120 PHYLLOTAXY, OR LEAP-ARRANGEMENT. 



that in which the members are reduced to two. This case is 

 so much commoner than whorls of three and of higher numbers 

 that it took from the first its special name of opposite, so that in 

 descriptions the phrase " leaves verticillate " implies more than 

 two leaves in the whorl. But it should be kept in mind that 

 "leaves opposite " is the same as " leaves in whorls of two." 



233. The greater number of phaenogamous plants (all but the 

 monocotyledonous class) begin with verticillate leaves, mostly 

 of the simplest kind (t. e. cotyledons opposite) : sonic continue 

 verticillate throughout ; some change in the first leaves of the 

 plumule or after the first pair into alternate, and again into 

 verticillate in or toward the blossom, in the interior of which the 

 alternate arrangement may be again resumed. As Nature passes 

 >-adily from the one mode to the other on the same axis, we 

 ma}' expect that the two may be comprised under some common 

 expression. But they have not yet been combined, except by 

 gratuitous or somewhat forced hypotheses ; so that for the 

 present the}' should be treated in morphology as primarily dis- 

 tinct arrangements. 1 



234. Yerticillate or Cyclical Arrangement. Here the leaves 

 occupy a succession of circles, or form whorls around the stem, 

 two, three, four, five, &c., in each whorl. According to the 

 number, the leaves are opposite, ternate, quaternate, quinate, and 

 so on. The characteristic of the individual whorl is that the 

 members stand as far apart from each other as their number 

 renders possible, i. e. they divide the circle equally. Thus, when 

 only two, or opposite, their midribs or axes of insertion have an 

 angular divergence (as it is termed) of 180; when three, of 

 120 ; when four, 90 ; when five, 72. 



235. The characteristic of the whorls in relation to each other 

 is, that the members of successive whorls stand over or under 

 the intervals of the adjacent ones. In other words, successive 

 whorls alternate or decussate. This economizes space and light, 

 or gives the best distribution which the cyclical S3'stem is capa- 

 ble of. And it is in accordance with the general conclusion of 

 Hofmeister's investigation of the origin of pbyllotaxic arrange- 

 ments in the nascent bud, viz. that new members originate just 

 over the widest intervals between their predecessors next below. 

 Thus, in opposite leaves or whorls of two (Fig. 237), the suc- 

 cessive pairs decussate or cross at right angles, and so four 



1 It is readily seen that whorls may be produced by the non-development 

 of the internodes between the leaves of a series of two, three, five, or more 

 in alternate order. The difficulty is that the members of the next whorl do 

 not follow the rrder that they should upon this supposition. 



