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 f^imilies a regular pentamerous flower with four alternating whorls each 

 consisting of five members, such as is found in the nearly related Linaceae and Bal- 

 samineae'^. 



Floral Formulcc. 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 SsPiSts+^C^ 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 andrcecium 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 S^P^ •S'^s^+s Q+s gives the 

 relative positions of the parts of the flower of Butomus umbellatus (Fig. 382). It 

 is distinguished from the previous one by the gynaeceum consisting of two whorls of 

 three carpels each, and the andrcecium having the typical three stamens of the outer 

 whorl each replaced by two stamens, which is expressed by the symbol i^. The 

 formula S^P^St^^-^C^ corresponds to the diagram of the flower oi Bambusa, Fig. 409 J, 

 and differs 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 A, might be expressed by the formula S^P.^Sti+QC^, the symbol Sti 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 S^P^^St^+QC^ which cor- 

 responds to the ordinary flower of Grasses represented by the diagram Fig. 409 B. The 

 formula S-i^P-^St^+iC.^ expresses the whorls consisting of decussate pairs which form the 

 flower oi Maianthemum bifoUum ; the formula .S4 P4 5^4 +4 C4 or S^ P^ ^^5+5 Q the 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 Dictamnus and of Ruta this is to be 

 explained by Celakovsky's theory of displacement. In the Oxalideae and Geraniaceae Frank has 

 found (Jahrb. f. wiss. Bot. X), in opposition to Payer, that the antipetalous 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.] 



2 Doll (Flora von Baden, vol. III. pp. 1175, 1177) and others suppose that a whorl has 

 become abortive between the corolla and ovary in Rutaceae and Oxalideae, 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 Epacrideae and Rhodoraceae 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 ; Gottingen, 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. 



