558 
BULLETIN OF THE BUREAU OF FISHERIES 
Table 6.— The increase of a principal at compound interest when the interest rate is decreasing by 
20 per cent each unit of time 
Prin- 
cipal 
Interest 
rate 
Income 
Prin- 
cipal 
Interest 
rate 
Income 
Prin- 
cipal 
Interest 
rate 
Income 
Prin- 
cipal 
Interest 
rate 
Income 
Per cent 
Per cent 
Per cent 
Per cent 
$0. 31 
152.6 
$0. 47 
$27. 72 
25.6 
$7. 10 
$70. 63 
5.4 
$3. 80 
$87. 02 
1. 1 
$0. 96 
.78 
122. 1 
.95 
34. 82 
20.5 
1 7. 14 
74. 43 
4.3 
3.21 
87.98 
.90 
.79 
1.74 
97.7 
1.71 
41.90 
16.4 
6.88 
77. 64 
3.4 
2.67 
88.77 
.72 
.64 
3. 45 
78. 1 
2.09 
48.84 
13.1 
6.41 
80.31 
2.8 
2.21 
89. 41 
.58 
.52 
6. 15 
62.5 
3. 85 
55. 25 
10.5 
5.80 
82. 52 
2.2 
1.81 
89. 92 
.48 
.43 
10. 00 
50.0 
5. 00 
61.05 
8.4 
5. 13 
84. 33 
1.8 
1.48 
90. 35 
.37 
.33 
15. 00 
21.00 
40.0 
32.0 
6. 00 
6. 72 
60. 18 
6.7 
4. 45 
85.81 
1.4 
1.21 
90.68 
.29 
.26 
1 Inflection. 
We are thus forced to conclude that the significant biological aspects of growth 
are not adequately shown by the plot of absolute size on age. Such curves indicate 
Figure 10. — Ratio diagram of growth of clams from Hallo Bay, Alaska, from larval 
stage to 14 years of age, with the slope of the growth rate calculated by two methods: 
Squares from the formula 
and 
1 dL Li — Li 
~L ’ ~dt~ Li 
r log,r 
r— 1 
when L= length 
U(U-In) 
and horizontal lines from the graph of log, (Alog.B) 
a slow growth at those early ages when each unit of protoplasm is actually putting 
forth a maximum of energy in the construction of new tissue. They further represent 
the most rapid growth as occurring at the “inflection” whereas it has been shown 
above that an increasing body size and a decreasing growth rate per unit mass at 
this age make a maximum contribution of new tissue. Therefore, if we analyze 
gross growth into its capacity and intensity factors we find that the rate is constantly 
decreasing and that the inflection neither corresponds to a biological epoch nor 
represents a real quantitative landmark. 
A GROWTH FORMULA BASED ON RELATIVE RATE 
Having emphasized the importance of relative growth, we may consider it more 
in detail. If we examine the curves of relative growth rate (fig. 9), it will be noticed 
that the descent is regular, suggesting the logarithmic-exponential relation. A plot 
