378 



BULLETIN OF THE BUREAU OF FISHERIES 



Table 44 shows the value of Tc for male and female lake herring taken in the fall 

 just before spawning. The lengths and weights are the averages for various age 

 groups, as shown in Table 32. The Ic averages for males (0.01132) and females 

 (0.01154) differ only in the fourth decimal place. In Table 45 age and sex are dis- 

 regarded, and the values for ^ are based on size only. The herring were arbitrarily 

 divided into size groups with definite hmits, which were selected so that a sufficient 

 number of specimens would be included in the group. Thus, the average, 20.4 centi- 

 meters, represents the 17 smallest herring collected; that is, herring 21.0 centimeters 



Fig. 46. — Length-weight relationship of Saginaw Bay herring taken in the fall ju.'Jt before 

 spawning. The curve is plotted from theoretical weights computed by means of the length- 

 weight formula W=k.L^, in which /:=0.01126. The crosses represent actual weights (see 

 Table 46). 



or less in length. It may be seen from Table 45 that the value of Tc changes com- 

 paratively little with size, and that the average foimd for the species is 0.01126. 



Substituting this average for the Ic in the above formula, I computed the theoreti- 

 cal weight of herring of various sizes and compared the calculated values with the 

 actual where possible. These various values are given in Table 46 and plotted in 

 Figure 42. If we e.xclude the largest size gi'oup we find that the average difference 

 between the actual and calculated values amounts to only 2.82 grams. For all fish 

 this difference is 5.10 grams. The crosses in Figure 42 represent actual measurements, 

 the curve the theoretical or calculated values. The agreement between the t'wo 



