104 
PHYSICS: C. G. ABBOT 
TERRESTRIAL TEMPERATURE AND ATMOSPHERIC 
ABSORPTION 
By C. G. Abbot 
ASTROPHYSICAL OBSERVATORY, SMITHSONIAN INSTITUTION 
Read before the Academy, November 21, 1917 
The earth's temperature depends mainly on the balance of incoming solar 
energy and outgoing terrestrial energy of radiation. These two classes of 
rays lie chiefly in two far-separated regions of spectrum. Of solar rays, 98% 
lie between 0.3 and 3.0 microns (jjl) of wave-length. Of terrestrial rays 
about the same proportion lie between 5 and 50 microns. According to Abbot 
and Fowle's researches, about 40% of the solar rays directed towards the 
earth are reflected to space. The earth must radiate to space 1.93 X 0.60 
X 0.25, or 0.29 calorie per cm 2 per minute on the average from its whole sur- 
face to keep a steady temperature in balance with the solar rays received over 
the area of its cross section. If the earth's surface was a perfect radiator and 
its radiation passed unhindered to space, it would emit according to Stefan's 
law 8 X 10~ n X (287), 4 = 0.55 cal. per cm 2 per minute. How shall we 
explain the discrepancy between 0.29 and 0.55 calories? 
1. Is the earth's surface a perfect radiator? Its surface is about three- 
fourths water. Of the remainder much is moist soil or moist vegetation. The 
radiative power of the earth must therefore be near that of water. My col- 
league, Mr. Aldrich, has lately studied the absorbing and reflecting powers 
of water for long-wave rays. He finds that of the rays emitted by lamp-black 
paint at 100°C. a layer of water 1 cm. thick transmits none and reflects as 
follows: 
Incidence 0° 30° 55° 63° 70° 72° 
Reflection 2% 3% 1% 10% 17% 22% 
As the absorption is 1— (Refl. + Trans.) he computes that of rays reaching 
a water surface from a hollow hemispherical enclosing lamp-black-painted 
surface at 100°, the absorption would be 90%. Experiments on lamp-black 
paint having shown nothing strongly selective about its radiation in this 
region of spectrum, we seem justified in concluding, in accord with Kirchoff's 
law, that water is a 90% perfect radiator in this region of spectrum. As is 
water, so is the earth's surface. Hence we conclude that the earth's surface 
sends out 0.50 calorie per cm 2 per minute on the average. 
2. How much of this does the atmosphere transmit? My colleague Mr. 
Fowle has recently published 1 results of a long investigation of this subject 
in which he studied the spectrum up to a wave-length of 17^t by aid of a spec- 
tro-bolometer with rock salt prism. He employed a very long tube in which 
the beam traversed paths of air up to 250 meters in length containing quanti- 
