642 
PHANEROGAMS. 
flower is tetramerous or pentamerous the number of carpels is usually less ; when the 
flower is dimerous or trimerous, or when the parts are arranged spirally, the number 
of carpels is not unfrequently larger. 
It will be seen from this brief outline that the relations of number and position 
in the parts of the flowers of Dicotyledons are very various, and cannot be referred, 
as is the case with Monocotyledons with but few exceptions, to a single type. Even 
the establishment of difl"erent types for the - larger groups is attended with great 
uncertainty, since the knowledge of development necessary in order to refer par- 
ticular forms of flowers to general formulae is often wanting. The too universal 
application of the spiral theory of phyllotaxis in the case of cyclic flowers has 
often increased the difficulty, and has even occasioned doubts which would not 
have arisen without the theory. 
For the great majority of Dicotyledons the floral formula may be given 
At This formula holds good for most pentamerous flowers 
and for those which are truly tetramerous (or octamerous as Michauxid) ; so that n 
is in these cases 5 or 4 (or 8 as the case may be). In the androecium an indefinite 
number of (alternating) whorls ^ must be assumed in order to include 
the large number of flowers iff which the androecium consists of more than one 
whorl (as e.g. Fig. 451). The mode of expressing the gynaeceum is intended 
to show that very commonly the number of carpels is fewer than 5 or 4 (or 8 as the 
case may be) ; m may be of any value from o to n. In the majority of gamopetalous 
orders and elsewhere there are very commonly only two carpels ; and in this case 
they stand in a median line posterior and anterior; but on the hypothesis that the 
typical gynaeceum consists of five alternating carpels and has been reduced to two by 
abortion, one must stand in the median position in front, the other obliquely behind. 
A similar difficulty is also presented when the gynaeceum consists of three or of 
only one carpel. It would carry us too far to detail the reasons which nevertheless 
determine me to retain the formula above given for the gynaeceum of flowers of this 
description ; it need only be mentioned that species or genera with the typical five 
carpels occur in the most diverse families and orders where a smaller number is the 
normal one. 
The diagrams Figs. 440-450 represent a selection of cases which can be 
reduced (if no further reference is made to the consideration mentioned above) to 
the general formula which here assumes the simpler expression -5*,; P,^ St^^ 
Fig. 440.— Diagram of Caprifoliaceze ; A Ley- 
cesteria, a Lom'cera, b Syinphoricarpiis. 
Fig. 441.— Diagram of Par- 
7iassia (Saxifragaceas). 
Fig. 442. — Diagram of Campanulacese ; 
A Campmntla, a Lobelia. 
