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Aftronomia Accurata\ 

ROYAL ASTRONOMER and NAVIGATOR. 

CONTAI.NIHG NbW IMPROVEMENTS IK 

Aftronomy, Ghronology, and Navigation. 

particulaTilt 

New and correa Solar and L^e-NAR TABLES; 

With Precepts and Examples of their U>b, according to Old or New Style, 

The EiiMiNTJ of the A1A4/ C«»oifoioci«ii, RULES tn4 

Meu ?lat*t and J^timt of chft TABLES. 

Plahtium] Satkllitbi. ■»,,«««»«« , . «..—>./. 

REDUCTION of die DATES 

A firm and Orrft? C*TAi.o«irj *f .^RAS. 

of STARS. ~ I „ . , , , „ 

WIdt Vwrwifd ud Ptrfttmai 

With their R;^^ Jfimjhm, Dttk» TIME-TABLES j fcrring for 

MMtitnt, and ./nuW Fa^Mtmi, ^j Year^ U|f , frtftai, or M 

{fspplying the Plice of Vha- g^g^ 

MoaaAPHiA Bkitahhica.) 

And ANSWERS taTify-thm ANSWERS to nxny Clmnl^ 

J QwjiTiom. tml QUESTIONS. 



OBS. 

V i\ 



The seaman's READY COMPUTER, 
Or New and Easy NAVIGATION: 

Shearing bow to keep an exafj Ship's Rtckomng ; with HxampUst according to all the Methodt 

oi SaUing in Practice, by only fumm'tng up a/rtt; Figuret, taken out of ?d*jfef. 
5*<i3«/iir Anfwers to all the CASES in Plain and Spherical T R I A N G L E S j and to all the 

CASES of SAILING. 
Aft a^A<iirf»Vfl/ TIDE-TABLE: An univerial SEA-COAST TABLE, of the Latttudts and Ln^tuda 
from Greenwich^ and alfo the Ifland of Ferrty of the moft rtmarkahU Sea-CoaA Pldat, Partt^ and Har- 
huri, ]y'mg ctHligmut round the WORLD. 

To wUth IK ulM 

An fxphmftrj COMMENT on the MOON's Thnry : An eafy Method, with ExampJet, of amputing the 

Lunations, and of Saiarf,aA Zuniir Eclipses. And itww to determine the Diffirrince of Longitude, 

from the ^•jw/Obfcrvatory, at Gritnwich, by obfcrring the Moorli Phce, under any dlflant Mtri£an. 

With y«K* ufcful Rtmarh-^tA Imprtvtmmtt on the Motion and Theory of COMETS. 

TheauWuinterTperfed with ■Variety of Mi-;^«ir)r Tabid, widrtUIn, fubfervieDt to the /irw prhicipal SUBJECTS. 

By ROBERT HEATH, a. Military Otiic^t.. ~ 

Hbvi HrarfH in all btr Glory ptnt, ami r^ttd 

Hit Mttiani, at tht Great Pirit MoveeV Hand 

Tirfi <uiburj ritir Coorfe. y Milton's Far. Loft. B. VH- . L. 499. 



LONDON: Printed fo^the AUTHOR. Price 15J. in Sheets. -M.DCcXx. 



(^ Tbofe Sttii not banng the Cafftr-Pltit of the Falltdium (Ttmt atut M^nrrw; »ffi«d to the 77*/*, or Fmiiffiicr .nd fi£ntd *"'' tj^* 
Aurbtr't ovti UtoA, ud feilcd widi hii Sen], (aG—tof Ami, atdUioartMpaU) or anj with the Fiootirpifce-rpicelaliSiiii^ in^riMi, 
t«inUTf.h,fi!fB-'d, otfirttid. And i handfeme «M«4r/i> herebj offeicd to any Pirfin uho flijll be pltaftd W dlftovti B> '1>= -J-/**-- "J lu=l« 
Book), publifliB), orifliibuttd, igwnft hU Knowledge or Confrnt.— All Putchiferi wh«fo«»(r miy be fupplied at Mr. CWf'i, M«*«m- 
licaili^nKmtt-wukr, \d FUafina, U-^, Succeffor to the eminent Mr, ITw^fa, with proper Allowance of Snm for 'l«P'>»0' ^"f™?!"' 
to in Book&Uen and their Country Cortefpondenti. Where «iA< the rraJi. in Town, may be fuppliei at thejf^ Fr"a, ''•."*^''J~7' 
.with Allowance of the ^««/ff-./-Hwrf«J »«*. beiideitheSe.enfor Six Boolo, Wfas IS^ttttf j by thofi tjentlenM Olimg tW""^"* 
^'' •ndi'ibtt «f Abode) orAitrcriUngfor vbitMiuiibcrlheyplMft. 



•Bw«. ^ 



' T O T H E ^iMiti^M- 

HOHODKAILE andREVEREKS 

^PIPNCER QQWPER, D.D. 

p'EAk^^. DURHAM. 
SIR, ! 

How UluftripgsflJii/eiiriobkd (J SCIENCE! wbin Per/em pf hi^ Bkth^ Honour, anJ 
Diflindion, become her Votaries, and voorflsip at her Altar ; while other humble Admrers 
are obliged to have Recourfe to the Favour and Intereft of their SUPERIORS to he admttud ta- 
her Smiles ! ' ■ /. 

Hadnft yottj Sr, veiuhfafed toe the Honoxir to iompefe the Comment m the' lanar Theory, 
to model the iinar. Eqpation-Tablcs,, and to lend me your Aid, in bringing the ROYAL' 
ASTRONOMER to Light, that ufefii] DcCgn mufi have ftill lain dormant in. Oblivion: 
Which being matured by your aftuating Genius, naturalhf feeksyour Patronage and Protcftion^ 

Jhe incomparable Sir ISAAC NEWTON laid the Foundation of a perfi£t lunar Theory and 
Computation, and pointed out the Means to his irrdefatigable Succeffors for accomplifhing Jo defire^ 
4thle an Attainment', to which the illufirioas Halicy, of our own Nation, the celebrated May fr, 
M, De la Caille, and ether ingenious Foreigners, have amazingly contributed. But you are the 
firft EngUfhman tttho fo eafily rejhlvfd.the._ difficult Q^^TRaL EQUATION OF THE 
MOON, in two Parts, and introduced fuch otbernt^ffS aCy lumr EQlJATlOliS, deduced 
fro0i the tiev/toniSinPriic^s of -Gravity, of have, oTtbe greaieft. D'l&^ace, rendered the Bnal 
Computation of the Moon ivithin tw<j Minutes of Tri^h i which the great Newton hipife/f left 
4/fl Diffprepfe e/ above five Miputcs, and Halhy' i Con^tatioH left at above eight Mitjutej i 
as appears by his ebferved and computed lunar Places, compared for a Plinian Period of iZ Tears \ 
in the noble (and before unequalUd) Correction be has given us' of the. lunar Theory. But your 
Computation, at a mean Difference from Tr^th, is not above three Fourths of a Minute ; as ap- 
pears by jour Tab\t «/ ope Hundred lunar Pkces coveted. IVhich great Accuncy is /hewn, in. 
ths^ following Work, /a he ^,prodigi(ius. Advantage in obferving the l,xingitude from Greenwich 
Ot)fervatory, in long Voyages, at Sea. 

Ihe celebrated Mayer of Gottingen, undertook /if arduous Tafk of correcting the lunar The- 
ory a^oa/ /if /aw^ 7V»m «j(/i'_yfi«r/e^. ^(?« iijw_^« adopted Wj concife Method of Compifta- 
tien in the Conftruftion of your Equation Tables, and fo far improved upon it, as to perform that, 
with equal Accuracy, by ten eafy lunar Equations, and one correSing Table, which thai celebrated 
Foreigner has conJiruUed thirteen different Equations, and as many different Arguments, to per- 
form. And as you have ixr.ufefuljy and elegantly improved and adorned the lunar Theory 
and Computation, you are, among other celebrated Improvers of the coeleftial Science, (of which 
KINGS and PRINCES have been Patrons and Promoters) jujlly entitled to your merited 
Honours ! 

Tour mat '^ixxi^lt. Sir, in encouraging and improving StAsnct, will not only do Service, but 
redound tiot\owr to thh Nation. And, as your Motive, in your indefatigable Purfuit of new Ac- 
quifitions in Aftronomy, appears to be the public Utility more than a View toyour own Reputation, 
your excellent Improvements will reflet Honour,, tu hii£ as tht SUN gives, and the MOON 
r^eSls^ Light. 

DigHizcd by VjOOQ IC 



DEDICATION. 

I ^a U mSt ues fl^it- ftrai^ to thofi who art t£i kaft atqoMnttd withyet^ NOBLE F AMILT* 
and your A^^anfffr the hcWt^ljexXKit (which you feem to inherit as much by Nature as Actjuifi- 
Hon) tha/you are a Lover «»ii Promoiser eftbe LIBERAL ARTS. 

rhe nobU ^arl the LCOID CHANCELLOR^ your FATHER, vjas the Omevunt of the 
4ge in which he lived. His manfy Ciceronian Eloquence, in debatit^ the weighty Affairs of State j 
Am Patriot Zeal, for the Liberties and Cenflttution of his Covntryj when attacked by perfidious and 
implacable Enemies, ; his uncprrupted Fidelity, in the Difcharge of Offices of the higb(/i Trufi i 
bis indefatigable Laietfrs* in the Difcovery of Truth ; and unbiajid Integrity, in the Ahiimftra- 
tion 6f public Juftice ; ore fa tnaiff Moauraents of the Greatnefs of hrs Mind, the Honefty of bis 
HeM'ly his vafi Capacity^ and unexampled Worth. The Rebel Lords, on whom be, as Lord 
High Stewardi pronounced Sentence of Death, were no lefs edified and cenvtlfed by the Force tflas. 
iUafotting, than they were inftruSed to embrace their Fate with a becoming Refignatien. 

But you, &U 'were pot educated to adorn the Profe^on in which that great Man, your Fz- - 
ther, was earfyand emnently dijHnguiJbed, but you were deftined to improve the COELESTIAL 
SCIENCE, and to injiru3 Mankind in the Knowledge of their true Happinefs j to encounter Vice,. 
avdreformdn immoral Age, by the benevolent Spirit of CHRISTIANITY. iVharein the Dig' 
nity af your Birth and n^le Alliance, (being Brother to an Earl and married to the Daughter of a- 
lite noble Lord) are of Advantage to the Doftrines j'Otf, inculcate ; in making tbegreater Impreffion 
on the Minds ofyifitr Auditors. 

But Imtifi intreatyeur Pardon, Sir,- for having thus fur tre^a/Jed on your Patience i oecqfiomi- 
iy the Dignity and Luftre of the SubJeS, as weff as by the Refpeft and Graeicude / »vte you, for ■ 
the finguTar Obligatims and Honours I have frequently received at your Hands. 
V>' , - 

\. Who am, vith the higheft Regar<^ 

\i 

f^ SIR, 

( 
(t- ■ 

^ .' Your mofi devoted, 

Moft obedient, 
Vpnor-Ci0le,_ Septal^ 2$, 

and moft humble Servant^. 

ROBERT HEATH. 



PREFACE, 

DigHizcd by VjOOQ IC 



PR E F A G E. 



FTER loneExpeOsti 



efbtion, we Iitve pobliflied otir Jfirtmmt^ Taihi of the Skm and Mam i which being eon- 
Sabjefti of CirMwȣj and Knt^affM, ws aic obliged, on Account of the Altentioii uid 
^ A. Ealirgement of oar origiiuii Plan and Dtfigm, to omit onr Afiranomy of die Plakiti and SattUitti ; referring 
our Reader to our Jflrtatmia PirftBa, or Supplemental Afirtntmtr aad Natli^tr, for SattifkAion in thoTe Subjedi, 
and in all others promifed and expeded, to complete our VndfiaJdMg. Which W»ri will be printed at foaa ai due 
Encouragement it given lu j but without proper £iicoDr»;ement (ai all SubCcribcri may, niutitimuUff, depend on oar 
Honour of firifily fu16lline our Engagement] no fnch ^fjt will be printed, fold/, at our own Hazard of Expencei 
though great Part of the Copy i) aSha/A finillied. 

To KM the coiTcA mean Piatn and Matitui of the PUiuti and S^tBiut (employlag the utmofi Skill and Indoilrjr of 
the aSiift Aflronomen, for many Yean, fiace the ImproTemeat of accural* Inftnuienti to obferve them) it » 4aff 
Attainment. But to fettle the Variation of thefe feveraf Modoni, by an Acceleration, and determine the Ftrwu and 
Bputini of the fereral Orhiu, (o that the cemfxiti Piacn may correfpond nearly with the Placei »bftrviiy for the pre. 
iiuit Cm/hj aftd remote AgM, ii a Talk requiring the ^Mf{^ Judgment and ASduity to perform. In which we have 
not wannd fr*^ ASftancc from oar ^Uft mtahimaiital Aftrvmnn, and for perfening which we are beholden to^- 
rtipt Oblerrationj moie than tbofe made at Ihmt, the more difficult to acquire ; and not obtainable at all but by the 
tfeepefi Atifict. One Britifi Ob/irmutr brooded, like a Mifer, orer his ObfirvaiiBni, depriving thit Nation, a^tia 
faid, of a pcrfefi lifiiar Tbmj, by fecreting fom^ and falfifyiog other, of his Obfervadoni, ordered Sir Jfaac Mw- 
foH I infiead of being nfefolly and gencioull/ csmnonicable of hit D^cvistriii, like the late Scibktipic and II- 
i^aTatODi H ALLEY I 

Ai to whatii pretended of the Difcoreriei of the ihdifaticablb and accitkati Dr. BRADLEY, neither ' 
the Uotion of the Earth' > Aphtrian (could it be cxaCUy known] the jiiirraihn of the lAght of the fcttd Start, nor 
theEqaationof the i*nfi^a of the cqniDo£lial Point*, nor that of the Nutaiia* of the Earth ■ ^zi'j, (all butimperfcd- 
Iv known, though pretended of fnch Importance by the great Hailt/i Prefoce Writer) are fufficicnt to account for tho 
Several runo/iiw, in the planetaiv Orbiti, where the computed Errorg, in each, partly depend on thofe of theBarth'a 
Orbit. And had the late Mr. Viatnfitad been acquainted with all thefe refined Maliiri, u we are at prefeut, ihey, 
probably, would not have reconciled the apparent Errtrt in bii Obfervation). 

The celebrated Helltjt Skill and Contrivance, in fupplying the QtfiSi of the ^«ar EqnaiiBtu, by a CorreiBion of 
£rn>ri ofthe lunar Computatioufor a/'/inian Period, ai recurring, after which, of the fame Magnitude, ara no lefa 
to be admired for the Invention thereof, than for the Viility and Importance of the Improvement, Which Method 
can only be exceeded by fome fach Una CorreAion of the iMar Theory and CtmfUatim, ai in oar Tablm ia 
attempted. 

Ai to what is given oi for HaiUfi dmpMittHtir, by hli Precept- Writer, feemi to carry a Miflake. For otherwife, 
what Reafon can be affigned for the /agaciaia HaUtj placing the Feurtb (or Nmotm't 6di) iefirt/iie central Eqnadon i 
if, » the Precept-Writer reprefcnti, it wa* deligoed to be ufed after the central Bqaation. tJfing it before leqniita 
an aukward CorreAion of it* Argument ; without which CoweAion he pretendi there will come out near ta(f a Mi. 
MMti Difirintei more or lefs, in the Error of Halkft Abacui of computed and obferved Placei. compared in bis 
Tabvl^e Lua^ Mtriiian*. Whereii if thii fourth Equation were defigned by Halitj to be ufed after the ctmtral 
Equation, ic had been preptrlf and naturally placed after it, immediately before hii Veriativn Epatian ; whereby the 
Are&nt tronblefame CorreAion of iti Argument, and confounding the Camputtr how tbii Eqnation ibould be nlcd, had 
hwx.»vvidid. But thii Precept Writer ^fl^fli^ miftakei, (iif.A, ^. HalitfiT^Us) 'vJjtri ht apphu tbtExctfitflht 
Sif>EqiiatiiB,anJSKm ef tht Meen' i Equaiim (rednced to Time in Mean Motion of the Moon from tht S^a) ta iht Timt 
tf thiMiaii fir that BflhtT rut Syxygyi withoDt coniidetingtlit Sin t/lbignatir ^antity, in tii /aid Exci/ii aadtbtrijm 
mifaku, in hii AcctanI eflbt true Sjv/gj fi-tuJiig iht Mian, er tb* Mtan priaSng thi 7nie : fThich intinly dtptnd in th* 
Negative »r Affirmative Sign of thi Sum »f tht Sun'i Ejuatiom viitb iti proper Sign, and of tht Mom'i EjuaJieni nvili a 
COHtniy Sign i labich- Sum, •uiilh in prvpf Sign, ii univtr/ailj iht Equalim ^ ibt laltcftX btfvMtn ihi Mcom and Trii* 
Syzygy, and mt as Halley'/ Prtcipi Wrilir de/cribei. 

We have given, what wai much wanted, the correAeft Co/tibjii/ of eminent fixed Stan of any extant, froroM. i7f 
&Ci(///iObrervatiooi,. with their Right Afitnfiani, Dtclinatim, and hmW Variationi ; by which the Moon'i Right 
Afiinfiiin or Flact On the Meridian, or at other Timei, may be readily determined ; ai alfo the Right Afceo£on or 
Place of a Fianit or Csmti, at any Time, moving in i» Orbit. This enrea Catalogue, fo far ii it extendi, may be faid 
to nar« than fupply the Place of the once promifwl ani expt&ed Uratcgrafhia Britannica. And itwere to bewiOicd, for 
the Honour of this Nation, that we had a Britannic Caia^giu fubViQied, of all the moft faithful, diligent, and corrcA ' 
Obfervations of the JixrdSiari, that have been made by our moll able and celibrattd Afirentmen. Since it is a Matter of 
Ugh Impoitance to thit Nation, thit alt tit Oifirvatitm mide at the RsyalOi/irvataiyat Grienwich, fhould be pub- 
Itlned It certain Timci, for the CbrrcAion of our Tittriti, and Improvement of Afirawtinj ) on which our Navigaiian fo 
■och dcpendi. 

I& 



,y Google 



PREFACE. 

Td tbe Pnfue to Hmiltj'» 7aiUi, it \s remtrked,' by hii PrtfattJfritir, " T"^.!' /^ Pmilkuivt of allronotnicir Ob~ 
" forvUiOBI h if vtrj grial Iroponance, « thry an/n- itaau obTolete Hit T«blei i irmf, tn tit ctntrarj, tht V/e/ulaifi 
'* tf fucb Oh/irvatimt ai art car^ulij made enJ failhfuily ddrvtrtd h grtaily tnbatKid hj thtir Antiq'iicf . 7hai tbt m*ri 
" di/igtaf oa Obferrer r/, ibt iB*rt ii the PaUit cwnttrmtd in tht Pretcrvitian (ind be might hftve Taid Pahiicalitm) ef hh 
" L^ttri, Bud iht leit /iafliiU ii tit Exptnc/' (of fucli Publication) •' /a /^ Circnmfitncei af aprroeli Ptrfiui."— 
. Yet we find that no Briiijb Obfervator, fioce the cominuRicutve fiaUej, hu followed the Sxanpit of the above pri~ 
etft i though the Prtttplffrittr hai iDrtdwufly fpoken of that great Aftntemtr and MmtbtmatiaoK in another Pan 
of hii Preface, ai not having publiOied hia Oiferviahni. Wfao(e Priltnci, tbu the Gr^rMwi^Obfcrraciar) are befl 
printed at the public Expence, " ai hfi fuitiJiit tt tbt Exftneis/ a frifMit Pnfiii" (while the Po/lW/am. Author, or 
«ny odier Prsmoter of Science, woald print ibem, were ibev open to Accefa) feem* calculated for a frndtat Aug- 
- meptatjon of the prefcDt Sa/u7, or elfc ispropofed fora f*(r;ju^/rio fome Favosrite '^^•tvf-Oi^Anvr. 

As to communicating to the Ledin, the Method of mitcing (aUftial Obferrationa, trom Gnemiiich-Hiil, (hewing 
them ' the rifing' Moon, and other ObjiSi of Pleafare and In pro cement, from that delightfbl View, we greatly ap- 
prove. AndwewiQi, thofc Zaifi«i, rainly attending on the ORACLE in the Old Baiitf, LeadtH, to confult tbeir 
Dffliaiti, ftnd other fatnre fvrisff, would henceforth, mart •aiijely, attend the rir/r^A/Obferraton i it being not abore 
an Hoar'* Travel further,-in their Coaches, to have infallible Proof of the^rrrfTranfaAioni amongalf the JrijA/ 
RaiiTt'vx the Heaven* I There they may fee the celebrated Mr. Gtui Mtrrii, enammred of the Gtddt/i tf Siitnci, 
walking Hand in Hand, and the renowned Mr. T. S. P. R. S. Ufurptr of the Vaditi Diary, holding ap her Trai ! 

The Change of Dic/iMatiaii of the fxtd Stan, according to Succeflion of Yean, happening with tlie Vsriaiftn 
of the Eelifiic Obli^ait^, or DiAuice of the Pole of the Ecliptic from the Pole of the World, ii no more to be 
wondered at than their tmnuai ProgreHion in the Sign* of the EctiplU, by the Prteiffim of the equioofiial Point*. By 
which Means, the DiAance* of the fxti Start are found to increare, or decreafe, from Atrtrtm of any Place, 
accordingto thar Miaaai Fariatim, ai Teen in odt Catalogue, So that the Variation of the Dtelina^R of the ^i^ 
Star, and of all other Stari, inferted in oar Catalogue, for any Number of Year*, paft or to come, and thence the 
j)refaat Declination of a given Star, may be readily and traly determined. 

Oar JitffJtmataJ EQUATION -TABLES, in the ptefent fferi, ufed with tke Ecctntritity of the Moon'* Orbit, 
and fittnd EquattM of the Moon'i Aptgii, are dcfigned for making Tiial asd Improvement of CoraptiMtion, by the 
(iifierent Kind and Number of tanar Equation* to be ufed. Mifr't lunar fiquationi are inferted for the fame 
Parftft ; va compare their Rtfuit with that from the /wwrSquation* marked C ; and alio with the Rcfvlt from oar 
other Eqaition*. 

The RiJI of our If^tri we leave to fpeak for itfelf, or the Critics for it. On which we obferve, thu we Oiall be fo 
for from taking it amifi from the ^vt/inovi Critic*, (hat w« Ihall be obliged to tbaa to mark oar Dtftdt, for the 
Improvement of Truth and Science. Hut if CaviKirt, inficad of Critict, {hoold preliune to 6nd Fauit with what 
they do not onderftand» or, according to the CnSom of fome Monthly JUvitmutrt, nfe Contempt, Derifion, and 
Abnfe, for Criticifin, on Subjefi* they are not Mailera of, we fliall have Kecourfe to fftrdi with the Pid/U/btr, in oiir 
Vindication, unleft hedelireri "a^Mw Emijfarien ai all foch Scafftn, and Prtttnitri to Science, are very eafily 
ufwered in their own Way ; being do more than fo many FUn noder the Briifh of a FUpptr, ^ one being now fick 
of a Smrti^m — — another maimed by a Stroke of Ridica/tf ■■■ apd a third difabled by a Strma given to hii 
Alltniian, lie ——Some have ventured, without Idtai on the SubjeO. to charaderize Mr. Smir/aa't Treadfei of F/axiaai, 
j/tbtbaniti, i^t, and fome to c-iticift and rvrrrS Nptotan't Prtatifia | bat aiai I how vain and iolignificRnt mnft all 
ihe{e Prtltndirt to Criticifni appear, when it ii coofidercd that they attempt to criticife fach nnequalled Pro- 
dodion*! of which SobjeAi we have but ve^ few Perfbni, in thij Nation, (now appearing} cMiuirr^ qaaliBed 
to judge. Who then, bot Men of equal Genias and Capatitj, (hall be able to jodge of the diflicalt yet' certain Truth* 
ana DemoDftrationi thofefew Perfoni of Ability write } It ii true their Miihad, ot Laagmage, may be cavilled at, to 
which all Method and Language are liable ; but thiiio Nothing to the Truth of their CiWi^vj, deduced from tSetiti, 
or Chain, of demonArative maihematicat Argument* ; whofe tight or wrong inference* are the principal Part 
of the Subjefi to be criticifed And though many /pua/utivi Truth* are not reducible to Practice, yet the 
Dimwftratiaat of tbofe Truth*, on affumcd Principle*, are not tlie left certain i a* will be found, where 
the Critic hai idtai and Judgmeut to purfue the intricate Chain of Reafooing. ■ Neverthelef* there 

are rataj fftculativt Truth* that are not DecelTary to be iTttroduced in Praftice; fucK aa building Bridge* on 
tirtalar Archet inRead of on elliptic or other Archei, full at fufriisBi, m ciicular Arche<, to anfwet the End 

Kopofed, andtolaftout (bf tAattrwh: Which Truth it in the Ptov'inceof the praflical £i.^iw«/-, more than with the 
tcnlative Mirimnf (Villi. There are other ^fa/a/i'vt Truth*, in AQtgnoniy. oot tciucible to Obfcrvation ; ai 
we find in the MifciUaactHi trails. — And we hereby adverlife tiie Jadi.hni Critic*, tbat we a.-e reiilible of the 
Breachei of Connexion and Method in our ff^ari, in out pramr/ ann Way or writing it, while the /'r0 waacHiployrdi 
which will be all redified in our /reand Eiliiia<i: TRUTH (which we have endeavoured t:i prcfeive through the 
whole) being our principal OB lECT ! 

Oar Kjijal Afiranamtr wai not begun on the Plan whereby it it now finilhed. It wai er-i^iM/^ deSgned to contain 
only a few ftlar and kaar Tabree, far acciriiely compnting the San and Moon's lem Piacn, to viV with, and make 
' Impntvcment on, the Pian sind Method of the uUhrattd Majtr'i Tables. But finding thit ^ccaracy of Computation 
woald not have its V/i unKfi appUtd to Na-vi^a'! n. (in obferving the Matn't Place under a di^nt Meridian, for 
determining the Difference of iangi/udi, at Sea, by the OilTeience of that Time, and the Time when the Moon haa 
the lane computed Place at Gremicirh, hy our Tailts) wr-farthet extended our Plan, to tne Royal Afiraatmtr anA Natii- 
£Mt9r, To which we found, that ffiraaa/e^, and lioinc other fubferrieat Subjefit bring added, would render ch* 

If'ari 



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V 



PREFACE. 

Vtri fiiU tbtm»r4 ffifiJ^ ac<fttMt te tit PMit. B«t, in thii pnigreftve ADgmtnutlon, oar EacovfiKmentTrom 
SabTcribcri, we aie {orijtQit.y, wu att fnftrtimaUt lo otu Ejoienoaa to oblige; and we And b«[ fi:w Encamntgcr* 
of Science in thia KiDcdotn. 

Mr. Emir/tm, in bii FrcfMfi to bii UttioMia, oUerrei to the fellowiDg Pnrpore. — 7itU m M»cen9>, i» this Agt, 
fi^ari la patrttiM ami fnliQ Scitmt ; that lb* Di^im cf Arit mai Sritncl ^ thinlul ii in 41 gr*at Mta/mrt tt»ing la 
tht fal/t JMtitiui and txtremi Aiiiarki tf tbt prt/tMt Agi, Ifibrm JKrn [unlike the tfWimr Soni of Scienci; and Bocoura* 
gen of Aj-U and Literature) Mt ititg aiit to Mft tbat Eyti ahevt thii Earth, maii Ntthime f» macb thiir Cart ei raimg 
ttgtthtr iht DraJ, it ^v4n Jlrivitig. £ii tut Mali, luha fifatl At loHb tht mtft SarSt In lUi PeJJt^n. (Whrne 
fome find more Plagoe to lalce Care of tbeii Atnatdttac; than other* to fapply theii natural Wami.) that 
nalarel KarviitJgt finli Ne/hiwg htl Ctu/trnfi j and that MJoerra yitldt la ' Pluto '[bat, if tht gtatrttl Di^tfiiian 



af Mankind had Ittn in aii Agti, ai in titir^tnt,hedttuba,'wi*litrvMjf^lgbavtiadeiibtr a Mi^l ib grind Oamjtr m 
Brtad\ •>•« Painp/««^«w m Waitr. ThA, it it « trifling &xtaft/af MtnintxalfrdStalian ttf/tad thtirUatKmimntm» 
•with Scitactifinet learning, tfiUiSarli, htu ittn fotr Atn^ nndir tht Cofi and SufiirialenJencji ef ibt GREAT : Who 



ought to fntta Mdtniata-i^t Stitntt wid iti Frtftjtrt, fn tht Pruntlif a/ fniiic Gasd. That Tnindfiif omdGtmr^ 
vrntg tin GrtMt art btrd la it Jkni. 

ScivB veluitomMi, meiccdeai lolnre Kmo. 

4MdlblItM^lht WwUhatfiftm hMu^U btttu^t ibirtan/e/fm Alexwdcrl. 

Aikd wo kMC oblarved, that inraitod ^tritt, rarmft NtW/, and other /a0 Anoreneiti, find nodi 
nt>re BKOsngnmu tiua « Trooife on real and nfeftd Kaowledgc 

Bat, thtt we mttf accoont to oar ww% SiUfiriitrj md S»etmagai *f Scitnet for the txtrtnu Dtla^ in the Delirery 
of e«r picfeRt Wtri, befidea the Tima Mf idicd to fi^9, «wry, and aMt> naidil oat feveral Material*, the moA for 
AdTKBO^ ia on sstendcd Plm, the NaMra of Printiag Aa Work hu been foch, and the Tisie rctjairecl to coavt^ 
aad coned tht Proofif dut, on Aecont of dtafa femal anexpeAcd HlndraMCt, it could not be encnted imI 
delivered l«OMr- — Aad wa hope that am Sobfcriben trill excvfe at (baviog fbared ia their rcfpeaive Uoeafineb) 
for thefe Boforcfeen Occafioas of Delajr. 

V^ ta ^ntnt all Jatb Umttf/mfi mMd Bififfmnlwma, tm ail Sidti Jtr tht fOnri, nut baa/t fttvidid fnffcitnt Mtam 
•t Vi/^th, firPriUiwg tnt ftcfiod Sdltion 1 a^ tar Sa^lomaaial AOronomer aad Navigator, 4[c mi /tm, at fittnrt 
itlhferihtrt JbaUbt t^d J^atutlf t» tmcmragi ibtfl fifmHI Wtrii^ M tbt'Ttrm frtftfid ia tar Palladlam /er ttt 
Ttar 1761. 

TO tit ENCOURAGBR6 amd IH.PROVBRS »/ ARTS and SCIENCES. 

Fittii Amtf Fatri0. - — — 

Virg..So.VI. T. 823. 

WHATEVR. ia ^Etf', Grttei, or ffmf wu known, 

^J^arf can boaft a GBmUS of her own ; 

VnOt lona'AvtihPaffiani SdeacetobtfrieBd, 

And TSri'd is A'li, Bnconragement fhall lend. 

While the ^fi attli Seop to a^tS Waji, 

Hii Warlti a taftiDg htaanrntnl fliall reife t 

Hii FrindpUt — at aoblc at bit SUtd~~ . 

Who afii in prirate for the/«Mc Gacd-^ 

Defcended ftooi a j^M^P'triot-Kace, 

Whom Trnfi ftill hononn, and m Jrti debafe j 

To StattJmiM, Strati, Gti/raii, allied. 

Tbax PRINCE'i Glory, and the Nation'i Pride f 

In Famt'% imperial Temple higbly plac'dt 

And Jimt with laorcl'd Honoura donbly gra^d — 
' O Sm if Scitntt, Merit ftill porfae. 

And, t^ Examfii, lixep the Frixr in View i 

Exert yooj Taamti ftill to blefi Mauldod, 
_.jAl id-)L RfwardyouT Sirvicti flull find t 
w'ffThoBgh laitM/aertd'Seim^a deplor'd, 
Jfik Ti"it T'rtiArt in t CQWPER ii rcfior'd I 
^^■' R. HEATH. 



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r-fef NEW tfi/«(r<^ SYSTEM, lately puklijhed in Lain, (in the Im>. Magazine, September n 60) 
for the true SYSTEM ef the WORLD. By F. B. 

qp HE mcSyfim of tlie World is not that of Puimj, fo much to be admired for its harmooioui Epkxd". noi 
J that of Cftrmtm. fo fataon. for explammg the feveral Pb^cwuna ; nor yet that of Tnh,. reprcfeotiuK a 
noBle, and, » « were, a G^thu. Sm.aure. Among the Andent., £f/A„„,„ the /Vi<«..,«;. aad ifo-^i^. 
of Pntu; among the Moderns, Onfawu, and L<mgtm„taj,ui werenotnnacquainted with this SyS,m, But Ifind noae. 
«^r Age, but *;.■««. &M^„ an Bv/f^««, r.V-r.fWfW/,, in RW*.^,>r, who hai mif Something in F.voi.; 
of thii Sy^m. Plate, after he had begun to make a Figure la Philofophy, wai pleafed with it ■ I own indeed 
that heifteiward. altered hi. Opinion of it. becaafe the true netrj of this Syflem. a. on«may Koefs. did cot occpr * 
tohiiThoaght.. The whoJe Syftem 1. thni eicplaincd on Priwiples confenianeoui both to na.aral Philofophy and 

"n,E^,hi.^. i^i^Cfi,tnef,hiW„U,^Jr.vol^,r>mulh,AxU/r,« Weft u Eall. '^Itr.hj UAt <md 

" carmd reuitd tbt Etrth frva -Weft /» 



The New Abfard- SYSTEM of the WORLD. By P. B. 
R M A M B N T. 



■ Eaft « tin Space rf tat Month, Mer- 

" cury anJ Veno* rrvalvi h a partic^a* 

" Mmivi ahttt tbt Sun ; tbt fonmr in «- 

" hut 3 Mnti/, thi Luttr in about 7 | 

" MoMlbi, aad »t tbt faint Timt art car- 

" rttJnmJ tbt Earib, ivtry Ytar, luith 

" tbt Sun. Man, JopitEr, ao^ Saturn, 

" rnJUbraugb their rt^tkiwOrbiii, (mar 

" tbt Outer »/ vtbicb the E^rib it ^Xcd) 

ibe fitft in t Ttart, the fccmd, taib bit 

.Satellites, m iz Ttart, md tbt Avi, 

f Saturn, -uiib bit, itt 30. 7be fixed 

Star* art at Rejl; ^/ebtiict ibi &uif 

HesTen ii ealUd, U fgmd Writ, tbt 

Firoumcttt. 

" W# Suttont and Retrogradadona 
»/ Veom mud Mcrcuy, I'x ibi trm 
Sj/ltm tftbt World, or, in ibt Coper- 
nican ttjfothtjii 1 aad in Tycho'r Sj^ 
Im art partiatUrijtxfUMtd; butllk 
Statitnt and Rttrtrradatrtnt, vbitb M. 
fear to Ibt Bji in Man, Jniater, m/ 
Saturn, frteitd fihij frtm lit On*' 
laHf *f ligbi jiim Weft r# Eaff, 
tebieb it frtater or it/j, atnrding mt tbt 
flamtt it m A fOetoa tr Pmgfon, trttt 

\\ \ -'^ ^ / / ,-jf « gnatir *r M Diaanet from tbt 

\ X ^ r""^ y / Jf " ^*'*' '' -^ -f 

\^ ^--.^^ ^^y^ / Jf *• 7/* Jlfaawr of thii Clrcolaiion <wi}t 

^ ^ ^^ ^■""^ / .-» « ritarlf afptar front ibe fiUnviing Ex- 

• ample. If a Stone faff fitm lit Fir- 
' mament /* ibe Earth, befiJe tbat M^ 
" tien, bf *vbicb it ii frtciftiatelj tmrriiA 
' lotvard ibt Earlb'i Center, ii mnft, 
' neitjari/f, fartak, if tbal fSotitn iSft, 
' ij 'wbitb all fhiagi ore tarritd fra» 
" Weft to EaS, atctrdSng to the general LAW of the World, ft'ljat ve ha-vi faid ef the Stone, ii to bi nnderfleod 
'• tiktviift of tbt Globoles tr Atom* 0/ Utbt \ ai ail other •Thingi are earriii altrg from Weft It Eaft, -uMl* ihty m6 
* from the lucid Baify la the Earth. And Ibe nearer the Planet ij lo the Earib, the lefs •willie the Greulalien ef LIGHT 
" from Weft to Eaft, ■u.fo* it reacbet ibt Eye. Tbe GrcuJaliin rf Light fuiard the ^aft in ov Hour, fir hpance, luiii 
'* beitfi than in two j tobence tbt Planets appear lo move ntsre fwiftly or «>»r;'flowly, or lo fland in ibe fame Point rf the 
" Heeime*, or it rtlnm tevairdtbi We&, ibtugb tbtj do reallj al'u/eiyi conlinne advancing te Ibe 'KaA." 

F, B. 
ONwhichWeQUERB. How will the Comen Ihiftfor themfeWn, in their regular" Orbict ; or what Center ot 
iMnu mnfl they obey, in their lefpeClive Motioni, to correfpond with Oblervaiiou, accordine to the 2bo*e eenfufed, 
or ahfordly conceived, Ssftm ? And how confiftcnt this Syllem with Che Harmony of a MuttiCude ot Sy^tmi, each 
Iwriog i fxed Star, or new Sua, for its Center f And how will aff the Flancti, according to tliii new Hjpoibtfii, 
defeHbe equal Areat io equal T^mes, about tbe San, at obferved in tbe Coperaiaut Syftem. 

