452 PHYLLOTAXIS OF CONES. 
LACK SPRUCE. ... . 80 Cones had 5 spirals to the right, 8 to the left: 
Sian for 1869, . a a ee “ “ 5u “ 
Saye wri 6c t To “ 
eee ee i “ c «6 g “ 
1 “ eae a é e é 6 & ‘“ 
3 éé “ 6 st “cc 4 L n se 
Same tree in 1870,...26 <“ Hah “ “6 “ 8 6 “ 
23 se ce 8 ce “ce “ce 5 ce ts 
ee co té “u “ A R “ 
AMERICAN LARCH. ..30 “ ait | é é “« 5 6s 
34 e “ 5 s “ “u E AE é 
3 o “ 4 “ aa “ 6 e “ 
1 “6 “ec 6 c s ve r Ro 3 “ 
1 (23 ét T “ s 4 cc 
i AAD wg & t “4&lo“ c x 
In all of these cases it was possible to see other spirals, but I 
have mentioned those most apparent in each case. For instance, 
in the most common forms of Norway spruce, there were spirals 
with three rows, eight and twenty-one one way, and five and 
thirteen the other way. Other cones showed three and seven one 
way, and four and eleven the other. 
To cut this article short, the fractions for xa cones of POPE 
spruce was 42, for others it appears to: be 34, and for others 3%. 
' By operating with the fraction 44 and other nambers of spirals on 
the cones in the same way as we may on the most common forms, 
we get this series of fractions, viz: 3, 3, +4, Tę, 44, etc. Other 
cones noticed in the table as having four and six nets had also 
two, ten, and sixteen. The fraction for these was 3%, and would 
be found in a series 2, 2, +4, 1, 42, 18, ete. The latter we ob- 
serve, when each fraction is reduced to its lowest terms, is the same 
as the first or most common fractions. mentioned. Most cones of 
the European larch had the phyllotaxis expressed by the fraction 
zr Others by 74, one,other by -&. This latter cone had three, six 
and nine spirals, and falls into the following series, viz: 8, 8 
Z 48, ete. Most cones of the American larch fall under the 
fraction 3, Othars “4 35, others 
In these few examples ‘he | same number of parallel spirals is 
about equally divided in the two directions, right and left. They 
also show that other series than the one usually accepted as 
almost universal, are not uncommon, as they may be found on a 
variety of coniferous trees, though in smaller numbers 
Plants with the leaves opposite generally have them four-ranked 
up and down the-stem, and then the leaves are said to decussate. 
If we start with a plastic stem of this nature we get a fraction A 
to express it; giving the axis a slight twist we get 2, another 
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