Visibility of Luna and Lunar Crescent

All thes. figu6 show ! lend for lhe Aveog. RiFn€s Funcrion lhal is indicaL<l
bt rh6&thal consitt ralions tud deEocr.at.d in figGs 3.3,6 b 3.3.9, c..ealy ihc
invisible ce$enr hav. Actu.l Rip€ne$ Fucrion vdu6 b.low lh. AwnC. Ripoess
"Cwe md lh. visibte cBcens have v!l@s rhal @ abov. rhc cle. Devi.tions oa
both foms ac prc*nt ald e discu$ed ,bove. A rh€orcricalty visiblc cG$en$ (aclual
Rip€n6s Funclion valu. noE rb& the avcRg€) is reponcd invisibt. $ar gendlty
.ounts s 'Positive E@lied lh.oErically i.visibte q€sc€m (acr@l Ripc.ess Function
valuc les 1ha lhc ave@g€) Eponed to be se.n, a..Negalive Edof,. The posirive ero^
dponed halc no atiecr on the modet as rh.se cm6 nay occurdue ro mdy uncontroued
fado6 ( like seather cond id ons and obseNer,s abi I ity to scn* lhe conr 160, Thc negative
cmB nay eirher by hiShty oprimislic bur inconect clains or they nsy rndicsre hcr of
authcnticity ofthe nodet both di$lsed abole ih derajlfor $e LunarRipenes Law
,a,n ovd atl @hprrisoi of the Lud Rip€ness taw wih thc Babytoni& oitcrion
shows lhat lhc Babylonie crjrelion huch noe succcssfut. .ltE succcs percenr,g€ for
pcllNe cs$ fq lh€ ipenqs law h 92.8% aeaitrsr 96.490 or Babytohid qiroion. Ior
the negatve si8]]iings lhc .iFne$ las succ*dr in 57.?ro css ,€ainn 59.9% for the
3,4 EMPIRICAL MODELS OF EARIY 2o.rr CENTURY
After lookine i o Ine deraits of tc success &d lne co.srE,nrs of rhe tupcness
Modd oftheMslinsa ctoser look in|o rhe figw3.3.1 ad tne eatysis of th€ obseryed
oara rn comparison to itc Lu.& RiFn€ss Las, d impond dp€ct is rcv.ated. The
following figee3.4 t whicb an exlhsion of fie 3.t,1, in addrrDn to Moon b€ing nonh of
$c rcfiptic. als shows rhe M@n b be sourh ofectipric. In lhis €6e though sign of
latillrde. pM oflhe M@n tats c@ ofwhcrher rhe tmgih HT is to be added or subrracted
nom ln - ,6 in equario. (3.1. r t) or (3.3.6) bur tuother qwsron becones rlever rn rhe
cae shoh in rhe tisuE for sane as tbe Moon is huch tunner away ror lhe Sun when
Moo. is south of $e Sun (in nonhem hemisphec), rhe cese n6 ldes m of tishr
108