abbot: solar constant of radiation 90 



grouped in the great bands made up of these fine Unes which 

 occur in the red and infra-red spectrum, and for them a special 

 procedure must be adopted, as was introduced by Langley. In 

 general, however, the bolometer suffices to give us atmospheric 

 transmission coefficients in sufficient number to deal with the 

 gradually changing transparency of the air for rays of nearly 

 adjacent wave-lengths. The proof of the formula for atmospheric 

 transm-ission for homogeneous rays follows. It will be seen that 

 the formula is one of extrapolation solely, and is not applicable 

 to computations of the transparency at different barometric 

 pressures, unless it be the fact (which is not usual) that the qual- 

 ity of the air from the different stations to the limit of the atmos- 

 phere is approximately identical. This indeed may be the case 

 at very high elevations of 4000 meters and over, but is not the 

 case for ordinary observing stations, so that in the use of the 

 formula of transmission it is generally erroneous to introduce 

 the barometric pressure in the exponent as was done by Pouillet. 



Proof of formula for transmission. Imagine the atmosphere to 

 be made up of ?i concentric layers so chosen in thickness as to pro- 

 duce separately equal barometric pressures, and let the number 

 n be so great that the transparency of any single layer is sensibly 

 uniform, although the layers may differ from each other in trans- 

 parency by any gradual progression. The index of refraction of 

 air is so near unity that there will be no sensible regular reflec- 

 tion in passing from one layer to the next, and the transmission 

 of each layer may be expressed exponentially by Bouguer 's for- 

 mula, but with different coefficients of transmission for the several 

 layers. 



Thus, suppose Eo to be the original intensity of a beam of 

 light incident upon the outermost layer at the angle whose se- 

 cant is m. 



Then after passing successive layers the remaining intensities 

 become 



E,=Eoar, E2 = Eoar-ao'"\ En^Eoa^ar- • • • • <"". (1) 



The value of the secant of the angle of incidence will change 

 slightly in passing from layer to layer from two causes: First, 



