VARIATION STEPS 181 



rectangular cross. In these examples, the observed symmetry- 

 is secondary, the number of segments is primary. 



Between symmetry and variation steps certain relations may 

 exist and probably really exist. In certain examples symmetry 

 may be the cause of the variation steps ; in other examples 

 symmetry is rather the effect, the variation steps being the 

 cause. It is impossible to express the relations alluded to in 

 one short sentence. 



This subject is in relation with very delicate morphological 

 problems. Morphological homology, mechanical concordance 

 (§ 65) and variation under the influence of external causes 

 (plasticity) ought to be taken into account ; the distinction 

 between hereditary possibilities and observable properties must 

 be borne in mind. 



§ 126.— THE SIGNIFICANCE OF AN OBSERVED VALUE 

 DEPENDS ON THE SERIES TO WHICH IT BELONGS.— 



In Senecio nemorensis, subsp. octoglossa, the marginal florets are 

 8 in number. Here the number 8 is a term of the Fibonacci 

 series, for other terms of this series are observed in other species 

 of Senecio (§ 124) and in other Compositae. In Epilobium and 

 Fuchsia 8 stamens exist ; here the number 8 is a term of the 

 series 2, 4, 8 . . . 2^ for this series is observed among the Ona- 

 gracecB (Circcea, Lopezia, 2 stamens ; Eucharidium, Isnardia, 

 4 stamens ; Hauya, Clarkia, CEnothera, Epilobium, Fuchsia, 

 8 stamens). From these examples (see also § 123, Remark) it 

 may be concluded that the significance of a given value depends 

 on the series to which it belongs, as often as variation steps are 

 at play. 



In other words, the series of steps through which the value 

 of a given property passes is the quantitative expression of 

 a certain specific energy of this property. Therefore the value 

 8 is the expression of different specific energies in Epilobium 

 and Senecio. 



This is of the highest importance with regard to the study of 

 heredity and variation. (See § 131.) See, in § 132, the methods 

 for discovering the series of variation steps to which a given 

 value belongs. 



§ 127.— A MEAN VALUE WHICH COINCIDES WITH A 

 VARIATION STEP MAY BE LOOKED UPON AS BEING 

 A CONSTANT. — In a biological curve a mean value which does 

 not coincide with a variation step has not the significance of a 

 constant. It is not the measure of something which has an 

 independent existence, and it is therefore quite different from 

 the mean value of a curve of errors. (See § 108.) Such a 

 biological mean is merely an indirect measure of the conditions 



