Miscellanea 
107 
Various forms of ray-flowers seen in the flower-beads of GuiUardia aristata x 11 . 
that 27 had mixed ligulate and tuh\ilar rays. Cohmms 6, 7 and 8 deal with percentages ; it is 
seen that 77'2 is the percentage of 13-rayed heads with all ligulate flowers ; 0"9 the percentage 
of 13-rayed heads with all rays tubular, and 21-9 the percentage of 13-rayed heads with mixed 
tubular and ligulate rays. 
It is seen that when the numljer of rays in a head is large both ligulate and tubular rays 
are apt to occur. While with fewer rays in a head there are some instances in which all the 
flowers are tubular and many in which all are ligulate. The normal head has all ligulate 
rays, but a percentage of 28'8 heads with mixed ligulate and tubular rays shows a strong 
tendency to vary from this normal. 
The accompanying curve of variation for the number of rays is computed from columns 
1 and 2 of the foregoing table. It includes all rays withoxit regard to their form. There is 
a well-devclo]ied mode at 13 and the usual skewness to the right which may be expected in 
all such studies as the present one. 
The 500 flower-heads examined had a total of 7709 rays. The larger part of these rays 
were three-lobed and ligulate but some had as many as six lobes and a single specimen had 
only one lobe. In the following table the records for all of these flowers are tabulated. It 
includes therefore both ligulate and tubular rays. 
It will be seen from the table on p. 108 that while the ligulate rays have as a rule three 
lobes, the tubular rays are more often four-lobed. The percentage of ligulate rays decreases 
and the percentage of tubular rays increases with an increase in the number of the lobes. 
14-2 
