272 GENERAL BIOLOGY 



The normal flowering head has eight ray flowers, and the 

 relatively fewer variants are nearly all on the side of the 

 lesser numbers. 



In the midst of such fluctuating variations there sometimes 

 exists a marked tendency toward a definite structural type. 

 Such is the tendency of the compound leaves of the smooth 

 sumac (fig. 165) to be odd -pinnate; that is, to have one 

 terminal unpaired leaflet, with all the other leaflets arranged 

 in pairs. A count of the leaflets of 2 730 leaves of this species 

 results as follows: 



No. of leaflets (classes) 56 7 8 9 10 11 12 



No.of times occurring (frequencies) 3 9 24 11 57 20 75 30 

 13 14 15 16 17 18 19 20 21 22 23 24 25 26 

 224 71 352 80 501 106 331 35 143 14 31 4 7 2 

 Here is a total of 1748 odd-pinnate and of 382 abrupt- 

 pinnate leaves. The broken curve which these figures 

 yield is obviously the equivalent of two similar curves for the 

 two types of compound leaf, and the greater height of the 

 odd-pinnate curve is the index of the tendency toward such 

 leaf type in this species. 



Study J5. Fluctuating numerical variations. 



Select some common organism or organ having parts that 

 can readily be counted and that vary in number, and study 

 the variation in numbers of these parts. Let the numbers 

 be small ones (for economy of time in counting, prefer- 

 ably not above 20). Such things as the seed spines, ray 

 flowers, or leaflets of a compound leaves just cited in these 

 pages, or leg spines, wing hooks, leaf lobes, etc., etc., are 

 everywhere available in sufficient abundance. Gather the 

 material at random. Count at least 100 specimens and 

 record the classes and the number of times occurring, as 

 in the first example cited (see fig. 164). Then plot the 

 curve of variation on a square of cross-section paper, lay- 



