310 BULLETIN OF THE BUREAU OF FISHERIES 



calculated from 22 scales varied from 6 to 11 millimeters and averaged 9.3 milli- 

 meters or 0.7 millimeter less than the actual. 



From the preceding review it may be noted that most of the papers devoted to 

 a study of the body-scale growth relationship are recent, having appeared since 1918, 

 and involve mainly three species of fish — the marine herring and the Atlantic and 

 Pacific salmon. From this review it is apparent that the question of the validity 

 of growth calculations based on the scales of fishes is still a thorny one, indeed. Not 

 only is there a difference of opinion among investigators employing different species 

 of fish, but also among those employing the same species or even the same material 

 (see Dalil, 1910; Mottram, 1916; Lea, 1913; and Molander, 1918). Most of the 

 investigators agree that discrepancies exist in the calculated growth measurements 

 of the nature described by Miss Lee as the "phenomenon of apparent change in 

 growth rate." But of these investigators, only a few (Lea, Jarvi, Menzies and Mac- 

 farland, and Nail) have attempted to show that Lee's "phenomenon" is also evident 

 in fish that belong to different age groups but to the same year class. There is also 

 much disagreement as to the causes underlying the discrepancies in computed growth 

 values and as to the efficacy of the various methods employed to eliminate these 

 errors; and yet, peculiarly enough, all the experimental evidences reviewed above 

 show, as far as they go, that calculated and empirical growth measurements agree 

 almost exactly. 



DIFFERENTIAL GROWTH OF SCALES OF A LAKE HERRING AND OF THE AREAS OF 



ONE OF ITS SCALES 



In the application of the scale formula (p. 272) to the marine herring (Olupea 

 harengus), Lea (1910) found that it is rather immaterial in what direction the meas- 

 urement dimension of the scale is taken if the center of the scale is clearly established. 

 In Table 8 is given, for a lake herring, the length in millimeters reached by it at the 

 end of each year of its life, as calculated from different scale dimensions of three 

 series of scales, one series representing uniform scales taken from the same area and 

 two consisting of scales taken from different places on the body. The calculated 

 lengths vary considerably with the different scale dimensions in an individual scale. 

 They vary less with the dimensions when the averages of several scales are compared, 

 though the differences are still significant. Comparing for each year the extreme 

 averages based on different dimensions of scales taken from the same area (series 

 A) and expressing the difference in terms of its probable eiTor according to the for- 

 mula given on page 284, I found that the difference between the averages was as 

 follows: For year I, based on the lateral and anterolateral radii, 18.47 times its 

 probable error; for year II, based on the lateral and anterolateral radii, 16.11 times 

 its probable error; for year III, based on the lateral and anterolatei'al radii, 7.15 

 times its probable error; for year IV, based on the lateral and anterolateral radii, 

 7.69 times its probable eiTor; and for year V, based on the anterior and anterolateral 

 radii, 2.68 times its probable error. The difference between the extreme averages 

 is significant in all years except the fifth. When, however, the scales are taken from 

 different parts of the body (series B), the discrepancy between the averages, though 

 still significant in the early yeai-s, is greatly reduced. 



