of the Fishery Board for Scotland. 



321 



Cm. 



No. 



Average. 



Cm. 



No. 



Average. 



26-28 



15 



13-6 



— 



— 



— 



29-31 



03 



13*4 









32-34 



256 



13-7 



26-33 



245 



13-55 



35-37 



108 



132 



35-43 



227 



13-47 



38-40 



22 



13-59 









41-43 



8 



14-1 









But since the groups are so irregular as regards the numbers of 

 mackerel in each I have divided the whole number into two groups of 

 from 26-33 and 34-43cms. By this arrangement a slight reduction in the 

 number of rays is indicated in the group of larger fish ; the averages 

 being 13 '55 for the less, and 13-47 for the larger. Two groups of 

 mackerel which Garstang compares with the object of showing this 

 decrease give more indication of the reduction ; e.g., 129 mackerel of from 

 5|-10^ inches gave an average of 12*49 rays, while 127 of from 

 12|-15| gave an average of 12*02. The discrepancy between the average 

 numbers of rays obtained by Garstang and by myself can only be due to 

 a difference in the interpretation of the term recognisable. And herein 

 lies the difficulty of counting the rays of this fin. In almost every fish 

 one ray at least was completely sunk beneath the skin, and, notwith- 

 standing its minute size, if its articular base was made out, it was counted 

 as a ray. 



Second Dorsal Fin and Dorsal Finlets. 



The average number of rays found by Garstang for this fin, viz. North 

 Sea and English Channel 11*946, Brest and Scilly 11*948, and for Ireland, 

 S. and W., 11 "933, agree very closely with what I found in the Scottish 

 fish, viz., 11*95 for Aberdeen, 11 92 for the Clyde, and 11*91 for Barra 

 and Stornoway. The average for the dorsal finlets of the same southern 

 localities were 5*009, 4*994, 5*011, while those for the Scottish districts 

 were 4*996, 5, and 4*96. Here, again, a close agreement is seen. 



The Correlation between the Variations in the Numbers of the Rays of the 

 Second Dorsal and Anal Fins, and the Dorsal and Anal Finlets. 



Garstang draws attention to the correlation between the variations of 

 the second dorsal fin and the number of dorsal finlets, and from an analysis 

 of the variation of these organs in a number of American mackerel makes 

 the following generalisations: — (1) "That the normal or modal number of 

 fin-rays (12) is constantly associated with the normal or modal number of 

 finlets (5) ; (2) that when the number of fin-rays is below 12, the variation 

 in the number of finlets is confined to deviations above the mode (5) ; (3) 

 that when the number of fin- rays is above 12, the deviations from the 

 modal number of finlets are exclusively below the mode ; (4) that the 

 normal number of finlets (5) is associated with a wide range of variation 

 in regard to the number of rays in the second dorsal fin (from 10-14); 

 (5) that when the number of finlets is above five, the number of rays is 

 constantly below 12 ; and (6) that when the number of finlets is below 5, 

 the number of rays is constantly above 12." Nos. 1. 5. and 6 do not hold 

 good for Scottish mackerel, as the following Table will show. 



Table to show the numbers of second dorsal fin-rays which have b^en 

 found associated with each number of finlets, and the observed frequency 

 of each combination in 474 mackerel: — 



