December 15, 1905.] 



SCIENCE. 



803 



So then in practise it will be necessary to 

 calculate from the formula only one of these 

 probable errors for a given distribution, viz., 

 the probable error of the skewness. Having 

 determined this we need only to multiply it 

 hy 2, by 4 and by a to obtain the values for 

 the other three. Kaymond Pearl. 



BOTANICAL NOTES. 

 hallier's natural system. 



In the July number of The New Phytologist 

 Professor Dr. Hans Hallier discusses fur- 

 ther his provisional scheme of the phylogenetic 

 .system of flowering plants. The general fea- 

 tures of his system are : (1) the Angiospermae 

 •constitute a monophyletic group; (2) the 

 Amentaceae are not an old type remaining in 

 a lower state of development, but as ' the 

 laighest and most reduced types of one of the 

 lines of Dicotyledons ' ; (3) they and all other 

 lines of Dicotyledons have been developed by 

 reduction of flower and fruit from the Poly- 

 carpicae, the latter group being derived im- 

 mediately from Bennettitaceae or other ex- 

 tinct Cycadales; (4) in the same manner, the 

 Liliifiorae and all other syncarpous Monocoty- 

 ledons have been derived by union of the 

 ■carpels, by reduction in the number of parts, 

 l>y epigynous insertion of the perianth, and 

 hy other changes in the structure of flower and 

 fruit from the polycarpous Monocotyledons 

 {Helohiae), which latter group originated 

 from the polycarpous Dicotyledons (Poly- 

 ■carpicae and Banales); (5) the Apetalae and 

 Sympetalae are unnatural groups. 



In applying these general principles, Dr. 

 Hallier has worked out the following arrange- 

 ment of the Dicotyledons, which he distinctly 

 ■says is provisional for all after the Piperales. 



1. PoLYCARPiCAE {MagnoUaceae, Canellaceae, 

 Anonaceae, Myristaceae, Calycardhaceae, 

 Monimiaceae, Lauraceae). 



2. Ranales (Berheridaceae, Menisperm- 

 aceae, Ranunculaceae, Nymphaeaceae, Cerato- 

 ■phyllaceae) . 



3. Ehoedales {Papaveraceae, Capparid- 

 aceae, Resedaceae, Cruciferae). 



4. Piperales (Lactoridaceae, Piperaceae, 

 fChlorantkaceae, Myrothamnaceae). 



5. Malvales {Sterculiaceae, Papayaceae, 

 Euphorhiaceae, Bombacaceae, Malvaceae, 

 Elaeocarpaceae, Tiliaceae, Rhamnaceae, Urtic- 

 aceae, Dipterocarpdceae') . 



6. Ebenales (Sapotaceae, Convolvulaceae, 

 Ehenaceae, Symplocaceae, Styracaceae). 



T. Geraniales {Zygophyllaceae, Cneoraceae, 

 Oxalidaceae, Geraniaceae, Linaceae). 



8. Myrtiflorae (Lecythidaceae, Caryocar- 

 aceae, Rhizophoraceae, Lythraceae, Myrtaceae, 

 Melastomaceae, Combretaceae, Geissolomaceae, 

 Penaeaceae, Oliniaceae, Thymelaeaceae, Elae- 

 agnaceae). 



9. Rosales (Saxifragaceae, Rosaceae, Ana- 

 cardiaceae, * * * * Meliaceae, Rutaceae, * 

 Leguminosae, ******* Sapindaceae, * 

 Celastraceae, * Aquifoliaceae, ***** Gutti- 

 ferae, * * Dilleniaceae). 



10. Ericales (Olethraceae, Pirolaceae, * 

 Ericaceae, * * * Biapensiaceae, * * Primul- 

 aceae). 



11. Sarraceniales (Sarraceniaceae, Droser- 

 aceae). 



12. Santalales (Olacaceae, Ampelidaceae, 



* Santalaceae, Myzodendraceae, Gnetaceae, 

 Loranthaceae) . 



13. TJmbelliflorae (Cornaceae, Araliaceae, 

 Adoxaceae). 



14. Amentiflorae (Hamamelidaceae, Myric- 

 aceae, Salicaceae, Juglandaceae, Betulaceae 

 (incl. Casuarineae), Fagaceae). 



15. Passiflorales (Flacourtiaceae, Viol- 

 aceae, Cistaceae, * * Passifloraceae, * * * 

 Onagraceae, * * * Gentianaceae, Aristolochi- 

 aceae, Rafflesiaceae, Loasaceae, Begoniaceae, 

 Cucurhitaceae, Campanulaceae, * * * Com- 

 positae). 



16. Centrospermae (Crassulaceae, Cact- 

 aceae, * * * * Portulacaceae, * Phytolacaceae, 

 Tamaricaceae, C aryophyllaceae, Polygonaceae, 



* * Amarantaceae, Chenopodiaceae, Batid- 

 aceae). 



17. Caprifoliales (Caprifoliaceae, Valerian- 

 aceae, Dipsaceae). 



18. Tubiflorae (Apocynaceae, Loganiaceae, 

 Rubiaceae, Bignoniaceae, Oleaceae, * * 

 Acanthaceae, Yerbenaceae, Laiiatae, Scroph- 

 ulariaceae, * Solanaceae, Polemoniaceae, 

 Boraginaceae, Hydrophyllaceae) . 



