LIFE HISTORY OF LAKE HERRING OF LAKE HURON 327 



based on the anterior radius than in those based on the diameter dimension when 

 two years intervene. The discrepancy in the former calculations increased 164 per 

 cent, that in the latter 46 per cent. 



Unquestionably, we would find, if actual values were available, that the dis- 

 crepancies in the computations based on the anterior radius increase rapidly with 

 each additional intervening year. Doctor Jarvi (1920) found this to be true in his 

 calculations for Coregonus albula. The trend of the available data at least indicates 

 that this is true in the lake herring. The available data likewise suggest that this 

 phenomenon is also present in the computed values based on the diameter dimensions 

 of herring scales. Whether it occurs in similar computations in other species of fish 

 is not known, as diameter dimensions never have been emplo3^ed before in life-history 

 work so far as I Icnow. It must be apparent at least that the increase in the dis- 

 crepancy in computations based on diameters wiU be much less than that in the 

 error in the calculations based on anterior radii. 



In the above discussion of the accuracy of length computations it has been as- 

 sumed that the values of measured lengths represented all the individuals of the age 

 groups considered. Strictly, this may not be true. As I shall show later (p. 334), 

 the lengths given for the 2, 3, and probably 4 year fish are in all likelihood nonrepre- 

 "sentative of these age groups and are too high, inasmuch as they are based on the mature 

 and presumably the bigger individuals of the age groups. If this be true, the cal- 

 culated and actual lengths for the fifth and older years of life should coincide, but the 

 calculated values of all age groups should be less than the measured for the fourth and 

 earher years of life. It has been shown that the latter statement generally holds for 

 all computations of length, whether based on diameters or anterior radii. 



As it is not known to what extent the measured length values are exaggerated, 

 probably no absolutely safe criterion is available by which to judge the accuracy of 

 the computed length values; but the following conclusions, previously stated, indicate 

 that the calculations based on diameters are more accurate than those based on 

 anterior radii: (1) The £'/!'" ratio is more constant with the individuals of an age 

 group and with the age groups of a year class than the K/ac (p. 323). (2) As both 

 K/V and K/ac ratios decrease with age, we know that very probably (almost cer- 

 tainly) the calculated values, in general, will be too low. However, the computed 

 lengths based on anterior radii will differ more from the true values than those derived 

 from diameter measurements, as the K/ac ratios decrease more rapidly with age 

 than the KjV. (3) Virtually all investigators who studied the accuracy of calculated 

 lengths concluded that those based on the radii measurements of scales are generally 

 too low, especially those length values computed for the earlier years of life. The 

 computed length values based on diameter measurements may, then, in all proba- 

 biht}^ approach the actual values more closely than those based on anterior radii. 



The data presented in this section are believed to show (1) that the diameter of a 

 scale grows in length more nearly proportional with the body than does the anterior 

 radius, (2) that the diameter dimension is less variable than the anterior radius, (3) 

 that the computed lengths based on the diameter dimension are always higher than 

 those based on the anterior radius, and (4) that the computed lengths based on the 

 diameter, though in general still too low, are more accurate than those based on the 

 anterior radius. 



99760—29 5 



