420 



SCIENCE 



[N. S. Vol. XL. No. 102& 



-|- 15° C, or 288° Abs., or if the temperature 

 regions alone are considered, a temperature 

 of +10° C. = 283° Abs. is thought to be 

 better ; and this is done by accepting the mean 

 air temperatures observed by meteorologists as 

 if they were those of the soil. Ordinarily, 

 this does no harm for places where the sun 

 shines at a low angle, or where the wind is 

 strong enough to make air and surface tem- 

 peratures coincide. But when the sun shines 

 at a high angle above the horizon, or in desert 

 regions with light airs, the astrophysicist must 

 know the temperature of the actual radiating 

 surface which becomes far hotter than the air 

 temperature. Even in regions by no means 

 of a desert character, surface layers of fairly 

 dry soil in summer and in the middle of the 

 day may be 20° or 30° C. hotter than the 

 shade temperature of the air as commonly 

 observed; and surfaces of rock in sunshine and 

 on calm days are still hotter. Even plant sur- 

 faces in sunshine, though much cooled by evap- 

 oration, are appreciably warmer than the air. 

 Taking the currently adopted thermal equiva- 



gram cal. 

 lent of radiation, a == 7.9 X 10-" ^^ ^ ^^^f ^ 



black body at 288° Abs. 0. radiates 0.544, and 

 one at 298° radiates 0.623 gram, cal./sq. cm. 

 min. Hence an arid region whose surface is 

 on the average 20° C. hotter than the assigned 

 air temperature during the sunlight hours, 

 will radiate 14.5 per cent, more than the 

 ordinary supposition indicates. On the other 

 hand, most surface material radiates less than 

 a black body (for example, a silicate, such as 

 glass, radiates 93 per cent, as well as lamp 

 black which, in turn, radiates a little less than 

 a truly black body) ; and since minute accu- 

 racy is not attainable, the supposition that the 

 earth agrees with an ideal black radiator may 

 answer as a first approximation. 



In summer, the radiation from a black sur- 

 face at •+ 25° 0. to the sky overhead, if the 

 latter be of a deep blue, may be as if to an 

 efficient radiator of the same quality at a tem- 

 perature of 0° C. 



In winter, under similar circumstances the 

 black surface at — 10° C. may radiate to a 

 zenithal sky as if to a screen at — 50° C, or 

 — 60° C. 



A mean of three days of good blue sky in 



winter and of three more in summer follows t 



Winter surface temperature ... =:263°.9 Abs. C. 



Summer surface temperature ... ^291°.3 Abs. C 



Effective temperature of zenithal sky, 



Winter =;212°.2 Abs. G. 



Summer = 269°.9 Abs. 0. 



By Stefan's law: 



Winter Summer 

 Terrestrial radiation (unabsorbed). .3819 .5685- 

 Eadiation from observed zenithal sky. .1601 .4196' 

 Difieerence. .2218 .1489 

 Transmission (winter) Tw = .2218/.3819 ^.5805 

 Transmission (summer) Ta = .1489/.5685 = .2619 

 Transmission (mean of summer and winter) = .4213 



We may say that a round 40 per cent, is 

 near enough for an approximate estimate o£ 

 the average transmission of terrestrial radia- 

 tion from land surfaces in mid latitudes. 



In a note in the Astrophysical Journal for 

 September, 1913 (p. 198), Mr. Anders Ang- 

 strom gives 0.15 gram cal./cm.^ min. as an 

 average value of the earth's radiation. This 

 agrees very well with the values which I have 

 obtained in summer, but is smaller than the 

 best winter measures, and to such an extent 

 that one would not suppose that Hr. Ang- 

 strom had ever observed under conditions 

 most favorable to large transmission. He also 

 declares his "belief that the transmission for 

 clear sky seldom is greater than 25 per cent, 

 and seldom is less than about 5 per cent." ' 

 The stipulation that the sky must be " clear " 

 rules out those imperfect skies affected by a 

 thin cirro stratus veil, which, as will be evi- 

 dent from my article in the American Journal 

 of Science, April, 1913, are included within 

 these limits. My observations, which have 

 been made repeatedly, give a fundamentally 

 different result for the best winter skies. 



In desert regions, or for hottest, midday 

 and dry summer conditions, it may sometimes 

 be necessary to increase the estimated sur- 

 face temperatures considerably, as has been 

 shown above; but this does not apply to more 

 than a small part of the earth's surface, and 

 the principal differences between air and soil 

 temperatures, where the soil is considerably 

 hotter than the air, occur during only a part of 



3 Op. cit, p. 200. 



