GROWTH AND MORTALITY OF PACIFIC RAZOR CLAM 
557 
about 0.01 centimeter and in the second from a clam already 12.25 centimeters long, 
the relative growths are approximately 340 and 2 per cent, and the growth during the 
first summer is 170 times as fast as in the twelfth. 
The definition of rate is important not only in early growth but also at the time 
of inflection on the absolute growth curve. Is the inflection as significant as its 
universal presence in the absolute growth curve would indicate, or as negligible as 
its complete absence from the relative growth curve would suggest? Brody (1927) 
claims several points of significance for the inflection, namely: (1) Maximum velocity 
of growth, (2) age of puberty, (3) lowest specific mortality, (4) equivalence in age of 
different animals. It is true that the inflection represents the greatest gross increase 
for a unit of time, but, as we shall show later, this is a mathematical fact of no biolog- 
ical significance. In the growth curves of man and rat the inflection roughly cor- 
responds with the age of puberty, but Brody also shows on the same page growth 
curves of eight other species in which the inflection does not correspond to puberty. 
In the clam the inflection occurs at lengths from 3.17 to 5.81 centimeters, whereas 
sexual maturity does not occur until a size of about 10 centimeters is reached. (Wey- 
mouth, McMillin, and Holmes, 1925.) 
The age of the inflection in man is the age of lowest specific mortality; but, 
since mortality data on other animals are not available, this generalization relating 
the inflection with specific mortality is unwarranted. As a “point of reference for 
the determination of equivalence of age in different animals” the inflection is a con- 
venient working basis, but this has no influence on its possible biological significance. 
Robertson (1923) claims no biological significance for the inflection but looks 
upon it as dividing the growth curve into two portions which Brody has designated 
the “self-accelerating” and “self-inhibiting” phases. These terms imply that the 
specific growth activity of the protoplasm increases up to the time of the inflection 
and thereafter declines. But this is not true; as many authors from Minot to 
Schmalhausen have pointed out, the intensity of growth due to an increasing pro- 
portion of inactive material in the organism and other causes is continually decreasing, 
a condition clearly shown by the relative growth rate of the clam (fig. 9) which falls 
without detectable change through the period of inflection on the absolute curve. 
The occurrence of a maximum gross addition which does not represent “die wahre 
Wachstumsgeschwindigkeit” will be clear from a moment’s analysis. 
An animal growing at a constantly decreasing relative rate will, if starting at a 
rate initially very high, show for a time an increasing absolute rate, each increment 
being, as in ordinary compound interest, larger than the preceding. But the falling 
relative rate will after a time more than offset the increasing body size; and the 
total gains will slacken and, having passed through a maximum, finally become 
progressively less, thus showing an inflection in the absolute rate. Viewed in this 
light, the inflection becomes a mere mathematical consequence of the course of growth 
and not a point which a priori might correspond to any physiological stage. 
A hypothetical illustration may show how an inflection results from a constantly 
decreasing growth rate. Table 6 shows the increase of a small principal at com- 
pound interest, the rate of which is initially very high but steadily decreasing. For 
a time the income (annual increments) will be larger each year, but there will come a 
time when interest rate is so reduced that the income becomes smaller each year. 
The income will then be comparable to the absolute growth rate, showing an increase 
to a maximum followed by a decrease; a graph of the principal will be comparable 
to an absolute growth curve and show an inflection. 
