50 
BULLETIN OF THE BUREAU OF FISHERIES 
slide rule. In the case of a few of the age groups in which the numbers involved 
were small, the calculations as far as the determination of the constants from the 
"normal equations" were done entirely on the slide rule, which gave exact figures 
to a sufficient number of places. The calculation of the constants from the "normal 
equations" was in all cases done by the use of logarithms. The following table 
(Table 12) gives the values of the constants a and h and the values of y when x is 
100 (the most probable average length on the one-hundredth day of the season — 
August 8), for each age group, both for fish taken in the ocean and in the river. 
Figures 14 to 21 show, for each age group, the average length observed in each 
collection and the calculated trend of the growth diu-ing the season, calculated 
separately for the collections made in the ocean and in the river. The upper and 
lower limits of twice the standard deviation is also indicated in the same manner 
as in the previous figures showing the variations in the size of the eggs. For the 
purpose of this study, both males and females have been included. The various 
age groups will be discussed separately. 
Table 12. — Data for the trends in length of chinook salmon taken during 1919 
Age group 
Number 
of speci- 
mens 
Value of 
y when x 
equals 
100 
FISH TAKEN IN THE OCEAN 
Ocean nuclei 
Second year 
Third year 
Fourth year 
Fifth year 
Stream nuclei 
Third year 
Fourth year _ 
Fifth year _ 
FISH TAKEN IN THE RIVEE 
Ocean nuclei 
Second year 
Third year 
Fourth year 
Fifth year 
Sixth year 
Stream nuclei 
Third year. 
Fourth year.-- 
Fifth year 
Sixth year 
121 
322 
194 
37 
117 
40 
11 
90 
99 
319 
166 
19 
115 
147 
17 
42. 97 
60. 20 
77. 65 
92.02 
48.57 
72. 10 
83.50 
79. 10 
111. 10 
104.70 
47.30 
75.00 
92. 30 
112. 05 
. 1193 
. 1410 
.0610 
.0979 
.1169 
.1064 
-. 0252 
.1989 
.0771 
-. 1051 
. 1546 
.0956 
.0671 
.0832 
.0600 
51.85 
72.14 
91. 75 
98. 12 
58.36 
83.79 
94.14 
42.02 
68.87 
86.81 
1 100. 59 
120.16 
56.86 
81. 71 
104.98 
106.05 
1 The fish of this ago group taken on June 16 and June 16 and 17, 1919, were unusually large. Both collections were taken well 
up the river, one at Seufert and the other at Warrendale, and it is difficult to escape the conclusion that these fish are representative 
of a large race. Omitting these two collections the constants become: o= 100.6, 6=0.0015, and the value of y when i is 100 is 100.65. 
FISH IN THEIR SECOND YEAR, OCEAN NUCLEI 
Figure 14 shows the variations in the length of fish of this age group. The 
differences between the fish taken outside and those taken inside are conspicuous. 
The trend of those taken outside is upward, from nearly 43 cm. on the 1st of May to 
nearly 52 om. on August 8, 100 days after the opening of the season. The change in 
length during the first 100 days of the season has been used simply as a matter of 
convenience in calculation and discussion. In the text figures the trend is extended 
