98 DEPARTMENT OF THE NATAL SERVICE 



in 1907-09, these were the more numerous among the samples of immature herring 

 from the north of Norway, and as might be expected (in view of the fact that the 

 samples consist of autumn-caught iish)' they are found in 1907 only among the herring 

 with four summer belts; in the following year, 1908, they appear in large numbers (95 

 per cent)^ among the fish with five summer belts, and in 1909 among those with six 

 (79 per cent). In the autumn of 1910, only a very few fish with seven summer belts 

 were found (seventy-eight in all, out of 1614 specimens examined). Of these, how- 

 ever, fifty-five ihad scales of abnormal appearance, and these fifty-five specimens 

 amount, after all, to 40 per cent of the total found. 



Consideration of fig. 21 and table 1, leads us directly to the question of possible 

 error in counting the rings of the scale. What would be the results, for instance, if, 

 owing to various difficulties, the investigator were unable to note with certainty the 

 number of rings on a considerable proportion of the scales? Would such inaccuracy 

 by any means be able to account for a filial result revealing so distinctly marked a 

 regularity as that here found in the case of the Norwegian herring? 



It is no difiicult matter to see that erroneous age determinations will tend to pro- 

 duce an age curve which, where it should exhibit marked differences in the number of 

 individuals in the various groups, assumes, instead, a more even contour,, with less 

 pronounced contrast and more gradual transition between the age-groups. The groups 

 most numerously represented will give ofi^ a greater number of individuals to the 

 groups adjacent than they receive from these. 



The experience gained in the course of the investigations with Norwegian herring 

 tends to show that the probability of error is greater when dealing with older fish 

 than with young specimens, and further, that the error more frequently falls to the 

 One side, thus placing the fish in a younger year-class than that to which it actually 

 belongs. And finally, it has been found that the majority of such errors are uniform 

 in degree, the fish being reckoned as one year younger than is actually the case. 



The effect of errors of this nature and degree will then be that, where a certain 

 sample contains one dominant age-group, the predominance of the group in question 

 will appear less than it should, and the younger group next following be credited 

 with greater number of individuals than is its due. We are consequently led to the 

 conclusion that the figures arrived at in the case of a dominant group are minimal 

 values, i. e., that the diagram shown in fig. 21i, for instance, would have presented 

 essentially the same features, but in an even more marked degree, if all the deter- 

 minations of age on which it is based had been correct. 



That errors and uncertainty are unavoidable in investigations of this kind will 

 be admitted by all who have had any experience of such work. The material may be 

 handled with the highest possible degree of care and attention, so as to warrant the 

 hope that a repetition of the determinations must give exactly the same results, yet on 

 going through the whole once more, discrepancies will nevertheless be found. As n 

 matter of fact, we are hardly justified in using the term " age-determination " when 

 dealing with scales ; " estimate^ " would be more correct, for there will always be 

 found, whatever may be the material under consideration, a greater or less niimber of 

 individuals whose scales must be classed as doubtful, and where the decision must be 

 based more or less upon personal judgment. 



In this respect, the herring from different localities will be found to vary,, and it 

 is therefore impossible to formulate any generally valid rule as to how great the 

 probnbility of error will be. And, indeed, any such estimate would always be a matter 

 of difficulty. Eepetition, of course, affords a certain guide in this respect, and this 

 method has also frequently been employed, with satisfactory results, in dealing with 

 the Norwegian herring. Another method is to examine the actual results arrived at 

 in the investigation of a certain stock. It would be altogether unreasonable to 

 suppose, for instance, that the age determination in the case of the Norwegian herring 



1 Excluding all fish with less than four summer belts. 



