210 



Part III. — Eighteenth Annual Report 



Body -height. — By this is meant the greatest distance between the dorsal 

 and anal fins measured from their bases. As already mentioned, this 

 dimension is taken in percentage of the total length of the fish minus the 

 length of tail and length of skull. Both by Duncker and Cunningham it 

 has been stated that this dimension was slightly greater in the females 

 than the males. So far as their data is concerned, however, this con- 

 clusion is not very evident, and it will be seen from Table XL, p. 230, 

 that such a conclusion can only be drawn with great caution. 



In five groups — the males and females of each group being directly 

 comparable as regards size and condition of reproductive organs — only one 

 group shows a clear difference between the males and females in the 

 fluctuations of the averages. This is the group of mature plaice from 

 Aberdeen, which are over 350mm. in length. The fluctuations are 62*50- 

 64*30 per cent, for the males and 65*48-67 "88 per cent, for the females. 

 The difference is certainly considerable, being on the average for a fish of 

 400mm. length about 8mm., or one-third of an inch in favour of the 

 females. The number of specimens in both cases is, however, small, and 

 it may be that this character is not well represented by them. In the 

 other four groups, where the specimens are more numerous, the fluctuations 

 of the averages overlap in each case, although the averages for the males 

 are slightly smaller in all cases than those for the females. From the 

 latter fact there is a certain amount of probability that a slight sexual 

 difference in this character does exist. 



In endeavouring to state the amount of th4s probability it must be 

 remembered that the individuals, the averages of whose characters are 

 here given, represent only a small fraction of the total in the sea, and yet 

 that the probability can only be based on the actually observed values. 

 On account of the former fact some might say that the averages given 

 may not even approximate to the averages that would be obtained from 

 an infinite number. Unless there is collateral evidence to show that the 

 specimens examined are not sufficient in number and are not representative, 

 however, the latter fact — that this is the only kind of evidence we can 

 have — forces us to trust in the amount of probability there is in the 

 results. 



As they stand in the Tables the fluctuations of the averages are calcu- 

 lated from five times the probable errors of the averages. This means 

 that if the averages did not overlap, then the probability is a thousand to 

 one that the differences observed correspond to true differences in nature. 

 The four groups in question will not give this amount of probability. If 

 the probable errors are only multiplied by 3, however, then, according to 

 Davenport (I.e.), the probability is only 19 to 1. Not one of the four 

 groups in question will give the amount of probability. Again, if the 

 probable errors are multiplied by 2 only, the probability is then 4 to 1 

 that there are real differences in nature corresponding to the observed 

 differences. But none of the four groups give even this amount of 

 probability. Lastly, if the probable error alone is used the probability is 

 simply 1 to 1. This amount of probability is given by the three groups 

 from the southerly North Sea, but not from the group of immature 

 specimens from Aberdeen. In conclusion, therefore, if the group of 

 mature specimens from Aberdeen be omitted, as being by comparison 

 with the other groups not true representatives of the values of this 

 character, then the probability of there being secondary sexual differences 

 in this character is only 1 to 1 — i.e., it is just as probable that there are 

 no such differences. 



Length of Skull. — This corresponds to a certain extent with the dimen- 

 sion taken by Duncker and Cunningham, called the " length of the 

 head." This latter was measured externally from " the apex of the lower 