. as - CONFUTATION 




^"^-^^i^^^'^)***^ 



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CONFUTATION «/(*</»•«;«■/« SYSTEM., 

liagna *fi Vtritai, H prtvaUbit. ^ 

Oifitvatigm 1. Tlie S^iuD-etof xiit ftriiJitai Timtt ue oblerved to be as the Cbu oflht mean DiHaDCeg from th» 
San, of all BodRi revolving round the Sun ; confidcied as the Fooacain ot Li^^/ and ///of, irraiiiated 'throogh the 
yiba\eC:^irnitaa &y&eai: V\ hich univtrjaj Law obfcivtd, ii, aioBce, dettroy«l, if the Earth ii cui^«rcd at A(^r 
Thirrfore f. S.\ Sj/lii* is ai/u-/. 

z. Tlie Times now obfervcil of the CoymiSuJii, Ofpspnni, and Kttrtgradansni of the f-Linets, ate not (ach U 
wbuldbe; if they revolved, in Orbit:, round the Earth at Ri/l. 

3. The Bodies of Mtrturj and ftnui in the lower Conjunaion with 'he Sun, are hid behind the Suo's-Body ; and. 
in the nppe^ Conjunflian, (in the ditmieiu SyOem) are feen cu pafs over the Sun's Body, in Furtn- of a Jeri r«iaii 
Sfef, which it imooffible to happen with the Eaith at Rcll. 

4. JAircBT) and Vnai arc ubierved to have two Conjunflioni wich the Sun, but 00 Oppoficion ; which, cannot 
happen unlefs thofe Orbiti are within the Earth's Orbit. And iherclore cannot happen in F. B.\ ini-m, 

y The Earih being at Rtjf, in tUe Center oi F. S'iSjfitm, will aot account for th-: dii&rent 5r;^i/n(/i wtiaffarial 
Diameter! of the pianitarj Bodies. VtMm'% apparent Diameter, when gnatifi,. u nearly 65' 1 buttvhcn Uafi oot above, 
9' {. Moi-j'i apparent Diameter, whengreatcft itaboatzi'i bat when kail not above z'^ ', which, f. it.'s Sjfitm, 
with the Earth at Stfi, will not account tor. 

6. The greateS Ekngaiuii or Diftance of Mircwiy from the Sun ii aboot 18 Degrees, zn^ that of Ftiaa about 4.7 
Purees, aDfweriag exa^v to the Ctpmuean S ySem { bnt cannot agree with f. B.'i Syflcm, with the Earth at Rtfi, 

J. Mari, Jttpiur, ani Sa/HrM, have e«cb their CoQJanftion* and Oppafitions to the Saik a/tcrnau , wtd /MCt/J^v* t. 
which cannot happen in F S.'i Syjftm. 

8. The Earth being placed in the Center of/". B'iSjfiim, with the Snn and Planets revolving round it, tk« Planeti 
miift then, like the C«meti in the Ctptnticaii Syflem, be fcorcbed with Heat, when ntarrfi to the Su* « and frozen with. 
Cold, atthcir mateft Diftancesi contrary to the Harmony of the C>/«rOTfo( Syfteia j proving ^. jS'g Syfiem abfurd. 

\' Mm tflgMtrauct taidOfitKiitlitmiiitirvtiiring /« rmiji Oeuhli amd ahfurd Opinien, ttnctning Jtitkd bhJ dtmtKfirat'fut 
KutviUdgt, fnmiUtl 0m E;ipirimtiii Mid Ot/trvatimt, art Emmin ItTrutb, n/efiJ Sciinct, and lb* PulSe, Newionienfia. 

t> 7'4#DattJ«/'r^Edipfeafi>/APaIladiaiBy^ \yti, fiJi/tt^iiit i» ibii Work, art »U *ccardmg to Htvi Stjit^ finet 
th Gnffuitn £n cMiMtxetd, Oaobel' j, 158a. 

REMARKS en tin Jaid SYSTEM. By mr ikgenious and /iarmd Correfpondenr, 
ARGUS BRIAREUS. (See PalladiMm for 1761, t. 76.) 

Ciariiii i Unthrh dtprtffa rtffirgil vtritai. 

.'f^Hfi precedinji SyAem, according to my View of it, makes a very abjkrd Aoiirratknal A^^taxaxivt, moi& 
\ I likely to be rejeded, than received ai Tniib, by the Aftr»namcn of thii Age. 

"The Author whereof would do well to affign a Reafon, why tht Earth Ihould be fa^ed in the Canter of the whole- 
^Syftcfn, rather than one of the other Planetf. To fay that it contains on it more noble' reaturef, filing) 0/ more exalted 
Faculties and Perfeaion*> and therefore ii the moft illnfiritus of them all, woold be a bold Allertioo, and llrongly 
lavouring of a Mind overmuch attached to this Ar/ABall, and-iu Inbabiiants. And yet, if. this be not allowed a- 

{nbfiaatial Reafon, I prcfume it will be bard to find another that is To. It nn»y be alked, why the Sua Ihould 

revolve roand the Earth and not rather ronnd one of the other fuperior or inferior PlaneiE ( feeing he i> allowed to be 
the great Sonice of L'g^t and Hiai to all thofe dark Bodies. And alfo, why the Sun be made the Center of the 
Orbus of ytmmt and Mircury,- while the larger and Aipcnor ?laneti, Mai, Jupitir, and. Saturn, perform their 
ReV^olotions round an inferior Planet, t'ae Earth, as their Center. Clear, rational Anfivtrt ic thefe i^ifinns may go 
a good Way to remove Objcflions to thii Sjfiim. If the Anfwer be made, ibai thcfe Things inuft neceHkriiy he fo, to 
■^ee with die Appearances of the planetary Bodies, it will folUiw that tbii SyJlem cjnnoi agree with Appearances t 
fboogh the prefent Ceptmitan Sjfitm folly and clearly folves all thofe Appearancei. T\itCtptrnitaa or Fytbagvia» lb' 
pahtfii not only effiefinally anfwers. that End, in agreeing with the xeji atcuraii Obreivaiioo), which theabfurd SyRem 
does not ; but is infiricely more fioiple, aniform, and faarmonioui in its ConliruAlon, and coofequeotly ii infinitely 
more worthy the Wifdom and Contnvance of the divine and matchlefs ArtkinS, 

Burfirdi*, Cat. Ntv. 1760. ARGUS flRIAREOS. 

EXPLANATION of TERMS. 

A. 

Jthtrjur. A blight Sur of the ift Magpitnde in £n4^w; obfeived by Dr. /k% at St. /f^vW, in 1677 { never 

riling at Gritmtiieh. 
Athramcal Sifirg aad Sittiar »f ibt Stan, When thcy rife in the EaAern Horizoii, in the Evening, as the Sun let* i 

and fctiatbe WclternHotizoa, in the Eveniog, with die Son. 
^rai. Points of Time) whence Chronologers bwln to compute their Years, Of which Acconnis of Time thers. 

are many Kind* i u the £n of Creation t the Ortfiiaa, Turij/t, f^e. £tt t fome tnore famooa Iban othen. 

CjOOQTe 



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EXPLANATIONofTERMS. 

jB^haraih , Aintrahie ^titiiefoT it Jixrd Star of tbe ill M^nitndf,. called the finll'i South Ey«. 

jBgtMih. A Stu- of the id Magnituds, to the right Side of Ptrfitu. 

Algel. A Sur of ihe 3d Mtga'tade in the right Side of Pir/iai, called Mtiifit$ H»d. 

jStii. A Sur ia the Tail of the great Bear. 

jUmoMtc. A Svcceffiooofa'lthe Weck-d«yi,MoiKh>days,andHo1y<la7i, coriefpondcDt, thronghoal theyear: No* 

thing wiihoui tbofe Seqnifices btiDgfrK.^aiid Artnu!^ an. Almanac. Which fixed, and not vui«bl« or aftrODOmio 

Computation), are it< chief Properties. 
AhaiMieb, T\te rime u ArSarm. 
^mpl'iaJt. Ad Arch of thcHori'son between the Riling or Setting of the j'jm, Mtmi, or Star, and the E«ft or WcA 

PoioM, of the lame Name (N. or S.) with their Dec'ination. 
Jmt/tmma. A Projcilion of ihe S) here, trihetruphicttUf, on the Plane of the Meridian, the Eye being at U wfatit* 

DifttttKt, placed ta a Liar pcrpeadicular to the Middle of the laid Plane. 
JmaUfj. The (aiDe as Proportion. 
JvtUBf hirtBiin. 1 'he Angle madeby che^jru of the MAon'i Oibicaod Jxii of the Earth, at the Center of th« 

EartVi D:flc. Of great- UCeiDconlttiiaing/e/or Bcliplcs. Id which ProjeAion, if 

^"" •" i?; 5' K^ %' b' n' } ^"*'* ^*" "■ '''" \ Uft"} *'*' ^^^ ^"^ "^-''^ Ecliptic. 

Jiigle ff Bi/tSian. The Dificrencc between the nean and tme central Eqaitioa of the Moon, in the tww Afimtrnft 

' ih« greateH Eveition Aoc'e beineabouri'io^in Qaadratnre. Or the Difference betwcni die leaS and trye centr^ 
EqoatKW, according to 5/rMr'a ComputatioDt the greateft Angle of EvefiiAn, tbit Way of compntiDg being abonC 
a," yf, ia Qaadriiure. 

AngU af RiJUBk*. The fame ai VariaVmt'itfUtaaa. of the Moon j being greateft in Oamtt ofthe Moon iron the 
iiun, or 37' 33', according to f^r/ft'iAQronom]'. 

Anmeif. A Plaitet't angular Diftance from the A.phetion Pdim,- or AnheS DiAance from the Sav^ 

A^M or ABJii., The Ring of Satm^ -, appearing like Handles to the Body of tiie Planet. 

Mtrti. A filed Star i»f. the 1 ft Magnitode, or the Snrfiiii't Heart. 

jhttetdtnii^. Accordingtoa prccediog or contrary OrderofSlgni ; the f<me taAtr^pWA/w*. 

j^j, or Af^Ai. The Extreme, or Exiresea of u Orbit'i Tranfverfe Djav^r. Sfgnifyhig alfe tkfl J^ttn and. 
/'fl-/jns, of the Mood's Orbit. •"* 

A*pmtMi ef Latiindt. The Diltance of the Moon from At NonbWafcending JKm!«, in Degree*, C^f. by which 
(be Moon') Latitude is determined. 

AfiuiJhaalGigirinct. The Difference between the right and oblique A(c««6w or DcfcenEoir 1 or the Ttloe An Snn 
rtfii and fill before and afier Six. 

AfitaJim, The rifing Point of the EcUptit. 

Ammntbi. Ftriictil Cirdci paffing throngh the Znitb and ffaJir : Which Term* Jit. 
6. 

Baij&a. A famoni and antient City in Sgyft. It fioodnpOD a, Sqnate of no Pnrlongi long, of 15 Mile* each 
way. Circomfercnce 4SoFui]ongi, or^oMilea. 

f S^7Z P / 5^*"'* 1 In ibe Walls were 100 G«l«, as on each Side, with 15 ffftw/r etch Way, 
Wi^ < 135^05 " Z^i^ Vcroffing one another alright Anplei t making ($76 S^^tm, each of which Wa* 
i. 480 Furimgi Rcuajj 4I Furlongs, on the Side, and aj Mitei round. 
Id the MiJ£t over Eufhrain, was a Bn^i no Vards long and 10 broad. The Temple of Sihi wai a Pntlong 
Sf»ari, confining of 8 Tower*, one above another, each-75 Fiit high. King tfthaehathnKxar enlarged it to a FurUngi 
on each Side, making a Mile he enlarged it round. The aid P^u* wa* 4 Miles in Circainfirtuci ; the aciv 8 Miles. 
The HangiKg Gtrdms, 4C0 Fut fiquare, by feveral Tirraffts, one above another, till the higheft became 350 Feet. 
The AJ<tnt wa« from 'Itrrafi to 7irra/i, by Stain of to Feet wide, built by Archei upon Arches, and a Wa// 22 
Feet til ck. Thii wonderful Ciiy like the famous and antient City of Tray, is yaniEhed out of the World, where 
fomany grejt Thingi were once tianfaAcd T And as magnificent Citic* and Empire* fucceffivety vanifh in Obli>- 
vion ; lb Ihall Sj/iaj of the fa-/-/>W Bodies, and all ib«ir Inhabitants, paf* away, like £i«i^4r'* bafeUfs Fabiict. 
of a fi^K, leaving^ not a WWrii. behind I 

C. 

Calaiar. The fame v^iib Aimnnac: Which fe(. 

CtHttr if tht Eqataii. The fame ai the upper Fatut of an Ellipfij, round which the Planetr unifotnly more. 

CanjimBteH irui. When the Center* of two Planet* (at of the SUN and MOON) are feen conjoined in a tight Line, 
from the £arth's Center. 

CanjiitSin afpM-tfii »r -vi/ib. When two Planets are fecn lionjolned in a right Line from the Earth'* Satftrt, 

Cawfipitaiia. According to a following Order of Signs, 

C^nitMj NiiMai. A Native of fiam, inPcliJb Pr^ffia, born in 1473, and died in t;43. A great Aflronomer and 
Reviver of the Pjthagartmn SyAem. 

C»fmt»iHifin tmj Siiiinr »f Start. Rifing in tht Morning with the Son, and Setting at the Son riles. 

CytUaf tba Sbta. A Kcvolotion of 19 Years, after which Time the mean ZamriMj rtltrn on the fame Month- 
days. The Nambcr of this Cycle i> the Golden Number. 

Cjc/f af laJiaitK. A Revolution of 15 Years, fnbftitoted in the Room of iheGrwi OfymtiaJti dcotning (he YaaKthe 
Tribme was (o be paid to CfJloMtim lit Grtmt 1 eftabUihcd 3 1 « fiitct Chrift, on Sifttmi4r 24. 



DigHizcd by 



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EXPLANATIONS TERMS. 
D. 

DMAritfitlal. Diff tf ihiSun^i Light, from SuD-iIfing (oSan-fettioc: Being the DiftinaioD of Dayi according to 
Cufftm, which » the greateft Auckont/ in the proper Ufe of Woi^s. 

D^Naiurel. Dty of ibeytiiT,tri^Hauri. The Timeof an apparent RcvoluttoD of the Son, freoiany HoorCIrcIa 
to the fane. ^ 

t>ffctnitM. Seiting Point of the Ecliptic 

Jiiiil. The Ivjil/lb Piirc of the Siin'i Diametei', in folar Eclipru. In /toMr Edipfe), the Moop'i Digit» ecltplcd may 
06 23; ill above 1 1 Digit! Qiewing how mncb the Earth'a Shadow more than covert the Moon's nearcQ >£dgc to- 
the Middle of that Shadow, or Eclipfe. 

Dirta. A Planet's Motion ia direfl, movtog according to the follow iogOrder of Signs ) ai fiom Jriei to Tmu-mi, 

Di/t tf tht 5an a»d Matn. Tbcir roQud flat Fam, a* they appear u a Di&ance. 

Dijk »/ tht Earib, Her Pace, as fcen from the Sua or Moon i or from other Plucti i being ci^iial to the Diftrt»c* 
between the San and Moon'i horiitontal ParaiUix. 

E. 

tarib. The Globe we inhabit; carded Toand its Orbit, called the Ecliptic, in j6; D. j H. ^ 8 M. 5(6, bat to the 
i%mt fixid Star '\n lii<i O. 6H. 9M. 248. keepinK its Axii always parallel la itfalf. Whofe fwift Roution 
canfei its Pignre to be fiaiieJ next it* Poles, and rweHed ont abont its Equattr. It* ifmttrial exceeds its fi»r Dia- 
meter by about 6] Mites ; Sir Ifaac NrwtM having proved the tjitatttial to the flar Diameter in the Rsth of 698 
to 6jf». — Whence, according to Ntrwatd't Mealure of ilte Miles in a Aegrcc of a great Cirde, the Eaitb'i 
Orenmftrttut '{OJJ-Sj'l 
Diamttr 7969-1$ >£«;'!^ Miles. 

Htight tj tbt Atmjpbtn 17-ni 

Ecctniricitj. The Diflance from the Center to the/onuof a Planet's Orbit 

Ekngatitm. A Planers fiutbcfl aaiMlar Diilsace from thcSoo. as Teen from the Eartb. MtrcMr/a Elongation ii oMee 
more than z8» 11' 6", norlcfs tbio 17* 35'+*". Vtmi'i never more than 47° ji'sj', not kfs than f^'s^' 14*. 

EiKtrfim. When a Planet, or Satellite, eclipfed, begins to recovcriti Light. 

Efaa. The Difftmit between the j^^ and Imar Year, of 365'' j^" 49"" and SS*' 8*49", ot 10* il''o"i being 
KdEoacd. 1 1, whtde Dtayi, the Days of the Month fooncr the Moon cbangu in the followingthait in a Cotmer Year. 
■ EpbtmirU. A yearly and daily Account of the Places of the caUJIiai Bodies. 

M/tmiiiTK . The Dif*r*»et between ctoc Quantity and another to which it is to be t^uUid. Ai th» D^tnwa between 
the Planers mean and itoe Placet, Anomalies, ^t. orEqnationof nieantOA//arwflolarTime. 

SrUamm. A Southern CooAellation, or the River. 

F. 

FomtAM. A Star of the/r>f Magnitnde in the Mouibof the Sonthero fi/i. 

GtUiu NtaAtr. The Nnmber of the JUWs Cycle. 

BiBtualRifng. When a £/v recovers from the Sun's Light to the frfffuvf-'/. foatto be Ceen agRin in the Mining 

4|Ar(the Son. 
Utiiacal Ssttii^. When a Stjtr fitft becomes invtfible, by the Sun's near Approach. The Moon being large, can be 

feen 17' from the Sun, when the other Plaoett cannot be feeo till they are near jo*dianit from him. 
HiBtcMtrif PUet. The Place of a Planet as feen from the Sun ; from whence all the Planets appear to move dire^, 

nccording to following Order of Signs t and the htiiactnlrU Latitude is the fame with the Inclination of the Plaaet'i 

Orbit wiu the Ecliptic. 
Uarnui. The great Circle of the Heavens, bounding onr Sight ; dividing the (ipper from the lower Hemifphetv. 

It is diftiognifhed into ftn^l§, as what we fee from the Eanh't SnrJac« •. and ratitnal Horizon, as what it woald 

truly appear, if we beheld itfron the Earth's Center. 
HttrGr^ii. The fame as Meridians i or great Circles cutting the eqninoAial right Angles, at any Hour of the 

Day or Night. , . , . 

Hjfibtfii. A Syllem, Theory, or Conjeaure, to explain Appearances by j which it the more coafiAeju with Troth 

and Reality, the more it correfpondi. in general, with Obfervation. 

JtiaififHtMn, otherwife«alledPAnwf«i7H»w*.' The twelfthPartof the Day [of the Son's Light) from Son Rifiogto 

^•,i,S«tling: nod the twelfth P»trfilK Night, from Setting to Rifing of the Sgn : Being the antieot y.-wj* Accown 
* of Time. 

IllaminatitM Mtaih. The Space of Ti«e the Mooois-vifible from Conjundion to CosjonOion, 

JmaurSaH. When a Planet or Satellite firft begins to be eclipfed. 

Jtfiar, Mailted U. One oftfae^m«oi Planeu, next to the liigkcft, or ^dftrra. He moves ronnd the Sun in 11 Yn. 
313 D. 5 H. 35 M. 4, S. Inclinition of his Orbit, f 10'. Diornal Motion, 4' 59'. The Law of his Moaoa. 
about the San it fueh, that tbeffaff'rof hi* periodical Revolution is aa the Oo^t of his «<«> i)(/«wr from the Snu, 
compared with that immotmtii Law, obfaved in the Motion of the Reft of the Planets ; firft difcoveTed by Ktfitr, 
and iince demonftratcd by Sir I/aac NrwM. JOi. FUmfitad and Dr. UjiH^j obfcrvcd that JnfittrtD-mtA tooj}ow by 
the ToWm, which were torrefied aooofdingly. 



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EXPLANATION of TERMS. 

K. 
Ktpkr, "Sihu. Of Wiiiimherg, in Qtrtntatj, HouriOicd in i6ao i ho wat Maihcmaticua and AOronotncr to thre* 
Emf^nn ( vxt wai the &rft who diroovered the tUtf/um/ Orbiu of the Planet:, ud that their fiHtJiiMt Tiin« were 
•( th« Cuiej «f the DiCbancn from dw San. And flXpUiocd ihe general Pi^mu»t»a oF folar Gclipfe!. Id the Veir 
l6iS he publifhed his Epitome, \atiiied J/fmomite Caftrsicanit : Ephttaaidtt J* Harmuid MuttA, Mjfitr'mm C^m»- 
graphium: Likewire, Di Metibui SteiU Martii, and Other PieCM of AUroDOm}'. 

LatiluJe«f aSittrer Planil. The Oiflance of either from the Etliptit ; rneafared on the Arch of a Circle of Latttade, 



paGag thravgti tkc Center of either, and the Paitt of the Ecliptic. 
l^bratian ' ' •' ,.■... ... ■. , 



Libratian tf thi Matn. i . In Lmgitiuit, being a Motion arifiug irom Ae Plane of that Meridian of the Moom in 
genera), ncjirly tutord.towuds as ; not diie£ted towardi the Earth ; but towardi the other Foau of the Mooq't 
tUiftie Ofbit t wlMteli/ to an Eye at the Earth flie appcaia to lihratt to and fro. i. in LaiiiiuU ariiing fron her 
Axil not being perpendicular, boi indincd to the Plane of Iter OrUt, whercbjr fomttiineB tiu of h« Polei and 
foqietiraes the fA^ dipt a liuk toward* the Earth. 3. A Zji»f(««, whereby one Part of the Moon it not reall/ 
turned towaidi the Earth at in the former Manner ; bat another ii illuminattd by the Sun. For her JjtU being 
Dearly perpeadkiilarto the Plane of tlie Ecliptic, when fbeiiat Iter greateft Soaihem Unit of the Pan* adjacent 
tobcrNoithPoie, wiUbeiUoaunaccd by therian, while thefmtfrer^.or Sonth Pole, wiUba involved in Darlcoefi.— 
Thefe Liiratient are completed in her fynodicaj Month. See Ntvit^t Pnadpim, 

limUt.tf Eeiip/ri. SuorMooo'iDtftaiccc* from the Node at lew lULfuU Moon, within which DiOucfli all >Utr-fr 
AiMf Sdipl'ci muft happen. 

Fr. Node. Lat.MooD. Greater than which DiRancet {i«m AeNode, orLaiiMde ofthe 
C M^»l\>t,i^ S^oov.'lii' x' s'S'" a'it'?MaoB, no Edipfc of the Moon or Snn can happen, M neaieft 
txrimyri^imn '^^^^ ^1820 4 ■J.i 3* 14 ^Diftanceiof the Son andMoon from the Earth. 

Fr. Node. Lat Moon. Greater than which Diftasce* A«ro the Node, tir Latitsde of tbe 
I 6 T'mt S^'ion'i loiQiJ^ofl > 7 Moon, no Eclipfc of the Moon w Son can happen, at fartbeft. 
t/^i,imn |g^^ 5163; 1 ^ I 15 30 5 DiftancM of the Sun and Moon from the Earth. 

Man. Matked ^^ One of the /ranrnrji Planet* 1 moving round the Sim,iii anOrbitbetweeDtheBtrth attd^a^/«r>,iil 
t Yr. 3»tl>. 23 B. 18 M. iBS. Uii iiarM/ Motion, }i' ^j'. The lu/iiaiimi of bit Orbit to the Ecliptic, 1" 
51' I being ic Timet left than onr Earth. Hit Coloar 11 nuidy like that of the StMiJ/M^'mBi and il ntr^Mt/i 



t Yr. 3»tl>. 23 B. 18 M. iBS. Hit iiarM/ Motion, 31' 27'- The At/MnrtM of hit Orbit to the Ecliptic, 1" 

--' ■- ■ "" '' ' irEarth, Hit Coloar it nuidy liketb" '" "^ - " — '" ' 

MaUiai Gr£. The Degree or Point of the fidiptie on the Heridia at any Time of the Day. 

Mtrary. Marked 9. One of thc^rrtMr^PIaMtit nravlDg throsgh his Orb next the San, iaS7D. 33 H. 14M.' 

^ S. Hit mean heliocentric i/;«n>«y Motion 4*' 5' S'*. Tbt luliiiMiia of hie Orbit with the Edipbc^ 6» (9^;. 

being never more dongated from the ^nn than 28" it' afl', aud thercfsrc fddomfeeo..— He appeal* retn)gradc 

4 or 5 Timet every Year ; and it 37 Timet lefs than, ow Edith. 
t/trUima/ Paris. Tablet fitted for the Ure of NavirathM, fn»n a Projedioa of the Earth's S«ffacc, where the Me- 

ridiant increafc it the Paralldtof Latitude decieah. For at all the Pandlih eitd in a PoiMat the Pole, to tlMi*«* 

ra/Zt/ Meridians, being infinitely continued, never meet; 
idicmuitr. An Inflnimewiaveaied by Mr. "Ttvinlj, fitted to a Teleilcope, fot takiwg ^k DiaoeUti of thi PlanMiL 
Mtntb, iiaar tr piriaJicaJ The Time the Moon it going throueh her Orbit, 27* ^^ 43". 
-— — Sjmadkm/. From htr Conjunfiion to the nejtt Coc^nnAion with the Siu>, in 29' 1 s*' 44". 
— ■■■ ■ Se/ar. Time of the Su going throagh one of the Sigst in the Bdiftic nbant 3^ Dayi^ but all o£ (G£ei«at 

Lctrgtb. 

• ' ^ tvmi/y*igbt D»pi. Neatly eqsalio (he perio^cal MonUt. 
" ■ — a/ tht CaUniar. Uorc or left Dayt at in the Calendar. 
JUmh. Marked P, ^Jtcndarj Planet) moving round the Earth, to the fame Gxed Star, in 27 D. 7II. 43M. jS;. 

but return) not in Conjanflian with the Sun, till 29 D. 12 H, 44 M. 3 S. ijc. While the Earth movei roond the: 

Sun in 365 D. c H. 4B M. 55 S. Htr CMw inttrftas the Bdiptic in two oppofice Poinu, called IMti. She ta. 

JO Timet 1b& than our Earth. 
MM^ilMtHnoHanaf birOrbit •with lb* StUflh. 4* 59^35' in ConjnnAIon and Oppofition-, 
5 17 30 in Qpadratare with the Son. 

fta£r. The Point of the Hcavent under die Earth 1 diametrically t^poGte to die Ztmth above it. 

IMti. The Poiai* where the feveral Orbits of the Flaaeuiuerfca the Earth^i Orbit, oe Edipiici haaing %. flow 

/rsfn^M Motion, as well at the '^»^>f«>i Poinit, 
fi^KOft^mlDtgrf. The 90th Degree or highcftPoiM of thcEcUptic atanyTime of the Day or Night; whofe A|. 

.tjtndc it alwiyi equal to thcAngle diat the Bdiptic make* whh tbcHoriooni whicA ii alfo equal 10 iheDifltnce 

between the Pok of the EcHpbc and Vertex or Zenith of the Race. 
Njthibtmtrw. KnaturalQKf in thePlanettt inctnding n Day of Li^t, wid Night, where die Sua feUin AdinraaL 

JtevolKKMt of ih^lnct t being with u 34 Honrc. 

O. 
OUi^tt J/amfiau. The Degree asd Minate of theBqniBoAialirifiiig with the ffa«, M—m, ori>J«a«ff»bianobliqo«Sphera. 
Om^DtJemfitm. TheI>^^andMiAiii«ofth»Eqmwftiil>fitti«gHilfathc&Hi,2lfn^or/^eAb^wu 



,y Google 



EXPLANATION of TERMS. 

OetaliaiicK. The Time that i Star or Planrt it hid from ai j when cclipred by the Interpofition of theBouy of the 

Mood, or fome other Planet, bciwixt it and oar Sight. 
Oriht^aphie FrajeBhn efiht Sfhtrt. Drawing the Superticiei of a Sphere on a Plane, cutting it in the Middle, the 

Hye l>eing placed at an infiaiit Diftance vertical to one of the Hemi^vlMret i in which all the Hosr Circlci btcoiue 

Ellipfei: The fame with iAtiUImMs. 

Parallax. The Z)u?ct«.m between thetraePlace of a Planet, aifeen from the Ear&'jCeitter, and iti apparent Place 

%* feen from the Earth's Sorface 
Parallax in thi annual Oriii. The Angle the Earth wonld appear Boder to the Eye, M each Planet, to be elongated 

ftosn the Snn ; being greateA and leall at extreme Pofitions. 
Path f/iit I'ertn. A Circle dtfcribed by aoy Pointof the Earth'i Surface, by the RotatioD abottt iti .^'i. Thii Point 

ii confidered as •veriical to the Earth 'i Center ; beiag the fame with Ftrttx or Zmiib. The Semidianeter of the Path 

of the yeriix ii equal to that of the Complement of Latitude of the Place defcribing it, 
pimmbra. A faiii Shadow, or ontmoil Edge of the dark SkaJvui of the Earth, in an Eclipfe of the Moon : It being 

difficak to determine where the dark Shadow begin*, and where the Light end*, in (/dor) Eclipfe* of the Earth 

by theMoon'i Shadow. The Pen umbra' ■ Semidiametcrii equal to the Sum of the apparent Scmidiamcter* of tb« 
- Son and Mood. For if, at any Time of the rrw Conjundion-of the £v« and JKm«. nooeof thKPtaamtrattXU within 

theEaith'iDiOc, the Sun will then hcne luhere feen cclipfcd. 
Ptrignn. A Fknet'i luartfi Diitanee to the £^h. When the Moon'a mean Anomaly it 6 Sigm Ibe ii then io Peri- 

geon, and her diurnal Motion about 15'. This Point ii oppofite to the Jptgun, both at the Exuemei of the 

vanfverfe tKamtter of her elliptic Orbit. 
Ptrihilim. A Plaaet'i nearcfi Difttnce to the Snn { the htiiaeenlric Mntion being here the fa-ifufi, with 6 Signi 

Planet'* mean Anomaly. 
Ptact if iht Sum cr Plantt. The fame with Longitude. 

Ptact irut aiutaffartni. A* feen from the Baith't Center and Surface, lefpcAively. 
Patlital RiJiiigaiiJ'Stni»i*f Stgri. AthranUal, comical, *.tiA Inliaeal, before defctihed. 
Prtttjjnn ef thi Equintxti. The fixtJ Star* are ifninoveablc ; the Eanh travels round the Sun in its mmiMal Otblt, 

with itsj^i'i carried 6£* 31' 30', inclined to the Plane of the Ecltptic : And by the Earth's diernal Motion EtiL 

round it* Axh, in z^ Hours, the EquinoAial Poincg are moved caalrarj at about 50* yearly j whereby the fixidStart 

nre made to go forward in a fallowing Order of Signs, yearly, as miich. 
Pr»jeSin tf ihtSfbtrt. A geometrical Delineation ot the Circles of the Sphere, or any affigned Part, on thePIine 

of any great Circle, U on the UariKom, MtriJioM, Efninaaia/, Ec£ptit, Calunt, or on the Trafici, &c. being cidier 

-fiirmreflHc, fuppofing the Eye 900 dlAant from, and perpendicular to the Place of PrnjecUonj or er/ierr^h, 

the Eye being at an i^mte Diftance, in the Center of PiojeAion. 
PttUarf. ciaadiiii Pnhmiia, A Nadre of Ptlxjuua, a City of Jfrita, in Egjft-, who flonriJhed 135 Yean after 

Ojrifi i and was Author of the Sjfitm known fay that Name. . 
K. 
ttaJiai. The Semidiamcter of a Circle. A mi>M Proportional between the Tangent and Ctiat^i of any Arch. 

A mtax Proportional b^ween Sia* and Sttax/ Complement of any Arch. 
Xtfis. The particnlar Rtlatiaa, m Habitude, of two Numbers. The Siailiiadt of Raiw lignifiei Propoition, or 

Analogy. 
Simflt, £iflkatt, trifHcait, f»adrmfik^t, &r. A»n'». I* the fingle, fqnarc, cube, 4th Power, He. of two Quantitiei. 
SabdupHcait, ivhtripUttat, (ke. SJili; Tht fyuart, ekbt Raot.&c. of two Quantities, {Jc. 
Tht/tfji^l'tati Ratii. Is the one and f or JPower. confequenity y«^/^>r/>/ifj:r< ^si/a, the |Root, and the fabqnin. 

top'icate Adfis, the \ Root, of any two Qixantities ; and fo of the Rift. LtaJbttttr, in bis Aftronomy, haa 

iDilreprefentcd what a Ruiia is, in every Cafe and Circumftance; giving a wrong /lini thereof. 
4 to ^ the fimplc. A* to t^ the fubdupUcaie. 

a* to ^ the doplicate. a^ to b^ the fubttiplicate. 

■ «* to h* Ibe fefqtuplicate. 



Ratiu. < «' to i* the triplicaw. 
ff*lO t* the biqnadraW. 



«i to b^ the fubfcfqoiplicate.' 
a^ to b"^ the fubquintuplicate, 



iat thereof. 
I Raliu. 



.,\ 



JUt^m *f til Efuha**). Goiog back of the EqoinoAial Poiau, about 50* in each Year; caafed by the Earth's 

^Wsi'a^/ Figore, in its diurnal Motion. 
RsdaSitutf tbiOrbil t*lbi EcliptU Plaef. The Angle between the ^m of the Ecliptic and .<£n^ of the Ptanu'iOrbiij 

being equal to the Ecliptic's Atch between the fuv Axii. 
RiftMitx. The Pole's Oiftance from the Horizon of the Dijt. — The fame as the Sun's Declinauon. 
XtfraiJian. Produced by the Atmofpbere, making a Star appear more elevated than it really is, 
Rttrtgrodaliam. Going back, in a eonttaiy Order of Sighs : as the Moon's North NtA moves mrograde upon the 

whole of it* Motions. 
Rigltt Afiiufim, Tiie Degree! of the E^»ai*l, reckoned from the Beginning of Jritt, coming to the MtriHam irith 

a Stv or Planet » or to any Hoar Ciick, «t right Antlee with tke EqoinoQjal. 



yGooglc 



EXPLANATION of TERMS. 
S. 

Stni, ChaUtM. Of i8 Yra. II* 7*43", when 4 Leip-Yoart iDtenrene — botoDlxiSYn. 10*43" when j Leip* 

Ycut iotcmns. ■— The fame u Pitman Period. 
SaitUitti. Secondary FUnets, revolTing round their rerpe^ve Primuiei, u the Moon rQand the Eatth ; tfae Sttd- 

liiei of Jupiltr &nd Staurn round ihofe Bodiei. 
SaiKTH. Marked biOaeofihe/riimu^PlaneUi the higheft in all oar SyAem i movui| round the San in 19 Yrt. icSD. 

13 H. 14 M. 4 S, His diurnal Motion i'. lacIiDJtiom of hiiO»it *• 33'. He u retrograde once evcr^ Year, 
Sttnagra^hic PrmtaiaH. The fane » FerfpeAive, 
SiJtrtalDay. The Time beiween toy fixtJ Siar departing fronii to iti Return to, die fame Meridian t being sj^ 

16=' 4* 6'\ Parti of & meflu folarDay. 
W*"aiTiar. The Time of ihe Sun going from afixed5'f«rtohii Return to the faoc, }6<* 6)> ^" 24*, C^r. 
ItlarYtmr. The Time of the S un'igoing f[o;n, to hit Return to, the fame Point of the EelipUc; called ^fi> <ni^«/ 

Ytar, of about 365'' s"" 48" 55'- 
Siriiii CcmpniaiiiiB. I . Haring found ibe Moon'i mean Anbmalyi Ap<%es, and Node ( yon find the Kttntrie 

Eqoation anfwcring to her mean Anomkly, which being added tOt 01 fnbtrafied fromt the faid Anomntyi 

according to iu Title, you have thence the 1. ejaated ADtmt^y of the Moon { to which adding the Moon'i Apo- 

ree, yea have i . ijBottd Piatt of the Moon. 

2. Froin ihe 1 1) t^uaiiJ Plan of the Moon take the Sun'g true Place, and the SiMii ia the piAance of the Moon ' 

from [he Snn, by which you may take one the Sqoation of Variation (as at P. 74, according to Htmx) which' 

tuUid to 01 fuitrailiJ from the } A fqnatt J Anomaly (before found) willgire the 2. (f>M//</ Anomaly of the Moon. 

3;. The fyneiUal Anomaly being found, as under that Termj tal^e iti Half, if lefs than 6 Signa, but the Half of' 

iti Supplement to 11 Signcj if above bSigng. 

4. To the Logarithm 3.640432, of the I^ametei of the Circle ai EvtBion, add the Log. Sine of the Moon from 
the Snn (btftre faunJ) which Sua, rejecting Log. of Radius, will'be the Log. of the Chord of EveAion. Thii - 
Logajithm to be taken from the Logarithm of the MoouVDi&ance from the Eanh (/simdin aTaiit) «dding the>- 
Logariihm of Radius to the Remainder, will be the Bengali of an Arch, fiom which rejcCt 4;^. 

N«W, fay. As Xtdiuy tB ibtTatigent tf tbii Rxmaiader, imDegriit,fi tbtTa^tmt »f ba(f tie fjntdictii Jntmaif, tr 
ranginl ef Haff itt Suf^ltiutnl to 12', (before found) tilhi7ttHgtnt if an Asth, ivbeji DiJirtKft frm tlial Half v/iii 
bi tBt Ere ftion -Equation ta bi oMid er fahirallid accerdiiig ai tbt •uiieit fynadUal Awma^ is wtri v l^i liam 6 ^P"- 
— With which E<vtSim-EqKation you mujt connect the Variation, or RifitSim, according to iti Sinn, (bcifrc 
found) for an Eqaationi which being connefied with the Moon a Place t. tMoted, will give hci Or^'-i'Arr i 
.which is reduced to her Elliptic Place, by the Red n ft ion- Equation, found aa ufual. 

The rrw Place of the Node (titfiuaai) being taken frooi the Moon'^ Orbit-PIa^, the Rcn>«i»dCT WiH kf th« 
Aigumtat tf Lalilui't. 
B/ (he DiAance of iheMoon from the Sun, yon find the £j|rr{/f of tb? greatcALstitade^bfve tW prefent LuitNde. 

