If there is only one ovule in these orders as in _Agathis_ (Fig. 265) and _Araucaria_, then the flower is reduced to a single carpel and one ovule, as in the case of _Dacrydium_ and _Microcachrys_. If two or more ovules are present, then the same number of carpels may be supposed to exist, the external integuments of their ovules being developed into leaf-like structures which collaterally coalesce to form a “symphyllodium,” or are suppressed. According to this theory, which is based on the researches of Celakovsky, the female flowers of the Coniferæ may be classed thus:-- 1. In all cases situated in the axil of a bract and collected into cones, with numerous flowers or with few or one flower. In _Ginkgo_ only, are they situated in the axil of foliage- or scale-leaves. 2. It is only in _Taxus_ that bracteoles are present. 3. They are formed only from rudimentary carpels, in which the stem takes no part. 4. The number of carpels in each flower varies from one to many, most frequently three, of which the central one remains sterile. 5. Each carpel bears only one ovule. The flower which is formed of only one carpel appears to consist of only one ovule. 6. The ovule has in Taxaceæ either a double integument (Podocarpeæ, Taxeæ), of which the external is the “aril,” or, as in the Cycadeæ, a single one, which is homologous with the two united together. 7. The external integument in the Pinoideæ is expanded to form a leaf-like structure--the ovuliferous scale--and bears on its dorsal side the ovules, which are thus only provided with one, and that the inner, integument. This later interpretation of the female cones in the Coniferæ is more probably correct than the older ones; that, however, which appeared in the former issues of this book, may also be stated. It was to the effect that each catkin-like female cone is in reality a single flower; the cone-scales in the Cupressaceæ were single leaves, namely carpels, which bore the ovules on the side which is turned upwards; the division into two parts which makes its appearance in the other orders, and becomes most prominent in the Abietaceæ, was compared with the division of a leaf into a barren and a fertile portion, which is found especially in Ophioglossaceæ and Marsiliaceæ, or with the ligule in _Isoëtes_.