Visibility of Luna and Lunar Crescent

c@dt in ln.e m, Providcd th.c is tro obscaing cloud in lhc sky The
rponed posilive sightings i. dr6e cascs e I 14. Tns it is @mble to consider
cscs wilh I > +0.216 10 b. lhose wbcn the cccnl is esily visible.
(B)
Fon obseryc^ rcporls it has been fou.d that, in gcneral, t = 0 is close to lhe
lowr linit for fi6t visibility ud.r p€lfecr ahosphenc co.ditio.s 3l s.. l€vel
withour Equirine op1ic.! aid. YatloP u$d his Tlble 4lo st lhis losd linn for
vhibility mot p@helyand he says thal from inspstion of Tabl. 4 ihe
siSnilidcc ofq - 0 @ b. str bul t = -{ 014 is &olhd Possible cul_of val@'
Thce @ 68 €Aes in Tabl.4 sith q in ihis Ens. in the daia u*d bv Ytllot wirh
48 positive siShtings. Th. data sed in this qotk (in app.ndixlll second lst
@lu.) thec aE lll ca*s with q > 4Ol4 bul les lhan +0216 Oll of th€*
l1l cse) rhe!. ae 6a posirive sighnngs withoul oPtical aL
(c)
Yallopusd hisia6L4lo fi.d|hecut ffpoinl *hs opti@laid isal@vs ne€ded
lo Iind the crcse.t moon by rutching lhe q_test visibilirv codc wilh scha'Iecs
.od.. The rcund€.I value of 4 = _O 160 @ cho*n for lhc cut_olT dirclion ln
Tablc 4 (YalloP, 1998), thcc \,w 26 cNs thar s Gfv rhis diterion t0'16 < q <
-0.014), only lhree ces out oflh.se wre positive unaided siSltings tbe tcst were
se.n vith hiMul6 or r.lceoFs ln Tlble i. appendixlll' *cond lat cormn
useii in this *ork therc 62 cses in rhis tuge ol q_valu€s oul of vhich I 0 s€E
unaided si8ltinSs dd 29 times lh€ cresced *as seen either vith bin@uktr oi s'lh
(D)
ln lhis ca* (-0160 > t > -0232) YaUop s Table 4 ha' roo lew enli's fton
which lo estinale a lowt limit for 4
The situalion is nade NGe bv thc fact lhat
whe€ thse is an €nl!v. in non cas.s' the Moon ss not scen even wi$ oplical
aid. ln f4t it h @€ fot lhc cc.dl to be obedcd lElo* 6 a9pae't clo'galon
ofabout7c5 (Fatoohi d al, 1998) Ydlop's Tablc 4 h6 14 cs's in lhis dg€ oul
wbicb 6 re positiv€ sightirgs thdough binoculss o! &le$ope ed one exl6
oiilinary ce of uaid.d siShing ln th' r'bl' i' app'ndixlll Gecold 16l
141