130 
] . If several leafy shoots from different plants be taken, it 
will be observed that many, probably the majority, have their 
leaves placed one at a time on the stem ; or, as botanists say, 
alternately ; e.g., the Garden Flag, a Sedge, the Oak, and the 
Holly The rest will almost always have two leaves at the same 
position (or node), but situated on opposite sides of the stem ; 
e.g. } Lilac, Privet, or Horse-chestnut. Of the latter, it will be 
also noticed that each pair of leaves stands at right angles to 
those above and below it. Such series of pairs of opposite 
leaves constitute what has been called the decussate arrange- 
ment. Extended observations will only strengthen the conclu- 
sion that leaves are for the most part alternate or opposite. 
2. Alternate Leaves . — If I take a branch of the May or Oa , 
and hold it vertically with any selected leaf before me, and 
then pass my finger upwards along the stem from that leaf to 
the next, and thence to the third, fourth, fifth, and sixth leaf m 
succession, I find, that the one last reached (sixth) is exactly 
over, or in the same vertical line with, the first ; and it I 
proceed further, I shall find the seventh is vertically over the 
second, the eighth over the third, and so on, the eleventh being, 
therefore, over both the sixth and first. 
3 The following observations will result from this examina- 
tion— Obs. 1. All the leaves on the branch are arranged m 
five vertical rows : from this fact such an arrangement has been 
called pentastichous. Obs. 2. The imaginary line traced by 
the finger in passing from leaf to leaf successively is a spiral 
line. Obs. 3. This spiral line coils twice round the stem be-ore 
arriving at the sixth leaf; the portion of the spiral intercepted 
between the first and sixth leaf is called a i qfcfe. O f®’ f ' t h« 
cycle contains five leaves , the sixth being the first leaf of th. 
SU 4 Ce The g method adopted to represent this arrangement is by 
means of the fraction f. The numerator (2) indicates the 
number of coils in a cycle . The denominator (5) shows the 
number of leaves in a cycle. # „ , 
5. Let a complete cycle be projected on a plane suiface, and 
represented by a “helix” (a spiral line like a watch-spring) 
having two complete coils, and let the corresponding positions 
of the leaves be marked upon it. Then ,f radii be drawn from 
the centre to the positions of the leaves, the ' 
those drawn to any two successive leaves will be two-filth.. ot 
whole circumference, or of 360°; i.e. it will contain 144 degrees. 
Prom this fact, the fraction f is called the angular divergence 
of the pentastichous arrangement of leaves. An observation o- 
* Leaves will occasionally be found grouped in threes or some higher 
number ; they are then said to be whorled or verticillate. 
