in the Air upon the Temperature of the Ground. 255 



Stefan's law of radiation, which is now generally accepted, 

 holds good, or in other words that the quantity of heat (W) 

 that radiates from a body of the albedo (1 — v) and tempera- 

 ture T (absolute) to another body of the absorption-coefficient 

 /3 and absolute temperature 6 is 



where y is the so-called radiation constant (1*21 . 10~ 12 per 

 sec. and cm. 2 ) . Empty space may be regarded as having the 

 absolute temperature 0*. 



Provisionally we regard the air as a uniform envelope of 

 the temperature 6 and the absorption-coefficient a for solar 

 heat; so that if A calories arrive from the sun in a column of 

 1 cm. 2 cross-section, ak. are absorbed by the atmosphere and 

 (1— a) A reach the earth's surface. In the A calories there 

 is, therefore, not included that part of the sun's heat which 

 by means of selective reflexion in the atmosphere is thrown 

 out towards space. Further, let f3 designate the absorption- 

 coefficient of the air for the heat that radiates from the earth's 

 surface ; /3 is also the emission-coefficient of the air for radia- 

 tion of low temperature — strictly 15° ; but as the spectral 

 distribution of the heat varies rather slowly with the tempe- 

 rature, /3 may be looked on as the emission-coefficient also at 

 the temperature of the air. Let the albedo of the earth's 

 crust be designated by (1— v), and the quantities of heat that 

 are conveyed to the air and to the earth's surface at the point 

 considered be M and !N" respectively. As unit of time we 

 may take any period : the best choice in the following calcu- 

 lation is perhaps to take three months for this purpose. As 

 unit of surface we may take 1 cm. 2 , and for the heat in the 

 air that contained in a column of 1 cm. 2 cross-section and 

 the height of the atmosphere. The heat that is reflected 

 from the ground is not appreciably absorbed by the air 

 (see p. 252), for it has previously traversed great quantities 

 of water- vapour and carbonic acid, but a part of it may be 

 returned to the ground by means of diffuse reflexion. Let 

 this part not be included in the albedo (1 — v) . 7, A, v, M, N, 

 and a are to be considered as constants, /3 as the independent, 

 and and T as the dependent variables. 



Then we find for the column of air 



0y0*=#yv(T*-0*) + *A + M. ... (1) 

 The first member of this equation represents the heat 



* Langley, 'Prof. Papers,' No. 15, p. 122. " The Temperature of the 

 Moon," p. 206. 



T2 



