130 
BULLETIN OF THE UNITED STATES FISH COMMISSION. 
Ill tlie Aiiiericaii, genera of Ciiprinidic the number of anal rays is usually fixed witbin 
two or three for any genus. In the group of fishes under consideration the number 
varies within 12. 
Now a word as to the charts. The vertical lines on plates 7 and 8 represent the 
number of anal rays, beginning on the left with the lowest number observed and end- 
ing on the right with the highest. A certain height (100 mm.) is taken to represent 
100 per cent. The height of the curve on each vertical line is made to represent the 
per cent of si»ecimens having that particular number of fays expressed in millimeters 
of height. ' • 
In the table below the numbers in the headings represent the numbers of anal rays 
found in siiecimens of iiltc/mrdsoMdis, and opposite each locality is given the number of 
specimens from that locality possessing the given number of rays. Thus from Idaho 
Falls, 2 specimens had 12^ rays in the anal, II specimens had 13i rays, and I speci- 
mens had III rays. At the bottom is given the nearest per cent that the sum of any 
given column bears to all the (300) specimens examined. 
Locality. 
Kiev a- 
Number of rays iu the aua). 
tiou. 
lU. 
12i. 
13^. 
\U. 
15J, 
16J. 
17L 
18i. 
19g 
20g 
21^. 
22g 23g 
24J. 
Feet. 
26 
12 
Columbia Basin. 
4. 712 
2 
14 
4 
2 786 
9 
6 
11 
4 
2 550 
1 
5 
4 
1 
2, 372 
1 
2 
0 
7 
8 
7 
9 
1 
1 
300 
1 
5 
1 
9 
1 
Fraser Basin. 
■ 1. 900 
1,300 
1 158 
3 
O 
3 
1 
1 
3 
13 
28 
8 
5 
1 
1 
1 
9 
7 
13 
25 
18 
8 
2 
9 
2 
9 
9 
4 
8 
13 
17 
11 
12 
8 
4 
1 
1 
1 
i 
Taking all the specimens recorded (300), adding the columns, and representing the 
variations in the anal rays in a curve,* we find that there is a certain number of shoul- 
ders or peaks. Each of these represents a distinct species or variety. The extent of 
intergradatiou can be measured by the depth of the valley between any two peaks. 
In well-separated species the slopes of the two peaks would not meet. Now it will be 
noticed that the depth of the valley between the two right peaks is quite shallow; 
and, in fact, I find the variation almost perfect between L. halteatus and lateralis^ the 
two varieties represented by these two peaks. The valley between the middle one 
and the two on the left is deep. In other words, L. lateralis is well separated in the 
character under consideration from L. liydrophlox and montanus, the species repre- 
sented by the peak to the left. On the other hand, the latter species merge into each 
other perfectly in the number of rays. 
I have represented in a double curve or composite iihotograph, as it were (plates 
* By au oversight this curve has heeu omitted. The height of the curve in millimeters at various 
points is indicated by the uumhers at the bottom of the table. With these the curve can easily he 
constructed hj' using the lines of plate 7 or 23late 8. 
