92 



Tlie proportions, while vaiviiii; considerably, do not show any wider tinmia- 

 tious than usual. The position of the dorsal, on the other hand, varies from mid- 

 way from Itase of the middle caudal rays, and from a point behind to a point 

 al>ove the middle of the eye. 



In the development of the keel behind the ventral fins we find again a sjreat 

 riuituation in speoimen8 from the same locality. In some, the keel is very sharp; 

 in others it is entirely absent, and between these forms, we have ail shades of 

 variation. If uniform, it would be of generic value. 



Now. as to the variation of the anal rays. The lowest numlier retorded is lo 

 ( alter adding "2 to tTJliiert and Evermann's lowest number), and the hishest is 24. 

 This gives a total variation of 12 rays. This would be a large variation for any 

 tish. but becomes phenomenal when it is considere<i that the variation in the 

 number of anal rays of the 175 Atlantic slope species extends only fmm <i to 14. 

 a total variation of but 5< for 17-'> species as compared with the variation of 12 for 

 a single species. The high number of rays reached is also phenomenal, for. leaving 

 out of consideration the two rudimentary sjiines, the highest number of anal rays, 

 22. is ten more than the nuud)er found in any other Pacific Cyprinoid, and eight 

 more than the nutnber found in any Atlantic species. The average uuml>er of 

 rays is seventeen. The variation to lower numbers extends throngh 4 rays to l:>. 

 The variation to higher numbers is luuch greater, extending through 7 rays to 24. 

 Not only is the e.xteut 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 average 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 numlui-. A more striking illustration of determinate variation could 

 not be wished. 



Figure 1 graphically re|>resents the variation of the species as shown by the 

 '^2o specimens examined. The total hight of tiie vertical lines represents the 

 greatest possible number, 100 per cent., that conid have the given numl>er of 

 anal rays indicated at the bottom of the lines. The curve shows the actual per 

 Cent, of specimens having each particular number t)f rays. Were the variation 

 promiscuous the curve would be symmetrical. The symmetry shows the inherent 

 tendency to a higher number of rays in this fish. It may be well to bear in mind 

 th^it no other si^>ecies has a higher number of rays — that no other species joins this 

 curve on the right — while at least ime, probably two, related species living in the 

 head-waters of the Snake River have fewer rays, ». e., joins this curve on the 

 left. The curve of Leuriscua hydrophlox will not only joiii this curve, but overlap 



