THE PERMEABILITY OF PROTOPLASM 



125 



line, but by a plane parallel to the base. To determine 

 the antagonism of any of the mixtures, it is only necessary 

 to measure the height of the ordinate at the point repre- 

 senting the particular concentration under consideration, 

 and, having also measured the height of the plane of the 

 additive effect (which is 55 for wheat roots, as shown in 







Sol.I. 100 

 D. 



FIG. 10. METHOD OF EXPRESSING ANTAGONISM IN MIXTURES 

 CONTAINING MORE THAN THREE COMPONENTS. 



Three of the components (A, B, and C) are combined in Solution 1, and 

 various amounts of the fourth component (D) are added; the ordi- 

 nates represent growth; the abscissae represent the composition of 

 the mixtures. Thus, at the point M the mixture contains 62 '5 c.c. 

 of solution 1 to each 37'5 c.c. of Solution D. The antagonism at 



- ON 



Table XXXI.), to subtract it from the total, and to divide 

 the remainder by the amount subtracted. 



When solutions of more than three components are 

 employed, Osterhout recommends the following procedure : 

 Starting with isotoxic solutions A, B, C, and D, a mixture of 

 the first three may be made, and named solution 1. To 

 this various amounts of D may be added ; taking the growth 

 in the mixtures as ordinates, a graph may be constructed 



