1874.] Dr. H. Airy on Leaf -Arrangement. 307 



roots, taken in connexion with their probable homology with 

 lateral shoots (the three ranks o rootlets in Polygonacece, 

 and the four in carrot and parsnep, illustrate variability in 

 number of ranks) ; 



(5) the two-ranked arrangement of leaves in the seeds of Mono- 

 cotyledonous plants, as compared with the more condensed 

 (though probably at first two-ranked) order in the more 

 highly developed Dicotyledonous embryo. 



Summary. The author is led to suppose : 



I. That the original form of leaf -arrangement was two-ranked. 



II. That this original two-ranked form gave rise to forms with 2, 3, 4, 

 5, 6, 7, &c. ranks, by " sporting," as opposed to any process of accumu- 

 lative modification. 



III. That of the orders so formed those with an even number of 

 ranks (except 2) have, as a rule, assumed a ivliorled arrangement, and 

 those with two or an dfld number of ranks have assumed an alternate 

 arrangement, under the need of lateral accommodation of ranks in the 

 bud (taken as type of close-packed forms). 



IV. That all these orders have been subject to vertical condensation, 

 under the need of vertical economy of space in the bud (taken as type of 

 close-packed forms). 



Y. (a) That such condensation, operating on a 2-ranked, or 3-ranked, 



or 5-ranked alternate order (^ ^, g, has produced subsequent or- 



ders of series A (1, -J, ?, | , , , |, , Ac.). 



(2\ 

 ,=j or rarely of a 3- or 4-ranked 



L ^) alternate order has produced subsequent orders of series B 



I 1 2 3 5 & \ 

 & 4' 7' IT 18' 7* 

 (c) That condensation of a 9-ranked m or rarely of a 4- or 5-ranked 



-r, -} alternate order has produced subsequent orders of series C 



1123 5 



' 5' ' 14' 23' 



(d) That condensation of a 4-ranked whorled order (whorls of two) 

 has produced successive orders of series a, with spirals in sets of 4, 6, 

 10, 16, 26, 42, &c. 



(e) That condensation of a 6-ranked whorled order (whorls of three) 

 has produced successive orders of series j3, with spirals in sets of 6, 9, 

 15, 24, 39, &c. 



(/) That condensation (if any) of an 8-ranked whorled order (whorls 

 of four) would produce successive orders of series y, with spirals in sets 

 of 8, 12, 20 3 32, &c. Higher numbers of ranks would lead to higher series. 



