278 MORPHOLOGY 
The preceding alliances are the so-called spiral alliances, in which 
the floral members are not definitely and constantly of the same num- 
ber. While the floral number three is a feature of monocotyledons, it 
is evident that it does not apply to the spiral alliances in the same sense 
that it does to the cyclic alliances. 
In the following cyclic alliances the almost constant floral formula is: 
perianth 3 + 3, stamens 3+3, carpels 3 (and syncarpous). Further- 
more, the perianth is the conspicuous floral feature rather than bracts, 
and insect pollination is well established. In other words, the real 
flowers of monocotyledons, as ordinarily recognized, belong to the 
cyclic alliances. 
7. Farinales (n families, 2000 species). This alliance is in a certain 
sense a transition group between the spiral and cyclic alliances; for al- 
though the cyclic number is established, many of the forms are grass- 
like herbs with bractlike perianth, as in the rushes (Juncaceae); but 
there are also forms with showy corolla, as the spiderwort (Tradescaniia). 
8. Liliales (9 families, 5000 species). These may be regarded as 
the representative monocotyledons, with conspicuous and usually regular 
perianth, and well-established insect pollination. Most of the mono- 
cotyledonous flowers of ordinary experience belong here. The group 
shows a distinct development from hypogyny, as in the amaryllises 
(Amaryllidaceae), to epigyny, as in the flags (Iridaceae). 
The two remaining cyclic alliances are characterized not only by 
epigyny, but also by the extreme irregularity of the flowers. 
9. Scitaminales (4 families, 800 species). These are the cannas, 
bananas, and gingers of the tropics. One peculiar feature of the group is 
the so-called false stem, which may be seen in the banana. The stem- 
like structure, which often rises to a considerable height, is built up of the 
heavy and overlapping bases of the leaves. 
10. Orchidales (2 families, 7000 species). The orchids are notable 
for the great irregularity and showiness of their flowers, and for their ex- 
treme specialization in insect pollination. The number of species runs 
very high, but orchids cannot be regarded as abundant. By contrast- 
ing the 7000 species of grasses and sedges with the 7000 species of 
orchids, it becomes evident that although the species of two groups may 
number the same, the number of individuals may be very different. 
The orchids may be regarded as the culmination of monocotyledons 
in floral structure, and that culmination is expressed by epigyny and 
extreme irregularity. 
