LIMIT OF THE ATMOSPHERE — KERBER 45 



The ratio of the astronomical refraction to the apparent zenith 

 distance is - = 57.3" according to the current tables of refraction 



c 



for the average condition of the atmosphere, 3 so that we can write 

 •° =57.3" (1 + J) (2) 



c 



where 5 7.3 "J represents any possible error of observation that we 

 include in our computations in order to show the degree of accuracy 

 of the results. Hence we have 



F' - R -(l +J) 

 57.3" 



= about 22 918 400 kilometers for R = 6366 .7 kilometers. 



> (3) 



The first focal distance of the atmosphere follows from the relation 

 according to which the distance of the two focal points from the 

 respective nodal points is inversely proportional to the ratio of the 

 refractive indices of the respective media. 4 Hence we have 



n' R 

 F = n'F' = (1 + i) = about 22 924 900 ... (4) 



57.3" 



where we assume the coefficient of refraction for the average condi- 

 tion of the atmosphere (b = 0.752 meters, t = 9.3 Cent.) to be 

 n' = 1.000282 according to Ketteler's determination. 



All celestial bodies except the moon are farther removed from 

 us than the focal distance F. Hence the atmosphere produces 

 as a whole and at the focus inverted real images of these. The 

 convergent pencil of rays coming through the atmosphere enters the 

 eye so that it also unites the pencil into an inverted image within 

 the focus <p of the whole eye (or it falls short of the retina) and thus 

 there forms on the retina under all circumstances for a perfect far- 

 sighted eye a circle of diffuse light, no sharp image, and thus the 

 spread of the stellar image over the retina finds its physiological 

 explanation. 



On the other hand, the atmosphere produces a correct upright 

 virtual image of the moon because she is within the front focal dis- 



* Bruhns: Astronomische Strahlen-brechung, p. 19. 



* Mousson: 2d Edition, section 731; 3d Edition, section 809 (4). 



