.304 Dr. H. Airy on Leaf -Arrangement. [Apr. 30, 



But there are phenomena in leaf -arrangement which are not explained 

 by condensation. We have still to account for (1) the origin of alter- 

 nate orders with 3, 4, 5, 7, 9, &c. vertical ranks ; and (2) the origin of 

 the different whorled orders, with whorls of two, three, four, five, &c. 

 (with 4, 6, 8, 10, &c. vertical ranks). 



The whole course of condensation depended on obliquity of ranks ; but 

 the distinguishing feature in these cases is that the ranks are exactly or 

 almost exactly vertical. 



All these cases are explained on the hypothesis that there has been in the 

 vegetable kingdom a variability (per salturti) in the number of leaf -ranks ; 

 that a plant originally having two vertical ranks has, by a stroke of 

 variation, produced shoots or seedlings with three vertical ranks ; that 

 three have varied to four, four to five, five to six, and so on ; and that 

 these " sports " have survived in some cases because of some advantage 

 which they enjoyed (probably the same advantage as that gained by 

 condensation the accommodation of the same number of leaves in 

 a shorter bud). 



This hypothesis is supported by the variability which is found at the 

 present day in the number of leaf -ranks in one and the same species. 

 For instance, Sedum sexangulare exhibits seven nearly vertical ranks in order 



?, or six exactly vertical in whorls of three. Frjaxinu-s exeelsa has nor- 

 mally four exactly vertical ranks in whorls of two, but may be found 

 with five nearly vertical ranks in order , or with six exactly vertical in 



whorls of three. (These three varieties may be found on shoots growing 

 from the same stump.) Whorls of three are often produced by plants 

 usually bearing whorls of two (e. c/. sycamore, lilac, laurustinus, maple, 

 horse-chestnut, elder, ash, &c.), and whorls of four instead of three are 

 seen in some species of JSedum and Verbena. Among these forms it does 

 not seem possible that one could be produced from another by accumu- 

 lative modification. 



Professor Beal has found well-marked variation in the cones of larch, 

 spruce, &c., the majority belonging to series A, but a considerable minority 

 to series B or series a. 



In dandelion-heads about 5 per cent, belong to series a. 



Different species of the same genus (e. g. Aloe verrucosa and varieyata, 

 HawortJda viscosa bud. pentagona, and different species of Sedum and 

 Cactus) often exhibit differences of leaf -order which can hardly be under- 

 stood but as resulting from direct variation in number of leaf-ranks. 



This hypothesis is also supported by analogy drawn from the animal 

 kingdom. Among starfishes there is variability in the number of rays : 

 Asterias rubens has sometimes four or six instead of five ; A. papposa has 

 from twelve to fifteen. Among mammals there is some variability in the 

 number of digits. 



