 specimens possessed 

 more than that number ; whereas, of 300 fish from Lowestoft, 1 % 

 possessed only 4 finlets, and only 3 % possessed 6; and of 300 Plymouth 

 fish, the percentage (3) of specimens with the lower number was almost 

 as great as the percentage (4) of those with the higher. On the other 

 hand, the number (100) is quite sufficient to show a marked difference 

 between the American and the British fish in regard to the same 

 character, since nearly 207, of the American fish possessed G finlets — a 

 percentage almost four times as great as that observed in any other 

 sample of 100 fish. 



In order to check the adequacy of this number as a unit-sample for 

 determining the frequency of the variations of more variable characters, 

 we may turn to table B (p. 290), which deals with the variation in 

 number of the black stripes or bars across the sides of the fish. We see 

 there that in each sample of 100 fish from Lowestoft, Ramsgate, and 

 Plymouth , the frequency of the values above 27 is constantly less than 



