SIC LTUR AD A S T M

Sonderdruck aus
SIC LTUR AD A S T M
Studien zur Geschichte
der Mathematik
und Naturwissenschaften
Festschrift für den Arabisten
Paul Kunitzsch zum 70. Geburtstag
Herausgegeben von
Menso Folkerts und Richard Lorch
2000
Harrassowitz Verlag . Wiesbaden
A Close Look at t,wo AstJrola.bc:sand tJhcir Star Tables
ELI,YDEKKER.
111 1993 Paiil Kiiiiii:~scli X?-rotea fast:iiiat.iiig palicr 'Ziir Probl<:niirtili dcr ;\strolaI>stcrri<i:Eiiic: weitere unbrau<:lil>aicStcrritafcl', iii xrlii<:li lic siiininari~e<l
all tliat c»iil<l
aiid <iid go ~x~roiig
iii t h r trariscript~iori«f lists of stars 11;- a nia<lic\-al scril><r.' Tliis
paf>c!r slioiil(l l>c <:oinf>iilsoryrea<liiigfor all stiideiits of iiic,<lirval astrol;il><:siiia<lc iii
thc Latin ~x:?-cst.:
l~ccaiis<:orily by iiiidcrst,aiidiirg tlic sort of crrors occiirririg iii tlic
iiiaterial iiscd by riialicrs of tlicse iiistriirrieiits~it. is possible t o iiiterl>r<,tthc st,cllar
data oii astrolabi~scorr<:ctly.
Tlic! si.u<iyof nir<li?val astrolal~osraises a lot of qiicstioi~s11-Ilicli arc of grcal iiit.<?r<~st
t o tlic i~ri<lcrst,aii<liiig
of t l ~ ci>ackgr«iiiid of riitr<liti~-al
star tables. Yet: for oiic rtrasoii
or anotlier the proper aiial>-sis iircrle<l for sii<:li a piir~>os(~
lias ii«t b<:cii carrie<S oiit.
To (latc scl-cral al>proaclicsar? liiion-rr: i>iit.fmx- havc combiii<.d th<,riaiii<,sof t,lic stars
witli tlieir posit ioiial da1.a."~-rr siiicc: I<iiriitzsc:li pul~lishe<liii I966 liis classic 13-ork
oii star t,a)>les,1ic Iias a<ivocat.e<ltlic ricn- t,liat it caii IIC! irc.r:- inislca(ling t« i(lcnt.ify
t,lie stars ori tho ljasis oF llieir 1>osit,ioiial«ri<>:'Es ist also I~csc~iidcrcr
%rr aiif (iic
¿;bcrciiistiiriinii~i~
I-oii Zairieii iiiid Ii«or<liiiat,ciizii lcg<:ii'."
S l i r pr<3sc!iit.stii<ly airris t o oiitliii<: a coiisistcrit n-2,- t o stiidy tlie stars plot.tc<l on
tlic rrt,c of astrolal>cs. Soirie o F t lic proi>l<!ins<:iicoiinterti<larc <lisciiss<i<lon t.li<:liaii<l
of tivo specifi<:ally <:iicisrri <~xariil>lcs.
111 addit,iori n-c Iiav<:coniparr~doiir rcisiilts ivii 11
t,hosc of tlici gralthic: rnctlio<l c ~ i r i ~ ~ l oI,?~ eStaiitz
d
a.ii<lpoiiit oiit tlic iiiriitatioiis of tllat.
iii1~tliod."
;\notlicr piirposc of tlic pr<.seiit papcr is t,o ilis<:iiss t.11-o iilcdi<~valstar tablcs, Kiiriitzs<:h Ty11c:s X1 ari<l 1.1; l>ccaiis<,tlicir origiii aiid ba<:kgroii~i<l
arc far froiii (:lcar."
Tlit:sc~tn-o t,ablcs ar? <:los<~ly
associat,<~<l
ivitli t,lie t,~x-oastroliilics iriciitioiled aljovc 1x1
also appcars rcgii1arl'- oii iiieriic.i-al astrolal->CS.'It is tli<?r<,foreiiiil><:rativci o start aiiy
i<i(:iit,ifi<:atioiii>rocc<Iur<,iiitli tli? iiaiiicSs.\lost iianics <:an I)<, foiiii<i iii i lic iiid~irof
Iii iliis \ia:- iicit oiriy tlic
stars naincs iii I<iiiiitzscli's \vork oii iri~!dici-alstav i.al>l<.~.~
st,ar caii l ~ i<lci~t,ificd:
c
11tit also l.lic inc<licval star t.al~l<:(s)that iiiight. liavr 1)c:cii iiscd
1): thc iiiakcr. T1ic: riest prol~loiriis liow i.o acijiidical cr l>ct,ivc<~ii
tlie possihlc typ<:s. .A
Star t,alll<:such as S y p c \'I11 lias i~ccii<:ornposcd of t,lic ilat,a from o i I ~ ( lists.
~ r Ii <:an11c
distiiigiiislicd froin otlirr tablcs oiily by iiot.ing srriall (IiEer~riccsl>ctmc<:ritlioii~.H<,rc
Ihe positionai ~1at.aof t l i ~stars 111a3- bo licll~fill.Positioiial dat a arc also \.aliial>lc iii
<:asest,liat a iiaine is not foiiii<l in Kiinitzscli's iiidex or a-licii that. iianic is f(>iiiidiii a n
«d(i positioii. Aiid positioiial data ar<. iiidis~><~iisal>ltr
to distiiigiiisli bcin-ccii rcliablr
aiid corriil>t.cddata of tli<,si.ars: oitlicr «ii tlie rctc of nii astsolal~ror in thc s t a r i.;~1>1<~
iiscd by its rriakcr.
For i h conlparisori
~
of iri 1>arti<:iilareorriipt positioiial datn it is <Icsiral>l<~
t,o liiioniv-hi<:liposiiioiis arc: 1.o bc osl~c~:l.cd.
IIo~v?i<:i-_
iii ordcr 1.0 yr<*<li<:t.
tlir posiiioii of a
lit,tlc is linoii-ii ahoiit
star oiio iice<ist o liiio\v ttic ep«<:hof tli~:siar list,. ~~r~forriiriatciy.
t.hc tlicori<:s of prrccssioii inv«lv<:d iri iiirciicval star lists. Tliercforc~rathcr tliari tlic
c~>o<:li
itsclf it. is bcst t o iise tlic ~>rcccssioii
<:orre(:t,iorias a iii<iasiir<!for t,lic cl>oclisiiicr
tliis caii l>c<Ictcriniiic<lfioiii 11i<!list itscif. Iii oiir stii<l?-tlic 1>rcrc:ssioric<>rrrct.i»iiof a
star t,al)lc is tlir iiicari valiic of tli<! <iiEcrcii~c:cs
l)<!t,i\--<~cii
thc e<:lil>ticloiigitiidos of tlie
stars iri tlic tal~lnaii<l t lic c«rrcspoiidiiig T-;iliic:s in rlic 1'iolciii;rir: <:aral«giic:. 1x1 «r<l<ii
1.0 r:al<:iilatc: it. oric has first t o c ~ ~ i ~ \tli?
- ~ ~iiicdiation
i-i
aiid <i<~cliriat,ioii
of <:acIi star iiito
<-clipt,icloiigit,iiclc aiid latitii<l<i;tlirii ~lctc!rriiiii<!
tlic <lifF<ir<:iiccsDI,o7i ;iiid DI,ril 11-itli
th<r cori.<~s~>ondirig
Pt.olcinaic. 1-aliios, aiid finally cal<:iilatc tlie iirc.2iii ialii<:s of tlic~sc
riiff<:rciires."
Siinplr as tliis iiia)- s<:ciii: oiic cari casil!- gct a iiieaiiiiiglcss rtrsiilt 11)- iii<:liidiiig
<:orriiptrd data iii tlie <-alciilat.ioiiof I lir iiicari valnrs. Iii or<icr t« a\:«i<l tliis oiic iici<i<is
a st.aii<iar<lt o (listirigiiisli l~<'i~vi-o<~ii
rc1i;rI~lcniicl corriipte<l(iatix. :I v<'ry dirc<:l \\-ay is 1)'
iisiiig thci diff~.r<:ric<:s
DLo,i aiid DLon. Siiico tlic latitii~l<x
is iioi aff~:ric<iI>? ~>rcccssioii,
oiic: nial- espn<:t tli<: ~:;LIIICSof DLnt to I><:C ~ O S Oto Oo. TIIC valiics «f 01,071 slioiild not
(1eriat.c t.oo riiiicli fi-oiii t,lic 111-nccssioii corrcc:i.ioii irilid for tlir. star t a l ~ l c<:oiicci-ii~~l.
Iii
pra<:t,i<:cit is rim-er <iifficiilt t o r<~«giiiz<x
stars n:itli a gr«ssly osccssiie I-ttliir for DLo,t
or D L o n S<:tt,iiigsii<:liw r y tiiitriistn-orth>-data apart. a rclial~lr111-cr.<issioir<:oi-i-<:ctioii
for t.li? star t a l ~ l ccaii I>c cstal>lisli<:<l.Tliis l>rcccssioricorrc<:tioii <:?insiil>sc<~iieiitly
I>a
usad t o ~:al<:iilat.c
tlie 'corr<~<:t'
~>«sitioiis
of i h r sl.ars xviili iiiir<:lial.~lc(1at.a; aiid iiiali<>a
iiiorC <lct.ailcd aiialysis of t.lic crrors in tlie st.ar 1.a.hlc or oii t lic ast.r~>lal>e.
3. S h c siars
oll
t h t retc of' S.\IYI ;\ST0370J0
Tlic rrtc «F t,lic asi:rolabe 11ST05iOin tlic collcct,iori of tlic latioiial Miiritinic l\Iiisc;iiiii
is slion-11iii Figiir<-1. 111311111<. 1 tlic: hasii! data of t.h<istars oii i h r retc arc r>rcscrit.c<i."
Tl><.stars lian<.I~ciciiord<:ro<iaiid iiiinil><:rc<i(first <:oliiiiiii)for iiicr<?asiiigvaliics of tlic
iri~:iIiati«ii.111 tiiii secoii<li!«liiriiri tlic riamr is giv<,iias ii. is eiigra.i.e<l011t,lic rctc. This is
f«lloi~-c<i
iii tlic iicsi <:oliiiiiiisby thc: ixieiiiatioii aii<ltlic decliiiatioii. Iii tlic last <:oliirnii
tlic idciitifi<:ati«iio f t lic star is l>resciiied, arid listc<lal«iigsi<lc ivitii tlic iiiinib<?rof tlic
stav c:oiii!criied iii tlrc slai- t,al>l(,assoi:iat,ocl n-itli this astrolal~e,Tyr>c XI." Iii iriost
cas<:s tli<lidcnt,ificati«iis agrcc witli tliosc iii Type XI: Iiiit tlicrc arc soiiic adjiistiiicirts
rcsiilting fi-oiii tlrc. aiialysis of tIi<:l>osit,ioiial<iat,a]>res<iiit<i<l
bcloii-.
Iii tlii: ]>rcx?iit.c:asc siiidy tlir i<l<~iit,ifi<:ai.ioii
of stars aircl tiic, riic<iic\nl star t,abl<:
iiiv~l\:<~<l
ivas iiot. ver? iliffii!iilt iii spitc: of tlic fact tliat iiiost t,lin star riaiiics riigrav(:<i
oii ilic rct,c <:oiilii liavc becii tal«c!n froiri <:ith<!r S y p c 111: XI or VIII. Tlie rcasori is
sirril>lr.tliat t,li<*rrari. tivo riaiiies tliat occiir iicith<!r i l i Ty11i: 111 nor iii VIII. Tlicise
arc i.li<!iiaiiics L-4LGL;IRJ' (for Cr\-) arid 'rILIELI1~'(for 6 Sc«). Tliese na.mcs (io
iiot occiir i r i aiiy otlicr I<ri»n-nsoiircc: aiicl iiiii<liiely <li:iiiie Type XI. Tag<-tlior ivit.11
tlic iiaiii<,sof t,lic ot1ic:r stars ]>rcseiitc<loii tlic astr«lal>ctliis csial>lislicshcj-ond doiil~t
i h r i h r stai. tablc i i s < ~I)?l tlie rnakcr was Typc S I . As Iiiiiiit:zs<:h hiixisclf piit it: tlic
noiiicii<:latiirc of T?-pc XI appcars oii tlic ra1.c 'gaiiz reiii;.'"
Bcforc \>-C (iisriiss tlic agrecrnciit b<ii.rir<:ii«f tlie positiorial data of ilii: astrolal>caiid
Typ(. S I ; ive iiec(l to say a TI-or<loii t,lic striictiirr of tliat stirr tirl~lc.T y ~ ) cXI is l<iioi\:ri
iii t.i?--o 1-crsii~iis:
t,o \vliicli \I:(: sliall refcr licrc as 11.1 ari<l X1.2. Iii T-ersio~i
X1.1, t,l1<:
(l(icliiiatioii of a star is givcn iii<iire<:tly iii t i m diff(:rciit I\-::iys\T-Iiicliarc disliiiguisli<!d as
S I . l ?I ('allitii<io') aiid as X.ll> (t.lir in<?ri<liaiiiiltitii<lefor Paris). Iii ordcr t o l>cabl<:to
coiii]);rrc tlic ~>osit,ioiial
(lata with tliose ori tlic astrolalx, i ~ o t l i'allilii<lo' arid iiicridiaii
altitii<i<,I\-orc i!oii~-(,rtcclI)> iis iiito <lcrliiirr.tioii." Tlic rcsiilt of rlics<:cal<:iilali«iis lias
I><:eii]>rcsentc(liii ? a l ~ l cS;ii-hcr(i t,li<.~>ositi«iiald a t a of a iiiirnl~cr«F star tai)lcs arc
<:oinparc<lfor rcasoir <Iisi:iiss~<i
iii riioro <letail bclml-. Tlrc riii.diatioiis in XI.la arc tlic
saiiic a s tliosc iii 11.11). aiid arc ]>rcseiit.c<liii Tiibli? 5 alorigsi<ii: tliosc of X1.2.
Th? agrccriic3iit bctiwcii t,li(: posit,ioiial dat.a of tlici st,ars oii tlie rctc of tlic astrolahc aiid t l i o s ~iri Tyi)<:S I is gciicrally fair. For esaiiil>l(~_
tiic (lat,a of t,hc gliost stiir
origiiiatiiig fioiii cv Gc:in. star n». 10 (lal>cllc<i:.4I<DI): agrco ivit,ii thosc iii hotli versioiis 11.1 an0 X1.2, n«. 10. Iii soirie cascis ili(, dccliiial ioii of a star «n tli? ;istrolab<i
(locs iiot. agrer xvitli nll T-crsions«f Typt XI. For iiistaiii!c, rlic d<i<:linatioiiof rl Ckla
(110. IG. I~il~clicii:
BESE,X.i:) agrccs bctfcr n.it11 XI.11) or X1.2 tlian 13-itli XI.la. .4iiii
tlr<, ialii(: i>f ilii: dci:liiiatioii of star nii. 28 (l;il>cll<~i:
HT71\IER."F:():) agrccs 11c:st.\I-itti
tlic <l<~riiiiat.ioii
iii SI.11). Otlior diffci-ciicrs harc b<,cii list<,il iii t,iir iiotrs t o Cnblr 1.
II I
aiii
gvrall? iiidcl>t<r<il o 11i- lio<mraii<lvaii iilctnipoci. Sackl<,r fclloi~of ilir Satioiial ilaritinic
foi ipioii<liiignic ii-illi !.li<! iii<!?isiii.ciiicr~is
IICC<~<:</for t l ~ < p~.<isriii
,
s1,uOy.
lliisriirii
I2 I<itiiiizscli il<IfiC>) I>!>. f i i - i l
.L Close Look at t,~vo;\strolabcs an<i t,lieir Star Tahles
181
.All in all: ~vi:<:ori<:liiclcttiat thc positioiial data of tlic: astrolabc stars agree t,olcrahly
~vc:llmit,li t,he dat,a iil X1ll1 arid XI.2 biit less so Tvitli tlrose in XI.la.
Tlic fair agrccrilciit bct~i~c:eiit,liti stars oii tlic rcac arid in thc s t a r tablo clocs iiot
n<i<:c!ssarilyiiicaii tliat t,hc (iata ar<:csccllciil.. Thiis tlic riest. stcp lias hcrri to <:omparc
thc <lat,a frorri botii tlie iiistriiiiiciit aiid tiie st,ar list. (vc:rsioii XI.11)) witli tlic valiics
frorn t,hc Pt.ol<:riiai(:<:at,alogiic,aiid t o cal<:iilat,cthe prc<:essioii correction for both
soiirccs.'g For t,liis piirposc xvr liavc coiiucrtc<it,li<:ine<iiation aiid d(~c1iiiatioiiof cöcli
star iiito loiigitiide aiid lat,it.ii<l<::iising a vtllue of of 24'. T h c rt?siilt is slioxvn in Tablc! 2
mhcrc t,lic re1ial)le st,ars haic: bccii list.c<laiid iii TaRle 3: iii xvliicti tlie corriipted stars
lra>-<-<. hcen <:ollect,<id.In botli Tablc?s 2 arid 3 t,tic stars ar<,ordc:n.d acc:or(iiiig t o their
nurnber iri Type XI. E<>rcacli star tlir loiigitiitie and tlie latitiidc is givcri as wcll as
t,li(: <iiffcreii<:es:DLon aiid DLnt: bct~\~c!ciitkiesc aiid t,lic I't,olcniaic n l i i c s as esl~laiiicd
iii se<:t,iori2 ahol-c.
