1914] 



OS TERHO U T—A N T AGON I Si 1 



273 



additive effect increases very rapidly. These methods usually 







25 



50 



75 



100 N ACL 



consist in mixing unequally toxic solutions or in keeping the con- 

 centration of some salt or salts constant while varying that of the 

 others. 



The method of mixing equally toxic solutions also has a great 

 advantage when the results are to be expressed graphically. As 

 an illustration of this we may take mixtures of NaCl+KCl+CaCl 2 . 

 In the case of wheat it was found that the roots grew equally well 

 in solutions of NaCl 0.12 M, KC1 0.13 M, and CaCl, 0.164 M. 

 Mixtures of these solutions were prepared and the growth of the 

 roots in these mix- 

 tures was measured 

 after a period of 30 

 days. In order to 

 show the results 

 graphically, the com- 

 position of the 

 solutions may be con- 

 veniently expressed 

 by means of a tri- 

 angular diagram as 

 drawn in fig. 1? 



CACLl 



KCL 100 



Fig. 1. — Diagram representing the composition of 

 various mixtures of KCl + NaCl+CaCl 2 : this serves as 



The diagram con- 

 sists of an equilateral 



triangle, the apices of the base of the solid model shown in fig. 2. 



which represent 



equally toxic pure solutions. Thus the point A represents pure 

 CaCl 2 (0.164 M), B represents pure KC1 (0.13 M), and C repre- 

 sents pure NaCl (0.12M). All points on the sides of the triangle 

 represent mixtures of two solutions only, the composition depend- 

 ing on the position of the point. Thus the point H represents a 

 solution made by mixing the equally toxic solutions NaCl o. 12 M 

 and KC1 0.13M in such proportions that in the mixture 50 

 per cent of the dissolved molecules are NaCl and 50 per cent are 



3 These diagrams are employed in physical chemistry and have been used by 

 S< hreixer and Skinner in plant physiology (Bot. Gaz. 50:1. 1910). Finely ruled 

 diagrams may be purchased from the Cornell Cooperative Society. 



