348 BOTANICAL GAZETTE [NOVEMBER 
direction. In other words, chemotropic forces which would cause 
a turning of slightly more than go° would bring all the B’s and D’s 
to A; but if the force were stronger than this, some of the C class 
would turn to the A direction. It is clear, therefore, that the 
number in excess of 75 per cent represents those which have turned 
from C to A; and that in this case those remaining in B and D 
must have been originally in the C class but have not turned 
strongly enough to become A’s. 
Accordingly, whenever the total number of hyphae in A exceeds 
75 per cent of the whole number, a correction must be applied; we 
must now subtract from our formula the number which have come 
over from C into A, to avoid counting them twice. We can ascer- 
tain, indirectly, how many of the C’s have so turned into A by sub- 
tracting the number left in C from the normal number, and by also 
subtracting from this result the sum of those left in B or D; for, 
as was previously shown, those now in B and D must also have been 
originally C’s. The remainder, representing the difference between 
all these and the normal number, will then denote the num- 
ber which have turned from C through the B and D classes to 
A. In accordance with this, therefore, we must subtract from 
our first formula [(n—C)—(B+D)]. The whole formula would 
then read: (A mm) Se [(m—C)—(B+D)]. or, simplifying, 
34 ? + 
t 
A—n+B+D 4 
em ercentage of hyphae reacting. As before, should 
the excess over 75 per cent be in the C class, the result of the cal- 
culation would be a minus quantity, and would indicate repulsion. 
THE EXPERIMENTAL ERROR.—In order to test the accuracy of 
the method, 10 preparations were made with conditions as regards 
number and length of the hyphae, and composition of the medium, 
essentially the same in both upper and lower films. Under these 
circumstances, in accordance with our hypothesis, there should be 
no more turning in one direction than in another. Hyphae were 
examined in the prescribed manner for 10 holes in each preparation, 
making too holes for the entire operation, or, if we count bot. 
upper and lower films, in reality 200 lots of hyphae. The results, . 
in the order in which the counts were made, are shown in table I. 
