488 LECTURE XXJX. 



these circles represent as it were successive transverse sections, and this so that the 

 outermost circle represents the lowest transverse section, and the following 

 ones sections at higher and higher levels. On these circles the organs which arise 

 at the different transverse sections are transferred in the order established by careful 

 study. In this way is produced in Fig. 324 a diagram of an entire plant oi Euphorbia 

 helioscopia in flower, with the exception of the root. It is only necessary to observe 

 that the leaves cc and i-io, and the central figure B which represents the first 

 terminal flower, belong to the same shoot-axis. The five figures arranged around the 

 centre, on the other hand, represent the diagram of five lateral shoots which have been 

 developed from the axils of the leaves 6-10 ; each of these five shoots has produced 

 only three leaves and a terminal flower B, and in the axils of the three leaves appear 



Fig. 324.— Diagram of a small plant of Euphorbia helioscopia. c c cotyledons ; 

 // the first ; i— lo the subsequent foliagre-leaves ; 6, 7. 8, 9 and 10 form a whorl ; B / 

 (in the centre) the terminal flower of the primary shoot ; Bl/ the terminal flower of 

 one of the five axillary shoots; ///in each case leaves of axiUaryshoot of second 

 order. 



again three shoots, each with three leaves. Without going more deeply into the varied 

 relations of symmetry of this entire system, I may simply remark that the shoot com- 

 mences with two opposite leaves cc (the cotyledons) upon which follow two foliage- 

 leaves (/) decussate with them. Further upwards, however (i.e. further inwards in 

 the diagram), the leaves i-io are situated, no longer in pairs but singly, at various 

 heights on the axis ; at the same time appear lateral displacements, so to speak, the 

 leaf 3 stands above i, but the leaf 5 stands not exactly over 2, as would correspond to 

 the original order with which the arrangement of the leaves began, and finally we 

 find the five leaves 6-10 arranged in a circle, and forming a whorl, whence the shoot- 

 axis which lower down puts forth leaves radiating in four directions is now surrounded 

 by leaves equally disposed in five directions. The central flower B also has five more 



