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LV. On terrestrial refraction

1919; Taylor & Francis; Volume: 38; Issue: 227 Linguagem: Inglês

10.1080/14786441108635984

1941-5990

A.R. McLeod,

Radio Wave Propagation Studies

Summary IN the following report, which was communicated to the Advisory Committee for Aeronautics in December 1918, the refraction of light rays, of various lengths and zenith distances, by the atmosphere is dealt with, and the errors in the Chauvenet dip-range formula are considered. The ordinary assumption that all rays are arcs of the same circle is considered, and the observed variable radius is accounted for numerically. The law of density of the atmosphere, obtained by assuming any given ray to be an are of a circle, is shown to be much farther from the truth than an empirical law, which is used to find the refractions for various zenith distances, and heights up to 8 km. The curvature of the light ray is considered in detail, and the refraction correction for instruments on the ground is dealt with. The errors in the derivation of the Chauvenet range formula are considered numerically, and better formulæ are suggested for particular heights. Table I. compares the densities obtained by the use of the approximate empirical law with the observed density for heights up to 15 km. The corresponding curves are found in fig. 2. Table II. gives the total refractions of a ray of wave-length 5000 Å.U., for various zenith distances and heights up to 8 km. The simple Surveyor's Formula for refraction is deduced, and its errors considered in § 4. The curvature of the light rays is considered in § 5 and numerical values for various rays are given in Table IV. The dips corresponding to a number of rays are given in Table V. In § 6 the refraction correction for instruments is considered; and in § 7 the Chauvenet range formula is shown to be valid, except for rays which pass close to the horizon, with an accuracy of 1 in 400 for dips not exceeding 5° and with an accuracy of 1 in 100 for dips not exceeding 10° Curves showing the errors are appended in figs. 6 & 7. The effects of a change of density of 2 per cent. are considered in § 8 and shown to be small. The refraction corrections are of use in accurate observations of the altitudes of aeroplanes, balloons, shell-bursts, etc., from the ground; or in observing objects on the ground from the air. They should be of interest to the surveyor. Further, it seems to the writer that the method followed is the only sound one to be used in obtaining astronomical refractions, when our knowlege of the upper atmosphere is more complete.