ANGIOSPERMS. 607 



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

 a general expression 5„ P„ Stn+n Cni+n)i 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 ( + «) 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 oo ; thus the formula for Alisma Plantago is 

 S^ /*3 5/3+3 ^"^ ' 



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 Gruciferae, Fig. 413, might be represented by Sc^+^P^^Stc^^.^ Cc^[+^),ihe 

 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 

 be placed after the number of the first whorl ; thus ^5 P^ \ St^ C^ might represent the 

 formula for Hypericum calycinum (Fig. 408), | St-^ indicating that the androecium con- 

 sists of five branched (s'^) 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 P5 5/5.5 Cg 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 S^ Pg 5/g Cg, the sign Pg indicates a gamopetalous 

 corolla of five petals, C2 a syncarpous ovary of two carpels. In the formula for the 

 flowers of Papilionaceae again ^g P^ 5/5+4+1 Cj, the expression 5/544+1 signifies that the five 

 stamens of the outer and four of those of the pinner 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 5^2/ bP^zi sSf^si ^ C^ , which indicates that all the foliar structures 



15 Is /2I °° 3' 



of this flower are arranged spirally, and that the calyx consists of five sepals with the 

 divergence ^/g, the corolla of eight petals with the divergence ^s? ^^^ ^^^ androeciuhi of 

 an indefinite number of stamens with the divergence 721' 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 -^ 52/ 5P3/ 8 5/8/ ao C 



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 Rohrbach, Bot. Zeitg. 1870, pp. 816 ei seq. 