5. To find the prcfent Laiicudo. — Ai Radim ta ibt Sim tf tb* jrgMpttit ^^ L^itud*, io \t lb* Sint rf iht grtnUfi 
Latitudt, to tit Silt e/ iht prefert Laiitudt. 

To find the Redu£ltDO. — As Radiuitp Ce/19* ^f tbt g^tat^ Latii^, £d iiToMgai ^ iIm Atffaunt ^^I^hiait Ut' 
Tengnt ef air Ai:glr, -whuft Difftrtmt /rem tbt farmn is ibi RcduSim. 

*,* Lfadtntir, in his AAronony, hu ufed Srrtfi's Logsiithmi of the DiAmce of the Moon from her Earth, . 
according to her mean Anomaly, ai he has alfo ufed Strtti's Diameter of the Circle of EveClton, and alfo Variation 
Equation, yet hat deviatc,d from this Compntation, in nfing ^rw/cn'i cantral Equation to the grtat^ ^cceptric^y, 
\a^ei<i nf Strtii"! Eciiniric; the Maximum of the latter being 5" 1' 43' andof thcformer but 4° 57' s6"i being 
3' 47' differedt. Lcadbitter'i Logarithm of the Chord of Eve^^on computed to erery Pegrce of. the Moon ^ Siio 
(avei no Labour ; being more difficult and left certain to proportion the Logvithm of the Chord of EveAion J.9 
the odd Minutes and Seconds of Moon a San, then to gain that Logarithm by nddiug the Logarithm Sine of A^Iaos - 
ii Sun to the g.ven Logarithm of the Diameter of Evcdlon Circle, in*. 3.^540432. 
Sun. The G1ob« of Fire placed in the Center of onr Syllcn>i rcvolfing round its Jxii in 25 \ Dajrs t ud giving 

Light and Heat to the whole. 
^miaii. '(crofs a trigoaFig.) jivM. X lii*ltifiicAli*», */ Square Xtti, T. Ttugtat. '.' fbmft/at 

o Rtqmred. -L. Drmjui,, S. &«. Cot. CttaMg^QTlf. : 1». 

R. Radiui. = E^ual. Cot. CftfworS'. • Digrm. t: 8» ii. 

+ Mof*' I. AngU. Sec. &tcamt. ' Mimm. A TrfMUglt. 

— W>- ^* Jng/tl. Ci)(K.Ct/t€anlOTf.»Stcml.'nird,iSc. Djfll*-/. 

SjmediialAatmaJj. From Syiygies to ^uadratnrn it the Moon from Sun lets than j or 9 Signi addid to the Moot'l - 
mean Anomaly z.tquatid, by her Eccentricity and Variation. — From the C2.aadratnres to the ^^zw>« it the Mocn ' 
from the Sun more than 3 or 9 Signs >&rA9r^fr(un tbe-^Moon't mean Anomaly t.tfaqitd. w before. Thiiii 
according to Siriti'i Lunar Tbeory ; who deteimine* ths Mwm's (rw Piatt, frum.her mean Place, at any Tiwe, -by 
Means of 3 Equations. The firft of her Center, for the gnattft EcccBttici^ (callod the tectniric Equation) the 
EimtSiait-E^atia» cortefpondent to the Diftrtni* of prsfcot Eccentricity from the greait^ (making together the 
■mbeU central Equation) and the third, the Variation- Equation (otherwife called the Refioflion) nicd before to 
equate the i. equated Anomaly. Which three Bqaatioas give (he Moon's Place fomctimes very near the Ob- 
fervatlon. However this Method of CoapvtntiOD ftemt CD WMt ImBCBVUU&h in n new Ciick of £vi^'fi ■ 
aew tcctntric Equation, and new Feriatitn, 

DigHizcd by VjOOQ IC 



EXPLANATION of TERMS. 

SjTy^iei. The ConJanAioDorOppofitioDof theSonaad Moon. 



Tiint aj RepUtian. The Time from the Middle to the End of ft ToUr Ecliprc. 
Tratifit, The PaiTmg of one PUoat byi or over, another. 

yiilar. A Line drawn from any Planet moving roand the San, or Ftau of iti Orbit, defcribing eqaal Jriat in eqaal 
'Hme). 

ymii. Marked ¥,Oneofthe^riW)i Fhncti; thebtigbcedofall. Whenlbe is Weft, it hergreateft Etongitioa from 
the Sun, flie rometimei Ifainei extreme]]' bright. She bat her Increafe and Decreafe of Light from the Sun, like 
the Mood i and novel in an Orb, between the Earth and MtrcMry, roand the San in ZZ4D. 16 H. 49 M. 14 S. 
'and it never farther from the San than 47° 3S' 3;'. She has the /r^ Etcmlricitj, but greateft geocentric Latitude, 
— For being in ~, retrograde, her Latitude ia above 8° N, and being in "B retrograde, Ihe has about 9" Latitude 
S. Id every 8 Years Ihe is feen in the fame P/ace of the Heaveni. 

fertex. A Syftem of Particlef of Matter, according Co the Carttfan PhiMophy, rapidly moving round like a Whirl- 
pool i by which the Frtntb Mathematician! endeavoured to folvc the Motioni of the cceleflial Bodies : But being 
proved abfard, and contrary to Ejcperience, by Sir J/aac Newten, it was exploded. 
X. 

Xphiai. The Sword-Fini ; a Sonthern CufitlUaitn. 

Y. 

Year. The Time of the Earth'* Revolution tbroogb the Fcliptic.'in 36; D. 5 H. 46 M. ;; S. called /w/iV«/ Year, 
or iu Retaro to the fame fixed Star, ins^jD. 6H. 9M. 24 S. called /itno/ Year. 
Z. 

Ztuiib. The Point of the Heaveni diredly over oar Head^, otherwife called the yerttx ; diametiically oppofite to the 
NaJir. , 

ZtJiac. A Zone or Girdle fnrroanding the Heavens, crofling the EquiaiSial, in Jrin and Libra, at an Aozle 
of i3« aS' 30*, equal to the Snn'i greateft Declination. The Middle of which Zodiac it the Etlipiic. The 
fireadth of the Zodiac ti iS" 30^; talcing in rbe Latitude of all the Planets. It ii equally divided into iiPaici, 
called Signs, denominated j^Vi, Taarui, Gimni, Cancer, Lit, Virge, Libra, Scerpia, Sagi/iary, Cepncern, Ajiiari»i, 
MadPifieii btmgCoHfieiiaiinti of thofe Names in the Zodiac. 

JS til firtroifg Grelii and Prtptrliti b/ the Earth mJ Heavens, are beft fieti *« Mr. Cole'i new imfrweJ terreftrial 
amteariejtiaJGlobei, (which no ASronomer fhould be without) ^War hit H»u/t in FleetHreet, London, being Succtffsr 
tube eimxtnt Mr. Wrigbt, Matbemaiital lafirament Mdler la bit iate Majt^y. Wbere Ukew'fe maj bt had all Zvrli tflkx- 
diematical Inftrumenti, Optical GlalTei, Ht. «rf«rd!iiif rvrif moft corTc&aa^ncwcft Improvement*. 



DEFINITIONS of (iDANTITY. 

Dif. I. Whatever Bung, or ObJtS, confifti of Fani, and ii capable of being augmented or dlmioilhed, ia called 
^Mniitj. 

Corollary i . Btmce there it ^iiantily af EMtenfiam, Nmnber, Jfeiebi, Memjnre, Meliem, Tim, Stc. taken mere #r Irfi, 
heamiervT ligbler, langirarjharler, Jhui/itrtrjk'wer, ice. relative It lot /am* Kind i ffcat and (iBtX\ being hat ten^arativ* 
Term far Thing, af the famt Kind. 

Z. Jndai iCpHncifa/Preptrljaf Qatatity it ia it, being taMiU ef more er led, tierrfart Q^Uttitltt BUfj he adJed It, 
fibtroMed Jtam, aaimnltiplitdby, amaaatber, ar divided into the farti tb^ ctnlain. 

Def. II. All ^antiiiei have their Parts united orfeparated, 

Def. III. Qoandty having Ita Parts feparated i* called Mu/tilndt, or Number, being the SubjeA of Arithuetic. 

Def. IV. Quantity having at Parts oniced is called Magnitude, being the SobjeCl of GeoyETar. 

De/.V. ThcnarWRelation of mw ^mnViVj of the fame Kind compared together, i* called a A4ft> t andtha 
Similitiide of Ratios of Quantities it called Pnfartien. 

Def. VI. The Knowledge of the Comparifons, Properties, and Relation* of ^aniititi {Kaiiti and Similitado 
of RatiaiJ is the Sutjeft Of MATHtUATiCi 1 including Fhtxitai, Algebra, 4rithmtie, and all fubordioate Mtthadi 
mi Computation. 

Corol. r . Hnee, a Part af S^uantitj ii tn/f cunjidtrid in Relatitn la tb* whole, trndnug bt taten ml an inJiviJthle Com* 
It af il, tr far tbafwbaje farthir Diirifibililj ii net ienfidired. 



\it\t fiffiifiit amf ^anlilj, etnfidired ai indivijible, 

Nombcr it a Nam ef ^miij eanfipng ef a CalUaitn er Sum af Vmtt, whether (tnfidendai Parti of a wM, tr 

9I1 ^MMlifji. 

Stmt 

DigHizcd by VjOOQ IC 



rfftverai'whaie ^uanlitiei ttgttber. 

4, Integer « oNaauaf ^uantitf ten/ldered at nnfiJUng ^ nubth Vmtt. 

5. ttaSiaaiiaNamtf ^SMtitjcen^dirtdaietMfi^grfPwUt/ enUnit, trtvhoJt^iumtit;. 



Hm Aniitnl Osd&VATioiJi {^ Solar 4X^LnQ«r ECLIPSES Maf^Arv^vit/i tbt Compnta&Mll /rwn /^ Tablet inth 
Roj'al AftroDomcr, nrrtaedhjth arwTatilttf Ac<lil.tt.iLTio», at P. 374> JeetrMag It D. C. 



I. A Tii/V Bdipfe of the San, Jint 16, AmuChr, 364. Accordioe to 

J\ Mr. DuMbmu. (St, Ph. tranfaS. Vol. XL VI. P. 168.) xt app.T. 

Under the Meridian of Grtunt-Uh the Moon w» in Cen/ij, with the Sun . . 

Tilt Sun's ZcHptKLtHgitudehyiheTaHuv/tttbea . . . 

Therefore the Moon't true Ecliptic LoDgitndc wii . . , 

£Dt by the Tablei thai csrreAed . . . 

2. h pattia} (oXti Eclipfe, Dtetmhtr 12, Amu Chr. 9771 at . . . 

Under tbe fame Afe-f^im the Moon wai in .^s(«ff/. to the Son . . . 

The Sno'i Ecliptic Longitude by the 7'«Jilj being then . . . 

TheMoon'i £c]ipticLoDgitude«j/}r<vf/wa* . . . 

But hy the TmHii wai . . . 

3. Another /«r/i«/EcIipfe of theSnn, on^wrfS, Autre Cbr. gyS, at . . . 

Under the fimcMeridiaa the Moon was in Cmi/ijmtinia . . . 

The San't LsngiiMJe by the ^abla waa then . , . 

The Moon'is^^/irivi/Ecliptic LoMjiM^wat therefore . . ■ 

fiy liitTahiti wat . . . 

N. B. The firfl of thefe wai obferred at AUxandrla, in Eiyft, hj Thttn. 

the fame u are quoted by Mafir in the Pt^tgtmtma to hi) T^hi. 



CMKpaiaiitm, 

o' o''39'4i' 

D as 9 49 . „ 

n 25 49 y> I Error — > 

°- \S « S4 I 3' 36* 



9'' "'"SO' '^■ 

— 43'3r 
/ »7 8 S3 
/ i6 as 14 
/ 26 26 12 I 



. Timt. 



Error + 
0*58' 

..Time. 



I* 16" lo* App. 

+ *9' 3* 
« 2' SJ I 
n at aa 4 I Error + 
n 21 aa 34 I o* 30* 
The two laft « Grtnti Cain 1 and are 



1:^ The atuiini Aftronomen were fo negligent in their Obfervat'uiH, that hardly any can be depended a 
tbtni Tcmark), for efttbliOiing the Ctrtmnt}, mucfl left the Qaanticy of the. Moon 1 Acceleration, at differ 



d 00, a* DmH' 

Qaanticy of the. Moon'i Acceleration, at different 'nme*. 
And yetthere are a/^^ attended wiih (uch lucfy Circta^ancti, that they ferre, a* be obCerves, not only to ellablilb 
the mpeibtfa, but to fctck the Quantity of the ActiUraiian of the Moon. I Jball therefijre odd thefe, « they lie in 
DaHtborH^i Letter to Mr. Mafin, and compare the Compatatioo) ftotn the eirriStdTt^Ui witb them. 

t. The£ri^ ii faid \>y Hiffarehiii, to have bees obferred ttSalgftn, in 
die 366th Year of Nahnaffar, the Night between the i6[h and 27th Day: 
tiflh^thi whenafraall Part of the Moon'* D^wateclipfed from the JVfri'i. 
Eaji, Half an Hour before the End of the Night, and the Moon (ct ecUpfed, 
Thi( wat in the Year before Chria 3S3, (faffely printed 313) Dittmhtr 22. 
The San rofe then at 7^ iz^ and at the Moon then had &>nth X«rifM!r, hei 
Setting moft have beea bmeihing fooner. 



2. It ii alfo faid, by Hifpta-thui, to be obferved in the S4th Year of the 
fecond Cal&pic Period, at Akxaniria, the ■6th Day of Mi£an when, he 
iayt, the Af«M began to be edipfed Half an Hoot before her Pijoii, and wai 
wholly clear again in the Middtt of the third Honr of the Night. Thii 
wat in the Year before Chrift aoi, Siftimbtr aa. The Son fet about 7" , 
after Jix 1 and the Moon being in Anttttd. witb N. tatiiudi, her true RiBog 'f*<*lt 
had been fomewhat (ooner ; bnt the Dt^Jfitn by P^aJiax, over and above '"" '' 
Refraflion, bringt theTimei toanear Eqnality. 

3. The moft anttent£f/i/yi recorded, it related hyPtelemj, to have been 
obferved w Baijk», the firll Year of Mardtitrnfad, in the Night, between 
the Z9th and jolh Dayi of Thvib, in which the Mws began to be edipfed, 
when one Hoar after her Rifing wat fully pafled. Thit Eilipfe Wat in the 
Year before Chrift -jit, on Marih to. The afpttmi Rifing of the Mmm 
waiats''46*>- The San-Setting at $"48'". 



Ctifuatin. "} lU ti. ijr O 
Beg. 71111m 30> fJ'H-rfl'f: tbm/t 
Midd.7 eg o (iflJlaahtji 
Dig. Ut. »" ii'J 



Tltfi Tima atrtfftmi mi 
tt txftStd, aad 
latmrintfiir tbt 
\j^rmB I tbtSmr tfibti m 



Ctufutatles. -J Tltfi Tit 
B'g- S* 34" 4»' t-r " "", 
Bad S 41 O fitfi^aMlC 
Di£. EtI, 9" o' Jfirmir i lit . 
fari/f atifi fnm itt aiMiati Durailn in'Kr im 
' u/l, farilfjhm lU tfimii iMgiladt t^Btbf- 

CtmfMtim. "> n* Befii"iit if ttU a^. 

Beg. 6*1 J7" lt< lepvi vtrj mrlj witb lit 

Mid. g 5t o tCnfmtMimi TiifFtrMad- 

Endio 4j a JmiiHnr pf Laiiitdt, But if 

Ki\>\\onfii*litnQ', a«7 HT jo' ErjO e^ Alci- 

I, bath CWirratini isill arrrffni; ani itr 

1 rftabyloit in nM tua ' ~ ' ' ' 

UDaji. 



*,* Inregard to the Acdltratitn of the Aptgu and NeA, fuppofed by Mr. Mirrit, if it had been founded on Ob> 
ftirvation, the foiar Bdipfii in 977, ard 978 were, of all oihert, the moft likely to have dtfcovered the ^eati^, at 
wellai Ktaliiyof it; At ihey happened one near the Pirignn, theother nearthe Apogconof theMoon't Oibit. Sot 
we (ta at near a Conformity of the Errer of Computation at can be expeAed. And the Acceleration of the Moon't 
Anomaly being then nearly eqoal to 40*1 it being the Sum of the CorrefUon of the Moon't mean Motitn, and twice 
the Acceleration of the Moon, the Sqaationof Zba^/'/W^ thence atifiog would be abont 4' in ihe Perigtan Neui Mnn i 
and 3'iD the j4^jH«. Which would give the Errert of the above £i'2j!/W, in I)<r">^T 977 • ■ +$'0' 

mjvu 978 . . — ? 30 
I do sot doabt bntJVfi^fr omitted a CorrefUon of the Apcjctm from the obferved Difagrecment with Qhftrveiim. 

Aa to tbe Acceleration of the Moon't JVtirf, \ ean fay Nothing to it lirom a Compaiifoo^of mcini ObicrvatlOB> j 



bnt I thiolcthere ii at little Reafon to fappofe-any. S. C. 



- UttmAwg, 1760. 



db.G^oo^le 



CONTENTS. 



TMe irf Cccofld Equation of the Moon** Apogee, ac- 
cording CO Nruilen, With decimal and lexagefimal 
** MuttiplicTi Sot greaceft Dif. under and above the Moon'i 
ceocral Equtioa, forpreCentcestralEqoatioD Page 64 

Second Equation of the Moon'a Apogee according 

R> Harrex. With deciioat and (exagEfimal MDluplier* 
(or the grcateft Difference under and above the Moon'* 
mean central Equation, for prcfent central Equation 65 

■^— IV. or liiean central Eqnation of the Moon, ac- 
cording to Nf^'fo'. With the greatelt Diilerencc of 
Eqnation (under and above the mean central Equation) 
cotrefpooding tothegreatcft and leaft Eccentric itiet 

from 66 to 68 

.- IV. OT mean central (or elliptic) Equation of the 
■ Moon, according to Herrax. With the grcateft DiiT. 
of Equation (under and above the mean central Equa- 
tion) correfponding to the greateft and leaft Bccenttici* 
tiei — firtjm 69 to 71 

—I. V. Equation of the Moon, or Moon'i greatefl'1 
and leaft Variation, according to Nmv/tn f 

.— Decimal Multiplier* for the foregoing Equation f ' 

Moon'g grcateft Variation in Oftanw ol DaO J 

~— — V. Mean Variation E.pation of the Moon '^ 

^ — Logiftical Logarithoi* for CorreOion of the V73 
foregoing Equation — ' J 

.1 V. Entire Variacion-Equation>of theMoon,ac-1 
cording to Herrax or flamfiiad \ 

.— VI. Equation of the Moon, orfecond Equation i 
of her Center. According to ^<w/m j^* 

— — VII. Equation of the Moon, or fecond mean I 
Variation. Accordingto Gngtrj. J 

•~— Correaion of Grrgarft Vli. or fecond Variation^ 

— VII. Equation of [he Moon, or fecond mean j 
Variation. According to NrtvtaK 1 

-^— Conefiionof Vll. E'quaiion foregoing, or fc- >?; 

eond mean Variation | 
Panher Corrcfi. of foregoing id M. Variation. I 

According to DiC of D'l Dift. fr, Earth and Sun J 

— Second Equation of the Moon'* Node, according to 
Nrutim. With decimal Multiplier) and Logiftical 
Logorithmi to be applied to the nvateft Exceffei of Re- 
duflion and Moon's Latitude. For finding the prefent 
Reduflion and Latitude. Alfo prefent Bxceftes above 
the leaft Inclination of the Moon'* Orbit and Ecliptic, 
for finding tl^e prefent Inclination -— 76 

Red udion- Equation of the Moon from her Or- '1 

bit to Ecliptic -- — 

—- Latitude of the Moon, for leaft and greotelt In- 
clination of her Orbic. With greateft Excd* of 
Latitude for finding the prefent Lat. Moon 

__ — Mean horizontal Parallax of the Moon in Con-' 
jnnflion and Oppolition of the Sun and Moon. 
With greateft Difference of horizontal Parallax 

—~^ Decimal Multiplicrg for greateS Difference of 
horizontal Parallax. To find the horizontal Pa- V78 
rallax for prefent Eccentricity 

^— CorreAion of foregoing horizontal Piralltz, 
ont of CoDJonfUon and Oppofitionof the Sun and 
Moon — — — 

_- — Eccentricitie* of the Moon'i Orbit. Difference of 
thofe Eccentricitie) from the mean, according to Htrrex 
and Flatafttad. With the Difference of £ccciitricitiet 
firoia the mean, according to Ntv/ttit 79 



Table of Bqaadon of mean elliptic Bqnation of the") 
Moon'* Center,to the mean elliptic Equation. Ac- ( 
cording to »V^i Hypoihefi* — 1 80 

ConftruAion of conftant Logarithms in follomng f 
Table, for finding the Moon'* central Equation J 
—^ Conftant ^garithma correfpondent to the different 
EcceDtricitie* of Moon'* Orbit. For finding the tins 
elliplic^quation of the Moon'i Center - 81 

-■^EqnatioO'Or Coiteaion of Half Moon't equated A- 
nomaly. For txpeditioufty finding (at one Operation) 
the tme Equat. of Moon'* Center fr. 8a to 83 

Elliptic Equation of the Moon't Center in all States 

of her variable Orbit, according to her different Ec- 
centricity. Wfth the Increafe or Decreafe of Equation 
from mean Eccentricity for evety 5000, Difierence 

of Eccentricity . - fr. -g^ to 89 

Equation of the mean to the prebnttroe elliptic E- 

qnation of the Moon'i Center. According to equated 

Anom. Moon, and Son fr. Moon'i Ap. fr. go to gc 

Ufe of the foregoing Equation — 96 

Of finding the true from the mean Anomaly univerfally 

andcorrefUy - .— .— n6 

MAYER'. LUNAR EQUATIONS. 

Table of Equation of Node and Moon'i mean Anom. 97 

L II. la. IV. V. Equationi of the Moon 98 

VI. VII. VIIL IX. X. Equations of the Moon 99 

^ ■ ■ XI. Equation, or Equation of Moon's Center 100 
——XII. Equation, of Moon'« Eveflion 101 

■ "" XIII, Equanon, of the Moon'i Variation loz 

XIV. Reduaiou-Eqnation to the Ecliptic ") 

Mater'* LA-nTvoa of tbe Moon. | 
——I- Moon'* mean Latitude — ^ 1 

II. Equation of the Hoop'* mean to her true j 

Latitude — — J 

Mateb's rokizoktai. Parallax of thi Mooh, 
—— Mean equatorial Parallax of the Moon 
■ — I. Equation of Mo 



103 



O.J. 
> 10s 



Moon** horizontal Parallax 
II. biuadon of Moon'i horizontal Parallax 
M. EULER's EQUATION.S of the MOON. 
Table of £qnation of the mean to eccentric Ano-"^ 
maly of [he Sun and Moon 
■ Snn'i mean Motion and Acceleration 

I. il. III. Equationiof theMoon 106 

—~' IV. Equation of the Moon — 107 

V. Vi. VII. and VIIL Eqnations of the Moon, wiA 

Remark* — - — — 108 

DIFFERENT METHODS of folvlng the KfliriM 
PROBLEM. 

A limited Corre&ion of IfarJ't Hypothefis, detennining 
the true Angle at the opper Foco* — 109 

Example* of leveral Solution*, by different Methods, ac* 
cording to Haiiej, BuIliaJJmi, and the foregoing Me- 
thod, compared together - fr. notour 

A Remark on th«'mifccllaneous Trafit — 1 14 

Univerfal and Ihort Method of folving the KtpUriat Pio< 
Uem — ^ — — gg 

RULES and EXAMPLES for A/tnmiigi odicr REOUI- 

SITES of ELLIPTIC ORBITS. 
Pr»f. I. To determine the Diftance of a Planet, or Co- 
met, from the Sun, from thetnu Anomaly aiid£ccen> 
tricity of the Orbit given ■ ■ ' _ ? ij 

Pnf, 



DigHizcd by VjOOQ IC 



CONTENTS. 



Prop, n. To deurmine the eccentric Anomaly of a FU- 
ncc, or Comet, from the true Anomaly uid Eccentricity 
giren. 

Pnp. HI. To determine the mean Aoomaly and Equa- 
tion corrcfpondcDt, of a PUnct, or Comet, from the 
eccentric Anomaly and Eccentricity of the Obit 
g^ven ■■- — — -■ ■■ _^^ II j 

Prvf. IV. To determine the Diftance of a Planet, or Co- 
met, from the Sun, flem i%.t eocentric d^f^ulf, tnw 
Anomaly, and Eccentricity of the Orbit giypo. „,^ 

Pr«p. V. Todetermtse thegreatcQ Eqoation of aPIailM, 
or Comet, or greats. Di^rence between its mean and 
troe Anomalie» 't • 1 1 6 

Prtp. VI. To determine the Eccentricity and other Di- 
menfiont of a Planet'tor Comet's Orbit from ths great- 
eft Eqoation given — fr. 1 17 to 1 18 

Remarlu on thegreatefi Eqnat of JIfortYry fr. 118(0119 

a PLACES and 



Decimal Table of the Sun's mean radical Places and Mo- 
tions : With Eqaations of the Sun's mean Placts in 
afironomical Table* to thofe in others fr. i aoto 1 2 1 

I. The Moon's mean radical Places and Motions. 

With Equations of the Moon's mean Places in agro- 
nomical Tables to ihofe in others — 131 

■ The mean radical Places and Motions of the 

Moon from the Sun. 

-^— Mean radical Placet and Motions of the five pla- 
netary Bodies, Mircurj, fiMm, Mars, Ja^ttr, and Sa- 
tur* — — — fr. 1 31 to 1 23 

^— ~- Planets mean periodical Sevolutions. 
Planets mean fynodical Revolutions, 

How to determine a PUcet'a mean Place at any Time, by 
it] periodical Kevalution, and the mean Place of that 
Planct/orfomeoneTimebemggiyen 113 

Comparifon of the Elements of ue Planet* mean Placet 
. and Motioni, according to late Improvemeott. 

Law of the five primary Planets Motion i a^ 



Remarks, by different AAroDOinen, on the PhKoomena 
and Properties of Satura't five Satellites ; and oaSa/um 
and his King. 

A general View of the Elements of the Theory of oar ^ 
plaoetuy Syfteffl " — fr. 117 to 118 



jffirtntmicgl and ChrcHolegUel DEDUCTIONS and 
DEMONSTRATIONS. 

A Table {hewing, at Sight, the Number of Daya from 
the ifl of Jmuatj to any Month-day of the Year foU 
lowing, in a common or Leap-Vear. 

■ For reducing 'JaiioH Years to Days, and the con- 

trary, 

With Example! of the Ufe of the foregoing Tables 1 29 

Table of the ;NuEa»,y£i!itr, Grtgerian, itA /jJtrtai Yeari' 
compared. 

With Examples of the Ufe of the foregoing Table 1 30 

Of thcPrcceffion of the Eqaiooxes. 

The mean annual Qnaniity deduced from Obfervation. 

Of the Progreflion of the Aphtlions and Nodes of the 
Orbits of the Planeti in refpe£t of the fixed Stars. And 
of the Progreflion of the Aphelion of the Earth's Or- 
bit. 

The Quantity of that Progreflion dedaced 1 3 1 

Of the Inequalities 0/ the Earth's Motion, canfed by the 
Gravitation of the Moon. 

Rules for determining the Quantity of Preceflion, Nuta- 
tion, and Changes thereby of Declination and right 
Afcenfion, in refpcA of the fixed Surs. 

Prefent Obliquity of the Ecliptic deduced from Obferva- 
tion — — — 131 to 13) 

Of the MEASURE of TIME. 

The fydereal and folar Day. 

An aibonomical or folar Day. 

The fydereal Day correftly deduced. 

ToregokK a Clock or Watch — '34^ 'SS 



EQUATION of TIME. 



Decimal Table of the radical mean Places and Modona 
of yH/iV(r'i four Satellites ■-■ 114 

Law of Motion of Japilii't four Satellites. 

Periodical Times, Diilancn, Magnitudes, and variable 
Motion of Jafiitt'f, four Satellites. With Obferrations 
and Remarks by Dr. PaimJ and Dr. Bradkj on the 
Phxnomena and Properties of thefe Bodies 12; 

Dedmat Table of the radical mean Places and Motion* 
of the five Satellites of Satan. Accordingto late Im- 
{HOve meats. 

I Of the radical mean Places and Motions ofthe five 

Satellitesof Satt^n dednced from their periodic Times. 

A Comparifon of the Orbits, Revolutions, and Velocities 
of Jupiitr and Sahim, with the Orbits, Revolutions, 
tod Velocities of their Satellites — r26 

Law of Motion of Satura't five Satellites. 

A Comparifon of the periodic Times and Diflancet of 5a- 
/ara't five Satellitea from Satuntt Center, in JEo^s of 
his Ring — — — — — I a? 



Examples of the Equation of Hme 136 to 137 

NATURE and DIVISION of TIME. 

Time meafured by Motieo, 

Variable folar Year. 

Mean aftronomical or folar Year, called alfo the tropical 

Yeir. . 
Near fydereal Year. * 

Near anomalitlical Year* 
Correa fydereal Year. 
CorrcA anomaliftical Year. 
Mean lunar Year. 
Civil Year. 

Mean Jnlian and mean folar Year compared. 
The falling back of the Seafon* before the Style wat 

altered. 
The Qnantl^ dedaced. — 13810139 

"^le, how — i4'> 

DlCitrence 



AlterttWB of S^Ie, how 



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CONTENTS. 



DifTercDce of Vein." 

Civil, folar, and lunar, complete, vacant, and Ronun 

Year, dcfcnbed. 
Difference of Months. 

AUrooomical, civil, periodical, fynodical, and antient. 
Divifion of the Year by the Antient* into 
Jtviijh^ Eg^plian, Arabic or Tarkijh, and Grt«(Wi Month ». 
A common Month- A Week. i|o to 141 

Da/, natural, utiGcial, aflroDOmical. 
Hours, equal, aneqoal. 
Minutes, Seconds, Scruples. 
Cycles and Periodi. 
Saa'i Cycle, Moon's Cycle, and lodiaion 141 

Of the FIXED STARS. 

Appear bigger to the naked Sight than through a Telef- 

cope. 
Made not on Pnrpofe to g^rc Light in the Nigbu 
Readily known. 

ConitellatioDi, a Table of their Namei 143 to 144 

Different Properdes of £xed Start. 
Milky Way, lacid and cloudy Stan, tSMgeltmut Clonili. 
Change! of, and periodical Stars. 
Changes in the Heavens, 
fidtpnc Obliquity changet — i44to '4S 

TABLE of CbrtMle^eJ .ERAS of great. EVENTS) 

According to the Year of JuUom Period of Creation, and 
of Chriji. 

An Account, and Example* of, tlieUfeof.£rai, Cycles, 
and Periods. 

The Birth and Death of Ctrijl. 

Sir I/aac Nnvtta't Method Of fixing the JErai of Chrono- 
logy, and particularly the Time of the ArgatoMtic Mn, 
by the advanced Places of the Conftellationi 146 to 
"47 

Chronological Tables, Ihewine. at Sight, the dominical 
Letter, or Letters, for any'^ar be^re Chrift, O. S. 
" For any Year fince Chrift, O. S. 148 

^1 ■ — For any Year before ChriS, according to N. S. 

_— ^— For any Year Gcce Chrift, according to N. S. 

I Shewing by the dominical or S'miey Letter of ei- 
ther Stile, the Day of the Week anfwering to any Day 
of the Month in that Year; for ever j +9 

— I.. — Shewing the Golden Number, at Sight, for any 

Year before or fince Chrift . 150 

^ Shewing, at Sight, the near Place or Sign of the 

Moon, by the Golden Number for the Year and Day 
of the Month given, N. S. — 151 

. Shewiug, at Sight, the Moon's Age, for any Day 

of the Month ^ven, N. S. ; — ica 

The Sun's Place through the Year, by which the 

Moon's Place may be found, and her Rifing and Setting 
nearly for Le«aba, or any other Part of the World. 

A Table of the Time of high Water at fevcral noted Pla- 
ces before or after high Water at £«uln , — TC3 

A chronological Table, to find, atSigh^thcTime of ta« 
Pa/cha/, or Eajtfr Fnll Moon, and confeqneutly the. 
Time of Eafirr far ever, by the Golden Number and 
Days that the lanar Cycle of 19 Ycvi, goct forwaid 
» any given Period, Hew Style. — 154 



A Table of the Number of Days, at Sight, the Mew, 
Full, or Quarter Moons, in the Grtgsrian Accouat, gd 
forward in the Months ; or how much the lunar C^cle 
of 19 Yean advances in the Month^ay, from 1600 
Beginning ~- ^ _ ir^ 

■ Shewing, at Sight, the moveable Feaft* by ttie 

dominical Letter and Golden Number. 

— ■' ■ ■ Shewing, at Sight, the moveable Terms, by the 
dominical Letter and Golden Number ■;; 

-s— ^-^^'^SUrtflng, at Sgtt, the moveable Feafti and 
Terms WTBver, by the dominical Letter aad Golden 
Number, for old Style — Of Ufe in antifnt Hift<wy 
and Chronology. 

A general Table of the Sun's Klfing and Settiug i^ E«^ 
Msi/and Inland, according tonew Style 156 

Remarks on .£ras, or Points of Time.. 

Controverfies concerning ^raa. 

Remarks on the Nature and Meafare of Time 157 

Of Reft and Motion of Bodies 

Of aatient and modern Hypochefei — — ijS 

PRACTICAL QUESTIONS in CHRONOLOGY, 



Of fuodry Kinds, anfwered 



IS91 



166 



To turn Time into Degrees and Parts of the Equator, and 
the contrary, arithmetically — -' 167 

A Table to find, at bight, the Nnmbcr of Days advanced 
and retreated by the Epafls and Lunations, in the 
Mondi-dajs, (from 1600 before to 6000 Years fince 
Chrift} from old to new Style from iSoo, and the con- 
trary. 

For determining the Epa£t and Fall of Eofitr, according 
to new Style, as fettled by Pope Crtgarj. Alfo to find 
the Epaa, O. S. for the fame Centuries 168 

Examples of the Ufe of the foregoing Tables i68tOi69 

Chronological Remarks and Improvements, 

Chronological Scale. 

ChronologicaL Rules, ariihmetical'y applied to Prafliceia 
anfwcnng many Kinds of chronological Queftions ) 
fuch as finding the dominical Letter, Week-day anfwer- 
ing to a given Month-day, the Golden Number, Cycle 
or the Sun, Rav-ait Indiflion, EpafI, i^e. for sew and 
old Style, before and fince O^ift, i^c. With memo- 
rial Couplets to affift the Memory 1 aud fmall chrono- 
logical Tables added for the fame Purpofe 1 yo to i^y 

A Table of Calends, Ides, and Nones, according to tae 
RgmoH Year. Of Ufe in Hifiory. 

An .Account of the old and new ccclefiaftical and dvil 
Calendar. 

With fevcral othei chronolo^cal Matten decided 17S 
to 179 

PERPETUAL T-I M E-T A B L E S, or GENERAL * 
RULES for CHRONOLOGISTS, HISTORIANS, 
NAVIGATORS, igc. 



Sealbn of the Year, pafi, prefcot, or to come, particoUr- 
lyufefnlfbr all Ferlbns writing Almanacs for the £/«- 
ri«Mrj Company. 
Rnlct for findug the moveable Fea£s wid Hi^dayi in 
my Year — — — — 1 80 

Namei 



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CONTENTS. 



Kames of ill tlte fixed Feafl-diyf , obfcmd in the Church 

of England. 
>JimeB of all the Vigiliand Fafi-dayt. 
The D&ys of Fafltng and Abftinence. 
Solemn Days kept, for which particular Church- Service 



apMin 



'3o 
Tab!<*of moTCable Feafli for ever, according to the Fall 
of Eafitr, N. S. 

Moveable Termi for ever according to the Fall 

of£fl/«r, N. S. — — i8i 

' Moveable Pealta from 17(9 to iSoo, N. S. ifiz 

Perpetual Tables, of the Month-day and Week-day cor- 
tefpondent, according to the dominical Letter ; with 
the fixed FeaRa, Holidays, remarkable Dayt, i£c. ^C' 
cording to N*. S. for any Monlh in the Year, 
Month-day of New, FuTl, and Qaarier Moona for any 
Uondi in the Year, according to the Golden Number 
183 to 188 



RULES for the proper USE of the RIGHT ASCEN- 
SION and DaCLINATION of the SUN and 
STARS, their Meridian Altitudei and Height of the 
Pole, in afirtncmcal OBSERVATIONS. 



Particalarly ufcful in Navigation 



189 to 191 



Table of the apparent Semidiameter of the Sua, Time 
of hi* paffingtne Meridian, and his Oiftaoce from the 
Earth for cvciy loth Day of t be Leap- Year, 17;6, 
N.-S. — — — 191 

A Solar Ephemeni, commencing 1756, and ferving, by 
Miani of fmall Equation), till iSoo. 

Being a mnntbly Table of the Time of the Day by a rc- 

a Hated Clock when it is Noon by the '^un : Stiewing 
c Equation of natural Days, and Advance and Re- 
treat of Clock-Time for Leap- Year. 
^ ■- The Sunt Place. Declination, and Right Afceo- 
fion, for each Day of the Month in the Year 1756; by 
which, and fmall Equationai hi« Place, Deduatioa, 
and Right AfccDfion are eafily determined for any fa- 
toreDay of the Year, illl 1800. 192 to 196 

TABLES in ASTRONOMY. 

