ANGTOSPERMS. 



529 



Floral Formula. The diagram may, under .pertain circmiistances, 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, sinte 

 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 S^P^St^^^C^ corresponds to the diagram of the Liliaceae, Fig» 375, 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 gynseceum 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 5*3 P3 St^^j^^ C^.^^ gives the 

 relative positions of the parts of the flower of Biitomus umbellatus (Fig. 351, p. 489). 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^ P3 5/3^.3 C3 corresponds to the diagram of the flower of Bambusa, Fig. 378 ^ (p. 525), 

 and differs from that of Liliaceae only in the suppression of the outer perianth-whorl, 

 represented by 5„. The numerical relations of the parts of the flower of Orchidese, 

 Fig. 379 A, might be expressed by the formula ^3 P3 Sti^^ C3, the symbol St{^f^ 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-^ 5^3+0 Q which cor- 

 responds to the ordinary flower of Grasses represented by the diagram Fig. 378 5. The 

 formula S.^ P,^ 5^2+2 C, expresses the whorls consisting of decussate pairs which form the 

 flower of Maianthtmio7t bifolium ; the formula S^ P, St^+^ C^ or S^ Pr, St^+r, C-, the flowers of 

 Paris quadrifolia, in which all the whorls are either tetramerous or pentamerous. These 

 and most other formula: for the flowers of Monocotyledons may now be combined into 

 a general expression 6^,P„ 5/„+„ C,, (+„), which signifies that the flowers belonging to this 

 type are usually constructed of five alternating whorls each with the same number of 

 members, two of which are developed in the form of perianth-whorls, two as staminal 

 whorls, and generally only one as a carpellary whorl ; the bracket ( + n) at the end of 

 the formula indicating that a second carpellary whorl sometimes occurs in addition. 

 The general number n may, as the examples which have been adduced show, have the 

 value 2, 3, 4, or 5; 3 is the most common. If a considerable increase of the number 

 of members takes place in a whorl, and if this number, as is then usually the case, is 

 variable, this is expressed by the symbol oc ; thus the formula for Msma Plantogo is 



As has already been mentioned, no further indication is given of the position ot the 

 whorls when they alternate ; when a departure from this rule occurs, this can be more 

 or less accurately expressed by special symbols. Thus, for example, the formula for 

 the flower of Cruciferae, Fig. 382, might be represented by ^2+3 ^xi St.2+2^ C^i+o), the 

 symbol Px4 signifying that the decussate pairs of sepals are followed by a corolla con- 

 sisting of one whorl of four petals, which are however arranged diagonally to the sepals. 

 In order to express the superposition of two consecutive whorls, a vertical stroke might 



' 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. 



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