AGE AND GROWTH OF THE CISCO 
239 
A fish with a length of 1 foot and a weight of 1 pound will show on the basis of 
the cube relationship a coefficient of condition of 1.00. In conformity with a rather 
general usage this quantity may be designated as K. If this fish doubles its length 
without change of form or of specific gravity its weight at the length of 2 feet will 
be 8 pounds, and the value of K will continue to be 1.00. If, however, the weight 
at 2 feet is 10 pounds instead of 8 the value of K at this greater length will be 1.25, 
and it will be known that a change of form 11 has occurred along with growth in length. 
It may be considered that 2 pounds of the weight of this 10-pound fish represent its 
change of form; this change is measured directly in the increased value of K. The 
10-pound fish is 25 percent heavier than the 8-pound fish and is 25 percent relatively 
heavier than the 1-pound fish (that is, the 10-pound fish corresponds in form to a 
fish tfiat would have a weight of 1.25 pounds at the length of 1 foot). Thus it may 
be seen that values of K, by reason of their calculation from the cube relationship are 
direct and quantitative measures of form or relative heaviness, and in this sense are 
directly comparable between fishes of any length. 
Now if the weights of 1 pound at the length of 1 foot and of 10 pounds at 2 feet 
were to represent actual average conditions within a population, the corresponding 
length- weight equation would be: 
IF=1.00Z 3 - 32193 
The coefficients of condition calculated from this higher empirical exponent are 1.00 
both for the fish at the length of 1 foot and weight of 1 pound and for the fish at the 
length of 2 feet and weight of 10 pounds. Thus it may be seen that the coefficient C 
fails entirely to measure in any way the change of form that occurred with increase 
in length. Further, the value of C for a fish that weighs 8 pounds at the length of 
2 feet is 0.80, and from this value it would appear that a fish that doubles its length 
without change of form actually suffers a loss of condition. Since the assumption is 
hardly tenable that a fish can suffer such a great loss of condition without undergoing 
any change of form or relative heaviness it must be concluded that values of C cal- 
culated from empirically determined exponents fail to serve as satisfactory measures 
of condition. Questions concerning the use of C as a coefficient of condition will 
receive further consideration in connection with the presentation of the data of this 
investigation on condition and the length-weight relationship in the cisco populations 
of Trout Lake, Muskellunge Lake, Silver Lake, and Clear Lake. At the present 
time, however, a brief review will be presented of the observations and opinions of 
authors who have used or suggested the use of C in equation (2) as a coefficient of 
condition. 
The observations of Jarvi (1920) should be included in this review, although in 
justice to that author it should be emphasized that he was concerned primarily with 
the calculation of unknown lengths and weights from a general length-weight relation- 
ship rather than with the measure of condition. Jarvi’s data are of particular interest 
here since he included a comparison of coefficients based on the cube relationship and 
as determined from equations of the type, W=CL D , with empirically determined 
exponents. His coefficients for the males, the ripe females, and the spent females 
of the ldeine Marane ( Coregonus albula ) were, on the basis of the cube relationship, 
11 The term “form” es employed throughout this section carries with it no implications as to details of shape, but refers only 
to relative heaviness of stature. 
