FREEZING POINTS OF NUTRIENT SOLUTIONS 353 



also exhibits satisfactory agreement between the present deter- 

 minations and the calculations of Tottingham. As that writer 

 employed the optimal series, the diffusion tensions apparently 

 varied from a minimum of 2. 36 to a maximum- of 2.66 atmos- 

 pheres, while he assumed this value to be constant throughout 

 the series and to possess a magnitude of 2.50 atmospheres. Con- 

 sidering the relatively low sensitiveness of ordinary plants to 

 slight variations in the total diffusion tensions of the medium 

 in which they are rooted, it appears that Tottingham's calcula- 

 tions are satisfactory for the preparation of nutrient solutions 

 not more concentrated than his optimal series. For the weakest 

 and for the medium concentrations, then, Tottingham' s method 

 of calculation (which assumes ionization of each salt to proceed 

 independently of any influence of the other salts) proves reliable. 



As has been emphasized, the highest concentration employed 

 by Tottingham exhibits much more serious departures from his 

 calculation of diffusion tension. The supra-optimal series shows, 

 by the cryoscopic method, a range of diffusion tension from a 

 minimum of 6.52 to a maximum of 7.53 atmospheres, while 

 Tottingham's calculation placed this value at 8.15 atmospheres. 

 Whether such a variation may be important in culture experi- 

 ments, with plants at best sickly from such high concentrations, 

 has not been determined, but it appears probable that an os- 

 motic influence may sometimes enter as an uncontrolled condi- 

 tion if Tottingham's strongest solutions are prepared according 

 to his formulae. 



Since no concentrations were studied between the optimal and 

 the supra-optimal of Tottingham's experiments, since the former 

 of these concentrations proves reliable as he prepared the series, 

 and since the latter seems somewhat unsatisfactory, it can not be 

 stated how concentrated such a series may be made without in- 

 troducing considerable variation from the diffusion tensions de- 

 rived by cryoscopy. It seems perfectly clear, however, that 

 Tottingham's method of calculations should prove satisfactory 

 for series of somewhat higher concentration than that of his 

 optimal solutions. 



