NO. i() Mi';ii';()K ouiuTS IN rill'; sdi.au sssriai — von niI'.ssi, m 



tnuoli loo heavy 'i wiMj^liI, siiico for tlicso this r;i(i<) of Ihc siiu's is a 

 very small fraction. 



If Ihc apjxiront i)alh be c-oiupiilrd iiol Iiy <i', 8', hiil hy liir .ipp.nciil 

 incliiialioii al the terminal ()oint, we shall eome nearest lo the eorrcct 

 values of the wciji:hts if we assume the mnnerator as unity. 



Tt is hest moreover as a matter of coiu'se in all special cases to apply 

 the indicated weight of the observed (|uantilies. 



The method hen; explained is based, as already slated, on the 

 assumiDtion that the lenninal point can he located with siiHicient 

 accuracy to justify the assumption I ha I Ihc apparent iK)silious m", 8i" 

 computed therefrom remain michanj^ed in delermininj;^ the radiant. 

 If this is not allowable, then the weij^ht of the individual tn", 8("'s 

 must he deduced from the averaj;e error in the determination of the 

 location and altitude of the terminal |)oint, and tlu-n a;i estimate nnist 

 he made of the weij^ht lo be j^iven the lirsl point m', 8i' of the orbit. 

 The corrections for both jxjints must tluii be determined as inversely 

 proportional to the weights />' and /»", Ihal is lo say, the rotation of 

 tin- apparent orbil is not around ihe point n", 8", but around Ihal p(»int 



in the orbit which is distant from this by the (inanlily ,' , • / and 

 from «', 8' by a (inantilv ,' „ • /. I f /" ret )rcscnls Ihe spherical dis- 



lance of this division point from llu- .issnmcd radiant a„, d,, then the 



factor becomes , „, 



/' / 



sm ,, , ,/, 



Vk= I' J' . (,'.) 



sni / 



I f we ( ainiol of (I<i not u ish to (htcrmine tin- terminal point of the 

 orbil b«'foicb.iii(I, tlicM in j;encr.il tbc two points a, fi' and n" , S" nntsi 

 receive e(|n.il weii;hts so th:it we must assume' 



. / 



^^-sin/"- <'7) 



II the radiant is determined from the linal co ordinales a, d, then 

 for each place of observation the arcs from a, d to a", 8(" will indicate, 

 according lo their positions, ihe improved apparent orbit. The normal 

 projections of the point a', 8' on this arc alTcjrd us on one hand the 

 improved apparent arc, and on the other hand the normal com|)onents 

 of the errors of observation projected on I lie p.ilh, I liose Ihal lay in 



' Oil tlio (Iclcnniti.-itioii of the radiant from lutiiioroits oli.scrvationit williotit a 

 pr-vioiis <lclcrii)iuali()ii uf liic Iciiniiiai points, sec also R. I.ciiiiiaim i'illi<-H 

 " Oil tlic theory of the shootinx stars, ]krlin, 1878." 



