GROWTH AND MORTALITY OF PACIFIC RAZOR CLAM 
559 
of the logarithm of the relative rate of growth on time, over the range of sizes for 
which we have data, closely approximates a straight line. (Fig. 10.) Therefore, 
where A = e a 
where c = ^ 
where B = e b 
This formula, which is that of a Gompertz curve, fits the growth curve of the clams 
from all localities from the first winter to extreme old age when the observed values 
tend to be high. Although expressed in a different form, it contains the same idea 
as advocated by Minot who claimed that the percental growth decreased throughout 
life in the animals studied by him; namely, the guinea pig, rabbit, and man. To use 
his terminology we might say that the percental growth rate declines at a constant 
percental rate. This growth formula was developed in ignorance of the work of 
Wright and Davidson, the latter now associated with the writers. Wright suggested 
(1926) and Davidson developed and later applied with Wright’s assistance, a formula 
essentially the same as that here given to the growth of cattle (1928). This is the 
first case, however, in which it has been applied to a growth curve including an 
inflection. 
DIFFERENCES OF GROWTH IN DIFFERENT LOCALITIES 
We have presented the general features common to all our growth curves which, 
as we have stated above, are representative of growth in 10 localities ranging from 
Pismo, Calif., to Hallo Bay, Alaska— a distance of over 2,500 miles along the Pacific 
coast and 25 degrees of latitude. It remains to consider the differences in growth of 
clams as influenced by the great differences of environment encountered in this 
unusually wide range. 
To analyze these differences, we selected for comparison a large number of 
constants derived from the growth curves. These we have studied by means of 
scatter diagrams and in many cases have calculated the coefficients of correlation 
between selected constants. As a result we have chosen five constants as the most 
significant for comparison and have presented their values in Table 7 and the 
coefficients of correlation in Figure 11. 
As representative of age and length the maxima, as defined above, were selected 
as most significant. The growth rate, while a single feature, shows such characteristic 
relation between its initial and its later course that two constants were necessary to 
represent it. Those selected were the initial relative growth rate and the rate at two 
P L = = relative growth rate 
log P L = a — kt 
where a = initial relative growth 
k = rate of decline 
t = time. 
d log; L 
dt 
- = e 
= Ae~ kt 
A 
log L = -—r e kt + b 
b — ce 
k t 
L = e b - 
= Be - 
■ k t 
