338 



BULLETIN OF THE BUREAU OF FISHERIES 



Table 25. — Comparison for identical individuals of calculated lengths, averaged after having been cor- 

 rected hy Lee's formula in the usual manner (that is, the formula is applied separately to measure- 

 ments of each individual), with corresponding calculated length averages derived by application of the 

 formula to averages of measurements of scale diameters and body lengths. (See text) 



In a more recent publication Miss Lee (1920) considers another factor as a pos- 

 sible explanation of the "phenomenon of apparent change in growth rate." It is 

 well known that scales do not begin their development until the fish has grown to a 

 certain length. The growth history of the early part of the first year of life is not 

 registered on the scales, therefore. This, if ignored, presumably introduces an error 

 into the computations of length, wliich are based on the assumption that the entire 

 history of the growth of the body of a fish is registered faithfully in its scales. Lee 

 supplied a general formula (see p. 306) patterned after that of Fraser to correct the 

 errors due to tardy appearance of scales. To determine whether such a correction 

 actually eliminates the "phenomenon" from my computed lengths, I applied the for- 

 mula to a series of calculated lengths computed from the scale-diameter averages of 

 Table 22. That is, I determined the average actual length of the fish of an age group 

 whose scale diameters were measured and from this length and the scale-diameter 

 averages (Table 22) computed the length attained by that age group at the end of 

 each year of life. 



That this method of length computation is valid may be seen by comparing the 

 computed lengths of the seventy-four 5-year fish of the 1920 year class, as given in the 

 left half of Table 24, with those given in Table 35. The former computations were 

 derived from the scale-diameter averages of Table 22, the latter in the usual manner — 

 that is, the lengths were calculated for each individual and then averaged. The com- 

 pared lengths are identical in corresponding years of life. To the average lengths, 

 determined as explained above, Lee's formula was applied. That this method of cor- 

 recting computed lengths is valid is indicated by the data of Table 25. I applied the 

 formula separately to the measurements of each of the 11 individuals of the second 

 age group (Table 25) and obtained an average corrected calculated length of 145 

 millimeters for the first year of hfe. I then ascertained the averages of the scale 

 diameters of these fish for the two years of life and applied the formula to these averages 

 and average actual length of the age group (208 millimeters). The corrected calcu- 

 lated length for the first year of life obtained in this manner was 146 millimeters, or 

 1 millimeter more than was obtained above. Repeating the above procedure with nine 

 individuals selected at random from the fifth age group, I obtained by the two methods 

 identical calculated length values for corresponding years of life (Table 25). Appli- 

 cation of Lee's formula to the averages of the body and scale-length measurements 



