238 
BULLETIN OF THE BUREAU OF FISHERIES 
wide range of variation. The values of c under various definitions (coefficient of 
condition, condition factor, length-weight factor) have been used widely by fisheries 
investigators as measures of individual or average seasonal and regional differences 
in the condition or “degree of well-being” of fishes. Some investigators have used 
the coefficient as a measure of the state of sexual development. Oth erp have con- 
sidered condition to apply only to the state of nourishment and have removed the 
gonads before taking the weight for the calculation of the coefficient. Yet others 
have used the coefficient merely as a measure of relative heaviness and have recog- 
nized the effect of both the state of sexual development and of the state of nourishment 
on the determination of its value. 
In addition to its use as a means of estimating condition, the equation (1) has 
been employed also to describe the general length-weight relationship in populations 
of fishes, and thus serve as the basis for the calculation of unknown weights of fish 
of known length or of unknown lengths of fish of known weight. The use of the 
equation in this latter capacity has met with indifferent success, due to the failure of 
the cube law to describe accurately the relationship of length to weight in many 
forms of fishes. Fulton (1904) who applied the law to the relationship of length to 
weight in several marine species stated: 
The law in regard to the increase in weight according to the cube of the length, although 
broadly true, does not accurately apply in the case of the fishes examined. With scarcely an 
exception, the weight at a given length is greater than the weight calculated from the law, so that 
if the specific gravity of the fishes remains constant they must increase somewhat more in other 
dimensions than in length 
Although the cube law does appear to apply to the length-weight relationship 
in some species (Crozier and Hecht, 1914; Hecht, 1916), these instances appear to 
be the exceptions, for the observations of Fulton in regard to the inadequacy of the 
cube law in describing the length-weight relationship in fishes have been repeated 
by numerous investigators and on many forms of fishes. In recent years a much more 
satisfactory method of describing the length-weight relationship in fishes has been 
developed through the use of the more general equation: 
W=CL n , (2) 
where W— weight, 
L— length, 
and c= constant. 
In this equation the values of both C and n are determined empirically. 
Such a relationship has been determined by Jarvi (1920), Tjurin (1927), Clark 
(1928), Keys (1928), Fraser (1931), Hart (1931, 1932), Tester (1932), Walford (1932), 
and Schultz (1933). 
Some of the above authors have, however, confused the two entirely distinct 
issues of describing condition and expressing the length-weight relationship, and have 
abandoned the use of coefficients of condition based on the cube relationship in favor 
of those based on an empirically determined exponent ( C in W=CL n ). That coeffi- 
cients calculated from the cube relationship and from empirically determined expo- 
nents are in no sense of parallel significance as measures of condition appears from 
the following simple illustration. 
