WEAKFISHES 
79 
due to the personal equation of the observer, because it is harder to draw a line between 
gill rakers and tubercles at the uppermost part of the gill arch. In the present study, 
therefore, the number of gill rakers on the lower limb (fig. 2) and also the total number 
(fig. 1) have been enumerated separately, the first because of the greater accuracy 
possible and the second because of the greater divergence shown. 
Number of Jin rays . — Figures 3 and 4 represent the number of articulate fin rays 
in the dorsal and anal, respectively. It may be seen at a glance that while there is 
considerable overlapping, each form shows a strongly marked mode. Furthermore, 
the mode is markedly conspicuous in both 
characters. While, because of the large 
number of overlapping individuals, these 
characters by themselves do not prove the 
distinctness of the two species very con- 
vincingly, yet they furnish additional proof 
when considered in conjunction with the 
other characters. The advantage in the 
use of the fin rays lies in that their numbers 
can be determined accurately in terms of 
exact figures and are not subject to varia- 
tion with the personal idiosyncracies of the 
observer or with the size of the fish. 
Using the following standard formulae: 
Standard deviation = <s = -*/ — ~ — 
probable error of arithmetic mean = E= 
±0.6745 
V n 
and probable difference = -jEf + Ef 
some statistical constants have been worked 
out for the numerically variable characters 
of gill raker and fin-ray counts. These con- 
stants are shown in Table 3. The numer- 
ical values of the ratios of the actual 
differences of the arithmetic means to the 
probable differences are high in every case 
and serve to emphasize the distinctness of 
the two species. 
o 
an 
u-l 
cQ 
10 II 12 13 
NUMBER OF ANAL RAYS. 
Figure 4.— Frequency distribution of soft articulate anal fln 
rays of Cynoscion arenarius and C. regalis. The last two 
rays, which apparently are united at the base, have been 
counted as one; 
Table 3. — Some statistical constants showing the divergence between Cynoscion regalis from the 
Atlantic coast and C. arenarius from the Gulf coast 
Gill rakers, entire 
first arch 
Gill rakers, lower 
limb only 
Dorsal rays 
Anal rays 
C. 
regalis 
c. 
arenarius 
C. 
regalis 
c. 
arenarius 
C. 
regalis 
c. 
arenarius 
C. 
regalis 
c. 
arenarius 
17.26 
.894 
.044 
.088 
3. 45 
39 
13. 81 
.829 
.076 
11. 90 
.570 
.028 
.057 
1. 77 
31 
10. 13 
.546 
.050 
27.26 
.862 
.042 
.063 
1. 39 
22 
25. 87 
.751 
.046 
11.72 
.502 
.025 
.038 
.69 
18 
11.03 
.476 
.029 
Actual difference divided by probable differ- 
