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AMERICAN NATURALIST. 
Vol. VIL.— AUGUST, 1873.—No. 8. 
HCH ORMDOD D2 
PHYLLOTAXIS OF CONES. 
BY PROFESSOR 'W. J. BEAL. 
Is the summer of 1870 I examined a large number of cones of 
several species of Conifere to see if there was any variation in 
their leaf arrangement. It has long been well known that the 
scales or leaves of cones show very plainly a certain number of 
parallel spiral whorls twisting to the right and a different number 
twisting to the left. A closer examination will also usually reveal 
other parallel whorls (one or more in each direction) with numbers 
differing from those most easily seen. By beginning with the 
simplest forms of alternate leaf-arrangement, as the elm (4), and 
sedges (1); and then to the more common but more complicated, 
as the cherry (2), and American larch (3), it is found that in these 
fractions the numerator expresses the number of times we pass 
around the stem to find a leaf directly over the one with which 
we started, while the denominator indicates the number of vertical 
ranks or rows of leaves up and down the stem. This is nicely 
Proven to be true in the case of a fraction with large numerator 
and denominator in the leaves of Yucca filamentosa, where the 
fraction is thirteen thirty-fourths, if memory is not at fault. In 
Yucca the bases of the leaves are so broad that they reach about 
half-way around the stem, so it is easy to see which is below or 
outside of all the others. The fractions above mentioned also 
express the angular divergence or show the proportion of the 
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AMER. NATURALIST, VOL. VII. 29 (449) 
