BIOLOGY OF THE ATLANTIC MACKEREL 179 



incubation period, stage B, from complete epiboly to embryo % around the yolk mass 

 constitutes 32 percent, and stage C from embryo % around the yolk mass to hatching 

 constitutes 33 percent (Worley 1933, fig. 5). The average time occupied by these 

 three egg stages was therefore 2.53, 2.31, and 2.39 days, respectively, and the average 

 age of each stage was derived by simple aritlimetic. 



The duration of each larval length-class was computed from the formula: 



duration (in days)= °o 01591 ' 



where li is the lower boundary of the length class interval in mm., 1 2 the upper 

 boundary of the length class interval in mm. The constant 0.01591 is the increase 

 per day of the logarithm of lengths computed from the straight line fitted to the 

 points of tbe S series (fig. 8). 



The average age of each length-class was computed by the formula: 



age (in days)= 1 -^=^f^+7.23 



where h is the length of newly hatched larvae (2.8 mm.) and 1* the midvalue of the 

 length class interval. Tbe constant 7.23 is the average age of newly hatched larvae. 



The boundaries of class intervals were as follows: for 3-mm. larvae, 2.9 to 3.5 

 mm.; for 4- to 25-mm. larvae, the designated length ±0.5 mm.; for 30- to 50-mm. 

 larvae, the designated length ± 5.0 mm. The mid values of class intervals were: 

 for 3-mm. larvae, 3.2 mm.; for all others, the designated lengths. 



Accuracy oj determination. — The resulting values for duration of egg stages and 

 of larval-length classes are given in table 7 to hundredths of days, thus expressing a 

 smooth curve that gives the most probable relationship for the body of data from 

 which they are derived. Purely from the standpoint of instrumental and sampling 

 accuracy, they have no such high degree of precision. The durations may be accu- 

 rate to the nearest tenth of a day for the egg stages, and of lesser accuracy for the lar- 

 val-length classes. The duration of the 3-mm. class, derived by extrapolation, is 

 especially in doubt, and may be in error by as much as a day. The other classes 

 probably are within several tenths of a day of true values. 



From the standpoint of variability in growth itself, the values are even more 

 approximate. While growth obviously follows a curve of percental increase, there 

 must be fluctuations about this curve due to local variations in environment affecting 

 accessibility of food and rates of metabolism. Furthermore, the particular curve of 

 growth given pertains only to the S group, which developed under a particular set of 

 environmental conditions. From figure 8 it appears that the earlier hatching R 

 group, developing, on the whole, in cooler water, grew more slowly than the S group, 

 while the later hatching T group grew faster in the generally warmer water in which it 

 developed. Thus the R group took 56 days, the S group 50 days, and the T group 47 

 days in growing from a length of 4 to a length of 25 mm., a divergence from the S 

 group of 12 percent in one instance, and 6 percent in the other. This is by no means 

 the extreme variation to be anticipated, for it is conceivable that temperature or other 

 influences might vary more widely than happened in these three instances, and corre- 

 spondingly greater differences of growth would follow. On the other hand, the S 

 group developed from eggs spawned somewhat early in a season that was slightly 

 warmer than average (Bigelow, 1933, p. 46) and thus in temperatures that would 

 likely be reproduced in the middle portion of less unusual seasons, and therefore 



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