424 



SCIENCE 



[N. S. Vol. XL. No. 1029 



sky, y is the radiant energy received at the 

 earth's surface, e is the " relative emissivity," 

 or rather, it is the ejfective emissivity from 

 the surface through the air, that is, the radi- 

 ant emission as affected by atmospheric ab- 

 sorption of rays of long wave-length, and 

 which is governed by the fourth-power Stefan 

 law, but it is distinguished from the convec- 

 tive loss, except in-so-far as these two overlap 

 according to the principle under discussion. 

 The coefficients a and b are numbers derived 

 from the observed transmission of instru- 

 mental radiation to the sky applied to the 

 meteorological data under clear, and cloudy, 

 nocturnal conditions, respectively. 



The equation rests upon the observed fact 

 that ATj : AT„ = 5:2, which holds good for 

 both tropical and temperate regions ; also upon 

 the fact that there is no difference between the 

 mean temperature of clear and cloudy days; 

 and the numerical coefficients are chosen on 

 the assumption that the average air transmis- 

 sion is the same for either day or night. This 

 I find to be justified so far as the radiation of 

 the measuring instrument to the sky is con- 

 cerned, but it does not hold, in general, for the 

 surface of the ground. Hence there arises a 

 discrepancy. For example, if we let T^the 

 mean day temperature, 292° Abs. C, and take 

 the average transmission of instrumental radi- 

 ation as 40 per cent, for clear sky, we have the 

 eft'ective transmission of a unit of energy with 

 a cloudy sky = 2/5 X 0.40 = 0.16, and the 

 average transmission for day sky, assuming 

 that there are as many clear days as cloudy, is 

 0.28. The mean transmission for an average 

 day and a clear night becomes 



a = K0.28 +, 0.40) =. 0.34 ; 



and the mean effective transmission for an 

 average day and a cloudy night is 



h =. *(0.28 +. 0.16) = 0.22. 



For mean temperate values, 

 T - ATi 292 - 10 



1 - .34 



292 



.9792, 



= (.9792)' = .9196, 

 e = .585. 

 But this is practically the effective transmis- 



sion of the earth's radiation, because the emis- 

 sivity of the earth is nearly that of a black 

 body. Nevertheless, e by the computation is 

 nearly 50 per cent, larger than the transmis- 

 sion of instrumental radiation with which we 

 started, so that, in round numbers, the equa- 

 tion as it stands raises the transmission from 

 .40 to .60, mean = .50, which is the value 

 adopted by Lowell. The explanation of the 

 discrepancy between the transmission obtained 

 from measures of sky radiation, and that 

 from nocturnal cooling, appears to lie in the 

 reconversion of a part of the heat abstracted 

 from the surface by convection currents, into 

 radiation which is added to the radiation 

 emitted as such from the ground ; but the large 

 part of the energy communicated to the air by 

 convection remains in the circulation of the 

 air so long that it does not affect the diurnal 

 changes on which the equation is based. 



A similar computation for the tropics gave 

 the result that e has only about one third of 

 the value derived from measures in the tem- 

 perate zone, while the discrepancy is very 

 much smaller and has the opposite sign. This 

 may mean that the excessive evaporation and 

 precipitation of the tropics bring thermal 

 losses and gains which still further complicate 

 the relations between radiation and convec- 

 tion. Evidently there may be some ambig- 

 uity about the term " terrestrial radiation," 

 unless we limit our definitions very carefully. 



As a check upon these measures I have used 

 my determination of the transmission of the 

 proper lunar radiation by the earth's atmos- 

 phere in which values as high as 48 per cent, 

 were obtained in winter. The transmission 

 of lunar radiation is relatively smaller than 

 that for terrestrial radiation from a land sur- 

 face by the same atmosphere, because, owing 

 to the higher temperature of the lunar sur- 

 face, its radiation invades regions of the spec- 

 trum where the atmospheric absorption is 

 especially large." Frank W. Very 



Westwood Astkophysical Observatoet, 

 December, 1913 



8 See r. W. Very, ' ' Sky Eadiation and the Iso- 

 thermal Layer, ' ' American Journal of Science, Vol. 

 XXXV., p. 379, April, 1913. 



