14^ ^'^- EE Zach*s Ajlronrymlcal Ohfervattom, 



Now for the hrft obfervatlon the angle of elongation \%h -- a\ 

 for the aDG:le ATG = arc AG = t 'f^-^K — t ^/5 G ^ lono-. o — lon^^v 

 eornet — b — a\ 



the anqle of the animal parallax S;;2Ti=""' ' ~"' =<:' : 



the angle cf commutation wST= jg^. - ^+ (3 — <3) =y; 



from whence the heliocentric longitude of the comet =^ 



The iiime at the fecond obfervatlon in I. 

 Angle of elongation =. /3 — oi ; 



Air I n ^'"'- v*^— *) '^ 

 Anjrle or annual pa^-allax g — ; 



Angle of commutation ^ = i3o^~" e +(/5 - a) ; 

 heliocentric longitude of the comet in I = /3 — 1 8o° + (p = ^ 7 

 putting now the heliocentrie latitude feen from S = /^ ;- 

 the geocentric latitude feen from T — /;.; 



17 1- • 1 • T '11 1 fin. /". tane. / , 



the heiiQcentric latitucie will be •-, - •' , ■ \ :=: tans:. ^ ; 



7 r • 1 Tr • "11 1 fin ® . tan<r. ^ i i* 



the lame with li« it wiii b€ — . ' ^ ■ ^ ■" - =-• tanp". y. heliocentna 



iin. (i3 — Ji) ° 



latitude in K. 



Having thus determined th-e heliocentric latitudes of two 

 obfervations, the radius ve6lors will eahly be found in the fup- 

 polition made for the fhortened drllances, for they are in the 

 lame ratio to the radius veftors as the coiine of the heliocen- 

 tric latitudes are to the radius = i ; therefore the radius ve6toF 



m of the firfl:. obfervatlon willbe=:~.- and the radius ve6lor of 



col,. ,4 



the fecond obfervatlon u — ——- . 



' col. y. 



Taking: now the difference between the found heliocentric 

 longitudes, we get the heliocentric motion of the comet upon 

 the ecliptic between two fliortened diflances, which is to be 

 redu-ced upon the comet's orbit, this heliocentric motion Is 

 tjiercfore 7 -.§■ =^ /^. Now to reduce this motion we have, firfl-, . 



finus 



