An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

234: TI1f,j PLNJ.A'.
Tl'hle mlcan angular motion being known fr'om tle periodic timl
of the ptlanct, it is then ascertainedt by observation wthen thtc
tvuec motion equals it, and thus the tiime of the greatest equation of the cellter is obtained. TN-ow) thlis occurs twice ilt tit
revolution, at i. atnd f; an.d half way between tlhese points lie
the apsidcs A and 13. lThlrefore,b obseriil tlTic tin etmc of the
greatest equation of tthe ccntcer, ]E anld it' and bisectilng thle in
tcrval, we have the tiie qf tihe planet's passing te/)erd1ihflio,
13. Jiut the same observatiols also determtinc tlhe hcliocClitric'3places of iE and:1', and thell middle of the arc I.E;Bl' is the place
of the perichelion.
3177.'T'le amount of the greatest equation evidently dep)el(ls on tite eccentzricity of the orblit, since it arises wholly'rom thle departure of the ellipso from tlhe iilure of a perfct
circle; lihence, the greatest equation attords the mlcans oft dtcrmningi telC eenlltnricitSy itselt In orlbits of small eccentricity,
as is thle case with most of the planetary orbits, it is tbunllt thlat
the arc lwhich meassures thle greatest equation is very nearly
eqal to tlthc distance bcetween the foci, wlict always equals
twice tlle ccccntricity, the measure of the eccelntricity being
tel distalce from tlhe focus to tile ccntel' of tile ellipse. The
ngular vralne of radius is 57i 17' 44"1.8; for,
3.1 5.-,;9 1:I 180~ 57:l7' 411".8.
Tlhle'refore, 57~1 P17' 44".8: radius h alf tile greatest equation
of the center' tIle eceeatrieily."
iThe foregoing exp)lanations of the metl.hods of finditng the
clements of tlle orbits, will serve ill gllneral to shtow the learner
how these l)alrticullars are or may be ascertained' yet the
metlho(ls actually employed are usually more refined and intrictate thllal these. l'n atstI ronomy, searcely an cllement is p1resonttdc(
sinploe and umnmlixed with others. Its value, whelln first isengaged, miust partake of tile uncertainty to wvticlt tie other clelents alre0 subject, and can be sup)p)osed to be settlbd to a
tolerable (legree of correctnetiss, onlly after multilplied observations and 1manay revisiolns. Indeed, a large part of th}e most
ardulous la)bors of astronoln-meris ]rave been emlnployedl ill findillng
VinCeo's C'.olplet e System, i., p. 113..- \Vootldhouse, p. Ci.9.