1914] OSTERHOUT— CRITERIA OF ANTAGONISM 181 



same or not. Thus, if a solution of A 0.05 M is just as toxic as a 

 solution of B o. 1 M, mixtures of the two will give a straight line 

 (as in fig. 1) provided their effects are additive. 



Emphasis should be laid upon the fact that the method of mix- 

 ing two equally toxic solutions eliminates disturbances due to 

 variations of osmotic pressure. If a molecule of A is twice as toxic 

 as a molecule of B, a solution of A 0.05 M will be just as toxic as a 

 solution of B0.1M, provided there are no other factors to be con- 

 sidered. But if the osmotic pressure of the 0.05 M solution of A 

 is less than that of the o. 1 M solution of B, there will in many cases 

 be better growth in the o . 05 M solution of A . In order to make 

 the solution of A appear equally toxic with the solution of B, the 

 concentration of A must be somewhat increased, say to 0.055 M. 

 We thus compensate for the variation in osmotic pressure, and 

 this compensation is not destroyed when the 0.055 M solution of 

 A is mixed with the 0.1 M solution of B. If the effects of the 

 salts are additive, we must therefore get a straight line, as shown in 

 tig. 1. 



furnishes a criterion of 



which for quantitative purposes 



All 



that is necessary is to determine what concentrations of A and B 

 are equally toxic, mix these solutions in various proportions, and 

 determine the amount of growth. The antagonism in any mixture 

 may then be expressed in a very simple manner. Let the curve 

 showing the growth in the mixtures be LKM. The antagonism in 

 a mixture in which the molecules are 50 per cent A and 50 per cent 



KJ 

 B may be expressed as -^ . JE is the growth which would have 



JE 



been obtained if the effect of the salts had been additive (that is, if 

 there had been no antagonism, but each salt had produced its effect 

 independent of the other). KJ is the increased growth due to 



KJ 



antagonism ; it is best expressed as percentage of JE or as y^ X 100. 



In the same wav increased toxicity (when the mixture is more 



J JH 

 toxic than either of the pure solutions) may be expressed as j^ . 



This sometimes occurs, but it is much less common than antagonism. 



