enough to be definitely outside the lower 
limits of the group. The resulting frequency 
distribution was then smoothed twice by a 
110 —— — moving average of three and plotted. The 
: descending slope of the second to the last 
wale group of eggs of this plot was then extended 
by eye. The amount under this extension at 
4 each size class was subtracted from the total 
2 ! _—___ No. 1002 WESTERN EQUATORIAL at that size to get the ascending slope of the 
| | NO. B472 HAWAIIAN most mature group and its mode. This is 
80 |- 7 illustrated in figure 3, By experimentally 
' shifting the extension to the right and left to 
70 t | its apparent limits, the mode was shifted 
| 0.04 mm, at the very most, If the shift was 
60 L \ too much to the left, the frequency distribu- 
\ tion of the largest group of eggs would become 
Ole i | bimodal, Overshifting to the right had very 
; little effect in the position of the mode, 
After 33 ovaries from the central 
equatorial Pacific had thus been investigated, 
a relation between modal position and relative 
ovary weight (ovary weight/fish weight) was 
7 sought. The diameter frequencies of the 
samples from these ovaries are listed in 
table 7 with asterisks (*) marking the modal 
NUMBER OF EGGS IN SAMPLE 
SS positions. As shown in figure 4, the relation 
exert] between modal diameter and relative ovary 
1.0 12 weight appears to be curvilinear, To deter- 
EGG DIAMETER (MM.) mine the best mathematical relation, three 
regression lines were fitted to the data, The 
modal diameter3/ and the relative ovary 
weight x 1034/ were used as the variates for 
one line; modal diameter and the logarithm of 
the relative ovary weight were variates for 
another; and logarithms for both modal diameter and relative ovary weight were variates for the 
third line, The sums of squares of deviation from these lines were 3396.91, 788.35, and 878.85 
respectively. The line of best fit, the semi-logarithmic relation, may be described by the equa- 
tion: 
Figure 2,--Egg diameter frequencies from 
ripest ovaries of Hawaiian and 
western equatorial Pacific areas, 
n 
Y = 0.7055 X - 0, 1478 
a 
where Y is the modal diameter in millimeters and X is the log (relative ovary weight), The 
regression coefficient (b = 0.7055) differs significantly from 0 (t = 9.965, P <0.001). The 
correlation coefficient (r = 0.88) is also highly significant (P < 0.01). 
Positions of the last mode for six ovaries from the western equatorial area were examined 
to determine if the same relation held for the two areas, The six ovaries were selected to cover 
the range of logarithms of relative ovary weights, ‘The frequency distributions are tabulated in 
table 8, The regression of modal diameter on log (relative ovary weight) was calculated, yielding 
the equation: 
F = 0.6178 X - 6.0597 
The symbolism is the same as that in the previous paragraph, 
3/ 
— Coded by using micrometer units. One micrometer unit = 0,022 mm, 
4/ 
— Called hereafter simply "relative ovary weight". 
10 
