i9o8] CURRENT LITERATURE 63 



BouLENGER/'^ from observations of the evening primroses growing wild at 

 South Kensington, England, and in La Garde St. Cast, Brittany, concludes that 

 O. Lamarckiana and O. biennis cannot be distinguished as separate "species,'* 

 and that O. Lamarckiana originated from O. biennis through some hypothetical 

 process of hybridization among the different forms of the latter. His conchisions 

 rest on an examination of the variability of the plants taken en masse in the wild 

 condition, and the unproven assumption that all the plants obse^^'ed at St. Cast, 

 Brittany, came from a single stock. Many different forms, both in Europe and 

 America, go under the name of O. biennis^ as MacDougal has shown, and if 

 0. Lamarckiana were capable of giving rise to any of these we might have expected 

 to find them in DeViqes' cultures. The study of the Oenotheras has long since 

 reached the stage where cultures are necessary to determine the relationships of 

 the various strains, and without such studies speculations drawn from casual ot^er- 

 vations of variability among forms growing wild are not likely to affect seriously 

 the results obtained from culture work such as that of DeVries.— R. R. Gates. 



A biometric study of Ceratophyllum. — A recent memoir by Pearl'? on varia- 

 tion and differentiation in Ceratophyllum presents an admirable illustration of 

 the successful application of mathematics to the working-out of important biological 

 problems. The work is too compact to allow a brief review to present all the impor- 

 tant relations which are clearly demonstrated by biometric analysis of the variation 

 in the number of leaves in a whori as related to the position of the whorl on the 

 plant. It is shown that the whorls on each grade of branches, e. g., main stem, 

 primary, secondary, tertian% etc., are differentiated as a class from each other 

 grade by several distinctive features of their variability. In all these grades the 

 correlation between number of leaves in a whori and its position on the stem is 

 considerable. It is least in the main stem and increases as we pass to the more 

 peripheral dinsions. The regression line is not linear, but logarithmic, being of 

 the t>-pe y = A + C\.og{x - a\ in which A, C, and a are constants, y is the number 

 of leaves per whori, and x the position of the whori. The curves so derived fit 

 beautifully the observed data, and allow the derivation of what is believed to be 

 a very fundamental biological law which b caUed the "first law of growth" in 

 CeratophvUum, and is stated thus: "On any axial division of the plant the mean 

 number of leaves per whori increases with each successive whori in such a way 

 that both the absolute increment and the rate of increase diminish as the distance 

 (measured by the number of nodes) of the whori from a fixed pomt mci^ases. 



By the fact that the equation fits data from plants collected fiom different 

 hnbit^R hv mprplv rhan-inff the factor A which represents the actual size and 



^ rrn— m ini'inii i iiii 



•6 BoriEXGEE, G. A., On the variations of the evening primrose (Oemtk^m biennis 



L.). J ox. Botany 45:333-363- 1907- 



.7 Peaex, RiViiOOT, assisted by OmE il. Pefpek and F-^-^^y^/' 

 Variation and difierenuadon in CeratophyUun.. Carnegie Inst.tut.on d VVashington. 



Ptihr Tin CS_ nn- tii6. ^Is. 2, fiZS. 26. IQO^. 



