1914I 



OSTERHOUT— CRITERIA OF ANTAGONISM 



179 



antagonistic action, but that it is partly due to the dilution of the 

 toxic salts, for it is evident that the concentration of each of them 

 has been reduced from o. 1 M to 0.05 M. 



It seems desirable to formulate the matter so as to obviate such 

 misconceptions and it is clearly necessary to provide a quantitative 

 criterion of antagonism which shall be both accurate and conven- 

 ient. A graphical expression of such a criterion is seen in Fig. 1. 



Molecular 

 Proportions 



CACL 2 NACL 

 100 



80 



60 



40 



20 



0" 100 

 NACL 100 



CACLi 



20 



40 



60 



80 



jOOjSoluti 



ions 



Fig. 2. — Curves showing the relation between the molecular composition of a 

 mixture of two solutions and its composition expressed as cc. of the component solu- 

 tions; see footnote 1. 



In this figure the growth of the plant in a solution of the salt A 

 0.1 M is expressed by the ordinate at C; the growth in a solution 

 of the salt B 0.1 M is expressed by the ordinate at G; as the ordi- 

 natcs are equal the solutions are equally toxic. The ordinates be- 

 tween C and G express the growth in various mixtures of the two 

 solutions; thus that at D expresses the growth in a mixture in 

 which 75 per cent of the dissolved molecul* are A and 25 per cent 



