174 FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



Table 5.— Number of eggs and larvae taken on each cruise in 1932, classified according to stages of eggs 



and le7iglhs of larvae 



(During cruises 1 to 7, tow nets 1 meter in diameter at mouth were used, and duriog cruises 8 and 9, tow nets 2 meters in diameter 

 were used; all hauls were obliquely towed and numbers caught were adjusted to represent an equal amount of towing per meter 

 of depth fished] 



i Eggs and larvae below 7 mm. were not retained in their full numbers by the coarse-meshed nets used on cruises 8 and 9. 

 3 The numbers given in this class are deficient, due to failure to occupy the usual number of stations at the southern end of 

 the area of survey where many of the larvare of this size were to be found at this time. For revised data see footnote on p. 192. 



The groups of more than average abundance were brought into prominence by 

 a modification of the conventional deviation-from-average-frequency method. The 

 average numbers per cruise of the larvae at each length ("observed values" of table 6) 

 were converted to logarithms and plotted against logarithms of lengths. Straight 

 lines were fitted to these observed values (figure 6) from which the theoretical values 

 were derived. These were subtracted from the logarithms of the frequencies of each 

 cruise, giving remainders which represent the relative amounts by which the number 

 of larvae of particular sizes deviated from the average number at particular times in 

 the season (last 9 columns of table 6). 



Since the average curve was, in effect, an estimate of mortality by sizes, the 

 deviations may also be regarded as frequencies from which the effect of mortality was 

 removed, leaving only the effects of rate of hatching, rate of growth, and, of course, 

 the random variations of sampling. Fluctuations of hatching (resulting from 

 fluctuations in spawning) give rise to modes, and growth causes the modes to progress 

 from one cruise to the next. If early growth of the mackerel is exponential as in 

 many animals and plants, the progress of modes should be along straight lines when the 

 deviations are plotted against logarithms of length, as in figure 7. This idea in- 

 fluenced the selection of homologous modes marked by corresponding letters R, S, 

 and T, in the figures. 



