196 THE QUANTITATIVE METHOD IN BIOLOGY 



the term parallel variation and are therefore confounded in our 

 mind. 



1 place in a first group the cases in which two or more sub- 

 species, species, genera, etc., resemble one another in certain 

 properties, without more. Examples : fasciated and twisted 

 stems, ascidiform leaves, eye-shaped spots on the wings of 

 butterflies and the feathers of birds. In certain Conifera 

 {Finns silvestris, etc.) certain insects (Chermes) bring about 

 cecidia, which resemble a strobilus by certain properties, etc. 

 Such resemblances are the expression of similar states of equi- 

 librium : they ought to be called mechanical concordances. 

 They are comparable to the examples given in § 65, in which 

 this subject is expounded. 



In other cases a SERIES of primordia, observed in a species 

 (genus, etc.) A is met with again in a second species (genus, 

 etc.) B. Examples : the above-mentioned horses of different 

 races which present the same range of colour. 



If there is no relation between the properties which belong to 

 such a series,! the term parallel variation ought to be avoided : 

 the resemblances under consideration are mechanical concord- 

 ances and belong to the first group. 



Second Group. — It may happen, however, that the pro- 

 perties imder consideration are terms of an embryological series 

 (§ 133). I bring such cases in a second group under the name 

 embryological parallelism. Example : in the species Myosotis 

 palustris three subspecies exist : white, rose, blue. In other 

 species of Myosotis and in several species of other genera of the 

 same family {Echium vulgar e, etc.) a similar series of subspecies 

 exists. The primordia white, rose and blue are terms of an 

 embryological series : therefore we may say that embryological 

 parallelism ^ exists between the different series of white-rose- 

 blue subspecies. 



In a third group of so-called parallel variations, the properties 

 under consideration correspond to determined values, a, b, c 

 ... of one primordium and coincide with variation steps. 

 Here the existence of the terms a,b,c ... in several subspecies, 

 species, genera, families, etc., depends on a mechanical con- 

 cordance of a peculiar kind which I designate by the term 

 parallel variation steps. Examples : the series 2, 4 ... 2" is 

 repeated in Pediastrum (number of cells, § 122), the OnagracecB 

 (number of stamens, § 126), the Mosses (teeth of the peristome, 

 § 122). The Fibonacci series is found in many Composites 

 (number of marginal florets) and UmbellifercB (number of rays 



'I don't know whether any relation exists between the colours of the 

 horses. 



2 The term embryological parallelism is based upon the constatation of a 

 fact and quite independent of the phylogenetic relations between the sub- 

 species alluded to. 



