16 The American Naturalist. [January,, 
formula is 2,5-4,1 or 2. The variation through ten different. 
combinations is exceptional. 
The proportions, while varying considerably, do not show 
any wider fluctuation than usual. The position of the dorsal, 
on the other hand, varies considerably. 
In the development of the keel behind the ventral fins we- 
find again a great fluctuation in specimens from the same 
locality. In some, the keel is very sharp; in others, it is en- 
tirely absent, and between these forms, we have all shades of 
variation. If uniform, it would be of generic value. 
Now, as to the variation of the anal rays. The lowest num- 
ber recorded is 13 (after adding 2 to Gilbert and Evermann’s 
lowest number), and the highest is 24. This gives a total 
variation of 12 rays. This would be a large variation for any 
fish but ,becomes phenomenal when it is considered that the 
variation in the number of anal rays of the 175 Atlantic slope 
species extends only from 6 to 14, a total variation of but 9 for 
175 species as compared with the variation of 12 for a single 
species. The high number of rays reached is also phenom- 
enal, for, leaving out of consideration the two rudimentary 
spines, the highest number of anal rays—22—is ten more than 
the number found in any other Pacific Cyprinoid, and 8 more 
than the number found in any Atlantic species. The average 
number of rays is 17. The variation to lower numbers extends 
through 4 rays to13. The variation to higher numbers is 
much greater, extending through 7 rays to 24. Not only is 
the extent of variation greater towards higher numbers, but 
the number of specimens varying in that direction is much 
greater. Of 825 specimens, but 22.3 per cent. have the aver- 
age number of rays. This is the largest per cent. for any given 
number of rays. Thirty-four per cent. of all the specimens have 
fewer than the average number of rays, while 42.9 per cent. have 
more than the average number. A more striking illustration 
of determinate variation could not be wished. Fig. 1 graphic- 
ally represents the variation of the species as shown by the 
825 specimens examined. The total height of the vertical 
lines represents the greatest possible number—100 per cent— 
that could have the given number of anal rays indicated at the 
