246 
BULLETIN OF THE BUREAU OF FISHERIES 
samples of a single population. It will now be shown that not only does n vary 
from population to population and from year to year in the same population but 
further that in two populations, at least, the values of n determined for a single 
year’s sample apply only to the length intervals for which the equations were fitted 
and do not hold for fish whose lengths lie outside these length ranges. 
If the equation, #=CX10 5 Z m , for each year’s collection of the Muskellunge 
Lake cisco is solved for Z= 100 millimeters the following values of K are obtained: 
1928, K= 2.59; 1930, K= 1.93; 1931, #=1.80; 1932, #=1.86. These values of the 
coefficient of condition indicate a fairly robust body form. Ciscoes of such heavy 
build are indeed found among the larger fish of the Clear Lake population (table 31), 
but it is very unlikely that such heavily built individuals may be found at the length 
of 100 millimeters in the Muskellunge Lake cisco population, or in any population 
of the same species. This view is supported by the comparison of the K values 
upon which the 1928 length-weight relationship was determined (table 29) with 
those of the 15 fish that were less than 145 millimeters long. Eight of these 15 fell 
in the 125-129 millimeter length interval and had an average value of 1.23 for the 
coefficient of condition, K ; the 5 individuals in the 130-134 millimeter interval had 
an average K value of 1.25; while 2 single individuals whose lengths were 138 and 
144 millimeters had K values of 1.29 and 1.34, respectively. These data show that 
in 1928 the values of K in Muskellunge Lake ciscoes less than 145 millimeters long 
were much lower than the theoretical length-weight equation (based on specimens 
more than 145 millimeters long) indicated they should be. 
The 1931 data for Trout Lake furnish another example of the failure of a length- 
weight equation to describe the length-weight relationship for fish outside the length 
range for which the equation was determined. The length-weight equation for 1931 
(see table 27) was based on specimens whose lengths ranged from 125 to 164 milli- 
meters. The same collections contained five large fish (189 to 225 millimeters long). 
Since the 1931 length- weight equation for Trout Lake indicates a continuous decrease 
of K with increase in length, these large fish would be expected to show small values 
for the coefficient of condition. Table 32 which contains a comparison of actual 
and theoretical values of weight and K for these five fish shows that they fail com- 
pletely to fulfill this expectation, for the actual values of weight and K are far above 
the theoretical values calculated from the length-weight equation. 
Table 32 . — Values of length, weight, and K for the 5 longest individuals of the 1931 Trout Lake cisco 
collection 
Age 
Length 
Calcu- 
lated 
weight 
Actual 
weight 
Calcu- 
lated 
value 
of K 
Actual 
value 
of K 
VIII 
189 
69 
100 
1.03 
1.48 
XI 
192 
72 
90 
1.02 
1. 27 
VIII - . 
203 
82 
122 
.98 
1. 46 
XI 
218 
97 
148 
.93 
1.43 
XII .... .. .. 
226 
105 
172 
.91 
1.49 
Observations on the failure of a single value of n to hold for all lengths of fish 
within a population have been made previously by Clark (1928), Walford (1932), 
and Schultz (1933). 
Materials for the comparison of condition in the different populations and in 
different^years are to be found in tables 28 to 31 and 33. The last-named table 
