of the Fishery Board for Scotland. 



■I'M 



are found drifting down the Belts into the Baltic may return later as 

 young to the Kattegat, as Heincke supposes, in a similar fashion as 

 those off the southern shores of Scotland return northwards. 



In drawing this section to a conclusion, it may be pointed out how, 

 starting from the characteristics of the groups into which a "species" 

 may be naturally divided, we attain by examples a clear conception of the 

 underlying theoretical meaning of the term "race." This has been shown 

 by Heincke with reference to the herring, and his definition adequately 

 displays this inner meaning — " A race is a collection of individuals which 

 live within like surroundings, and which through the intermingling of the 

 sexes stand in close blood relationship." This definition gives a picture 

 of the " race," and the observations recorded here show that such collec- 

 tions of individuals may and do exist. 



Conclusion. 



At the end of the section on the " average age at first-maturity," the 

 usefulness of the results therein obtained was discussed, and it is now 

 advisable to give a brief review of the contents of the succeeding sections 

 on variability. In such an abstruse subject it is somewhat difficult to 

 explain the theoretical and practical bearing of the work, although the 

 underlying current of thought and relation of part with part may be 

 comprehensible. The chief endeavour throughout has been to utilise and 

 display those portions of the mathematical method of treating variations 

 which are most essential in fisheries research. The work of past observers 

 in Scotland, England, and the Continent has shown that many problems 

 in connection with the fisheries can never be satisfactorily solved until 

 large quantities of material from different places and different times have 

 been examined. The reason for this lies in the great variation displayed 

 by everything. One cannot rely upon a few scattered observations here 

 and there, but must be prepared to amass the facts, not only by the 

 hundreds, but by the thousands. 



When the facts have been collected they have to be sorted into groups, 

 and the average value of each group must be calculated. Even this is 

 not sufficient. It is necessary to remember that a thousand facts repre- 

 sent only a fraction of the possible millions in nature, and the amount of 

 probability that the averages of the observed facts represent the true 

 averages must be calculated. As with all new subjects and methods, the 

 work is at first extremely laborious. The calculation of the averages and 

 of their true worth is comparatively easy ; the labour arises from the 

 need of carefully selecting and arranging the groups so that no confusion 

 may arise later, and that the conclusions may be justified and self- 

 evident. 



In the preceding pages only a few of the total number of characters 

 examined have been described because of the time taken to find the best 

 manner of grouping the facts. As arranged at present each Table serves 

 three purposes. Sex-, growth-, and race-variability can be read directly 

 from any of them without confusion, and this has seemed the shortest 

 and simplest method of arranging the groups. With greater quantities 

 of material it would be possible to sub-divide certain of the groups still 

 further, as, for example, those displaying growth- and race-variability, and 

 finer conclusions might then be drawn. With the material in hand, how- 

 ever, the groups could not be further sub-divided. The characters chosen 

 are perhaps the best for all purposes, but some of the others may be of 

 importance. The latter will be considered at a future date, it is hoped, 

 along with various other points of importance which have only been 

 lightly referred to in the present paper. 



