
366 BOTANICAL GAZETTE [NOVEMBER 
ture efficiency (w) for any Fahrenheit temperature (é) is the eight- 
eenth root of 2 effected with an exponent equal to the given 
temperature minus 40. From this the values of u may be directly 
calculated. Only one cycle of eighteen quantities, however, needs 
to be so determined in any case, for the coefficients of the second 
cycle are double the corresponding ones of the first, etc. ; 
The following table presents the approximate values, derived 
as above, for the efficiencies corresponding, respectively, to the 
temperatures (in whole degrees) from 40° to 99° F 
APPROXIMATE EFFICIENCY INDICES FOR TEMPERATURES, IN WHOLE DEGREES, FROM 
40° TO 99° F., ASSUMING THE EFFICIENCY TO BE UNITY AT 40° AND TO 
DOUBLE WITH EACH RISE IN TEMPERATURE OF 18 DEGREES 







jenn Efficiency (u) Fist rg Efficiency (1) Ponta ge Efficiency (#) 
Bes Os, 1.0000 Since ba 2.1603 6: eS 4.6662 
rane Lye 1.0393 | ON cea 2.2451 Mote 4.8490 
Ae 1.0802 O20 ake a. 244% Le Sen aa 5.0396 
fhe aep gar Aba 1.1226 Os. fern 2.4245 Baier. 5.2384 
44. 1.1666 Osis wees as 2.5198 Bailes oa 5.4424 
He ae t. 2123 2, Fe RIG 2.6192 eRe 5.6568 
PR ge baad I. 2599 ee aes 2.7212 86.5 eo 5 8782 
Oi. is I. 3096 Pee 2.8284 seat he 6. 1090 
Be. 1. 3606 08 2.9391 bt alae aia 6.3496 
Mo 1.4142 Oe ates 3-0545 ere 6.5972 
sic 2 Bet SB peas 1.4696 ve Ae aR Ces 3.1748 Ossi 6.8566 
Beare pak 1.5273 Evert oud, 3.2986 QP keh 7.1258 
ck i ag 1.5874 Fe, pena 3.4283 pe eierae ei 7.4048 
Soi vee Ges 993 Y.. 3.5629 63.0 ee 7.6960 
Shes wee une 1.7142 Pe ee 3.7024 ci Pereae epee 8.0000 
Se iaccie,s 1.7815 Mi Ais. 3.8480 pe er ee ee: 8.3144 
Sia EA ene 1.8512 a ee Fe re hed ge 2 8.6412 
oo... 1.9240 Ved teers 4.1572 ET 8.9804 
58.. - 1 5 ea R SS 4.3206 Dy. Darlene aA 9.3324 
bc Grae yer: 2.0786 Or ask 4.4902 OD crise enh 9 








Efficiency indices and direct indices for the mean frostless season 
in the United States 
All of the climatological calculations involved in this study 
have been carried out, and at least once repeated, on a apace 
machine.” The stations employed (179 in number) are those 0 
_ 7 The authors wish here to acknowledge with thanks that they have had - ; 
assistance, at various points in this work, of Mrs. Eprra B. Sareve, Mr. H. E. ee 
and Mr. J. W. Suive. It is also a pleasure to state that the study was made poss! 
by the Department of Botanical Research of the Carnegie Institution. 