I. ACatalogneof i40TemaikabIeFlXEDSTARS,witb 
their Magnitadea, Longjiudei, and Latitudei^ H. S. 
According to Dr. //««^ — — 197 

II. CatalocDc of 69 remarkable fixed Stara, with their 
Right Aicenfibn in Time, Degrees, and alfo Dodina' 
tion N. or S. According to the Foreigneri 1 98 

Equation- Table of the middle Time in Second*, between 
the Timet [by a Clock or Watch] of Forenoon and 
Afternoon, equalAltitudeiof theSun. Correfpondent 
M the Increafe or Decrcafe of the Sun'i Deainition 
daring the Interval of Obfervation - 199 

Table 01 renu-dinrnal or femi-doration Area, joi finding 
the Rifing and Setting of the Sun and Start zoo to zoj 

Table of the Snn'i Amplitnde of Rifing and Setting > 
for finding the Variation of the Compau 204 to 207 

III. Catalogne of 307 eminent fixed Stars, in the North- 
ern and SonthemHenifpheic; WUhtheitPlac«inth« 



Conflellaiioni, correfi Right Afcen^on, Decliaation 
for the Year i/co, and their annual Variation. Ac- 
cording to the laft improved Obfervatioat to8 to 2 1 3 

Small Equations of Clock-Time, and of the Sun's Place 
and DeclinatioQ, for every 4ih Year from 37^0. (or 
from any common, or Leap-year after) to 1 Koo, N S. 
Which will fetve, with contrary Sign, back to 1700J 
N. or O. Style. According to M.'£)« ia Caillt\iAo- 
tioni — — — 214 • 

Equations of the Sun's Right Afcenfion in Time for every 
4 Years. 

Sun') apparent Diameter for every 5th Day in the Year 
1760. 

Equation of the horizontal Semi-diameter of the Moon, 
to her apparent Semi-diameter in Altitude. 

Ecliptic Obliquity for given Years _ 215 

Table of Clock- Time at Noon by the Sun. 

Sun'i Right AfcenSon, Complement of Right Afcenfion, 
01 Diftance of Jriti from the Meiidian, in Time. For 
each Month and Day in the Year. Reduced to the 
Meridian of Grtemaci Oblervatoiy ai6 tozt/ 



UIL.Principal ASTRONOMICAL QUESTIONS ap- 
plied to NAVIGATION i prailically anfwered by 
fpherical P/opprtion and Logarithms zi8 to zjo 

The Nature and Caufe of Twilight — 224 

XXXIX. Sigijlien. To find the apparent Place of the 
Moon, from her Longitude, or true Place, and Lati- 
tude given. 
Wherein D. Cirwftr't new and IhortMediod offinding the 

Pajallaftic angle i» exemplified. 231 

Rules of applying the Moon's Parallaxes 233 

Equation-Table of the Ecliptic Right Afcenfion to the 
Right Afcenfion with Latitadc. 

Equation to be fubtraficd from the Latitude of a Planet, 
for the Equation of the ecliptic Declination to the De- 
clination with the Planet's Latitude - 3S> 

Tabli of the Longitude and Right Afcenfion of the Mid- 
heaven, with the near Longitude of the nonagefimal or 
90' Degree from the Horizon, correfpon^nt in Latj>' 
todeof London — ' — — 252 

Table for determining the near Time in any Day, when 
the Sun, Moon, a Planet, or Star, is in the higheft 
Point of the ecliptic Latitude of Lt>td»n 2(3 

Rules and Examples to find when the Sun, Moon, Pla- 
nett, or Stare, will be in the iwnagefimal Degree 

ij+tois5 

Sexagcfimal Tables for proportioning the Diflerence of 
Bqaations at Sight — -■'■ ■ j;6toa;9 

Table of the vifible Eclipfes of the Sun, and Fluenome- 
aa, for a I principal Cities of £«»//. 

The vifible Edipfet of the Moon, and Phsnomcna fior 
Gnnrtuicb Obtervatory. 

Ukewife the invifible Eclipfes of the Son and Moon 260 

The New, Foil, and Quarter Moons or Lnnadoai tw 
Grumvicb Obfervatory to the Year 1765 261 

Table of the (emidtoraal Arci of the Son to every Degree 
of his Longitude in the Ecliptic, ibr Landan. 

Semidinrnal Arcs of the Moon to every Degreeof 
her Lonntude in the Ecliptic, at Soothing, without La- 
titude, ntlMAm "— — — 2^* 
TaWf 



Bigilizod bi 



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C O, N T E N T S. 

Table (hewing, by the Moon 'i Age, the near Time of ber Of coiredinei Ship'i Coarfe fteered by theCompafi* 
Aifing and Setting in Eitgiand or Irtleudf when Ihe ia Correfiion of a Ship'i Conrfe by the magnetic Variation.' 
in the Beginning, Middle, or End of each Sign in tbe Magnetic Vanation from i ;8o to 1 7^9, 
Ecliptic (fuppofing her without Latitude) her mean Farther Correction by allowing for Lee- W^ 307 

Place and Age being known at Sight, hyfai. P. 241, General Rnletof Lee- Way from the Sails let or furled. 
2ji -^— — — — 261 Correction of the Courfe and Diftance, by trying the 

Eqaation of tbe tne horizontal Diameter of the Moon, Swiftnefi and Setting of a Canent - 308 

to the apparent horizontal Diameter, according to tbe Of Meafuring the Sbip's W^y. 

Moon'i Declination. Of tbe Seaman'i Compart", Log-Line, Log, Half-minate 

^qoation of the horizontal Diameter of tbe Moon to tbe Glafi, and Log-board — — 30^ 

apparent in Altitude. Example of a Loe-board. 

Reduction of Paii mean Place* to Grttmvieh Places 263 Seaman's Compais. 

A Table ihewing the proportional Difference to be added Day's Reckoning on Board the Drtadnnuglit 310 

to or fubcrafiedfrom tne Sun, Moon, or Planet's Pla- Rnlesfor corre^ng a Ship's daily R'eckooing 311 

ces, Deditfation, Right Afcenfion< t^c. at a firfi Me- Remark on tbe fotegoing Method of correOiDg • Ship'i 
ridian for tberefpeClire Place, Declinaaon, Right A f- dead Reckoning. 

cenfion, i^e. undera diftant Meridian 264. Remarks on Mr. B. IdartiiCt new Navigation, in a ft- 

Equation of the Difference of Right Afccnlion, in Time, cond Letter from a Correfpondent - ~ 311 

at Noon, between the Snn, Moon, Planets, and Stars, Dimenfiom and Weight of Shot, 
to the nearer Time of their refpeflive Southing at PJaceof Turning 10 Windward. 

Grenrmicb .<• — ...- 265 To compute the Didance of a Head-Land, or Cape, at 

Sea ' — — — 313 

To meafure the Tonnag:,' or Burthen of a Ship. 
LOGISTICAL LOGARITHMS. Beft Position of tbe Sail), and Rudder, in wotting a 

Ship - — _ _ 3,4 

Their Nature and Ufe — ■ — aM ThcPropertiesof Magnetic Variation. 

Table of LogiAical Logarithm* 267 to 272 Rnlei for determining the Quality and Quantity of Va- 

riation — — ___ jij 

Practical Rales for finding the Latitude of a Ship's Place 

The SEAMAN'S READY COMPUTER. of Obfervation 316 

Geographical Rules for finding the tabular Difference 
An Improreroent in Tabular Navigation 273tO 280 of Longitude. 

Remarks on the dilTereot Beginningi of terreflrial Longi- 

Ufe of the Seaman's Computer exemplified a8 1 to aS? tudes — — — — j 1 7 

Our new Method of Computation, without Scale, Com-. A Journal «f a Voyage in the Drtadmugbt Man of War, 

pafles. Chart, or Canon, exemplified in Anfwers to Y'^taa Engiandia MartinUa — '31SI0319 

the five Cafes of Sailing, propofc'd by Mr. Martin, in Nearnefs of Sailing to the Wind % and Rates for refolr> 

hii new Principles of Navigation 1 according to Sailing ing a Ship's Traverfe geometrically ; by tbe Line of 

by the Spheroid' — 18310237 Chords with Scale and Compafi — 320 

Table of meridional Farts on Mm-a/«r*B Chart, accord- Of Trade Winds and Monfoons 321 to 312 ' 

ing to tbe Sphere. Variation of the Compafi, at obferved at different Time* 

Table of meridional Parti according to the Spheroid and Places. 

2S8 to 293 Remarks on the vulgar Error in Books of Navigation 
The Length of a Degree, or Number of Degrees, being of fuppofing meridioDal Diltancc and Departure to be 
elliptic Arcs of the Earth's Meridian in Minutes of the alike, and of fixed Quantity — 313 

Equator, and Hundredth Parts for any Latitude. Ac- Table Ihcwine the Miles and Minutes of the Equator, 
cording to Don Juan, making a Degree of Longicude in any Latitude. 

Length of the Meridian Arcs of the Sphere by Mr. Mar' Divilion of the Earth and Ocean — 324 

^ocjt,com pared with thefbregoing Arcspf Donymnar'a General AffcCHon of fphetical Trianeles 32; 

Spheroid — — — — Z94 AffeClions of right angled fpherical Triangles, 

Dimenfions of tiie Earth aa a Spheroid confidered, from Some Properties of Sines, Tangents, (Sc. 126 

295 to 301 Anfwen to all the Cafes of right-angled fpherical Tnan. 
Properties of right-angled plane Triangles. gles, in Symbols and Words — 327 

Properties of Sines, Tangents, (Je. 302 Anfwen to alt the Cafes of oblique fpherical Trianglei 

Anfwers to all the Cafes of plane Triangles in Symboli 318 to 3*9 

and Words — — 303 The Properties of fpherical Trlandes 33010331 

Rules and FropOrtiODS for anfwctiog all tbe Cafes of Sail- Some general Obfcrvations on the Tides.' 

ing — — — 304 To 6nd the Time of High Water, at a given Time and 

Tabular RnLe), in one View, to anfwer all tbe Caluin Place . — — 332 

Sailing — — — 305 An alphabetical Tide-Table from the belt Authorities: 

Examples in anfwcring the principal Cafes of Mtrcmtr fhewing tbe Time of high Water at the moft remark- 

Sitline — — 306 to 307 able Sea>Ports, and Sea-Coaft Placet, at New and Full 

Mood — — 333 » 33+ 

Obfervatioiu 



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C ONT E N T S. 



Obfervttioiit on the different Beginningi of terreftrial 

LoDgitudet. 
Ad aftrooomical Qiieftioa.of Vte in Navigation. 
Spherical Qveftiooi anfwered — «S 

Obrer?aiion« on the AnfWen to Manin't or MatAcb't £x< 

uoplea. 
Variation of Cafe 6thiof MerM^lfki^. 

Thii Mariner'* Univeifal Se«-Coa» Table. Of the ptin- 
dpal Pom, HarboDD, Head-I-anda, Bays, Rivert- 
Moadia, and Idanda, lying contignona, or nearly fo, 
roond the World. 

With their Lautndes, North and South, and Lonriraju 
Eafl from Firm Ifland. Alfo their Di&— ^^^JrEon- 
girade Eaft or Weft from^Gr— '"^'Obfervatory 337 



Of UaebttT iThcory of the Moon 37910383 

Of Dt la CaiUii Theory and phyfical Rules of the Moon'i 

Motion — — '^^ 383 to 38+ 



Of LUNATIONS and ECLIPSES. 



Aa alphabeuol Table of the Latilndei of promifcuon* 
and remarkable Placet, with their Longiiades, from 
the Ifland of Ftrre, and Difference of Longitude from 
Grtenivicli Obfervatory ■ 345 

Captain B>rv;iii Direiliona for the Safety of homeward 
boond Shipi, coming into the E>iglifi> Channel. 346 

REDUCTION of CHRONOLOGY. 

Commencement of the m(^ famont ^ai in Yean car- 
rent and complete, before and fince Cfrr^, Julian 
Style, — — 347 

Table for Redaaion of Chronology. 

I'ablc for redncing ^wEiiM Years into Daya, and the con- 
trary. 

.. Reducing turhjb or Arabic Yean into Dayi and 

the contrary. 

Several Example] of the Redndion of Chronology. 

348 «> 3SS 



INTRODUCTION to the COMMENT on the 
MOON'» THEORY. 

336 to 3S7 

An explanatory Comment on the Moon'i Theory. Ac- 
cording to which Ptinciples the aftronomical Table* at 
the Beginning of onr Work [preceding the Supple- 
mental Tablet} are conftru£ted 358 to 371 

Of determining the Qoantity of Evefiion-Equation 371 

Table of the Moon'i Longitude computed from the Ta- 
ble* to a 1 00 Placea, and compared with the refpeflive 
Obfervation* — — 37* to 373 

Total CorrefUon of the Moon'i mean Motion. Accord, 
■ng to the Correfiion of her mean Motion, and Acce- 
leration allowed — I 374 

Table for correfiing the Snm of the VI. and Vlf . Eqoa- 

I liooi of the Mood, at the Bennning of the Tablei. 

A Compatifiin of the Nomber, ArgnmentJ, and greateft 

Equations of the Moon — ^ 375 

Method of determining the Maxima of the fevcral lunar 

Equations (C.) at the Beginning of our Work 376 to 

377 

377 



Table of the mean Time of the firH mean New Moon in 

Ja/manj, from 1700 to iSoo, O. S. 
Place* of the San't mean A aoaia^(t.*»«fi'f Argument, 

and Son from MMtf'*»_iS.p*«ee'."SiTelponding. 
Monthly Sfciiofia*? lE« feme — 385 

ji— vnitsins of the Moon to the Sun, next after JhAos 

Centuries — — _ 386 

Pliman Period of folar and innar Eclipfei. 
344 Equation of Time for a '*<?>'«« Period 387 

Radical mean Flacei and Motions of the Moon from the 

Sun ; for determining the mean Time [by Meani of E- 

quationi) of the true Orbit or Ecliptic New and Full 

Moon — — — — 388 

Mean Motions of the Moon from the Sun, (^t. for 

Month*, Days, Hour*, Minutes, and Second* 389 
Equation of the Moon's Center (and fecond Equation 

fupplemenul) compounded, at New and Pull. 
The Moon's Latitude, Inclination, and Rednflion, at 



New and Full 



Aftronomical Table* equated to oihen 
Explanation of Niwian't lonar Theory — 
Bxplanation of JUof&V* lonu Theory * — 



378 
37J 



— — 390 

The true hourly Motions. Diameteri, and Parallaxes of the 
Sui] and Moon in Eclipfes. 

Times between the true Ecliptic Conjundion or OppoJi^ 
tion of the Sunaod Moon, and Middle of BcUpTe 391 

Angles which the Way of the Moon from the Sun makei 
with a Circle of Latitude, in Eclipfes - 392 

Examples of compoting the Times and Places of the New 
ano Full Mooni in Eclipfei - 392 to 397 

Precepts for compating the Times and Places of the Or- 
bit New and Full Mooni — 39} 

What an Eclipfe of the Moon is — J97 

Precepts for computing an Eclipfe of die Moon. 

What an Eclipfe of the Sun ii. 

Precepts for computing an Eclipfe of the Sno, by Pa- 
rallaxei — , — _ 338 

To find the Places, on tha Earth, of the principal Ap- 
pearances of folar Ecliplei, by ProjeAlon 399 

Method of 'computing the greatefl Number of Ecliples 
of thi Sun and Moon that can happen in one Year. 

Of the PlinioB Period of Eclipfei, and iheirRctoins. 

Of antient Eclipfes. 

Plurality of Eclipfes. 

Hiftorical Edipfes of the Son and Moon, at great Erents. 
' 400 

Redo&ionof aftronomical Tables, with Examples 401 

Geometrical ConftruAion of a lunar EcUpfe . 403 

Table of the Angle of the Hoar Circle (paffing through 
the Sun and Moon) with the Ecliptic ^03 

Examples of computing the parallafUc Angle, according 
to different Methods. 

Explanation of different parallaAic Angles 404 

' PrecepCi of the lunar Contpntation. 

To find the Moon's true from her apparent Place. 

Remark on Dr. HaiU/% Tablet 40$, 

Of Hailey'i Method of detexnuning the Longitude by Ob- 
fetvation. 

Of D* UCmOit Method.. 406 



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CONTENTS; 

Of obferviag the Losgitn^ at Sea by the Mooa*8 The- Correffion of the lAittidile of &t Son, and Sim'i Dlf- 

oiy ~ II II ■-' — ■ ■ I- 40^ UDce from the Euui. Accordioe to M^tr 410 

. Account of a Pamphlet pmcndlng ^vOifcovcry of the A Table and Emnplefbt this Redudion-ttf k Comet's 

Longitode. Lon^tade from the Perih^ion in a parabolic, to that ' 

Example of ccmputiilg the Diftrence of Longitude from fromthePetiheliOttHiandliptic, Onit, bytheDiSe- 

GritwJiich — — ^ • 407, Tence of Motion in dtofe Orbits - 411 

A new Method of malciug a limar,&phemerit. Compntationof.an Oppo&tion (^ the Sad and Moon, 

Of the Motion of Comets — — 408.' - with their Place*. 

txampleof 1uDarCom^autioD,.accordiDgtoD.C. 409 Conclusion, 01 Laud '•■ '— ^t^ - 

xample of .C^pQtattoD. Accoiding to JIAt^. 410' - " 

CORRECTIONS o/I'W"! «rf typographical HRROKs-tom«,uUjp bt mUU -uiitb tit Fm, hfirt nrWOtiK. 

it fi/fd. "^ ~ ■ - 

f^ Mtfi ef itt Jilltniiig Bmrt art t^m ami ir'^ing i *..< ^. -ff-n.f«/n f,r.„t^tam/ ^j-^ wwifajnf 
N, B. mart b II flaccdtfitr lit tUmtir »J t Uate, itjgtifia ibt Ntmbv »/ ibtt Liat, Jnm lU Botton if A.^^, 

PACE 1. Line 6. i. Foroii iii" i6> ind 1049' 4" P. 117. L. 7. i. C/.1>II. For tf ifi" 6* ««f. r. 8 i+oj?'!?". 

Read □ 7 16 ind 1 4a 4^ P. i^, L. 11. Cc/. UA. For 44 Yra EwT. Chr. r. 4$ YnW. Cbr, 

L. ij. i. Tor Lima S6<>49' o" 1. 76° 49' o", L. 1, f. For, from 47 11, r. from 4714. ■ ■, . 

P. 1. L. I. ForJVaM* o"" ij" jj' ind 6" 13148" E, P, 147, L.4. For 47 13 Year Jul.Petkiil, r. 47(4, Vt, 

Rnd o D 56 and I 44 o W. Im 5. Far Dif, 1954, r. DiC ig jj. 

L. 14. TorFerta BiOs Sg" jo' 6" r. 79* 50' 6". P. t6$. L. 10. b. For diiilibU b74, r. dItiGUebr ■, 

P. II. L. j6. For OAs^ I I. ahitir 5. P. 170. L, ifi, Cg/. i. Forirfuiiri, t. rtpiri, 

P. ij. L. »K. For e?").}* 31" r.67040'31''. P. 17J. L. 16. W. ». ForVaii JhiaClalR, i.YanMinChim. 

P,14tO«7. RightHindCoI. For © PI. in Deji. r. inCotnp.tOjOB, L.lg.rameCi/.FarFen'sa^roluppciwd, r.^flWlbluppeiicd. 

or iriTeit in writing th( Degren in that CtimnD b]< Paper pallet P, 193. L. i. he\mr the Ttilri, For arrtaing st beginning, r. aw 

over its Length and Biuddi. ■««■; or bediming. 

P. 71. L. (. b. Far 1. (. 7,14 X any L.E^. =0, D. i, i. <. ,im6 P, »i. L. i3. t. CtLt. For, from a>u D«cIinitioD for cth Arr. 

X iny L. Eq. = O. D. r. hemfdsr Dillince for the 5Ch Arc, &<. 

P. 71. L.8. i. Fori. J a© C*^™" next ^aifrwiire or Sjiiygjf) fff. P. i34. L. 10. Co/. 1. For, To theNo, of Earth's Diuutteri, r. To 

r, S. a. J i © (from next Qijidratun; or Syxjgy) ! S. Pref. the So. of ihe Eanh') Semi-DjametHt. 

M. Variation, SSe. P. 137. MIdd, tkl. 1. For 1.1187, '■ ii'S?- 

P.78. L,i4. *. unde»C(i/.7. For + r. + — . ' L. 7. lower. For3^,ia, r. 3l',67. 

• P. 97. L. 1!, Cc/. a. For 00 38' 35" r.o" 18' 15". P. l6j. L. 1. under Tab. (kl. i. For inii Semi- Dim. T.trmt Dttm. 

f. 100. L. 3!. Cdt. Forfi°59' 18" r. s" Ss' S^". F> aSi. L. 18. Cel. i. For, MhUle Latitude be V^i ttud 45s, r be 

P. lot. L. 7. ai. 8, 10, 13. For +, +, 4-, Car Tif ; r. — , — , — . ^Jiw rhan 4s-. 

P. no. L.I. For elliptic T«;(f7iMi(, r. elliptic Trfljjflorifl. L. 19.1 —r— For, It ;r«un-than 4j«, r. if /r/i than 4c'. 

L. 10. For Wbtretl:kemeaaandtTueMotiaDisfquil, r. Where P. 197. L. i:. (. For, a> a Meant for the DeftQ, r. ii AnenJc 

the mean and true Anomallei are equal. . irni/c for the Defefl. 

- - fi.+i+i9457 ,f™ f '■— '4 19 45 P. 311. L. 0. ForiMllein iD/</i. r, iMileinio-srr. ■ 

rlT't Y^ ■{'■+»^3g 3.1 *Y™'-{»--»8 39 3' P. 3.7. W<Wof 3<1 C»;. «.A.. 6iff. Long. 5" S4' W. r. Dif. Long. 

*^" ■ l3-+4» S9 >7J t3--4» 59 17 J" 14'W. 

P. WI. L. !- CW. J. For +,97017915137, r. + ,9701786191, ffc. p. 313, L. 3. Ctl. i. For B.J?iii'i Ba^, r, fla^'i Bay, 

290 y 19* 17*4 in a Lunit. P- 1*4- ^-^S' C"'- *■ ^'"'> ^"'1 fi-^' Ift"^, t. laifimiotbaipcJi. 

L. a8. Ct/. 1. For, from lEooand 1700 reduce to, r. ftona L. 3. i. Far, From the i>j'ci/bM, r. From the £)j«^^. 

L. ir-^sx + 4' J-. .. .' .-. ■■•=■'• ■■■ ••• '•' ^'.,» ! "■" *•• '■ S'.™ } ■'■■ .-■ 

L. 33. C>/. lafl. For, from 1600 and 1700, r. ftom 1700. L. 19. i. For Rad. = to, t. Rad, =: i, 

' "' - "-- tt" 36iT, r. ailv ^6v. P. 3»g. L. 6. QJ. 7. For, Sum and Dif. i. Sum wDIf. 

S" jB"'i4J* !"'38i»a4v. P. 3591 L. ta. '■ For i.ooo 10 1787x5 r. 1000 to I78rze. ' 

4"6iv, e-c. 4'"oi», 6fr. L. 9. *. For 178715, t. .78,7»5. 

3" l5iT »3i« I s». L. 5. b. For, «f the bme Time, r, in the Ijiiw Time. 

9" l^" g^iSiv. P. 360. L. 5. h. For, gravinte mcr. tow»tdi, ffc. r. grancate itfn 

[1* 4{iv HIT 4^T. or Irfi towardi the San than the Eitth. 

S" 6* 5* *Ii. Ift J. b. After KT — introduce, ij vihiib rbc Hfiai ij «/!• 

11* 31". . tttraaid Hvierii Itt Etnb, in the former Cife, 4ft. 

i" ji" iiiv 11* jiiTiiT. P, J71. Obf. 16. For 6« »9« 19', r. 5* 19a 39' ]) a 0, 

g^^Sif iSiv^Sr, P.376. t, la. *. &/- a. J'ufr. For 357,45, r. 356,50. 

" 14" 14!? 6* i4iTi4v. L. 4. *. Marg. For 111,16, r. Ii9,x6. 

5* 35iT 1511 jjv, P, 390. Ctl. %. 3' leo . . for 3"4o'ai'', r,4» 40' ii», 

i''47'' itiv ii'47iTit>; '^•397- ^- iS. Ctl. I. For, EcfiptieCnv. r. Zdiptic <Tp/D/&i'M, 

ig^jii'i ^(. loivjiv, Gfc. L, 18. Ctl.i, For, Ecliptic Cmt'. r. Ecliptic Op^nsn. 

8' 13" iiiv %*' lyv iiv. L.11. bJotCel, For, Ecliptic toB4]> Dif. i.iam^itDif. 

lOit 33*. \>lot Ecliflit. 

•tin 57T. L. 3. ForEiamp. xt, r. Eiamp, a. 

11*81*. L. 10. i. For 10 64111, r. 10 74111. 

7i>'»OT. THE Readet if defirtd to emnfe and cotreft whit ether E/Ia/n, or 

V 1* j6iv 14T. Jnmairetin, he Gadi, unatoidably ■riCng, in To targi a Wrrk, from 

n, &r. r. 1<1 (8^ i;", &c. h«r(e*(iu either of X\m Albtr eiCamf^tr, or Both. 

rj- Arf maliriat Zrrort anlnhiJ, <fcaflnf eur Oi/trviHieii,- v)iS>aI/ii cbSgidii lii Ma rf J^ifiOKataeJ Cc\tici it jeiM ml. Se/ar/rm 
oar liihg fiicb Nsiiu ami/i, lh*l vit btritj ^ or Tbatla tf aity, vit fi)aU bt p!taf<d H'^na cir h'lfttAti, (ftft^g ttt PoAage >/ (ter Lirtiri, 
frttkifg ibtm, trfMtklj ir/irm'^ laj that TRUTH (%Bli(b it aa piiKipal Vi**) awjr it gt ■■ 



r 


111 


I..1 


b. Col. 3. For 






4- 


*. fame QJ. 
i. Col. 5, 

*. ccl. 6. 1 












4 


*. r>me Q/. 
*. Co/. 7. 






4 


4. ftmeCii/. 
*. fame Cs/, 


p 


x»3 


UiJ 


W. 3. 






14. 


&/. 4. fr 








fame C>/, 1 








Co/, e. ] 








fame &/. 1 






3- 


C./. 7. 8 
fame CW. 1 
i. C^l. 3. 3 
i. fame Crf. 
*. Cel, 4. 
^ faike C>/. a 


p 


>*4 




i. &/.1. For 



db, Google 



THE 



ROYAL ASTRONOMER 

AND 

NAVIGATOR. 



A GeoQtArBiCAL TABLE of vary imntiit ancl rmarUbh Placii la the World, with thnr correa teippo- 
nry Difierence of MtriJiau aiul Longitudti Snta Grishwich Ossrrvatort i asd their coneA LatiiKAt. 





Djf. Time 




DIf. LoncH 


- 1 


Lititdde 


1 




Of. Tim 


. 


Dif. Unpt 




Litinde 


FUcttNuati. 


fcftwMBrf. 


tiftOT Weft. 


•fottbnSoa. 1 


PUaetNi»c 


AFcaotBtT. 


EiK or Wclt. 


NanhorSc 




h > . 




• ' ' 1 




B » < 






;■; iJ 




E 


18 s 


N 


iJ«««..*, P.Jk*^ 




A 


.841 


E 




jB.x«i«isfti, 


















t 






J6«7 O 




36 IJ 10 




EdM.rlb, 










5S S> 










jS 1 






o+i >8 










Ar: in M^i, 


5 «5< 




7*44 » 


E 
E 


Z64, c 


N 


rr«cfin. 






«)S - 


1 

E 




'&'^' 


rs^ 


A 
A 


17 »o o 


n *s »i 


Gta, Enfi-In^a, 


:si^ 


A 


73 45 " 
6 »t> 


;ii; ; 


Z^M., 


ol, i« 


A 


4 Sg o 
7 ■ 33 




S» " 45 




CmiHwiCH OMtTV. 










SI tS JO 


jtMita, 




A 




43 34 io 




ss^. 


1 11 10 




H so 




3' 5! •= 


J^. 




A 


448 33 


£ 


4J S7 «J 


N 


04? 30 


A 


.iLL»_lS 


1 




^r 


.S. 6 


41 46 JO 




:fj^^*, Pfr>, 








A 


J. >6 .5 


t 






jC^,Or^l»*«,CfM. 


4 if" 


B 






Ui\ 


SJ SO 
S 44 « 


A 


ir^': 


E 


S> 33 


N 


X«fao, 


J 7 ig 


B 


¥\% 


W 


" I »s 

SI 10 40 


aS«? 


.iS « 




43 46 30 


E 


13 »' 


u 


U/h«, 


0,6 JO 


B 


8 57 JO 


^ 




ji««U,' 




A 


a 11 


41 i6 


L!^JP>i^. 


o 19 




ff^dDW, 




> +4' 




43 »9 »' 






1» JO 










s!i^, ru/r, 


a4fi »*;* 


4 30 4S 
M J7 


E 


44 JO 


N 


Lifi, Fla^,r,. 


.0 49 10 

11 17 


A 


It 10 
1 4 16 


E 


S" "9 14 


«i>nw ^ra, ytnnn, 


1 5» « 


■ 


jS I 


W 
E 
E 


34 JS 


K 
N 
N 


Msjnia, iujff. 


*4i >o 


A 

B 
A 


40 »o 


r 

w 

E 


S5 J" 




•1" 

1 8 J5 


/ 


J4 19 

1 3*44 
17 »5 JO 


44 50 '8 
JO 43 J' 
S> 3 




liiH 


IO» J 


43 '7 45 
401s 




VVl 
























Q^.fG^Fv. 










H 




8 I 10 


B 




^ 




Carr^nu, Amtncm, 


5 »46 


E 


H >6 


.0 .6 1, 


M.»i....W^^l^^ 




605845 




^tir- 










4.S* t 
























36 11 3' 




Mtxin^ jimmca, 


























Mto, 


,o|J.o 






E 






oS-.e 




y49 i 


£ 


5° S7 3- 


N 






A 




E 




C—i»f. 


<^S5S 




3 I3+» 


to la JO 


UmfOUr, 


IS ji 


J S> 44 




x::"- 


























e j».. 




! * * 




5°aSS < 




Mu^, 


04^10 






E 


4I . 


C^a.,imtU. ■ 
















1444 






t 






I 19 lo 






JO >o e 






oigifi 


■A' 4 S' 37 




JO .4 



;^^ — ii>-^./fjift'-*f'*iHM^'3/*f^^ o^i,/^— ;j2^' 



,, Google 



The ROYAL ASTRONOMER 



GiocRAFHiCAL T A B ■ E Continued 



PiKii tMemterj, 



Si. Mafi, 
Si.Omrr, 



Uj' 



m6 


u 




r. 






•d 


so 




»*+! 








1 














77 


fi 




"J 

+ 


3 
7 


li 




•9 


'S 




i?4H 




» 


IV 






47 ■! 

40 s; 45 
4* 1* 



S 13 


s 


47 S4 4 




1' 'i Si 




S" 4S ■= 




48 so ■<= 






N 






it 13 »7 


N 


9 JJ S 












46 3S = 








N 


11 17 





49 '4 3* 

49 a6 13 
48 38 S9 

50 44 46 



7r^; Btrimj, 



Tifjfibma, Tiakm, 
Vaifrit, am. 






r 36 J, 
I 5* o 



> i *9 



I >6 13 

« 30 o 
.1 8 o 



4 30 

li ,0 



>7 45 





w s«r> 


" 33 


1° 


71 IJ 




s f 


" 



18 s8 
59 M. 
f* 34 ! 



„,» 


♦1 


7 »4 


■i» 


S3 4° 






47 




6s 


JO JO 


♦3 


3S S4 


IB 


19 


404""= 














4a 


4* IS 




..48 


S' 




« 


51 s" 


^^ 




1? 


»:: 


i" 





USE b/ tit firtgmmg TABLE. 

Wtwn it» IX It Noon, Men Time, U Civwmii OUmtuij, whil ii Cha Hour, or M«n Time, »t Ptru Bifia, in Amri. 
EXAMPLE I.— AgBoft firtv S'jVi, id t&c Table jnu find Cbt Timt ii {I' i9iii ao* A<^rt the Time at Cctfint 
Tberetbn, Fracn is^ o" o* U Crumv/ij, 
Dedoa - - J 19 10 



40 40 TiiM In (he Moi 
It Gnfnpicb, or idd it ihoreCc 
ic antrtiy, whin the Ti 



ing 1 



Vr* B(A, rtq<l. 

1 the Time it after that it Grtar- 

It any PJlvi, to find the Tia 



— The DilTereocf or Degree in ffifl or Eajt Lm^tuile, between the /Utridian of two Placei, conTcrted into Tim^ 
■llowint >;■ to la Hour, it the Time or Houi il one PUee ^in or mfltr the Mean Time at mother; (tbc ^^ Lonfitude »r/i^t, 
Eti Longitude afl^) ehere«ire, the Ofmrntt or Sum of the Timei of taj two PJicei from the Titne at Crtmwith Oj/nuiiij, » . , 
are both B or A, or one B, aod ooe A.GmtMci-Tlme (ufint A^rr and Biftn Co GrMtwiVt, inftead of Btfm and AJiir ham tbcncej will 
be the Tiine at one Place in Reference to the rime >t uolhet. 

EXAMPLE II.^-^7f>Wf*(SwirdC Babylon, *r Grand Cairo, nriniV /i 10 iXkFdriWM ■tUfBor Cafth f 

57 A, at Crmd Cain, tbe Tint (t (JM» CjIj^. 



TiaKUE^HMrCflU B. tbtt tt(7r«WCnie, orlXIIereacc 



Tinw at CraaiCalrt - 11 3 tj Ate-noon required. 
EXAMPLE Ul,~~rtfiiiJtbtTimiatQxioti-aAail hNtmrniKamtt 



TSmaitaifMB. Timeat JtMf. Sbd o 
Time U Oxfiri referred to Haipi i^ 



59 Foteoooo requ< I fceug >IKIwC>fn ibitcinbippen. j 



,, Google 



. 






■snd 


NAVIGATOR. 






i 


M». k,A^ HAdli of .ta bUt(. md Brd Sl.r of Jn„. froo M. t» „ 


(2, old STYLE. 1 


'juUi 
Style. 


M.P1..0. 


M.W2.AP.0. 


M. K i+v. 


6*y?ft 


M.m.o. 


M. 


*lll.Ap.0. 


a*, n. i*<ir 














b. I6s3 
S3 

Si 


9 ao 36 12 
9 20 21 ix 
9 20 7 }2 
9 >9- SJ 'J 


3 


«:4.7 

6 s6 »o 
« !7»I 


a8 18 56 
>8 19 +6 
c3 a8 30 37 
i» IT 17 


B. 1700 

z 
J 


9 20 ;S 3 
9 «> 43 43 
9 2o 29 23 
9 20 IJ 4 


3 


7 45 a9 
7 44 3<> 
7 4! 32 
7 46 33 


28 59 20 
29 10 
29 1 1 
0,29 I ,1 


B. 1656 
S9 


.9 20 j8 1 
,9 •<> '} *• 
9 20 9 21 
9 '9 IS " 


3 


65.., 

6 S9 24 

7 26 

7 ■ «7 


iS 31 18 
□ a8 2} 8 
»8 23 59 
i« tii 49 


Bj 1704 

1 

7 


9 20 S9 S3 
9 w 45 53 
9 "> 31 "3 

9 20 i6 S4 


3 


7 47 35 

7 48 5' 
7 49 38 
7 (■> 39 


29 2 42 
29 3 32 

29 4 2J 

29 r 15 


B. 1660 
6( 

6f 


9 "■ 39 S' 
9 '" 'S >< 
9 20 11 II 
.9 19 S^ S» 


3 


7 2 29 
7 3 30 
7 4 3' 

7 < !3 


»8 as 40 
aS zo 30 
38 37 SI 
■ 18- rt n 


B. 1708 
9 


9 21 1 4« 
9 20 47 22 
9 20 53 2 
9 20 IS 4J 




7 5' 41 

7 52 4» 
7 S3 44 
7 54 4! 


29 5 4 
29 6 54 
o «9 7 45 
29 «3! 


b. 1664 


, 9 20 ,1 40 
9 20 27 20 
9 20 13 
9 "9 S» 4>- 




7 « SS 

' I 'J 
7 8 j8 

7 9 39 


38 39 3 
38 39 53 
38 30 4J 
38-3T J3 


B. 1712 
«S 
■4 
'S 


9 21 . 3 )i 

9 20 49 II 
9 "> 34 SI 

9 20 20 32 


3 7 5S 47 
3 7 5« 48 
3 7 57 SO 
,3 7S8S1 


29 9 20 
29 10 16 
29 II 7 
29 II 57 


69 

71 


9 20 43 29 
9 20 29 9 
9 20 14 49 
9 20 JO 


. 1 


7 i« 41 
7 " 42 
7 " 44 
7 '3 45 


«8 33 3+ 

t 3« 33 14 

28 34 5 

38 34 S^ 


B; 1710 
19 


921 . s 20 

9 20 SI ° 

9 20 36 40 

9 20- 22 21 




7 59 S3 

8 2 J7- 


. 29 ,2 48 
29 13 38 
29 14 29 
29 15 19 


B. ..67. 
73 
74 
7S 


,9 >»4S i« 
,9 iojosS 
.920,16 38 
9 20 , 2 19 


■3 


7 »4 47 
7 "S 48 
7 1' S» 
7 17 !' 


