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eponed in rhe Explanation Io the ln.l<strong>lo</strong>h Attranonical EPle,cfir $al is basd oi<br />
Schoch (Sch@b, l9l0). In allrhe* worts for dei€miriry lhe day ofrhe fi*r liribilir) ot<br />
new cE$o! ARCV (arc ofvirion) b shoM to be a sMnd d.8Fe pohomial runcrion<br />
of DAz (claive uinuth). The* edly €f<strong>lo</strong>rc !rc only empnical in natuF N rhe critcria<br />
dc!.<strong>lo</strong>ped de bsed on lluing rhe dau so rh8t mo$ ofthe obs.oaiions arc conshlcnl<br />
TlE* nelhods do not hke into cosideElion lhe vidth ofcE$enl Btuii (Bruii,<br />
1977) co.sidd rh€ ihpodahce oacE*cnt widtn fld his Dod.l desqibes ARCV (in<br />
rems ofannud. of cr.scent above horizon plus tn€ solar depRssion be<strong>lo</strong>v lhe horizln)<br />
os a funcion ofthe crescenr widtn. The Nodel ofBruio. ho\rever, kkes $e {idlh !s a<br />
funcion ofih€ RCV ond DAz md a fircd Ddnh-Mmn dislaftc (in lemsolfixcd * i'<br />
dirnrl'ler ol fte lu.ar disc). Hc sas ale thc fi6t \no consid.rcd phJsical .stkcs<br />
dsociakd *nh $c problen like blightnds ofskt and thar oflhe M@n. Thus tu nrodcl<br />
due <strong>lo</strong> Bruin is the lirsl drolelical node<strong>lo</strong>fr|t nodern timcs Using the nrodels tur thc<br />
briShhess oalhe lull M@n as a fuhcrion of altilude (Befrporad, 190,r) lnd $c s[t<br />
brighhe$ duri.g lNililhi (Kooncn ct al., 1952, Si€denbpl 1940) Bruin delc<strong>lo</strong>p lhc<br />
visibililt cu^6 r€lnrin! the aldudc olcrc*€d sirh the slar dcpGsion. A<strong>lo</strong>nS lhc$<br />
ctrrvcs the bdehb€ss ofcrcscem (modellcd on $e basis of lirll Moo.) is al leasl ds much<br />
os tlhl ofrhe twiliShl sky. He aho delc<strong>lo</strong>pcd cuNes sholvnu rel{lDn berwccn ARCV<br />
and sl.t depesion rhll ldd prorcd to bc crucial for lunhcr nodellihg ol canics'<br />
Yal<strong>lo</strong>p has edne lbr funho improvemenr ond consides cece *idth as a<br />
funclion ofARCV. DAZ and lhe acllal scmi-dianeter ol lhe Moon (rhar depends on Lhc<br />
Eanh-M@n disrucc) al $e time ofob6endion (Yal<strong>lo</strong>p. 1998). \vilh de!€<strong>lo</strong>pinS a model<br />
<strong>lo</strong>r lhe besl time of yisibiht YaUop s nod.l al$ onsideF ARCV 6 a ihi.d d.gtce<br />
polynomial tunction of $e actul cresc.nt oidrh ar the ben ime of visibihJ. Such<br />
polynofrial is oblain.d by applying leasr square appbxination on a basic data sel This<br />
blsic data s€l *qs d.duced bt Yal<strong>lo</strong>p fom lhe limiling lbibilil, .uvs of bnrin b!<br />
slctins ARCV for a Sircn sidtn from tlr ninin@ oh lhe componding limilin8<br />
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