130 PHYLLOTAXY, OK LEAF-ARRANGEMENT. 



may most naturally be produced by the non-development of the 

 internodes between any two, three, or more alternate leaves. 

 Two proximate distichously alternate leaves would thus form a 

 pair ; the three leaves belonging to one turn of the spiral in the 

 tristichous (^) arrangement would compose a trimerous whorl ; 

 the five leaves of the two turns in the pentastichous (f ) arrange- 

 ment, a 5-merous whorl, &c. Verifications of this conception, by 

 whorls breaking up or reverting to spirals, are occasionally met 

 with, and the successive overlapping in spiral order of the 

 members of a trimerous or pentamerous whorl is very common. 

 The few instances among phaenogamous plants in which the 

 leaves are opposite and all in the same plane 1 (that is, the suc- 

 cessive pairs superposed) may be deduced from the distichous 

 alternate mode becoming opposite without further change, by 

 the simple suppression of alternate internodes. The frequent 

 disjunction of the members of the pair in similar and analogous 

 cases goes to confirm this view. But the characteristic of whorls 

 ordinarily is that proximate whorls alternate, that pairs de- 

 cussate. We cannot homologize this with spiral phyllotaxy ; 

 for in this lies the fundamental difference between the two plans. 

 We can explain it only by a reference to Hofmeister's law, which 

 generally governs leaf-origination as to position, namely, that 

 succeeding leaves appear directly above the intervals between 

 the nearest preceding (241, note) : this gives decussation or 

 alternation of successive pairs or whorls. 2 



247. Hypothesis of the origin of both. Instead of regarding 

 the spiral path on the stem which connects successive alternate 

 leaves as a purely formal representation, it may be conceived to 

 be the line along which the members in some original form were 

 physically connected, in the manner of a leaf-like expansion 



1 As in Loranthus Europaeus, &c., according to Braun. See 236, note. 



2 This renders the verticillate an advantageous arrangement, perhaps no 

 less so than the distribution which spiral phyllotaxy effects. Both must be 

 considered to have been determined by and for their respective utilities, and 

 to have been independent determinations. For " there is no continuity or 

 principle of connection between spiral arrangements and whorls " (Chauncey 

 Wright) ; since, although individual whorls are easily reducible to spirals, 

 each succession is an absolute break of that system. 



As whorls of four members often (as especially in calyx, bracts, &c.) may 

 and sometimes should be viewed as two approximate pairs, so even the spiral 

 of five members, as in a quincuncial calyx, has been conceived to consist of 

 two whorls, one of two, the other of three leaves, the second alternating with 

 the first as nearly as possible. But this appears far-fetched and of loose 

 application. It is much clearer as well as simpler to regard the alternate 

 as the fundamental phyllotaxy, and to deduce individual whorls from spirals, 

 if need be, rather than to imagine spirals as somehow evolved from whorls. 



