i9 1 2] CURRENT LITERATURE 79 



and that in tri-dimensional material such as fruits, the modes are related in 

 similar manner to the cube roots of the Fibonacci numbers. The absurdity of 

 such a view will be obvious when it is considered that nature takes no note of 

 such arbitrary units of measure as the millimeter and centimeter, and that the 

 choice of any other unit of measure would place the modes on other values. 

 Vogler 1 ^ shows by a much more extensive series of measurements of leaflets 

 of Cytisits Laburnum that while the curves are multimodal, the modes can not 

 by any sort of manipulation be made to fit the Fibonacci series. 



In another paper, Vogler 1 * performs an important service by summarizing 

 the statistical studies which have been made upon the heads of Compositae and 

 the umbel rays of the Umbelliferae, together with a few of the more important 

 investigations upon the flowers and inflorescences of other species. The list 

 of Compositae includes 45 species and of the Umbelliferae 10 species. The list 

 gives not only the names of the species and the particular organs studied, but 

 also states the number of counts upon which conclusions regarding the several 

 species have been based, the apparent modes, and references to papers in the 

 appended bibliography in which the results are recorded. This bibliography 

 contains 63 titles. 



De Bruyker 1 * makes an extensive study of variation in the umbels of 

 Primula the motive for presenting a discussion of the entire subject of statistical 

 variation. This simple and concise presentation of the subject should occupy 

 for Dutch readers a place similar to that held by Johannsen's 16 discussion for 

 readers of German. It is not necessary here to consider the general treatment 

 of the subject of variation as given by De Bruyker, but only the new results 

 relating to Primula officinalis, P. farinosa, and P. elatior. The modal numbers 

 of flowers in the inflorescences of these three species fall with considerable 

 regularity upon the numbers of the Fibonacci series, but collections taken at 

 different parts of the season show a gradual decrease in the average number of 

 flowers per inflorescence as the season progresses. Plants growing in a favor- 

 able environment had the mode on 5, and in less favorable ones on 3. The 

 similarity of results in collections from good and bad surroundings, and in 

 early and later parts of the season, convinces the author of the correctness of 

 the interpretation of the gradual fall in mean number of parts during the 



Vogler 



Beih. 



Bot. Centralbl. 27:391-437. figs. 12. 191 1. 



14 Volger, P., Probleme und Resultate variationstatistischer Untersuchungen an 

 Bluten und Bliitenstanden. Jahrb. St. Gallischen Naturwis. Geseils. 1910:33-71. 

 1911. 



15 De Bruyker, C, De statistische methode in de plantkunde en hare toepas- 

 singen op de studie van den invloed der levensvoorwarden. pp. 226. figs. 33. Gent: 

 A. Siffer. 1910. 



16 Johannsen. W. t Elemente der exakten Erblichkeitslehre. pp. vi+516. figs. 31. 

 Jena: Gustav Fischer. 1909. 



