LIFE HISTORY OF LAKE HERRING OF LAKE HURON 



341 



definitely whether the Iviiovm ratios are too low or too liigh. However, in view of the 

 facts that the actual observed ratios undergo a rapid drop during the first year of life, 

 and that each year thereafter the ratio continues to fall, it seems reasonable to believe 

 that the observed ratios of the older fish are lower than they should be theoretically. 

 Tardy scale formation may be ignored, then, as its effect upon computations of 

 lengtli is counterbalanced by that of disproportionate growth of body and scale. 

 The latter factor, rather than the former, may, at least in part, be responsil)le for 

 Lee's "phenomenon" in the computations of body length. 



It is to be noted that Lee's formula proposes to ehniinate the "phenomenon" 

 from calculated length values that involve computations based on mathematical 

 proportions. The larger the number of proportional computations involved (as in 

 old fish) the greater will be the correction for the first computation (that is, for year 

 1; .see p. 339). Lee's formula assumes that the "phenomenon" is purely the result 

 of the method of calculation from scales. Obviously, then, late scale formation can 

 not be a factor in the "phenomenon" found in direct measurements of scale diam- 

 eters, as in them no computations are involved. Even so, there is no relation 

 apparent between the late formation of scales and the progressive decrease in the 

 length of scale diameters with age (Table 22) in fish of the same year class. Tardy 

 scale formation was not considered, therefore, in the discussion of scale-diameter 

 measurements (p. 331). 



A correction for the disproportionate increase in length of body and scale is 

 possible. If, for example, the body-scale (K/V) ratio of a higher age group equals 

 95 per cent that of a lower, the length value computed for the lower age group from 

 the scales of the higher will equal 95 per cent of the true value; that is, the calcu- 

 lated result \vill be too low in the same proportion as the scales grow relatively too 

 fast and an error of 5 per cent is involved in the computation. 



Table 26. — Average of actual measured lengths (K) of all available Bay City herring lohen arranged 

 in age groups; also, in each age group, the calculated lengths for each earlier year of life, calculations 

 based on measurements of V of X and nan X scales ' 



' The number of specimens employed is shown in parentheses. 



