530 F. H. Bigelow — Thermodynamics of the 



primary physical question becomes the natural rate of radiation 

 of heat at certain low temperature wave lengths. In any event 

 the marked change in the loss of heat, from —140 to —362 per 

 1000 meters below and within the isothermal layer, is involved 

 in the physical conditions of the phenomena. Before crossing 

 the boundary of the isothermal layer there is an increase in the 

 heat supply, as at the values marked with a cross and omitted 

 from the summation, as if there was a congestion or accumu- 

 lation of heat, in the cirrus cloud region, before changing from 

 the slow rate of loss —140 to the rapid loss —362. It is appar- 

 ent that further studies of these data are likely to lead to a differ- 

 ential equation of radiation, which differs from the theoretical 

 equations that have been hypothetically proposed by several 

 authors. 



The Entropy (S^—SJ increases with the height, but more 

 rapidly on entering the isothermal layer; it increases generally 

 from the equator towards the poles, except in the high pressure 

 belt, from 3000 to 8000 meters elevation. 



The work expended ( W 1 — WJ diminishes with the height, 

 and more rapidly towards the temperate zone except in the 

 same region of the high pressure belt. 



The inner energy (U,— U ) is substantially a constant, about 

 7200 per 1000 meters, except in the strata near the surface 

 where it is smaller 7000, and in the isothermal layer where it 

 is larger and increasing to 8000 or more. 



The radiation energy K,„ = — is of course similarly 



distributed and ranges from 94,000 near the surface to 13,000 

 at the 18,000 meter level. The loss of radiant energy is accom- 

 plished by means of the complex thermodynamic processes just 

 described, and it is quite unavailing to discuss this problem by 

 means of generalized simple equations that take no account of 

 the mechanical and thermal requirements of the atmosphere. 



rm /> t ■ a 1°£ K" — log K n . . 



J he exponent of radiation A = , "„ J . ' is about 



1 J log A - log T 



4 - 00 in value, and the atmosphere conforms to the radiation of 

 a black body. In the lower levels this exponent is larger, prob- 

 ably due to the heat contents of the condensing aqueous vapor. 

 This can be separated from the dry air as follows : 



A 4'00 + (A - 4-00) 400 A-4-00 



dry air vapor 



Thus if A = 5-50, 



4-00 1-50 



*-(*)•*.(*)■ 



dry air vapor 



