ANTAGONISM 133 



25% CaCl 2 ; the line EK represents mixtures in which 

 the dissolved molecules are 50% CaCL ; the line DL mix- 

 tures in which the dissolved molecules are 75% CaCl 2 . 

 In the same way FG means 75% KOI; EH, 50% KC1; DI, 

 25% KC1; GL, 25% NaCl; HK, 50% NaCl; and IJ, 

 75% NaCl. 



The point M is on the line FJ, meaning 25% CaCl 2 ; 

 it is also on the line EH, meaning 50% KC1 ; and likewise 

 on the line GL, meaning 25% NaCl. It therefore repre- 

 sents a mixture of the three equally toxic solutions, 

 NaCl 0.12 M, KC1 0.13 M, and CaCl 2 0.164 M, in which the 

 dissolved molecules are 25% CaCL + 50% KC1 + 25% 

 NaCl. In the same way the point represents a mixture 

 in which the dissolved molecules are 50% CaCl 2 25% KC1 

 + 25% NaCl. 



It is obvious that the composition of any solution can 

 be represented by selecting a suitable point on the dia- 

 gram. At any such point an ordinate may be erected ex- 

 pressing the growth of the plant in that solution. When 

 this has been done for a sufficient number of points, a 

 solid model may be constructed which gives a complete 

 description of the growth of the plant in all the solutions. 

 Such a model is shown, in Fig. 54. The ordinates represent 

 the aggregate length of roots per plant of wheat at the end 

 of 30 days. The ordinates in the pure solutions are equal 

 (55 mm.), showing that the solutions are equally 

 toxic. The ordinates were in part determined directly by 

 experiment and in part calculated from data obtained by 

 growing plants in solutions of approximately the same 

 composition as those represented. 



From such a model the antagonism in any solution 

 may be determined at once by measuring with calipers 

 the height of the ordinate at the required point, subtract- 