Csiiig t,hc data « i tlic 22 relial~lc~
stars list,ed iii Ta11lo 2; 7l-c <ie~tci.iiiincdrlie iiieaii
valiics arid t,lieir st.aidar<id<:viatioii of DLon and DZot. Tlic rcsulting valiies slioiv
t,liat tlic latit,ii<lcs of tlie stärs iii Type XI aiicl oii tlic inst.riiriic!nt (10 ori averagc
iiot dcviat,e <:onsi<i<-1-al)ly
froni tlie Ptolmnaic valiics. Tlie loiigitu<lcs of the st,ars iii
Type S I arc oii aicragc iii<:reas<?di>ytlic <:orist.ant.ainoiiiit. of 13.9'i 0.5' 13-itli rcspect
t,« t,lic I't,olciriai<: loiigit,iidcs. Tlie diff~:rcriccsl~ct,!vccii the dat,a of Type XI aiid t,lie
astrolat)<:of lcss tlii~ii(]..so arc n.cll ~\;it.liint,li<:liinits iridicabcd by tlir c!rrors iri t,lie
incaii valiies.'"
Thc urircliable st,ar positioiis n-crc casily rc<:ogiiize<i1.~1-tlicir esc:essiue dci-iations iii
the mlii(+sof DLnt aiid DLon (sec: Tablc 3). Th<:\-alii<rof DLon dcx-iatcs l>y10" or 111oi.e
from t,lie3meaii valii<?«f aboiit 14" for all stars (is<:eptrios. 2 aiid 9 f«r T\-lii<:liir«n-c!icr
t,lie valiie of DLnt dm-iat,cs niorc t,lian 5'. T h c nunibcr of stars n-ith corriipt,ed data
is tlic sanic for tlie iiistriinic!rit. arid tlic star t,able. itldicatiiig t,l~at.tlie errors iiivo1vc:d
arc inbrinsic: t,o T>-peXI."
Usiiig a ialiic of 14' for tlie precessioii correction, oiir ncst st:cp lias bccii t o cal<:ulate
tiie corr<x:t.positioris for tlic stars list,<>d
in Tablc 3; t,ogc!tlicr ivit,li tlic posit,ioris of soinc*
iiciglihoiiririg st,ars. Tlie r<,siiltsar(, siiiriniariz(:d in Tablc 1;arid TI-illI)? <iis<:iissc<i
liere
in soinc dctail iri orflcr t,o sliow tlic siii>tlcties of t.lic idriitiii<:atioii proccdiirc.
Tlie first ~>r«blern
to c:onsidcr is the idciit,iiicatioii of star S I 110.2. Kiiiiitzs<:liassiimes
t h a t it,s narnc 'algoii' st.<:irisfroni 'algcbii' whicli is sliort. for 'algeriib', ttie iraiiie for
n Per; brcaiise t,liis agrccs \T-itliIiis hypotliesis tliat. Type XI is aii cstract fioin VIII.
Most iiiariiiscripts of T y ~ SI:
e lio~l-cv<!r,
liarc 'algon iri frorit,e algoriis' r~liicliappciirs
In
\Ve preiei. Lo iisr vcisioii S l . l l > ior oiir cornparison becaiise tI,al is tire vcisioii iuhich agicrs ivith
1 h r astrolel>r daia ior iiit criii<:ai si.ai- iio.24. See also footnotc. i'L b~lon..
I 6 I'trc riilcs o f statisiics teli 11s thai. t i i r sian<lar<i<leviatio~iiiiciicalci O n averagc t l w erroi. i i i t.!i~
data of an ii>diui<liialstai. aiid i.iiat I h r erroi- i n tile meaii ~ a l i i eol a g i o i ~ po l st;iis is ohlaiiied
I7
i>y divicling iiie slan<lard iic\-ia,tio,i I>.riic sqiiarr i o o t o f tli<: niirnl>er o l si.ars.
1.11~data of ti>e positioris ii>l\-pt S i ; w tlicsr iinvr bern e<lilr<iI>? l<iiiiitzscli. tiaic
l>een ~.epiacc<lI>? variai~ir<!>i<iiiigsiul>irli ar<. iii<lical.cd i n his notrs to I ~ y p c X l s; ~ iiiiiiitasrii
c
(1966) pp. 7 0 - i . \\Y ihavc iii<licate<ltiris i n 1.iie ~ i o l e s10 oiir 'Jii>lr2. .As a iesiilt l.iie niimb<,r a i
reliahlc stars i o i T y p c S i . ) b Iwcarne idenlical to tliose loiiiici rar i l i c instiiiment.
Soinc of
to Ijc <:oiiiicct,e<l
1i-it.11Typo I11 aliere it is idciitificd 11-iili fi Pcr.'?r\lso tlrc? 'alt,ituclo'
»f 71" of star XI. 11o. 2 is thc sarnc as t,liat of (I Per in Type I11 iio. 24. It is t,riic t,liat
tlic ~~ositioii
agrces bcttcr witli <,I Per. :lssuiniiig aii rscess in longitiido \vit,li rcspcct,
to P l . o l r m ~of~ 14' (T);pe S I ) i ~ fiiid
c a iiic<lia.t.i«nof n Per of Tau 7' mcl ü dccliiiat,ion
of $G0. For 0 Per t,hc nicdiat,iori is Tau 5" and tlie <ioclinatioii 38'. Howeier; t,hr
positiori is iiot alw-ays dccisiic; iiiid in t,lic liglit. of oiir nclv liypothesis for t,hc origiii
of Typc XI: wc! thiiik t,hat 9 Per is t,lic proper ideiit,ification."
Tlrc o<hi positioii of thc gliost star si.<:rnniiiigfrorri rr Geiii is ii:c!ll est,ablislicd. Thc
positioiial data of tliis star agrce ~x:ii,lrtliose! iii Ty11e XI (i~~e<Iiati«ii
Lc:o Goj dccliiiatioii G o ) . Slic c<:lipii<:loi~gituticaii<i la.titudc! of cr Geni aro 98' (01: ai:cordirig to a
variaiit rcading; 103') arid 9.3') resp~<:tii-el'. assiiiniiig a prccessioii corrcct,ion of 14'
(T!-pe S I ) . FI-oni tliis a rri<idi;~tioiiof about 98' (or thc iariaiit virliic of 104O) and a
<l<~cliriatioii
«f ailoiit 33" arc ol>t.aiiicd. Tlic ]>ositi«ri of ihc star oii thc astrolal~ean<l
1.h~:l.al>ledocs not CT-CII C O I I I ~ S ii<iai.to this: aiid tliis star t,li<?r(:forcccrt,aiiily d<~serv<~s
lo b<:coiisi<lcrcclns a ghost.
Tliat. d<!riatioiis occrir iri Ilic ~~ositioiis
of tile Stars of Lrsa Xlajor (scc! Tabir 3) is
not siirprisiiig l>c<:aiiscof their closrricss to tli<,iiort,li p«lo. T11c (1i~t.aof t,lic ast,rolahe
Star rio. 9 ügrrc fairly mcll witli thos<i of Typt XI.1b ('egregcz': iiic<iiatioii Ciic 24":
deciiiiatioii aroiiii(1 46'). I<.cccritly Kiinitzs<:li has concliidc<l t.ha.t. its iiaiiic arid t,lic
\-ariatioiis of i t iii<li<:ate!r CYla." E~rcnivit,li tliis iicw i<lciit,ifi<:atioiitlic positioii,
<!sp<:ciailyi . t ~ d<:ciination,
<~
rciiiaiiis corriipt. .$ssuiiiiilg agaiii a ~>rcccssi»iicorrc:<:tion
of 14'; t,lic i~ic<iiiitioii
of 1, UXia slioiil<ibc Ciic 26" ancl its <ic<:lii~atioii
al~oiit51". For
tlrc d;it,a «f astrolabe star iio. 13 a similar story ciiii he told. Its data agrcc fa.irly ivit,li
tliosc of Typc S I . I b ('alru<:aha.', rnc<iiat,iori1-ir 17". <Ic<:liiial.ioii49"). Alt,lioiigh thc
iiainc iii<licat<!sB LMa. tiic iiicdiatioii sccin to l~oiiitto / I 'Cl~la.Tl-ii.11 a prccession
<:»rr<~c:i.ioii
of 1.1' 1%-efiiid tlic irir<liatioii of B LMa as Lro 5' aiid its de<:liiiation 5j0.
For 11 C l l a tlir iii<idiatioii is Lco 18" aii<lt,li<.dc<:liriai.iori5 " . Iii I>oi,licascs tlic c«rroct
d<~ciiiiation
<Irriatos froin tlic wliir of tlic astrolabc star arid tliat iii Typc S I . Also
iii tlic liglit of oiir 11c.i~Iiypothcsis f»r tlin (11-igiiiof T)-p<:S I ; n.r Iliiiik tliai B ChIa is
tiir, prop<:r idcntificatioii."'
T1ie sitiiat,i«i~for r Del is orily slightly diffcrciit. Again th<?<lat,aagrce fairly witli
Type XI ('cl<:lfiii'; inc<liatiori .Aqr 10": dc(:liiiat,ioii Go). For a 1>rcccssioi1a>rr<bct,ioiiof
1-1' t,lic incdia,tioii for F Dcl slioiil(1 bc c:qual to Ca11 29'; aii<l t,hr de<:linatioii aboiit
9'. Iii otlici- x\-or<is2
tlrc incciiatioii of tlic ast,rolal><!st,ar aiid in thc tal>l<:arc al>«iit 10°
siar is n>nic ci>niiiio$ilylal><?lli:<l'algol'. altliougli 'aigoii' is also iise<l iir tiiis
l.i.ir<iii.i«ii. sec! I<iiniizs<:li (i<>iS)asirolehr sl.ai-s 810. 14; 11.G9, aii<l (:iiiilli<!r (1<132) p . l O i .
I 9 C\ \
tliink tllat 'Type \'I11 ans roniposc<i o f X I aii<l \'I;aiid that iii<!
wioiig posii.ion o l SI, iio. 'L
l:oiifiisc<l t l i r aiitlior o l I \ - p c \:I11 iilieii iic c o i i i ~ > o s <Iiis
~ l s l a i tal>ie. lir al>l>?al.s10 Iha\-C.inatclic<i
1.he s t a i 7 I'P~
(X1 ii<>.
2) w i t h il,s iabrl 'algoii i n Iroii1.c algiinis' wich n Per (V1 no. 8) ii-ith its
laix!l -iiigeinl> i . laius ~>PI.SC~<Iexi,~iiin~.
TIie ~namri n V l l l iio. 7 siiiIl 1bca1.s Li1c c v i d e n c ~o i this
inat.clr: ,algciiil> rroiis algoiiis'. ll. esplaiiis ii.h? 0 l'ci does iiot iigiii-c iii I - y p c V l i l .
similaii i i a i c l ~ i i i gei-roi- i v a i n i x i r lby llie aiitlior of \I(31s I): See Iiiiiiiizsch ( l ~ l i 6 J11.45, iiotc 8.
20 1'iivai.c coliimiinicalioii ( L e t t r r »f 2:i .liily l<)<J<J.)
2 T i i c i>osiiioil o l ast.rolal>c siar rio. 13 agices iiell i i i t l i tiiat. of ??!>C 111 no. 26 (scr '?abie 5) a ~ i d
iiol wit.11 tliai. of V l l l no.21. 'i'iiis agi-ees ivitli our ~5siirnpi.ioi1lliat 7 y p r \'!I1 ivas <:ompose<lo l
X1 aiid \;I.s<%,also fo<iliiott .!fi l>clo.;.
'il>t<iatn < > I 0l:\iiiaiid ji i \ l a as pirsciil.c<l011 astr«lal>r~s
aiid iii s l i i i i.iii>l<,sai-c so coiif~isiiigtiiat iiiey ~Icseri-r2. sq>ai.aic sl,t~<ly.
18 lii Type I11 tiiis
.\
A Closr Look at
t\vi> Ast,rolabcs aiid
tlicir Star Tdhles
183
Ii:ss t,iian mhat t,hey slioiild Iia.\-<:11>1.cn.Errors of 10" arc iiot rar?; but iii <:ont.rast1.0
tlic corruptioiis discusst:d ahov(! tlie orror iii tlic in<,diat,i«ir of c Drl is i ~ o tfoiiiid iri
Type 111 biit. i t oc<:iirsonly iii Type XI aii<l VIII but. ii«\vlicrc clsc.
Of great. intrrcst arc t.lic iiiirclial>lcd a t a of the rcniaiiiiiig stars nos. 19 aii<i28. Tlicrc
is good agr<a?inaitl>etii<:cii tiie data of astrolabc s t a r 110. 19 aiid Typc SI ('aliclis';
mcdiat,ioii Sc:« 17": dccliiiat~ioii10'). Ho~i-cvcr:tlic iiairie corrcsi>oii<lsto 3 S<:oj fcir
wliicli ivith a prcccssioii c«rre<:tiori of 14' a nictiiat,i«ii of Sco 21' aiid a <lecliriat,i»iiof
17' arc oi~tainc!<i.Tlic. p«sitiorial <I;it.a of st,ar 110. 19 (lab<!lle<l';~liclis') appear t o fit
precisely t,iio posit,ion of n Si31 (inediatioii Sco Li", dtc<:liriation 10"). Tl]<! agrceinciit,
is so closc! tliat, we bclicvc this t o bc a c:asc iii ivliich thc ~>ositi«iiof oiie star is
<:«iiiicct,cd mit,li a \i-rong labcl, t,kic iiainc! of another star. Ttiis sort of crror is iiot
rcally esccptioilal iil rncdicval star lists; a s we siiall ~ ( ~ cinc oiir dis<:iissi«ii of thc otiior
astrolahc selcctcd Iicrr.
:
I
siniilar but lcss <:lcar casc is star 130. 28 ii-iii<:liis lahcllc<i 'Iiiiincriis <qiii', oiic of
the ilanirs iiscd f«r 3 I'cg, bitt h h ~
positioii <iiE(!rs froin that of 3 Peg, as is shoii-n in
Tahlc 4. Ttiis st,ar is 11rosc~iite<i
tivic:c 011 tlie asirolabc aiid iii T ~ p Sc I . Tiic star 110. 27
is labeilrd: 'Iialfc!raz' or .;ilf<:rai.': one of tlie otlicr iiai1it.s fcor fi Pcg. aiid blic positiuii
i><il»ngingto it. is compatil>lc ii-itli t,hat iiarric. Siric:e [j Peg is alrcarly pr<~scntr<l
lvr
giit:ss t,liat tliis agaiil is a case iii irliich a lahcl «f oii<i star iias 11ccn att.a<:lic?dt,o t.li<*
position of aiiot.lit;r st,ar. Iri<i<~cd;
t,lic positional dat,a of star 110. 28 oii thc asrrolal~ean<l
iii vrrsiori XI.1b (rnecliat,iori Psc 17"; <lec:liiiatiori52') app<:ar to iii<iicat.ctlic positioii
of 4 Cas. Csirig a prcct!ssioii corr<.ct.ioiiof 14" \\-C find fou 3 Cas a iric<liatioiiof Psc 19"
an<l a dccliiiation of 54'. Thiis t h r posit,ioii «f s t , x iio. 28 oii tlie iiist,riiincrit arid i i ~
SI.II> agrces faii-1. xvi;<.lIn.it.11 that of ,;j Gas."Slie ast,rolirhc stiiriicd hrre w-as iric:lii<led iii a rcbcont st.ii<ii1- St;~iitzivlio lias aiialyzecl tlic st,ars oii thc retc grapliicall!-. It. is t.lrcr<:f<)rcof iiitc~restto sec hon- Iris
iiictliod <:omparcs with tlic prrsciit. analysis. So starr n.it,h, \V<: iiot,e tliat tii? I>rcc:<:ssiori <:orra<:t,ioi,of alx~iil,1.1' oi~taiiicdbl- us <:«irir~arrs\vcll T\-itlitli(9 valiic of 14' T'
iisrd by t,lic Islairiic astroii«nirr rlriacliiiel for liis star t,i~l>Ie
for t,lir cpocti of 106617
('Iypc XII).'" Tiiereforc, tiif stars prcseiitcd in T!-[>(! XI agrec ii.it,li tiic sky aroiin<i
1070. Shis cpocli prccctlcs tlic d a t r ass«<:iat,c~i
that star tahle (1223 or 1233) by iiiorc
t,ha.ii 150 -cars." .In' agr<:c3niciitfoiiiicl »ii thc hast of tlic grapliic: <lispla\- pr<:s<:iit~t.<i
by St,aiitz of t,lie stars of Typc XI n:it,h rnodesii <lat,a calciilatc(1 for tlir ycar '1223, is
22 Ilir <ieclinaiioiioCs1,nr no. 28 iii vrrsion S I 2 is 2 i 0 hiit sincc ilie wri~olai>e
aiid X J . l b agrec iliis
coi>l<ii.icll h~ n Iatcr ~i)riiij>li<>i>~
j>r>ssibi,vi n or<lrr to niake i.Ii? rrioilroiis Iiamc 'liiimcri~s<,rjili'
agic<,;~bir1.0 tlir posiiioii. (SI3 Tlie aiitlinr oC X1.2 is in01 iiectssar.ily i<lriiii<ai io ttic r l ~ i t h o i
ol S1.i.) Ti>is'cori~c~cl,e<l'
posiiioii was PO ivc lliiiik siihse<(iici,liyidriiiifird I>? itic autiioi.
oC T y p c V111 iyitli tliat of n Arid rif 'lypc V1 iio. 2 ivi1.h tlie lai><,i'al~>lierai'.
