504 Mr. J. J. YTatcrston on Solar Radiation, 



Let w Q} m x be the secants at which the radiation is r 0i r u we 

 have, according to the projection -~ — =-' = k } a constant quan- 



tity so long as the physical condition of the atmosphere remains 

 constant ; and to find R, the extra atmospheric value of r, we 

 have 



11 11 



Hence tw = ^ and ^ = t-. Since R is constant^ we may 



k k 



put ^ =e, so that r= ■ . This expresses the presumed law 



of absorption or interception. 



The essential nature of this law is seen by studying the pro- 

 portionate differential of r, 



~ kSm , — Br Bm ~ r , — Br Q 



— e>r= 7 rg and = =bm T : hence -^ — 00H. 



{m-\-ey r m-fe k bin 



Thus the sun's rays, in passing through a constant element 

 of the thickness of the atmospheric medium, loses a proportionate 

 amount of its power that is not constant, but that diminishes in 

 the simple ratio of that power. 



As an example, suppose with ?- = 30°, the value diminishes 1° 

 in passing through 1 mile; it would only lose J° in passing 

 through the same mile if r = 15°, and -g-J-o-tli of a degree if r= 1°. 

 We might thus expect, when the atmosphere is clear, it does not 

 intercept any sensible proportion of the heat radiated from the 

 earth's surface into space. 



§11. Compare the value of r with one sun and with two; 

 the supply from each, supposed equal, doubles the value of r, 

 which, measured at the extremities of the mile nearest and 

 furthest from them, shows that for the same element of the 

 thickness of the medium the proportionate decrement of r is 

 constant. Let a. represent the angular space occupied by the 

 sun's disk, and t the potential temperature of its radiating sur- 

 face, then toi represents the supply of heat by radiation from it 

 upon a unit surface, and is measured by r; so that if at becomes 

 2at, r becomes 2r. Now the factor 2 may have reference to a, 

 the magnitude of the sun's disk; 'or it may have reference to t, 

 its temperature. The fluctuating value of r from change of 

 altitude or climate represents a fluctuating potential value of at; 

 but a being constant, the change is similar to what would take 

 place above the atmosphere by a change in / alone. At different 

 parts of the earth's orbit the value of a changes ; so that with 



