300 Dr. H. Airy on Leaf- Arrangement. [Apr. 30, 



this fact of mutual pressure, we can see that leaf-order is useful iu these 

 close-packed forms by securing equal development of leaves and therefore 

 economy of space. If the whole space is to be occupied, and the leaves 

 or shoots are to have equal development, there must be orderly ar- 

 rangement of some kind. The principle of economy of space under 

 mutual pressure is put forward as of chief importance in leaf-arrange- 

 ment. 



It appears that economy of space is especially demanded in a longi- 

 tudinal direction, for the sake of protection against vicissitudes of tem- 

 perature and the attacks of enemies. In a bud, for example, it is evidently 

 important, on the one hand, that as many leaves as possible should attain 

 as high development as their situation will allow, in order that they may 

 be ready at the first approach of spring to complete that development 

 and enter on their function without loss of time ; but, on the other hand, 

 it is evidently important that the embryo shoot should be as short as 

 possible, in order that it may be well within the guard of the protecting 

 scales and less exposed to danger during the long period of bud-life. 

 These claims will be satisfied by a vertical condensation of the leaf -order, 

 such as the state of mutual pressure of the embryo leaves and shoots is 

 calculated to bring about. 



That the arrangements represented by the lower terms of the above- 

 mentioned series A, B, 0, &c. would, under a force of longitudinal con- 

 densation, actually give rise to the successive arrangements represented 

 by the higher terms of the same series, is shown by diagrams, in which 

 the necessary consequences of each step of condensation are made 

 apparent to the eye. In these diagrams a leaf or shoot is represented 

 (for mechanical considerations) by a sphere, and the spheres are numbered 

 from upwards. Taking, first,' series A, the lowest order of that 



series, -, is represented by two vertical rows of spheres, those of each 



row being in contact and alternating with those of the other. If these 

 two rows remain vertical, no longitudinal condensation can take place. 

 The first step towards such condensation must be their spontaneous 

 deviation from the vertical. (Instances of such deviation in nature are 

 found in the genus Gasteria and others, to be considered further on.) 

 The next step required is some force of vertical compression, such as 

 would result in nature from the stunting of the bud-axis (due directly to 

 cold or indirectly to the advantage of protection gained thereby), attended 

 with less, if any, stunting of the leaves. Then it is seen that the succes- 

 sive stages of condensation, beginning with the order T , will bring succes- 

 sively into contact with (zero) the following numbers, 3, 5, 8, 13, 21, 

 34, 55, 89, 144, &c. ? alternately to right and left, producing in succession 



