420 FOURTH GROUP. SEED-PLANTS. 



corresponds to the ordinary flower in the Gramineae. The formula S2 P2 5/2 + 2C2 

 gives the numerical relations of the whorls in the flower of Maianthemum bifolium 

 formed of decussate pairs, the formula 54 P^ 5/4 + 4 64 or 55 PS 5/5 + 5 C$ shows the 

 flower of Paris quadrifolia consisting of whorls of four or five members. These and 

 most other formulae for monocotyledonous flowers may be united in a general 

 expression 



SnPnStn + n Cn( + n), 



which means that the flowers belonging to this type are usually composed of five 

 alternating whorls each with the same number of members, two of which are developed 

 as perianth-whorls, two as staminal whorls and one usually as a carpellary whorl ; the 

 bracket ( + ri) at the end of the formula indicates that occasionally there is a second whorl 

 of carpels present ; n may have the value of 3 or 2 or 4 or 5, as the examples show ; 

 usually n = 3. If there is a considerable increase in the number of members in a whorl 

 and the number, as is usual in such cases, is a fluctuating one, the fact maybe expressed 

 by the sign co ; the formula for Alisma Plantago is 63 P$ 5/3 + 3 Coo . 



It has been already mentioned, that there is no sign to indicate the normal alternation 

 of the whorls ; an exception to the general rule may be expressed with more or less 

 preciseness by concerted symbols ; for instance in the formula for the flowers of the 

 Cruciferae (Fig. 347) 52 + 2 P x 4 5/2 + 2 2 2 ( + 2) the symbol P x 4 would mean that 

 the decussate pairs of the Calyx are succeeded by a corolline whorl of four members, 

 which are placed diagonally to the members of the calyx ; to show the superposition of 

 two successive whorls, a vertical stroke might be placed after the number of the first 

 whorl, e.g. S$ P$ | 5/5 V C5 ; in this which is the formula for Hypericum calycinum 

 5/5 v might indicate that the androecium consists of five branched (5 V ) stamens super- 

 posed on the members of the corolline whorl (Ps \ 5/) ; lastly, if it is desired to show 

 that the members of a second whorl are interposed between the members of an original 

 whorl -at the same height, the number of the new members may be simply placed beside 

 that of the first whorl, as in the formula 55 P$ 5/5.505 which corresponds to the 

 diagram in Fig. 349. 



In the formulas hitherto given no occasional cohesions have been indicated ; they 

 too may be easily shown, if necessary, by concerted symbols. Thus in the formula for 

 Convolvulus 55 PS 5/5 C2, the sign PS would indicate a gamopetalous corolla of five 

 members, C2 an ovary formed by the cohesion of two carpels ; in the floral formula of 



the Papilionaceae 55 PS 5/5 + 4 + I Ci the symbol 5/5 +4 + 1 would mean that the five 

 stamens of the outer whorl and the four of the inner cohere and form a tube, while the 

 posterior stamen of the inner whorl remains free 1 . 



The construction of the formulas must vary according to the special purpose which 

 they are intended to serve ; the greater number of relations it is desired to express the 

 more complicated they must become, and we must take care not to render them obscure 

 through the accumulation of many symbols. 



All the formulae hitherto given express cyclical flowers ; the spiral arrange- 

 ment of the parts of flowers may be indicated by the mark ^ placed before them, 

 and the angle of divergence may be put after the number. For example, the formula 

 5^ 5/ ) ^f 85/^^ 8 T ooC^3 will give the relative numbers and positions in Aconitum 

 according to Braun's views, and mean that all the organs of the flower are spirally 

 arranged, that the calyx consists of five leaves with the divergence f, the corolla of 

 eight leaves with the divergence , and the androecium of an indefinite number of 

 stamens with the divergence TJ T ; it would however be sufficient to put the symbol for 

 the spiral arrangement once before the whole formula, since it recurs in all the parts of 

 the flower, thus, ~5f 5 Pf 8 5// T v oo 3. 



In flowers arranged cyclically it is generally unnecessary to indicate the divergence, 

 because the members of each whorl are usually formed simultaneously and so placed as 



1 See also Rohrbach in Bot. Ztg. 1870, p. 816. 



