CLIMATIC CONDITIONS OF THE UNITED STATES. 213 



activity in general doubles with each rise in temperature above 40° F., 

 at which temperature the rate of development is considered as unity. 



(4) Physiological Indices of Temperature Efficiency for Plant Growth. 



All three methods so far considered for deriving temperature effi- 

 ciency indices from temperature indices assume that the rates of plant 

 activity increase continuously as the temperature rises. If these 

 various series of efficiency index values be plotted as ordinates on 

 graphs whose abscissas are the temperature indices, then the graphs 

 for direct and remainder indices both take the form of straight lines 

 with an upward slope of 45°. The graph for exponential indices, on 

 the other hand, has the form of a curved line slightly concave upward, 

 which much more nearly approaches being horizontal in the region of 

 chmatic temperatures than do the other graphs. In other words, 

 within the range of temperature indices encountered in climatology, 

 the calculated efficiency index increases much more rapidly with rise 

 in temperature for the direct and remainder methods of calculation 

 than it does for the exponential method, as adopted by Livingston and 

 Livingston. None of these graphs, however, shows a maximum, and 

 we know that the true graph of temperature efficiency for plant 

 growth must possess two points where the ordinate is zero and must 

 have a maximum somewhere between these points. This maximum of 

 the graph has a relatively large ordinate and its abscissa is the index 

 of the optimum temperature for growth. It thus follows that none of 

 the methods so far discussed can possibly furnish true indices of tem- 

 perature efficiency for plant activities, excepting, as has been empha- 

 sized, within certain limits of temperature range. If a perfectly satis- 

 factory method of calculating efficiency indices from temperature 

 indices is to be devised, it must be of such nature that both low and 

 high temperature values will give efficiency indices of zero, and inter- 

 mediate temperature values must give indices whose graph shows a 

 well-defined maximum. 



Livingston^ has attempted to obtain efficiency indices from the 

 variations in plant growth-rate experimentally determined for different 

 temperatures. As has been said, the best study of the actual relations 

 between temperature and growth is that of Lehenbauer, and Liv- 

 ingston has employed the results of that writer in this connection. He 

 considered the average hourly growth-rates of shoots of maize seed- 

 lings exposed to the same temperature for a 12-hour period, the tem- 

 peratures included in Lehenbauer's study ranging, by increments of 

 one degree, from 12° to 43° C. Lehenbauer's curve, plotted with 

 growth-rates as ordinates and temperature indices as abscissas, was 

 first smoothed by the use of a flexible spline, so as to give a generalized 



* Livingston, B. E., Physiological temperature indices for the study of plant growth in 

 relation to climatic conditions, Physiol. Res. 1: 399-420, 1916. 



