VARIATION STEPS 193 



AMPLES : Chrysanthemum carinatum, p. 184. In the number 

 of flowers of the inflorescence of Primula elatior a Fibonacci 

 series of the second degree is observed. According to DE 

 BRUYKER, in the state of nature, the predominance of a 

 given term depends on the conditions of hfe (for instance, on 

 the quantity of water in the soil) . 



FIFTH METHOD : Variation steps may be discovered by 

 observing the variation produced by gradation. (See Part 

 VIII.) EXAMPLE : the Fibonacci terms are rendered observ- 

 able in Chrysanthemum carinatum by comparing the flower- 

 heads of the successive lateral branches. (See p. 184.) 



SIXTH METHOD : SELECTION. In certain cases the 

 successive terms of a series of variation steps have been brought 

 into evidence by selection. DE VRIES, starting with two 

 specimens of Trifolium pratense, which had a few leaves with 

 4 leaflets, obtained by selection a form with numerous leaflets, 

 the most frequent values being 3, 5, 7 • . • (series of the un- 

 even numbers). (See also the example of Chrysanthemum 

 segetum, § 129.) 



From this method the discovery of new series of variation 

 steps and the elucidation of the true significance of certain 

 values (§§ 126, 131) may be expected. 



SEVENTH METHOD: CURVES OF DEVELOPMENT. 

 In the course of the individual development many primordia 

 pass through successive values till the definitive value is 

 reached. Ordinarily the increase seems to be gradual (con- 

 tinuous) . It may be expected, however, that in the develop- 

 ment (growth) of a primordium in which variation steps exist, 

 jumps may occur, the passage from a term (step) to the next 

 one taking place suddenly, or more rapidly than the passage 

 between two transitory values. 



It may be anticipated that in such cases the variation steps 

 might be indicated by abrupt changes in the direction of the 

 curve of development (see § 49), these turning points of the 

 curve being more or less distinct according as the series of steps 

 under consideration belongs to the first, the second or the third 

 degree. (See § 124.) Therefore the use of curves of develop- 

 ment for the discovery of variation steps may be suggested. 



§ 133.— SERIATION OF THE PRIMORDIA ACCORDING 

 TO THEIR DEVELOPMENT. EMBRYOLOGICAL SERIES. 

 — Since each term of a series of variation steps represents one 

 of the states of equilibrium of a primordium, the arithmetical 

 relations between the terms of a series correspond to more or 

 less complicated mechanical relations, and very probably in 

 many cases to morphological relations, and also to embryo- 

 logical relations. (See § 132, Seventh Method.) 



