118 
PACIFIC SCIENCE, Vol. II, April, 1948 
gression of greatest body depth on total length, 
and the regression of length of longest first dor¬ 
sal ray on total length do the intercepts fail to 
differ significantly from zero. For the pectoral 
insertion to insertion of first dorsal, and length 
of base of first dorsal, the regressions on total 
length have y intercepts differing significantly 
but yet so slightly from zero that the expression 
of these measurements as percentages of total 
length would result in a negligibly small error 
from this source. This is also true for the re¬ 
gression of length of maxillary on length of 
head. For the remaining characters, the size of 
the fish has a considerable effect on the dimen¬ 
sion expressed as a percentage of total length, 
and the same is true for diameter of iris ex¬ 
pressed as a percentage of head length. 
The lengths of the second dorsal and anal 
fins are in proportion to the 1.69 power and 
1.83 power of the total length, respectively. 
This very rapid increase of fin length with fish 
length follows the equation 
y=cx h ...(1) 
where y is the fin length, x is the total length, 
b is the value indicated in Table 2, and c is an 
arbitrary constant depending on the units of 
measurement. (Here, where the measurements 
are in millimeters, £=5.45 X^O -4 for the anal 
fin and c=1.30X10 -3 for the second dorsal.) 
The standard deviation from regression, con¬ 
verted from logarithms as expressed in Table 2 
to percentages, amounts to 8.7 per cent for the 
second dorsal fin and 10.0 per cent for the anal 
fin. If the deviations were randomly assorted 
by fish size we would expect to find in about 
one case in 100 a fish with second dorsal fin 
varying as much as 23 per cent from the aver¬ 
age for a given size of fish, and a fish with anal 
fin varying as much as 29 per cent from the 
average for a given size of fish. Examination 
of the data, however, has shown that the devia¬ 
tions are not entirely randomly assorted, but 
that they are to some degree related to size of 
fish, the variability, on a logarithmic plot, being 
somewhat greater for the larger fish. This 
means that at the larger sizes, say over about 
a meter in total length, the variation may be 
expected to be somewhat greater than the 
numerical values indicated, while for small fish 
it will be less. 
The deviations from the average for a given 
size are not attributable to the sex of the fish 
in any case. No sexual dimorphism of fin lengths 
or other measurements has been found from our 
data. 
The exponents b in (1) for anal fin length 
and second dorsal fin length are so nearly equal 
that the regression of the latter on the former 
is linear or nearly so. The least-squares fit to 
this regression indicates that, on the average, for 
any given size in the range investigated the anal 
is somewhat longer than the second dorsal. 
The pectoral fin grows more slowly than the 
length of the fish over this range of sizes. It 
was found that, for this range, the relationship 
between fin length y and total length x may be 
expressed in the form 
y = 446 log 10 x —1068 (2). 
There is no recognizable difference between 
the measurements of the two observers with the 
single exception of the character "length of base 
of first dorsal.” Examination of the data indi¬ 
cates a tendency for the measurements of this 
distance by Mr. Marr to be a little smaller than 
those of the author. The statistics of the linear 
mean-square regressions, computed from the 
data of the two observers, are: 
Schaefer Marr 
Number of specimens.. 21 24 
Mean total length (x 
in Table 2).1047.6 879.8 
Mean length of base of 
first dorsal (y in 
Table 2) . 250.0 198.1 
Standard deviation 
from regression . 7.35 7.29 
Regression coefficient 
(b in Table 2) 
0.2330 0.2090 
