320 



BULLETIN OF THE BUREAtT OF FISHERIES 



1-year fish is not doubled; the percentage of increase in length is not the same in fish 

 and scale — it is less in the former. 



The scale formula, however, is based on the assumptiori that the lengths of the 

 body and scales maintain a fixed relationship after the first year of life. The formula 

 demands that the body-scale ratio of a fish at death be the same as it was at the time 

 of the completion of each annulus on the scale, irrespective of the actual growth rela- 

 tionship during the first year or during the intervals between the periods of annuli 

 formation. The lengths are calculated back to the periods of annuli formation. To 



test the scale theory of growth determinations we may then study the j/ ratios, 



Fig. 13. — Body-scale length relation-ship of adult lake herring (Leucichthys artedi) arranged 

 according to their age. The continuous curve is plotted from the average total lengths of 

 the body, the broken curve from the average total lengths of the scale shown in Table 14 



which the theory demands must remain constant with the age groups strictly with 

 those age groups that have completed their last year's growth but have not yet 

 commenced the new year's growth and thus have formed a completed annulus at 

 the margin of their scales. My herring were taken at the end of a growth year, in 

 the fall of the year. 



Now, since it has been shown that the body-scale ratios gradually decrease 

 with age in the lake herring (p. 315), we may conclude that the demands of the theory 

 are not fully met — that the percentage of increase in length of the body and of the 

 scale is not the same but that this percentage is greater in the scale. The actual 

 growth increments of the body and scales in the course of time, however, may have 

 increased in direct proportion even though the body-scale length ratios decreased. 



