F. IF. Very — Transmission of Terrestrial Radiation. 519 



tions than the vertical, where special reduction to the zenith is 

 required ; but nevertheless, with a clear sky, my method of 

 observing the zenithal sky gives nearly the same observed 

 radiation as Angstrom's method, as has been shown already. 

 The differences appear only in the further treatment of the 

 observations by diverse and irreconcilable theories. The neces- 

 sity for my mode of treating the data arises from the fact that 

 the absorption of terrestrial radiation takes place in a layer of 

 air of small depth immediately above the surface. Thus we 

 may regard earth and " sky " as two widely extended parallel 

 surfaces in close proximity ; and if we assume them to be 

 " black bodies," we can compute their effective radiations by 

 Stefan's Law. Hence, on the supposition of a normal trans- 

 ference between the two, the zenithal observation of sky radia- 

 tion virtually integrates the natural process and gives the rate 

 at which heat is lost, rendering unnecessary any complicated 

 summarization by zones. Nor can a small thermometer bulb, 

 for whose radiation a zonal summation would be appropriate, 

 represent the radiation of an extended surface. But each ele- 

 ment of horizontal surface may be considered as in radiant 

 exchange with the vertical air column of equal section situated 

 directly over it. 



The hemispherical summation of sunlight diffused by the 

 sky upon a given point and the radiation from an instrument 

 of limited area to the sky follow different laws. For if we con- 

 sider the case of a zenithal sun, it is evident that, within a 

 given solid angle, the reflected skylight comes from greater 

 depths of air according as the direction approaches the horizon, 

 and the light therefore increases in intensity at the low alti- 

 tudes ; but the earth's radiation to the sky, as represented by a 

 circumscribed measuring instrument, is more absorbed in direc- 

 tions near the horizon than at the zenith, and therefore earth 

 radiation (as thus measured) proceeding outward diminishes 

 just where the incoming solar radiation, diffused by the sky, 

 increases. Thus in the summation for the hemisphere, skylight 

 from the hemisphere bears a larger ratio to skylight for a 

 given solid angle of high altitude, than terrestrial radiation to 

 the hemisphere bears to the same solid angle at the zenith. 

 This is the reason why Angstrom, who measures the radiation 

 to a hemisphere, always gets a positive value for radiation 

 received from the sun-illumined sky in the daytime, but a nega- 

 tive value for the night sky, while I find the zenithal value 

 always negative, whether by daj T or by night. The apparent 

 discrepancy is just what we ought to expect. I have not access 

 to the observations of Homen, who also found negative sky 

 radiation both by o day and by night, but if his method at all 

 resembles mine, Angstrom's conclusion "that the observations 