° !2 '1 *^ 
.0 a8 36 36 

38 37 37 

38 3? 17 


B. 1720 
21 

22 
23 


9 21 7 10 

9 » s; 5° 
9 20 38 30 

9 20 24 II 




8 3 59 
1 i ". 
8 7 3 


29 16 10 
29 17 
29 17 5^ 
29 ■« ,. 


b. ,6,. 
77 
78 
79 


, » 20 47 8 
. 9 «° .3' 4» 
. 9 20 18 28 
9 20 4 9 


1 


7 18 S3 
7 "9 54 
7 20 s6 
7 " !7 


38 39 8 
38 39 58 . 
28 40 49 
38 .41- 39 


B. 1724 

27 


9 21 8 S9 
.9 20 54 39 
9 20 40 19 
9 20 215 


3885 
.3896 
3 8 10 8 
3 8 " 9 


2y 19 32 
29 20 22 
29 21 13 

29 i-2 3 


b. lOBo 
81 

83 


9 20 48 57 
9 » !4 37 
9 20 20 17 
9 20 f 58 




7 " J9 
7 'i •> 
7 2; 2 
7 26 3 


z8 43 30 
38 43 W . 
28 44 1 1 
38 4S . 1 


B. ,728 
'9 
3° 
3' 


9 21 10 48 
9 20 56 28 
9 zo 42 8 

9 20 27 4, 


3 


8 11 I2 

e 14 14 

8 1; „ 


29 22 54 

29 23 44 
29 24 35 

29 2-5 2! 


■ ll 

87 


9 20 5« 4i 

9 20 36 26 
9 20 .22 6 

920 7-47 




7 »7 S 
7 28 6 
7 29 8 
7 30 9 


28 45 SI 
38 46 43 \ 
28 +7 33 
38 48 «3 


B. 1732 

33 

34 

. 3S 


9 21 12 38 
9 ao 58 18 
9 =0 4! 58 

9 ao ag }9 




8 16 17 

8 17 le 

8 18 20 
,8 19 >i 


29 26 r(l 
29 27 11 
29 27 57 
29 28 47 


B. lOUb 
8, 
90 
9- 


9 20 52 js 
9 20 38 ij 
9 20 23 S.J 
9 20 9 Jli 


1 


7 ji 11 
7 32 " 
7 33 14 

7 34 IS 


28 49 14 
a 38 so 4 
38 so SS 
18 51 45 


& i7j<. 
39 


9 21 14 27 
9 31 7 

9 '» 4S 47 

9 20 „ 28 




82023 
8 21 S4 

8 '22^ 

8 23 27 


29 29 38 
29 30 28 
■0 29 31 19 
29 32 9 


B. 1692 

. 93 

94 

9! 


9 20 J4 i; 
9 20 40 s 
9 20 «s 45 
9 2U,II z6 


) 




38 53 36 

18 53 36 
38 s4 >7 
38 s? 7 


B. 1740 
41 

4» 
43 


9 21 16 16, 3 
9 II I 56] 3 
9 20 47 36, 3 
9 20 3) 17 3 


8 24 .9 

8 2J JD 

8 26 32 
8 2, 33 


29 33 
29 33 JO 
29 54 41 
29 51 ,. 


B. ,696 
97 
98 

. . ?? 


9 20 s6 14 
9 20 41 54 
9 20 «7 34 
9 20 ij ir 


1 


7 39 »3 
7 40 2J 
7 4> »° 
.7 42 '7 


18 SS $1 
»8 56 48 
38 57 39 
28 58 39 


B. 1744 

47 


9 21 iS s 
9 'I 3 4S 
9 20 49 25 
9 20 35 6 




82835 
8 29 3« 
8 30 38 
8 ji 39 


29 36 23 
29 57 12 
29 38 J 
29 38 53 


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B. .748 

49 
5° 
S' 


9 " '9 iS 

9 a' S 3S 

9 » s; •! 

9 20 36 56 


3 


8J241 
8 33 4« 
8 34 44 
835 45 


29 39 44 
29 49 54 
29 41 25 
2942 IS 




•Br 1-752 


9 21 21 44' 3 


8 J647 


2Q 43 6 












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* 




n< ROYAL ASTRONOMER 




Mmo Radical PLACES of ihe SUN. ind firft Star of" ^r.>j, (rom i7« to i8«»."New S 


rvU. : 


Gregonan 
Siyle. 




M.Pl.Ap. 0.|M.Pla.i*r. 1 


Gregorian 
Siyie. 


M. Pla. 0. 


M.Pl.Ap. a. 


M.Pla.i,^ 




■ • ' • 






I <• / ff 




B. 17S> 
!! 
54 

ss 


9 "> 3; '3 
9 10 16 S3 
9 10 a 33 
9 9 48 -4 




8 564s 
8 37 4S 
8 38 4« 
8 39 49 


«9 43 5 
9 '9 43 55 
29 4446 
2, 4S 36 


1800 
3 


9 9 53 55 
9 9 59 35 
9 9 25 15 
9 9 10 j6 


3 9 «S 57 
3 9 28 58 
3 9 28 
3 9 29 I 


I 23 29 
1 «4 19 
t 25 10 


E. ,7,6 
!9 


9 10 33 a 
9 10 18 42 
9 10 4 22 
9 9 SO 3 


3 


8405. 
841 S2 
8 4» 54 
8 43 55 


29 46 27 
29 47 10 
29 48 8 
29 48 J8 


B. 


I804 

1 
7 


9 -9 55 44 
9 9 4' 24 
9 9 27 4 
9 9 '2 4S 


3 9 JO 3 
3 9 3" 4 
3 9 32 6 
3 9 33 7 


I 26 51 
I 27 41 
1 as j2 


iL. 1760 
61 

63 


9 "o 34 51 
9 10 20 31 
9 10 6 II 
9 9 5' 52 


3 


III' 


29 49 49 
29 JO 39 
29 51 30 

29 J2 20 


B. 


litOB 

9 
■ 10 


9 9 57 33 
9 9 43 "3 
9 9 28 S3 
9 9 14 34 


3 9 34 9 
3 9 35 '0 
3 9 36 ■« 


1 30 13 
1 31 3 
1 31 54 


B. 1764 
67 


9 >° 3' 4" 
9 "O " "' 
9 10 8 1 
9 9,53 4' 


5 


« 49 ! 
8 JO 4 
e;. 6 
85a 7 


29 sj II 
29 J4 I 
29 54 52 
0295542 


B. 


1812 
'3 
•4 

'S 


9 9 59 23 
9 9 4S 3 
9 9 30 43 
9 9 16 24 


3 9 38 IS 
3 9 39 '6 
3 9 40 18 
3 9 41 19 


■ 9 3J 35 

1 J4 2. 


69 
70 
7' 


9 10 38 30 
9 10 24 10 
9 10 9 JO 
9 9 5! 3' 




8 53 9 
8 j6ij 


29 5' 33 
29 57 as 
29 j8 14 
29 59 4 


B. 


19 


9 10 1 12 
9 9 46 52 
9 9 32 32 
9 9 '8 13 


3 9 42 21 
3 9 43 22 
3 9 44 24 
3 9 4S 25 


• i> 57 
' 37 47 
1 38 38 


B. 1772 
73 
7+ 

75 


9 10 40 19 
9 "O 2! 59 
9 '<> "39 
9 9 57 »o 


J. 


8 57 '5 
8 s8 18 

8 S9 >8 

9 0,9 


a9 S9 ss 

; I ?ji 

1 a z6 


B. 


1820 

22 

=3 


9 10 3 1 
9 9 48.4' 
9 9 34 21 
9 9 20 2 


i 9 4"^ 27 
3 9 47 28 
1 9 48 30 
3 9 49 3' 


I 40 <9 
1 041 9 
I 42 

I 42 so 


B. .776 
77 
78 
79 


9 10 42 9 
9 10 27 49 
9 10 13 29 
9 9 59 ,0 


3 9 I 21 
3 9 2 22 

3 9 3 24 
3 9 4-5 


I 3 17 
I + .7 
I 4 58 
I s 48 


B. 


.824 

2I 

27 


9 lo 4 SI 
9 9 SO 3' 
9 9 36 11 
9 9 21 52 


3 9 SO 33 
! 9 5; 31 
3 9 S2 3' 


2 43 41 
1 04431 
I 45 22 


B. 1780 
81 
81 
8} 


9 "" 43 57 
9 '9 29 S7 
9 10 15 <7 
9 .0 ;8 


3 


9 5 27 
9 6 28 
9 7 SO 
9 831 


( 6 39 
I 7 »9 
I 8 20 
1 9 10 


B. 


1828 
29 
30 


9 10 6 4u 
9 9 52 20 
9 9 38 
9 9 23 41 


3 9 54 39 
3 9 SS 40 
3 9 56 42 
3 9 57 43 


1 47 3 
' 47 53 
1 04844 


B. 1784 

II 

87 


9 '9 45 47 
9 10 31 27 
9 10 17 7 
9 10 2 48 


3 


9 9 33 
9 ■" 34 
9 " 36 
9 •' 37 


1 10 1 
I <o 51 
I 11 42 
1 12 32 


B. 


i8j. 
33 
34 
35 


9 10 8 a, 
9 9 54 9 
9 9 39 49 
9 9 25 30 


3 9 58 45 
3 9 59 44 
3 10 48 
3 10 1 49 


1 so 25 
1 51 It 

I 52ie6 


»9 
9° 
9- 


9 '9 47 36 
9 10 33 16 
9 10 18 s6 
9 ■■> 4 37 


5 


9 '3 39 
9 14 40 

9 !S 4- 
9 16 +5 


1 13 «3 
1 14 13 
I IS 4 
. IS S4 


B. 


1836 

39 


9 10 10 18 
9 9 SS 58 
9 9 4" 38 
9 9 27 19 


3 10 2 51 
3 10 3 52 
3 "> 4 54 
J 19 5 55 


■ 9 53 47 

■ 54 37 
1 55 28 


B. 1792 
91 
94 
9! 


9 10 49 26 
9 10 35 6 
9 '" "> 4' 
9 10 6 27 


3 


9 18 46 
9 1948 
9 20 49 


. .6 4S 
1 17 35 
1 18 26 
I 19 16 


B. 


1840 

4' 
42 
43 


9 10 la 7 
9 9 S7 47 
9 9 43 27 
9 9 29 8 


3 10 6 57 
3 10 7 58 
3 10 9 
3 10 10 1 


I 57 9 
I S7 59 
1 s8 50 


B. 1796 
99 


9 10 s; IS 
9 'o 3« 55 

9 10 22 3s 
9 10 81^ 


' 


9 21 5' 
9 " 52 
9 *3 54 
9H5? 


1 20 7 
I 02057 


B. 


1844 
4S 
4<> 

47 


9 "> '3 57 
9 9 59 37 
9 9 45 17 
9 9 3'' 58 


3 10 11 3 
3 10 ,2 a 
3 10 IJ i 


. 1 J, 
I 1 1 21 
1 1 2 12 


Ftr.J^tmf^t tftaiing M ikt Numbtri afiir Jannary 
«■(/ February, Biffiratile Yeari Blaciiori adfuauiita 

Nacn ^ Jacuary the i/l. 


*• 


.848 
49 
50 
5" 


9 10 IS 40 
9 10 1 26 
9 9 <7 6 
9 9 32 47 


3 10 It 9 
3 10 16 10 
3 10 17 12 

3 10 18 13 


■ ' S 53 

' ■ 4 43 

■ ' 1 31 
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W NAVIGATOR. 



M«an MOTIONS of the isUNand/r^^STARS for MoHTHs and Days. .. . 


i 


JAHUAKY. 


MARCH. 


APRIL. 


M. MM.O.' Ap. 


*•. 


M A. Mot. 0. 


Ap. 


4ci. 


M. Moi. e. 


Ap. 


*2. 




2 






2 


2 a / r 




« 


2 

' 3 

4 
1 


S, 8 
I J8 27 

2 S7 «S 
3 S* 53 
4 !5 4« 






1 1 29 1 19 
I 1 7 28 
1 2 1 6 36 
> ' « 5 45 
• I 3 4 53 


10 

.10 


8 
8 
8 
9 
9 


2 29 41 38 

3 40 47 
3 I 39 5! 
3 2 39 3 
3 3 58 II 


'5 

;i 

16 


■3 
■3 

13 
'1 


6 

5 

9 

lo 


1 s4 s; 

7 S3 7 
S 32 .; 

9 SI 2J 






■ "441 

• 7 ■ ■' 

I 2 8 35 


II 

12 


9 


3 ■ 4 37 20 

3 5 3« ■! 
3 6 3; 36 
3 7 34 4! 
3 8 33 53 


16 

t6 
17 
17 


13 
'! 
13 
14 
'4 


'4 
'5 


10 50 3' 
II 49 40 
12 48 48 
13 47 57 
14 47 ! 






1 2 8 59 43 
1 2 9 58 ji 
I 2 10 58 
1 211578 
I 2 12 .56 16 


12 

U 
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3 9 33 1 
3 10 32 10 
3 II 31 18 
3 12 30 26 
3 13 29 34 


'7 
17 
17 

■|'8 


14 
14 
U 
14 
14 


16 


15 46 1) 
16 4j 22 

0. 17 44 30 
18 45 38 
19 4' 47 






1 2 13 55 2S 
1 2 14 54 33 
1 2 15 33 41 
1 2 16 52 SO 
I 2 17 51 58 


■3 
■3 
■3 
13 
■3 




3 14 28 43 
3 15 =7 51 
3 16 27 
3 17 ■« 8 
3 IS 25 16 

3 19 '4 2S 
3 20 23 33 
3 21 22 41 
3 22 21 so 

3 23 20 58 


18 
18 
18 
18 

19 
'9 
19 
19 
'9 


■5 
■5 
'5 
'! 

'S 

■il 
16 
16 


22 

■s 

24 

?! 


20 41 s! 
21 41 3 
22 40 12 
23 39 20 

24 38 28 


4 




2 .8 J, 6 
1 2 19 50 14 

1 2 20 49 23 
1 2 2. 48 31 
I 2 22 47 40 


13 
14 
'4 

14 




26 
»7 

2& 

30 


2; 37 37 
26 36 4; 
27 35 S3 
28 3S 2 
=9 3< "O 


s 




1 2 23 45 48 
1 • 24 45 5* 
> » »S 45 5 
1: • 26 44 13 
2 27 43 2 


14 
■4 
■5 
'5 
IS 




3 24 .0 6 

3 2| 19 15 

3 28 18 23 
3 27 17 3' 
3 28 16 40 


19 
20 

20 


16 
iS 
16 
li 
16 


3' 


. 033.8I 5l 4 


2 28 42 3c 


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T»/W ti. Meu PlK< if ti-Sun, i« Apo|««, «rf*/ fA* i*r, " March 27, 175!, -( iftc, Nwf Style 
EXAMFLX L, 

AP. ■♦v. 

N. S. Ytir 1758. 9 to 4 21 ] I 42 54 « 29 48 S 

Minh 27 2 24 4S 5* +14 + 22 


- 


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A.;«. - 1 « 4 JO Hi i 1 43 « • 29 4l .o| 
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Tht R C> V A-L AST k NO M E R 






Mean MOTIONS oMhoSDNitnd/^/StARS for MoKTa^andDAYt. ] 


f 

f 
J?.. 


MAY. 


■^ JUNE. 


JULY. '"] " 


■ AUGUST.- "• 


M.Mot.0. 


Ap. 


**■ 


;M. Mot. © 


Ap, 


;*«. 


M. Mot. &. 


Af 


*«-■ 


M. IWot. GT. 


/tp. 


*t. 


' 




' 


. " 




* 


21 

22 
22' 
22- 
22- 
22 


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4 o 
4 ' 
4 2 

d-JL 
4 4 

M 


»S 4« 
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■4 5 
13 13 

12 2! 

" 3? 
10 38 

946 

8 3 


■-TT 


1 '7' 
>7 

■7 

.8, 


4 2g 49 6 

5 0,4! 15 
Is- ' 47 *3 
is 2 4«,, 

S- 3 45 S9 


16. 
26 
.26. 

2<5 

26 

■27' 

. 27: 
- 27- 


^ 29 23 lb 
6 22-24 
b I 2r y, 

D 2 20- 41 

f5 3 '9 49 


3' 
3« ' 

3> ■ 
31 ' 


2S 

25 

25. 


t> 29 51 34, 
7 55 42 
f'l ;4!i 
7 • 2 5J 59 
7 3 S3 7 


36. 
.j6. 

J: 

37 
37 

37' 
■37' 
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29- 
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30 
30 

J2_ 
31 
3» 
30 


'S 4 44 4» 
5 S 43 !<■ 
S ■':41 4 
5 :7 42 13 
5 .814, 21 


.6418 58 
6 5 18 6 
6 6 17 14 
6 7 16 22 
6 8.; 3, 
6 9. 14 39 
6 10 13 47 
.6 II 12 y6 
6 .2 r2 + 

'6 13 II 13 


. 3« 

32' 
32 

3* 

3« 
32 
33 
33 

13 


26' 

■26. 
261 

'261 
.a6. 

37 
27 
27 
27 


7 4 5"= 16 
7 ■ S Ji *4 
7 6 50 !2 
7 7 49 4< 
7 ' 3 48 49 


4 y 

4 lo 
4 " 

4 12 

4 '? 


6 20 

4 3' 
3 45 




18' 
i3 
18 
18 
.9 


5 9 40 *9 
5 19 3? 3« 
5-11 ,i fi 
5 12 37 5! 

5- 13. 37 3 


a? 

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tS 

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22' 

23. 
*3 

21- 


7 9 47 57 
7 10 47 6 
7 11.46 14 
7 12 45 22 
7 13 44 3' 


3« 
18 


3' 
31 
31 
31 
31 


4 "4 2 53 

j;i ;..; 

4.17. a. 8 
4 '7 S9 *6 
4 ■» 58 35 
4 '9 57 43 
4 2056 J. 

4 21 56 

4 22 55. 8 


-?- 


'9 
'9 
'9 
'9 

20, 
20 


S >4 3S 11 
5 IS 5! 20 
S. 16 34 28 

Si 17: 3S 3' 
;■■ '8 S« 44 


2rf 
23 
2S 
2S 
29 


2J 
*3 

23" 

^4. 


6.4-2r 
6 >s 9 29 

6 .6 8 37 
6 17' 7 40 
6.1S 6 54 


J3- 
33 
33 
34 

14 


27 

27 

23 

28- 


7 14 43- 39 
7 IS 42 47 
7 16 41 56 
7 17 41 4 
7 18 40 12 


3» 
33 
39 
39 
10 


31 
3* 
3" 
3" 
« 


i-*9 31 S3 
5-203" I 
S- 21 30 10 
5 22 29 1-8 
5- 23; 28 26 


. 29 

29 

29. 
29 

3a 


2+ 
2+ 

24 

2 + 


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6 20 5,1 
6 21 4 19 
6 22 3 zS 
6 23 2 36 


34. 

34 
34 
3+' 

■1^ 


28 
28 

28- 
28- 

28' 


7 '9 39 21 
7 2o 38 29 
7 21 J7 3; 
7.22 36 46 


J9 
39 
39 

40 


32 
3' 
32 
33 


4.23 S4 16 
4 2453 2S 
4 2i 52-33 
4-26 S'.4i 




20. 


S'.H 27 3s 
5 25 26 43 
S.«« 2; sj 

;. 37 2S 1 

5 28 24. 8 


■ 30 
3a 
30 

. 3* 
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24 

■25 

2? 


6 24 > 44 
6 25 52 
6 26; 1 
6 26 59 9 

6 27 5S .7- 


■ 3S-- 

3S' 
35 
35 


29 ; 

11 \ 
,29' ' 

29 


7 24 35 2 
7 2S 34 " 
7 26 33 19 
7 27 3* 27 
7 28 31 36 


■5I" 
40 
40: 
40 


33 
33 
33 
33 




4 28 


« 5SI 25 1 21 1 


■ 






6 28 57 21. 


36 


29 7 29 30 44 


41 


33 










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nnd N A V I G 


A T S 












* 


]»«. MOTIONS ofliw SUN, and /i«^STARS, for Mopxtis fitiXlAVi. | 


1 


SEPTEMSeR. 1 


OCTOBER. 1 


NO V£MB b k 1 


D 1; t: i. M 8 E R^-. 1 


M. Mot. 0. 


Ap. 


*.fl. 


M.Mot.0. 


Ap.' 


*s. 


M. Mot. 0. 


Ap. 


*». 


M. Moi. G. 


Ap. 


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a •> , n 


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H 


9 » 3 10. 


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5t 


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1 


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47 


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42 


34 


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11 483 


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47 


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57 


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19 


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S' 


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47 


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39 


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43 


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11 


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41 


35 


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K 


J9 


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H 


41 


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'5 


48 




8 II 20 24 


■4% 


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9 .'o 5+ 34 


4« 


19 


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^4 


44 


11 11 2 2 


58. ,4» 




8 12 19 ja 


4^ 


IS 


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8 .5 a6 57 


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36. 


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11 14 so .3J 


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48 


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3t.- 


9 *^ -9 «4 


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H 


44 


11 i& 56 52 


49 


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8 18 14 2r 


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^6 


9 V 48 3! 


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40 




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,11 17 s6 


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49; 


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8 19 13 30 


44 


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9 18 47 40 


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49: 


21 


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4' . 


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44 


11 19 54 .7 


60 


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8 21 u 47 


4^ 


37 


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44 


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37 


9 «■ 45 5 


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49 


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45 


12 2S SO SO 




!<= 


-i6- 


£ 2$ 8 20 


4? 


m 


9 =>4 4' 3* 


!9 


41 




" H '5 49l"SS 


46 


>' 24 49 58^1 60 


SO 




8 26 7 25 


4S 


37 


9 'S 4' 35 


5° 


4' 


10 2b 14 57 


S" 


<f 


11 2S 49 : 




SO 


-28 


8 27 6 35 


4b 


■ 37 


9 26 40 47 


^' 


4- 


10 27 14 i 


,('> 


46 






so 


29 


8 28 ! 4J 


«6 


37 


9 *7 39 55 


V 


42 


10 28 13 13 




46 


11 27 47 2 


«' l.iol 


30 


8 29 4 s^ 


4t> 


IB 


9 28 39 ^ 


(I 


^ 


10 29 12 22 


!» 


4<> 


11 28 46 32I 61 1 50 


3' 








9 29 38 12 


S' 


4« 








■ ■ 29 45 40I 61 I .50 


Radical Mian Placi* and Motiohs of the Sun, ftom fevtr^ Authokitcis. | 




MJ-i-Ap-QJ 


1. tiat..Q. 


U. UM,At>. 


t rnfan Solu 


EMtnlrr 


Gnaftft E^. 




Tuliu Style. 


luHuSiylc. 


. loojuiiu. 


in ,00 JolUa 


y..,, 365 






According to 


J,n. 0.170,. 






"">■• 


lOOOOO. 






, D / # 




• • ' ' 












9 »0 4J 4* 


3 7 44 1° 


r.o°,.,v.,:r 


1 4jr 

Ap.i*«i7 40 


t.f " ♦' 


Ii,> 


1 si .0 


Sir Ifaac Nnaim' I lilt Edit. Prmcifia. 
t°..l'.«".*.iEs'<iii<ooJ.{'... 






45 31 

S«5. [io'" 




5 48 i4 41 


Cud. 


bflie 


Dr. EJ. H^lbr'l T.hlci. I70t, i*i« 
Gatl SYarrrrAft A(>R.[or.ioo,o'.io". 


fl «> 41 51 


3 7 4MO 




».. ., . , 




I* 






4S 47 


I 45 0: 5 48 ti 7 




I Si 30 


1^<uMtycr, of Gtllairn,Gtrmain, 














9 »4»3' 


J 8 S41 


046 


» » »S Soj W8 47 57 


■ 1,4 


1 55 >S 


r. R. S. fro«hi.T.Wn. ^' 


, »4»" 


J 7.6 


ti 41 S5 


.0 I lO « 


LV"*" 


>7J» 


<. .S, 6 


9ir«..Srr.«f. t;.coliM TaUM. - 


9 «.« « 


J 7 44 30 


4S 1» 


1 4» 30 

*o ..410 


S 48 S4|4* 


.»>i 


. Si 50 


0.romT.bl=. 





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9 




The ROYAL AS T;R O N 


M E 


R 




Radical Meah 


Placbi ud MoTioift of the Son, hit Apocbi, and of tht Fixid Starj, for 
yaiUn and Grtgoriait YsAai. 


Julian Style, 
fincc Chrift. 


M. PlaceiO. 


M.Pl.Ap.0. 


M.pi.i*.^. 


G»gori> 
a» Style 
Years of 
Chrit 


M. Placei 0. 


MJI.Ap.O 


M.H,,,,,. 




s / 2 








a - / f 


B. IDOD 

B. 900 
B. 800 
B. 700 


9 
9 
9 
9 


02839 

1 14 n 

' 59 4J 
' 4! "S 


1 "1 3S 59 
1 13 18 29 
< 2; S9 

I 26 43 29 


I. 21 6 JO 
II 22 31 

II 23 ii 10 

II 25 19 20 


S. lOoo 

: 1700 

1800 

1900 


9 10 21 8 
9 10 7 32 
9 9 S3 55 
9 9 40 19 


36 57 
3 7 43 27 
3 9 25 57 
3 II 8 27 


27 35 9 

28 59 19 

1 23 28 
1 I 47 38 


B. 600 
B. joo 
B. 40D 
B. 300 


9 
9 
9 
9 


3 3J47 

4 16 19 
! > i' 
! 47 »! 


2 
2 


28 25 59 

8 29 

1 50 59 
3 33 29 


II '6 43 30 
II 28 7 40 
II 25 3, 50 

jS 


B. 2000 

2100 

■ 2200 

2300 


9 10 2S Ji 
9 10 12 IS 
9 9 58 38 
9 9 45 2 


J 12 so 57 
3 14 33 27 
J .16 IS 57 
3 17 58 27 


1 3 II 48 
1 4 35 58 
1. 6 8 
I 7 24 18 


B. 

}.Ja1.Period. 100 

B.47.3B,Chr.^ 


9 
9 
9 
9 


K I' SS 

7 -3 «7 
a 3 !9 

8 4^ 31 


2 
2 


I 'i S9 
6 58 29 

8 40. S9 
10 23 29 


3 44 20 

0' s « 30 
6 32 40 


B. 2400 

2600 
2700 


9 10 30 34 
9 10 16 58 
9 10 3 21 
9 9 49 4S 


3 19 40 so 
3 21 23 26 
3 23 5 56 
3 24 48 26 


I 8 48 28 
I 10 12 38 
I II 3648 
I IJ S7 


B. 200 
8. 300 
B. 400 
B. <iOO 


9 
9 
9 
9 


9 3S 3 
,0 3S 
II 6 7 
II SI )9 


2 


" S 59 
13 48 29 
■5 SO 59 
17 13 "9 


7 S' 50 
921 
10 45 10 
12 9 20 


B. 2800 
J960 
3000 
3100 


9 10 3S 17 
9 10 21 41 
9 10 8 4 
9 9 54 28 


3 26 30 50 
3 >8 13 26 

3 «9 55 S' 

4 I 38 25 


1 14 25 7 

I IS 49 17 

I 17 13 27 
1 ■» 37 37 


B. 600 
B. 70c 
B. 800 
B. 900 


9 
9 
9 
9 


•37 II 
■3 M 43 
.4 8 IS 
'4 53 47 


2 


2<> 38 25 
22 20 59 
24 3 29 


13 33 30 
14 57 40 

16.21 JO 

17 46 


B. 3200 9 10 40 
3300 9 10 26 24 
3400 9 10 12 47 

Biflextile Yean PlacM are 


4 3 =0 55 1 ?o 1 47 
4 5 3 25 I 21 2S 57 

ativaiicetl a Day'i Motion. 


B. .000 
B. 1100 
B. 1200 
B. .300 


9 
9 
9 
9 


'! 39 19 
iS 24 SI 
17 10 23 
■7 S! 5! 


2 

3 


•5 45 59 
27 28 29 
29 10 59 
53 29 


19 10 10 
20 34 20 
21 58 30 
23 22 40 


From H.ivlrBl. of run C^t^ma M.O Ibdr /Wni [k- 
jcfting Fr.aiaiuJ .nd ttw Uttuiniit will ha fiaal la Uie W. 
ol D<fi then irr b[, in any N^. of Cn^^it, Yoin Ifau theie 
.r« la the tame N". of Vtm JnUm, /ton ifioo. Whtaee U 
had the Diff. of MoOon bttween ^.^aa aad f^ialaa Yeaia. 

EaaMrLii. 
. la the Yaoe jaoa. la the Year 3756 
— 1600 1600 

i i6|oo i.ilsi 
-4 — S 

la Day. left 16 Daya lefe than ia 21 
rthaitiaifiHaad. Y't?./. (Haadred Yeaia >£... 


B l^n 
B.' 1600 
B. .700 


9 
9 
9 
9 


18 41 27 

19 16 S9 


3 2 35 59 
3 4 .8 29 
3 « o 5; 

J 7 43 29 

3 9 25 59 
3 II 8 29 
3 >" 5° 59 
ranced 2 Day 


24 46 50 
26 II 
27 35 10 

28 59 20 

1 23 30 
1 1 47 40 

.'. ' " s" 

I Motion. 


B. 1800 

B. 1900 

B. ■ jooo 

BiiTeztile Years 


9 «' 43 35 
9 23 29 ; 
9 *3 1+ 35 
Piacca ajc ad 


Julian Veart, 


M 


Mot. ©. 


M22. Moi. 
Ap.®. 


MoanMoi. 

fixed 'Stan. 


Giegoii- 
20 Yeara 

from 1 600 


M. Mot. G. 


Mean Moi. 
Ap. 0. 


Mean M«. 
fixetl Stan. 






S , ff 








B. 100 

b! 300 

B. 400 







45 3' 

1 31 4 

2 16 JO 

3 ' a 


° 


1 42 30 
3 25 

5 7 3'-. 

6 5= ■. 


I 24 10 
2 48 20 

4,12 30 

5 30 40 


200 

300 

B. 400 


II 29 46 24 
II 29 32 47 
II 29 19 11 
4 43 


. 42 30 

3 2S 

s 7 30 
6 50 


I 24 10 
2 48 20 
4 12 30 
s 36 40 


1: l^ 

a: 700 

B. 800 





3 47 40 

4 33 12 

1 '8 44 
6 4 m 







8 32 30 
10 IS 

ti S7 30 
13 40, 


7 so 
8 2J 
9 49 10 
II 13 20 


». 800 

b; 1200 

B. i6ct) 
B. 2000 


9 26 
14 9 
18 s? 
23 ,5 


13 39 55 
20 29 59 

27 19 58 

1 4 9 58 


II 13 19 
1649 59 
22 26 38 
28 3 18 


a. 900 

ri! 2000 

B. 3000 





b « 48 

7 3! 2» 
1; 10 40 

22 46 




1 


15 SI 30 
17 5 
4 10 
21 IB 


12 37 30 

14 1 40 
028 3 20 

1 12 s 


B. 2400 
B. 2800 
B. 3200 
B.- ,600 


28 1.8 
33 1 
37 44 
42 27 


1 10 59 57 
1 17 49 57 

1 24 39 s« 

2 . 1 29 SIS 


1 3 39 58 
1 9 iJ 37 
114 S3 17 

I 20 29 56 


3. 40<=° 
3, jooo 
3. 60D0 


I 7 56 40 
I i^ 32 


2 

? 


8 20 
2S 2S 
12 30 


1 26 6 40 

2 10 8 20 
2 24 10 


B. 4000 
B. 6000 


47 10 
1 10 45 


2 8 19 ss 

3 ■• "9 S3 


1 26 6 36 
'24 9 54 




















MtM 



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.!! ; 


iW,/ ifi AVIIG-A-T4*. 






^ 




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fe 


M. Hol.to. 


ComE. 


Mat.ei 


MottHm. I 


&■ 


M. Mot. 0. 


Comp. 


Mot' 
ApoiT*- 


Mcu Mol. 

-liiEdSnn. 




4 / # 








• « , . 


'~< 




• . 1 . 


.2 

B. i 


» I ■a9 17 1 
0,0 1 ^ 


14 20 
2i ^» 
4» !9 


1 1 
■• 3 


so 

1 41 

2 31 

3 21 


1* 
S" 

B. 5; 


7 31 
n 2913 It 

11 29 ]i J! 

23 41 


2?*! 


50 13 
JI IS 

52 16 
53.18 


41 14 

42 5 

43 4* 




" «9 V W 
11 ^ It so 
» » 3 » 


12 31 
2« 50 

41 10 


1; 


4 12 

5 3 




e 21 

11 29 SS I 

II 2940 42 

2S JO 


4 S9 
19 18 


54 19 

56 22 

57 »4 


44 3« 

45 27 

46 17 

47 8 


9: 

B. I'z 


11 19 49 19 
" «»34f» 
11 19 «o 39 
•0 5 rt 


10 41 
•5 ■> 
39 "■ 


9 13 

^o IS 
II l« 
Ik 18 


9 IS 
10 6 


15 


11 10 
11 29 s6 so 

u 29 4I .1 
17 !9 


3 lo 
17 29 


58 25 

59 *7 
I 28 
1 .1 l" 


47 S8 

48 49 

49 39 
. 5" 3° 




11 ,9 4 » 

ii »9 3448 

11 «, IS m 

-0 7 17 


« 52 

37 3' 


■J '9 
1421 

'J " 
18 24 


.. S6, 

"47 

" 57 
13 2! 


61 
62 

B. 6i 


q 12 S9 
11 29 s8 39 
11 29 44 20 

29 8 


1 al 
IS 40 


1 2 3I1 
' 3 « 
' 4 3*' 
1 5 S6i 


5' »o 

52 u 

53 1 
S3 52 


'7 


1' »9 S» S7 

11 :m >4 rt 
9 A 


7 3 

21 22 

IS 4« 


17 «S 
■"2 

19 28 

20 )0 


14 18 

15 9 
. ■! 59 

iS so 


^1 


r4 48 
28 
.1 I94S 9 
JO sS 


'3 S" 


1 6„ 

' 7 39 
I 840 
1 942 


S4 42 
!7 >4 


31 


u <9 S4 46 
11 29 40 s6 
11 .9 .6 7 

10 ^ 


S "4 
■9 34 
33 S3 


21 )l 
21 )J 

24 j5 


17 40 
1! 3» 
1921 
20 12 


69 

70 


16 38 
0.0 2 18 
11 119 47 55 

3.2 47 


12 1 


1 .10 43 
1 11 45 
1 12 46 
1 1348 


5! * 
1 36 


'A 
,. S 


u 19 s' J6 
11 19 4t t6 
If J9 17 S7 

-0 15-4; 


3 24 
17 44 
S« 3 


»S 37 
26 59 

3,1 


" 5) 
«• 43 

. : »3 34 


73 
74 


18 27 

0047 

11 29 4, 48 

". 34 .3? 


10 tv 


1 H49 
1 i?ii 
1 rtsJ 
' "7 54i 


1 1 16 
1 a 17 

'I 3 7 
1 J S« 


B. li 


<i «9 s« ir 

11 J9 44 S 

11 J9 J9 46 
.0 14 54 


• 3! 
>S SS 

JO 14 


»9 43 

30 4S 

31 46, 
. 32 48 


T4 24 
26 si 




■0 -o 20 16 
s s6 

11 29 SI j7 
J6 26 


8 23 


1 19 57 
^ 26.5! 
i il 


I 4-4» 
I 5 39 
i 6 19 

I 7 2b 


34 

.. 11 


0-14: 
" "9 4S 54 
11 29 Ji Si 

16 24 


Mi 


33 4S 

34 5', 


■274* 

28 !7 

29 27 

30 li 


Si 

B. 15 


-0 22 6 
d 7 46 
11 29 sj 27 
jS 15 


« 33 


"4 5 

Hi i 


-1 8 10 

1 10 42 


11 
B. Jl 


» T 
11 29 47 <4 
11 29 31 25 

6; i8 1, 


12 iS 
16 3! 


3? 55 

3»SJ 

39 (8 

.. 41 <i 


52 8 
3' !9 
3' 4» 
3! 4<1 


*. 15 


-0 23 55- 

» = 935 
11 29 55 tt 
0. . 40 4 


] 

4 44 


h3 i 
'1 29 10 
1 30 1^ 


1 11 32 
1 12 23 
1 13 13 
1 14 4 


4> 
B. S 


» 3 J3 
■" 29 4,4j 
II 29 3s 14 
,9 «i» 2 


•4 K* 


42 I 

•43 » 
* t 


34 39 
Si »' 

30 11 

37 2 


^9 


6 25 44 

II 29 57 s 
,« 4, s! 


• S* 


1 31 13 

* )»-i4 
. 33 16 

I 34 >^ 


1 14 54 
.2 -IS 4i 

1 16 35 
■1 17 M 




S 42 
11 ,9 SI 22 

11 29 37 3 

21 SI 


S 38 

22 S7 


4« 7 

48 10 

49 12 


37 S» 

3« 43 

39 33 

. 40 24 


93 

•94 

B. ,'l 


27 33 
.0 13 13 
II 29 58 54 

". .« 4J 43 


I 6 


I 3! 19 
t j6 21 
1 37 22 

1 38 24 


1 18 1« 
1 19 7 
1 1937 

1 20 48 


Oa-a iW. Mcni«»i wM. Pl«n fer-»iiole Ha.- 


B 

W 


29 2J 

IS 3 


— 


I 39 25 

1 40 27 


1 21 ;i 



,, Google 



Til R O Y A L A S T;R-ON.O ME R. 











' -- 


. "... 


: 


JfwiPtACES of the SUN aaJTV«/rrARS:&rK4«r/«nd Moaff/OU-^ 




iKmSi,!,. , \ 


1600 


Juliui Stylt. 


1600 


Gregoriin Style. . 1| 


Momlh.. 


Mt.1. PI. 0. 


M.Pl.Ap.0. M.Pl.i*=ir. 


Montlu. 


MeuPl. 0.. 


M.Pl.Ap.G. 


