282 BULLETIN OF THE BUREAU OF FISHERIES 



for different size groups of Bay City lake herring of various ages. A detailed exam- 

 ination of those averages that include a SLifficiently large number of specimens shows 

 that, with four exceptions, the averages of the females are higher than those of the 

 males. The averages are higher for the males of the smallest size group of the 4-year 

 fish and of both size groups of the 5-year herring of 1923 and of the larger size group 

 of the 3-year fish of 1921. It is to be noted, however, that the 4-j^ear males of 1923 

 average somewhat more in length than the females of this group. The larger averages 

 in the scale number of females can be correlated with size in the 4-year fish of 1921 

 but not in the same aged fish of the other two collections. When the grand averages 

 of the scale number of the males and females are compared it may be seen that 

 those of the females are slightly higher in every age group except the fifth of 1923, 

 irrespective of the average size of the females. If the differences between the mean 

 scale number of the two sexes of a size group are compared for all age groups, it is 

 found that the differences vary from 0.53 to 1.70 in those cases where the averages 

 of the females are the higher and from 0.20 to 2.35 in those cases where the averages 

 of the males are the higher. When the dift'erences between the grand averages of 

 the two sexes are compared (fifth year of the 1923 fish with a difference of 1.27 ex- 

 cepted), it is found that they vary from 0.10 to 0.99 and that their mean approxi- 

 mates 0.55. If these differences in the average scale numbers need l)e considered, I 

 may state that they lie well within the limits of personal error in scale counts, as I 

 shall show later (p. 283), and therefore have no significance. The number of scales 

 in the lateral line, then, is shown not to vary with the sexes. 



Further examination of the averages of Table 3 shows that the larger individuals 

 of both sexes of an age group possess, on the average, a greater number of scales in 

 the lateral line than the smaller. The scale number increases consistently with size. 

 The dift'erences between the average number of scales of the small and large males of 

 an age group vary from 1.34 to 4.25; of the females from 0.20 to 3.26. The range in 

 the differences between the grand averages (male and female) of an age group extends 

 from 1.27 to 2.44. The mean of these differences is approximately 2.09. The 

 difference between the scale number of the small and large herring of an age group 

 is therefore about 3.8 times as great, on the average, as that between the sexes. 



Are these differences significant or are they due to errors in scale counts? To 

 answer this question I reenumerated the lateral-line scales of most of the 4-year 

 herring collected October 29, 1921, and of a random sample of the 1922 herring. 

 The 1922 collection was selected for the recount because a large percentage of its 

 individuals had lost many of the lateral-line scales, and inasmuch as scale pockets 

 are overlooked more easily than scales the discrepancy between two enumerations 

 in these fish should represent the maximum. No counts were taken when the scales 

 of the caudal region were lost. 



The results of this recount are summarized in Table 4. It will be noticed that 

 averages were made at various stages of the recount to indicate the trend or direction 

 of the personal error with the increase in the number of variates. In both series 

 the discrepancy decreased as more individuals were employed. 



