3^ 



THE QUARTERLY REVIEW OF BIOLOGY 



better correlated if they be plotted in three 

 dimensions. A model was therefore con- 

 structed (fig. 6) representing the rate of 

 elongation plotted against pH by erect 

 cards, standing on a platform, the two 

 dimensions of which are spaced to cor- 

 respond to the hydrogen ion concentration 

 and the molar concentrations respectively. 

 It is found by this arrangement that the 

 alkaline limit falls in a straight line, and 



0.120 

 0.112 



Fig. 7. Idealized Floor-plan of Tri-dimensional 



Graph for CaCl 2 . Dotted Lines Indicate 



Maxima 



that the acid limit forms a curve at low 

 concentrations and at higher concentra- 

 tions forms a straight line intersecting 

 the alkaline limit at neutrality and a 

 molar concentration of theoretically 0.185. 

 This relationship can better be shown by 

 a map or floor-plan of the model (fig. 7). 

 In this also it is shown that the alkaline 

 optimum and the acid optimum form 

 straight lines, with the median minimum 



between. It need scarcely be pointed out 

 that it is necessary to incorporate the 

 graph for calcium hydroxide in these 

 models and maps inasmuch as it may be 

 looked upon as representing zero con- 

 centration of the salt. 



From this model and map there can be 

 readily pointed out the relationship be- 

 tween the effect of the respective ions 

 present namely, Ca, CI, H, and OH, and 

 their mutual interaction. For instance, 

 it is seen that no growth occurs in acid 

 solutions of low calcium content. This is 

 in harmony with the agricultural experi- 

 ence of the inadequacy of acid soils low in 

 calcium, and indicates a possible explana- 

 tion of the beneficial effect of adding 

 calcium to an acid soil, if by so doing the 

 root hair elongation is changed from zero 

 to the maximum rate in any concentration 

 of this salt, namely at a concentration of 

 about 0.010 and neutral or slightly alka- 

 line solutions. The growth of root hairs 

 in acid solutions, with moderate calcium 

 present, indicates that the latter ion has 

 an antagonistic effect upon the hydrogen 

 ion. This is also in harmony with the 

 results of others upon studies in plant 

 development. At still higher concentra- 

 tions of the calcium, however, a new 

 relationship is brought out, namely that 

 the hydrogen ion does not have an an- 

 tagonistic effect upon the calcium ion, 

 that is, in higher concentrations of calcium 

 chloride no growth occurs in very acid 

 solutions. In like manner relationships 

 may be pointed out between the chlorine 

 ion and the hydroxyl ion on the alkaline 

 side. The interpretation here is however 

 complicated by the difference of interpre- 

 tation of alkalinity as due either to the 

 presence of the OH ion in excess or simply 

 to the decrease in amount of free hydrogen 

 ion. It is also complicated by the fact 

 that the calcium seems to play a direct 

 part in the growth of the root hair, and 