Siricc i l ~ eiiarric
'al(>liciaa'wa.5 also in usc as a n uiicinatiie iiamc for 'liii~iicriisrqiii tlr? atitlior 1.ook 1ivr.i- ttlc
da1.a on tiiis slar Crorn XI aiid <iropc>ciiilir star \'I no. 2. I1 txplaiiis nliy <i \n<i clocs iiol figiii-C
i n 'Vypc VIII.
23 In IiiiniVascii (1966) p. 71. tiici-C:is siill sciinc niicertaiiity ahoiit il?? ipiccis<i<'porli of ' l i l > r S I I .
bii: tiiis was <:ori.<~cir<l
i n Iiiiiiitasch (1980). P. 19i.
I Tiiis coiiclosioii
aiica<iyo!>lainr<ii i i aii cai-iier s:~i<ly.scr 1)ekker (1995) 11.35. tablc 10. l i i
I.i>ccriiiiiiies i>i-ec~dii>g
llic :\lplioiisini. el>ocli (1252) the iisc 01 ali :\inl>ic ~>reccssiori
ralc of l o
in 66 )-ra1.scaii lbr ,iiistifi<~<i.
\Vii.ii it aii rj>o<:li
ol 1070 is obtairie<ifoi i\-pr XI.
.i
Closc Look at txvo .Isrrolabes aiid tlicir Star 'Tahici
18.5
d ~ i s t , r y . "Sc<,ii
~ against t,liis hacl;groiiiidj it rna!- I>c iio coincidcii<:c i.liat. tli<: siiape of
thc rc1.c of AST0570 (Figiirc 1) fit,s well into t,he st,+-lc:of ast,rolal>rs ma<ie iii t.lic srcoiid half of tlic~clcv<iiitli cciitiiry iii Sorth<!rii Spairi. Espccially tlic so-callcd Solo<$»
ast,rolai>cof .lD 1067 sli«ii.s cliara<:tcrist,icswliicli ii-(? caii r<:cogriizeagaiii in tlie Xkfkf
ast,r»labc aiid 11-liictian: so t,~l>ical
for tliat period: (thrce) praycr iii<:li<isoii tlio ciiit,rr
frariit~,coiinter cliaiiges 011 t,lic cast,-\vcst bar aaii<l t,lic siiiail I>ar along tlic iiicri(1iaii
liiic? coniic<:t,iiigtlic ccliptic n-itli tlie c<?nt.ralring aroiiiid t,lic cmitrc."' Also tlic st:l<i
of t,hc! ]>oiiitcrsis qiiitc siniilar.
SIiiis thc ~>rc<:cssiori
corr<:ct,ioii of alioiit 14' of Sy]>c XI agrccs n-it,li llir sliapo of
rlir r e t e Tliis is tlici l ~ a s cfor oiir liyl>otlicsis tliat t,lic stars I>cl«iigiiig t « tli~:st,ar t a l ~ l o
T>:~>CXI
\+-er<:
co]>iccl iii Paris aroiiii<i 1223 (or 1233) froni an ast,rola.be of SpaiiisliIslaniic origiii: tliat. n-as rnadr in 1070 or thcirt. al>oiit. Iir tliis s<:<,riario ivlii<:h claiiiis
a soiircc: for Typc XI tliat is iiidcl>eiidcnt of Type I11 or 1'111 there is iio riccti for
Ei111 agr<J<:iiicritl>ct~~-i-ccii
Typns I11 an<l XI. h dire<:t <:oiiscclii<iii<:e
of il is: lio\t-e\-cr:
that T>-l>cV111 was coiiil>oscd of stars froiri Type XI aiid T!-[><:VI. siiicc only iii lliis
way <:an oiit cxpliiiii tlic. spc<:ial fcaI:iir<'sthat oiily T y p t XI arid Ty1><:1.111 liav<: iii
crIllllIloll
T h c idea tliat T:-pc: X1 iiiiglif Iia\-e I~ceiicopicd fioiii aii irist.riirn<~iilis iiot oiitragcoiis. Loiig ago it ivas siiggcst.c<l tliat tlic positioiial d a t a of t,lic stars of Type 111
wcrc <:ol>ic<i
froiii aii iiist.ruint:iit,.'" Tlic sariic siiggcstioii n-as iiia<lc for the origin of
'Type I\'.":' ?vlorc«v<:r:i<iiiiit.zs<:lislion-cd t h a t tlic (irawings iii MS Paris, I3.X. lat,. 7412:
rcl>rcsciit,cda copy of a Spariisli-,\rabi<: ast,rolabc froiii aroiiiid 1OOO."" Indec~d,it. (iocs
iiot scc!iii ainazirig tliat. iiist,riiniciiits \\-er<%
airiorig t,hc first, t~raiisinitt~crs
of östr»rioiiiical
iiiformatioii t,o t.lic Latiii sp<:akiiig worl<i. An iiist~~iiiiiciit
is tlic sorl of <:iiriosity tkiat,
at.t,ra<:t.stlic attciitioii of a \videi- aii<ii<-ii<:<:
tliiiii tables iii leariiecl t.rcat,is<:s\\-irich rnay
C\-cn shy pc?o~>l<off.
S h c iclca tliat aii iiistriiinc~iitiin<i<.rliest,li<: data of Typt XI is sii~>l>ort.cd
qiiitc
iridcpcn<lciit,lg I>!: t,li(- sf.ar list ibscif. ris lias bcc!ii ilot,ic<,d ai>ovc, iii Ilir rcda<:tioii
of tlic tablr X1.1; thc decliiiat,iori o<:c:iirs twicc: first. as tlic 'alt,itii<lo' an<i sc<:oiidlv
;is t l i ~mcridiaii altitiidc for I'aris. Poiillc corisi<l<!rc<itliis as cvideiicc tliat Type XI
was a r<~-xvc.«rk<:d
X-crsioiiof ?)-]X 111. IiIc rcasonrd i;liat. tlic odd 'alt.it.iido' <:oordiiiatr
was coiisid(?red iiisiifficiciit aii<i that iii 1223 (or 1233) tlic incridiaii altitiides of tlie
stars ii-<:r<,iicn-iy ohs(?rve<iiri Paris in ordcr 1.0 iinprovr iipon tlic! fault. 'aititii<lo'
coordiiiat,~~
of t,lic s t . a r s . : ' ~ l i i stlicri woiil<l also csplain \\-liy t.lic3t ~ v oiiltcriiati-i-o15-ays
of csl>rcssiiig the dccliiiation of a star arc listcd toget,hcr. Onc is in<:liiic<iIo licsitate
n.licri ol>serial:ioiis in tli<x kfirldlc .lgrs arc niciit,ioiicd: I>i~t.
apart fiorri t liat t licrr is
aii»t.li<?rwi-;i?-for <isplaiiiiiig tlic iise of thc inrridiaii altitiidc.
30 'l'iic Stili scnic OS liiis iii<lilsti.? iviil oiiiy becoiiic ciear ivheii ilir caialogiir i n i>rcpai-;ttioii oi l i i i i g
will bc piii>iisiic<i,sce l i i i i g (li)<Ii).
31 Ciinl.iiei- (1932) rio. 118. pii.253 5. Soc ;iiso l l i v groiij> OS acti-olabcs l a b ~ I l ~I>?
< iSl.a<iiiai \Y10 I:?
an<i alii<:iiai<r <lale<iSroin 106O IO<lO; S l a o t i (199i) [>I' 5
6i.
X2 J l r ~ c k r r(1931).
33 Iiiinitascli (1966) 1>.31 iiotc 2.
3.1 I i i i i i i l z s i i i ( I 99s).
:ii I'ouiic (lOi(i) i>i>.31TS .
70c:opy a star list, fioni aii Islariiic iiistriiineiit iii ir~c<licral
tiines was a iriorc difficiilt
I>rol>lcrxitliari sucli timt arc iir<!t ii»\va<laysin descril~iiigt,lic ri:t,c of an ast,rolal>c.First,
of all; for tlrc nicdieial stu<i<:ntt licrc cxist,cd a s<:riouslairgiiage problcin for readiiig
off t,li<?~iairics»f thc stars. And alt,lioiigli thc in<!diatioirs of 'lrc stavs coiild be read off
straiglit aiT7ay:t,lierc ~ v a stlic problcin of liom to dcteriniire the dei:linat,ion of tlic st,ars.
Tliis pr«l>lciriof fiii<iiiigthc <l<:c:li~~at.i«ii
has hccir at. thc bottoiii of thc usc of t,lic odd
'alt,it,iido' coordiiiate recorded iii Type 111." .kn alterriative \vag for tlic dl:!t(!rn~iiiatiori
of t.11~deciii~atioiisof t,h<:stars oii the rct,c of ari ast,rol;ii>cis I,» rcad off the rn<-ricliai~i
altit,iidcis n-itli tlic liclp of a lat.it,iidt: plat,~!.~'
All onc! lias to do is t,o bring thc star
poiiiter iii tlie iii<-ridiarilinc aiid rozl off i1.s position oii thc iinderlyiiig latitiide platc.
Tliis easy rn<it,li»dwas also firsl apl>lied in tlic coiit<~st
of Tvpc 111. Tlic odd numl>crs
of t,lic 'latit.ii<l«'iii tlie st,ar list in 14s Paris, D.X. lat.. 7412; fol. Sv: <:aii bc eiplaincd
as tlic iiicri<liaiialtitudcs for a geogral>liicallat,it,iidl:-of 38.2'i 0.2". Thcsc <lat,a<:oiild
t,liiis h a w hccii obtaiiicd bu r<!adiiigthciii off frorn a 1ai;itudc platc for 38' 30'." Arid
if oiir 11:-l>oi,lrcsisis <:orrc<:l.
- tlic saint iirethocl for fiiiriing t,lii. dc<:liiiaiioiis was at t,lre
l~ottorriof thc rc<:orcliiigof the incridian altitu<lcof Paris Type XI. All tliat is needed
is a latitii(i<:lilirt~for Paris or a platt of t,ii<,scr~iit,li(:liiriatc; t,li<! lat.itu<ieof ~vhicliiii
B.';. lat. 7-112; is girrri as 48" 32'.'3n
Slie dosc a>rreIat,iori cxist,iiig bci\~-cciithc star iiainl:?s iisod in Type I11 and XI
fiirtlicr siiggcsts tliat. our Parisiaii autlior t,ricd to orcrcornc liis t,ranslatioii probleni
\vitli tlir. iist of T y ~ >I11
e in liis liand. Tlic coorcliiiatcs prCsciited in rcxsion XI.1 slio~vs
in oiir aic~vt,liat oiir aiitlior tricd to riiatdi tlic positioiial dat,a of liis iiist,riimeiit with
thosc: of Sype 111: aiid siihsc<liiciitl):!n:rot,e <io\vna list of thc star rianies he liad foiind
011 liis a s i r ~ l a b c . 'Ciifortuiiately
~
t,he list of T):!pr 111 did iiot solx-c all liis 1>r»bleiiis.
Tlic astrolabc iriclii<icstivo stars for wlri<:liiio iiiforniatioii is pr«i:i<lcd in Typ? 111: XI
iio. 11 (rr Hya) aiid XI rio. 19 (p»sit,i«ii ik S<,r)..$iid for onii star: XI iio. 28 (~>osit,ioii
ß Cas) oiily a vcry corriiptcd position is giv<,iiiii S):!pr 111. I7or t,licsc stars -- so ive
irn>~giiic- tlic I'arisia.ii aiithor liad to <!inploy »i,li<~r
\va):!s 1.0 find ilie iiam<:s of tliese
stars, aiid ap~>ar<~rii,l\;
Iie i\;as su<:<:essfiiloiily iii tlic r:asc of rr >I>-a(XI iio. 11). Hoir- he
arrii-cd at. tlic iiairic of t,liis st,ar or a t tliosc of tlic t~\:ootli<.r stars rciiiains in tliib darli,
l>iit siircly liis soliitioris for tlie lattcr two are way off. Clcarl):!; our Parisian aut.lior
<li<liiot iiiidc?rstaiid .$ral>ic, aiid tliis rosultcd iii a rccor<iof aii odd si,ar nanic! for t,lic
~~
tlic iise cifliie &?trolabr ?
,I j>scii<l«-llasalialla; see Giii>tliri- (1'129) ~01.2..1, L20 $ 10. 'i'liis is l h e
firsl strp iii ilie mei.liod ricscril>e<l Tor (iiidiirg Llie <lecliiialioi>(srr (:,iiii.tici- (1'129) voi. 2; p. 221.
2 20) los i f i n r?<l<lilioiriirc iiiei-i<liari all,iLiidc of rlie lhegiiii~iiigoi t l i r sigri a i hi.i<:s or o l I-ibra is
<iciei-rni?i<,<l.tlic <iecliiia.lioii can br calcnlalc<l Siom i l i e <liifcitii<:r I>c<~I.cPI>
llie star's rneridian
altilii<lc aiid I.lial. o l llir ~<~,iiiios.
18 I n aii eniliri- si.ii<i)- I>?iiiii~itdsciiaiid Uekiiei. (19915) p.66i; a g<~ograpiiical
Iatitiide of c.39' iyas
incntioiie<l. i l i i s raliic inusl bc ii.jeclc<i lbociiiis? tlrc circiiiii~>oinislei-s ivem irot tiealeil correcl.ly.
:\llri- ioi-l.crl.iiig foi- siicli Stars l h c pl.esei>l valiie i?f 3S.2"1 0.2' is obi.aiiicd. \\i.
i i o t . ~Iiere tliat a
iulii.ii<le ,>laLe of :ja0 10' ( l o i Covdoi-a) was iiicliidr<i iii lI,r so-callc<l 'lblcdo asti.olabi! dt-scribc<l
in. <:iinI,l?cr (1932) p.222; ser I\iiig (199'1) 1>.2.1 5.
:3D K i i i i i t i s i l ~( I <J<)$)
116.
411 :\,I csaniiiieoiao alreinpt to malcli I!<-o slai- tai>l<,s(betivreii 111 and I\;) is seen iii tlir illiistraiio~r
o i llie iahle o i i ' y p c I V i n <:iiiiiiier (1921) \<>I.
1 , 1>.20i: sre also I<iinilascli (1966) 1>31
C r t in IVj hc:caiisc iri some iriaiiiis<:ript.s«f Type XI this star iias I><:<:ri
ad<lcii.11. is
iiot <:l<.ar7,-licthcr tliis is rriatod a t all t o tlic star iri Tj-pc 11'.
Siirrirnirig iip ivc cari sa>- tliat tiici iicm iiypothcsis «n tiic origiii of Type XI caii
cxplairi t,lic <:lost i>iit.iiot coniplct,r corrc!lati«ii bct.ivc:c:n tlic iraiiic material of Type 111
arid XI; aii<i also tlic <:orruptiori of t,ii(: iiarncs of B Cas aii<irr Cer. Scitlicr is t,hcrc an
ol,jcct.ioii t o ac<:cpt.ttiat Typ<%
V111 ivas coiii~~ost!cl
oiit «f of T y l ~ eXI aiid 1:I. Tliis iri
t,iirii esplains tlic special frat,iircs ii-liicli Sype: XI and V-111 liai-r in <:oriririori.Tliercf<~rc;
tlicrc is 110 iiccd t o i-iolat<:t.lic datc of 1223 (or 1233) asso(:iat.ctl ivitti Typt XI. Tlic
11e.~hypothcsis oii thc origiri of S y p c XI also iinplics aii c a r l ~datc for t.h<: XkII\.1
ast,r»labc bccaiisc if it is iiidccd a copy of tlie iiistriiiiiciit tliat camc 1.0 Paris in 1223
(OS 1233) it vrry likcly ~ - a iria<ic
s
iri Paris ar«iin<l tlic sariic tiirit, t,hai. t,hc t,al>leivas
<lraivii ti[>. Tiiiis a rarc aii<l iiiiosiial c«nibiirat~i«iiof Latiii text ori aii otiierii-isc iii
ei-cry rrspcrt Islaniic looking iiistriimcnt <:eine irito bciiig.
Cr
5.The stars on thc rct,e of thc great. Sloanr astrolal-jc: 1311 SI,. 54
Tlie star mal> »f tlie Sloaii<!astrc~labcin tlic collcci.i«il of thc ßritisli llusciiin is oll<:
of t,lic, rriost c~scliiisitrprotiiicts «f irie:dicval tiiiies (sec Figurc 2). :iri<i its priricely- sizci;
a <liairirtcr of c. 47 <:iii_iiiakcs it estrcmclg siiit,ablr to arisn-c.r sii<:h qiic:st,ioiis of lioiiacciiratc a rcrtc of an ast,rolabr <:«iild l>c corrstsii<:tc~diri t,iiosc (1ai;s. S i i r stars oii thc:
rctc liai-c bccir stiidiod iiiorc tliari oiicr; biit iioiic of t,li?s<,stii<lic,scoiribiiicis iiamt:s
arid positioiis, aii asp<:ct tliat canriot. 1>reinpliasizc:<lsiificient,lj-."" Iii Tal>lti6 tlie l~asi<:
data of tiic: stars oii tiie rc:t,e of thc Sloaiic astr«lal><:.tiic rii~i~i<>s,
iii~<Iia:.ionsan<l <Ir~liiiatioris~
are p r < : s ~ i i t < ~Thc
d . " ~st,ars haar l>ecrior<ierc<laici iiiiiiihrr<i<I(firsi. <:oliiniii)
agairi for iiicr~asiiigi-aliics of thc inc<liatioii.Iii tlie sccoiid coliirnii tlie ri;iriios are 6'
'ii-cii
as <:rigrai-cii 011 thc rct<,. This is folloivcti in t,lic iicst <:oliiiiiiis hy t,hc ine<liat,iorisaii<l
l.lic <Iccliiiiit.ioris.Iii tlic last <:oluiiiii ttic! idciitifi<:atioiis of t,lic stars art: 1>rcsciitc:d,arid
liste<l aloiigsi<lc ivitli tiic riiiriil>cr of tli(x star <:ori<:erii<i<l
iii Ilic star Lal>lc! associat.<:<l
ii-itli ttiis astrolatje: 'I'ypc: VI."' Iri inost <:ascstlic idriitificati»iis agrce ivitli t,liosc iii
'Ty~'t?1.1: l>iit tiicr(! arc soinr ac!justirient,s rrsiiltiiig froin t.iic: analysis «E tlic ~>ositiorial
data to I>c ~>sesent,ed
bcloii-.
