1916] GRAVES—CHEMOTROPISM IN RHIZOPUS 347 
of the normal number in A we get the total number affected. In 
order to get the total percentage of reaction, we must divide this 
number by three-fourths of the total number of hyphae counted 
in the whole area, since we are dealing with only three-fourths of 
the hyphae, the one-fourth represented by the normal A’s being 
unaffected, at least visibly.5 
If we denote the normal number to be expected in each region by 
n (one-fourth of the whole), the number actually in each region by 
its corresponding letter, and the total number of hyphae in the whole 
(A a os 
area by #, the formula will then read as follows: 
or, simplifying, Sy = Percentage of hyphae reacting. “Th case 
a repellent force exists, raising the number of C’s above the normal, 
the final percentage will then be a minus quantity, and it is so 
expressed in the accompanying tables. 
One objection to this method lies in the possibility that some 
of the normal C’s may have been attracted so strongly as to have 
turned from C, through the B or D areas, to A; these would then be 
counted twice over, for they would be included in the gain to A 
as well as in the loss from C. It is of course quite impossible to 
determine for a large number of holes how many hyphae have 
so acted. The objection, however, is not a serious one; for, as a 
matter of fact, when the number of B’s and D’s is fairly large, indi- 
cating a force not strong enough to draw them all into the A class, 
we know that the probabilities are much against the force attracting 
any from the C class into the A class. 
However, when more than three-fourths of the total number 
point in the A direction, we can fairly assume that all which were 
originally B’s and D’s have now turned to the A direction; that 
is, of this 75 per cent, 25 per cent consist of those originally in A, 
and 50 per cent must have been derived from those nearest the A 
class, namely B and D; thus any number above 75 per cent must 
have come from those which were originally growing in the C 
5 Just what individuals among the normal A’s have reacted to the stimulus we 
cannot of course judge, since by their original chance position they are all oriented 
toward the holes, but the proportion would correspond essentially to that for the 
remaining 75 per cent of the hyphae 
