Sir J, W. Lubbock on Shooting Stars. 83 



if il' = 883000 jR = 7916 2) = 95,000,000 



Let 



— — =<7 = -004605 



j.*(sin2^— y2cos2^)-)-2jr{siu 6 cos e-\-q-&ui 6 co%^\-^y^^z'^SQ,Q%- t-q^ siu^ 6\ 

 +2i?|.r(sin i cos e-\-q- cos Isini—q cos ^)+r(cos2 S—q' sin* ^+y sin 6) \ 

 = R-\sm"i{\+q-)-2q sin 6^ 



The origin being at O the place of the spectator, the axis Os 

 being drawn from O to the zenith, and the axis x having the 

 the same azimuth as the sun, if the azimuth of the moving body 

 be reckoned from that point in the horizon, 



a.' = psin ^cos a ?/=psin^sina ^=pcos^; 



and putting these values in equation (1.), 



^2 I |sia- ?cos" a. (sin* 6—q^ cos* f)-\-2 sin Z cos a cos ? /sin ^cos ^+y' sin i cos 6\ 

 +sin*?sin*« + cos*? jcos*^— }*sin*^[. I 



+2f iJj sin ?cosa {sin ^ cos 6 -\- j'cos ^sinrf— y cos^j- 

 ^-cos ? jcos*^— g*sin*^+y sin^[. I 



=iJ*{sin*^(l+j*)-2?sin^}. 



Hence it is evident, that if the place and time of disappear- 

 ance of the moving body are known, the distance p from the 

 spectator can always be determined by a quadratic equation. 

 Moreover, as the cone limiting the earth's shadow envelopes 

 the spectator after the sun has set on all sides, wherever the 

 shooting star disappears, a value of ^ can be found which will 

 satisfy the problem as far as the disappearance alone is con- 

 cerned. 



U, as a first approximation, we consider the earth as a 

 sphere, and the shadow of the earth as limited by a cylinder, 

 such that the axis of the cylinder is a line drawn from the 

 centre of the earth to that of the sun, the equation to the 

 cylinder is 



{xsm^+{z + R)cos^^ + y'^=zR% . . (2.) 



p2 { sin^ 5 cos^ a sin- fl + 2 cos a cos ? sin ? sin fl cos fl 

 + cos^^cos^fl + sin^^sin^a} 

 + 2p/i{sin?cosasin6cos9 + cos?cosfl2j=^2sijj2g 



When j/=0, that is, when the shooting star disappears, 

 G2 



