VARIATION STEPS 189 



and 8-10, mean 7-20 ; for undulatum : limits 6-93 and 9-10, 

 mean 8-02. Here the difference between both curves is small. 



Suppose now that the two species under consideration were 

 doubtful (critical) species, and that for each locality the collected 

 specimens were confused in one series of measurements, the 

 result would be : in A, two separate curves ; in C, a two-humped 

 curve; in D, a one-humped asymmetrical curve; and in B a 

 regular, symmetrical one-humped curve. If we limit ourselves 

 to one series collected from one locality, we are in danger of 

 being completely deluded : the curves obtained from the 

 localities B and D point to the existence of one species, whereas 

 the existence of two specific forms seems to be demonstrated by 

 the figures obtained from A and C. If the curves obtained from 

 the four localities were compared, we might perhaps be tempted 

 to believe that transitory forms between two species exist. 



In reality, the differences between the four localities depend 

 merely on differences in the conditions of existence. Compare 

 Mnium hornum in § 127, p. 182. 



From the above examples (and many others which may 

 easily be found) it may be concluded that continuity and dis- 

 continuity in various degrees may be observed in the variation 

 of any primordium whatever in a given group of specimens, 

 and that any conclusion about the existence of one or several 

 species among the observed material is questionable, if not 

 verified by other methods. 



When variation steps exist in the investigated primordium 

 we are still more in danger of being deceived if we draw any 

 conclusion from a supposed relation between continuous varia- 

 tion and specific identity or between discontinuous variation 

 and specific difference, for a monomorphic (one-humped) curve 

 may be easily transformed into a dimorphic or a polymorphic 

 one by a simple change in the conditions of existence or under 

 the influence of gradation. See the examples of Chrysanthe- 

 mum and Primula in § 128, pp. 184 and 185. 



Many attempts have been made in order to discover, by 

 means of the biometrical method, whether a given critical 

 species consists of one or several specific forms, and also in 

 order to find characteristic differences between two or more 

 allied critical species or between specimens of a given species 

 collected from various countries or localities. In the researches 

 alluded to much importance has been ascribed to the mean 

 values, the correlation constants and the form of the variation 

 curves.^ Several authors are tempted to believe that a sufti- 

 cient degree of discontinuity in the variation curve of a given 



^ This subject is expounded and illustrated by a number of examples in 

 VERNON, loc. cit., chaps, ii. and x. Examples are also found in the review 

 Biometrika, passim. 



