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BULLETIN OF THE BUREAU OF FISHERIES 
0.00848, 0.00989, and 0.00830, respectively. 12 The coefficients as calculated from 
formulas with empirically determined exponents were, for the males, ripe females, 
and spent females, 0.0050, 0.0020, and 0.0056, respectively. The exponents in these 
last three formulas were 3.2 for the males, 3.64 for the ripe females, and 3.16 for the 
spent females. The comparison of the coefficients derived by the two methods shows 
clearly that those based on empirical exponents fail completely to reflect the relative 
heaviness of the fish groups to which they pertain. Whil e the values of K based on 
the cube relationship show that the ripe females are on the average the relatively 
heaviest group, followed in order by the males and the spent females, the values of the 
coefficients calculated from equations with empirical exponents follow exactly the 
reverse order. Thus on the basis of the values of C of equation (2) the relatively 
heaviest group of fish would appear to be in the poorest condition. If the values of 
the two types of coefficients are compared in relation to the values of the exponents, 
n, it appears that while the values based on the cube relationship depend on the 
relative heaviness of the fish upon which they are based, the values of the coefficients 
calculated from equations with empirical exponents depend primarily not on the 
heaviness of the fish but rather on the value of the exponents. A large value of n is 
associated with a small value of the coefficient — and the reverse. 
Clark (1928) appears definitely to have confused the two problems of describing 
condition and expressing the length-weight relationship. From her study of condi- 
tion and the length-weight relationship in the California sardine ( Sardina caerulea) 
Clark concluded: “The weight of sardines increases at a rate slightly greater than 
the cube of the length. For the data studied the correct formula for the weight- 
1000 W 
length factor was found to be F= ^ 3 - " 5 — But for the purpose of the present study 
the formula F= 
1000 W 
U 
was sufficiently accurate.” 
Clark evidently believed that the coefficient of condition (weight-length factor), 
to be accurate, should tend to hold a constant value at all lengths of the fish, for she 
stated: “The more a species departs fiom this general weight-length relationship 
[cube relationship], the greater the error involved in the factor.” Concerning the 
changes in the value of the factor with increasing length she observed further: “Due 
to the error introduced from calculating F on the basis of the cube of the length, the 
, . „ , . 1000 w . . , , , ' 
curve resulting from the equation F = — ^ — rises consistently throughout the range 
of sizes represented in the commercial catch at San Pedro.” 
Clark’s conclusion that the failure of the cube law to describe the length-weight 
relationship makes inaccurate the use of coefficients of condition (weight-length 
factors) based on the cube relationship is scarcely justifiable, particularly in view of 
the fact that coefficients based on empirical exponents fail to reflect differences in 
form or relative heaviness while those based on the cube relationship offer a direct 
measure of relative heaviness independent of general length-weight relationships and 
comparable as measures of relative heaviness between fish of any length. Clark 
actually studied variations in the weight-length factor on the basis of values calculated 
from the cube relationship, but did so only because she considered that the use of 
these values introduced “only a minor error into the work.” 
i» In the data from which these coefficients were determined weights were recorded in grams and lengths in centimeters. 
