CLIMATIC CONDITIONS OF THE UNITED STATES. 209 



This method of derivation assumes that the rate of plant growth varies 

 proportionally to the environmental temperature. Any thermometer 

 scale may be used and a set of efficiency indices thus obtained may be 

 transferred from one scale to another by arithmetical treatment. The 

 assumption here is exemplified as follows. If a plant grows 2 units per 

 time period at 2° C. it should grow 10 units per time period at 10° C, 

 25 units at 25° C, etc. While direct indices of temperature efficiency 

 (on the absolute thermometer scale) are of great value in studying 

 simple physical processes, such as the expansion of gases, they do not 

 promise much in connection with the study of physiological processes, 

 and need not be seriously considered in our practical applications. 



(2) Remainder Indices of Temperature Efficiency for Plant Growth. 



The derivation of what we shall here term remainder indices of tem- 

 perature efficiency is but little more complicated than that of direct 

 indices. A constant difference between the temperature indices and the 

 corresponding efficiency indices is assumed (or derived from experi- 

 ment), and this difference is subtracted from every temperature index, 

 thus giving the required efficiency indices. It will be seen that this 

 method virtually does nothing but alter the position of the zero of the 

 thermometer scale, after which alteration it employs direct efficiency 

 indices as these have been defined above. Thus, the rate of plant 

 growth at 40° F. may be considered as unity and it may be assumed 

 that this rate becomes 2 at 41°, 10 at 49°, 50 at 89°, etc., the constant 

 difference above mentioned being here 39. In the phenological studies 

 tha,t have employed this sort of efficiency indices it has been assumed 

 that if the plant does not attain the particular growth-rate that is 

 taken as unity, it does not grow at all; that is, with a temperature of 

 39.5°, for example, no growth is supposed to occur, when unit rate of 

 growth would be obtained with a temperature of 40°. It is clear that 

 the method of direct indices of efficiency is a special case of that of 

 remainder indices, the constant difference being reduced to zero in the 

 case of direct derivation. 



The integration of temperature data by these remainder indices has 

 received the attention of workers in phenology for many years and a 

 large amount of literature bears upon this subject. For a review and 

 citations of the earher phenological studies, the reader is referred to 

 Abbe's Relations between Climates and Crops, already mentioned. 

 Because of their close relation to our special field of study, Merriam's 

 researches upon the zonation of temperature conditions in the United 

 States must be considered here. The conclusions arrived at by this 

 author have been largely adopted by plant and animal geographers 

 in this country, and Merriam's zonal terminology has come into very 

 general use, despite the exceedingly tentative nature of the data on 

 which this is based. 



