

1874.] Dr. H. Airy on Leaf -Arrangement. 301 



a series of orders which exactly resemble those found in nature, repre- 

 sented approximately by the successive terms of series A : 



] 2 3 5 8 13 o 



3' 5' 8' 13' 2T 34' 



The first two or three stages of this process may be illustrated by 

 mechanical experiment. Attach two rows of light spheres in alternate 

 order on opposite sides of a stretched india-rubber band, give the band a 

 slight twist, and relax tension ; the system rolls up with strong twist 

 into a tight complex order with three steep spirals, an approximation to 



the order - : if the spheres are set a little away from the axis, the order 

 3 



becomes condensed into (nearly) , with five nearly vertical ranks ; and 



o 



it is plainly seen that further contraction, with increased distance of the 

 spheres from the axis, will necessarily produce in succession the orders 



<J p- Q 



(nearly) -, , , &c., and that these successive orders represent suc- 

 cessive maxima of stability in the process of change from the simple to 

 the complex. These results are not invalidated by the consideration 

 that the natural development of leaves is not simultaneous but succes- 

 sive. 



By other diagrams it is shown that the same process of condensation 



operating on the orders represented by the lower fractions of series B 1^ 

 \ &c.\ will produce the higher orders of that series. 

 The same is also shown for series C (-, p , &c.j. 



From the striking correspondence thus brought out between fact and 

 theory, the conclusion is anticipated that we have here a clue to the 

 secret of complex spiral leaf-order that it is the result of condensation 

 operating on some earlier and simpler order or orders, the successive 

 stages of that condensation being ruled by the geometrical necessities of 

 mutual accommodation among the leaves and axillary shoots under 

 mutual pressure in the bud (taking the bud as the type of close-packed 

 forms). 



From this point of view, Hofmeister's law, that every leaf is found at 

 that point in the circumference of the stem which has been left most open 

 by the earlier leaves of the cycle, means that every leaf stands in that 

 position relative to its neighbours which gave it most room for develop- 

 ment in the bud. 



Allusion was made above to deviation of leaf -ranks from the vertical 

 as a necessary first step towards condensation. A series of six diagrams 

 shows the gradual transition presented by different species of the South- 

 African genus Gasteria, from a form in which the two ranks are exactly 



