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SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



(3) The principal points h and h' for which object and image are 

 identical. 



As in all complicated systems whose constitution is not known, 

 so here, the location of these cardinal points can only be found 

 experimentally 2 based on the astronomical determinations of the 

 refraction of light by the atmosphere. 



Let m in fig. 2 be the center of the earth, c the location of the 

 observer; cc' a small arc of a great circle of the earth; bb' the inter- 

 section of the circle with the boundary of the atmosphere; a a fixed 

 star; abc a pencil of rays from a toward c which is refracted at c 

 toward the direction cf so that the apparent zenith distance 

 £ determines the astronomical refraction p; am the axis of this 

 optical system whose first medium is the vacuum for which the 

 refractive index is n = 1, and whose last medium is the lowest 

 stratum of air whose refractive index is n', and which is assumed 

 to have no limit. 



The nodal points of the atmosphere coincide at the center of the 

 earth. For, because of the concentric boundaries of the refracting 

 media a pencil of light passes through the atmosphere in a curve 

 whose tangents are never parallel to each other, so that only one 

 ray, moving in the medium n' toward m, can proceed farther in the 

 same direction. 



The location of the second focal point f is easily found when we 

 consider the ray starting from a as originally parallel to the axis. 

 It is deflected from its initial direction by the amount of astronom- 

 ical refraction p and in the last medium finally proceeds toward 

 the second focus of the system or f . The corresponding focal dis- 

 tance F' is found from the triangle c. m. f ; in this triangle we have 

 c m = R, y = r and since in this case ab is parallel to af there- 

 fore a' = p hence 



F' = >-R. 

 P 



(1) 



Mousson: Physik, 2d Edition, section 731; 3d Edition, section 810. 



