Smithsonian miscellaneous collections . F — F and thence by substituting from equations (3) and (4) in — 1) Rmh = mh = !_ (1 - A) = about 6463 kilometers . (5) 57 .3 Therefore the two principal points, like the nodal points, coincidein one point h, that is 6463 km. distant from the center of the earthor = 6463 — above the surface of the earth at c ( or fig. 3). Therefore according to the definition of the principalpoints the object and the image coincide at the point h, that is to 6 We determine D experimentally by measuring the distance at which anintense flame is sharply see
Smithsonian miscellaneous collections . F — F and thence by substituting from equations (3) and (4) in — 1) Rmh = mh = !_ (1 - A) = about 6463 kilometers . (5) 57 .3 Therefore the two principal points, like the nodal points, coincidein one point h, that is 6463 km. distant from the center of the earthor = 6463 — above the surface of the earth at c ( or fig. 3). Therefore according to the definition of the principalpoints the object and the image coincide at the point h, that is to 6 We determine D experimentally by measuring the distance at which anintense flame is sharply seen. 8 Mousson: 2d Edition, section 731 (2); 3d Edition, section 809 (2). LIMIT OF THE ATMOSPHERE KERBER 47 say, all rays that in vacuo are directed towards h, diverge after theirpassage through the atmosphere from this same point h. If, forinstance we imagine a planetary nebula between any iixed starand the earth and the star-like image of the nebula located at thepoint h (see fig. 3), ymich is now to be considered as the luminous. fig. 3. object seen through our atmosphere, then will the rays ab converg-ing toward h be so refracted by the atmosphere, that on theirentrance into the last medium 11 they will appear to diverge fromh in the direction cd, and hence an identical virtual image should beseen at that same point (h) at which a real star-like image musthave existed if there had been no atmosphere. 11. FIRST APPROXIMATION TO THE HEIGHT OF THE ATMOSPHERE By reason of the nature of the curve of the beam of light abed,which has its concave side toward the center of the earth, it is evi-dent that the principal point must lie within the if e, fig. 3, were the principal point, then a pencil of rays that invacuum may have the direction ef must necessarily on its entranceinto the medium n go on farther in the direction egk, if an identicalimage of the object is to be formed at e; but this is impossible be-cause ef and gk cannot be tangents to the same curve at
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