342 SEMI-CENTENNIAL OF TORREY BOTANICAL CLUB 
Weisse (707) attempts to refer the position and number of 
flowers in the head to the mechanism of phyllotaxy, as conceived 
by Schwendener (778, 85). According to this view, the arrange- 
ment of lateral organs, as leaves, is determined by the pressure 
they exert upon one another when in the embryonic condition. 
The arrangement and relative position of matured organs is hence 
not definitely related to divisions taking place in the growing 
point, but is dependent on the mutual pressures between organs 
already present and above which the new ones are being formed. 
Weisse's observations were made on 141 main flower heads of 
Helianthus annuus. 'The most definite facts revealed are that 
as the ray-flower number increases more disk-flowers are laid down 
before two are in contact and that there is much variation in the 
phyllotaxy immediately below the flower head. "There seems to be 
an increase in ray-flower number with higher values of phyllotaxy, 
but the great range of variability (13 to 82) in ray-flower number 
and the small number of cases do not permit of a very definite 
conclusion. { 
ПІ. SPECIAL CRITICISMS OF FACTS AND THEORIES 
Vogler ('12) discusses especially the theories held by Ludwig. 
He points out that Ludwig ('87) at first related development of 
flowers in a head to processes concerned with the mechanism of 
leaf position, but that as early as 1888 he (Ludwig, '88) refers the 
phenomenon to certain types of rhythmic cell division which were 
later more fully formulated by him (Ludwig, ’95 and '98). Vogler 
points out that the two processes (1) the mechanism of phyl- 
lotaxy and (2) periodic divisions are not necessarily exclusive, and 
that leaf arrangement may be due to the same kind of periodic 
cell-divisions as are involved in the production of flowers in a head. 
Furthermore, Vogler (712) appears to contend that the develop- 
ment of certain numbers as maxima rather than others does not 
involve the reproduction of Anlagen according to the scheme of 
Fibonacci, but results from the continuation of the phyllotaxy in 
the arrangement of the number of parts of the flower head. “Піеве 
Bevorzugung bestimmter Zahlen ist nicht die Folge einer Ver- 
mehrung der Anlagen nach dem Schema des Fibonacci, sondern 
ergiebt sich aus dem gesetzmassigem Anschluss an die Spiral- 
