RELA TIVE POSITIONS OF LA TERAL MEMBERS, 



193 



-cases of decidedly bilateral construction the genetic spiral might be imagined just as 

 well, and with the same divergence, ascending right or left, by which of course it 

 loses its importance for any morphological conclusion, as much as if one supposed 

 it to change its direction from leaf to leaf. 



It is principally in upright axes with solitary leaves arranged in three, four, 

 five, or more directions, that the spiral construction appears conformable to 

 nature, and agrees with the symmetrical relationships of plants, of which more 

 will be said hereafter. The spiral construction proves to be opposed to nature 

 in bilateral structures, especially in creeping or climbing stems, and in lateral 

 branches. 



In those cases in which the spiral construction may be employed naturally 

 to elucidate the relative positions of the members, two cases may be distinguished, 

 ^according as the divergences, on the one hand, are very unequal and change 

 .abruptly, or, on the other hand, are nearly or quite equal to one another or 

 .only change gradually. In the first case the members appear to be arranged 

 irregularly and without order, as the foliage-leaves on the stem of Fritillaria 

 ■iviperialis (Fig. 151), the flowers on the rachis of the raceme of Triglochin 

 palustre or of many Dicotyledons. When the change of divergence on the same 

 axis is abrupt, it may also ap- 

 pear more natural to represent 

 .the phyllotaxis by two homodromal 

 spirals instead of one, as in many 

 species of aloe, where the shoots 

 commence with leaves arranged in 

 two rows, and then pass over into 

 complicated divergences which lead 



■finally to rosettes of leaves radiat- fig. 152.— Transverse section of a shoat of ^/,?i'.S-?rr«. 



ing on all sides. This occurs, 



e.g. in Aloe €iliaris^ latifolia, brachyphylla. Lingua, nigricans, and Serra. Fig. 

 152 shows the transverse section of a shoot of the last-named species; the 

 first six leaves are arranged alternately in two rows with a constant diver- 

 gence \\ at the 7th leaf this arrangement is suddenly changed; instead of 

 being placed over 5, its position is between 5 and 6; but the 8th leaf exhibits 

 .the divergence \ from the 7th; the 9th again changes the divergence, instead of 

 ^being placed over 7, it is between 7 and 6; the loth leaf again diverges about \ 

 .from the 9th; and so on. The leaves 7-15 are evidently arranged in pairs, 

 the pairs being 7, 8; 9, 10; 11, 12; 13, 14; each pair consists of two alternate 

 4i.e. not opposite) leaves, the divergence of which is \\ but the pairs them- 

 , selves diverge from one another by smaller fractions. If it is desired to unite all 

 the leaves from i to 15 by a genetic spiral, an abrupt alteration of the divergence 

 would occur in it. The relative positions are shown, however, more simply 

 and clearly if, keeping in view the bilateral origin of the shoot, two spirals are 

 constructed, each of which commences from one of the original orthostichies, and, 

 r50 to speak, continues it in a spiral curve ; the one contains all the leaves with an 

 'even number, the other those with an uneven number; the two are homodromal, 

 ^running in the same direction round the stem. The bilateral origin of the shoot 



o 



