139 
or | x 360°. But as the spiral arrangement is continued up 
the stem and into the terminal bud, the leaves seem to “ right ” 
themselves, as it were ; so that the appearance of the spiral in 
the neighbourhood of the summit is more accurate than at the 
point of departure from the highest pair of opposite leaves. 
Ex. 2. Change from the tricussate arrangement into the f 
divergence of the secondary series. A change from verticils of 
threes into the f was frequent. It takes place in the following 
manner : — The first step is to cause the three leaves of the dif- 
ferent whorls to separate slightly by a development of their in- 
ternodes. Then, if any two consecutive whorls be examined, 
the order of succession of the six leaves (No. 1 being the lowest) 
is thus : — 
6 
3 2 
7 9 
4 8 5 
1 
In which it will be noticed that the fourth leaf, instead of being 
over the interval between the first and second, is over that 
between the third and first, so that the angle between the first 
and second leaf, or between the second and third, is double that 
between the third and fourth. These latter, it will be remem- 
bered, are separated by a long internode. The same order ob- 
tains with the succeeding whorls ; the nodes, however, are now 
much more widely separated, while a true spiral arrangement, 
with the same angular distance between all its leaves, is ulti- 
mately secured, and is henceforth continued uninterruptedly 
into the terminal bud, and represented by the fraction -f-. 
31. From very many observations on stems of the Jerusalem 
Artichoke, it appears that to resolve opposite and decussate 
leaves into spirals of the primary series and tricussate verticils 
into those of the secondary series is more easily accomplished 
than any other kinds of transition. To reverse the process, or 
to bring back spirals into verticils, seems quite contrary to all 
nature’s tendencies to change. Stems of the Jerusalem Arti- 
choke occasionally had their leaves arranged spirally below, and 
verticillate above ; but then the change was abrupt. The spiral 
suddenly terminated, and the last leaf was succeeded by three 
in a whorl. 
Conclusion . — I have now endeavoured to give a brief and as 
clear account as I can of the main facts and principles of Phyl- 
lotaxis. But, if we venture to search for a cause of such 
definite and exact arrangements of leaves, it will probably be 
fruitless, for as yet no satisfactory explanation has ever been 
given. It is not enough to say that it is a wise arrangement 
that leaves should not all be over one another, so as to exclude 