M.pi.4*v; 






s. / .# 






January , 

Ftkrmn 1 

March 
AfHl 


9 !o IJ Ji 

10 10 +5 +9 

11 18 11. 4« 
18 (, , 


36 59 
3 6 .1 + 
, 6.-9 
3 S I 14 


27 35 10 
» «7 33 .H 
<J 27 35-« 
17 35 22. 


ftbrum-y I ' 

- JMi^i— 
jfj*.<7 


9 10 21 83 ,6 .0 57 
10 10 54 26 3 ,6 I ,3 
n ■« 30 .9 3 6 1-7 

9 9 3 38r3 * I 12- 


■i •? 35 9 
27 35 13 
2I7 35- 17 
27 35 21 


A/fljF 
Juni 

7^^ « 


1 ia 29 11 

3 i« 36 39 

4 19 9 ;7 


3 I 19 
3 6 1 24 
3 6 1 29 
3 6 1.33 
3 6 I 40 
3 6 1 4S 
3 6...S.. 
3 6 ■■ !S 


27 3S >7 ■ 
2J 35 31 
27 35 35 
27 35 39 
27 35 44 
27 35 48 
27 35 52 
27 js 56 


Maj 


I 8 37 47 
29116 

3 845.6 

4 9 18 34 


3 6 1 17 
3 6 1 22 

3 6 127 

3, « ,1 33 


27 35 26 
a 27 35 JO 
27 35 34 
27 35 38 


Siplimbtr 


5 '9 -U 'S 

6 19 17 J) 

7 "9 5° +J 

8 19 Z4 53 


Sibtimblr 


! 9 s; 5' 

6 9 26 2 
• 7 9 S9 20 

8: 9 33 3» 


3.6 'i J8 
3' I 43 
3 .6 > 48 
3 6 153 


27 35 43 
0. 27 .35 47 
27 35 51 
27 35 55 


•1700 ' 


ulian St/lc. 


,700 


GregotiRO Style. 1 


Mmd, 

4.w; 


9 20 si _ 3 
,0 21 31 21 
II 19 . 7 14 

19 49 33 


3 7 4! «9 
3 7 43 34 
3 : 7. 43 39 

3. 7 43 44 


^ 59 20. 
23 59 24 
0.28 59 28 
0. 28 59 32 


Afril ^ 


9 lo 7 3" 

10 10 40 so 

11 8 1S43 
8 50 . z 


3 7 43 i7 
3 7 43 32 
J 7 43 37 
3 7 43 4' 


28 59 19 
28 .59 23 
28 59 27 
,8159 3 


«,- 
J" 0, 


■ "9 H.« 
. .9 4? I 
3.19 " " 
4 19 !S '9 


3 7 43 49 
3 7 4J !4 
3 7 43 S9 

3 7 44 ! 


9 28, S9 37 . 
28 59 41 
28 59 45 
a 28 59 49 


. J^, 


.1 8 '4 I? 

2 8 57 30 

3 8 JI 40 

4 9 458 


3 7 43 47 
3 7 4! S' 
3 7 43 57 
3 744 3 


,28 59. 36 
0,28 S9 4« 
0.28 59 44 
028 59 48 


Siplrmbtr 
0.«.Ar 


5 20 '8 47 
620 2,7 

7 20.36 15 

8 J^o .10 2s 


3 7 44 '° 
3 7 44 IS 
3 , 7 44 " 
S 744 «S 


28 56 5, 
28 S9 58 
29 ; 2 
[29 6 


1 Stptemitr 
ftt™&r if 


5 9 38 16 

6 9 12.26 
7: 9 45 44 
8.. 9 19 54 


3 7 44 8 
3. 7 44 "3 
3, 7 44 >« 


2> 59 S3 
28-59 5? 
o.'a9 ; ( 


1800 


.. ulian Style, 


.iMao.: 


Gtcgonan Styles | 




9 *> 43 3S 
iS 22 16 S3 
II 19 52 46 

26 26 5 


3 9 ^5 59 
3 9 =J 4 
3 9 25 9 
3 9 26 t4 


I 23 30 
I 23 34 
r 23 38 
1 23 42 


K^ib 9 

4.„y J 


9 9 S3 55 

10 10 27 13 

11 8 3 6 
83625 


3 9 25 S7 
3 9 26 2 
3 9 26 , 7 
3 9 26 12 


, 2J 28 
I 23 32 
i ij 36 

I 2J 40 


M, 0. 


1 20 IS 

2 1=9 '33 .33 

3 »0 ■ 7 « 

4 20 41 - 1 


3 9 26 19 
3 9 26 24 
3 9 26 29 
3 9 26 35 


'. « 23 47 , 
I 23 SM 
1 23 55' 
1 23 59 


W« 9 


1 8 10 34 


3 9 26 17 
3 9 26 22 
3 9 =5 '7 
3 9 '6 35 


1 23 45 
1, 0-23 49 
1 23 53 
. 23 57 


Oathtr 
Dumhra' 


6 20 4B 29 

7 21 21 47 

8 20 55 S7 
Inl«p-y™tj 


3 9 26 40 
3 9 264s 
3 9 26 50 
3 9 »"■ SS 
Ite oflt [ke Mob 


WAt 

tb D«r Mc^D. f<r 


Oaihir 
Ncvmitra 
Dtttmitr. 


lilt 11 


3 9'f38 
3 9 29 43 
3 9 '5 48 
3 9 26 sj 
Udi Stylet. 


I 24 2 
I 24 ( 
I 24 10 
I 24 .4 




ex;a-m 

. .°/ .. 
9 U .. J. 

14 3. 


P L E I. ' 
», O.S.f 

! • . S 
!■ 4 


B »7 3i 'o 
2^ S6 


7c Jhd lit Pltti 

rt.s.oa.o.ti'^ 

Y«n >o 
Diy7 ifl 


E-X A WP 

■"Sin-* 

■» I! • 


L B tl, 

3 # 2» 43 

20 .10 


; i*r . 


[).«.7m.iM6i 


to c ig al 


1 * JJ 45 


il , 7 


t r/.s.oa.is,itio 


7 7 4» 37 


3 9 47 t! 


( 41 



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-«»i ■I^'A-VrGA'TO R. 



Fti. 



-M'^' 



JU««» aI'otion of the Si 
Jtf. Mot. 0. 



Ma; 



03. 



1 of tbe Fixtd Sittri, continued,' for MoDths, Days, (jt. 



«r-- ;-- »- ^ 



33 i8 
„ 9''' 
J »» 4a 30 



■ 3 »» 16 40 
4.28 49 (8 

5 28 24 8 

6 28 57 aiS 



7 29 30 +4- 

8 39 4 54 

9 29 38 lA 



Take out i Day feoner for Jannoj 
and Ftinuoy, in Leap.yeu. 



I s8 
' S7. as 

3 S* 33 



6 S3 j8 
I S3 

8 SJ ij 

9 5' 



■6 10 50 3; 
o II 49 40 
O IS 48 48 
o »3 +7 S7 
° '* 47 



. 15 46 1 
I 16 45 i 
' '7 44 30 
' 18 43 38 
' '9 4^ 47 



o 22 40 12 
o 23 3020 
o 24 38 28 



o »S 37 37 
O 26 j6 45 

o *7 35 S3 
o 28 35 2 

° '9 34 'o 



■ o 3? '« 



* * . 4" 



Chronological j£nu belbieand 
- finceChrift.'- 



Qifwipiadi, ^Twi 



KabomUTir, Fcbniiryat. 
D«(* Alci. the' Cnal, Nor. 11. 
45 CtlaJatfaiMij t. CmL Ua. t. 

oBSnio/ceHJl. . 
iT4[DiocJel!iii, XagiiH t». 
-■Gmnila/iria. 

HmM./TorLt, Jolj .6. . 
7(7<*«(V>^perr».ni,Juno,6,0.i'- 

Bigan IK En(l)nd, ScpL 3, O, S. 
Sept. 14, JJ. ^. 



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"TxTmpTTT" 



To /W ^i« Mmii P/aet ef ihi Sat, hii 
get, anilhtfirfi iff^ Janiiary 20, 

__ otNoea, Netu Style? 



'7se| 



M..E1» Q. . Ap. ©, 



.8 n 19 

+.4*49 



OM.Aooi 



M.Mo. 



456 
O J 24 
" 9 SI 



o 14 47 
17 IS 
'9 43 



o 27 6 
*9 34 



l.Mo.ol 



EXAMPLE II. 



39 16 
o 4' 53 



o 46 49 
49 '7 



S" 45 
54 13 

6.5643 
59 8 

' 36 



6 52 



II 27 
■3 55 



n, The Grtgerian is [rdnc 

And; the coniruy, by idding the Dii»« Diffi; 
'w Diffkrat, k,tvi\xi New *ni Old Siylc; 
ki7t». From the Hnndredi of Cmiij' 



*<V, January i, at Midnigbi, 1804., 

Q 

? 51 5S 

.+ ' 49 



33 38 
36 6 

38 3* 



' +5 57 
43 25 



S5 48 
58 16 
o 44 



S 4" 
8 « 
10 -35 



'5 31 



B- !»"■«« j 



9 SS 44 

+ *9 i* 



EXAMPLE IIL 

To find tht PLci of ibt SfiB, Jfagte gnd 

■ ♦'¥•» February jg, igh 13" ti\,P, M 

848, Nn^Siflt? " : . 



2 17 59 
2 io 27 
2 12 SS 

2 2S 23 

^ '7 50 




Tte fame may be performed by redu- 
cing the Day) of the Monthi' in ihe'above 
ExaJupUi to the Old Style. 



■i«g equjiiy for ConpuiMion) by f-btMaing the Number of D^« Diffi^ce 
. u redoced to the Cr^,« Style. 3i i«r«« uaiMrfiJl/S* N^lj 



EiAMFtB.— in i7J4a 

(teiB. .10 IbitDiffemm. 



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Tbt ROYAL ASTRONOMER. 



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M O 38 5' 



44 »4 
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ij 48 

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t9 



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3" ' 
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34 54 
36 2 



Si 49 



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44 S4 

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54 55 



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55 45 

is 4 9 



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38 16 



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7"» *.-<*«■«» ii(i)i#rf£»M«M>. All" or 60* DifferoiM of Argurotnt [i lo «,™(o Md S«-=i.fl!., Dif. of E,iHt»n, To antlie Uln' id. 
Sec<Dif. of ..«p«ar above whole DceRM Id tbeMJD'iad Sect [>n>p<)ni<iail Dif. oF Equation, to be idded to, or rnbtriQed Amu, tht>i 
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AA rSfMcd bj So : whieb Ma>ti[dinROD lod DinBon {by f »»; tht above T,bU peifoimt, >t Sitht, 


£>AHit< I. ■Ibt&m-tEjwmmJir ■• ]5<> jf 57* 5<m>'i yflwHd^ h njv^idT 


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The ROYAL ASTRONOMER. 



EXAMPLES t/.pnptriiiniing iht Dirpii.«NCB f/^ £ (^U A T-I O N S. 
BiAMTti II. S«ii'j Ptati t iftM, Jau lo, 1756, n f 9"- 5*' o" rtfinnd til Et[b JflcastM r 
OPl- R. A. ' 

n«o 5 7g 7 4 
AiDif. iO-+, J i«i65'. I". Dif, inecetfioi ! 

Uj TABLE. 
X ec . . . s»' 
,S ■ ■ ■ JtOi 



( Atg'. than Dei*. ) + 56*. ae". 51'". Pmpl. iEqw", a i^'^^^- 

:acb 
X "I 



, 5» 



R, A. itqnirad . 7!! jS 13 
«oiiiMAt.s ire thui CurMd ii 



MCIMALLY, 
S)jj8io.!j» 



i'l S= *7 6. » 
ItiluRltbii 



SEXACBSIUALLV. 



Xd 






Prop'. Aqitl^i vyjji>|Wfoj« cut iff ) iakjnr 

CIMA19, and the cODtiirr, withenC gj' Ih Sixaoiiimj 

. ■ Taile. W^nin X Afin'a = -5 

i/i> firrW ran Decinuli •/ a Jfui,/,, j. Jiviiiit ibim hj G, ^itmiJi X ^ttwb = Fw^ii 



6)33810" _ 

e6' »o" ji"' Prop'. jEaua" 



iliuU Mtrt ibt SteiaJl 
fmmJlt,, &4. 



. . __,, Ibifjfi Daimal, iba^. 

fitmJ, Hundredtht, tec. ixtrpt vittn ttr Sitetdi 11 

'—J-J tr i) vnS be HmnA-tJibi, lU axt TIuhi- 



ibtri a, a muflfiaaJit fatb', Placi. 

tuntallj luriid iiut Decinub 0/* De 

;_.A./-o. — i fc, .^ -ampk K til Rigbt}. Aidii'- 
.uotient, ami ihi ntiX Driwmi- 
tbt Dccimili of Stxggtfmidi art 



hieh. 



rhirdi into Dtdmalt •/ 1 Second, ^c. (Si 
tiiJing liii loweA Danmiiviim ly 6, lim lb 
,Mio« bitbrr by 6, m fat at Digna, tr He 



Dicimil. C'f Dipm, H>an, .«/ a//™, Ordtr) ar. ani^t^faUy w™«/»M 
Stxagifimah. iy ^/iifhing all lb. D„,maU „ lb. Right HW tf 6, t-i c^"i':g 
4 ihe Pr^a ./ tUjrfl lUciaut. -uilb -uihal 11 carrildfnm ,b, rrjl, fir Ibl n,x, 
0««./wri.,/™ff, a,/,WBft.— Two or th™ D«; ' ' " ' " ' " ' 

noltiplied bj 6, will deterauoe the faUt of the a 
uSi^b), 



thiRightof 1 Scxegifimtl baa% 
ind ^1 cbt Figurci to the Left diiidcd by 6, will give tlit 
VAae of ChiC Produa, in Snigerimal), a Denonunabc 
—The Raa'Kdrr, befbre the Figure cut olf, to I 
before chM f iture, for the Vilue of Ihe /nwr Deac 



»9.'573°i, ■ ■ "9'J4«3 



'9'.!7J0S5S4( ^. 
J4",j8j33ia; Fi(|urc denote! ■ concinl 
■i"'g^)}44 -> Repetition (ram tbcncc 



rrfsj' ss" DiftTiiu,,fJtrg««,^r 

SEXACSSIMALLY. 
jOif .«,«. 39'v4°"U9' I 40" 

- ;li£lLi5lL_ii!L 



40" 5 Oif- JB-fi. 
Si" f Dif. Ar,. 



40". 



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3J »S »8 10 Propl ^qi 

By LoCDTtCAL LoOAlItHMI 

L.L. 

Ltgiflica/ tegarliimi fnfrrtUii til tafir/l, biitnfl ataiajiittfuiei^, «> 
'*'-'"'- ■'" — ■■— liaii Ibl ran'Bg (bttkaarJ aaiifertiiarJJ mr Lunm, 



ao6|7" I3<|5"' 140^' 
4+' »7" . . »»"45"'. *3"'ioi» 
35 io"' 



mf.Ajt". S3' 35" latsOM*. TbifiL^JUclLogari 
Olf. ^qa. 39 40 j 1797 L i,l>fidifii.rii„gi,jb!nlin 
PrI. jEq». 35 ij I »SiJ 



35 3; aS 10, correfUy. 

4irlBMa«:ir, «£»£ 



JO', i- «o' . 16' 
6- TO**"' ■ S.35S 

4o''-5-£: - 



39*. 4c/' . 3S''4'J 

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UNIVERSAL! Y 
L, S3' js" of 39>,G66 



4!'.,8x.''.ji ,, 
5- SXi'- 3.30s 
JO". ,SX «'■ 



S3' 35' 
Pom, «/ »Ay»*( Farti if rLj 



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Multr x^»i\A\' 
u iiunj TrMif- 
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39' 19" Jo 44' 51" » 7*' 3" 47" 
39. Ji fo 44, (^ to 76',044=76' s' 



tDi7/ a^iJiu lit aitvr Prtf 



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39'4o" j Sl'.jg 
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md N -A -V I G A T OR. 



rke SUN", /n^tu/ DISTANCES (rem the EARTH to the Suo'. Man Diltmce from th«.ce, looim.- 
-. . .. Tie Ecctotridty of tie E>rth'. Orbit j«Sj of fuch Part.. 


— .rfjTOW. SUN-, Mem Aiion.1,. - . 


An. 


6.g.o 


Dif. 


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10 168 J 
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5 

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6 

7 

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8 
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12 
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I 01466 
101 4S2 
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101 jBy 


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23 
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33 

24 

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100864 
100839 
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100788 
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26 

27 

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28 

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28 

28 

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29 

29 

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9»!9 
99910 
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3" 
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29 
29 
29 
29 
29 
29 
29 
29 
29 
*9 
29 
29 

:i 

28 

28 
28 

iS 
iS 

a? 
27 

11 
26 


99180 

99"!4 
99129 
99104 
99079 
99054 


26 

'S 

2S 

25 

'! 
•5 

24 
24 

23 

22 

20 
•9 

;i 

18 
17 

'7 

\l 
16 

■s 


98550 
98535 
985.0 
98506 
98492 
98479 


'5 
■S 

>4 
'4 
'4 

'3 

12 
11 
10 
10 
10 
9 

i 
8 


3« 
*9 
28 

27 
z6 

25 


6 
7 
8 
9 
to 


191676 
IO1673 

,0,66? 
■01660 


101372 

"o>3SS 
101338 
1013ZO 
101302 


100709 

100682 

I 0060 I 


9,852 
99823 
99794 
997's 
99736 


99029 
99004 
98980 
98956 
98933 


98466 

98454 
98442 
98431 
98421 


2+ 
»3 

20 


12 

'3 
'4 
'S 


1.16SS 
1016,9 
10i6« 
101636 
101629 


101284 
10136s 
101346 
101226 
ioi2«6 


I 00s 74 
100547 
1 00s 19 
10049. 
100463 


99707 
99678 
99649 
99620 

9959" 


98867 

9!"4' 
98824 


98411 

98401 

?sW3 
9837s 


19 
13 

\l 

IJ 


i6 
■9 


101612 
101614 
101606 
101597 
.01587 


101186 
i«ii6s 
.i«ii44 

101100 


10043s 
100407 
100379 

I 003 so 
109321 


99562 
99S34 
99506 
99478 
994!'> 


98803 
98782 
98762 
98742 
98722 


98367 
9B360 
98353 
98347 
9834> 


'4 
•3 

tz 
11 

i" 

3 


23 


101577 
101566 
1015SS 
101543 
loisji 


101077 
101054 
101031 
101008 
10098s 


10029Z 
100163 
100234 
10020S 

100.76 


9942! 

99366 
99339 
99312 


9S68J 
98666 
98648 
98631 


98337 
98333 
98329 
9j3>S 
98322 


26 

2i. 


loijio 
101506 
101493 
101480 
101466 


1 00961 
loocjjS 
100914 
100889 
■00864 


100147 
100118 
100088 
100058 
100028 


99285 
99259 
99232 
99206 
99.80 


98614 

98565 
98550 


983.9 
983,7 
983.6 
9831s 
983.5 


SM. 
An. 


0*0 


Dif. 


o^e 


Dif. 


©10 


Dif. 


©•e 


Dif 


o>e 


Dif. 


.©ie 


^^- OM. 
Ad. 


Sig... 


Sig. 10 


Sig. 9 


Sig. 8 


Sis- 7 


Sig. 6 






1 


Con 
JUhilci 

H.B 

tuDtOC 


TRUCTIOH. A> Sine { true Anom. ; Sine j emnt. An. :i -i^ PeribdioD Dift. : v'Difi. fi. SiUi the Stum of wbich ii tbc 
, 01 lb* dMUcd LopitthB, the Log. tt the DiAince (mm the Sun tr^uired. 

' ' ■" Com. Log'. 
iTineAmOin. 14 31 jj.j . . Sintl 0,6006415 Co. 
' ^«Wi. Anmo. ,4 4s « 1 . . Sine g.+ofiioss 
^PetOuDift. gSjis. . .. i . 1 2,4963099 

rMrottioiuI DiAuict fiom the Sun 101466 . . ^^aoliiii Doahhi. 

one oal coma : The abon T«ble bcini > Work of «teit L.bour. 



uxitarmm 



,, Google 



tbt R O V A IL -AS t ^ O K b M E R 



LOGARITHMS of the foregoing propaRLODml DiRancei of the SUN from the EARTH, to the Mnn Difluce. 
looooo; UK](he£cceiitrici^oftheEuA*iOrtHt i68j. 



SUN'* Mmm A»i>UM.-r. 



Sig. < 



■^5^ 



Logar. 



Logjtr. 



LogBr. 



_!£I 



S'g; 3 _ 



Logar, 



Lag« 



5,0071568 
5.007*568 
5,0071516 
5,0071483 
S.BO7I393 

5.007Z3I1 



5/>o72i94. 
5,0072056 



5,0071714 
C.00715 01 



:5,0062< 
.5,0061964 
5.0061311 
5,0060636 

iS,005$9o3' 



<5.oo50LfteL 
15,0058451 
5,00577*3 
;5 ,005 695 1 
:5 .00561 60 



5,0055408 
5,0054594 
5,oo;j779 
5,005191, 
5,005 tofcj 



5.005 IZ04 
15,005630 
5,004040 

5.0048456 
is .0047 5 



5/J037361 
5,0036285 
5,0035208 
5,0034088. 
5,0032966 
5,00311847 



5,0030683 
5/5029518 
S/)Di«353 
5,00x7188 
5,0026033 



S,Ooz4g;7 
5,00x3691 
5,00x2481 
5,ooTi 273 
5,0020061 



5.oo«i2i6 
4»99999>3 
4,9998610 

4.9997350 
4,9996090 
4j9g94829 



4.9993*68 
4,9952306 

W99'04+ 
4,9989783 



5,00 18S; 
5,0017640 
5,0016418- 
5,0015174 
5.oo'3 " 



4,9967256 
4,9985993 
4,998+729 
+^983465 
4.P9B 



5,0046523 

5.004s 535 

5, 00445 ,& 

'S>oo43SS7 
l5,oo4t5W' 

\\l 5.^4'579 

S«7 



S'4 



5,0013663 

5,0013407 
jrooiotiji 
5,0006894 

5,0007637 



4,9980936 

4.99?97i5 
4*978483 

4,9977270 



4,9964141 
4,9963102 
4,996 «>07 
4,9960911 
4,9959816, 
4,9958720 

4^99576*4 
4,9956517 
4.99SS47+ 
4*99S44«i 
4799534" 



4,9952446 
4.995 '480 
4*99505 '4 
4^949547 
4199486^4 



4,99748*5 
4.997360Z 
4,997*378 
4,9971198 
4*99700 '7 



4.9947701 
4*9946778 
4,9945899 
4*9945' 
4.9944 '39 



4.9943304 
4*994*467 
4.994' 675 

4,9940883 
4.9940134 



Sig. 11 




Sig.9 



Sig.fl 



419999386 
4.9938637 
4*993793* 
4.993656 6 
Logar. 



4,9936566 
4.9935905 
4.9935*4+ 
4,9934627 
4.9934010 
4.993343^ 



4.993286J 
4.993«334 
4,9931804 

4.993 '3 '9 
4,9930878 

4.9930436 
4.99*9995 
4.99*9598 
4,9919101 
4.99»8»47 



4,9918494 

4.99»8i«5 

4.99*7876 

449*761 

4.99*739° 

4.9927170 

4,99*6993 

4,99x6816 

4,9926640 

4,9926507 



«Jg-7 



*'99»637, 
4,g9i628( 
4,9916142 
4,9936198 
*,99'6it?8 

L«gT. 



Sig. 6 



EiAHKS. TtJudl^LftaiitmffihtSum'tDiJU-fnfwTinguibtiiia 



Anonuly 4' ifi" . * . 4.9<r37]Sd 
Tor JsT 37" . . — »45 



I Mcu AimmimIjf 41 afi* j^i j^'ir . 



Log. O ' @ ,4>9939>4l nquited. 



17649 
7«*4 
'J7»7 



60' or !■ . . 


-7W 


ii.f=i' 


ir ..,3x1 


»»4.7 
».J, 
.■7.J 


,««a=," 



,, Google 









,:t r ' 


! i%a. <Nl41V.l GATOR. 






f 


7 
- -1 




BJpA^nON of ^SUK-s Wj&NOMALY, or PLACE, to the MEAN. 




■ , . . Ar^uwunt. SUN-» tru' ANOMALY. 




© 
An. 


S,|. 


Dit. 


Sij. > ^ 


Dif. t % ^ 


Dif. 


Sig- 3 


Dif. 


Sig- 4 


Dif. 


SifS 


Dif. 




An. 




+.-■ 


+ ■ 


+ "■ ." 












4- 


7~7 




o 


/ « 






' -' " '. * 


' ■ " 




' ' 




' * 


• . * 




(J 


000 


- 


•»■ 5» 34 


I At '4° S^ 


S4 
° S4 


> SS S' 




t 39 42 


' 3 

; I 


57 '7 


4' 

. 48 
.-48 
. so 
. 50 


1° 




I 






■i 19 


1 44 
I 41 
I 41 
1,4* 

■ 39 

111 

■ J! 

■ 34 
' 33 
1 3» 

1 17- 
1 24 
i -13 


1 41 56 


• SS v> 




1 58 39 


" SS 3' 


*9 




2 


046 




' 2 3 


> 42 54 


■ 55 43 


6 


■ !7 3' 


053 45 






3 


II.! 


! 3 


> 3 45 

1 ! '7 


I 4348 

> 44 4' 


1 SS 37 
■ SS. =8 


9 


1 ,6 30 

■ 3S '3 


» 7 


51 59 


% 








a ■ » 




> 4S 33 


0:50 
0.49 
44 
043 


A 55 J2 


17 
18 


1 34 13 


1 12 
1 12 
I 14 


48 23 


Ti 




7 


i». >6 

1+ 18 


, • 8 47 
1 10 z6 


.■44 23 
1 47 12 


' SS 5 
I 5448 


» 33 ' 

1 31 49 


46 33 

04443 




■ 8 




*. 


1 IS 1 


1 « 5' 


I 54 30 






42 52 




31 




9 


|3 11 


2 , 


■ 13" 37 


. ■ is 39 


■ S4 '4 




. 29 19 


I IS 


4. 


' 53 
1 S' 

■ 54 

Hi 


21 






10 iz 


« ■ 




I 49 20 


938 

9 39 
36. 

iw 

IS 


■ S3 51 


24 


I 18 


39 7 


>9 




■ (1 


a. 13 


. 16 44 


r 49 58 


' S3 27 


1 26 43 


37 >S 




IZ 


1+ 2+ 


■ 59 
' !9 

■ 59 

■ S8 


I 18 H 


' 5° 37 


.' 53 2 


n,« 






35 2. 






'3 
■4 


16 .13 
50 :. 


>. '94J 

. 1 »i 13 

. .240 


.1 Ji 'i 
» 5' 44 
1 52 17 


■ S-' 34 
I S' S 
1 51 3- 


34 
J2 


1 2^ 37 

1 21 l( 


J 24 
t 26 
, 26 


3,3 *7 
, 3. S3 
,0 .9 36 


'7 
'4 




i6 


32 .9 


I 24 4 


IS2 4* 


1 so 59 


' '? *l 


27 4. 






54 ■« 


1 ijl ' 'S ^7 


' S3 '? s6 


I so 24 


038 

jg 




1 3' 


»S 44 


n 




.18 


056 .J 


;5? 


1 2b 4^ 


I 


■ 53 3' 22 


1 49 46 


t 16 47 


S3 47 


VI 


12 






0,8 .0 


I 29 28 


1 17 


r 54 


12 


" 49 7 


• 15 17 




2. so 


11 




lO 


40 ff 


■ si 


. 54 22 


i\i 




43 


> '3 45 


» 34 
I 33 


.9 so 


■ 58 

> S9 

ii 

■ S9 
'59 






ZI 


0.+= ' 


1 30 43 


' 54 39 


' 47 39 




.7 S« 


9 




11 


•43 S! 


1 32 


1 S4 55 




I 46 1 


47 




.5 SI 






, as 


45 4: 


■ S3 
1 S« 

■ s> 

' 49 

I 49 
■■■4J 
.47 




■ "3 

I 8 
1 A 


1 Si 10 




II 

% 




.'36 

■ 39 
' 39 
\\ 
> » 
'J 


.0 ij 51 


y 






» 47,4" 
49 3' 


■ 34 »1 

■ 3S3« 


I ss 22 

> 59 3" 


10 

8 
n 6 


, 4, 28 


\\% 


,1. 56 

1" 9 S7 


J 




>6 


sr >i 


' 36 44 


' " *J 


' 43 33 


:i2i 


,0 ..7 58 


; 4 




■ »7 


(5 I 


I 37 so 




» 55 4» 




I 42 3 


9 S R 


. 3 






ss c 


• 3! 5! 

1 39 s; 


I. 1 


1 SS 5° 




■ 4' 4 


V'X 


. ' 04 


jo 4.f 


-.3 




29 


0564; 




• 55 S' 




' 40:45 , ' 

• 39 4I ; 


59 . 




s.'s 






30 


j8 3 


I 40 5S 




• 55 5' 




57 '. 


.->o 











— 












— 


— 



























P*. 










An 


Sis- i. 




Sig. 10 




Sig. 9 




SiE- 8 1 ■ 


Sig. 7 




1 


A. 




CoMiTiacTiOH. From the Eijuitiof erf' the SuM'iCenCei.— Aj the Compl. ta (oi of the Dif..of.anr Equit^pn, ind'-tfic not E^itii 




idllowlnc, M fir » the rrfdf iff. Gut Dir^-l-jo' beyond ihtGriatifi, 11 re that Dif. /e /i the fDnnei Eqution of ihc two, to the PrMriim 




(>ouititTEi>beiddcdto>orrubti>aedfrom,th>tf«a]etE<j<HtiQn (Inooluig ai itii<cr«f^ or d'frrwl^i; 1* th« iwr^a SftHi^ M tke tru 
. |biM.Aa.cbrrerFi.]t(ili)eNiimberofOeB.ertbe:true,e<]ualt<itbeDe£. ofM. An. ol'thcSan'iCanter} bnlwiiha »MranS»i>. 'TbuPi^ 
j portion .rifei ft™ hrn«. A, swj her. ,f,ru, A- : r«-rr/>.,/-». <^ DaK cj E^u^h. „r rh*,„M, „ U. v«.: :: «w, ilh^Sir. ^ irm A 










I. EXAMPLBI. T.>i<i»£p-»»./«w»Af.AB*>i. »0(n«..tp.-SUa? •'■' 




M.An. Sutr.An. . Eq.SiiaCeuer - ' n ' ■ lift. Utft*. ■ ■ 












+ I 18 i4^.™a. J 'n>+ I jii 1.49SJ . 




'. ," 


. ; ..r . . 




; 








D 








• exAMriJia 





DigHizcd by VjOOQIC 



The ROYAL A S T R ^O WO M E R," 



EXJUrfPLES of tht CONSTRUCTION "nd U8^ of tk» fertyiiBg TAflLE; 
EXAMPLE II. Ti J!«J lb, EfKiiii^ fir t' ig" i>Ti, ^K>maly r 

M. Aa. OtrocAo. *<], GC M Wr ■ r ■ 1 

4" 190 (4' '7 4»' 47" 7 +'° '7' n" «=V '♦" J, , ., . i ■ " 

. «..»P 1* tg. 44- i» i +1 ij 4* . '3 4 «o J««'««rA«. - t «I-H» 3 

ArfW. locr. 1 " 1 jrfe.Hq.+*<i'):i"ir3if-Sl.*«crllJ 1* iT'iV-il's^ ( ^'^ ' 3 

.„^^: I .^ — t- sidtia.. . I l""?*^-! - 

rfdliljatCutflUSm'iCeMlir, t^ ' 






(■49M 



'4. 10 Ij 17 H. AKMii. leq' 



M B. The ArffWr^&nfiiuaiflil fi»i!i riietq««i 
MT, when iVfe B^Kioni ^nd their DiAerenctip 
of i", <M i''. "BioBB tlwfr ffj"/'-w or D(fn 
ifmSiiRtaka Pi *■ -'■ ->--'■- — 



n of ikc ttM f rata tbe 
■ aJma. Bulntu ' 
nil' aan u Zitar 



tfr.)M.Ottr 



to which inTwcn 



bit Mem Anonnt)' iam(l\y enimib, ^om tbe iwiutJiii «/ (At £■«' 
^ pttif Mfiutim, whW tfael>{^nwn an nty Ibull, u Bm 
«f ■", M Mate, ia pT«r<>tioMD|. WhcicfcH' the foUiwlngOH' 



Rule.— Ai ■^'FmElSTR , s/AtJ». &!it. . t Xm. t t m e AiwAi . > T«ii. I tc 
low, by the N.m« of a Piahit'i or Com^t'i MotlJrt in *b eKpdol Orfii, 



■ 'pT«r<>tioMDf. 

mtffOrliii^tMjmtrr 
nc Anom; 'wliiclt dooEftlttf ' ii tlie Br; Abobii 
cioln of TriEOniHiictrr.^ At Sem. Tranf.' (i 



How, iiytheN.m«of >PiAH«T-ior CoMkT'.Moril>iin«Bel«pda! Ori.il, •«! tlwP. -,.■.* .- . 

Bid.) 1 S. .SiccatT. An " Z.eoitrieit* ; Lenjth Atth L, wh»r« Degrew D, »« th» Diff. of th« Depee. of dje Afi««b#« thoft of 
Extntr. Aa*aalf. Therdbre RicU : 59^195779 •■' ^ i D, D««re«, Wl«i*W to ttaEawHritfctteliir4» A™, r^^ 

In Ih. Ewth-. OrHt, the Z««*oLcity u i&S c Of fueh P«rti u (he »m. TM»r.*ffc or fc«»n DU. Q < © = looooo, the P.nh. DiA. 
olkifud Aph. Di*. «i6Bs, Md let it be reoniie* to dettnhiile tfce Muin from the Irat Anmyiei. ind MafeijilcBtly tbe £f*«ia., 
»'. It". IS". Bo", uoo. 0.0. 01*. as", 04°, Jini 9i*- Hewe, from tie aliint Pw^rtwni, 

T.. —- — . ^ ..-. _ ™* f JarLo|.Tin. (D^rtaaf EsuiRric Anonul;, And 



Tl, As, ;lquil 



Dif. Tr. Aa. B 



SS S' o o j * ♦ 
EXAMPtE. I OonT. log. 



SS 41 
JS 17 
55 aS 



ici^piJ 



o ir I p. 1?. 
< EICAMPLE. lOonr.bog. v lULAMfl^ ICoof. Log. T ^T JT'*^'* "> 

I tf. An. 44*. T- ^914)71 l»' S/ S*'*««' ^fei^S^-K^Jr^'^'i 

tE<44".i(r.ST",iir 9.9911557 I P. 57 si + ..U9-a»4tii» \ („,„(,,, 

*<• SM4.<* JO-W.A. JV Jf 49-,«» *M.Aa.r«(.-'jj,,^ ^^ 

m. Aaom. no 

[hit ID. Anon 

Bv QOrTdM*. Apcpc ( 



To Cte?. £<X' 9-t>47>*' •^■' L°(- S- EMbilric An. {lej. Kad.) Foi 

.f 1.__,., I, ^^^ to the De^ee. erf Etcen- 

01 Aaotatif teqnired. WlKnct 



r» fiii A nm ^ ill sti»*i -zm 
tr ■■* Sifts* ^po^r 0- , 
I » 



At fM.^U«A^O 
<b I TMePlMeQ 
«4. ^ Tne Aacm. © 

tiaelCornfeoniJEq*. *— t sf 
- Lw- ««•*•*© ^,.^_2_4. 

ftt.r)>o«.&.*7j> 



aiMaj 




a 17 59 5I reo) 



Byw 

W. S. Ye»f 



BylTmrtHrFath. AiPerih.D». : A^. DiS. : ; Tin. j k. As. t 

Coinaion') Aa Sna. Con]. : Son. Trenf. ; : Tu^ 
Ajion. tho'. y M. An. 1 Tea. coneOed U. Aac 
CarrtQloa. J maty. , 

Hc«cE, coniL Lof, o-ot^Sjjo + L. T^a< ( tr. An. ^ L. ^^ 
m. Aaom. no krcnteded. Asdconlt; L. a.a««o6r7 4'L.Tui, i 
thit m. Anom> :9 Log. T. corteSel AOt for the f-aKk't-Orlil. 

T* A«f <& Si/Hf. >,«, p,Ww n rb 

M- PI. — 



t TM; pi. Ap, O 
e I Tnii PUce © 
q,'< TneAliain. Q 
ntl C«mf{lt. Eai ~ 
1 M. Pl.ce C 



M. PI.Q44. S. I7ti 



Hema 14 • • 
Himitoi 58 ■ • 
Seooadi i61/^ 



Apo^p. 



3 8 46 »5 

*+ 1 lo )7 
'1 4' y 



% aa JJ"^ 



TrarMVp 

o.v"i'7r 

Abe; 14 

in it 



BtfU. OU«t*e (he Day m ^ich the San ea-'> 
tai^ thit SifB ^ lwD« Kf benierii on the Lean- 
YeirfitcaiiB|tfa(TiatrBfwrc4. Then from Ai 



Apogtc O 
I ' 4» S4 



M. Pl. © 4 a3 4» jT 



'¥1 



S 46 19 ' 
'I 4' >7 



n*c4 hrilial^me tafiirtd, nki Saa' 

j»ipi, and tlw laa'a teat Aa. irill remain i 
6nH whencf let the Emian af irw M nnn Ab. 
which add to St fabtiaa AoM the Su't tne PI. 



M«.ktbt'jfaMh.&f,«><^4aMa,^«wW^«h>-laeiaafe;«F Hi«< 



the Uot. for Haara, Ac. 




that Til 
It iieWdeat, from ato»e*, thit the'Suliiiwrni^o ih^f^ P«^ '/j}' .^j''f!" 



the former Year 

hiiM.Pi. or Aaam. turned into 7a . 

Soha Yt ibbia jSs D«, 10 



irbrth<ia«.orDe<^af^^f < 
and added to or MrireilH ftooi 1 



13 



the SmtfAa af oarawan Soha 

tf.B. lacteafcJE^iJ — ") 

Dec«afe|— I + l 



J+JTW. 



of the Sun' 



ffaue, A» M. An. ft deawalat in the ww Year or '1 **'"'* V'J*f/^, 



A«<^Ti"'tl«*J-"T«»r) by whkh Dw. of th. Saa'e M. An. incMJt trai Year, the 



,y Google 



Old NAVIGATOR. 



