1913] LIVINGSTON—T EM PERATURE COEFFICIENTS 367 
BIGELOw’s paper already cited, with a few omissions on account of 
the lack of corresponding frost data. Each series of summation 
indices was placed upon’a large map of the United States, and the 
map was then divided into areas by isoclimatic lines, in the usual 
way. Thus were obtained two charts, one showing the geographic 
range of the efficiency indices and the other the corresponding 
range of the direct ones. 
It was at once observed that the relations of the different areas 
to one another are surprisingly similar in the two charts, so that one 
chart appears about as valuable for bringing out the temperature 
characteristics of phytogeographic areas as does the other. A 
detailed study of the two charts, however, made it clear that they 
differ, as regards the relative form and relative numerical charac- 
teristics of their respective zones, in many particulars. The two 
charts are here presented as figs. 1 and 2. The numerical efficiency 
data ‘from which these charts were derived (with the aid, at certain 
points, of probabilities based upon topographic contour lines repre- 
sented on the original maps*) are each placed near the position 
of the corresponding station, the latter represented by a small circle 
(for the names of the stations employed, see BIGELow, Joc. cit.). 
To compare the two series of indices, the ratio of each direct index 
to the corresponding efficiency index was obtained, thus giving a 
ratio for each station. These ratios have been placed upon a map 
in a manner quite similar to that used in charting the indices 
themselves, and the resulting chart, with its isoclimatic lines, is 
presented as fig. 3. 
The interpretation of our charts as regards plant distribution 
will not be taken up here. They are to be studied, of course, in 
connection with Day’s chart of the average length of the frostless 
Season, with the charts given by B. E. Livincston, and with any 
vegetation map of the United States which it is desired to interpret 
along these lines. 
As has been mentioned, the charts of figs. 1 and 2 show a 
marked similarity in the form and position of the isoclimatic lines 
which are represented. Of course it is at once to be observed that 
the direct summation indices are uniformly much larger than the 
* U.S. Geol. Survey contour map of the United States, 18X28 in. 
