﻿M. H. Wild on the Absorption of Light by the Air. 295 



the sun or diffused light should appear equally bright to the eye 

 of the observer at all distances ; if, therefore, the more distant 

 one is less bright, this arises from an enfeeblement of the light 

 in passing through a layer of air twelve times as thick. The 

 more strongly the air absorbs, the more will the ratio of the 

 distances differ from the true theoretical one of 1 : 12. 



Beer was the first to give a theory of the diaphanometer based 

 on the principles of photometry*. He assumes that the pheno- 

 menon would not be materially altered if the disks consisted of 

 white circles on a black ground, and that in this case the two 

 different-sized white spots would send an equal amount of light 

 to the eye at the moment of their disappearance. In fact, 

 according to this view also, the disk twelve times as large would, 

 at twelve times the distance, send to the observer's eye the 

 same amount of light as the smaller one, and disappear simulta- 

 neously with this, only if the air were quite transparent. If 

 it is not so, the light which is lost by absorption in the thicker 

 layer of air must be compensated by a greater apparent diameter 

 of the disk. On this assumption the coefficient of transparency f 

 a of the air (that is, the fraction of the incident light which tra- 

 verses a layer of air of the unit thickness) may, according to Beer, 

 be calculated from observations with the diaphanometer by the 

 formula 





in which d and D are the diameters of the two disks, e and E 

 the distances at which their spots just disappear. 



By this formula Beer has calculated the coefficient of transpa- 

 rency of the air at two different heights, from observations made 

 on the Tyrolese Alps by H. Schlagintweit with a Saussure's 

 diaphanometer J. He finds that, referred to a unit of length of 

 1000 Paris feet, at 



2300 feet above the sea . . . a — 0*9029 

 12000 „ „ ... a = 0-9985 



The development of the above formula of Beer necessitates two 

 suppositions which call for a more minute discussion. It is as- 



* Grundriss des photometrischen Calculs, by A. Beer: Brunswick, 1854, 

 pp. 91-93. 



t Both here and afterwards I designate as the coefficient of transparency 

 what is usually called coefficient of absorption. The first designation ap- 

 pears more convenient and more in accordance with general usage, because 

 for greater values of this coefficient the transparency and not the absorption 

 increases. 



298. 



