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XXII. On the Calculation of the Distance of a Shooting Star 

 eclipsed in the Earth* s Shadow, By Archibald Smith, 

 Esq., of Lincoln* s- Inn, Barrister-at-Law, late Fellow of 

 Tritiitij College, Cambridge*. 



1, TN a paper in the Philosophical Magazine for February 

 J. 1848, Sir John Lubbock has suggested that shooting 

 stars may be small planetary bodies which shine by reflected 

 light, and that their sudden disappearance may be occasioned 

 by their immersion in the earth's shadow ; and he has given 

 a formula for calculating, on this hypothesis, the distance of 

 a shooting star, at the moment of its disappearance, from a 

 spectator on the earth's surface. The formula, however, as it 

 is given in the paper in question, even when simplified by 

 supposing the earth's shadow to be cylindrical instead of coni- 

 cal, is not well adapted for numerical calculation, and may 

 repel some who would be inclined to pursue the investigation 

 if the necessary calculations were less laborious. 



The data assumed by Sir J. Lubbock are the zenith di- 

 stances, and the difference of the azimuths of the sun and of 

 the star at the moment of its disappearance. In repeating his 

 calculations, I find that by introducing the angular distance 

 between the shooting star and the sun, or rather the point 

 opposite the sun, the formula is very much simplified, and 

 thus the time requisite for calculating a distance does not ex- 

 ceed a very few minutes. As this is a point of some import- 

 ance in furnishing a test for the theory, this communication may 

 not be considered inappropriate to the Philosophical Magazine. 

 2. Let the centre of the earth be the origin of co-ordinates. 

 Let the axis of Z be directed to the zenith, of ^ to the north, 

 and of j/ to the east. 



Let x,y,x be the rectangular co-ordinates of the shooting 

 star at the moment when it enters the earth's 

 shadow, 

 p its distance from the spectator. 

 5, « its zenith distance and azimuth. 

 a,h,c the co-ordinates of the vertex of earth's shadow. 



S the length of the shadow = V'a^ + 6^ -f- c^. 

 Z, A the zenith distance and azimuth of the point in the 

 heavens which is diametrically opposite to the 

 sun. 

 ^ the angular distance of the shooting star from the 



point opposite the sun. 

 R semidiameter of the earth. 



* Communicated by the Author. 

 N2 



