1915] 
effect. 
OSTERHOUT—ADDITIVE EFFECTS 
233 
For example, it will be seen in fig. 3 that a growth of 
20 mm. may be found at 30 M or 60 N; ora growth of 15 mm. may 
be found at 40 M or 80 N. 
If this relation holds throughout (even 
approximately), we may consider the effect of M as equal to the 
effect of 2 N. 
line in fig. 4 (cf. table I). 
as will readily be seen, is the same as 
determining the additive effect of M 
mixed with another solution of M 
which has been diluted 
to a definite degree with 
water (each 100 cc. of 
the mixture of M+[M 
diluted] being itself di- 
luted to 200 cc.). This 
is in fact the method 
suggested in a previous 
paper.? 
A relation such that 
the effect of M=the 
effect of XN will be 
found to hold (at least 
approximately) in most 
cases. If it does not, 
the additive effect may 
If we grow plants in culture solu- 
tions made by taking sufficient of M+N to make 
too cc. (and then diluting this mixture to 200 cc.), 
we shall get an additive effect which is not con- 
stant but which will always be the same for any 
given mixture, whether calculated as M or as N. 
The additive effect obtained under these 
conditions is shown as a curved and dotted 
This procedure, 
to ee BOR. 
Fic. 4.—Antagonism curve showing growth in 
various mixtures of two solutions of salts, M and NV, 
of which the dilution curves are shown in fig. 3: the 
ordinates represent growth; the abscissas represent 
the number of cc. of the solutions of salts which 
are taken and diluted to 200 cc. to make the culture 
solution in which the plants were grown; thus N 75, 
M 25 signifies that 75 cc. of N were added to 25 cc. 
of M and the whole diluted to 200 cc.; the additive 
effect is shown by the curved dotted line; the 
antagonism at the point O is OP+PR. 
be calculated in terms of a third curve drawn arbitrarily or by 
taking points midway between the two (measured vertically), as 
previously explained. 
4 Bor. Gaz. 58:178. 1914. 
60 M.M. 
