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LV. On Terrestrial Refraction. By A. R. McLeod, M.A.+ 

 1851 Exhibition Science Research Scholar of the Universil// 

 of Toronto, and Wollaston Scholar of Gonville and Cains 

 College, Cambridge *. 



Summary. 



[N 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 arc 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 Ch;iuvenet range formula are considered numerically, 

 and better formula? are suggested for particular heights. 



Table I. compares the densities obtained by the use of the 

 jipproximate empirical law with the observed density for 

 heights up to 15 km. The corresponding curves are found 

 in fig. 2. Table IL gives the total refractions of a ray of 

 wave-length 5000 A.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 

 \ alues 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 

 accur cy 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 obser- 

 vations of the altitudes of aeroplanes, balloons, shell-bursts, 

 etc., from the ground ; or in observing objects on the ground 



* Communicated by the Author. 



