Astronomical refraction has had a long and fascinating history. Cleomedes (100 A.D.) and Ptolemy (200 A.D.) were aware of its existence and understood in a qualitative way some of its properties. Alhazen (1100 A.D.) quite correctly suggested that the flattening of the sun's disk near the horizon was due to astronomical refraction. Tycho Brahe in 1587, however, was the first to make direct measurements of the magnitude of the refraction. The first theory of astronomical refraction based on Snell's law was that of Cassini, who in 1656 looked upon the earth's atmosphere as being of constant refractive index up to its upper limit at which all the refraction took place. Extensive investigations of the physical properties of the atmosphere modified these ideas and led to the “concentric spherical shell model” and the “plane parallel layer model,” the latter being an approximation for the former. Attempts to evaluate the “refraction integral” for the concentric spherical shell model have led to the theories of Bessel, Bradley, Gylden, Ivory, Laplace, Mayer, Simpson, Young, and others. At the beginning of the twentieth century, investigations on the physical properties of the atmosphere extended to higher elevations, and new physical properties appeared which were not anticipated by the earlier workers. This led to the celebrated work of Harzer, who for the first time was able to compute the astronomical refraction purely from meteorological measurements. Harzer also made the first detailed investigation of the applicability of the spherical shell model, which is used almost universally by workers in this field. Harzer's work has served as a source of inspiration, but much remains to be done. This paper attempts to give a brief chronological description of some of the more significant theories of astronomical refraction for the purpose of pointing out the types of problems which have existed, how these problems were attacked, and the problems which still remain. It also gives adequate references for those wishing additional information.
A. I. Mahan, "Astronomical Refraction-Some History and Theories," Appl. Opt. 1, 497-511 (1962)