340 BULLETIN OF THE BUREAU OF FISHERIES 



The corrected values for year I, however, may be too high. It has been found 

 ah'eady that the calculated length averages for year I, based on the measurements 

 of scale diameters, averaged 13 millimeters higher than those based on the measure- 

 ments of anterior radii (Table 16). A correction now by Lee's formula raises 

 these averages from diameters approximately 17 milluneters (computed from Table 

 24) more — ^a total average raise, therefore, of 30 millimeters. These corrected values 

 from diameter measurements for year I, however, at times appear to be rather high. 

 (See year classes 1920 and 1921, Table 24.) Measurements of young herring from 

 localities other than Saginaw Bay suggest that the corrected values for year I of 

 Table 24 are rather too high than too low. A herring of year I, taken in September 

 at Alpena, Mich., from Lake Huron, measured 108 milluneters in length; another 

 taken from an inland lake in Michigan in October also measured 108 milluneters in 

 length. Clemens (1922) gives a length of 75 millimeters to Lake Erie herring (artedi) 

 of age group L Six whitefish (C. clupeaformis) 7 months old (whitefish grow as fast 

 or faster than herring), which were reared accidentally in the ponds of the bm-eau's 

 hatchery at Northville, Mich., and which subsisted on the natural food found in the 

 pond, ranged from 97 to 111 millimeters in length. 



Lee's formula does not take into consideration the rapid increase in length of 

 the scale as compared with that of the body, especially the rapid increase occurring 

 immediately after the scale appears (see Tables 10 and 13, and figs. 12, 13, and 14) dur- 

 ing the first year of life. The effect of this relatively rapid scale growth upon the cal- 

 culated lengths is exactly opposite that produced by the late appearance of the scale, 

 and the former neutralizes the latter, at least in part. The relation between the 

 two factors — tardy scale formation and the relatively rapid increase in the length 

 of the scale — and their effect on computed lengths may be stated as follows: If we 

 assume for the moment that the body and scale begin their growth in length at the 

 same time and continue that growth at the same relative rates throughout life, the 

 body-scale (K/V) ratio will remain constant throughout life and lengths computed 

 from the scales will be correct. That is, if the body-scale ratio of an older group of 

 a year class equals the true ratio of a younger, the calculated values for the younger 

 group, based on the scales of the older, will be accurate; but as the scales of the 

 herring do not appear until after the body reaches a length of approximately 35 

 millimeters, and are at first so small as not to be in contact, the actual body-scale 

 ratio at this body length is much higher than it should be; that is, higher than the 

 true theoretical ratio. As the scale immediately after its appearance grows rela- 

 tively very much more rapidly in length than the body (Table 13) it follows that 

 the actual body-scale ratio is lowered rapidly, approaching, with the growth of the 

 fish, the true theoretical ratio. If the actual and the true theoretical ratios coincide 

 during the first year of life, and body and scale thereafter grow directly proportional 

 to each other (that is, the body-scale ratios remain constant with age), calculated 

 length values will be accurate, and no correction for late scale formation is necessary; 

 but if the scale continues to grow in length relatively more rapidly than the body, a 

 correction is necessary, not for tardy scale formation but for the disproportionate 

 growth of body and scale. We do not know what the body-scale ratio (the true 

 theoretical ratio) of the herring should be, therefore we have no means of determining 



