292 BULLETIN OF THE BUREAU OF FISHERIES 



fication of an assumption which is of fundamental importance for the biological valuation of the 

 results of the mathematical analysis * * *, Xhe investigation [Lea's] has been an attempt to 

 decide the following question: Is it possible that herrings of several age groups may form a shoal, 

 for which the curves of frequency with regard to length as well as to age have such a shape that 

 there may be adjusted theoretical curves of variation with considerable "i^robability of fit" [p. 6] ? 



From a consideration of hypothetical and actual samples Lea concludes: 



From the above it will be seen that empirical curves of frequency, of which the similarity to 

 theoretical curves of probability or variation can not be doubted, may arise from and represent 

 processes which have nothing to do with variation and variability in the sense given to these terms 

 by Prof. D'Arcy Thompson. The curve of frequency for the length of the herrings in a random 

 sample may easily show sufficient degree of similarity to a theoretical curve of variation, even 

 though the individuals in the sample belong to several age groups, and the curve of frequency for 

 the number of rings on the scales may also have a form, which is so like a theoretical curve of varia- 

 tion that it might be mistaken for one, without this fact arguing against the assumption that the 

 rings are annual rings and that consequently the curve of frecjuency represents the distribution of 

 age in the shoal from which the sample comes. 



But if that is so, the results of Miss Sherriff's analyses justify the conclusion that the rings 

 on tlie scales are annual rings as little as they justify the assumption of the contrary. The method 

 does not carry us any further towards the solution of this problem, in one or the other direction. 

 It is not a method for an investigation to determine the nature of the scale rings, as it does not 

 suit the problem to be solved. 



The problem concerning the rings on the scales of the herrings is -per se a problem concerning 

 the rate of formation of rings in the course of time. 



A general criticism of the age hypothesis, which probably did not receive due 

 consideration by the critics in the past, is (16) the scarcity of convincing experi- 

 mental evidences. Such data are lacking even now for most of the species of fish 

 whose scales have been employed for age determinations. The experimental data 

 are probably adequate only in the case of the carp, the Pacific and Atlantic salmon, 

 and the whitefish, while they are fragmentary in about a half dozen other species of 

 fish. It is partly due to this factor, "it has never been proved," that Prof. D'Arcy 

 Thompson persists in liis attacks on the age hypothesis in fishes in general (1917) and 

 in the marine herring in particidar. 



Most of the 16 criticisms listed above are specific — that is, they involve only 

 the particular species referred to. It is not improbable, however, that had a critical 

 study accompanied each new investigation some of the vaUd criticisms would now 

 have a much wider application. Further, all the criticisms do not have the same 

 importance; it is now definitely Icnown that some are untrue [2 and 7 (Jacot, 1920)], 

 or, though acknowledged as being generally true, do not disprove necessarily the 

 age hypothesis (1, 9, 14, 15, and 16); some are questionable, supported by no defi- 

 nite data (8) or supported by controvertible data [3 and 6 (Arwidsson, 1910); 7 and 

 15 (Sherriff, 1922)]; and some, though valid, apply to exceptional cases .only (4 and 

 13) or permit corrections (5) or make age determinations doubtfid in the species of 

 fish involved or in certain individuals only [4 (marine herring, eel), 5, 6 (Rich, 1920), 



10, 11, and 12]. 



INDIRECT EVIDENCES 



The indirect evidences that were believed to support the age hypothesis are as 

 follows: (1) By following the growth liistory of the marginal portion of the scales of 

 fish collected at intervals throughout a part of a year, or for a longer period, it was 



