ANGIOSPERMS. 



423 



arise at an equal height, that is at an equal distance from the centre of the flower, or 

 not ; if they do, the arrangement is that of a whorl ; but if the members arise in 

 acropetal order at different heights, approaching the centre of the flower with each 

 step in the divergence, the arrangement is spiral ; this appears actually to be the 

 arrangement in many calyces, but it is a question whether it always is so, when the 

 sepals are formed with a or divergence. 



We must once more notice the cases which have been already mentioned, in which 

 new members are formed between the original members of a whorl at the same height 

 with them 1 . In the Oxalideae, Geraniaceae, Rutaceae and Zygophylleae an entire 

 whorl of five members is interposed between the previously formed stamens'-; in 

 Peganum Harmala, according to Payer, a circle of ten stamens is thus formed in pairs, 

 and not between the first five but below them at the base of the petals ; whether the 

 later formed stamens arise at the same height as the first or below them obviously 

 depends on whether more space is supplied by the changes in form of the growing 

 torus. A still greater deviation from the usual rule occurs in the Acerineae, 

 Hippocastaneae and Sapindaceae, where, according to Payer, a staminal whorl of five 

 members is first formed alternating with the corolla, in which an imperfect whorl 

 of from two to four stamens is subsequently interposed at the same height, as appears 

 from that author's drawings. In Tropaeolum on the other hand we learn from Payer 

 and Rohrbach 3 that three stamens first make their appearance after the commencement 

 of the petals, and five others are afterwards formed between them, but at a greater 

 distance from the centre of the flower than the three first formed. 



Symmetry of the flower *. Actual symmetry and decided bilaterality occurs much 

 more frequently in floral than in other shoots. Sachs avoiding the lax terminology of 

 many botanists here also considers those forms to be symmetrical which can be divided 

 into halves, each of which appears to be the exact reflection of the other ; if a flower 

 can be divided in this manner by one plane only, he terms it a simple symmetrical 

 structure or monosymmetrical; if it can be symmetrically divided by two or more planes, 

 it is said to be doubly or repeatedly symmetrical (poly symmetrical) ; the term 

 zygomorphous applied by Braun may be used equally for monosymmetrical flowers and 

 for those doubly symmetrical ones, in which the median section gives differently shaped 

 halves from those produced by the lateral section, Dielytra for instance. Sachs calls 

 a polysymmetrical flower regular 5 , only when the symmetrical halves produced by one 

 section are the same as or very like the symmetrical halves produced by any other 

 section, or which comes to the same thing, when a flower can be divided by two, three 

 or more longitudinal sections into four, six or more equal or similar portions. 



To determine exactly the relations of symmetry in a flower we must first distin- 

 guish between the relative positions of the parts as shown in the diagram and the form 

 of the whole flower produced by the complete development of its organs. 



1 See on the other hand the statement of Frank concerning obdiplostemonous flowers mentioned 

 above (page 419). 



2 See also Pfeffer in Jahrb. f. wiss. Bot. VIII, p. 205. 



3 Rohrbach however (Bot. Ztg. 1869, No. 50, 51) explains these observations in a different way; 

 but the equal or even greater distance of the later stamens from the centre of the flower proves 

 decisively that we cannot in this case suppose a spiral formation advancing from without inwards. 



4 [See notes on pages 349 and 411. The older terms zygomorphous and actinomorphous are 

 adopted by Eichler in his Bluthendiagramme for the monosymmetrical and polysymmetrical condi- 

 tions of the text and are now in general use. 



5 English and French writers use the word ' regular ' with a different and older signification 

 as regards the flower. According to their terminology a calyx of which the sepals are all alike 

 in form and size is a regular calyx, and similarly a corolla of which all the petals are alike in form 

 and size is a regular corolla, and a flower which has a regular calyx and regular coralla is a regular 

 flower. If one or more sepals or petals differ markedly in form and size from the other members of 

 a calyx or corolla, the calyx or corolla is said to be irregular and the flower also becomes irregular^ 



