Transgrcssive Variability. 431 



systematist. The vast majority of systematic species 

 are made and described on a few specimens; and where 

 large numbers of individuals have been available the in- 

 vestigator has contented himself with the general im- 

 pression they produce on him. The result of this is 

 that we have a knowledge of the typical forms of species 

 but no exact idea of their limits. 



Statistical investigation, as we have already said, is 

 necessary to determine what these limits are.^ Such in- 

 vestigation teaches us not only what the mean of a char- 

 acter is, but also the range of its variation. In the fore- 

 going section we have seen that the deviations are often 

 so large that neighboring curves sometimes overlap. This 

 is the phenomenon which I call transgrcssive variabilitw 



Let us choose a particular example to make this phe- 

 nomenon clear. 



We will select the common species O. biennis L. and 

 O. ninricata L. which, as every one knows, can be easily 

 distinguished by the size of their flowers. In the former 

 species they are large and project horizontally from the 

 stem; in the latter small and erect. 



But let us subject this familiar and obvious and con- 

 venient distinction between two species made by Lin- 

 naeus himself^ to statistical analysis.^ We measure the 



^ Beautiful examples of transgressive curves are given in a zoo- 

 logical article of P. P. C. Hoek^ Nciiere Lacks- uiid Maifischstudicn 

 in Tydschrift d. Nederl. Dierk. Vereeniging. (2) VI, 3, S. 231-235. 

 See further G. Duncker, On Variation in the Rostrum in Palac- 

 monetes vulgaris. Americ. Naturalist, Vol. 34, No. 404, 1900 and of 

 the same author: Variation uiid Asymtnctrie bci Plcuroncctus iicsiis 

 L., Wiss. Meeresunters. Helgoland, Bd. Ill, Heft 2, 1900. 



^ Spach in his monograph of this genus also separates these two 

 forms as species (O. vulgaris, Spach. = O. biennis L. : O. chrysantho 

 Spach. =^ O. muricata L.). 



^The types indicated in this book by the names O. bioniis and 

 O. muricata are those found all over Europe, which are probably 

 the prototypes on which Linnaeus based his descriptions. In Amcr- 



