194 
MORPHOLOGY OF MEMBERS, 
may be followed in this manner up to the terminal rosette of leaves. Similar 
phyllotaxes appear to occur in Draccena and in some Aroidese; and at first sight 
present the appearance as if the leaves were placed in two rows which have become 
changed into spirals by the torsion of the stem. 
If we now turn to those cases which clearly gave rise to the erroneous 
hypothesis that the primary law of phyllotaxis is a universal spiral arrangement, 
we find the leaves placed singly, and their divergences almost or quite equal or 
gradually passing over into some other value, thus corresponding to the second 
case named above of spiral arrangement. In these cases the spiral construction 
affords a simple expression of the law of phyllotaxis; the only thing required 
is to name the constant angle of divergence; — according as this is \, \, \, f, |, 
<S^c., the phyllotaxis is termed simply one of \, \, J, and so on. It is usual in 
such cases for the divergence not to remain constant for all the lateral members 
of an axis; shoots w^hich form numerous leaves mostly begin with more simple 
arrangements, as \, and then pass over into more complicated ones, an arrange- 
ment being considered more complicated 
when the numerator and denominator 
of the fraction of divergence are larger. 
When the divergences between lateral 
members placed solitarily with a spiral 
arrangement are equal, they must also 
TU Stand in straight rows, the number 
of which is expressed by the denomi- 
inator of the angle of divergence. If, 
for instance, the divergence is a constant 
one of I, as in Fig. 153, there are eight 
orthostichies, the 9th member standing 
on the same median plane as the ist, 
Fig. i53.-Diagram of a shoot in which the leaves have thc lOth aS thc 2nd, thc I ith aS thc 
a constant phyllotaxis of i. ■ o i ii • • 
3rd, and so on. In a f phyllotaxis, m 
the same manner, the 6th member stands over the ist, the yth over the 2nd, and so 
on. In some cases the orthostichies are very obvious, as, for instance, in cacti with 
prominent angles to the stem, the angles corresponding to the orthostichies of the 
spirally arranged leaves, which, however, in this case mostly remain undeveloped. 
In verticillate leaves also the straight rows are mostly conspicuous if the shoot be 
looked at from above, as, for instance, in the decussate two-leaved whorls of Eu- 
phorbia Lathyris, and the cactus-like E. canariensis . 
When the members of a spiral phyllotaxis with a constant angle of divergence 
stand sufficiently close to one another, other spiral arrangements are easily seen, 
one of which may be followed to the right and the other to the left, and more or less 
completely concealing the genetic spiral. These rows are called Parastichtes, and 
are particularly clear in fir-cones, the leaf-rosettes of Crassulaceae, the flower-heads 
of the sunflower and other Compositse, and the spadices of Aroidese. They may be 
seen in every spiral phyllotaxis with a constant divergence, and can always be made 
clear in the diagram, or when the arrangement is represented on an unrolled 
cylindrical surface. The consideration of these constructions leads to definite 
