THE LEAF 229 
in time the mature leaf is developed. The primordial leaf is 
formed by a portion of the dermatogen of the growing stem apex, 
which becomes epidermis, a portion of the periblem, producing 
mesophyll or leaf parenchyma which grows into this, and a part 
of the plerome, which becomes vascular tissue within the 
mesophyll. 
In the sub-divisions of cells around the growing stem-apex, 
the primordial leaves (primordia) do not arise exactly at the same 
time. ‘There is a tendency toward spiral arrangement. 
PHyLLoTaxy.—Phyllotaxy is the study of leaf arrangement upon 
the stem or branch, and this may be either alternate, opposite 
whorled, or verticillate, or fascicled. It is a general law in the 
arrangement of leaves and of all other plant appendages that 
they are spirally disposed, or on a line which winds around the 
axis like the thread of a screw. The spiral line is formed by the 
union of two motions, the circular and the longitudinal, and its 
most common modification is the circle. 
_ Foliage leaves are usually arranged in separated fashion along 
the stem, one occurring at each node. This is the form of spiral 
arrangement called the alternate arrangement, as shown by most 
plants. 
The alternate arrangement is said to be two-ranked, when the 
third leaf is over the first, as in all Grasses; three-ranked, when 
the fourth is over the first. Example: Sedges. The five-ranked 
arrangement is the most common, and in this the sixth leaf is 
directly over the first (counting the leaf from which the start is 
made), two turns being made around the stem to reach it. 
Examples: Cherry, Apple, Peach, Oak and Willow, etc. As the 
distance between any two leaves in this arrangement is two- 
fifths of the circumference of the stem or 144°, the five-ranked 
arrangement is expressed by the fraction 74. In the eight- 
ranked arrangement, the ninth leaf stands over the first, and three 
turns are required to reach it, hence the fraction 3g expresses it. 
Of the series of fractions thus obtained, the numerator represents 
the number of turns to complete a cycle, or to reach the leaf 
which is directly over the first; the denominator, the number of 
perpendicular rows on the stem, or the number of leaves, count- 
ing along the spiral, from any one to the one directly above it. 