T h c i<lciitiii<:atioriof stars 1)' tlicir iiaiiios prcs<:ritc.<l oiily »iir problein. Th<:riarnc
of star iio. 2; labclled 'RJGII.;\LS.4BIE', <iocs iiot o(:ciir iii th<iiirclex of star iiariics in
I<uiiitzscli iiy11er1. Hoii::cvcr; tlic iiaiiic lias becii iiicliidc<i iii i h r list of ast.rolal>estars
disciissc<i iii Kiiiiit.zsc1i Ste7.nnurn.m as a riamr for .4iiid." All the «thcr st,ars wcrc
ccciil?- i<l<:iit.ifie<l.
\lost «f tiic star naiiics <~ripravc(l
«ii t,li(, rct,c OE the Sloaiio ast,rolabc
i:oiil<i Iiarc l~ociit.akcii frorn citlirr Type 1'1 or Type \ X I ; Init tlicrc ar<: tivo stars
I:$. iwittr tl,<. lal>cl 'aIrii<:a.ha') aiid ,i i;\la (V1 iio. 1'1) foi- alii<:iiaiily a, ~ l r s ~ : i i g i . i o n
is proi-i<le<l. n i i l a iiaiiic. T11s neinc iii V111 iio. 21 bcars sl.ill l i i p cvi<lpiic<:o i l l i i s irini.<:li: 'alrii<:öi>a
iiiii.l t l c posilioil r<:ri<,ct tiial <>i
V1 no. 1'1. I 1 csplains iviiy j i Il\la <lo<!siiot ligiiie iii I.yl>t VILI.
Siniilar matclirs ai.r dcscril>e<i in oiir iiolcs 19 a i ~ d22.
<:iiiitii<!i- (1932) ~01.2.no. 2g0. p. 463; <:iiigciirli (1<>87):SI.aiilz ( l < J < J ipp.
) $16 -<J<). siici figiirr . i a
"Ci P. 2
".
I aiii grcaaiy iii<icblr<i to I>r Siikr :\<:k<,rnianti.l i i e <ilrati>i- o i tlic l i r i t i s l i \lus<,iirn; ior pro\-icling
rn? i v i l l i l l i e iricasiiicmr~iisiiecdrd lor i.iic pi-rseni, siiidy.
I i t ~ o i t a s c (1966)
l~
pp.39 .i6.
K i i i i i t i s c l i (1<l59)0.68.
0 L \ i a ( X I iio.
15
16
17
.18
A Closc 1,ook at (71-n ristrolabes ari<itlicir Star 1;ibics
I89
that Iiclp t o distiriguisii l>eti\-ccn i.lics<:tn:o typc?s bccaiis<~of tlicir occiirr<rric(Liri 1.1
oiilj-. Ttic first oiic is p ITkla, ~i:liicli is lal~clled'COXILXCI'E' ('T~ISII~
6; iio. 18); a
phrasc stcinniiiig froin tlic <icsc,riptioii of tlic star iii Typc 1.1 no. 19: 'siih siiiistro
11cclc ij~siiisnrse ~ > o s i ~ r ict
o rsnnt
~
diic con,i?i~lcbe'liny iialicsj. Soinetiin<?stkiis star
is lat>elle<l:'siibpcdc' aiid tiic, labcl 's<~lla'(for 'stclla') Iias also bcx~rirecord<~<l:'"Thc
ot,ticr st,ar \\:liicli uiiiqiicly dcfincs Tyi>c V1 as tlic star t,al>ltl iiscd by tli? iiiakcr of
tlic Sloiiiic astrolabc is <I Aiid. \\:liich is labclled '.ALFER..AZ' (Tablc 6'. iio. 40). Tb<,
namc 'alfr:raz' is iiscd iii Types 111: S I anil \;I11 f t ~ rtlicx star 9 P P < :so
~ ; oiie Iias 1.0
rnalic siii-<:that 011 tlic Sloanc astrolabc rcallj- <Y -4iid is rncant. Sincc tlic: <i~~clirii~ii»ris
of n Arid and !
3 Pcg arc irior<,or lcss tlie sairie (25' anti 23': resi><:ctivcly)tliis cari
only be decidcti hy tlic incclia,lioiis: for ru Aiitl it shoiild bc ;iroiintl Psi: 22' aiicl fnr
3 Pcg aroiirid PS<:io(coriiparc Tablc: G : 110s 39 aiid 40). Tliiis 39 oiit of JO stars caii
bc tracctl hiicl< t o Typc \;I. 1 s Kiiiiitzscli ~vi.oiil<l
1iar:c g~iitit: tlic iioiiiciiclatiiro of 1.1
aI>pcarsoii th? rctc 'fast gaiiz rein'.
T h c positional dat,a of Tyi,e V1 arc kno\vri iii tii-o vcrsioiis, t,» n-hicli \\-C sliall rcf<:r
licrc as VI.1 ariii VI.2. Iii T>-pc 1'1.1 tlii: cclipti<: <:«ordinatrs of ttie stars arc list<.<l.
111 thc otllcr vcrsioii: \-1.2_ \vIii<:ti is fi>iiiiii iii only oiic inaiiiis<:ript, iii addition tiie
niediations arid tlir ilccliilatioiis arc givcii. Thus a dircci coniparisoii for iirosi of tbc
astrolabc stars with T'1.2 cari 11c iiia<lestra.igtit alvay. Iii ord<:i-r» comparc tlic riosit,ioiial clata of t,li<:;istrolal~cstiirs ii.it,li t,liose iii 1'1.1 13-cIiavc corircrt<~dtlic rnc!iliaiioii
aiid ttic i1ci:liiiatioii of cacli star 011 tlic astrolahc iiito lorigitiiiic aiid latit,iidc, iisiiig
a ialiia of F of 24". Tiris n-C!\v«iild I ~ T -doiic
c
aiiylioxv a s part of oiir aiial'sis of thc
rcliabiiity of t,lic l>«sit.ional data. Tlit. rcsiiit. is skio\i-ii iii Tablc 7 \i-litxi-<,
ilic rciiaiiic
stars liai:c l>ccii list,cd arid in Tai,lc 8:iri mlii<:h iiiircliable stars havc bccii collct:t.c<l.
Tri hoth tahlcs tlic stars arc riolv «r<icredaccnrdirig t,« tlicir riiiri~l>(?r
iii Type 1.1. For
ciii:li st.ar ttic Ioiigitiidc: aiid tlicx laiitii<icis givcn as 13-cll as tlic diffcrciic:cs: DLon aiiil
DLat: hets+-c:<?iitlrcsc aiid tlic Ptolcrnaic ralucs.
T h r agmrnicnt bct,it-ccritlic p«sitioiis of t l l ~
st,ars oii slic rctc anil iii Typ(: \-I. 1 liste(l
iri Table 7 is fair. In gcricrai tiic asi;rolahc (lata arc I<,ssac<:iisatcthaii ttioso of Typt
1'1.1: t,lic lorigii,ii<iesoE n Cop (\:I iii). I ) aiid o Leo (1.1 110. 21) arc3off I,>? aljoiit 4"arid
.So r o s p c ~ t i v ~ linit
~ : , tfi<i(1ai.a of tlic «I licr stars agrec w<:ll.Tliiis tlic iicsi: stc1.o Iias bccri
t,o dctcrrniric tlic ineaii ialiios a i ~ dtlic si.aiida.r<ldc~i;itioiisof DLon aiid DL(i1. Tli(>
rcsiilt,~s l i o ~tliat
~ ~ t.lie latitiidcs of tlie stnrs iii Type VI.l aiid t,lios<:011 tlic iiist,riiniciii
do imt dcvii~t<?
on th<i averagcLc«iisid<?i-ahlyfrorii t,lic I'tolcriiaic i-aliics: aritl tliat - also oii ilic i1vc:rage -- :.lic Iorigitiid<:s of t h r star t,ablc arc iricrciascd by a coiistaiit
aiiioiirit «f 151.3~1-0.2" ivitli rospect. tn th<-Ptolciriaic Ioiigitiidos. Thc loiigitiiilcs of
t,lic astrolal>c stars arc iiicri:asod I)? aii arnoiint Iiat is onl? sliglitl!- <liffcrt:iit, 15.4"
i 0.3". Tlic diiicr<:ni:c is 13-cll T\-it,hiritlic liinits iiiciicatcid I)?- thc rrrors iii thc ~ i i ( ~ a r i
i-aliit.. Tliis g«o<i agre~~riiciii.
rriay ii-cll I>(:csi>laiiicd h - tiic sizc of tlio iiist.riiinciii.
I 9 1 . i ~namc 'siihj>ctic' is rrcoi<ic<l oii
nii a s t ~ ~ o i a l >
iiir t i i c r o l l c c i i o i ~of t i i c d l r i plaiirtnriilrn.
Mrnsirig 26: s r r <:iiritli<ri. (l(132) ~ i o2%
.
aiid \\l.i>stcr (1998) I>)>. .4O I. l'iic iiaiire 'srlia' occiirs
oii t.lic asl.rolal>e <lcs<:rihr<ii n tlic sales catalog,ic <:liristic's Soi>tii Kcnsingiori 251 Sri>trnii>ci
1991. l.ot iio. 136. l t iras iklcnliric<i & l i i i i i i i i s c i i (aftci t i i r <Icsciiptioii of t l i r asli-oiah<, iiad i~ccii
l>iii>lislicti) as i.i,r star <Its<:rii>r<liii \IS i o r i i f i ci><i.T.1.I.
l i l v (i>ieiioiisly 1,lS Iiliiiigsb<~i-g.11..
cotl. lal.. 1i3n) as: .$eil<<
'siil>p<~<i<:
siiiistso inaioiis iii-s<.oi siiot diic ~ t e i l c<-oiiiiiii<t<: Ir>,?.
itr~li<sl.
190
Ellr D~likci
I'licrc arc 110 stars mitli corriipteci data ainorig tliosc of Typc V1; iiidicat,irig 'hat.
t,hi! crrors inl-olrcd might n:cll 1ial.c bccii introduccd i ~ h c r irnabiiig tlic: inst~rii~nent."~
Tlic iinr<:lial>lcsaar positioiis oii tht. rete of tlie Sloanc astrolabc are easiiy rr<:ogriize<i
by tticir esccssii.c dcviatioiis iri tlic ialiies of DLnt or DLon (sec 'Ial'ühlc 8 ) . The valuc
of »Lot of astrolabr s i a r iio. 3 1 (ieaiates inore tliari '10' aiid tlic x:aliic: of DLorr of t,lic
orhcr stars d<!viatcs hy 7" or rnors fi.oiii tlie irieaii ialiir «f 15.3".
l:siiig t,lic \.aluc of 1S.3' for blie pre<:cssioii corr<:cti«ii oiir ii<!xt step tias becri to cal<:iilatc: t,ki<:correct positioils for t.hc stars list,c<iiri x~l'ühlc 8 ; l.ogctticr 1vit.h thc poiitioiis
of soin<:ncigliboriiig stars. TIic rcsult is suinniarizcd in Tahlc 9. Tlic corsiiptiori of t h r
d a t a of tx\-« stars. n Aiir C.(\ 110. 11) i\nd 1 Dcl (A 110. 34)) ciiii L><: rcdii<:ed t o 'crrors'
;hat arc, iniiltil>lrsof 10' in ni<~diatioii
aiid in latiiiidr_r<:spe!ct~ircl~-.
For coiiiparisori xve
rc:diict:<i tlic Ptolt:iiiaic cclipt,ic latitiidc of Dcl by 10'; aiid calciilat<:d thc rcsult,ing
iiiodiatiori aiid <ic<:liiiatiori(sec Tablc 9)
Of riiorc iritcrcst. arc! tlic rf:niainirig stars: -: .liid (A 110. 2); 3 ;in<! (.% iio. 3) aiid
3 l'cg (4 iio. 36). .4s is sliolvii in Tahlc: I): tlic ~>osii.i«iialdata for r Pcg (V1 rio. 37)
fit pr<sc:is<:lytiio posit.i«ii of tlic st,ar poiiit,cr lahcillccl: '\,IESKEB' (.:I iio. 36). Ttici
ag~-<~cirioiit
is so ciosc ttiat 7%-ebclievr this t o 1)c a case iii l~:lii<itlic p»sit,ioii of ono
star is <:«iifnsed xvitli tli<!labcl of aiiother. Ttiiis it <:aiii<:t « Iiap~jciittiat the iiaiiic of
R P<,g is presciitcd tmic<!oii tlic instriiincrit; o11<:ra s '\IEXI<EB' for r Pcg aiid o i ~ c < ~
iis 'BED4LFEl?AZ' for ?! Pcg.
More c«inpiicat,cd arc tlie ~>osit,i»iial
crror.: assocint,ed xvit,h i.li<:iiaiiies of y .\iid anrl
3 Aii<i. H<:rct,o« \\-P l~clicvetliat a mroiig lal>cl Iias b<icri attaclicd t,o tlic posit,ioiis of
i;lic stars. Tiic tn-o stars 1vliict1 rraditiorially slioiild II~I-cl>ecii plotted oii tlic astrolabe arc rx Cas aiid 0 .lii<i. iVc Iiave t,ticr<:forc c«inpar<~d
th<, positioiis of tticsc txvo
st,nis
.. ivitli tliosa of .\ iio. 2 arid A iio. 3. Ii. t1it.n tiiriis oiit tliat t,tic iianie of A 110. 2
L
('RIGILALS.4BIE' for 7 Arid) lias becri iiscd f«r tlie star poiiitcr xvitli tlic positioii
«f ;j Aiid. Sccoiidly; tlir lal~olfor 3 Arid; ('~IIR.,\C.-ISDR.0:) iias h<:cri attaclird t,o
ttie star 11ointc:r .l rio. 3 li-lii<:lircflc<:ts a corriiptcci positioii of <I Cas. Tlie ecliptic
loiigii.ii<ic of tlie ~>oiiitfr.4 iio. 3 agrccs mitli t,liat of o Cas 1jiit ttic latibiidc is 2G0
iristcxad of l G O (c:oinpare Tablc 7 iio. 5 witli Tablc 8 110. 3). It. riiay X\-cllbe ttiat t,hc
corru~>ted~>ositi«iiof i.\ Cas - an error of 20' iii e<:liptic latit,iidc tias iiidiiced tho
iiiakor; 01: rriorc prol>ably aii ast,rononicr iiii.olvc<l iri tlir <:oristrrict,ioii of tlie ast,rol a i ~ c ;t o look for a niorc iicarljy st,ar: arid lras addctl crror t,o error 1):- attachiiig t,li<.
iiairic of tliis ot.hcr 'nciv' star t o thc wrorig star poiiitcr. On<?can not say that tlie
corruptcd p«sit,ioii of a Cas agrcc:s ii:<!ll witli tliai of 7, .\nd. hiit it is <:<:rtaiiilviri its
ii<~ig-lii>oiirlioocl.
FIo~\-ei.ertlial. iriav hc,, it is of grcat. irit.<*rcstt o ol~scrvct,iiat first of
all it was rc<:ogtiiz<~<l
t,hat t,hc f a i i l t ~positioii disagrccd ivitli tliat. of (1 Ca$. aiid t,liat
iii tlin groccss a iirlv Arahic iiamc was iiit.roduce<i."'
.5O Somr of tlie dala of liie i>osilioiis iri 'I'vpc \'I. ni tl,?s<: liaia I><:<:ii c<lite<lby iii~rrilasci>.Iiavr
breii ~.c]>la<<,<i
by i-ai-iaiii readiiigs wliidi ai-r iri<licar<4i i i Iiis i i o t r s 1.0 'lypc \:l. sec liunit~as<:h
(1966) p[>.-i;IC>. have in<licale<llliis i i i t1,e n o k s ta oiii 'iablr i . :\s rl iesult. tlic ntiiiibw of
iini.ciial~lrstars foi- 'I'y!>r \'I rciliicnci LO zcro.
51 i\ dcscripLian oi tiic iianies of 1.Iic st.ais on a groiip of moinoipliic asitroiabes xas publisli~<lt>y
(:ingeri<:li ( 1 9 8 i ) . biil 110 ~>ositioiial<Iril.aarc pi-ovicle<l.\ccordirig i o tliis IisL Ilierr aie at lrasi,
liuo ollici iiist.iiiinciits ~ i i l i h r iianir Iiig<rlalsabir (oi Iiigcl).
<:rtiat.ed.Tlic qiicstioii ariscs wlictlier t,li<ia<:t,iiityof Johii of Loiidoii dicl OS did riot go
bcy»n<I siicli vcrifi<:atioiiof data. Or to piit ii, <liffcrcrit.ly,x\~lictli<!rtiic clata iri t,lic list
of Type \'I (10 really rci>rcscrit a set of dircc:t. rcc«r<iiiigs ivitli ari arriiillary splicrc.
