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BULLETIN OF THE BUREAU OF FISHERIES 
Van Oosten (1929), Clark (1928b), Weymouth (1918 and 1923), Reibisch (1911), 
Crozier and Hecbt (1915), and others. 13 
Of the above authors some employed the cube relationship in the study of the 
length-weight relationship (Thompson, Van Oosten, Weymouth (1918), Crozier and 
Hecht), while others used empirical exponents (Clark, Weymouth (1923)). 
Because of the serious objections to the use of coefficients of condition based on 
empirical exponents, condition in this investigation has been measured by coefficients 
calculated from the cube relationship. The comparison of the equations W—KL 3 
and W=CL n reveals an interesting connection between condition and length in popu- 
lations that deviate from the cube relationship. The equation, W=CL n , may be 
written in the form: 
W=f(LU(L), (3) 
where 
f(L) = CL ", 
<t>(L)—L 3 , 
and 
m=n—3. 
Thus it may be seen that where weight can be expressed as a parabolic function 
of the type W—CL n condition can be expressed by a similar function of length. 
While this definition of condition as a function of length is valid only insofar as the 
equation (3) actually describes the length-weight relationship, the failure of equation 
(3) has no effect on the value of coefficients calculated from the cube relationshie 
as measures of relative heaviness. Where the coefficient of condition does behavp 
as a parabolic function of length (hyperbolic if m<o), the value of m=n — 3 measures 
the rate of change of form or condition. 14 
In order to have the most complete data for the study of condition the value 
W 
of j(L) =— was calculated for each individual specimen. Since lengths were recorded 
13 This statement of Dr. Schultz as it pertains to the studies of other investigators is in some points inaccurate. Van Oosten 
made no use of the coefficient of condition to study the state of sexual development but was interested primarily in deriving a general 
length-weight equation; he did, however, quote Thompson (1917) as to the effect of sexual state on the value of the coefficient. Clark 
used the weight-length factor chiefly as a measure of the state of nourishment or fatness as the following statement shows: “The 
monthly and yearly fluctuations in the weight-length factors of sardines were due, therefore, to some changes in the composition 
of the body tissue of the fish, presumably an increase or decrease in the fat content, and not to the amount of food in the alimentary 
tract, or to the growth of the sex organs.” Weymouth (1918 and 1923) was concerned with the general length-weight relationship 
and not with any individual or seasonal fluctuations in the length-weight factor. Reibisch’s coefficient was calculated neither from 
W—KL 3 nor W=CL ", but was a “ Dickenkoeffizient ” with the formula 5 == __ / 40000. (J , (< 7 = weight in grams, L=length in 
\ TT L 3 
centimeters). Reibisch discussed the effect of sexual state on the state of nourishment, but, in order to make £ describe only the 
state of nourishment, removed the gonads before weighing. Crozier and Hecht were concerned with the determination of a general 
length-weight equation. They stated: “All the fish examined (over 400) were either spent or unripe; so we are sure that none of 
the weights recorded are influenced by the ripening of the gonads.” (The date of issue of Crozier and Hecht’s paper was 1914 , 
not 1915 .) 
n The differential equations corresponding to the equations W=CL n , and f(L) =K= CL m are: 
dW dL 
TF = "i’ 
and 
dK 
K 
djj 
L ' 
Now —• \ i and —• where t=time, are the relative rates of change in weight, length, and condition, respectively. The 
dt W dt L dt K 
exponent n describes the ratio of the relative rates of change of weight and length, while m describes the ratio of the relative rates 
of change of condition (form) and length. If n=3, m= 0, and growth proceeds without change of form. If n±3, then m±0, and the 
values of the exponents measure the rate of change of form. 
