ANGIOSPERMS. 
607 
and most other formulae for the flowers of Monocotyledons may now be combined into 
a general expression Pn ^fn+n Cn( + n)y 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 00 ; thus the formula for Alisma Plantago is 
As has already been mentioned, no further indication is given of the position of 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. 413, might be represented by 5^+2 5/2 + <2'^ C2(+o), the 
symbol Py^^ 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 
be placed after the number of the first whorl; thus S^P^ \ St^ Cr, might represent the 
formula for Hypericum calycinum (Fig. 408), | Str^ indicating that the androecium con- 
sists of five branched (5^) stamens which are superposed on the petals. If, finally, it is 
desired to signify that members of a second whorl are interposed at the same level 
between those of one already in existence, the number of the new members may be 
placed simply beside those of the original whorl ; thus the formula 5^ Pr, 5^5.5 C5 would 
correspond to the diagram Fig. 414. 
In the formulae already given no cohesions of any kind have been indicated ; they 
can however under certain circumstances easily be expressed by special symbols. 
Thus, in the formula for Convolvulus Pr, St^ C^, the sign P- indicates a gamopetalous 
corolla of five petals, C2 a syncarpous ovary of two carpels. In the formula for the 
flowers of Papilionaceae again P^Str^+^^-i^ fhe expression 5/544 + 1 signifies that the five 
stamens of the outer and four of those of the inner whorl have united into a tube, while 
the posterior stamen of the inner whorl remains free'. 
The mode of writing the formulae must vary according to the object which one has 
in view; the greater the number of relationships it is intended to express, the more 
complicated will they become; and care must be taken that they do not lose their 
clearness by being overladen by too many signs. 
The examples of formulae which have hitherto been adduced all illustrate cyclic 
flowers; those parts of flowers which are arranged spirally may be denoted by the 
symbol placed before them, and the angle of divergence may also be affixed to 
their number. Thus, for example, the relative numbers and positions of the parts of 
the flower of Aconitum, according to Braun's investigations, may be expressed by the 
formula S^ii ^P^zi sSt^si , which indicates that all the foliar structures 
15 Is /21 ^ 3' 
of this flower are arranged spirally, and that the calyx consists of five sepals with the 
divergence ^/^, the corolla of eight petals with the divergence ^g, and the androecium of 
an indefinite number of stamens with the divergence • It would however be sufficient 
in this case, since the spiral arrangement runs through the whole flower, to place the 
symbol only once before the whole formula, thus 821 öPsi sStsi oo C 
/ 5 / 8 / 21 3* 
In flowers with a cyclic arrangement of their parts a statement of the angle of 
divergence is generally unnecessary, since the members of each whorl usually arise 
simultaneously, and are arranged so as to divide the circle into equal parts. When 
they do not arise simultaneously but successively in the circle with a definite angle 
See also Rohibach, Bot. Zeitg. 1870, pp. 816 et seq. 
