48 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



securely protected * in the bud, has long been a favourite biological 

 explanation of bud-structure ; to the common disregard of the fact 

 that actively dividing cells are capable of sustaining enormous 

 pressures from the surrounding tissues ; and that as shown in the 

 apex of Pteris, younger cells can grow and remain turgid at the 

 expense of all older ones. The case of pressure against a sclerosed 

 framework may be considered separately, but as far as parenchy- 

 matous structures are concerned, there is no reason to suppose 

 that primordia are not strong enough to resist all the pressures 

 that can be brought to bear on them in the bud, and the greatest 

 pressures are of their own making. As already indicated, so long 

 as they are formed in orthogonal series, all such mutual pressures 

 will only tend to alter their shape but not their arrangement. 



From this standpoint of a special packed system. Airy formulated 

 a scheme of phyUotaxis, in which all systems were to be derived 

 from a type presenting a constant "ideal" divergence angle by 

 longitudinal compression. The same idea has been put forward 

 by Schwendener.-f and his first figure illustrates the action of a 

 vertical condensing force on a spiral series of the Sehimper type, 

 the natural effect of the latter being to change an orthogonal 

 system into a hexagonal one. Without going into further detail 

 as to Schwendener's standpoint, or considering how such a vertical 

 condensing force could be obtained at a plant-apex, the problem 

 may be attacked in a different manner. 



If a set of equal spheres be arranged in orthogonal series, all 

 forces of contact will act at right angles to the curved surfaces, 

 in this case circles, and will be represented by the sides of the 

 exscribed square areas. The whole system is in equilibrium. 



But since the forces acting along the sides of a square are also 

 represented by the resultant forces along the diagonals, it follows 

 that the same contact pressures wiU give rise to lines of equal 

 pressure in a secondary orthogonal system. In other words, two 

 methods of arrangement are interchangeable (fig. 21) and equally 

 in equilibrium without any disturbance of the original forces. 

 The diagonal arrangement is equally in equilibrium as is the 



* Cf. Airy, Proceedings of the Royal Society, vol. xxii.,.1874, pp. 297-307. 

 t Mechomische Theorie der Blattstellungen, Leipzig, 1878, Taf. 1, figs. 1-4. 



