VI 

 THE LIMIT OF THE ATMOSPHERE OF THE EARTH 



BY DR. A. KERBER 



(Dated Chemnitz, February, 1881) 



[Annalen der Physik und Chemie, New series XIV , whole series 250. Leipzig, 



1881, pp. 117-128] 



I. THE CARDINAL POINTS OF THE ATMOSPHERE 



For small zenith distances the atmosphere constitutes an optical 

 system of refracting media separated by centered spherical sur- 

 faces of small aperture, so that the theory of such optical systems 

 developed by Gauss and Mobius 1 can be applied to it. The impor- 

 tant matter is the determination of the "Cardinal points" by this 

 theory. It is well known that the cardinal points are : 



(1) The principal foci / and f in the first medium A and the last 

 medium A' (fig. 1). At either of these points are united the rays 

 that come through the opposite medium parallel to the optical axis 



(2) The nodal points k and k' having the property that every 

 ray (ab) passing through the first medium in such a direction as 

 would pass through k, when it reaches the second medium goes on- 

 ward in a direction c a' passing through k' parallel to its initial 

 direction ab. 



'Gauss: Dioptrische Untersuehungen, Goettingen, 1840. Compare also 

 Helmholtz, Physikalische Optik. Braunschweig, 1861. In the present arti- 

 cle I refer to the Physik of Mousson, which is widely used. 



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