^ trf TIME, fbr'riie S u n's ArooiK in BB j*, about 177+. With Ae "SiEtrJiMMt* EattMihn 

of fwy, to which By idon, for 58 Years, or i Ptgrg* Jiwf«i^or Diiret>/i of tlte Swi'a Apogee, from tbatqfsgg* 



Jrpaii»t- SiTN'i true Pi 




KT(b. p. 10 . . Siu'i PI. n 
Tne Adob. Sm> 



- 4M 50' lftEqD«»TiBe. 

J ad EfuiB Time. ( 
7~Akr>ES'^^'A-taM. Tunc, 1 



..11 7 o » >.— « 47 

By Tik f. 17 KiBtJOM — e 45 47 1 

Ci)n«kniB>tU.AthSa . . . ti ( 14 tj J , 



i. £^ATt6M 



,, Google 



The R O Y A L A S T R O N O M E R, 



I. E<iw aVi'o'n of T£ME ; of App' 
Uean npd Meaa to App'. 



Argnment. -SUN's crue pi; 



lif 46 



8; 37 



£17. 



2_|d| 



.6* S3 
•6' !' 



9 46 



9 3 



irt TSSTi the 
Diff. bttwKD tbe Siin'i trut Long, and tha 
R. A. ronvritei into Timr, ^ihkh fli/< to 
Appl in tb« »J i»il 4th iiyaJnatra, ind 
ruhiiafli therefrom in tlie ill and id Siva- 
Jrllara, for thi Af, "Tlml iOi the Itn'rarj. 
N. B. The Corapicmenl cf iny Dift'. to 
6<f PI Deg. R< A. (in Tily K. A.) con- 
Kiicd inn Time, and luUiil to ibe Eiiuat. 
of T, fo. any pweding D.(. Qtr. Place, 
»far« W ,7',otf™,Ey„./.Time,wm 
b. the Eiuat-T. in tbt above Tak. romfp. 
, , the fucceedioi Deg. of © tnie Pl^ce,- 
Bnt the Diff. efR. A. abore 60' beyosd t) 
>t>. or [be treateS Equat. coDTttted lalo 
fr. the Equat. of T. br 



Tim:. toiJMmtliJ' 



iquat. of 
_., precediDg Deg. Q true PI. will 
E^t. "t. ctcnIpwndiBg to cbe (iKifeedint 



11. EQtrATioii»fTIM£; of Apparent to Mean and Mean to Apparent. 



jfrguaUMi. . SUN'a Mfi'^n An"n"'i' 


(^ 


SiR, 




Sig. 


Sis. 




sig- 




Si,. 




SiR. 







^ 




g 




3 . 


% 


1 



Si 


XV 



Si 


5 


1 


s 




A.M. 


A M 


"AM, 


A.M. 


A.M. 


P 


_ + 




— + 


— + 




- + 




— + 




_ + 




" 


M . 


' 


" ' 


B • 


' 


■ '. 


< 


■n • 


■ 


n . 


« 











fl 


3 47 


7 t »' 




7 43 


' 


6 45 




1 s(' 


7 

I 


10 


I 


0, 16 


!8 


3 J4 

4 ' 




7 43 
7 41 


"3 


6 4, 
6-37 


3 49 
3 4» 


*9 
>8 


1 


0' 14 




4 8 


7 43 




b „ 


1 34 


»7 


4 


32 




4 «i 


7 41 


l* 


29 


, 27 






( 


0' 40 
47 


? 


4 «' 


t, 56 




7 4* 





6 H 


3 ao 




6 


, .8 


^ • 


7 4= 


i 10 


3 '» 


7 


i> s^ 




4 34 


ti *<■ 




7 4" 




«. 15 




I S 


»3 




' 3 


7. 


4 4« 




7 4» 






' (7 




22 


9 


I 11 


4 47 


/.' ' 


7 39- 




" 5 




1 4V 




2t 


10 


1 ly 






j' " 




7 3« 








2 4z 


20 


11 


I 27 


7 


4 59 


'•' '5 




7 37 




5 55 


^ 


' 3* 


:t 




' 3+ 




6? '* 




7 35 




5 49 








'3 


1 42 




S ■■ 


6? " 




7 H 




' *l 


^ 






'7 


'4 


1 10 


8 

1 

s-7- 
8 


S »'7i 


6 7 'S 




7 12 




5 3« 










'5 


< ^a 


S S3 


"7 "5 




7 3= 




5 33 
5 27 


6 
6 


1 54 




1 

.'4 


16 


= 5 


! "S 


J 7 «7 


7 "8 


'7 
18 


a 13 


! 34 
5 39 


;7 •9 




7 't, 
7 «3 




S 21 
S '5. 


'6 


i.tS 




.'3 


'9 




5 45 


5 7 »3 
» 7 JS 
;7 3' 




7 «i 






6 


I JO 




11 


iu 


^ 39 


S 5° 




7 '9 





S 3 


7 
6 


1 12 




~9 


1j 


I 43 


5 SS 


7 l6 


4 5" 


I 14 


22 


I 50 






'7 37 




7 1!^ 


4 50 


6 








21 


2 ,8 




« 5 


^7 39 




7 ■<> 


4 44 


7 
7 
6 
7 
7 
7 
7 

a 


T« 




7 


Z4 


^ S 




« io 


; 7 40 




7' l7- 


4 17 


49 




49 


1 " 




6 .5 


'7 4- 




7 14 


4 30 


4' 




J. 


.26 


, iq 


6' ,0 


7 4. 


7 


4 24 


33 


.27 


, 2b 


8 


6 ., 


7 4" 




57 


4- '7 


2^ 




' 


19 


3 34 


6 89 
6 3! 


1? 43 
t? 43 


.0 


5 S3 

6 49 


4 '0 
4 3 


17 
8 


? 


2 


30 




Q 


« 37 


' 7 43 


B 


45 


3_Si 

+ — 





>9 





as 


F) 


+ — 


+ — 


+ - 


+ — 


+ — 
AxM. 


S 


A.M. 


A. M. 


fa A.M. 


A.M. 


A.M. 
7 




10 


= 9 


8 


■6| 


P 


Sig. 




Sif. 


S,f. 


■i.,g. 




s.§. 


1 Sig. 




p 



CoHiTiocTWH. The afco** 7«*/* ia onljf the Eauation^f the Suo'i Center, cortef- 

pondeat 10 the given Meiu Attmafy, converted into Thre, whirh fublnO-j from the Appi- 
rent in the ifl iM Srpn, and «dd= thereto io the hjl Six Sigii, for the Mean Tim*, and 
the contMry.-Hence lie S«m ./ 'fc Ift an^ 1 Id £y-i«W,/=r ,6, gif^u't Ei^lin >/ Trm, 
■will it otoflji <»m/ w <i' P'J. tf" f ** O '' *■ -A ""^ *" '''™ i"g"l"l' "rarrltd tfU »W. 
N . B. Mua TiJfc ii confidered irt jfyfartM Tim cotreipondent to it. 

Eiam; 



By TMt I. ;t »3° is" , . a to M . . + 7" 



lAnt 1* 4 to nfurtJ. 



iU»AC.TUN. 



,y Google 



md NAVIGATOR. 



iCK*ACTiowef-iinrnT-(btt. OrmFtu/f^ OBftr-vatory), and 
Parallax of die Su>. Tfa^yfri? to be fubOsfleilfrom 
the apparent Aldmde of the lumimHs BiJj, and the ItUtir 
to be wided to theappareift fef thfe rta! AliiiiiJt 6f the" 5un. 



Argmtnt. Apparent Altitude of the Sm 



^||Ap. 
O. Alt. 



33 45 
jo Z4 
a; 5S 
as >i 

'3 7 



10 



Ap.liilef. Par, 






vw\ 



39 



Hourly Motioh, and Apparent 
Stm-Diamtler of the.SvM. 



jfr^. bnn'i Mean Anomaly. 



Mean Mot. 
Aoom. 



Babaia, 



Rjyi 



kifraflnn ot Light vinci with the Latitude, Almofpheie, or 
r ; cffcciillj anr the Htrixn.— In the Year i6g;, in Latit^ic 
, pn Just 14, II Hau[> P . M. the Sun't Center being depretTcd 
leHoriMii 40', at P,lh, lo Milet ooithwari of Ftnmm Wefletn 
He wat obOrred, b/ Reflation, to be two Diaincieii in Al' 
above 1°.— The common tiperltnent of pouring Water af- 
,f S!h^, in a Bafcn, to bting it in Sight (when unfeen be- 
ret the Elemion of Objeai by Light pilliog from them thnnigli 

a rarer Afrjitm, Tthe (ontrary happening from » rarer to a 

1 DO the VatiaiJoDcrf'tbe rcAaaing Mtilium the diffeient De- 
RefraAioo depend. 

paffing through OH of Tarfaunt and through f^ltr, pre the 
of RtfbQiMi diffcrcnl, proving the diSireilt Denfitiei of thofe 



I of the Sun ii the Angle ihe Sao ii ffcn lo 



Earth'! SntftM-lhan it muM WAm f ii»iii Center. 



ir from the 



'S S4 


'S 5S 


"S 57 


,5 ,« 


•S W 



»4 



g 33 



16 24 



COHITllVOTIOV, Toyiurf lif Sim'l 

ha<trtj Mttlun cat.JftaJivt K ^' 6°, Sui\ 

' frfli Aettlra!) f 

ByEiiiialiDnTjb.Sun'iCenter, p. 11 

4^1 tie M, Ad. + t' 10' dir.Eq. 14^. 

, ■ • ■ +59. g M .Me.a^H, 

in't tr. Mo. inai^ 60 iS U-K. 

Whciii:* 1 ]i Houilf Moi 
(aa by Tablo) re<iuired, 

lefad '1 ^. Smi. DUm. iei>iff. It 
6* M. Jii{. Ibijlfl. S. Ditm.ao* M.jin. 
brinwiva 15'}!"? 

By tab. L. Sun^iuopl Did, fr. @. p.t6. 
KtafrKtltt. [Co; 

otM. AD.Pt.D.Oloi6S;..L,4,gfi7 
Soa'aap, S. Diam. ■ j'ci'.. IuL.o.jtSi 
6' M. AB.P».D.g, 9J3t6 ■ . L-»,9qa6 
Suo'tap. S. Dnm. i6'i4*.. L.L.o,c6]4 
'-- >- ■^-•- > — ' •"•- ap. S. Diam. OC 
'''t)ift:iQ. 



.^i:f//irr«/f«K>rthe 
./Em^* J accord. 
iDgtOauamfolai 



3 56 
7 S* 
II 48 



o 27 3 
o 31 a? 
o 3J 
o 37 
o 43 



o 47 n 
6 SI 
o SS - 

o 58 j8 

' "■■ 54 



6 JO 
lo 4f 



! jb 



■I ^o 26 

I 3+ I- 
' 38 1: 

* 4* 1-3 



',46 
1 S-^ 



ai above, fboi 
the Meridian, each 
Diy, thaa on 

The ttoe Time ot , 
the ^rf Stan A«c- 
deration it the h- 
cnk^f of the Sud'iR. 
A. eicK Dar con 



&f . S-i'a'i Inii jUl 

is" o' •" 
Iq.Ref. 
E^. Paril. 



ijLil 



DECIMALS 



=d by Google 



fht ROYAL ASTRONOMER, 



DECIMALS of • 




M1NUTE9. 


SiCOHDt. 


ruiADs. 1 


MiD. 


Decim. 


Mia. 


Decint. 


8ec. 


Dcdm. 


Set. 


Dccin. 


Til'. 


Decim. 


TI1-*. 


D«ia. 


1 


.016^ 




.5'6? 


1 


,oooi!f 


3" 


.0086/ 


I 


,000004^29 


3" 


,ooo)«/i8 


2 


•033* 


1" 


'S337 


2 


,0005/ 
.oooSi 


3» 


.00888 
,0091^ 


2 


,DQ0009^S9 


3' 


,o«..48/48 


1 


'Mif 


13 




3 


33 


3 


,00001381 


33 


fi^ii'li 


+ 


34 


,566? 


4 


,0011/ 


34 


.0094/ 
.~97? 


4 


,pooot8|i8 


34 


,000157^07 


5 


.083^ 


" 


.383? 




,0013$ 


■n 


J 


rf)O0O23A8 


3! 


,000162^37 


6 


,1, 


,6 


.6. 


6 


,0016? 


36 


,01. 


6 


rfWOM??/ 


,6 


,0001666^ 


7 


,i.«; 


37 


,6.6> 


7 


.0019^ 


37 


,oio2y 


I 


,000032^07 


17 


,000171^ 


» 


.'33J 


3» 


.633/ 




,0022/ 


3« 


,010s/ 


.000037^37 


38 


.000175^25 
,0001803/ 


1 


'Mif 


39 


•'I-- 


9 


,0025. 


39 


,oio8j 


9 


.oooo+i66« 


39 




4» 


,666^ 




.0027^ 


- 


40. 


,011./ 


10 


/x)oo46jfc,6 


40 


,oooi8s/83 


11 


,.8„ 


4" 


.683^ 


.OOJOJ 


4' 


,o..!j 


II 


,DOOOSOiJ(25 


4' 


,oooi89<J4 






4» 


.7- 




^53J 


4* 




12 


.0000555^ 


4' 


,0001944^ 


'1 


,2i6il 


43 


.7i<i» 


M 


,~3'/ 


43 


,0119* 
,0122/ 


i\ 


,oooo6o/8s 


43 


,000199^7+ 


1+ 


.'33^ 


44 


.7S3i 


14 


.OOJ88 
,0041^ 


4+ 


14 


,00006+^14 


44 


,000203^03 
,0002083^ 


'S 


,'!■ 


4! 


.7!- 


'5 


4S 


.0125. 


•s 


/>ooo694^ 


43 


16 


,266; 


46 


.766> 


16 


.0=41/ 


•46 


,0127/ 


k6 


/)00074^74 


4« 


,000212^62 


>7 


."i3 


47 


.7»3i 


'7 


.•047^ 


47 


,0130* 


>7 


,000078^03 


47 


,000217/92 




■3- 


4« 


,8. 




,O0J. 


48 


,0133^ 




,0000833^ 


48 


,0002222^ 


19 


.3.6> 


49 


.8l6|! 


'9 


.»os>y 


49 


,o,j6J 


»9 


,ooooe7a;63 


41 


,000226831 


so 


.333? 


f 


.83M 


20 


.0035 < 


SO 


.o.38« 


so , 


,000092192 


50 


.»=02J./Sl 


2t 


.35- 


?' 


fc, 


31 


■0058^ 


3' 


,0141^ 


It . 


.Oooo97a;i 


31 


,0002361/ 


22 


.3«? 


3« 


22 




3' 


.oi44< 
jO 147)1 


22 


,(»oio6j§i. 




,ooo24oy4P 


■» 


.3«3« 


33 


.883i 


'3 




33 


*3 


33 


,000245^0 


*4 


>4- 


34 


*,- 


==4 




34 


,015. 


»+ 


,00011.1^ .* 


34 


,00025. 


»? 


rf.6? 


?s 


,„6)( 


4i- 


- 


53 


,0152/ 


2^ 


.00011 s^+o 


33 


,000254^29 


2( 


.433i . 


!« 


.9333 


S6 


,oiss» 


«6 


,pooi 20370 


,6 


,000268/ls 




•«•,- 


t? 


%, 


'7 


•007s • 


37 


."'S"! 


«7 


,00012$. 




18 


.4«» 


<» 




.007 7y 


38 


,0161/ 


z!« 


.000119(1*9 


38 


"0 


rfSjJ 


39 


.98Mr 


'9 


.0080/ 


39 


:r4 


29 


•^.%\' 


g 


,oo<.,7j/4« 


30 


.5- 




I. 


f°. 


.0083^ 




30 


.0002777^ 


K >. In tke 1 


lore Ttblc, li. 


FigDre w^^ 4 jGm Smh tr^i it, Jen 


us m ««/mW R^tituH aftbt r.t^tvr fi\ 


^«>«rf«« 


Kt. Jhd4ij>0t\ 


) ,r Full Point, *»»■ . DreioiJ, A 


mtuhi 


,«^r<ilm. 




EXAMPLE 


Ai 3* 19' 23' 


b to 40* t9' 33» 40», fo it n» 


B'H 


18», u 144. 


S- 2j» s6», »t. 


I, A, 


TtUe 




i..».'l 


xt4 




'H" 


3I6MJ . ! A. 


3'.3>30S< » 4o'«l'«<S' '• ' 


'9t 




.}« = 


oo658» 












3*305/ 


B, ... 


Logarilbiu 








,,' = 


0001 851 


■ J'.S'SOJ* ■ 
40.4926851 


9.4784624 CO. [t 


144' 


y.l99 
3<94 
S''.4 - 


«*; 


'^z: 


11. 82619^. 


1.072S4S0 






144M066 










4»"'«5" 










~ 


«>9444/ 
000083.} 




tf^^Af 


Scdiuls ta Sexsgcfiinalf, J 








/VWw. OrJIr, 


b t, ria 1 


?fc 


■£'S>*'*™ * * '"'**' ^' 


r>™« 


bt Exanplc) «&>«#, ak/m | 




826194^ 











,, Google 



6kd N A XiIG A t 6 R; 



SON*! DfccynAti'OTi from the EiiyriiocTiAi,, uuUMekidiah ANGLE with the Ecliptic. AccordiaK 
O tkt Meu EcUptk Obliqui^ aj" ^^l f 




■Jrffmati. SUN'i Vac Place in the Eci 



Taonu « ? i si, 
Scarpio ^37 ^' 



Gemini U 
Saglttarim -f 



n^ 




AgMTiu* 



Leo a? 



;Sig. 



0l)echiijl>ifc[ivjend.il, uif. 



30 10 5c 
10 23 

" 35 3;|i 

30 +7 II 

30 56 46 



a: 70 21 
II 30 +c 
21 +0 3, 
21 49 56 
21 SB ;8 



7 34 
22 15 4; 

" '3 J 

22 3D S 

37 47 



22 44 
22 so 11 
" Sf S' 
'J ' 7 



•3 

23 13 S9 
»3. "7 «3 
23 20 

1 



23 24 52 

23 26 27 
23 K 3S 
23 2tl 16 

3 '« 3' 



, ,,77 44 SS; 

;; 78 28 M : 

: tj 78 SO 47 
, .8a-l|-S2i 



fuss's? 

'* 80 22 8 



,5 (8 
35 iS 



ei)«ci. I JJit. tM^ria.^ 



4S 49 
S3 10 26 
!3Ji 



84 
842; 
84 so 
84 'S 46 
'i 41 



& 4s ■ 

16 32 28 : 

16 se •! 

'7 «♦ 3 

'7 ♦I' y; 



'S 54 
4' Si 

7 U 
3J 57 



2C 
1 Jl-i 









B^ 



£iiLio 



Cancer as c } c:„ 
Capricorn b*. ? 9 ^' 



ExAHFLS I. Ta /■< (i« Smn'i PttSitiitM nrrijfm im i U y 
9,l494»j; ■■■" ■ " ' 

)>44g74H J p icfcnt Dnlinitioa, 



ToprrinicDua li^\t'%^'^ S. 

ZxAWfLS JI. 7ifi^ tUMtrHiaa^gU 



AiltaHo 

To LoDC- Su to* . . . Csf. 
So p. Dcdi A]0 s>'4 T«a|. | 



Ad4 S. Loni- Sao t. 

Sam(R}enu|Rid.j 

f icfcnt Dnlinitioi 

JHcpcc 
AddCi 






:: S. R.A.O : S. Mcri4[u ^. 



rrlffHHliM ti n 

I^g "■ 

Cof. Siin'« Loni, fioin V •¥ A 

[KJeOInrftxI.] «mbC tlw| 

-Wftc^iDBft letikRi, UK 



,, Google 



fht R O Y A. L" A S;TRON O M E R,- 



T AfCBHtiOH, fromjfriti, accordiogtothe Mean.fci^ftVOBLitipiTy x^* %V i. 




Ciii»TMV«nON> A< K*4. 1 Tang'. Long. Q frwa oat EqninoSul Point : : CbT. Rnttlt Dtcliiuliaa : to Tang', 
EXAMPLE I. T,J!«l ibt 5»*> Rigbi AJctnpm atr^p^ia n ioP. l^^iiyJ-Jhm *r ■' 
Com. Logi. 
' ' ~ - - " -^t the Cu0. Lig. I |9.9£i4S«i 



» 7' 6" T, 



o -) H<nce to 

ii>.7;}6aii f AdilTing. 

9.9614801 r S'ra((iedii< 

r J 



110,7,61613 



rr.a. mrfng founithiltiKfitAfr". fo (o' 
WlowftomOitneeto i8o» : btLng the Stppli 
mer (laim tttJeaarii) to 180" ;/■ '*« ihiK.A. tf aiy lfiim-_ 
Ur i/Sigmi ami Digrra tf tbt Sun t Pit" tnug glvn iiijir 90", , 

Cat iKofc Signi utd Degrcea to 6 Signi. 
EXAMPLE. »■ ii" K. A. 7rf> 19' j!" 
Suppleatcnt 3 iS R. A. 10; ^o j> SappIoBeM 
'60 180 o o Pwflt 



(*ieddaingR.)=:T.R.A.| 

[fromT-l 
$L al ? i T« Con<t. Log. i-gifi^tot 

I Addjjo.T. ■ 9..7)S78<>t . 



B *o tie J'ly/if- 



,, Google 



NAVIGATOR. 




N.B. Whto the Sub ii ia the jf^ J^difrdM of the Ecliptic, T. (J. n. C" '" the Fittt EiAMfLiJ ilm f<mrrb7<rm, or Arch, i 
R. A. fcan^i'o. Whtnthr Sun ii in tie 5mm/^M.fr«>f, SB, JL' "O!' 'lira the Founh Term, or Arc, mail be deduced from i!o' 
thcSun'iR. A. frQm<r- Wheo [he Sua 'aiatbeliirdSiMMlrinl, ^k, 1?!, /. the Fourth Term, vr Arc, maft be added to i3o°, fat 
'• R. A. rrom <¥*■ And when tbe Sua ii in thtjaini gmaJnui, iy. iS, K> ibe Fuuttb Term, or Arc, muft be deduOed from 360° 
:heSaa'iK>A. Tion ly, 
EXAMPLE III. r*/*^ lir 5H't Xifitf Afif-im arrtlfadal it f ix* i To conJL L^. . . g.9ei4Soi 

f »* = »5a°3:7*''>bcve iBo". AW 72° T. . . ■o.48Sis4« 



EXAMPLE IV. r> /fl/rfc fm'i Jl.ff ( ^^cflj/Cgi nmfft-d„a iiXi'' 
X J<'=3J3« = is3»»b««.go'>i Sappiementjs:*?*. 

If.B. The Right Arceafioa to the liHt 6 Sipu of tJK Son's P>ce taint 
fvuiul, tbe Hi^bt Afanfiau to the lift 6 Sigiu foUow, bj >dilta| i8o> 
to the Right AtceoGon of the fonner. 



\\°J ''' 


3S"T. 


10.4307041 


Aid.,. 


i^-- 


i-jslso; 
9.70716S9 


74- ■ 


I7"T 


5.669S460 



Pif- JH W $ "^ *■ Wfi^' 



DigHizcd by VjOOQ IC 



16 



ibt ROYAL, ASTRONOMER, 





ArpmtM. SUN*! true Pl»ci in the EctiFTre. 



PI. 


Sig-O 


DiL 


s^-.. 


Dif. 


n 
Sig. a 


Dif. 


Sig. 3 


Dif. 


a 
ai.4 


Dif. 


.91g. , 


Dif 


Pf 


o 




B '• 


k m I 


■ ■ 




» • 




» • 




- • 




» • 


* 


Z 

3 
4 


O o 
O.J 40 
o 7 ao 
olio 
o 14 41 
o 18 zi 


3 40 
3 40 
3 40 
3 4< 
3 40 
3 40 
3 4> 
3 41 
3 41 
3 40 
3 4« 
3 4* 
3 42 
3 4* 
3 4> 
3 43 
3 43 
3 43 
3 44 
3 44 
3 44 

\% 

3 47 

IS 

3 49 

3 V) 


> S> 37 
' SS a? 
1 59 17 
a I 7 
a « 59 
z 10 51 


3 S" 
3 SO 
3 S° 
3 S= 
3 Sa 
3 sa 
3 S3 
3 S4 

' 'J 
3 S6 

3S6 
3 57 
3 57 
3 58 
3 S9 

3 S9 

4 
4 i 
4 a 
4 a 
4 3 
4 4 
4 S 

:i 

4 7 
4 7 

4 8 
4 9 
4 10 


3 S' 'S 
3 iS at 

3 59 3« 

4 la iz 


4 10 
4 ■■ 
4 11 
4 13 
4 la 

4 "4 
4 >4 
4 IS 
4 "5 
4 IS 
4 17 
4 >7 
4 17 

;:i 

+ 18 
4 19 

4 '9 
+ 20 

4 a" 
+.ao 
4 21 
4 *i 
4 ^1 
4 zz 

4 2J 

4 *' 

4 " 

4, 32 


600 
6 4" 
6 .843 
f *3 J 
S 17 rf 

61. +a 


4 aa 

4 ai 
4'a 
4 al 
4 " 
4 al 
4 ai 
4 al 
4 ao 
4 a» 
4 ao 
4 '9 
4 ao 
4 19 
4 "9 
4 I! 
4 ■« 
4 17 
4 17 
4 17 
4 "S 
4 '5 
41s 
4 '4 
4 '4 
4 " 
4 "3 
4 " 
4 1" 
4 "0 


» 845 

8. ass 
8 17 4 
8 ai la 
8 as 19 
8a9z6 


4 10 

Jl 
4 7 
4 7 

♦ « 

♦ S 

♦ 5 
4 4 
4 3 
4 a 
4 a 
4 " 

4 
! 59 

' '? 

3 S* 
3 57 

' 5? 
3 S' 

3S« 
J 54 
3 54 

5 53 
3 sa 
3 sa 
3 5' 
3.50 
3'50 
3 50 


to 8 33 
10 la 13 
10 16 1 
to 19 40 
10 33 36 
10 37 Z3 


3 49 

1^' 
3 ¥ 
3 47 
3,46 

1*4 

3 45 
3 44 
3 44 
3 44 
3 43 
3 43 
3 43 
3 4a 
3 43 
3 43 
3 4a 
3 43 
3 40 
3 4' 
3 41 
3 41 
340 
3 40 
3 41 
3 40 
3 40 
3 40 


30 

2 

34 
3! 
aa 

ao 

'9 
18 

\l 


6 
7 
8 
9 

lO 


za 1 
o as 4' 
o a9 aj 
o 33 4 
o J6 44 


z zz 30 
a z6 Z4 
z joao 


4 16 a6 
4 Z040 
4 a4 SS 
4 a9 10 
4 33 as 


6 a6 9 

6 3»30 

5 34 5' 

6 39 .1 
643 3Z 


8333a 
8 37 37 

5 ♦' •*! 

845 44 
84944 


10 31 9 
'o 34 54 
10 38 40 
10 4} as 
10 46 9 


'3 
'+ 


o 40 a6 
044 8 
47 SO 
St 3a 
!S >4 


z,4i6 
a 38 13 
a 4Z 10 
a, 6 8 
a so 7 


4 37 4a 
4 4; SS 
4 4'' ■' 
4 5° 34 
4 54 sa 


' 47 5a 

6 sa 11 

65631 

7 so 
7 5 9 


8535. 

8 57 S3 

9 ■ S4 
9 S 54 


"49 53 
10 S3 37 
10 57 ao 


i6 
'7 
i8 


05857 
1 a 40 
1 6 aj 
1 10 7 
1 13 51 


a S4 ' 
a 58 6 
3 a 7 
3 6 9 
3 10 II 


4 59 ■" 

5 3 a9 
! 7 49 
5 IZ 8 
5 16 a8 


7 9 a6 
7 '3 44 
7 18 I 
7 aaiS 
7 a6 35 


9 '3 !' 

9 17 SO 
9 ai 47 
9 as 44 
9 a9 40 


II 8 z8 

11 IS S" 
11 19 34 
11 33 16 


'4 
'3 

12 
11 

10 

I 

■I 
..f. 

4 
3 

0. 


2? 


• '7 35 
1 ai zo 
.as 6 
. zSji 
■ 3a 37 


' 'J '1 
3 18 18 

3 aa aj 

3 a6a8 

3 30 34 


5 ao49 
S as 9 
S a9 JO 
S 33 S" 
SSS.a 


7 30 JO 
7 3S 5 

7 !9 ao 
7 43 34 
7 47 48 


9 33 36 
9 37 30 
9 41 a4 
9 45 17 
949 9 


II 36 56 
" 30 37 
II 34 18 
■■ 37 59 
It 41 39 


26 


I 36 a4 
. 1 40 11 

1 <n 37 


3 34 41 
3 38 48 
3 4a 56 
3 47 S 
3 SI 15 


S 4J 34 
s 46 is 
5 S> "7 

I'J'o' 


7 s; 

7 s* "3 

8 a4 


9 S3 ■ 
9i<i 53 
10 43 

" 4 33 
10 8 ±1 


1 1 45 19 

" 49 

" 5;*> 

11 56 ao 
13 



PI. 


Arit,. 


Dif. 


VW... 


Dif. 


Geaeu. 


Dif. 


C»ar. 


Dif 


Z<f. 


Dif. 


nv 


Dif. 




PI. 


«/■ r«£/M, ». 34, as) as &r M go-, the Right AfcenBon from thtace, in-Tjnu, to l8o", will be the Con^timMt 
-,[ the former Right Alcenfioa (ttOn la^hiwdij to tz Hoari of Time, fo that the Right Afcenfion in Time to 
my Number of ^gns ami Degreea of the Sun's Place being given, the Complement thereof to la Hoon will be 
^he Right Afccnfion in Time to the Supplement of thofe Signi and Degrcet of the Sun't Place to 6 Sign. 

eXAMFLS l< !«• R. A. «' s4- ^ 1 
♦ 14 9 S !♦ t 

« o la o o PteoT. J 



,, Google 



md NAVIGATOR. 



RIGHTASCfflfSrONof tke SUN in TIME, toth. prrfc.tMtao 0«Li<!»iir of the EciiMic, ij'iS'i. 


Jtjanl. EUN-i ttuc PI.ACB in thi Ecliptic. 




PI. 


Sif^* 


Bif. 


Kg. 7 


Dif. 


-'■' 


Dif. 


Sig. 9 


Dif. 


Sig".o 


Dif. 


X 

sig. 11 


Dif. 



PI. 


" 




a ■ 








m i 




a 3 




■ s 






" 


3 
J 


la J 40 
ta 7 ao 
M it b 
ra 14 +1 


340 
3 40 
3 40 
3 41 
3 40 
3 *o 
3 41 
3 41 
3 4' 
3 40 
3 4' 
3 4= 
3 4* 
3 f 
1 V 
J43 
343 
3 43 
3 44 
3 44 
3 44 

IJI 

1$ 
3 47 
3 47 
3 48 
3 49 
! 49 


■3 5' 37 
'3 K >7 
'3 59 •? 

14 6s9 
14 .0 SI 


350 
3 S" 
3 !° 

U' 

3 J3 
3 !+ 

3 34- 
3 S& 
3 S^ 
3 S7 
3 57 
3 58 
3 S9 

3 59 
4- 

4 1 
4 a 
4 2 
4 3 
4 4 
4 S 

4 7 
4 7 

4 8 
4 9 
4 10 


IJ SI IJ 
'S is 'I 
'i 59 3« 

id la 11 


4 10 
4" 
4 "' 
4 13 
4 la 

4 '4 
4 14 
4 'S 
4 15 
4 'S 
4 17 
4 '7 
4 »7 
4 ■! 
4 18 
4 i» 
4 19 
4 ao 
4 19 
4 20 
4 al 
4 20 
4 " 
421 
4 a' 
4 22 
4 21 
4 aa 
4 21 
4 »a 


1^ 
18 4 22 

18 843 

'! ■' 1 

18 17 a6 
18 21 4S 


4 2a 
4 " 

4 22 
4 " 

4 *^ 
4 •! 
4 a[ 
4 21 
4 20 
4 ai 
4 ao 
4 '9 
4 20 
4 19 
4 "9 
4 18 
4 ■« 
4 17 
4 "7 
4 '7 
4 IS 
4 1! 
4 15 
4 '4 
4 14 
4 1* 
4 13 
4 " 
4 1' 
4 10 


ao 84s 
ao 12 55 
•0 17 4 

ao 25 10 

20 29 28 


4 10 
J t 

4 3 

4 I 

3 59 

ill 

3 57 

l\l 
3SS 
3 54 
J 54 
3 S3 
3 Sa 
3 5' 
3 S^ 
3 5° 
3 SO 
3 5"^ 


22 8 23 
aa la la 
aa,« 1 

11 life 

aa a7 a3 


3 39 

IV> 

3 47 
3 47 
34* 

3 45 
3 4t 
3 44 
5 44 
3 43 
3 43 
3 43 
3 42 
3 4a 
3 42 
3 42 
3.4a 
3 40 
3 41 
3 4' 
3 41 
3 40 
3 40 
3 41 
3 40 
I 4» 
3 40 


30 

It 

«7 
z6 

■+ 
*3 

23 

SI 

If 
[I 

It 
13 

la 

to 

4 

3 



\ 

9 
to 


la 22 1 
la a; 4a 
la ag as 
>a JJ 4 

la 36 44 


'4 ^4 43 
14 18 j6 
14 at JO 
14 26 24 
14 30 20 


i« 16 ad 
r6 20 40 
16 24 55 
16 29 la 
16 33 .; 


,8 a6 9 
18 30 3D 
18 34 51 


ao 33 32 

ao 37 37 
20 41 4a 
ao 45 46 
20494, 


22 31 9 
" 34 S4 
aa 38 40 
aa 4. as 
aa 46 9 


IS 

n 

H 

«7 
18 
>9 
so 


la 40 a6 
"44 8 
la 47 so 
la J. ja 
" SS "4 


14 34 16 
14 3» 13 

>4 50 7 


16 37 41 
i« 41 S9 

16 so 34 
16 54 sa 


185431 

19 so 
'9 5 9 


ao 53 51 
>» 57 53 
21 I 54 

" 5 54 

zi 9 S3 


"a 49 S3 

" S3 37 

22 S7 ao 
»3 1 3 

23 4 46 


la J8 S7 
ij a 4« 
13 6 *3 
13 10 7 
13 ij SI 


14 54 6 
1458 <■ 
•S ' 7 

15 « 9 
■S 10 It 


16 59 10 
'7 3 '9 
'7 7 49 

17 12 8 
17 16 2$ 


19 9 a6 
"9 "3 4t 
19 18 I 
19 aa 18 
19 26 35 


ai 13 5a 
21 17 50 
21 ai 47 
ai 25 44 
21 29 40 


23 8 28 

23 12 10 
23 IS S> 
»3 19 34 

aj a, iS 


SI 
3S 


'J '7 35 
13 ai 20 
13 a; 6 
,3 as SI 

IJ a* 37 


\\ \i ;i 

■5 30 34 


17 20 49 
'7 as 9 
17 a9 30 
'7 33 SI 
17 38 la 


19 30 50 
■9 3S S 
19 39 20 
19 43 34 
19 47 48 


ai 33 36 
ai 37 30 
ai 41 a4 
21 45 17 
ai 49 9 


.3 .6 s« 
■3 30 37 
23 3+ iS 
•3 37 S9 
■3 41 39 


36 

IS 
>« 

4 
PI. 


■ ; J624 
13 40 11 

•3 43 SS 

•3 47 4« 
aj ^1 37 


■' 't *'. 
■5 38 48 
IS 4a 56 
'5 47 S 
15 S' >S 


'7 42 34 
'7 4'' SS 
■7 5' "7 
>7 Si^ 38 


1,5a 

19 56 13 

20 24 


21 S3 1 

21 56 S3 

22 43 

"til 


"3 45 19 
23 49 
Z3 5a 4» 
a3 56 ao 
a4 


Mr«. 


Dif. 


S<»^.. 


Dif. 


Stgiiur,. 


Dif. 


Ct>i^. 


Dif. 


Jp^n^. 


Dif. 


P.Ji,,. 


Dif. 




PI. 


H. B. Tht Right AfceoBon in Time to the M 6 5,p, of th« Sun'. Plae hdag foand (in TM, f. i6) to th 
Oqiieei of Ri.H Aftmlio. (in the former Tnble., p. J4, =s) " f" " 'So*. *« Ripht Afcenlion, u T.me, ti 
leM 6 Sign., wiU b. h«d 1., iMmg iz Hogn » die Right Afceniion of the Ibiejom, Tible. 

EXAMPtE. 7< JU li, Kiill ^•fn i.Tim, u lh< S^i in> PItn "• "• J/ «'' 
rfklS'ij'' 6» aj' lExcefeofthe Son's Place above Degree* 27' +7' 0.33441 

+ 1 44 ^flif. Time for iBegreslBire . . 3" ♦+■'■'<*■ j.i,^/WZ.i«r;H«,. 




B0.I13 8 7 J R. A. 


reqni 


ted. 






1-44 


'|1.S40SJ 






1 



E^ 



DigHizcd by VjOOQ IC 



The ROYAL ASTRONOMER, 



For redocing PARTS of die EQUA-I 
TOR into TIME. ' 



?ar redactng TIME info 
Paiti of the EqjrATOK. 



iRlFKACTiOH and Pakallaz O. xcconUng 
to the Paw-Obfcivat^ry. 



Argiaaft. Apparent Alti tude 
Alt. Refria. Ah. Rcfwa. ..j'Ri 



— O _ 



Jrpmeat. Psrtt of the EqoatOi 



HiA^'mnt/. Hotin, Mintilei, 
Secoodi, f3c. of Time. 



9 20 
10 o 
■ o 40 



1+ 40 



22 40 



6 30 



32 20 
27 56 



12 48 



I 10 
> 7 
' S 



S 2» 

4S8 
4 32 
4 '2 
J_£t 



o 59 
o 58 
o 56 
» 54 



eJ_ 



■Jfy.Gap.AI, 



'3 -5 
■3 30J 
1L4S 
14 o 



4 30 
4 4S 



7«/iidihtBeurf in 230*. I5'. i6'/ 
230*. = IS*. 20". 



