1895.] Leuciscus Balteatus, A Study in Variation. 21 
not found below 1475 feet, that only one of the seven having 
an average of 16 rays is found below 1000 feet, and that but 
one of the eight having an average of 17 rays is found below 
1000 feet. From the last but three specimens are known. It 
may be further emphasized that three of the five localities 
having an average of 19 rays, are found below 1000 feet, and 
that two of the three having an average of 20 rays are found 
below 1000 feet. Generally, the lower localities have the larger 
number of rays, to which there are several notable exceptions 
—Lake Washington and Snake River at Payette. These facts 
can be presented in curves for groups of localities. Taking the 
specimens from the different groups of localities we obtain the 
following : : 
| | 
r Number of Number of Extentof | General aver- 
TRO localities. specimens. variation. age of anal rays 
| | 
| 
Feet. 
1 to 750 8 | 189 11 | 18.4 
-1078 to 2000 12 234 10 Boe 
2001 to 3100 8 388 10 17.5 
5000 to —— 1 10 16. 
Whether we consider the number of localities having a high 
average of rays, or whether we consider the average of all the 
specimens from a similar horizon, we find that the largest 
number of rays is found in the lower horizon. Furthermore, 
the extent of variation for the 189 specimens, from 1 to 750 feet, 
is greater than the variation for 234 and 388 specimens of the 
higher horizons. The variation for these three horizons is 
given in the three curves of figure 3. 
In the above we have considered the localities regardless of 
the system to which they belong. Lake Washington and 
the Newaukum and Skookumchuck Rivers belong to separate 
short water courses. Eliminating these and considering the 
localities of the Frazer and Columbia systems separately, we 
get the conditions described for the Frazer system. above and 
for the Columbia system the following, arranging t the localities 
in the order of elevation : i 
