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Appendices to Fifth Annual Report 



these in combination is so much reduced as to lead to results of no special 

 value. This of course depends much on the amount of variability affecting 

 the characters, and especially on the artificial divisions of such which we 

 must make for the purposes of comparison. In Heincke's paper the varia- 

 bility of each is divided into three classes, and this may be sufficient where 

 the amount of variation in the whole of the fish examined is so great as to 

 point to the probability of its representing a distinction of races. In other 

 cases, however, such as we have to deal with, the divisions to be reliable 

 should be more numerous. We have in most of the characters a more or 

 less common ground of variation, i.e., a region in which the character 

 appears so commonly as to be entitled to the term normal, and an extreme 

 of variation on one or both sides of this, and more or less great. By 

 dividing the total variation into three equal divisions we perhaps in some 

 cases include the normal in the first, in others in the second, or it may be in 

 the third division. This would not necessarily be very confusing, but 

 further, as in some of my cases, part of the normal cases would be included 

 with one extreme of variation, part — probably an entirely different quan- 

 tity — with another. If for facility in the investigation, so few artificial 

 divisions of variation as three are used, they should be not equal in extent, 

 but such as to cover a normal condition and an upper and lower extreme of 

 variation, except where the variation is equally spread over the individuals. 

 It has to be noted that with regard to every one of the characters — position 

 of dorsal and anal fin centres, position of pelvic and pectoral fins, length of 

 head, tail, dorsal and anal fins — there is in no case a marked division between 

 the number of fish exhibiting each grade of variation. We never find either 

 of the extremes of the ground of variation affecting a large body of the fish, 

 while only a small number may be possessed of the intermediate condition. 

 Taking the summer and winter fish separately, or both combined, we invari- 

 ably find that the majority have a central ground of variation, while the num- 

 bers decrease gradually to the extreme on each side of this common area. 

 Had a considerable portion of the fish been found showing one extreme of two 

 or more characters, while another set presented a markedly separate condition 

 it would be almost certain evidence of racial distinction, but none such is 

 to be found in the herrings I have examined. Moreover, in every case the 

 commoner condition of these characters in the summer fish — although they 

 may, when compared with the winter, show a more or less striking diverg- 

 ence in any particular direction — are found either identical with or over- 

 lapping, or, at most, adjacent to the similar condition as found in the 

 winter fish. Hence, if we combine the summer and winter fish, we either 

 find no alteration in the result, or we only find that the commoner, and, as 

 has been said, the central ground of variation is somewhat enlarged. 



It is quite true that we may consider it a ground for viewing fish as of 

 distinct races in the cases where we find, e.g., in Table XXV., some fish with 

 the centre of the dorsal fin holding the position of *448 to *460 of the body 

 length, while others have it from '533 to *545, but we see that these ex- 

 treme conditions are connected by a gradually increasing number of those 

 in which the intermediate condition of the character is found. Hence it 

 seems more probable that these extremes do not represent any real racial 

 distinction, but are merely the outlying exaggerations of the typical condi- 

 tion. In addition, an extended investigation of the number of herrings re- 

 presenting each degree of the variation — a modified example of which is 

 seen in Table XXIV., where the ground of variation is divided into eight 

 classes — shows us the difficulty or even impossibility of fixing on any dis- 

 tinct line of racial demarcation, for up to a considerable limit we find the 

 same gradual increase towards the centre of variation occurring. Conse- 



