APPENDIX. BOOK I. 95 1 



When all the bundles lie in a ring, the characteristic structure of a young dicotyledonous 

 stem is seen in a transverse section ; when they do not lie in a ring, the appearance pre- 

 sented by a section is that of an abnormal stem. In the instances mentioned above the 

 latter is the case ; but a more marked instance of this is afforded by Podophyllum, for 

 example, in which, owing to the irregular distribution of the primary bundles (which are 

 here all leaf-traces), a transverse section of the stem somewhat resembles that of a mono- 

 cotyledonous stem. 



The account given in the text of the formation of the cambium-ring in Cbavica 

 (Piperaceae) will be correct if for * cauline bundles ' ' inner leaf-trace bundles * be sub- 

 stituted : that given of the Begoniaceae, in which the internal bundles are cauline, is 

 correct. 



Section 19. For an account of the laws according to which cell-divisions take place 

 in growing organs, see Sachs' important paper Ueb. die Anordnung der Zellen in jiingsten 

 Pflanzentheilen, Arb. d. bot. Inst, in Wiirzburg, II. i, 1878. The following are the more 

 important points to which he draws attention : — 



1. The walls are formed at right angles to those which they intersect. 



2. The planes of the walls in a growing-point are classified thus : 



a. Periclinal, those which are curved in the same direction as the surface 



(seen in longitudinal section). 



b. Anticlinal, those which intersect the surface and the periclinal walls at 



right angles; they thus constitute a system of orthogonal trajec- 

 tories for the pericHnal walls. 



c. Radial, those which pass through the axis of growth and intersect the 



surface at right angles. 



d. Transverse, those which intersect both the axis of growth and the 



surface at right angles. 

 The relation of the periclinal and anticlinal planes are illustrated by the following 

 cases : — 



a. If the outline (in longitudinal section) of the growing-point is a para- 



bola, the periclinals will constitute a system of confocal parabolas of 

 different parameter, the focus of the system being at the point of 

 intersection of two lines of which one is the direction of the axis 

 and the other of the parameter. In this case the anticlinals being 

 the orthogonal trajectories of the periclinals, constitute a system of 

 confocal parabolas the axis and focus of which coincide with those 

 of the periclinals. 



b. If the outline of the growing-point is a hyperbola, the periclinals will be 



confocal hyperbolas with the same axis but different parameter; 

 the anticlinals will be confocal ellipses, with the same focus and axis 

 as the periclinals. 



c. If the outline of the growing-point is an ellipse, the periclinals will be 



confocal ellipses ; the anticlinals will be confocal hyperbolas. 



It must not be supposed that the outline of a growing-point is necessarily one or 

 other of these well-known geometrical forms ; they are selected merely because they serve 

 to illustrate clearly the rectangular intersection of the cell-walls as they are formed, and 

 because, when the nature of the periclinal and anticlinal curves is unknown, their relations 

 may be inferred by analogy. 



An interesting deviation is found in those roots (such as those of Papilionaceae) in 

 which the apex of the plerome are open, /. e. are directly continuous with the tissue of the 

 root-cap ; this is to be ascribed to the fact that the periclinals at the end of the root 

 become parallel or even tend to diverge upwards. 



3. The arrangement of the cell- walls in these planes is most perfectly seen in the 



growing-points of plants which do not possess a single apical cell but in 

 which there is a small-celled meristem. A large apical cell interrupts the 



