1908] DANFORTH—VARIATION IN DAISY 353 
modes is to be sought in an explanation of phyllotaxis. As is well 
known, this is a subject which has given rise to a great deal of 
speculation. Although, perhaps, there is even now no satisfactory 
explanation of the rules of phyllotaxis, the facts themselves are 
familiar and only a brief reference need be made to one or two simple 
conditions. 
As has been frequently pointed out, TABLE V 
five-ranked leaves may be regarded as DISTRIBUTION OF RAYS IN Two 
arranged on the stem according to any ee as Pears pray 
one of several different schemes. In WAY, JUNE 22, 190s; Lor A 
one light they may be imagined as FROM SOUTH SIDE OF ROAD; 
situated regularly along a line coiled Bae gla err 
spirally around the stem in sucha way 
that the sixth leaf falls very nearly Rays ae 
above the first. In this case, if the 6 . 
line is considered as running around 17 4 
the stem in one direction, it encircles . : 
it twice in passing from the first to a9 zi 
the sixth leaf; if in the other direction, . 26 5 
It encircles it three times in passing en 3 5 
between the same two points. On 25 : : 
changing the point of view slightly, the - 4 ie 
leaves may be imagined as all arranged a : 3 
along two parallel spiral lines running 30 4 # 
i one direction, or along three similar : 5 2 4 
lines Tunning in the opposite direction, 33 ; Pe 
which case either spiral embraces a te 
five leaves in each revolution. This < 3 
'S equivalent to regarding the leaves 38 
as though they were placed at the points [ . 
of intersection of two opposite sets of 
Spirals, one composed of two lines, the other of three. Once 
More, the leaves may be regarded as placed along five nearly vertical 
but still slightly spiral lines. Of course these are merely different 
ways of Tegarding one and the same thing. 
While these conditions, on the whole, are quite constant, never- 
theless when the stem is increased in diameter or shortened, thereby 
