243 
AGE AND GROWTH 1 OF THE CISCO 
in millimeters and weights in grams, the actual values oij(L) were quite small. To 
avoid the use of such small decimals the coefficient of condition K as actually used 
was defined: 
K—j(L) X 10 5 (4) 
In the Trout Lake, Muskellunge Lake, Silver Lake, and Clear Lake populations 
the variation of condition with length, and of weight with length conforms closely 
over certain length intervals with the conditions defined by equation (3). Conse- 
quently it was possible to determine equations describing condition and weight as 
functions of length by fitting parabolic equations to the observed average values 
of K at different lengths. 
The assumed relationship between K and L indicates a linear relationship between 
the logarithms of their values: 
log K=a J r m log L, 
(5) 
where a=log (7+5. 
It is possible to determine the values of G and m by fitting a straight fine to the 
logarithms of corresponding values of K and L. The determined values of C and m 
can be used in writing not only the equation for K as a function of length but also 
for writing the equation for weight as a function of length. 16 
Table 27 contains the equations obtained for K=CX10 5 L m and W=CL a . 
The data from which the equations were determined are found in tables 28 to 31. 
The tables mentioned last contain also a comparison of actual weights with theoretical 
weights calculated from the length-weight equations of table 27. 
Table 27 . — Equations for K = CX10 5 L m and W<=CL n as determined for the various cisco collections 
Lake 
Year of 
collection 
Sex 
Number of 
specimens 
Range 
of L 
K = CX10» L«“ 
O 
II 
is 
1 1928 
cf, 9 
138 
125-154 
K=6. 5232 L-°- 3S7jl _ 
W=6. 5232X10-* L2-«“». 
\ 1930 
d\ $ 
483 
125-169 
K-4. 8834 L-°-«»” 
W-4. 8834X10 -5 L 2 *7i033 # 
l 1931 
d\ 9 
338 
125-164 
If =38. 7640 L-°-«™» 
W =38. 7640X10-8 L2-3°™>. 
| 1928 
cf, 9 
263 
145-179 
K=4, 668.9 L-i.««™ 
W =4, 568.9X10-8 Li.37710. 

1 1930 
eF, 9 
244 
140-179 
K=567. 36 L-i-23)cj 
W =567. 36X10-5 L>-™538. 
] 1931 
d\ 9 
605 
130-179 
K = 141. 92 L-O-Mku 
W = 141. 924X10-5 L2-05088. 
l 1932 
d\ 9 
93 
145-179 
K = 182. 87 L-o-MHi 
W = 182. 87X10-» L2-0MS5. 
/ 1930-31 
s’ 
110 
130-199 
K=0. 25532 L»-32S™ 
W=0. 25532X10-5 L3-3»™. 
\ 1930-31 
9 
160 
135-204 
K=0. 12322 L0-«37> 
W=0. 12322X10-5 L3-«372. 
f 1931 
cF 
85 
160-359 
K=0. 10104 L°-«°“° 
W=0. 10104X10-5 L3-50530. 
1 1931 
9 
105 
170-379 
K = 0. 04555 L0.IHM1 
W=0. 04555X10-5 L3-8MS1. 
1932 
cF 
100 
160-379 
K=0. 04954 L»-«2U8 
W=0. 04954X10-' L3-82U«. 
( 1932 
9 
85 
150-389 
K=0. 03652 L"-«s«» 
W =0. 03652X10-5 L3-«s««, 
11 For the purpose of fitting the equations the specimens were divided into length groups (10 millimeters in the Clear Lake 
cisco, 5 millimeters in the other populations) and the average values of K and L determined for each interval. A straight line was 
fitted to the logarithms of these values by the equating of moments. Combinations of the sexes and of different years’ collections 
were made wherever the data justified the procedure. In Trout Lake and Muskellunge Lake the sexes were combined in each year’s 
collection. In Silver Lake the sexes were treated separately, but the 1930 and 1931 collections were combined. In Clear Lake 
each sex and each year’s collection received separate treatment. The data upon which the equations were based include only the 
size ranges for which adequate numbers of specimens were available. 
