of the Atmospheric Ahsorption. 291 



tion (i. e. four fifths of the remainder) would be transmitted 

 there also, and that the light would be the same kind of light 

 as before, and only diminished in amount (in the proportion 

 -| x |). The assumption originally made by Bouguer* and 

 followed by Herschel and Pouillet, was, lhat it was in this 

 manner that the solar heat was absorbed by our atmosphere, 

 and that by assuming such a simple progression the original 

 heat could be calculated. (The minute expenditure of energy 

 in the actual warming of the air is of course to be included.) 



Let us (to repeat Bouguer's reasoning) divide in imagina- 

 tion any homogeneous absorbing medium into successive 

 strata of identical thickness and chemical constitution. 



Let A be a source of radiant heat or light whose intensity 

 is reduced by passage through the first stratum to (let us 

 suppose) a fraction of the original represented by p, so that 

 what was A becomes Ap. Then, since the second stratum 

 is identical with the first in constitution and amount, and 

 must (it is assumed) have an identical effect, it will, on 

 Bouguer's hypothesis, transmit p of what enters it, and Ap 2 

 will emerge from the second, and so on, the fraction p trans- 

 mitted by the unit of thickness (the " coefficient of transmis- 

 sion ") being evidently the common ratio of a geometrical 

 progression, so that if the original heat be A, the amount of 

 heat after passing through e strata will be Ap e , and the amount 

 transmitted at any point will be proportional to the ordinate 

 of a logarithmic curve. 



To apply this to the estimate of the heat outside the atmo- 

 sphere (i. e. before absorption), let iSJ be a small portion of 



the earth's surface, and EK the upper surface of the atmo- 

 sphere, which is here supposed to be of uniform density and 

 constitution. (The effects of the actually unequal density of 

 successive strata can, it is assumed, be calculated and allowed 

 for.) Let S be the observer's station, then ES would be the 

 direction of a ray where the sun is in the zenith ; and, to fix 

 our ideas, letFS = 2ES, GS = 3 ES, KS = 4ES, &c. The 



* Bouguer, ' TraiU de la lumtire,' Paris, 1760. 



