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



having the same azimuth as the sun, p is given by a simple 

 equation 



Ji(l-cosg) 



'~ sin ^cosa sin 9 + cos ^cosS' 

 If i? + c be the distance of the moving body from the 

 earth's centre, 



a;2 + / + 22=p2 



p2 + 2^22 cos ?=26-i? + c^ 



from which equation c and 72 + c may be found. 



The azimuth of the body reckoned from the meridian, or 

 the angle SZP, must be found by adding to a. the azimuth 

 of the sun at the time of observation. If we consider the 

 spherical triangle ZPS as seen from the centre of the earth, 

 the angle SZP is the same as the azimuth of the body at the 

 place of the observer; ZS the zenith distance is given by the 

 equation 



tanZS= ^ ^l p 

 pcos i,+ K 



sin dec. = cos az. x sin ZS x cos geogl. lat. 



+ COS ZS sin geogl. lat. 



. , , sinZSsinaz. •/.,,• ti a \ 



sm hour angle = i = sm (sid. tmie — K.A.). 



° cos dec. ' 



By help of these equations, and the distance of the body 

 from the centre of the earth, the position of the body in 

 space is known. If, therefore, all the observations of the dis- 

 appearance of meteors on any given night were examined, 

 they might be discussed in two ways ; either upon the hypo- 

 thesis of their accompanying the earth in its orbit as satellites, 

 or upon the hypothesis of their moving round the sun, by 

 changing the origin of co-ordinates to the sun's centre. 



A body just skimming the earth's surface would revolve 

 round the earth in 1^ 26"". This, therefore, is a lower limit ; 

 and I find that if the semi-axis major of satellite 



h m 



= 2, the period =2 56 

 = 3, ... =3 40 



=4, ... =4 50 



the period of the moon's revolution being 27*^ 7^ 46% and her 

 mean distance 60|. 



If 8a, is a small motion in longitude, as seen from the centre 

 of the earth during the time U^ e the eccentricity, /x a constant 



