24 
BULLETIN OF THE BUREAU OF FISHERIES 
39, and 40.) It seems altogether probable that the differential growth of the eggs is 
begun simultaneously with the onset of the growth period of the last year. 
Another disturbing factor, which undoubtedly makes the accurate determina- 
tion of the relative maturity from the size of the eggs more difficult, is the fact 
that the various collections contain a mixture of races, which, as has already been 
mentioned, have not been segregated, and it is known that there is considerable 
variation among different races in the size of the fully matxire eggs. 
In determining the relative matm*ity it has been found necessary to compare 
the size of the eggs of the fish taken in the ocean with the size of the eggs of the 
undoubtedly mature fish taken in the river at about the same time. Moreover, it 
has been found necessary to consider the entire distribution of egg sizes as ex- 
hibited in each collection in determining whether any particular group of fish was 
mature or immature. The tables have been carefully scrutinized and the size of 
the eggs in the particular group under consideration compared with the size of 
the eggs of the other fish taken in the same collection. If necessary, comparison 
has also been made with the size of the eggs of the undoubtedly mature fish taken 
in the river. In making these comparisons, not only the mean, but the range of 
the distribution as well, has been kept in mind. If a frequency distribution of 
egg sizes was found to be unimodal, the position of the mode and the extent of the 
dispersion were considered in relation to the position of the mode and the disper- 
sion of other groups — ^especially those known to be matirre. If the given distri- 
bution were bimodal or miiltimodal, the position of each of the modes and the 
distribution of individuals about these modes has been considered separately and 
compared with the mode and dispersion of other groups. It has proved impracti- 
cable to pubhsh all of the detailed tables, but representative examples will be 
found on pages 81 to 88. The interpretations of the degrees of maturity have aU 
been made through a study of such detailed tables. 
In this study the logarithms of the observed egg diameters instead of the 
actual measm-ements have been tabulated and plotted. This has been done as a 
simple mechanical means of reducing all measurements to a strictly proportional 
basis. As has already been stated, it was thought during the early stages of the in- 
vestigation that the egg size would indicate whether the immature fish were des- 
tined to mature during the year following their capture or not for two or more 
years. With this in mind it seemed essential to emphasize not the actual but the 
proportional variations, since a difference that would be relatively insignificant in 
the case of the larger eggs might be decidedly significant in the case of smaller 
eggs. For example, a difference of 0.5 mm. in eggs averaging 7 mm. in diameter 
would be of no great significance, while with eggs averaging only 0.7 mm. the 
same difference might be of decided importance. Therefore the logarithms of aU 
measurements were found and the tables prepared from them. Although the final 
results of the study do not entirely justify the use of this method, the labor in- 
volved in retabulating the data, recalculating the constants, and redrawing the 
graphs is so great that it has not been attempted, particularly in view of the fact 
that such modification would in no way affect the conclusions that have been 
drawn. If it be remembered that this use of logarithms is only a means for show- 
