6o6 
PHANEROGAMS. 
and drawings that the same process occurs in the nearly related genus Ruta, And in the 
families Oxalideae, Zygophyllaceae, and Geraniaceae included in the same circle of affinity; 
viz. that in these cases also five stamens are interposed between those already in 
existence^. If the five interposed stamens are supposed to be removed, there remains 
in these families a regular pentamerous flower with four alternating whorls each 
consisting of five members, such as is found in the nearly related Linacese and Bal- 
samineae^. 
Floral Formula:. The diagram may, under certain circumstances, be substituted, at 
least partially, by a formula composed of letters and numbers. In a floral formula of 
this kind the relative positions of the parts cannot indeed always be represented with 
accuracy; but it has the advantage that it can be expressed by ordinary printer's type, 
and, what is perhaps of greater importance, is capable of a wider generalisation, since 
the numerical coefficients may be replaced by letters. 
The construction and application of these formulae will easily be made intelligible by 
a few examples^. 
The formula SzPsSts+^Cs corresponds to the diagram of the Liliaceae, Fig. 406, and 
signifies that each of the two perianth-whorls -the outer whorl or sepals S, and the inner 
whorl or petals P — consists of three members, the androecium of two whorls each of three 
stamens St, and the gynaeceum of three carpels C. The diagram shows in addition that 
these trimerous whorls alternate without interruption ; but since this is the usual case 
with flowers, it need not be specially indicated. The formula 53 P3 5/3^+3 C3+3 gives the 
relative positions of the parts of the flower of Butomus umbdlatus (Fig. 382). It 
is distinguished from the previous one by the gynseceum consisting of two whorls of 
three carpels each, and the androecium having the typical three stamens of the outer 
whorl each replaced by two stamens, which is expressed by the symbol 3^. The 
formula S^^P^St^ + ^Cs corresponds to the diagram of the flower of Bambusa, Fig. 409 J, 
and diff'ers from that of Liliaceae only in the suppression of the outer perianth-whorl, 
represented by S^. The numerical relations of the parts of the flower of Orchideae, 
Fig. 410 ^, might be expressed by the formula ^3 P3 Sti+Q C3, the symbol Sti q indicating 
that all the members of the inner staminal whorl are abortive, while on the other hand 
in the outer whorl the two posterior ones are suppressed, the anterior outer stamen 
being perfectly developed ; the two dots over the number i* are meant to indicate 
that the absent members are the posterior ones ; were the anterior ones deficient the 
dots would be placed beneath the number, as in the formula Pg-^^g+o which cor- 
responds to the ordinary flower of Grasses represented by the diagram Fig. 409 B. The 
formula S.yP^St.+^C.y expresses the whorls consisting of decussate pairs which form the 
flower of Maianthemum bifolium ; the formula P^ 5/4+4 Q 01* "^5 ^5 ^^5+5 Q ^^e flowers of 
Paris quadrifolia, in which all the whorls are either tetramerous or pentamerous. These 
^ [These are all cases of obdiplostemony. In the case of Dictammis and of Ruta this is to be 
explained by Celakov>ky's theory of displacement. In the Oxalidese and Geraniacese Frank has 
found (Jahrb. f. wiss. Bot. X), in opposition to Payer, that the antipetalons stamens are developed first. 
It is therefore difficult to give a satisfactory account of the obdiplostemony in these orders. Eichler 
regards it as due to constant deviation from the normal acropetal development of the whorls of the 
flower.] 
Doll (Flora von Baden, vol. III. pp. 11 75, 1177) others suppose that a whorl has 
become abortive between the corolla and ovary in Rutacese and Oxalidese, a hypothesis which is 
not supported by the history of development, and which is superfluous on our hypothesis. To 
assume abortion merely because certain whorls do not alternate seems to me to be going too far. 
Besides, the ten stamens of Epacrideoe and Rhodoracese cannot belong to two but only to one whorl 
in which five are of earlier origin, and five have been interposed. (Compare Payer, Organogenie de 
la fleur, pi. 118.) 
^ Grisebach (Grundriss der systematischen Botanik ; Göttingen, 1854) has denoted the relative 
numbers of the parts of flowers in a different manner, placing the numbers of the members of a 
whorl simply one after another, and indicating cohesions by strokes. 
