82 Sir J. W. Lubbock 07i Shooting Stars. 



ceases to be visible by its passing into the earth's shadow, or, 

 in other words, is eclipsed. 



Upon the two former suppositions, the fact of the star's 

 disappearance conveys to us no knowledge of its position or 

 of its distance from the earth; and all that can be said is, that 

 if it be a satellite of the earth, the great rapidity of its motion 

 involves the necessity of its being at no great distance from 

 the earth's surface. — much nearer than the moon ; while the 

 resistance it would encounter in traversing the air would be 

 so great, that it is probably without the limits of our atmo- 

 sphere. 



But although the two first suppositions leave us without 

 instruction as to the orbit or position in space of the body in 

 motion, the case is far different on the third hypothesis; for 

 knowing the time when and the place in the heavens where 

 the star disappeared, the elements of the geometry of thiee 

 dimensions furnish the means of determining the exact di- 

 stance of the body from the place of the spectator or from the 

 centre of the earth. Nor is this observation difficult; for if 

 seen on a starlight night, by attending to the configuration of 

 the neighbouring stars, a close approximation may be found 

 to the place of disappearance, which, in the event of such 

 bodies existing, will be most valuable in the interval which 

 must probably elapse before any orbits will have been deter- 

 mined with sufficient precision to enable us to anticipate their 

 arrival, and to make preparations for obtaining more accurate 

 data. 



I propose to consider the third hypothesis. 



Let W = sun's semidiameter, 



D = the distance of the sun's centre from that of the 



earth. 

 It = earth's semidiameter, 

 a = azimuth of the moving body at the instant of 



disappearance, 

 ^ = zenith distance of the moving body, 

 p = the distance of the moving body from spectator. 



X, 1/, z the rectangular coordinates of the moving body, and 

 also at the instant of disappearance, of a point on the surface 

 of shadow. 



6 = depression of sun's centre, so that 90°-|-fi= sun's ze- 

 nith distance, the sun being supposed to have set, the equation 

 to the cone limiting the shadow of the earth is 



{-a-cose + (z + .R)sinfl} J ~ \ 

 ;=R-i {xs\nQ + {z + R) cos ^'^+i/\K - (!•) 



