1895.] Leuciscus Balieatus, A Study in Variation. 19 
place. The variation from the normal, which is 19 rays, to a 
higher number of rays, is as great as the entire variation for 
the next locality. At Sicamous, a much larger per cent. has 
the normal number of rays, but the normal number has been 
decreased to 17. The curve for Griffin Lake is interesting, 
because the normal number of rays has again been decreased 
by two. In other words, the higher the altitude the fewer the 
number of rays and the narrower the limit of variation.’ 
Moreover, the curves are not symmetrical for any of the three 
localities, but, in the aggregate, the more gradual slope is on 
the side of an increase in the number of rays, a condition, 
which, considering the general variation of rays on the Pacific 
slope, seems to indicate that the number of rays of this species 
in the Frazer system is increasing, and that the increase is 
progressing from lower to higher altitudes. 
A glance at the remaining curves will be sufficient to show 
that no two curves are alike, that the per cent. of specimens 
having a given number of rays differs with each locality. 
Naturally, the curves constructed from a large number of 
specimens represent the true conditions better than the curves 
constructed from but few. The extent of the variation varies 
largely with the number of specimens examined ; that is, the 
probability of securing extremes becomes greater with an in- 
crease in the number of specimens collected. The greatest 
extent of variation for any locality, as far as known, is through 
9 rays. This has been found only when over 70 specimens 
have been compared. It decreases to about 5 rays with 10 
specimens. The total variation for the species has not been 
found at any one place. 
The question of variation, with elevation, is an interesting 
one, and may be taken up in some detail. 
In the following table, all the localities are grouped, accord- 
ing to their average number of rays. 
5 In their recent paper, Gilbert and Evermann have raised this specific state- 
ment, which occurs in my paper quoted above, into the dignity of a “theory ” 
and “generalization” which it was never intended to be, and their arguments 
against it as a “theory” and ‘‘ generalization ” are, therefore, not appropriate. 
