THE VAKIATIOX, llACES AND MIGRATIONS OF THE MACKEREL. 271 



The size of the fish in these samples, irrespective of sex, is given in 

 inches and quarters in Table A. lu the enquiry before us, however, it 

 is inadvisable to have too many size-groups, as that would reduce the 

 number of fish in each group to a very small number. I have there- 

 fore subdivided the Irish males and females into groups according to 

 the integral number which expresses the length of each fish in inches, 

 the fractional differences being neglected. The fishes in each group 

 have then been sorted according to the number of the rays in their dorsal 

 fins. The same has been done with the males and females of the 

 Channel and North Sea fish, and the resulting distribution of values is 

 shown in Table F (p. 294). The upper half of the table represents the 

 observed frequency of the various finray values, the lower half embodies 

 the same facts reduced to percentages. The mean number of finrays 

 for each inch-group of fishes has also been calculated, and is to be 

 found in the column to the right hand of the frequency data for males 

 and females alike. 



The results contained in this table are particularly interesting. If 

 we neglect the values ascribed to the extreme inch-groups, viz., those 

 containing 11- and 17-inch fish, which are naturally erratic on account 

 of the small number of observations, we see that on the whole ther'e is 

 a distinct tendency for the percentage of high values to diminish with 

 increased size of fish. The Irish results are clearer than those for the 

 Channel in this respect, owing to the greater number of large Irish fish. 

 I will, therefore, direct attention to them in the first place. We see, for 

 example, that for Irish fish of 12 and 13 inches length, whether males 

 or females, at least 40^0 possess more than 12 finrays; whereas for 

 fishes above that size the percentage of high values {i.e., above 12 rays) 

 never exceeds 33 % and in most cases does not exceed 30 %• On the 

 other hand, the percentage of low values {i.e., below 12 rays) does not 

 exceed 22% for fishes of 12 and 13 inches, but is increased to 30% 

 or more in the case of fishes of 15 and 16 inches in length. This 

 general tendency is expressed fairly accurately by the mean values, 

 which vary between 12-24 and 1235 for the smaller fish (12 and 

 13 inches), and between 11-90 and 12-05 for the larger fish (15 and 

 16 inches). 



We reach, accordingly, this general result, that, among Irish fish, 

 whether males or females, the average number of finrays decreases as the 

 length of the fish increases. 



Of course, this generalisation only applies to fish within the size- 

 limits of the present investigation, i.e., to mackerel of marketable size, 

 between 11 and 17 inches in length. I have not hitherto received any 

 small first-year fish from Irish waters, and cannot, therefore, say at what 

 stage the maximum number of finrays is present. Some remarks on 



