1904] SHULL—PLACE-CONSTANTS FOR ASTER 335 
Il. MATERIAL AND METHODS. 
This study is based upon the flowering heads of Aster prenan- 
thoides Muhl. collected thrice a week from the same area which 
furnished the serial collections for my earlier studies (SHULL 1902). 
This species is in some ways an ideal subject for studies of this kind. 
The heads are beautifully regular, as may be seen in fig. z. They 
are little subject to injuries, and almost the only heads which must 
be thrown away are those 
in which insect larvae have 
hatched and subsisted tipon the 
developing flowers. Such cases 
are not numerous, amounting 
to less than 2 per cent. of the 
heads collected this year. 
The personal equation was 
éliminated in the same manner 
as in my former work, 7. e., by 
the collection of every head 
that bloomed on a naturally cir- 
cumscribed area. The method 
used in making the counts was 
also the same, the heads being 
completely dissected. This 
method prevents the errors 
Which will frequently occur in 
the Counting of rays without 
complete dissection — errors 
