RELATIVE POSITIONS OF LATERAL MEMBERS. 



191 



in simultaneous whorls \ as the petals, stamens, and carpels of most flowers; or 



even in successive whorls where the members are formed in advancing order right 



and left, as in Characeae and the flowers of 



Reseda (Fig. 145). In the successive whorls of 



Salvinia naians the construction of a genetic 



spiral would be equally impossible. Fig. 150, B 



shows the diagram of the stem of this plant 



with three consecutive three-leaved whorls ; in 



each of these the leaf w is formed first, then 



the leaf Z^ and finally 



the leaf Z, 



If 



attempt be made 

 must pass from w 

 again 

 to Z„ 



an 



it 



to construct the spiral, 

 over Z„ across to Z,, then 



Fig. 149. — Transverse section through the convolu- 

 tion of the ieaf-sheaths i — 6 oi Sabal ttmbraculifera ; 

 in the centre is a young leaf-blade. The arrangement 

 of the leaves is a ? divergence. If the numbers i — 6 

 are united by a line, the genetic spiral is obtained. 



'1' 



in the same direction over w across 

 ,2, the figure thus formed is a circle, in 

 which the divergences of successive leaves vary 

 greatly. If we now pass to the next whorl, the 

 line proceeds in a spiral direction to the next 

 leafw; but then, to retain the genetic succes- 

 sion in the second whorl, the line must be continued in an opposite direction ; 

 and this is repeated with every new whorl. It is evident that no clear conception 

 can be obtained in this forced manner, and the whole construction appears alto- 

 gether superfluous, since it is _ 

 required by no feature in the 

 history of development. The 

 stem of this plant is construct- 

 ed, as Pringsheim has shown, 

 of two rows of segments {G, 

 RJ, K, &c., in Fig. 150, A), 

 which arise alternately right 

 and left from the apical cell. 

 Even before the production of 

 the leaves each segment under- 

 goes various divisions, and in 

 this manner the stem is built 

 up of transverse disks which 

 are in alternate succession 

 nodes and internodes. Each 

 nodal disk consists of the 

 interior half of an older 

 segment and the posterior 

 half of a segment next younger in age, as shown in the figure. An internode 

 is formed of a whole segment of one row and of two half-segments of the other 



Fig. x^o.—A the cone of growth of the stem of Salvinia natans, regarded 

 diagrammatically and looked at from above; xx projection of the plane which 

 divides it vertically into a right and left half; the segments are indicated by 

 stronger outlines, their divisions by thinner lines ; the succession of the segments 

 is denoted by the letters F—P; B diagram of the stem with three whorls of leaves, 

 its ventral side indicated by v v ; w the first-formed floating leaf; L\ the aerial leaf 

 formed next ; Li, the second aerial leaf of the same whorl formed last of all between 

 the two first (after Pringsheim) , 



* Many writers employ even in such cases the conceptions borrowed from a spiral arrangement, 

 considering arbitrarily as of successive origin the members of the whorl which arise simultaneously; 

 but this is not in harmony with a true scientific method. 