.-\lrea<lj- in 19GG Kiinitzscli <lrcm attciit,ioii t o t,lie fact t h a t tbc ~)»sitioiialdata of
Typt 1;I.I i+zrr<iiiot siinp1~-<?st,ract.?<l
froni tlic Ptol<~iiiaiccatalogiie a.ft.cr correct,ioii
-fcor pre<:c.ssioii. as is iisiially tlre case for siar tab1c:s wit.11 c:<:lipt,i<:coordiria.t.cs."' In
a<idit,ioii,iic slioi\:<-(ltliat soiiic! of t,lir tcxtiial cIcs<:riptioiis of tli<! stars iii t,lic list <lo
not folloi\: tlir Pt,ol<,niaictra<iitioii biit sc<!rir t11 +>C! 'dcrivc<i iioin Iiis jt,lie obser\:cr'sl
or\:ii p(?rsoiial rinm of tlic sby.." Tliis st1(:rns to iiidicatc tliat t,lic stars iii t,hc tablc
ivcrr iir<lc<~<l
»l>taiiiocl 1))-ol~sc-rviiigt.lic>ucal SI;?. L.\ coinliarisc~nirith i.lic rcal slq; inay
thiis bc iiist.rii(:tivc.
Tho iiioclcrn sourcc: iicarc,st: in time; an11 iiide$>cii<loiitof tli<, Ptolciiiaic catalogiic.
tiiat caii 1>ciakciri as a rcliable stairdard for tli<?real sk?: is tii? st,ar cat,al«giie of Ty<:ho
Br;rlie for tlie <?lo«<:irof 1601. Tliis cataloguc is I<ii«~\-ii
1.0 bc frcc fiom systcinatic:
c:rr»rs. It. is thrrc.lorc siiit,ablc t o iise it. iii oiir aiial:-sis. For tlic saixx »E disciission
Iiaae als» c»iiipar(?cl thc Prolcniaic ~ a l i i e s«f tlic stars inclii<lccl in T y l ~ o\;I .ii.itli
Tyclio's catalogiie.
Tli? r<,siilt.of t,li<irarioiis <:oi~i~>aris«iis
is pres<!iit<~d
iri Tablc 10. H<:r<-t.lic stars havc
I>c<:iior<lcr~<l
fc~lloiviiigt,lic iiiii~il,c!rsin Type \'I (first <:oliiinii).Iii t,lic se<:oiidcoliiriiii
tli(3 i<lciitifi<:atioiiof tb<>st,ars is givcii as it is in<licat<!<l
b;- tlic~iiaiiic. Tiiis is f<~llowc~i
in tlie iirst roiiiniiis b)- i.lic iongitiicie aiid t,hc lat,itude for Ty11v L'I.1 (coluniiis 3 and
-1). 111 tlie iicst. coliirniis tlic <liff(!r<~ncrs
in loiigitiid<: ((:«liiiiiiis 5 2nd G) a i i ~ llat,itiidc
(<:oliiniiis7 aii<l 8 ) l>ctn-<-<.n
ttic valiics talccn froiii thc catalogiic of Sy<:lio ßralic aiid
\'I_ as 13-cll as tlic <iiff<.r<:n<:c
l~ctxvcciit.ti<:~riliicsfroi~ithc catalogiirs I>' Tyclio and
Ptolciriy: arc pr<iscni.(!<i.
First. ivr d<-riicfi-oiii ?al>lr 10 t,li<i'triic' cpocli of Johii of Loncloii's si.ars list aiid of
tlic 1't.olcrnaic cat,iilogue. By 'triir' \\-Cirieiii tlic cporli for ivliidi tlic star posit,ioiis in
tlic: tablc ;igr~c<i
ivith thosc iri tlic sky ox:crli<:a~i.Siiicc it is ~>r<!siirnc<l
:hat t,lie data
coii<:<~riic~l
ii-<,re«I>iaiii<~l
1 ) ol>scrvabiori
~
a m«d<im rat.? of pi-t:ccssioii of a1)oiit 1' iii
12 j-cars caii l>ciisc<l for tliis piirIjoso.
Tlic ineaii iriliic: «f tlic <liffcrciicchrtivi.<iciitlic loiigiiiidcs of Tyciio aiid Pt.«lciny
i.li<!iiiiiciic:at.cs a triie el~ocliof ilic lattt>r of .$D 55 i 5 ycars. 'This rcsiilt <:oiifirins thc
71-rll-liiroi~iianil>iguity of Pi.olniny's cataiogiic: tlie data. do iiot c,orrcspoiid to ttic rtval
sky aroiiiicl .\D 137: tti<i c1a.t~:iiicntioiitid in tiic Ptoleiiiaic: catalogi~o.~"
This nicari
tliat citlicr a sj-steinat,ic error aI>»iit 1.2' was introdii<:cd iii tlio observat,ioiis, or bliat.
Piolciny <li<liiot iiiadc tlic obscr~-ationsliiinsclf arid intro<lii<:edaii crr«r in <:orrccting
aii cxistirig tabl<i for ~>rc:ccssioii.
Tlic r(:siilts For tli<, data iri Type VI.l poirii. t o a siiiiiliir ainbigiiity. Coinl~ariiigtli?
in<>aiivalii<,sof tiic Ioiigit~idcs«f Tyclio aiid Typc
ivc find a trtic epoch of Type \'I
«f .%D I l l G i 15 ycars. S h c clata in Jolin of Londoii's strir- t,ablc do t~liercforciiot
(:orr<~slooii<l
to tlic rcal SI<?-aroiind AD 1246. :lgaiii tliis ni<>aiistliat <iit,lrert,licrc is
-
A Closc Look at txvo r\st,rolai>csarid tli<.ir Star Tal>lcs
193
a systemati<: crror of about, 1.3' caiisc!ci hy ihc ol>scr\-atioiiiii~~th«<i
iiscd Ijy Johii of
L«ii<Ioii or tliai. 11<: <li<iii»r inadc tlic «bscrlr?t~ioiishiriisclf.
T h r iicvcr cnding <Icb:i.te oii t,he origiii of tlic Pt,olcmai<:caialoguc shoms Iiow difficiilt
i t is t o at1jiidicat.c: bctsi:<:cri t11c t,\vo possihilitics. >lorcovrr; in tlic casc of JoIiii «E
1,ondori t,hc!re is a n additi«rial f~roblciii.111 or<lcr t o a~>prcciat<.
it; oiic llas t o rcalizc
that, iii ari ol>scrr*itioiial coiit,cst ttie standarci dei:iai.ion «f a s<it of data rcflccts i,li<.
iiii<:eri.aiiity iri thc iiieasiirc!iricrii of an indivi<iiial star. Its vaiiic is t.li<!rcfor<:closcl!rclat,cd t o t,lic a.<:<:iira(:yof t,lie scal<?sof t,lic iristriiiiiciit iiscd for tlie ol>scrvatioiis.
Tlicrr is iio rcasoii t o siil>pose tliat iii ari aniiillary sptierc. t,lle scale for ih<: cir<:lc
aloiig 1i41icli tlic I«iigit~ii<ic
is nieasurc!d is tiiffcroiitly diri(1ctl froni tliat for mc!;isiiriiig
the lat,it,i~dc."~
Tlicrcf«rc; thc st;iii<iard d<,i-iati«risof a sct of obst:r\:ati«ns ob:,ainr<i
hy aii armillar:- sl>lic!rc slioiil<l bc iiiore or lcss cqual iii l>«tli <:oordiiiat<~s.
Tliis is
iiid(i<dtlic case fov i.iie rlata froiii itic Pt.olcrnai<:catalogiie (<:oriiparcTahlc, 10. coliirris
6 and 8 ) . Tlic valiic of ahoiit 0.5" iriorcwvcr agrecs ii-dl T\-itli n scale <ii\-id<.<i
iiiro
\vholr <icgrcrs. Hovr-evrr, i,ti<x(lata froiri Typc V1 <lo iiot agrcc mitli oiic aiiotticr. T1ir
st,aiidard dcviation iri I«iigitii<iccx<:ecdsiirorc thaii twicr tliat in latitiicie. This is 11ot,
i o hc cspccted for st,ars «i>si:r\-?<Iivitli aii arrriillary sphnre. I t appcars as if <~si><l<:ially
tlic! d a t a iri loiigii.ii<lc(io iiot rrprcscnt a <lirc<:tol>scrvatiorialrr<:or<l.Tliis <:«iicliisioiiis
iiiicicrliric<i1' ;iii«tlicr fc!atiir<!of tlie star list: of tlic 1 0 loiigitii<lcs:35 arc <sxprcsse<l
iri
ivtiolz clcgrecs, a s integcr iiiirril>rrs.ari<I3 iii a. fra<:ti«iiof a <Icgrc~e.Hcrc to»: tlic data of
tlic latit,iidos arc iiior<-iii liiic 1%-itlisii(:li as oiic ii-«iil<l~ s p e c froiii
t
<iire<:t.ol>scrviiriorial
rccords: thosc of 17 stars arc <~sprrssc<i
iii i~liolcdcgrc~csaiicl t,lic rciiiaiii<lcr is fairly
ivcll distribiit(;cl ovrr tlic X-ariousfiactioris of a dcgr<!(~."'111 otiicr n-orcis; tiic! T-aliics
of thc latitii<lcs s<:(?iiito agrcc mit11 ttio Iiyl>ot.lit:sis tliat thc stars ~r1!r(?ohscrrc~ln-itli
an aririillary splicrr biit tlie valiies of tlit: lorigitiidcs 1:crtaiiily <lo ii»t. .ililioiigli it is
diffic:iilt t,o say n-liai. exactly tliis coiicliisioii iinplic:s: we c;tii tliirik of at Icasf. t,lir(:c
cIist.iii<:t.esy>laiiati»ris tliat. <:oiil<laccoiiiit for it..
S h c first ~>ossil>ilitv
is tlrai t,lic star ]>ositioris iii Type V1 a r r iiidr<s<lbaso<l oii
obscrvat,ioiis iiiadr 11y Jolin of L»ii<loii iii 1216 hiit t,lia.t iii tlie proccss of transmissi(111
t,lie clata in Typ<!V1 liax-c hc<:ri corriil>te<ljan<itliat iii ]>articiilar tlic fia<:tions of th(*
(icgrcics of thc .inliics of i,li<.loiigitii<i(?sivcrc los:.. lT:<? (10 iiot favor tliis (:x]>laiiatioii.
<:oiisicicriiigtllat a siinilar corriipi.ioii slioiild llavc like\\-isc afk:<:i,cdtlic! fractioiis of tli?
clcgrces «f tli(! valiics of t.lic lat ii.ii<lcs.
Anot,li<:rcxplariation coiild b r tliat tlii. data iri ilic t.al>lcivcrc copicd froiii aii asir«lab(,: a iri~~ilio<i
for oi>iairiiiig iiei?- daia tti;it secins t « have hreri qiiit(: l>ol>iilariii
Ilic Mi<i<llc.:\gc:s."'
Tlin fact t.liat t.lic list is os~>rcssc<i
iii <3clip:.ic<:«ordiriat,cs is iii
it,sc>lfiiot an ol>,j(,<:t,ioii
t o tliis Ii>-l>otlic:sis.=\iii«ng t , h ~lat.itii<leplat,os of ;in astrolabc
60 For a <lisciissioiiol aii ai-iiii1l;ii.y spiirvr <liiiing llic i i i i i ~o( :\Iioiisits X. sCr Soi iiistail~r.Soll<'
( l W 2 ) p1>.?6 35.
($1 :\ri,ang liic raiiirs oTl,Iir l'tolririaic lc~ii~irii~lrs
oFiiie 10 siais i i i 'lypc \,.I. l i i < ~ iaic
r i cn~~irsir<l
in
i\-liol<!
<i<:gr<~cs.
12 iiai-c a Fiaclion oi $0'.arid i.hr remi~iii<lri
in <iivi<lr<l
ovcr llir otliri- lrarli<>i?s:
Lkw
JJtol<imai<:
liil.ilii<l<,s
s11nw ;an cwii I>rll.rrdisli-ihiilioii: I5 viiiiics ai-C.cpl-rsscd i i i wiioic <icgrecs.
aiid llic rciiiaiii<l<,s is ciisl iibiit<<<lci-ciiiy ovcr tlir ol.ii<!r Iracti<iiis.I b r ii coni]>i<!lc<lis<iissioi,OS
ilir <lis,.i-ii>iitioii l i w l~.c<~iiriirirs
OS tlic h.a<:lions of < I c ~ , ~ c c i ~ liflr I't<li<>iiiaic
<-:il.;iiot;iic ;is ;i
~ilioir.s r r <;rasslioii(1990) pi>. I56 7.'+.
C2 'l'liis possibilily was niipa<iyiiiciil.iiiii<~<i
i i i l<iiirilzs<li (l9861i) 1,. 5%
t,licrc «ft,cii is f»iind one, for a latitiidc of 66". This so-callcd 'plat,c of tlic scalc of t,he
spidcr', \ras a platc 1%-it,hcclcstial longitudrs arid lat,it.iidcs ivliicli \ras aii iinportant,
ai<i iri tlic <:onst,ructioiiof thc star map." Vice tiema it cari he iiscd t,o read off thc
posit,ioiiai dat,a of t,lic stars iii eclipt,i<:longitiidc an<$Iatitiidr. Rcadiiig data from aii
astrola.b<*in this way- <:ariaccoiint for a differonc<biii thc stanciard cleviatioiis Lc<:aiise
th<-parallels t,o tlie c<:lipti<:ai-c iisiially drawii ci<>ry2' or 3' ivlicrms tlir circ1c;s of
latitii<ic (the inrridiaiis t,liroiigh t,lic ccliptic pol<.) ar<:di-aivri oiilj- oocry 5" or Go. For
iiistriiirit~nt,sof t,lic size of tlic great Sloaiic astr«lah<:a 'platc of thc sc:alc! of t,tic spidrr'
<:aii hai-e pai-allels to tli? ecliptic draivti cvt!ry lo an<i circlos of latitiide erory 2". It
is iiot. difficiilt. to imagiiie that. in a list of data ac<jiiircd froiii ari iristriiinent iii t,his
may. i?..lielorigitii~iesi v ~ r crriorc oft,en than riot csprcsse0 in wholc dc:gi-ees. Orie caii
also iriiagirie tliat oncc such a list ivas obt,aiiicd t,lie ii<:cd ~ 3 - fclt
a ~ to vcrify tlir <lat,a
in it. This i;c!rific:at,ion iria:: liaic beeil carricd oiit witlioiit affc<:tirigtha tablc a t all.
Th<,last arid i~iostplaiisihlr possihilit,y is that t,hc list it-ith tlie origiiial ohscri-at,ioiial
rr<:or<lswas part of t,lie saino iiiikiiown Arahic s<iiir<:ras frorii ivhicb t,lic naincs \wre
cxt,ract.od.Siii<:ct,hc stars iii S y p c \'I refiect t,lit! s k - aroiind riD 11501onc! <:ansiil~posc
that i h r star tablc ii-as ohseri-cd by aii Islainic astroiioiiicr at t,liat t,iinc. Iii this casc
the iist of data was oiil>;izcrific<lhy Jolrn of Lon<loii,not ncmly ol>s<!r~-P<$.
Siircly sonic
sort of ohscr~~at.i»i~
m s carricd out. 111 a letter to a stii<iciit.lic \%?rote
rs]>licit.ly t,liat
lir iiiinsclf 1-erified t,tic star list mitli t,be armillary ~ ~ l i c r e .Fiom
~ ' l tlie lcttcr it. is also
clcar t,hat I><%Iiad rcad a niirnbm of autiiors oii tlic problcm of preccssion: ariiong
T%-lioiri
al-Battärii aiid Thabit ibri Qurra, \vIios<itlicories of ~>rcccssionlie r<:jc<:tcd.
Iristeaci Iic ac:<:cptndthat siiicr t,he days of Ptolcmy the lorigitiidcs of thc st,ars liad
incrrasccl Ly aboiit 1.6" aird siiicc t,lic days of Hippar<:tiiis by 19'. Diit tie dicl iiot
c:alc:iilatc a rirtc of pr<~ccssion:rior did iie disc:riss a precossioii tlieory of liis oii-ii. Aiid
iri qiiotiiig tlic abovc riiinit>crslie <:crt,ainlydid not show aiiy amarcricss of t,hc sort of
prc<:isioii ri(,ccssarj- to carry oiit ail obsci-vat,ional jolj. His 'ucrificatiori' m q csplaiii
t.li<idiffcr<!iit patteriis «I>scrl-<:diii tlre loiigitii<icsan<l latitii(1es iii liis taljlr. Hc i i i q
liarc lcft. thc lat,itiides of tlir origiiial tablc: alone - - lic kiic~vof i:oiirs? ttiat thcsc: ivoiild
not liavt, cliaiigcd - and hc may liase chaiigcci tlir origiiial lorigitii<lcs to ualiics more
appropriate to his o i m liking. If so: tlic re.sult is not re>tlly oiitst,atiding even for a
nicdici-al ast.r<~rioincr:
and as siicb it is reassuring. Hon.rv<:r,if m<iii-arit to esplain the
raIri<~s»f t,lie sbaiiciard dci-i;rti»iis of tlie data iii tlic star tat~lc,it niust bc! assiiin<d
that .Joliii of Loii(loii ern1)lo)-ed a rougli sort. of roiiiidiiig-off-prii<:t,icc!t,liat csceedc<i
the st:alc «f liis iristriiiiieiit.
Ui. <lo not thiiik tliat. a t prrsrnt it is ]>ossil>lcto ciecidc, t,hc iriat.t,cr of thc origiii of
:Typ<?VI. It, ii-ould t,licreforc bc! riglit to I<ecpaii o~jeiimiiid for altcrnatii-C:csplaiiat,ions.
