284 



BULLETIN OF THE BUREAU OF FISHERIES 



was divided into two size groups. The lengths, in millimeters, attained by the indi- 

 viduals at the end of their first year of life, as computed from the scales, were then 

 averaged according to these size groups. It may be seen from the table that the 

 large fish of each age group were also the large fish of their year class at the end of the 

 first year of life. Thus, the average size of those fish of age group III, taken in 1922, 

 that were less than 230 millimeters long (average length 222 millimeters) was 137 

 millimeters at the end of the first year of life, while the average size of these fish of 

 the same group that exceeded 230 millimeters in length (average 236 millimeters) 

 was 142 millimeters at the end of the first year of Ufe. Similar differences appear in 

 Table 5 in the other age groups. This presumably explains why the large fish of an 

 age group possess more scales than the small ones. The fish were longer during their 

 first year of life, and more scales were laid down in the longitudinal rows. 



Table 5. — Average calculated length, in millimeters, at end of the first year of life of Bay City lake 

 herring of different size groups within an age group ' 



* Numbers in parentheses indicate the numbers of specimens employed. 



The data indicate for the lake herring (1) that the number of scales in the lateral 

 line does not vary with the sexes and (2) that the number of scales in the lateral 

 line is greatest, on the average, in the large individuals of an age group, due to the 

 fact that these fish were also the large individuals of their year class at the time of 

 scale formation.^ In our discussion of scale constancy, therefore, an allowance must 

 be made for the deviations due to personal errors and to the size of the fish as well as 

 to random sampling. 



If we find, when comparing the means of the scale number of the age groups of 

 a collection with ojie another, that they remain constant with the year classes, then we 

 can conclude also that in all probability they remain constant with age. I have 

 constructed Table 6, therefore, in which these averages for each age group of each 

 collection are shown. In order to determine whether the differences between the 

 averages are significant, I computed the probable error of the extreme means accord- 

 ing to the formula, P.E.m=— — 7= — > in which a = standard deviation and w=the 



number of variates, and then determined the probable error of the differences between 

 the means according to the formula, P. £'. mi ~ m2 = V(P- ^- mi)^ + {P- E. mz)^, the difference 



8 It may be suggested here that these facts, as well as the one relative to the discrepancy in scale counts, may have special sig- 

 nificance in studies considering the variation of meristic characters in fish. Hubbs (1922), for example, accepted a difference of 0.40 

 between the average scale number of two year classes of Notropis aOtainoides as significant. 



