of the Fishery Board for Scotland. 



313 



the dentary (I De). These six characters are alone those in which any 

 sexual distinction appears. In the distance of the first dorsal from the 

 snout (d 1 D) the female average exceeds the male in the Aberdeen lot 

 by "03, in the Clyde group by '07, and in those from Barra and 

 Stornoway by '08. In the distance of the anus from the snout (d A) the 

 female exceeds the male average by '1 for Aberdeen, '2 for the Clyde, 

 and by *06 for Barra ; and in the distance of the anal spine from the 

 snout (d As) the differences are — Aberdeen -08, Clyde -18, Barra *06. 

 The greatest difference between the averages is in the case of the distance 

 of the anus from the snout (d A) in the Clyde fish, in which case it is "2. 

 It is, however, necessary to apply to these differences the test of 

 probability. The averages are not really different unless their fluctuations 

 fail to overlap. Now, in the case where there is the largest difference 

 (•2) just cited, the averages are -female 63*68, male 63-48. The male 

 average has a fluctuation of from 63 , 3-63 , 64, which approaches the female 

 average so closely that its fluctuation must necessarily overlap that of the 

 former. So with the other differences ; none of them are sufficiently 

 large to warrant the averages being regarded as indicating sexual 

 differences. Again, the male average exceeds that of the female in the 

 length of the skull (Z Sk), length of the mandible (Z M), and length of 

 the dentary (Z De). The greatest difference does not exceed *15 — a 

 difference which is not sufficient to prevent the overlapping of their 

 fluctuations. The conclusion is, then, warranted that of the characters 

 treated none are of sexual variability. 



Comparison op the Mackerel from the Three Districts. 



The group average by which the three lots of mackerel are to be 

 compared is the average of the males and females combined. This 

 combined average is given for each character in Tables IV. and IVa. 

 The fluctuation of the average has been calculated for certain of the 

 characters which were capable of more exact measurement than the others 

 (Table IVa). So far as the characters in Table IV. are concerned, the 

 averages of the three groups approach each other very closely, and, 

 allowing for the fact that the dimensions are not capable of very exact 

 measurement, they may be regarded as practically coinciding. In the 

 following characters — then, girth at three points,, viz., in pectoral 

 region, at beginning of second dorsal fin, and at the root of the tail, the 

 lengths of the dorsal groove and of the superior ramus of the tail fin, 

 the positions of the pectoral and ventral fins and of the anus — the 

 mackerel from Aberdeen, the Clyde, and Barra and Stornoway show no 

 appreciable difference. 



On examination of Table IVa. a very close agreement is seen to exist 

 between the three localities in respect to the characters there entered. 

 In this case the greater or less resemblance will be tested by the 

 fluctuations of the Means of the dimensions. In these characters, the 

 means of which for the three localities overlap through their fluctuations, 

 viz., the length of the snout (Z Sn), the length of the mandible 

 (1 M), the length of the dentary (Z De), and the length of the 

 tail (Z T), complete agreement is demonstrated. They do not, so far 

 as the evidence in this paper goes, afford any indication of racial 

 differences between the mackerel of the three localities. In the remain- 

 ing characters, viz., the length of the pectoral fin (Z Pf), the distance of 

 the first dorsal fin (d 1 D), the distance of the second dorsal fin (d 2 D), 

 distance of the anal spine (d As) from the snout respectively, the length 

 of the skull (Z Sk), the three Means do not overlap, but in each character 

 the Means for two localities do so. Thus, for example, the Clyde and 