Oir<:da' a soiirct?: a tcist or aii ast.rolal)r, iriay tiirii iip tliat <:anaccount iiaturally for
Llic ]>r«l~iciiis
licre <icscribr<l.
siii C = (1 - 1 ) / ( 1 + X). If n-<iappl3- ttiis csprcssioii for r to tlio tmo astrolabcis rr-e
25.4' f«r S1:ILIAST0570 aiid r .: 2-1.7' for B1,I SL. 54.
iial-r <isamiiic<l:\\-C fiiici t
Tlicsc 1-alii<:sarc ii«t acct:~>tai>lc.
Iri <!arl>trcatises oii tlic! consti-iictioii of t.hc ast,rolahc
a valiic «f 21" is inentioiio<l. 'l'hc Ptolcriiiai<: X-aliieof 23' 51' does iiot deviatc niiich
froin tliis \-aliio. Latrr iiiaI<crs inay Iiavc iise<l a. ~ - a I u rof 23.5'; r<ifIrc:t~iiig
tlic valiie
«C 23" 33' applicci I>? Islairiic ast.r»noriicrs. 'I'lic a1)ovt: vtxliic-s for tlic tn-o ast,rolabcs
clrarly <ioriot coiiic c l o c 10 (!itli(:i 23.5' or 21'. Tq,.r tlicrcfore Irtivr woi.lx5doiit airotli<:r
may of firi(lirig t,lic [ ~ a r a i r i < ~ t < ~ aiicl
r s 6.
Let thc poirits P„ (11.= 1: . . . . 12) ii1dira.t~tlic I>cginiiiiigs of t.lir sigiis oii thc c!clil>t,ic
riiig of aii astrol;il>c for wliicli tlie racliiis «f tlic c<jiiator is R,. Thiis Pi is tlic, first
p«iiit of .\rics; fi tliat of Taiiriis, etc. Lct R„ h c tlir dist,ai~c:c:t o tlic centre of t,hr
l>oii?l I:,. If its iiic<liai.i«ir is / L „ aiid its <Ic!cliiiatioii 6„ \V<. hal-c: /L„ = 30(iz - 1):
siii 6„= siii ji,, siii r aii<l X„ = I?, taii [(90 - 6„)/2].
Lsiiig tliosc esprcssioris a7c c-alciilatc<it.li<.<lc<:liriatioiis6„i «E t lici points I:, aft,cr
c:lio»sirig aii arhitraq- x-aliic for r ; saj- C , . Shcii ivc <Ictcirir~iiic:<l
for rach riicasiirc<l ~:aliic
X,, (lisicd iii Tal>ic A l ) a T-aiiic~ >tlic
i raciiiis «C tiii? i,cfiiator I?„, . Siiiis r ~ Iiavc
i ~
',
siii h , , ~= siii / i n siii C , = siii [30(7>- I)] siri r i
X„,
E
X,,
/ tari [(90 - 6-1 )/2]
S m t \Te ~I~t<?riiiii>e
<R,>; Ihc rncan \aliic of thc scrics X„: . . . Rd2. T \ < .also
ralciilat,c<ltlr<>staiidard < l < ~ i a t i oof
i i tlic? scrics. Tlrcs<~<:al<:iilat.ioiisivcrc rcpea.t,<:df»r
iiv<-~-aliicsof F. T h e resiilts fos I>otliastrolabcs arc gi\-(in iii Table .:I2 M o n - . It. tiiriir<i
oiit tliiit tli<. racliiis is iiot i-er' sciisitii-C:to thc cli«i<:<<
»f the I-alii<:of C. Tlic radiiis
«F t,h? c<luat.or c:ari tliiis b r coirsidcre<l as fiscd. Oiir also iiotes tliat thc, st,aii<lard
(ic~iatioiiis ri~iiiirrial\\.hcii r is ccjual ii)24". Th(?rcfor<!\v\;cc«ii<:liide t,liat tliis 1-aliic
\r-as nrost prol>ably iisc:d iii inakiiig tlic iiis:riirri<~iit,.
Iii orcler 1.0 coiifirrii tliis Iattcr <:oiiclusioii~i:cliax-ecal<:iilai:<:<l
D„l>ywliicli n-c iii<li<:ato
tlit, tlicorcti<:al 7-aliie of 1:lir clistaii<:r t o tlie cciitrc of t.li<x poirit P„ n:liicli caii l>c!
<~s1>rctc<i
if tlic raciiiis of tlie cqiiat,«r is crjiial t,o <R,>:aiid tlic ohli(iiiit,>-of tlic
cc1il)t.i~is f 1 . T\-<? in\-?
siii
= siii / I „ siii C I = siii [30(71, - I)] siri f~
I c s t . \W iravc d<,t<~ririi»cd
ttir cliifcrc?ii(:<:sAR.„ = R„ - D,, aiid ailciilat.c<it,iic niraii
T-aliic<AR> aii<lthc stari<lard <ir\:iatioi~.Tlic rcsiilts arc! also sho~~:i;i>
in Tahl<!.42 for
five valiit7s of C. t<>r l>ot,liiristriiiiic!rii.s the rneaii valiic a.ii<it tic st,aii<iar<l<i<n:iatioiiarc
agairi rriiiiiiiial ii-lieii t is ciciiial t,o 24'. 3'his coiifiriiis tlrc ai>o\-ccoiicliisiori that ttic
riiakcr iiscd a ~ a l i i cof 24' iri coiistriicting tlic rctc of t,lic astrolab<:.
.AIt.cri~ativclyons cari <:alciiiat.ot h c inran \-alilc of r froiii ttic nirasurcd valiir.s X.„
oiic:c t,lici mcair valiir of tlic radiiis «f t,liri cqiiat,or: <X,>:is lirio\\:ii. Csing tlic esprtissioii 6„ = 90 - 2 arctaii (12„/<R,>) oiie firids for <:acli 1-aliieof n (cscluding 71, = 1 and
= 7 ) a raluc F,, fsoin ttic relatioii C,, = arcsiii [sin 6,/ siii 30(n - I)]. Tlif: obliqiiit,y
of tlia ccli~>ti<:
is siil>sc<jiieiit,lyfoiiiid l>ytlic, inran 1-aiuc of F,, . R > r SL.111AST0570 n-C
A Closc Look al.171.0 Astrolabes aiid tlieir Si;r T a h l ~ s
197
foiirid thiis a nieaii valiic: for tlio ohliqiiity of blic ecliptic: of 23.9' I 0 . Y ;~iiiifor B11
SL. 54 a inwiri X-aliicof 24.1" 0.3'. Tlies(>data coiifiriri tlie earlicr roiiclusioii t.liat
for both iiist~ruiiiriitsa. T-aliicfor thc ol>liqiiity of 24" ii-2,s iiise<l.
+
Tahlc -41: Disi;aiiccs fi-orri tlic ccintrc of thc astrolaI,t! of tlic first poiiits of thc sigris.
* ;\I1
ciist,aiiccs are iri miii
Tal>le A2: <R,> aiid < A ß > aiid tlirir staiidard dcviations for diifcrcrit valiies of r .
SM11 .4STO5iO
B1.I SI... 5-1
DCI<KI?R:
E. (1992): 'OE .4st,r0lal)e~ aiid Dates arid Dcad Eiicis'. Essaj- rci-i(:i\- iri
An7,nls of .Scien,ce 49 (1992) PI>.17>18?.
Dci<r<i:n, E. (1995); '.411 Ciirci(:or<ictiSicdiclai Ast.roIabc (Jiii~<iraiit.C:. 1300'; Annnl.9
of Scierrce 52 (1995) 1111. 1 1 7 .
D E R J (1931); 'Hcriiianiiiis Coiitra(:tiis iiber (las Ast.r«lah', I ~ i sI6 (1931)
PP.2 0 0 in.
Fozi'i.:';; l\l/oxsrc~iii](l897.:8): 'Lc iriailuscript dc Jcaii <lc L«ri<lres', B7rlietiri ilc
l'A!:ndin,ie des Sciences, Iri~cri1117o~1,~
ef ßelle.3-Leltrei. de To7ilozlse: i (Toiiloiisc.
ISST-~8)PI>. 146--60.
C,I\(.I..IIICII;
...
0. (1987)_ .Zooinor]>iiir astrolabcs aiid tlic iiitrodiiction of i\ral>i<:star
iianic!s into Eilrop<:', iii Fmn1 Dejem:n,t to Eq7rnn.t: o 7jol7rrr!,r of sturiies in llte hislory
of scien,ce in the An,cie71,t nnrl Medievnl Neur East in Iiorror of E. S. Ken,nu?dy,
cditcd I>? D. I\. King arid G. Saliba, Armals of thc i\relr; Ibrk Acode7n,?l of Scien,ce
,500 (1981).
Gii!~siioi:i:~G . (1990); T11e Hi.ston~of Ptolem!~'.~
star cotfilo,gne, (Tcm Yor>rl<>
Urriiii;
1990).
Gi:s,riii:ic, R . T. (1923); Eorly Science in 0:zfolrl: (Osford, 1923) \.ol. 1.
G r : s r i l E i i ~R.. T . (1929): C/~fiu.ceranfl A$'f:s.sfiiiull(i. on tlir Astrolnbe, (Osford. 1929)
Tliis \vas piiblistic<l as T-ol.2 of R. T . Giiiitlicr; Enrlq Scier~cein Orfold.
G i : s ~ i i ~ : i iR..
. T. (1932); 7'1ie Astrolobes of tlic T'Vorld; (Oxforfi; 1932). R.cl>rinted in
Loiidoii iri 1976.
ICisc: D. .%. (1991). "\I<!<lic\-alastroii~;i~iical
iiistriiiiicnts. 4 <:al.alogiicin pr<!parat,i»ii':
B7illetin of illre Sci(~~tlJic
Ir!.strt~ni,f~7it
Socicty 31 (1991) pl>.3 ~ 7 .
ICis<:. D. A. (1999): 'Bririgiiig- Istrorioriril::al 111struiiicrit.sBal::k t,o Earth -- Tlic Gcograpliical Data oii klccii<!r-ai ;lstrolal>cs (i.o ca. 1100)': iii Between Ilern,on.stmtion,
ri7id Ininqinutior~,.E.ssa?j.s i?i the Ifi.sto?.y of Science n?i<lPlrilo.sopln?l, Presented to
.l«hri North; cl:lir~cl:l!)I I.o<li Saiil a iiii<l :\sjo \~aii<ll:?rjagi:
(Lei<lcii; 1999) PI>.3-S!.
ICr:sil-zscii, P. (1959). Arri.bisr:lie Sier~lnrirnen.i11 fii71,ropo~
(\Vicshadcir; 1939).
I S : I I . P . (1961). -Das Fisst.nrn\-c~rzcicti11is
iii fl<br .'Persisclicii Syiit,asis" dcs
Grorg-ios Ctirys~>l<okli<~s:
13:i/:(~i1l,inischeZeitschrift 57 (1961) 111'. 382---411.Rc:printcd
in Paul 1iiiiiil.zscli. Thp A ~ r i (17rd
s
tlie stnrs (V:irioririn Rc11riiits: Colle<:tcdstiidics
scsics CS30i. i o s i i a i i i ~ ~ : o i 1989):
i,
cha.pter IJ.
I : S I S I P . (19(%). Plpen non Stern;~ierzeic/ini.ssen 172 o~tl~r~.orn,i.s~hen
Hmdsi:l~,riftcndf?.~
Z P R T A ~ ~ 1)i.s
? ~ ! ~~iiem<!I!,riten
.J<~hrli.un.(lerti;
(\f;i<!sbadcn. 1966).
Iii-SI-iis<,ii.
I". (1970). "Abii XIa'Sar, Johaiin<:s IIisi>alc,iisis iiild .\ll;aincliiz', Zeitsch7.ifL de? Dr?it.sc/ier~,I/lo~:qf?r~liindi.vcI~~cn
Gesel1,sr:linft 1211 (1970) pp. 303-23. R.c~>riiitl:~l:i
iri Paiil Iiutiitzs<:li; Tlie Ar(1b.s nnd thf? stfirs (Varioriiiii R.cpriiits: C«llc<:t,cd
stii<licss~isicsCS307, iorthat~iptori,1989); c:liapt<:r S1;II.
I<i:si.rzscri; J'. (198O); ''~\\;cJ St.iir 'I'ables froril k1iisliiri Sl~ain':Journnl for t l ~H
i i~tory
of A ~ ~ r o i i ~ 11
o ~(1980)
n ? ~ ]>L>.
192.-201. Rc:pri~itcl:liii I'aiil Jiiii~itzs<:h~
Tlic Ambr nn,d
the stnr.s (\>rioriirii Rr.priiits., Collcc:t.cd stu<iiessrrics CS307, T«rt.liariiptori, 1989):
<:l~aplcrI\;.
Iii;sil-~scri:P . (1981), 'On tlic .Aiitlicrilicity of tlie %<vitisc on the Coriipositiori aiid
Csc of tlic .%st~rolal>l::
ascrib<?clto kIessalialla': Ar(:liioes Iri.2er?anLion.alesd'Hisioire
df?s Scier~cer31 (1981) pl>.-1i262. Rcpriiit,c<l iii Paul Kiiiiii:~s<:ii~T l ~ eAlubs and
t h stnr-r. (Varioriim Rrl>riiits, C:ollected stii<iicsscric3sCS307; Sc~rtlian~pton,
1989):
c:liaptcr X.
1ii:zii-zs<:ii, P . (1986a): "3ar Catalogucs aiici Star Tahlcs iii Yi<?cliacralOrieiit,al aii<l
Eiirol>caii Astr01ioiii)-', Indian. .Io?~rrlnlof Historll of Scierice 21 (1986) pp. 1 1 3 ~ ~ ~
22. R.cpriiirccl in Paiil I<iiiiitzsch, TIi,e ilr1ib.s a7rfl tlie stnm (\~a'auioriririRepriiits,
Collect<:cistiidics scries CS307, So~.tlianipt.ori,1989); <:tiapt<:rJ.
J<i:~i-I-ZSCI~.
P. (19861,): '.Jolin of Loiidoii and his ii~il<ii«\r-ri
Aral>i<:soiircc2~
.Jotrrn,c~l
for tlie H2stol.y of Astrono7i~?y17 (1986) 111,. 31-57. Rcl>riiitl:?din Paiil J<unitzs<:li,TIic
A m b ~find tlic stnrs (Varioriitii Reprints; C«lle<:t,e<lstiil:lies s c r i c CS307, Sorthaiiil>t o ~ i ;19S9); ciiapter S S I .
Iil.:SI'i-zS<:ir~P . (1986f:): 'Tlic Star Cal.alogiic <:«ninioiil~-appeiidcd to t,hc .Ilfonsiiic:
Tablcs', .Jonrn,al jor the History of Astron.orri?l 17 (1986) pp. 89--98. Ropririt<?diri
:
I
Clos<,I.ooh a.t in-o Ast,rolabes arid their Star Tahles
199
I'aiil I<i~iiitzscli:Tize A7.i~b.s nnd the sti~rs(Varioriii~iR,cprint,s; Collectcd stiidies
scrics CS30i; Sortliariipt~c~ri,
1989); chaptcr XXII.
I<L\-rrzs<:ii, P . (1991): C ~ ~ Z L <Pto1emitr.s:
~ ~ I L S Der Sternkatalog des Al7~~agest.
Die
ami>.z.sr:l~-mittelnlterlici~e
T?-i~rlitiun~:
7iol. 3. Ge.samtkon,kord<~~i,z
der Ster~zi;oordi7rnte7r;
(WicsBa<lcri, 1991).
I<i:si?.zsc:ii. I'. (1993); 'Ziir Problcinatik dcr .i\strolabst.criic: Eiiic x:citcrc> ii~ihraiiclibare Stcsiit.af~:l',ArclLioesI~i,tern,atio~2ales
d 'Histaix de.9 Sciencea 43 (1993) pp. 197-~
208.
I<rixirzi;cii: P. (1998), 'Traccs of a t~~!~~tli-~:erit~iir~Spai3isli-.L\rahic .5strolabc', Zeit~ c h l l f fir
l Geschici~teder nrabi.sch-islarni.~clie7>Wi.s.selirchaften, 12 (1998) pp. 113
20.
I<iix~'rzs<.:i~:
P.: ünd DCKKEII: 33. (1996); 'The, stars o i ~the rctc of t,lie so-cdlr<i
"Caroliiigiaii ast,volahc?", iii ßnm Bagdad to Barcelona. Sttrdies in tlre I.sli~m,icEmct
Scien,ces i71 110not1.r of Prof. .Jn.an Ve~net;cdit,<i<lby Josep Casullcras arid .Jiili«
Sains6, llnunri de Ii.loiogiia (Cnii-crsit;it, dc Barcelona) XIX (1996) \i>l.IIj 65.5 7 2 .
Planisphcric .kst,rola.b<:(1976): TIx Plnn~i~spizeric
Astrvlnbe, Greenwich, Sational Uarit,imc >Iiiseiiin 1976.
Zor:i-E;; F. (1922); Die Armillnr.sphür<:,(Erlaiigcii; 1922).
Por:r,r,~<~
E. (1956); 'P<iiit.-oridat,cr I<:s ast,rolabes rnr<liCi.aiis?', Retitre de l;Fli.stoirf?
des Scie7rces et lel~rnq~plicationi.9 (1956) p11. 301--22.
Poiii,i,c; E. (1964): 'Rcrriar<l dc Vcrdiiri ct Ic tiir<juct': Isis 59 (196.1) 1>~>.200-203.
S i i r ~ r :I&'..L (1872); A treatisc on tiie astrolnbe; nddreiseil to hi.5 .Ton Loui?).? by
Geoffreg C11,ascer. A. D. 1391; (Loiidon, 1872). Reprintcd in .Anist,ordarn iii 1978.
