276 



BOTANICAL GAZETTE 



[SEPTEMBER 



may be added and the results plotted as shown in fig. 3, in 

 which the additive effect is expressed by the dotted line and the 



1 



growth in the mixtures by the unbroken line. Antagonism at 

 any point may be easily expressed. For example, the antagonism 



at the point M is 



MO - MN 



MN 







Sol. I 



% 



D 



25 



50 



75 



100% 



FlG. 3. — Method of expressing antagonism in mixtures containing more than 



three components: three of the components (A, B, and C) are combined into solution 



1 and various amounts of the fourth component (Z>) are added; the ordinates represent 



growth; the abscissas represent the composition of the mixtures; thus at the point 



M the mixture contains 62.5 cc. of solution 1 to each 37.5 cc. of solution D, the 



OV 

 antagonism at M is ^— . 



MN 



By the method of mixing unequally toxic, pure solutions or 

 by the method of keeping the concentration of one salt constant 

 while varying that of the others, the dotted line would become a 

 curved one. 



Summary 



The measurement of antagonism in solutions containing more 



» 



difficulty 



mixm 



nism 



v-» x j x^ ■■ ■■ ^ — - ^^ — 



Methods are suggested for the graphical expression of antago 



ARVARD 



