202 Part III. — Eighteenth Annual Report 



of each group would be required, and even now no definite rules can be 

 given. Some characters are more valuable for the research than others, 

 and fewer specimens are necessary for these than for other characters. It 

 is necessary, further, to sub-divide each group according to size or sex, and 

 if the differences between each group are small the number of specimens 

 examined must be greatly increased. In the present work it has been 

 found that two hundred specimens about the same size permit definite 

 conclusions to be drawn. If the number in the sub-group falls below 

 fifty the conclusions become uncertain. 



The choice of characters is also a matter of moment. There is no doubt 

 that numerical parts (" integral variates "), such as the vertebrae and fin- 

 rays, are the easiest to manipulate and sometimes the most suitable, but 

 this is not always the case. Even over a wide area, such as the North 

 Sea, these characters may not show any appreciable change in their 

 averages. This will be shown in the case of the plaice, and it probably 

 occurs in many other forms. Differences do occur, however, in some 

 forms, as in the herring and the plaice of the Baltic, and it is always 

 advisable to choose these parts for study. Of more importance, however, 

 are the " dimensional " and " substantive " variations. These arise from 

 linear parts, length, breadth, form, &c, and from the mass or weight of 

 structures. These have been disregarded hitherto by most workers on 

 variation, chiefly on account of the difficulty of obtaining exact measure- 

 ments. The reason is quite valid, and great care has to be exercised in 

 the choice of the dimensions, and of the conditions under which the 

 measurements are taken. If possible, fresh specimens should be examined, 

 but if preserving agents are used then the contraction or expansion of 

 each measured part has to be determined. This gives rise to a great 

 amount of labour, and it is better to examine only fresh specimens. Soft 

 or flexible parts should also be avoided, because the errors arising from 

 faulty observation may be considerable. Matthews and Heincke have 

 shown, however, that certain characters in the round fishes are valuable, 

 although they involve the measurement of soft and flexible parts. Such 

 characters are the relative distances of the fins from the snout and tail. 

 The changes that take place in these during growth are well known in 

 the cases of the sand-eel and young herring, and they are therefore of 

 importance for investigation. It is preferable, however, to choose the 

 dimensions on the skeleton — e.g., the skull and vertebrae — of which the 

 measurements can be made accurate to within half a millimetre. 



In the present work the large majority of the measurements consisted 

 of these dimensions on the skeleton. Exceptions were the height of the 

 body and length of tail, and in these cases the error of observation would 

 be within 1.5-2mm. only. It is on account of these possible errors that 

 such dimensions are unsatisfactory. In a large number of specimens the 

 errors will be distributed almost equally about the mean, and hence will 

 not affect the average of the character, but they will affect the standard 

 deviation, and hence the fluctuations of the averages. These will be 

 presently defined ; at present it is sufficient to say that the conclusions 

 that might be drawn from the averages are thereby rendered uncertain. 



The number of characters that should be chosen depends upon the 

 object desired. If it is desired to ascertain whether groups or races exist, 

 or to investigate the variations due to sex or age, it is advisable to examine 

 a large number. This part of the study is still somewhat unsettled, but 

 a few general considerations may be stated. The changes that arise 

 during growth, or from differences in the environment, are, apart from the 

 " integral variates," changes in the relative proportions of the structures 

 of the body, and these are concerned with the movements of the animal, 

 its balance or equilibrium. It is necessary, therefore, to choose such 



