AGE AND GROWTH OF THE CISCO 
241 
Clark’s data on the correlation between weight-length factors (calculated from 
the cube relationship) and the fat content of the sardine offers convincing evidence 
that measures of condition should be calculated from the cube relationship. Her 
data show conclusively that variations with length in the value of the weight- 
length factor are reflected closely in corresponding variations with length in the fat 
content of the sardine. Inasmuch as relative heaviness is thus showed to be de- 
pendent on fatness (condition), changes with length in relative heaviness must be 
considered also to represent changes of condition. In view of this fact it does not 
appear valid to measure condition in terms of a quantity that tends to be constant 
for fish of all lengths regardless of actual changes that may occur in relative heaviness 
of form with change in length. Since the quantity C in the equation W = CL D tends 
toward this constancy and fails to measure relative heaviness it must fail also to 
measure the differences of fatness (condition) upon which differences in relative heavi- 
ness depend. 
Tester (1932) likewise appears to have confused the two problems of measuring 
condition and describing the general length-weight relationship. Concerning his 
method of determining the general length-weight relationship in the smallmouth 
black bass ( Micropterus dolomieu ) he stated: 
Following the method used by Hart (1931) and others the relationship between length and 
weight for bass from Perch Lake [Ontario! was obtained by plotting average lengths against average 
weights on double logarithmic paper and deriving the natural slope of the resultant straight line 
drawn through the points. It was found that the weight increased by the power 3.1(7) of the 
length. * * * 
Tester assumed, however, that the failure of the cube law to describe the length- 
weight relationship made the use of coefficients of condition based on the cube rela- 
100 W 
tionship invalid. Concerning the equation, K= — employed by Hile (1931) to 
describe condition in several species of Indiana lake fish, Tester stated: 
This equation is only approximate and might be better expressed — 
K = 
100 W 
In the case of the Perch Lake bass the power x would have a value 3.1(7). If the power x = 3 is 
used, the value of K tends to increase with the length of the fish whereas it should remain constant. 
Tester used the value x =3. 1(7) as determined from the Perch Lake bass to 
compute coefficients of condition for his smaller samples from Phantom Lake, Lake 
Nipissing, and Georgian Bay, but observed that, “To be strictly accurate, the value x 
should be determined separately for each of the latter three bodies of water. * * *” 
Had Tester actually determined the value of the exponent for each of the bass 
populations he studied he would probably have become aware of the difficulties 
involved in the use of coefficients of condition based on empirical exponents. 
Schultz (1933) expressed the relationship of length to weight in the bay smelt 
( Atherinops affinis oregonia ) by the equation W=FL 2 - 59 . He also employed the quan- 
tity F as a measure of seasonal changes in weight, dependent on the state of develop- 
ment of the gonads. That Schultz considered the length-weight factor, F, identical 
in significance with factors calculated from the cube relationship is apparent 
from the following statement: “The length-weight factor, F, was used to estimate 
the state of development of the gonads, as has been done by D’Arcy Thompson (1917), 
24535—36 3 
