1913] LIVINGSTON—TEMPERATURE COEFFICIENTS 371 
corresponding ones of the other series, and simple inspection of the 
two charts seems to indicate that the former indices are rather 
uniformly about ten times as great as the latter. No ratio between 
these two indices really exists which is common to all our stations, 
but what we wish first to emphasize is that the two charts are 
outstandingly and even surprisingly alike in the general form of 
their isoclimatic lines. The stations for which data are available 
are so irrationally distributed over the country (being relatively 
closely crowded in the eastern part, with low climatic gradients, 
and widely separated in the west, with high gradients) that an 
average ratio, or any other statistical function of the ratio series, 
must be without meaning, but it is clear from the ratio chart (fig. 3) 
that ratios between 9.00 and 10.00 characterize almost the entire 
area of the United States. In other words, for the great majority 
of stations the magnitude of the ratio in question does not depart 
more than 5 per cent from the value 9.50. Considering that all 
our original data must be regarded as only roughly approximate, 
this appears to indicate a very good agreement between the results 
of the two methods. We may state, therefore, that for most of 
the area of the United States, the two methods here employed for 
estimating temperature effectiveness for plant growth give results 
which agree within the limits of a plus or minus variation no 
greater than 5 per cent. It will be noted that this statement 
practically involves the placing of the phenological method of 
direct summations upon a much more satisfactory basis than this 
method has heretofore possessed; it now appears that the direct 
summation method gives the same general form of chart as does 
the other method of temperature integration, and this empirical 
treatment really ascribes to the former method some degree of the 
theoretical foundation upon which the latter rests. 
The similarity between our two summation charts, however, is 
only approximate and superficial. If it held rigidly, either of the 
two charts would suffice for both, and any efficiency index might 
be deduced from the corresponding direct index, merely by dividing 
the latter by the proper constant. The efficiency indices are not 
uniformly ten times the summation indices, nor is there any ratio 
other than ten which may be assumed with the aim of attaining 