ST.<;\~XZ~
B. (1997); Uriterit~ch7~n,gen
tion n~athe7naticci1,-c~stro71i17~l~i~scil.e7l~
Dnwtelhr?~gen auf 7nittelalteriiciir.n Astriilnbiei~z.slarnircii,er un,d e7iropäiscAer Hiillr~~,~tft:
(Bassurii, 1997).
Trionxnii<c; L. ( 1 9 4 j 6 ) ; 'Frarico (ic Pol«nia and the tiir(jiirt'; IFls 36 (1961) ]>P.6 7.
Tononi:, R. I<. E. (1989): '.L\ ii~at.h<~mat.ical
syst,cin for iiicnt,ifyir~gtlir stars »E aii
astrolaLc aiid fiirtiing it,s age', ,4strolr~bica5 (1989) 1117. .53~-76.
\Vi:i3si'cn; R.:
aii<lT%,-i:nc.i.i-ii,11. (1998), W?.sterii. A.strulahcs: (Cliicago: 1998).
.\ Closr Look at t\\-o -\st,roiai>esand tlieir St,u Tabirs
201
TaI11c 1. Star table of tlie in<:clicval astrolabe N?.ll1 :lST05iO
Xamc
Sigii
Idciitificat ioii
:I'.Yl.-\SC.AITOZ
-\I.GOS
Ari
Ta.11
Taii
Geiii
Gen1
Gern
Cric
ciic
Cnc:
Lco
Lco
Lco
Leo
Kr
Lih
Lib
I.ih
s<:o
CF{.
Per
Ta11
.A11r
Ori
Ori
Clla
Clli
LX4a
Gern
tiya
Lco
Clla
Crv
Vir
Clla
Uoo
Ci-B
Sc0
Cer
S<:o
01>1i
Lyr
AriI
Cyg
Caj'
»(.I
I'cg
Pcg
Cas
Ccr
.AI.,DF;T..AR..X
:iLH.&IOC:
:RIGI?I.:
.ALGESIE
:.AI.H.ABOR.:
.ALGO>~IEIZ.A:
EGGEZ:
:\LDI
:ALF.&RD:
COR.
ALR\,.C.VB
:ALGL.AII,I:
:.ALCHI\IEC:
BEXES:I:
ALR.A\IEC
E1.FEC.A
ALIELIL
positioii
:C:\LBALAGII.-\:
ALH.Ai,'XI
:V\;EG:\:
AI-T:III<
:\l,I?.lF:
:LIBEDESEB:
DELFIS
'\I.FEII -4%
H\-YIER" E<J:
j>«sitiorr
:DESEBC.AITOZ:
*
i
Sc0
Sc0
Sgr
Ca[>
Ca!>
Cap
Ac1r
.k*r
Psc
Psc
Psc:
a
n
3
ri
n
o
,.
(Y
(1
0
fi
7,
n
11
n
a
3
<i
n
Cr
n
ru
o
6
f
3
;?
;i
I
t
i
i
J
i
-~
:i
i
J
Tllc <:alciilaiioii of tli<, <iocliiiar.i«ilis based oii a ~ a l i i cc>ftlic raciiiis «f tlic, eqiiat,or
of 11.7 rnril.
Tlic i~iiixihrrsarc iliosc »F T:-j>c XI.
Sec th<: notc follon-iiig iliis tabI<-.
T y j x XI is kiioiri~in ti\-o vcrsioils, brrc rcf?ruc(i to as XI.1 aiirl X1.2. Iii oiic of i,hcsr_
11.1: IIi? d<!<:liiiatioiiof a star is given indirectly iii two diff<lroi~tways ~~lii<:li
a1~:
clistiiigiiislic<l as I I . l a ('altitlid«') and a s X.ib (tlic iii(iri<liai~
alr.it.ii<icfor Paris). S h o
-4 Cl«sc 1.ook n t t i ~ os t r o l a l ~ c sa.n<itiirir Star Tablcs
203
corrcsporiding x?iliics of ilic! <ic<:iirial.i«iihacc becii listcd iii T a l i l ~5 Thc: riotcs arc
arrangcd t o the 110s. of coliiiiiri 1.
Thc inc<iiation a$cC.s 11cttcr tviiii the valiic iir XI. 1 (Tau 7') tlian timt in
X1.2 (Taii 10°). Iiiiiiitzscli idciit,iiies this star as <.I Per. Tlic clioicc of J I'cr
is jiistifiecl oii pagc 181 1 8 2 .
S c . 9: R.cc:riitly Kiiriitzsc:li Iias coiicliidcd (privat,c coininiiiiicatioii: Icttcs of 23 Jiilp
1999) tliat tlic iiarii<:'cgrcgci' aiicl its i-ariat,ioiis iiidicatr 1. C\Ia: iiot LMa.
S o . 10: Tiic: ~>«sii,ioiialclata of tllis gliost star agrcc xitli tiiosc iii XI.] arid XI.2.
.-llrcad>- iii alrc (aarliest list «f 1,Iaslaina of .%D 978 (Type Ia aricl 1.4) i hc
[>«sii.ioiiof t.tiis star is c:orriipi. T1ie iiarn? 'alciiraaii' coiil ii~iiedto cxisi iii star
tablos aiid astrolaiirs mitli tliis c:orrilptcd l>ositiori.
S o . 13: Rr~ceritlyKiiriilxsdi lias coiiiirrri<:d privat.^ <:oiiiriiiiriicai.ic)ii~
Ieticir of 27 Juiio
1999) tliat tiiti incciixtioii of tliis siar in Tppc XI: iio. 13; is riot iri \Tii-go: I>iit,
iri Lco.
S o . 16: Tlic mc<iiatioiiis ofF 11)- -1' coiiil~arcdt o bhc valiics iri XI (Li11 18'); soo T a l ~ l c5.
So. 19: Tlici ciecliiiatioii agrrcss n-il:li XI.1 (10'. I>iit it ciiff(3rs 5" ttitli tlic valiicx cIiioic<l
iii XI.2 (1.5'); scc Tal>lr S. For tlic iiIc:i~tifi<:ationof the positioii ivitii (X %r:
see l>agc 183.
So.20: Tlic dccliii;itioii ;igrccs ii-ith XI.2 (23'); l>iit it ciiffrrs 10' ivitii II.11) (3");
sce Taljlc 5.
X(>.26: I<ii~iii:zs<:licoiriparos tliis star tvit,li VIII iio. 41 arid cioos iiot iclciit,ify it. n.itii
r Dcl. H « i \ - c ~ ctliere
~ , caii b r iio cl«iil>ttliat r Del is tlic star Iicrc iiiteii<ic.ci.!]I
tlic iiairie.
S o . 28: Tlie dc<:liiiatioii agra:s ivitli XI.11) (51.5"). l ~ u tit ciiffcrs 26.5' ivith tlic x~aliic~
<liioteci iri XI.2 (25"); sc3c Tablc 5. For tlie i<icritificatioii of t,lic posii.i«ii tvitti
iJ Cas, sc!c pagc: 183.
So.2:
Fahle 2. T l i ~iongitiid<~sarid intitii<i<~s
of thc rcliahlc stars iii ' I ' j ] > d I . l h arid tiit?
;rstr«liiI.>cS\I\,i AS1'0570: aii<li.licir <liffcrc!iiccs(DT.oii aiid DLat) xi-ith respcct t o tlic
Ptolciiiaic valiifs.
Ast
iio
liodcrii
naiii<'
I
3
4
.5
6
7
8
11
12
14
1.5
16
17
18
20
21
22
23
2.1
25
27
29
C C<!t
rt Taii
<Y :111r
3 Ori
Ori
n Clia
<t ClIi
oHya
o Lco
sCrv
n Vir
71 C l l a
o n««
o CrB
n Sc« i:
o Ol>ii
c> 1,yi.
rr .-l<]I
o Cyg
& Gap
.? Pcg
i Cct,
I.«ii*
Sl.lb
Loii*
Ast
1,;it"
SI.1b
Lai*
.-ist
DLon
X .
D1,oii
.Ast
Dl.at
XI.11,
DLat,
Ast
:
1,Icaii \ - i i l i i of 22 stars
Staii<lar<l<l<!iiationof 22 stars
Error i i i ~ h iircaii
c
r-aliic,
" .4 i~iliioof r = 2.1" n7isiisccl iii thc r;il(:iilatioiis.
i: Src Ilir
i ~ o i F~~lloiviiig
<~
t iiis tal~lc.
TIic iiicriclian altiiii<i<bOS cr Taii iii I l . 1 i i lias I>e<iiirc~~la<:c<l
11)- a varia.iii
rcadiiig: 59" iiistc,a<i OS $9'. 'This <:liaiigcs tlici <iccliiiatioii 1))- 10' Sroiri 5
' ro
1.s
S o . 20: Tlic <Iccliii;itioii «f o Sc« iii I I . l i > iiiis l>r<>ii
cli;iiigc<l 11y 10' froiri --31.5" i o
-21.5".
S o . 3:
:i Closr i.ook at tx-o :istrolal>cs ;iiid tlirii. Star T~rblcs
205
Taljlc 3. Tlic! lorigitiidrs aixi lat.it,iiclcs of t,lic rcjcct,c(l stass iri Typ<: XI.lb arici tIi<:
ast,rolabc SlIkI ASTO57O. aiid tIi<,ir<iiff?reil<:c!s(DLoii aricl DI,at) xvitli rcspcct. i o t h c
Ptol<ii>iai<:
I-alri<:s.
26
28
r Dcl
.9 l'eg
L.ori*
XI.lt>
Loii*
.Ast
Lat*
XI.11)
Lat*
.Ast
DLoli
XI. 111
DI,oii
Ast
DL.at
XI.1.b
DLat
.Ast
48.9
109..5
129.1
126.0
215.9
317.1
17.7
-17.6
107.4
128.8
2 . 9
218.5
317.6
1.5.6
30.6
23.7
11.9
31.0
23.3
23.8
,503
29.3
211.3
12.6
32.0
26.0
24.9
18.9
19.2
14.0
40.8
24.3
2.6
29.4
5 .
17.9
11.9
10.3
2L2
2.2
30.0
13.5
i.6
-5.6
--21:1
4.0
21.0
-5.4
19.3
6.3
8.0
22.1
-3.0
24.7
-1.1
li.9
Sablc 4. C«m~>arisonof thc 1)ositioiis of tllc rcjcct,e!<l st,ars of Typc XI aiid Sl'IAI
.-IST0570 ivith tliosc cal<:ulatcd fi-oiri Pt,olcriiaic ialiics iising a prcccssioii correctioii
of 14" ( - - P t . l l o ) .
St.,LI -"
i
Soiircc
: 1-1"
Pt . l 1 °
S1.1a
Pt.
X1.lb
XI.2
:ist,
Pcr
:j Pcr
5 Per
!j 1 % ~
3 Prr
t.;lI?~
r
I31a
I
Pr -1-1'
Pi. . 1-1'
jr
1
C41a
H LlIa
H I-lla
H I:\la
P t .-1-1" r Dei
SI
i Dcl
Ast
F Dc1
P t - 14'
P t - 1.1"
P t . 14"
51.2
SI.It1
.:Ist
Taii 7
Taii S
Taii i
Taii T
Tao 10
Taii 6
46
38
37
17
46
1.5
110s. ciosci t,o :i! Per
pos. of a Pcr
110s. <:lost t,o a Per
I„%
of a Per
EGGEZ:
Ciic 26
Cric 24
Cnc 21
51
16
41
110s. <:osriipt
110s. c>rriipt
-13
13
13
alriicai~a
.-\LIIYC\:D
L<:o 18
1.~0 i
Li!o I T
Lco I 9
-19
iO
110s. corriipt.
i>i>%(<:«rriii>t
26
26
dclfin
DELFIS
Ca11 29
;\qr 10
.k]r 10
10
7
8
cri-oi-of 10" iii rritbd.
crror of 10' iii i~ie<l.
ali<.lis
;\LIELII.
S<:o
Sc0
Sco
S<:o
liiiiri<:riis cqiii
Iiuiiierns cqiii
H\;?IER"EO:
Psc 3
I'sc 20
Psc I 9
I'sc 18
I's<: 17
PS<: 16
3
1.
Pt. - 1-1"
Pt 1.1'
SI
;Ist
D?<.
i r P<!r
Pt - l l "
SI
:ist,
XI
.Ast,
41a(I
Sainc
I
Sc«
Scr
:'? Sc0
i, Sc0
2
2
2
2
algoii
algoii
algoii
LGOS
9
9
cgrcgcz
;j
ii
:j
19
19
II'<?g
(1 .-iii(I
.j Cas
I'i:g
I'<.<i
0
.? I'CE
j:
'j
28
28
28
21
IT
Ii
I/
Coinm<iii:
--
.ii,
-li
10
10 110s. of <r Cer
10 po% <r Scr
23
21
S4
2:
52
iO
110s. <:losi?to o :iii<l
110s. cios<!t,« 3 C a
710s. closc. to d Cas
i Tlie i<lci~tiii<:atioii
Iistcd 1i1.r~f«r ttin ast,rolal~<.
aiiil T y > cS I is I>as<?<l
on tlic iiaiii<:.
.A C:los(, Look al. li\.o .Astrolabes aiicl thrir Star Bbles
207
Ta.blr 5. Coiriparisoii of ttic i>ositioiialdata of thc stars of Typrs 111: XI: aiid 11;.
Type nos.
111 XI I\'
C'<!t
:'? Pc:r
rr Ta11
i
Cct
(1 A11r
1' Ori
n Ori
o Clla
a Clli
i LlIa
( 2 Gcrri
{ Hya
rr 13ya
n Lco
i
(1
0
,, 1:>121
?'
<Y
I,
:
$
I
i
i
i
Crv
Vir
i;>I?I
Cr Boo
o Crß
o Sci-
i
n Opli
n Lyr
a .XqI
n C'-g
h' Ca11
t Dc1
3 Pcg
$
5 C,!as
I
I
*
1
n S<:o
I
C<.t
If tlierc is a diif~rcricrb e t ~ ~ ~ ~tllc
i ~ eralii<:s
ii
of XI.1 (or XI.li>) ai><iS1.2 both ~-alii<:s
arc iriclii<i<!daiid scparalc<l l>y j.
s 71ic star lias l>crii assoriatnd \i;it,li tli? star list ~oiiccrii<~<l.
$ S<,cttic note foll«\~-iiigthis tal>lc.
Xotc5 to 'r;iblc 13
TIie 'alt,iiii<io'aiicl thc iii<iri<iiaiialtit,ii<icof Typ? S1.l liav<,b<:cii <:«iivcrtc<liii1.o clorliiiaiioiis. iisirig a l;itit.ii<l<-of Paris of 18.S0, as iii<iil;!atril11;- ttic ;iiii:li«r of T y g r XI
(sec. t,lir iiiai.licm;~t.il;!al<~sprrssioiis
es~>l:!iiiiciiiii Ap~>oii<lis
I). TIie rio4.i.s are arraiigc<l
t o i,liix 110s. of a Type a.3 listr<i iii coliiiiiiis I 3.
T']>" I11
Tlirr<, is aii crror of 10" iii tlic iii<~liatioii
of n 01)Ii.
Tlic iii<-diatioiiof '-; Cas is g>liil;!c<l
iii ili<isigii of Taiiriis i~iitit l><:loiigsto t,liat
of Pisci3s.
S o . 22: Tlio i>»sit.ioiiof (I Getii is ic'r?. l;!orriipt
S o . 26: Tlic ~>osii.ioii
of 8 L\,la is corrupt.
S o . 27: Tlic ~>ositioiiof I CSla is corriipl
S o . .3:
S o . T:
T'lx:
XI
S o . 2:
S o . 3:
So.9:
S o . 10:
S o . 11:
S o . 13:
S o . 19:
S o . 20:
S o . 26:
S o . 28:
i"1>"
S o 4:
Sc<.tlir <Ii%ussioiioii :j Pcr oii P. 181 182.
F«r tlie clrl;!liii;itioii (>E Cr T;iii rariaiit. rradiiigs tia\-<*1)rr:ii list(:<l ( S I . l a : 'aititiiclr>' 59" iiisi.?a.cl of 49"; S I . l h : iri<~ri<iiaii
altitii<lr 5&S0 iristca.cl of 16.5").
Tlic ~>ositioiiof I CSla is corriipt.
Tlir i>'~sit.ioriof (I Gcsrii is rcir>-corriipt,.
For tlic <le<:liiiatioiiof 1:r Hga a variaiit rcba(liiig (11.2: 8 iiistcaci of 18) hör;
l><:crilist<~<i.
Tlic liositioii of 8 C \ i a is corriil~t.Shc iric<liat.ioiiof B I X a agrrcs I>ettcr mitli
rliat of I\' iio. 13: 11 I:\Ja. 711is iriay <-splaiiia sn.itl;!li froin B V\'ia t o / I I:\la
iii T:.II<: I\'-.
Srv tlio <iisriissioii (111 8 Sco aiid (r Scr oii 1). 183. Tlit d<!<:liriatioiiiii S I . 2
S I I ~ I I I I CI )~C Ino.
Thrre is aii (irrer of 10" iii tlir <icclinati»ii of o Sro i i i 21.11).
TIici-r is a n c'rror of 10" iii t l i ~in<,diatioiiof iD(4.
Sc<%
tlir <lisl;!iissioiioii 9 Pcig aircl 5 Cas oii P. 183.
IV
T h ? star n Cci. lias also 1x:cii I-ri.ou(ic<lin a iiiiri~l><~iof iii;rriiisrri]>tsof X-crsioii
XI.2 l>iit,iioi iii all of rliciii aii<l not iii tlios<, of vi.rsi«ii SI.1.
S o . 10: For tlic cIc<:liiiatioiiof r. C4Ia a variaiit r<,atliiigIiavo 1)ccii listc<i (50' iiistca<l
of 12").
