CLIMATIC CONDITIONS OF THE UNITED STATES. 211 



instances being too far apart, still enough are at hand to justify the belief that animals 

 and plants are restricted in northward distribution by the total quantity of heat during the 

 season of growth and reproduction. 



Merriam's chart (1894, plate 12) of the summations just described 

 is here reproduced in its essentials, as our plate 37, for purposes of com- 

 parison, and because of its pioneer nature and present scarcity. From 

 this map it is seen that the warmest zone of the United States, as here 

 indicated, is characterized by a summation temperature of 26,000 on 

 the Fahrenheit scale (14,500 on the centigrade scale), and that this 

 zone is restricted to the lower Colorado Valley, the extreme southern 

 portion of Texas, and the southern half of the Florida peninsula. The 

 zone characterized by temperature summations below 10,000, F. 

 (5,500 C.) occupies, in general, the highest portion of the Cascade and 

 Sierra Nevada Mountains, the Rocky Mountains, northern Minnesota, 

 a little of northern Wisconsin, the northern half of Michigan, and the 

 northern half of Maine. The isoclimatic lines for 11,500 F. (6,400 C), 

 and 18,000 F. (10,000 C.) are seen to have a west-east trend, but are 

 more or less markedly displaced southward by the western and eastern 

 mountains and northward by the Pacific and Atlantic oceans. 



Our own work with remainder indices will be presented farther on. 



(3) Exponential Indices of Temperature Efficiency for Plant Growth, 



As has been stated in our earlier discussions, it appears that some 

 possibility of advance lies in studying climatic temperature conditions 

 with reference to the chemical principle of Van't Hoff and Arrhenius, 

 and a first attempt in this direction has been made by Livingston and 

 Livingston in the paper already cited. This principle states that 

 chemical reaction velocity usually about doubles (or somewhat more 

 than doubles) for each rise in temperature of 10° C, or of 18° F. It is 

 to be understood that the principle of Van't Hoff and Arrhenius is 

 applicable, even in purely chemical problems, only within certain 

 temperature limits, and it is sufficiently clear that the same general 

 sort of limitation must influence its applicability in physiology and 

 ecology. We are primarily interested here in growth processes and their 

 rates, and, obviously, there may occur natural temperatures either 

 above the maximum or below the minimum for growth, so that here 

 are unquestionable limits for the application of the principle just 

 stated. Furthermore, the principle itself supposes that the process 

 considered increases its velocity with each rise of temperature between 

 the limits of applicability, and we are well aware that increasing tem- 

 perature is not accompanied by increased growth-rate throughout 

 the range from the minimum to the maximum for growth in plants. 

 An optimum temperature can always be found above which the pre- 

 viously increasing growth-rate begins to decrease. Thus the applica- 

 bility of the Van't Hoff-Arrhenius principle to organic growth phe- 



