VARIATION STEPS 183 



enced in a certain degree by the existence of the variation steps. The curve is 

 governed not only by the laws of chance ; it is also under the influence of the 

 specific energy which finds its expression in the variation steps. 



If we compare the examples given in this paragraph, we see 

 that in the case of Mnium the mean is merely a product of 

 chance ; in Senecio the influence of a specific energy is quite 

 predominant ; in Chrysanthemum the latter influence is less 

 important ; in Centmirea ^ it is still more in the background. 

 It is, moreover, quite thinkable that variation steps might 

 be still more concealed than in the case of Centaurea, their 

 influence upon the mean and upon the form of the curve being 

 stiU smaller. In the present state of science, we must content 

 ourselves with a rough estimation of the influence alluded to. 

 We may, however, anticipate the possibility of calculating it 

 exactly. 



However skUful and subtle the mathematical methods used 

 in biometry may be, biological errors may be committed in the 

 interpretation of a mean value if the eventual existence of 

 variation steps is not taken into account. 



OTHER EXAMPLES : Professor PEARSON counted the number of 

 stigmatic bands on the 4443 seed capsules obtained from 176 Shirley poppies 

 growing in a single garden, and found the following frequencies (Pearson, 

 Grammar of Science, 2nd Ed., p. 443. Quoted after Vernon, p. 89) : — 

 Bands . . 5 6 7 8 9 10 11 12 



Frequency . i 11 32 56 148 363 628 925 



Bands . . 13 14 15 16 17 18 19 



Frequency . 954 709 397 155 51 12 i 



Professor PEARSON counted the segments on 3212 fruits of Nigella 

 hispanica, and found the following frequencies (loc. cit.) : — 



Segments . 23456789 10 



Frequency . 10 7 20 303 412 534 1552 223 59 



Segments 11 12 13 14 15 16 17 18 19 20 



Frequency 35 43 6 — — 6 — ■ — — 2 



In both curves the material is not homogeneous. Terminal fruits and 

 lateral fruits of successive order being brought together, the influence of 

 gradation (social cause, see § 128) has been overlooked. In other words, 

 there is no social equivalence among the material. 



In spite of that, the most common form coincides in each curve with a 

 variation step (respectively 13 and 8) which belongs here to the Fibonacci 

 series. Therefore the hump of each curve may be looked upon as being a 

 constant. 



The mean values (12 "51 and 7 46) coincide approximately with the most 

 frequent values. In reality, however, the mean values (if not compared with 

 the humps) are here a vague expression of the conditions of existence of the 

 examined plants. According to my observations, the number of stigmatic 

 bands in Papaver (poppy) is very variable according to the conditions of life, 

 and this is undoubtedly also the case in Nigella. 



§ 128. — RELATION BETWEEN THE VARIATION 

 STEPS AND THE CONDITIONS OF EXISTENCE. TRANS- 



' By counting the ribs of the shell of Scalaria communis (more than 1000 

 specimens, Flemish coast) a variation curve was obtained more or less similar 

 to that of Centaurea cyanus (MACLEOD and WASTEELS). 