S o . 1I: T11c (icclii~atioiiof ( TI>-a.slioiild i>e7 iiistczi<lof -7. Tli<~ii
tlic posit,ion of ( I-Iya
agrccs ~ i - i t l it.iic iiariici 'Barta scrl><riitis'.R>r ili:!ii. r<:asoii t,lic ideiitifil;!atioii h;:
Iiiiiiitzscli sh«iil<i I>(: cli;iirgcid fror11 o II'a t o ( Hxa.
S o . 19: Tliarc is aii error of 10" iil thc iri<:<li;~tioii
of <Y Ser.
:I Closc Look at in-o -4strolahcs a ~ i dtlieir Star TaI>lcs
Tai)lc 6. Star t,al>l<.of t.li<:r i ~ < ~ d i c astrolabc
lal
DY1 SI.. 54.
X«
Xaiiic
DESEBC:IITO%
RIGIL:Il.S.\BIE
p«sit,ioii
3 l~IIR.~\C~ASDIZO
posiition
4 B;\TESC:\ITO%
5 C:IPI;T?\R'
G :\L.C:ElIB
7 l,fERl<?\13
8 .ACGE'TE?;.AR
9 :\LDEDR;\S
10 R.IGI1.
11 :\LIi'\IOC
12 BEDELGEVZE
13 !\I.Ii.AUOR
11 C:II'I:TGEYISO
1.5 :iLGOIIEIZ;i
16 l1111IkED
17 >\LE-IIII)
18 COSII-SCTE
19 CORLEOSIS
20 EDLB
21 C:\LDI\LEOSIS
22 1 . c : o n . m
23 .\C:llIhIEr
24 BESESAZ
2
I.R!\lIEC
26 .ALFECA
27 IED
28 C:ORSCORPIOZIS
29 .ALII.\I:E
30 R:\%T.A13ES
3 1 .\I,IT!iC::\
32 :\l.:TAIR
33 ALREF
3-1 iIF:l,FIS
35 :\I,IIF;R.AIlI
36 lIESI<EB
f~osiil.ioii
37 llF:SI?D;\I.GEJ>I
38 SC:E:IC
Sigii
I
2
Mctl
Dcc*
Xof
(1
-22.3
40
8.0
32.5
4
4
5
3
G
8
7
9
10
11
12
13
14
1.5
16
17
20
19
21
18
22
21
25
23
26
27
28
29
30
31
32
33
36
3-1
I
39
37
35
38
Idrnt
3 Cet
? .41i<i
:\ri
Ari
.Ari
11.0
1.5
23.0
T,ili
J..;
Ta11
Taxi
7.0
23.0
33.6
14.8
20.0
46.1
0.9
-1.5.9
c:r11>
10.4
1.5.0
16..5
2.0
8.0
12.5
21.0
8.5
19.0
2L.5
0.0
11.0
22.0
10.0
9 5
29.0
18.5
26.5
27.0
1.1.0
23.0
2.0
16.11
29.0
i.(i
11.0
-8.4
44.1
7.4
1.3
33.8
7 .
22.1
. 1.j
14.3
13.7
64.9
18.6
-13.8
--7.5
2.1
23.0
29.2
2.3
1 7
12.0
50.7
37.7
G.?
42.1
3.2
G0.6
13.0
11.0
29.j
6.9
-20.1
20.0
-c;<:1ii
Grrn
C~:llc
C11c
cric:
C11c
L130
T.<!«
L<\o
Yir
1-ir
1-ir
Li11
Lil]
Lil)
Sc0
s<:o
Sc«
sgr
Sgr
Ca11
Ca]>
C:ap
.\qr
..\<[T
3 :ir~<i
j:,
2\ll<i
t
r i Cns
C
C:rt
.4i-i
<% P r r
o C<.t,
7E1.i
<I Taxi
: j Ori
<i
(1 .4111-
11
Ori
Clla
<:ciii
C.Xi
Piip
Hva
ClIa
n
L.<!«
(I
ri
<i
o
p
rk
i
$
<u I;l,Ia
3 I.co
7 Cr\\-ir
11 L l I a
<r ß o o
n Crß
fi Opli
o Sco
rr Opli
7 Dra
o L>-r
o :\<XI
<I C:yg
Dcl $
(I C'<,I>
Y; I'cg $
C I'cw
t,
6 Cap
6 :\<ir
209
~~~
~
So
Same
Sign
l:lr<1
Dcc*
Sot
39
BED.ALFER.-IZ
ALFER;\%
Psc
Psc
1 9
21.2
25.2
39
2
.SO
"
t
-I .
Idcnt..
8 Peg
n ;\nd
Tlic c:alc:iilatioii «f d~!,cliriatioriis l>asc!d oii a \.aliici of t,lic railiils of t,hc cqriat,or of
141.6 miii.
Thc iiiiiiil~c:rsar<: tbosc of Type VI.
Src tlic iiot.~!f»llo\i-iiig tliis tal~lc:.
Sot<xs t o T:~I'ablo G
Typt V1 is kiio~viiiri tn-o \-(~rsioiis;here rcf<:rr<:rit o as V1.1 aiid V1.2. Iri \,T1 thc
~jositiiori is givcn iri ~cliptic<:o«r<iiriat,es,in tlici otli<ir versioii tlic mecliat,ions aiici
<lecliiiatioiis arc listccl. 111 tllc riotcs bcloiv tlre riiiiiiljcrs rrfw t,« tliosc of roliiiriii 1.
So.2: Tlie riariic, corrcs~>oii<is
t o ? :\nd brit tliis star aiid irs iiamc is not part of thci
Sc). 3:
S o . 9:
S o . 11:
S o . 19:
S o . 34:
S o . 36:
tradition asso<:iatc<imit11 Type \-I. Tlic positioii of t,kir star ori tho astrolab<,
is tliat. of /j Ari(1. Csiiig tlic c<:lipti<: (:o«r<Iiirat<,sf«r 3 .kiicl «f Type \'l.lj a
iiiccliatioii of .4ri 7.3" eriti a tleclinatioii of 32.5' is foiiiicl: xi-liidi agr<?rsrvitli
thc: v;ilii<~soii t,h<,astrolabc.
Thc iiairie c«rr<~sl>oiids
t» ;i rliid l>iit thc ~>osit,ioridisagrccs. T h r niediat,ioii
shoiiid 1,c Ari 7.3' anci its d~cliiiatiori32.5' (sce iiotc t,o iio. 2) l>ut tlicse <lat,a
ar? asso<:iat<dwitii star 110.2. See, t,hc clisciissioii oii 11. 190.
Tlii:rc arc rio positional ciata oii (X Taii I><:c:aiis<~
tlic ~>oiiit.c,r
is I~rokciioff.
SIir rncdiatiori of n .4iiu (Gcrii 15') (liffcrs hy 9" froin tlif i - a l u ~iii V1.2
(Gciii 6").
Tlic iiic~liatioiiof r> I.eo (Lco 22.5") (Iiffcrs hy aliiiost 5
' froni tlic valrir iil
1.1.2 (I.co 18').
TIi<: clccliilatioii of 7, Del (3.2") <iiff<~rs
I>?. aliiiost 10" froiii tlic i-aliic iii VI.2
(12").
iiairic kleiilich <:orrcspo~idst o ?: Pcg. Sliis riaiiici is associatrd xvith t,lir
positiori listrti for F Peg i i ~V1.2. The poiritrr For 3 i'cg itsclf is also rnarked
ori tlic astrolahr as 'I>c<ialfcraz' (no. 39)
A Closc Lo«k at tivo :\st,rolabcs aiid thcir Star Tabies
211
Taljle 7. Tlic loiigit,ii<icsarifl Iatitiidc:~of t,lie rcliahlc stars «E T:-pe! V1 aiid thc ast,rolabc
Bk1 SL. 54, and thcir <iiffereiic<?s(DLon aiid DLat) n-it.11 r<:sl>c<:tt o thc Ptolcinaic
7-al11cs.
1;IAst
iio n o
I
2
3
4
35
40
4
20
21
22
23
24
2.5
26
27
28
29
30
31
32
33
33
35
36
37
38
17
19
21
24
22
23
25
26
27
28
29
30
31
32
1,Iodcrii Loii
nüiiir
V
n Ce11
n Arid
C Cct
:7 Ail<l
:>
r i Cas
6
5 n 11ri
7
7 o Cct
8
6 <I Per
9
8 7 Eri:
10 9 n Tiiii
11 10 ß Ori:
12 - n Aiir
13 12 a Orit
14 13 n CMat
15 14 0 Gniri
16 1.5 n C\ii
17 16 p Pli])$
I 8 20 rr I;\,la
19 18 / I I:lla
37
33
38
n Hya
cr Lco
9 I.co
71 UMa
y Cr\<Y Vir
<r B«o
rr CrR
6 Ol111
<i Sco
<r Ol>li
7 Dra
n I,yr
rr :Iql
7Drl
6 Ca])
ri Cyg
t Peg
h' Aqr
1.0
1.0
10.0
20.0
26.0
27.0
32.0
50.0
12.0
58.0
65.5
70.0
75.0
93.0
99.0
106.0
119.11
121.0
130.0
135.0
138.0
1.5QO
166.0
179.0
191.5
193.0
211.3
232.0
238.3
250.5
252.0
271.0
290.0
306.O
313.0
321.0
321.0
327.0
Loii*
;\st
Lat
VI.l
Lat*
Ast
DLon
VI.1
DLon
-1st
DLat
1:I.l
DLat,
Ast.
\'I Ast
rio iio
39
40
39
1
lIo<lcrii Loii
iiariic
1
Lori*
.Ist
1,at
\I.
Lat*
Ist
3
349.7
350.5
31.0
20.0
31.1
-20.3
I'cg
!7 Cct,
350.0
351.0
lIet111 \-?iliic~~~
Stüii<iar<ldrviatioiii
Error iii tlic iii<iailvaltic
DLoii
.-Ist
DLat
\'Tl
DLat,
.-Ist
17.8
1x3
17.5
14.9
0.0
0.3
0.1
0.0
1.53
1.2
0.2
15.4
1.8
0.3
0.0
0.6
0.1
0.3
0.8
0.1
DLoii
1
*
I
-4 va!ii<: of r - 24" ~\:i-as iisc~liii t,lic cal<:iilatioiis.
Sr:e tlic Iiote follon-iilg this tahle.
i h r \Tl all 10 stars ar<: i~iclii<Icd;for tiic ast,rolal>eo i ~ l y31 stars.
Iii 1 . h ~iiotcs l>eloii:l.hc iiiirni)ci-s rcfcr to t,liosr of <:oliiiriii 1.
X . 9:
Xo. 11:
S o . 13:
Zo. 14:
S o . 17:
Tlic loiigit.iicic of V1 has l>cc~iircl>la<:cc!by a vaiiaiit rcaciiiig: Taii 12" iiist,c<a<l
Of 'rtllaii 2 2 O .
T111!, loiigitiidr of \'I Iias I>c<:iire~>la<:<rd
1., a \ariaiit rcaciiiig: Gciii 5.5' iiistead
of G<:ixi 21.5".
Tlici sign of t,lic latit,u<li!iii 1.1lias berii cliüiigc<l:froin 15.io t o -~15:i0.
Tlic loiigitii<lc iii \:I lias hecii rcplacod 1);- a variaiit r~adiiig:Ciic 3" iiistca<i
of Cii<: 18'.
Tlic loiigitiidc iii V1 Iias l~<!<!ii
rc!pla<:cd h' a \ariaiit readiiig: Cnc 29' iiistca<l
of 20".
2 CXosr 1,ook at t\vo Astroiabes a.ii<it.licir Star 'Tat~lcs
213
Tahlc 8. Tlie longit,ii<lesand latitudes of the iirircliable st,ars of t,lie astrolabc BX'I SL. 54:
arid t,lic:ir differentes (DLon ariti DLat.) mith respect t,o t,lio Pt,olcinaic ~-:iliics.
*
+
l
laiiie
Ideritiii<:;it.ioii+ Loii*
2
3
11
34
36
RIGIL!\LS?\BIE
>IIR.AC.A';DRO
.\Lli.AIOC
DELFIY
\IEKkEB
7
3
<r
7
3
-
-\nd
.ii~<i
iir
Dcl
Pcg
Lat,*
DLori
DLat
26.6
25.5
20.8
22.9
23.1
4.0
226
22.5
13.4
-11.8
1.4
-0.8
20.7
2.5.9
77.j
306.6
320.4
-l.i
--10.2
-7.9
A valiic of f
24' was uscd iii t,lic c:ai<:iilaii«ris.
Tlic id<?iit,ificat.ionis based «ii thc? iiaiiic.
Tablc 9. Coinparisoii of the posit,ioiis of tlie rejcc:trd stars of B41 CL. 54 ~ i t tliose
h
of
T y p c i ' I arid t,li»sc calc:iilatc<l fi-oin Ptolcmaic ~ . i I u eaftpr a prc<:cssioii cori-cclioii of
19.3' ( P t ---15.3').
Sonr<:c
Pt
-:
\'-I
Start
15.3' <r Cas
3 I
\;I
Ast
rr Cas
3 I
\'-I
.ist.
<r Aiiin Aiir
P t kk1.5.3O -;. Del
V1
7 Del
Ast
7 Dcl
V1
V1
1st.
t
,8Pcg
t
8
Pag
Pce
l o
Zaine
lIc<l
Dc:c
Coiiimciit
35
sec riotc a
inirach
s<:e<icr
\IIR:\C.AXDRO
.4ri 1 1
.iri
7
Psc 29
.iri 14
alliaiotli
.\1.11.A10C
Gcin 6
Gc!in 15
,34
11
44
m m r in iric,cl. of 10"
3
(lelfiii
»E;LFIS
Ca11 29
i
1
4
12
sec r i ~ ~11t c
34
34
39
37
iii<iiikci>
ciiif .i. iniis. (eqiii
>IESI<EB
.-\<P i
rklr 15
.:\<ir 13
4
3
3
12
i
36
-
33
51
34
3
33
6
7
corr. 110s. of <I Gas
cirsor iii lat,. of 20"
corr. ~ > o sof. 7 Dcl
ci-i-OTin lat,. of 10'
110s. of
P<!h
i
Ttie ideiit,ificatioii listed here for t,hc asl.rolabc aiid T>-II"V1 is I~ased0x1 tlic: xiaiiir.
l o t , c a: Tliis positiori was oi~tainedaftcr rc!dii<:iiig t,hc lat,it,iidc of ri Cns by 20".
l o t , c 11: Tliis positioii was obtaincci aft,cr rcdiiciiig tlic Iatit,iidc of y Del hy 10".
Tablc 10. Thc ioiigit,ii<icsaiicl latitiidcs of riir st,ars of T y p r V1 (rersioii \'I.l): and
tlicir differcil<:cs (DLon arid DLat) with rcspcct. t o tlic data of Tyclio Brahe (1601),
as ivcll as tiic corrospoii<iiiig diffcrcnces betwr;ecn tlic ciata of Pt«lcin)- aiid Tyclio.
lIo<i<!rii
l1?llIl<i
<Y
C<.i>
n ,Arid
C Ckt.
:? .4lld
o Cas
r l Ari
ri Cct
n I'cr
Erit
0 'Iail
3 Orit
r~ Aiir
rr Orit
o Cllai
(r Gciri
o C\Ii
p Piii>r
rr C l I a
/L C l l a
r i Myii
/Y 1.<-o
;'? Leo
71 C l l a
-;C'ry
fl Vir
B««
Crß
6 Ol>ll
n
(I
(1
s<:o
O~>il
7 Dra
r i I,yr
/I A<li
7 Ilrl
6 Cap
/I
(1
C:'-g
r I'<.::
6 ;\qr
DLon
T)--V1
6.2
4.8
6.4
4.8
6.3
5.1
6.8
6.3
6.3
6.2
.5.8
6.3
8.2
56
5.7
4.3
6.9
.X6
.5l
6.8
6.3
7.1
j.2
6.2
6.8
5.6
.5.3
1.7
j.9
6.3
10.4
8.7
6.1
7.9
j.0
8.9
5.4
6.1
DLat.
sy-T.I
1.1
0.3
0.3
1.0
0.6
0.7
0.4
0.1
0.2
0.5
1.0
0.2
0.1
0.0
0 .I
0.9
0.2
0.0
0.6
O1:
0.9
0.1
1.1
1.1
0.0
0.5
0.2
0.2
O:1
11.7
1 .(I
0.7
o.:i
0.3
0.0
0.6
~4.9
~11.5
DLat
Ty-I't
0.1
0.3
0.3
0.4
0.2
0.6
0.3
0. l
0.1
--0.3
0.3
0.3
0.9
0.3
0.5
0.2
0.0
0.7
0.5
~~1.9
03
0.i
0.4
0.4
0.0
0.i
0.1
0.3
0.3
0.1
0.1
-0.2
0.2
0.4
0..3
0.1
0.4
0.7
A Closc Look ar t\\-<-oAstr«lal>cs anci thrir Star Tablei
Typ<. kI«<lcrr~
no iiame
LOII
V1
\,Ieaii ialur
Staridard tlciiatioii
Error in tlic niriiri valiic
T'
Pt
i
-
Lat
1'1
DLoii
'
V
DLoii
Ti--Pt
6.2
1.3
0.2
21.5
0.j
0.1
DLat
T
21.5
DLat
I
Ty-Pt
0.1
0.6
0.1
0.1
0.;
0.1
Tyclio Brahc
Pt,olcmy
iiidic:atrs that tlir 1-ariant rra<liiigcsplaii>c<liri tlic iiot~cst,o Tal~le7 lias 11cciiiisrd.
-: