LIFE HISTORY OF LAKE HERRING OF LAKE HURON 287 



Applying the statistical formulas, I found the probable error of the mean of the 

 3-.year fish of October 29, 1921, to be 0.3318; that of the 5-year herring of 1923 to be 

 0.2421. The probable error of the difference between the means equaled 0.8344, 

 which is contained 2.06 times in the difterence, 1.72. The difference, 1.12, between 

 the fourth age group of the October 29, 1921, collection and the sixth age group of 

 the 1923 collection was found to equal 1.08 times its probable error. Thus, the Httle 

 evidence a comparison of the averages of different age groups that belong to the 

 same year class produces confirms the conclusion previously arrived at that scale 

 number remains constant with age. This conclusion, of course, involves only the 

 herring 3 years of age and older, although it would apply undoubtedly to the juveniles, 

 also, which, unfortunately, are unprocurable at the present time. (See footnote, 

 Table 6.) 



Throughout the preceding discussion we assumed that all sizes were represented 

 in correct proportions in each age group. This assumption, however, probably is not 

 warranted. (See p. 334.) The third age groups, at least, probably inchide a dis- 

 proportionate number of the larger individuals, and this would tend to raise the 

 averages of the scale number above the more representative values. The average 

 (80.54) of the 2-year fish suggests, however, that the averages of the 3-year fish are 

 not very much too liigh, if any. 



In this section an attempt has been made to learn whether the number of scales 

 of a fish remains constant throughout life. If the number of scales increased or 

 decreased with age, the growth rate of the individual scales would vary accordingly 

 and they would not grow in direct proportion with the body. Further, there is 

 evidence that in at least some individuals of certain species the number of normal 

 scales is reduced as the adult stage is reached. Herring of the same year class and of 

 different year classes were compared. These methods rest upon the assumption 

 either that scale number does not vary with the sex or the size of a fish of an age group 

 or, if so, that both sexes and all sizes are represented in correct proportions in each 

 age group of the samples. Data were obtained that indicated that the number of 

 scales in the lateral line did vary with the size of a fish but not v/ith the sex. It was 

 ascertained further that the greater number of scales in the large fish of an age group 

 could not be attributed to an error in scale count whereby some of the scales of the 

 smaller individuals were overlooked, but very probably was due to the fact that the 

 large individuals of an age group were also the large individuals of their year class 

 at the time of scale formation, so that more scales were laid down in the longitudinal 

 rows. A comparative study of the average scale numbers of the various age groups 

 of the three collections considered indicated that the number of scales in the lateral 

 line remained constant with the year classes and with the age groups (III and older) 

 studied. 



ANNULI AND NUMBER OF YEARS OF LIFE 



That the annuli of scales are truly "year marks" has been conceded in the past 

 by most of the investigators who employed the scale method. In many instances 

 the basis for the acceptance of tliis assumption has been the fact that the scale method 

 actually worked in practice. Masterman (1913) states it as follows: "In studying 

 the average sizes, average weights, and seasonal occurrence of the different age groups 



