438 Rev. S. Haughton on the General Law of Phyllotaocis 



10. E. hyemale. Mexico and Berne. Sheath whorls alter- 

 nate, 16 in each. Fruit whorls (9 in number) alternate, 8 in 

 each. 



11. E. (sp.). California. Sheath whorls alternate, 16-24 in 

 each. Fruit whorls (28-29 in number) alternate, 16 in each. 

 Branch whorls 16-20 in each. 



12. E. debile. E. Indies. Sheath whorls alternate, 24 in 

 each. Branch whorls 4 in each. 



13. E. giganteum. Peru. Lower sheath whorls alternate, 

 24 in each. Upper ditto alternate, 12 in each. Lower branch 

 whorls 24 in each ; upper ditto, 12 in each. 



14. E. fluviatile. Berne and Limerick. Sheath whorls alter- 

 nate, 24-30 in each. Fruit whorls 16-20 in each. Branch 

 whorls 20-30 in each. 



15. E. arvense. British. Branch whorls of barren stems 

 13 in each. Sheath whorls of fruitful stems 8 in each. Fruit 

 whorls alternate (14 in number), 8 in each. 



From an examination of the preceding, I conclude (rejecting 

 the branch whorls, which are generally deficient in number) 

 that the number of leaves in the alternate whorls of the Equise- 

 tacese are represented by the arithmetical series whose first term 

 is 4, and common difference also 4 : 



4?, 8, 12, 16, 20?, 24, 28?, 32?, 



the terms to which I have appended queries being more doubt- 

 ful than the others. 



I at first thought there were two series 



4, 8, 16, 32, 

 and 12, 24, 



formed by simple dichotomy; but the case of the Nilghiri 

 Hill Equisetum proves the occurrence of 8 and 24 on the same 

 plant, and the Californian Equisetum shows the concurrence of 

 16 and 24, thus proving that there is only one series of num- 

 bers, and that a series in arithmetical progression. The whorl 

 of 8 leaves, which, next to that of 16, is the most common, 

 is the only one related to the phyllotaxis of alternate-leaved 

 plants. 



III. Filices. 



The rhizome or root- stock of the Ferns presents many irregu- 

 larities, the leaves being sometimes apparently alternate, but 

 often truly arranged in whorls. The genus Cyathea, or Tree- 

 fern, from the Feejee Islands, is that which presents most ana- 

 logy to the fossil plants of the Old Red Sandstone, so far as the 



