14^ M. VE Zach's Jjtro?iG;nical Ohfervatlons. 



. Islow fortlic hrfl: obfervation the-angle of elongatien \^b^n\. 

 for the nnglex^TG = arc AG =; T v^-^ A - T vjQ =: long, o - long* 

 cornet —d — a -^ -': 



the angle ot tneaniuial parallax b/w i = — ^ — = e'} 



the angle of commutation ;;?ST=r ^g^o - e -{- (^5 — a') =-f\ 



from whence the heliocentric longitude of the comet =3. 



The fame at the fecond obfervartion in. L 

 Angle of elongation ~_/2 - ^ ; 



Ancle CI anjiuai paraijaxe — — ;.- 



Angle of commiiiation (^= , ^^-, — . £ + (/3 - a)- ; 



t 



heliocentric longitude of the comet in I = /3 - 180^ + $::= 9^;-. 

 putting novy the.beriocentrie latitude feen.from S'^^i;. 

 the geocentric latit-ude feen fro-m T = /;.; 



Ill' • 1 • 1 'n 1 lin. r. tan?. / t 



the heliocentric latitude w.nl.be - ' ■ ■ V ~ t^TJis;. k ; 



-I. r -IT'- Ml 1 fi" <^ • tansr. ^ ^ 1 1- 



the lame with \>^n it- will be ^ — ttt—^ =• tan8[. ;5 heliocentric 



lip. (p ---■«_) ^ 



latitude in K'. 



Having tfiiis oetermined th^ heliocentric latitudtes o^ twa 

 obfervations, the radius vectors will eafily be found in the fup» 

 pofiticn miade for the fhortened diflances, for they are in tha 

 famd'ratio to the i-adius ve6k)rs as th-e cofineof the heliocent 

 tric^ latitudes are to the radius = i ; therefore the radins ve6lo? 



m of the firft obfervation will be =:—.-, and the radius vedor of 

 the fecond obfervation u = —r-- . . 



'^ COi. X 



Takinp- now the difference between the found' heliocentric 

 longitudes, we get the hejiocentric motion of the comet upon 

 tlie ecliptic betweeii two fhortened diflances,, which is to he 

 reduced upon the comet's orbit, tliis heliocentric niotiou is . 

 therefore y -^=.w. Now to reduce this motion we iiave, firfl:, . 



fllUJS 



