188 THE QUANTITATIVE METHOD IN BIOLOGY 



hereditary possibilities (possible primordia). In the variatioi 

 of a given primordium continuity or discontinuity may exist 

 within the limits of a complex group of specimens (including 

 two or more specific forms), just as within the limits of a mono- 

 typic group (including one specific form only). In § 21 I have 

 called attention to this fact. (See also § 128.) 



Here a distinction must be made between primordia with 

 variation steps and primordia in which no variation steps exist. 



I take as first example the length of the longest leaf of the fertile 

 ste?n in Mnium serratum, spinosum and undulatum. These 

 three species (Acrocarpic Mosses) are distinctly different and 

 easily recognizable. I have measured the mentioned prim- 

 ordium in a number of specimens collected from several 

 localities. No trace of variation steps could be discovered. 

 The limits of variation were (in mm.) : 



Serratum 



Spinosum . . 

 Undulatum . 



According to these figures, which are specific constants, ^ 

 absolute discontinuity exists probably between serratum and 

 spinosum (the difference between 471 and 5-01 is, however, too 

 small to be decisive) and certainly between serratum and 

 undulatum. Between spinosum and undulatum continuity 

 exists, for 6-93 < 8-10. 



The aspect of the question is completely changed when we 

 limit the comparison to series of specimens collected from 

 given localities. 



We may find, for instance, in a locality A, for spinosum : 

 limits 5 -20 and 7-60, mean 6-40 ; for undulatum : limits 9 and 

 13, mean 11. Between both variation curves discontinuity is 

 absolute. 



In a second locality, B, we might possibly find, for spinosum 

 limits 6-93 and 8-io, mean 7-52 ; for undulatum the same 

 figures. Here both curves are identical. 



Between identity and absolute discontinuity all possible 

 transitions may occur. 



In a third locality, C, indeed, the figures may be, for spinosum : 

 limits 5-50 and 8, mean 675 ; for undulatum : limits 7 and 10, 

 mean 8-50. Here transgressive variation exists ; in other words, 

 both curves overlap one another. This results in partial dis- 

 continuity. 



In a fourth locality, D, we may find for spinosum : limits 6-30 



1 It is possible that these constants will be corrected later on, but this is 

 of no importance for our subject. 



