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IOWA ACADEMY OF SCIENCE 
flowers on it were counted. Only imperfect, and partially de- 
stroyed heads were discarded. Great care was taken in counting 
the rays, and in recording the counts, that no mistakes be made. 
Table No. 2 records the results of the counts. 
TABLE No. 2. 
Condensed table for all the varieties studied, showing all of the 
MAGNITUDES AND THEIR CORRESPONDING FREQUENCIES. 
Rays 
per 
head 
Rudbeckia hirta 
Rudb’kia 
triloba 
Helianthus grosse-serratus 
Ames 
Center 
Point 
Hedrick 
Total 
Ames 
Council 
Bluffs 
Ames 
Total 
2 
1 
1 
3 
1 
1 
4 
1 
2 
3 
5 
18 
18 
20 
6 
1 
4 
19 
24 
83 
7 
4 
5 
52 
61 
192 
1 
1 
8 
45 
1 
576 
622 
306 
1 
1 
9 
36 
9 
294 
339 
91 
13 
13 
10 
42 
9 
249 
300 
32 
2 
27 
29 
11 
53 
21 
233 
307 
11 
6 
65 
71 
12 
87 
23 
340 
450 
4 
16 
124 
140 
13 
230 
47 
1,050 
1,327 
1 
34 
320 
354 
14 
43 
5 
192 
240 
. 2 
23 
215 
238 
15 
12 
3 
59 
74 
21 
143 
164 
16 
2 
35 
37 
10 
76 
86 
17 
12 
12 
7 
51 
58 
18 
1 
5 
6 
4 
41 
45 
19 
9 
9 
2 
26 
28 
20 
1 
1 
2 
25 
25 
21 
4 
4 
35 
35 
22 
4 
4 
7 
7 
23 
3 
3 
24 
25 
1 
1 
1 
1 
26 
27 
1 
1 
28 
1 
1 
Tot. 
558 
128 
3,161 
3,847 
742 
125 
1,171 
1,296 
It will be seen by inspection of Table No. 2, and Plates I, II, III, 
and IV, that heads of Rudbeckia hirta containing 13 rays greatly 
predominate. The characteristic mode is at 13, with a very 
marked mode at 8, and smaller modes at 19 and 21-22. This very 
closely agrees with the results obtained by Lucas, '04 (Am. Nat., 
38:427-429). He says that Rudbeckia hirta has a primary mode 
at 13, and secondary modes at 8 and 20-21. It is possible that a 
