THE DETERMINATION OF ADDITIVE EFFECTS 
W. J. V. OSTERHOUT 
(WITH FOUR. FIGURES) 
It was pointed out in previous papers‘ that in measuring antag- 
onism it is of importance to determine the additive effect; this is 
the effect produced by dissolved substances in a mixture when each 
substance acts independently of all the others. It was also stated 
that when two equally toxic solutions are mixed the additive effect 
may be predicted, since it will be equal to that of one of the pure 
solutions. In this discussion it was assumed that if two solutions 
are equally toxic they will not become unequally toxic when both 
are diluted to the same degree. This is true (either completely 
or with negligible error only) for cases which have hitherto come 
under the writer’s observation, but other cases might possibly 
occur to which it would not apply, and it seems desirable to 
discuss briefly the treatment of such cases. 
As an example of this we may consider the influence of dilution 
on the effects of two solutions, A and B. These may be mixtures, 
but for the sake of simplicity we may assume that they are pure 
solutions of two salts, A and B, and that roo cc. of solution A, or of 
solution B , diluted to 200 cc. will permit the same amount of growth ~ 
to take place, as shown in fig. 1. In this figure the abscissas 
represent growth, while the ordinates represent the number of cc. 
which are taken and diluted to make 200 cc. of the culture solution. 
Thus on the curve A, A, the abscissa at 60 represents the growth in 
a culture solution made by taking 60 cc. of solution A and adding 
water to make 200 cc. Similarly on the curve B, B, the abscissa 
at 40 represents the growth in a culture solution made by taking 
40 cc. of solution B and adding water to make 200 cc. 
Ordinarily we should expect these curves to be almost or quite 
identical, but we may imagine cases in which they diverge, as shown 
in fig. 1. It is apparent from the figure that while roo cc. of either 
? Bot. Gaz. §8:178, 272. 1914. 
Botanical Gazette, vol. 60] [228 
