;>. PHANEROGAMS. 



be placed after the niiniber ol" the first whorl ; thus 5,-^ P^ | St^' Q might represent the 

 formula for Hypericum calycinum (Fig. 377, p. 524), Str^ indicating that the androecium 

 consists of five branched 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^ Fr^ 5/5.-, C5 would 

 correspond to the diagram, Fig. 383, p. 528. 



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^P^Str^C^, the sign P^ indicates a gamopetalous 

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

 flowers of Papilionaceae again S-^Pr^Sff+^^^C^, the expression Stf^^^^ 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 formulce 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, m.ay be expressed by the 

 formula 8,^2 5 Pr^.-. s ^^^^k/. 00 C^.^, which indicates that all the foliar structures 

 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 ^ g, and the androecium of 

 an indefinite number of stamens with the divergence V^i- It would however be sufficient 

 in this case, since the spiral arrangement runs through the whole flov.-er, to place the 

 symbol only once before the whole formula, thus — So p, o 6*/^ Co 



In flo\\ers 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 

 of divergence, as in most trimerous or pentamerous calyces, this can be indicated by 

 placing the angle of divergence after the number of the members; thus the formula for 

 Linaceae would be Sr^i . Pr,St^C^. If, on the other hand, the members of a whorl are 

 formed in succession from front to back, this may be shown by an arrow pointing 

 upwards ^, as in the formula for Papilionaceae S-] P^T 5/-t45t Q. If they are formed 

 in succession from back to front, the arrow may be made to point downwards \, as 

 in the formula for Reseda S^i Pni Stpi^gi Q., where the number of the parts is expressed 

 by letters instead of figures in consequence of its variability''^. 



Order of Succession of the Parts of the Flo-iver. The foliar structures arise on the axis 

 of the floral shoot, as on other axes, in acropetal order below the growing apex. It is 

 however not uncommon in the formation of flowers for the apical growth of the axis (o 

 cease altogether or to become extremely slow, while the receptacle continues to increase 

 in breadth, and to develope transverse zones of intercalary growth. When this is the 

 case the acropetal order of development is disturbed, and new whorls may become 

 interposed between those already in existence. But even within the same floral whorl 

 the individual members may be formed in a very different order of succession, according 

 as the zone of the receptacle which bears the floral leaves is developed in a uniform 



* See also Rohrbach, Bot. Zeitg. 1870, pp. S16 et seq. 



^ See Payer, Organogonie tie la fleur ; also our Fig. 137. p. \(X). 