4 Anfwer. 



" 34 
o 33 
o 31 



Ttfiidlhi Dtgriti /« i;i>, 21 
I'. 4'\ if Tim r 



IS>. = 22!'. 
""•= S '5'- 



Spm, 230 15 16 Anf. 



1 38 

' 34 



Z 



Ex A ur L >. 

7". Ap. Alt, — 7'. 44». RefraftioD. 
+ o 10 Parallax. 



Sum — 7 34 deduS. 
From 7« o o O Ap. AIl 



0*( tnie Alt. 651 26 reqnired. 



Digitized by 



Google 



and NAVIGATOR. 



Pot redodng PARTS of the £Q1JA> 
TOR, {paffcd over by the Eab.th"» 
Rotation, and Pkookession, or 
Sun'i appaTeot Motion, from Noon to 
Nood] into Mean {olu HOURS. 



Argianent. Parta of the Eqnator. 




For reducing Mtan foUr HOURS into 
PARTS of the EQUATOR ; paiTed 
over, from Noon to Noon, by the 
Earth's Rotation on its Axis and 
PaocREGsioN in iti Orbit. 



JirgimieHl. Mean lolar Hours, Minutes, 
Seconds, Es'f. of Time. 




M 
7: 


. / # 


M 




•" , / . 


^ ■ * iv 


r. 




1 15 1 21, 

3 JO + s6 

3 4S 7 >■( 

4 60 9 ji 

5 75 " "9 


3 
4 

s 


1; 23. 

30 S32 
04; 7 33 

1 1034 
1 i; .2j; 


7 46 16 

8 1 ,5 
8 16 2? 
83. 2, 
8 46 26 


6 90 14 47 

7 loj 17 15 
> 120 19 43 
91JS IX II 

10 150 24 3E 


6 
7 
8 
9 


1 30 i; 
■ 45 '7 

2 20 
2 15 22 
2 30 2; 


30 

37 
38 

39 

♦0 

4' 
42 

» 


9 1 29 
9 16 31 
9 31 34 
9 46 36 
10 1 3, 


1116; 27 6 
»2 180 29 34 
"3 19s 32 2 
14210 34 30 

IS"; 3' 58 


12 
13 
14 
'S 


' 45 '1 
3 JO 
3 IS 3' 
3 30 34 

3 4! 37 


.0 16 41 
"> 3; 43 
10 46 46 
.1 .48 
.1 .6 ;i 


16 Ha 39 26 
■7>;; 41 S3 
18270 44 21 
19 28; 46 49 
20300 49 17 


16 

■9 

20 


4 39'46 
4 IS 4'47 
4 30 4448 

4 4; 4749 

5 49;o 


12 I j8 
12 17 1 

12 32 3 


"31s 51 4S 
"330 54 13 
»3 34S S<i 40 
24 36o»;9 i 


■3 
■4 

'S 


s IS 52 

5 30 54 
S 45 57 

6.1'! 


1 


-47 i 
13 ' 8 
ij 17 11 
13 3' 13 
13 47 16 


"J o» « 1 *<W 


26 
27 
28 

29 

30 


6 46 7 

7 ' 9 
7 16 11 
7 31 14 


14 2 .8 
14 17 21 
14 3' 23 
■4 47 26 
.; 2 28 



EXAMPLE. 
71 find tit Dig. if lit Earih't Rmtilm m 
» Ijt sS" 4> 7>fc tfrnanftLu- Tim, 



^9 S9 J9it 17 



The DiPFtasKCB of 
tAem/tiar above fyde- 
rial HOURS. 



H. | M.S.T .|H|M.S.T 



+ 2» 7579 " 49 

t 3S 59589 31 40 

+ 4S 5059^9 41 3 

,4 55 4'lool9 5' ». 



CoiiiT«veTio)r, 

7. /bJ ibtEnetfi of 14 man/a- 

Jar i/Hiri, ajrw 14 hdaial 

H^ fnean ^ j(a>. 59', !"• 

10'". br Euth't Ratation. 
- s6.. 






or Che lime Poiit of the r,««s,4(murr. to the /«r «WjV« j m>ki» 






Digitized by VjOOQ IC 



s» 




rbe 


ROYAL 


A S r R N OkM E R, 






A TAktt, Itcwmii iSSTrf.V...o, b.wccc ,lc yji^.6'.(.ri^ tni S,!^ V...., ton. 


600. 






rk.i». 








ri«t»>. 


W'iwifD' 




£nW-Ye>n from 1600. 


jrfrof 


noiiO- 




Sctar Yean front 1600. 


■itli of 


Dif. k« 


Ytin 




19 y<aii 


Dif. bet. 

?.'o!:i 


Y«w. 




, v.. 


Ji»Col' 
Theiw, 


GrieariaH Yeui 
from i6oo. 


Hoon 


Sin 


GrtgtHan Yf*. 




Ki. 


of - 




rub. (r. 
at add to 


chejuj. 


L»r.Cjtl, 


of 




iddto 


JlrOMM/. 


'*'''«, 


J./: v.. 


bay. 
■ddto 


from vUEo 
1600. J,l. y*. 
t„.. lotO,. 


ChriJI. 


11600. 


Gregor- 
for Solar 
Vein. 


rub. it. 

,C.l. 


theG«j. 
Account 


Chnf. 


Voir.. 


D»tP" 
lab. fr. 
9 Col. 


ward in 

th«a^ 

Account 


Ceirturin. 


N-ColM. 


2. 


3- 


4- 


5- 


■ d.- 


7- 


8. 


9- . 1 . ■<>. 1 


II. 


thcDavi 








Add 10 Dayi to tha D«yi in the 3- tod 9 


kCal>, udllicSumoillk 


4600 
1700 


I 





the Gnitriam U forward of the JidiaM Acooont, or D* 0\(. betw. N. udOld Style. | 


_ 6 


i 




5300 


37 


z8 


+ 11 


12 


16 


1800 


2 


a 


— II 




S400 


J» 


•9 




'A\ 


17 




3 


3 


— 17 


t 




j6oo 


,19 


30 




17 




4 


3 




■f 




40 


30 




•3 


•7 


3IOO 


5 


4 


— 4 


.f 




S7<» 


4> 


31 




I3f 


18 


BlOO 




5 


— 2 






5800 


4« 


3' 




■li 


18 




7 






'i 




S9O0 


41 


33 




■4, 




.400 






+ 4 


■* 




6000 


44 


33 


ti 


4* 


>9 




9 


7 


_ 2 






6100 


4( 


34 




.4t 




2600 


10 




— 7 


si 




6200 


4I' 


35 




>4l 


to 


2700 


II 


9 


T'l 


li 




6300 


47 


1' 




'S 


21 


2800 


12 


• 9 


4 




6400 


4« 


36 




■ii 


*. " 


2900 


>J 


10 


+ 


4; 




6joo 


49 


37 




■si 


21 




1+ 


11 


— s 


4t 






!0 


3« 






. 22 




•S 






S 




6700 


^' 


39 




i6i 


*3 


3100 




12 


+ 8 


sf 




6800 




„ 39 




"■\ 


21 




>7 


13 


+ a 


5i 




690a 


53 


40 




■7 


23 


3+00 




H 


— 4 






i4 


4" 




■7i 


»4 


?IS 


19 


•! 


— 9 




9 


7100 


'^ 


4> 




■7! 


' *4 


20 


'5 


+ 1 


<■; 


* 9 


7«oo 


4* 




18 


*4 




21 


■6 


+ 4 


'i 


9 


73DO 


57 


43 




:?l 




3800 


22 


17 


^ 2 


7, 


10 


7400 


5» 


44 




% 




»3 






75 


* II 


7500 


^o 


45 




■9 


4000 


«+ 




+ 11 


r; 


10 


7600 


45 




-■9i 


tS 


4100 


li 


»9 


+ 6 


8 


11 


7700 


6t 


-fS 




■9t 


rt 




ao 




»i 


12 


7800 




47 




30 






27 


21 




»5 


»« 


ygOT 


bl 


48 




.o{ 


38 


+400 




41 


+ -J 


9 


12 


8000 


64 


48 




»oi 


27 




29 


22 


t 7 


?i 


13 


8100 


,6, 


49 






28 


4600 


JO 


n 




13 






SO 






*9 


4700 


3' 


»4 


T + 




H 


8300 


67 


S' 






29 


4800 




>4 


+ 1^ 


10) 


14 


8400 




1' 




. SB 


39 


+900 


33 


U 


+ ft 


■°I 


H 


8^00 


6g 


5' 




.^j 


30 




34 


+ 4 




■ '5 




70 


S3 


. zx 




5100 


3S 


i7 


— 3 


■■i 














&c. 


Sioo 


36 


27 


+ "7 


"i 


'S 














TgXX 


^t'Lb of the USB. Ik 10 Hundred JuUaa r»>r. /^» ^ 10 i/»^ n«r. Ctn^oriu «„ 


8 i>*r. 


Mi 10 J 


umlnJ Solu iuti, iDuft—j Hwi: fi that thi Gregorian Y««« s«tf. inlfmt pMio*, h %t>t 


rpftrv/an 


=//i*JM 


Mlb Daft of the Julian Rttiminr. And th, Stefm, of thi Solar Yita^,. in that limt. imll b* 7 Hour 
egorian ^^fMui/. ^o ^^ sJar Sta/en,, ar rtart, •uiUl ht 8 D^,—; OKn/trmwdtfthtMa* 


Lh^. 


,//AeG 


tb-Dtgt h 


../r Jutia 


Q RKkmi>ig. 


























l>Of tt ' 



,, Google 



.. . . - ■ ^ ■■- " . . ■ „ .,. ' ■ ■ V. ■,....■! '■■- 

CONSTRUCTION of the FO&EGOING TABL& 

AcGoant of Time, .from which Ptu/ the mregoiag 7^e&£( is compofed ; IhewiBg, uSuht, the Diffmmc4, in Dwi, 
betwixt the Julim, Grigtrian, tai Stiar Yetn, Wherein you iniy fee htrw maiy ^ys the Gr^tHaa Yean, ia 
given Centunef, adnnce (wid) RefpcA to Month-dsri) of the fame Noabar of Veari yu£a». Aad how 
nnay Uaun die 5«^ Yetra.w SmfiMi, to fofwud ar ntteac, (with RefpeA ro the Month>daTt) iatkeJkme 
Nnaberof Ca)ti*ieaof GngtrimtYtttu At al& the Number of Diys and Ho>n the&^<v Sealou, or Yean, 
-etreu (with ReTpeS to tAotttii<iayt) in th« yuUmi AoamM. And the Nnmher of Dayi the Lmmmt CfiU (of lo 
Yean} frUs Inck in the Moaif « of the ^£48 Reckomog' in t given Penod. By comparins which RettrdadoD 
>f Ae LDn&r Cycle, in the Month days of the Julian Account, with the Month-dayi 'ailvanced t^ the Gr'tfiiriak 
>f rthe JuIioM Rtciimii^, in the fame Period (refening to cue Siaodard], the Diftraui, qr Exceft, will be 
Jic Dayi that the Ltw- Cycle ii carried forward ia the Month-day*, (in the Cune Period) of the Or^eri^ 
Accoont. 

Hnce, the Reafon of the CeUat Nimitrt bting caniad fbnvafd by certain Daya, in certun Feriodt, iA ^ 
ari of MattitifiiWa nrmu SW/r for fiadtng- ff^ff- Fnti Kfoos; and hence the>fyflery of ^e two lafi TaUtt 
a the Siylt-M ia anfblded. 

Nui, A Solar Tear i» here ftated at jS;'' j"" 48" cj*, wanting ii" j* of a 7ifi«(r Yew { by which Ae odd 
tlonrsin the4ib uid i«tb CsAMMt are a>mpnted. ' The Juliait Antiripation of the Zjhuv Cycle of 19 Veari h 
iccordine to that of a Day in 310,7 JuSan Yeart; whence the 5'" and 1 1'^ Coltimna are computed near tht 
Truh. Wherein ahenu btdf a Day is taken ibr another tiuheU Dsa ; but lefi than half a Di^ more ia taken for 
Nothii^ more. Our Table cotredj, in feme Period), by a taheb Dmf, the Stjk-jta 7gUi. 

Thtrthtng \tfici<^ Oa/iim ^OoGrigniaHlTtari, «r 3 O^sUfiiihat in ibe fanu Tfumitr tf Tiari jMXaMi 
4 h ■ a ih ' 
h 19 Grigerim Tean tb*H •vdllht 6939 14 54 48 o =a 69J9<,6o7j 
£ia in z^^ SjmUfaiMaUh ttman:6tf3^ 10 }■ (6 30 = 6959.688848 



r Cycle, ih Dijtrivu i 

Witme, ia aioMt 233,56 I'/ari Grtfm<i«, if th Grtgma* Yatr vift rtffdarlf ftrwarJ ^ the JuJuui, tu t» th 
Mamth-J^ ^ tath Acemit, «New arf mW Mmn tMtild ht advaiuid oat XoK&^-da.y, hj tithra^r CjeU, inlbtGr^triat 
Actema. SMt 1 2 Dtyi compleliij art aJruanctd in 2800 Gregariait liars. Jjtd mr TaiU jht^i that iht Vmiatr ef 
Ooft 3, 6, 9, 12, CiTf. fi>tald fiand agaiMfi 2200, 2900, 3700, 4400, fJc. ai ihtf fiand in tbt Style-Ad Table. 
■Mlin/oasdiMt 8 /banU fiaaU agnnfi \bBo, n aod not vn^iafi 3900, andxt and sot £0, ^ainfi 6400, cor- 
red^ ^ Emm ia the Style-AA Table. 

Ekamplb. Tb fiid tht Miicifatim »f tb* 1.K0U Cycle in th* }\i\.M JeetKut, fir arf Ifwnhtr ef Yiart Julian 
/i^^f 2300 frmtb/TiariBoo, If. S.f 

As 310,7 Years : i Dtay :: 100 Years : ,312 Etay, neadyj a m^&m/ Xnii^tr (at Hondredi. Whence tjyi 
321 = 7,4 Day», or 7 nearefl, rtjnirid. 

Tht Grtttrian MoRth-days beine then adrznced 1 8 Days forwird of the JmUoh Mbndi-dayi, therefofi iS— 7: 
[ I Days, ue Lmiar CftU is then advanced in the Month^days of the Grtgcrian Account, and mt 10, ai in tbt Stji" 
MTabh. 

7« ,fii^/i( Julian, Gi^oriJu, ««/ Selw Yean, »r *U igmm JtamUt rf^imtt twrt^aadtMitttaebatitr? 

ExAuM.1. 1400 Jul. yns i^ooOreg. ¥>*+ It' Days, the Grr^tn'M Accomitof Time. 
i40oGr. Y"+ 1400 X W^^vmiipo — ■•' ■+ to'' 18'' 36" 40*, die 5«/*r Account. 

J^^.'A. The Jnlianis then fboftof? Dtff. — 5 23 ao (at by ?'«Jik> the W«r Accotint islhon 

the Gregorian Account by 11 Days. 3 ef theGt<^«rMa. 

By the above ^Jt the 4th and t«h AhMUU arc-cooltrafted. 



=db, Google • 



3» 



rtt ROYAL ASTRONOMER, 





DECIMALS of 


• DAY. 




1 


If.B. ATi^WwtbttfintStr^rnfiil, i>n»Hiihai tbtfiUt-uAigDtdmdiripttaJhmtbeutU JjUa\ 


Dot (.) ^tr tuiy Figiirt, Jtnttis that Drama/ le Ar arrta. 








'" Mc^.,. 


M.«UTa,. 


ijica 


NDl. 




Ho. 


Decim. 


Min. 


Decim. 


Mln. 


Decin. 


£eo. 


Decim. 


Sec. 


Decim. 


1 


0,0416^ 


■ 


:^SI 


11 


.»"S>< 


1 


,0000115/40 


1« 


,0003587362 


2 


o»o«3W 


3 


31 


fiajirf 


3 


,000023448 


1* 




3 


0,115. 


3 


,00108^ 


33 


.01291^ 


3 


,000046/96 


13 


/»o38i94^ 


4 


o,i6S6? 


♦ 


•«"77i 


34 


.02361/ 


4 


H 


,000393^18 


5 


0,2083^ 


5 


.~347^ 


3S 


,02430/ 


5 


,0000578/03 


3! 


.0004050^2^ 


6 
7 


oiigie? 


6 
7 


,00416^ 
,004 S6/ 


36 

17 


,025. 

,02569/ 

.02638I 


6 

7 


,00008 1 oJb5 


36 

17 


y«04.666/- 
,0004182^7 


8 


o,S333J 




.">S!S/ 


1« 




,000092^92 


3« 


,000439^14 
,000451 38 ( 


9 


l;j;ii? 


9 


,00615. 


39 


.02708^ 


9 


/x>oio+i6(l 


iq 




10 


,00654/ 




.02777^ 


10 


,000115^+0 


40 


,000462962 


11 


■>.««3i 


II 


.00763? 


4" 


,02847/ 


11 


,0001273/48 
,00013688$ 


4' 




12 




12 


.ooSjji 


4» 


,o29iM 


12 




,00048611/ 


13 


".S4i6? 


ij 


,00901^ 


41 


.02986/ 


■3 


,0001504^29 


41 


,0004976^51 


> + 


"iSlilS 


> + 


,00972/ 


44 


.03055/ 


"4 


,0001 62^^37 


44 


,000509259. 


>S 


0,625. 


'S 


,o,04,|J 


41 


,03125. 


■5 


,00017361/ 


4? 


,0005208^ 


"6 


c,6666i( 


16 


,01111/ 


46 


SiitJ 


16 


,000185/65 


46 




>7 


0.7»«3i 


17 


,01180^ 


47 


■7 


,0001967/92 


47 


,0005439^14 


18 


0.7S- , 




,0115. 


4« 


,omu 




fioozoim 


+« 




'9 


o,79i6|I 


rg 


■°'3;ii 


49 


.03402/ 


19 


,ooo2i99j!(74 


4P 


,0005671^96 




0.83J3J 


«o 


,01388! 


50 


.03472/ 


20 


,ooo23i'48 


^0 


,000578704. 


21 


?.;;&, 


21 


.ol4!»*. 


5' 


.0354' > 


21 


,00024305^ 
,000254^ 


S' 


,0005 902 ;y 


22 


22 


.<"S<7/ 


i' 


,03611^ 


22 




,0006018/18 




0.9583^ 


«3 


•"'SJ^iS 


!3 


,03680/ 


'3 


,0002662337 








I, 


** 


,01666^ 


S4 


■°'?' V 


*4 


/)oo27777y 




,00061;. 




J. 0+16^ 
1.0833^ 


2q 


.01736.1 


53 


,03819/ 

.03B8SJ 


'5 


,ooo2S9)^i8 


■;? 


,0006365^40 


26 


,01805/ 


56 


26 


,0003001(25 


^f- 


,000648/48 


*7 


1,125. 


27 


.01875. 


57 


.03958./ 


27 


,0003125. 


57 


,00065 972 i 


28 


1,1666^ 




.oi944lf 
,ozoi3lf 


58 


,04027/ 


28 


•0003*4.074 


^M 


,000671^96 


^^ 




29 


59 


.04097/ 


'1 


,orx)3356^ai 




,ooo6S2«yo3 


..3° 


1,25- 


30 


.oio8:i,T 




,04,66|r 


'° 


,00034722 i 


60 


•00069444/ 


"A TABLt ot 1. 


e NuMB^i. ot DAYftrom any ooe Day 


in any Mom i h, to the lame I>ay in any other | 




Month to. dwir 


•■■ 




1 


Month). 


i.„. 


Feb. 


March. 


April. 


M.7. 


Jme. 


Jill,. 


Augnft. 


i-cpr. 


otV 


Nov. 


Dfc. 


January 


I'l 


3* 


S9 


90 




'5' 


181 


212 


'43 


271 


304 


334 


February 




36^ 




59 


y 


120 


150 






242 


273. 




March 


,06 


337 


365 


31 




?' 




'53 


184 


214 


MI 


275 


AprU 


»7S 


,ob 


334 


365 


30 




91 


122 


•53 


iai 


214 


244 


Mv 


24s 


^76 


304 


335 


36s 


3i; 


«1 


92 


123 


151 


184 




>« 




«+S 


173 




334 


30 




92 


122 




■83 


July 


184 


215 


243 


274 


304 


335 


365 


3» 




92 


123 


'S3 


Auguft 


■S3 


.B4 


312 


"4? 


• »73 


_!i!t. 


,334 


^, 


. ,,3' 




9> 




September 
Odober 




'S3 




Ill 


H2 


'73 


303 


3H 


365 


30 


.61 


91 


^^ 


i»3 


'S' 




213. 


'43 


'73 


304 


335 


l*'^ 


3* 


hi 


November 


6, 




120 


■S" 




212 


242 


273 


304 


114 


,65 


30 


December 


3" 


62 90 


121 




212 


.^4^ 


274 


?°+ 


1?? 


365 




f.be added whsn tebnuvj ol ixap- year com 


et between two Monthi. 








nJtht SuT^tr ./ Vofiiti^ixt December 19 


1759, Wjnlj.s4.ysa, 


^mff 






7111V 19 following, we find, to the Right, 


againlt Die, and nnder 7ju 


r. 2., 


Dayi, (aiding 1 
>h) the Sum it 


Tor M. of Leap-year 


coming between) to which j D»y» mOre bi 




24th 3 


ji8D 


V» rtfiariJ. 








































M.4. ■ 



,, Google 



«»</ NAVIGATOR. 



33 



IMiAH Motion of the SUN forMoiiTBi 
and Days, to Thirds of a Dbckki, 
for corredly confiro&ing Tablbs, p»g. 
S. ^' 7- 




EQUATION of the Points of the E<tuiNocTijtt.,fbrthc couipu 
ted Lti^i'uiUt of the Sun and Moon, rrom the Mean EtiipiirOe- 
i.iquiTY,a3*' a8' 30*. Alfothe Equat. of the M. to the tr.Edifiu 
OiLJQOiTY. Together wich the jiKwual Pntif.- of t\iK Equ*. fioiii 
the Nutation of the Euth's^A'jj, doting one Revol. of the S'tti, 
■CCOi> to Dr. Bt ablky's Improv". of the R. Oiftno. at GrttJnuirh. 



8 201 o 10 
I 58 16 39| o ic 
» 57 »♦ S9 o 30 

3 S6 J3 '9 o 40 

4 » 41 39l ° ?o 



f 54 49 S« 

6 {3 {3 tS 

7 S3 6 38 

8 S» "4 58 

9 S' '? '7 



o 10 JO 51 37 

C5 11 49 J. 

o 11 48 41 

o 13- 4.; 56 j6 

o '4 47 4 i6 



I 16 45 >i 36 

' '7 44 »9 55 
I 18 43 ji 15 

■P •*' *^ ?^ 



o >o 4» 54 55 
o «l 41 3 14 
o ai 40 ! 
o *3 » '9 S4l 4 
o ^4 38 »8 14 



*S 37 36 33 

o 26 36 44 53 

o 27 35 53 13 

0*835 1 53 

3°) O '9 34 9 5» 



o 33 18 111 s 13 



o 58 



3 3: 
3 4* 
3 S» 3 " 



±^ 



ConeaCoNtrmcTtoii of 9"«t. p. 5, 6, 7. 



Jtt^ 



^a; 30 



•OSahiT 
]3L 



3 18 16 39 30 
° '9 34 9 5' 



8 *9 4 54 
18 43 38 '5 



9 -*7-4* S* »sRF^4« 



i-a 



45 5« 
3 ■» 



■ OB of tha Moow'j Node, from the 'EfuiatxT 




[oo 41I itf. Tit Sv »*d Mtam'i nmftlid 
Etliptic'Obliqnit)!) iq» 'lj« 34' ^C, lait o' lo" »7' 
_ , .. . ^ .... , .... •-licOhSjtiMf 



tfgUaiii (frwn ... , , . , . 

•o", i ^ Bntfy, ttjiii lit Q mi 5 '1 cirrefl /■/«(« ftribtinit ul'ftir MBfiy 
O conn. PI, ]) c«ispt PI. 

M< .j» sf- 4*" : . o« .0^ »7' »o" 
Bjr tha AifMNat, Eiguitmn — 17 . . EyMtion —17 
CMnAPlKC0 lo 1] ]4 1$ . 9 . o 10 17 ] rtfn'n/ 

Ton Si^Hic OUifwu »3« if AV'I^itttiifAMtJ^titHBV'''* 

Aoara] PmxffioaM thcfffn'ujr . > ■ 4g j }'' Q> ^^_ 



,, Google 



i* 


Jit ROTjCtrASTRQTiTOMER 




kMai Men RACES of ik. MOON. I,m iS 


2to,7s = , o/jstyu. f 


'Julian 
Style. 


M.PI1. 1. 


M.Pl.Ap. J). 


M.pi. a. 


Julian 
Stylo. 


M.Ph. B. 


MPl.Ap.J. 


M. PI., a. 














B. .(.ja 

53 
S4 
55 


9 »7 H '9 
J 6 47 2! 
6 16 10 26 
,0 If 3; 30 


4 24 24 34 

6 s "4 M 

7 '5 44 15 
3 26 24 6 


IS 8 49 
II 25 49 6 
II 6 a9 23 

10 17 9 39 

9 27 46 46 
9 8 27 3 
8 19 7 ao 
7 29 47 36 


B. 1700 

3 


10 1' a! to 
a a4 44 14 
7 4 7 18 


9 27 37 LO 

II 8 17 

18 5651 

1 29 36 42 


S 16 44 13 
4 a7 24 JO 
4 8 447 
3 ■»4! ! 


B. i&s6 
!9 


3 .8 7 s 
7 !7 JO 1. 

f S! "5 

4 16 t6 19 


10 7 10 37 
It 17 so 27 
28 30 18 
2 9 10 9 


B. 1704 

1 

7 


II 26 4056 
4 6 3 59 
8 '5 a? 3 
24 so 7 


J 10 23 13 
4 21 3 3 

6 1 42 54 

7 12 22 45 


2 39 22 10 

a 10 a 27 
I ao 4a 44 
1 1 aj 


B. ,660 
61 
61 
63 


9 8 49 S7 
1 18 13 
! =7 3' 4 
10 6 ;9 S 


J ig S6 40 
S 36 JO 

7 ;i ',6 V, 


7 10 24 43 
6 2( 5 
6 1 4S 17 
5 " "5 3? 


B. 1708 
9 


5 '7 23 45 
9 26 40 48 

l ' "«' 

6 15 32 s6 


8 2j 9 16 

10 3 4, 6 

1 1 14 28 S7 
25 8 48 


12 7 
1 1 aa 40 24 
It J ao 41 
10 14 57 


B. 1664 
67 


2 29 3J 46 

11 18 18 53 

3 "7 4' S7 


9 « 4" 43 

10 IJ 22 JJ 

11 H 2 24 
■ 4 42 I! 


4 23 2 4« 
4, 3 4a 5» 

5 '4 a3 '4 
a as 3 30 


B. 171a 

■ a 
14 


,1.8 6 34 
3 17 a9 37 
7 a6 S2 4" 
6 .5 45 


' 5 55 19 
J 16 3S 9 

4 27 IS 
« 7 54 51 


9 »4 38 4 
9 S-*8 31 
8 IS s8 38 

7 a9 38 54 


B. 1668 
6, 

7° 
71 


8 20 IS 3S 
29 J8 38 

S 9 ' 4' 

9 iS 24 46 


2 IS 28 46 
32! 8 36 

6 17 18 18 


a 5 40 37 
1 16 20 54 
27 1 II 
7 41 27 


B. 1716 
■9 


4 28 49 23 
9 8 12 26 
■ 17 35 30 

5 26 s8 34 


7 18 41 aa 

8 a9 at u 

10 10 I J 

11 20 40 54 


7 7 .6 . 
6 17 56 18 
5 a8 3S 35 
5. 9 I' 51 


B. 1&71 
73 
74 


2 ,0 58 24 
6 .0 21 27 

10 19 44 31 

3 9 7 3! 


7 <8 14 49 
9 8 54 39 
10 19 34 jo 
14 21 


II 18 18 34 
10 28 58 SI 
10 9 39 8 
9 20 19 24 


B, 1720 

22 
23 


to ,9 32 1. 
a a8 ss 15 
7 8 18 19 

II 17 41 a3 


1 1 27 as 
a la 7 IS 
J aa 47 6 

5 3 a6 !T 


4 19 53 58 1 
4. 34 1! 1 
3 " 14 32 , 
a at 54 48 


B. ,!,,<, 
77 
7» 
79 


8 1 41 ,j 
II 4 16 

4 20 27 20 

8 29 so 24 


I II S2 

a 21 40 42 

4 a 20 33 

5 IJ 24 


9 56 31 
8 II 3648 
7 ai 17 5 
7 2 57 21 


B. I7a4 
a7 


8 19 38 4 
0.9 . 8 
5 8 a4"2 


6 14 13 2« 

7 a4 53 18 
9 5 33 9 

to 16 13 


2 a 31 ss 
1 19 la 12 

023 52 29 

o; 4 32 45 


B. 16IJ0 
Si 
8> 

83 


1 22 2, 2 

« • 47 S 
10 II 10 9 

2 !0 33 13 


6 23 46 55 

8 4'f4! 

9 'S 6 36 
10. as 46 27 


6 13 34 a8 
5 "4 14- 45 
5 4 55 a 
4 '5 35 »8 


B. I7a8 
»9 
30 


10 6 57 so 
a 10 10 H. 
. S '9 41 f7 
10 a9 7 I 


It a6 59 ji II 15 9 sa 
I 7 39 ai ro 25 JO 9 
a 18 19 la 10 6 JO a6 

3*a8 59- 3' 9 17 10 4a 


B. 16S4 

Si 

«7 


7 13 6 51 

II 2! 2, S4 

4 1 5' 58 

8 It 16 a 


632J8 

1 17 la 48 
a 27 52 39 
4 » J2 30 


3 a6 la as 
3 6 Sa 4a 
a 17 3a (9 
1 28 IJ IS 


B. ,73. 
53 
34 
35 


3 at 40 35 

8 ■ I*; 

to 20 46 

4 .19 «. SO 


5 9 4! 34 
t 20 2s 24 

1 1 5 ■! 
9 11 4, 6 


J 19 3 23 
S 29 48 39 


»9 
90 

91 


" 3 49 40 

1 '3 12 43 
9 " 35 47 

2 I ,1 ,1 


1 19 19 I 
6 29 58 SI 

8 10 j8 4a 

9 at 18 33 


1 8 so 22 

19 JO J9 
10 so 
It 10. SI la 


a: -1736 
39 


I9 la 23 as 
1 2. 4ftja 

» > 9 35 

10 10 J2 39 


10 22 31 37 

"3 II 27 

1 IJ Jl i« 

a 24 31 9 


6 JO as 46 

f SI 6 3 
5, I 4f ao 
4 12 a« 36 


B. 169. 
93 
94 
9! 


6 24 3. 29 
II 3 55 3; 

3 '3 18 3« 

7 22 41 4« 


II a 5 4 

«2 44 54 
■ 23 a4 4s 
3443' 


10 ai aS 10 
10 2 8j6 
9 'a 48 53 
8 aj a9 9 


B. ■ .740 
41 
4a 
43 


3 3 6 17 
7 12 29 ao 

II 21 52 24 

4 t IS 2« 


4 5 >7 40 

5 I! 57 30 
8 28 37 at 
8 7 '7 "a 


3 33 3 43 
3 3 44 
a 14 34 17 
■ as 4 33 


B. .&,6 
97 
9« 
99 


IS IS 18 
4 24 38 21 

9 4 1 35 

1 1) 24 20 


4145' 7 

pit 11 
9 16 so 39 


8 4 6 16 
7 '*t6 35 
6 as a6 so 
< i 7 6 


B. .744 

4I 

47 


8 23 49 . 6 
I 3 12 9 
5 " 35 '3 

9 21 5' <7 


9 ■»■ 3 43 
10 28 43 33 

9 a3 a4 

1 20 J IS 


I s 41.40 
iti 31 S7 
11,37 3 14 
It 7 4* 30 


LUNAR TABLES. 


B. 174a 
49 
50 
5' 


a H 3^ 55 
6 23 54 58 
II J 18 . 
3 1241 6 


3 49 46 

4 ira9 j6 

5 aa 9 27 
7 a4, 1« 


10 18 19 37 
9 38 59 54 
9 ,40 1. 
8 ao 20 27 


*• -Tf 


> 5 H-44 


813 35 49 


8 47. ^4 



















,, Google 







mJ NAVIGATOR. 






S5 


R»dic.l Ma<, PLACes of th, MOON, f 


™i7siioi«s2. Bfm-STYLe. 




Gregorian 
Style. 


M Pla. t. 


M.Pl.Ap. B. 


M. Pl..a. 


"Kl" 


M. Pla. J. 


M.Pl.Ap. B. 


N 


. Pla. ^. 










• or* 


■•■ • ' ' 


S4 
55 


) 10 !« 19 

7 19 4' »» 
1 1 29 4 a6 
4 8 a? JO 


8 1-2 22 1.7 

9 23 2 7 
11 J 41 58 

14 21 49 


8 1 ja 31 
7 1. ,a4S 
6 22 S3 s 
6 3 33 21 


1800 

2 
3 


11 s 41 32 
3 '5 4 35 
7 24 27 39 
3 so 43 


I I.; 28 .2 

a 28 8 2 

4 8 47 S3 

5 17 27 44 



tl 
11 


3 11 5 
13 51 22 
»4 31 39 

S " 55 


B. 1756 

11 
!9 


9 . . 8 
I ro 24 11 
S '9 47 '5 
9 29 10 >9 


1 2i 8 20 

3 5 48 10 

4 16 28 1 

5 27 7 52 


S 14 10 28 
4 24 5" 45 
4 5 31 2 
J iS II i! 


B. 


.80, 

1 

7 


4 26 24 21 
9 5 47 24 
1 15 10 28 

5 24 33 32 


6 as 14 IS 

8 8 s4 5 

9 19 33 58 
II 13 47 


9 

1 


■5 49 a 

28 29 19 
7 9 38 
■7 49 52 


B. 1760 
61 


2 ar 43 57 
7170 
[I to 30 4 
! 19 53 8 


8 18 34 13 

9 29 14 4 
"9 53.55 


2 26 48 25 
2 7 28 42 
I .8 8 ;, 
aS 49 15 


B. 


1808 
9 

ll 


10 17 7 10 
2 26 30 13 
7 5 53 17 

11 IS 16 21 


II 18 

1 21 40 8 

3 2 19 59 

4 12 S9 50 


7 
I 

6 


28 26 59 
9 7 16 
19 47 33 
. 27 49 


B. .764 
'7 


8 12 26 46 
21 49 49 
! 1 '2 SJ 

9 "O 3S 57 


20 40 26 

2 1 20 16 

3 12 7 

4 22 39 58 


926-22 
11 20 6 30 
11 . 46 so 
lo'ii 27 12 


B. 


1812 
»3 
14 
■5 


4 7 49 59 
8 17 13 2 
26 36 6 

5 5 59 'O 


S 23 46 21 
7 4 26 II 
> IS 8 2 
9 25 45 53 


5 

♦ 
4 
3 


.1 4S« 
21 4! IJ 
2 25 30 
13 5 4« 


B. 1768 
«9 
7» 
7' 


; 3 93' 
6 12 J2 38 

10 21 il 42 
3 I ll 46 


6 J a6 a9 

7 14 6 19 

8 24 46 10 
,0 S 26 1 


922 4 19 
9 2 4* 36 
5 13 24 S! 

7 24 5 9 


B. 


18,6 

17 
18 
19 


9 28 32 48 

2 7 55 SI 
6 17 ,i 5; 
10 26 41 s9 


II 6 32 24 

17 12 14 

1 27 52 s 
3 8 ji sS 


t 
t 




'3 42 S3 
4 2J 10 
■S 3 27 
25 4J 43 


B. .77. 
7! 
74 
7S 


7 23 52 24 
3 >5 27 
4 "2 3« 3' 

8 22 13; 


11 10 12 32 

26 S2 22 

2 7 32 13 

3 .1 1. 4 


7 4 4" " 
6 It 22 33 

S 28 2 JO 

5 « 43 «. 


B. 


.8ao 

»3 


3 19 15 37 
7 28 j8 40 
8 I 44 

4 17 24 48 


4 19 18 27 

5 29 s8 17 

7 10 38 8 

8 21 17 59 




10 
10 


«7 41 '"4 
8 ai 40 


B. 1776 
77 
7« 
79 


5 ''l "« '^ 
10 3 ai ao 
2 12 44 24 


+ 28 58 35 
i 9 38 2; 
7 20 18 16 
9 58 7 


4 17 20 13 
J 28 JO 
3 • 40 47 
a 19 ai 3 


B. 


.8h 

'.I 

27 


9 9 58 26 
1 19 21 29 

5 28 44 S3 
10 8 7 57 


10 2 4 30 

11 12 44 20 
23 24 II 
•442 


9 

8 
8 
7 


18 s8 47 

»9 39 4 
ao 19 21 

» S9 57 


B. 1780 

82 


7 5.» 2 
11 14 4> 5 

3 24 4 9 

8 3 27 .3 


10 11 44 3* 

11 22 24 28 
I J 4 "9 

I 13 44 10 


1 29 s8 10 
1 10 38 27 
21 i« 44 
I S9 


fl. 


1828 
19 
30 
3' 


3 41 "5 
7 10 4 18 
II 19 27 22 
3 28 so a£ 


3 14 50 33 

n?orj 

T 16 50 s 


I 

5 

! 


■ 3844 
12 J7 1 
22 S7 I» 

• 3 37 34 


B. .784 

U 

87 


a6 51 

9 '4 4' 5* 

1 24 10 2 


3 24 30 41 

5 5 ■>> 3' 

6 13 50 22 

7 26 JO IJ 


11 12 j6 7 
10 23 16 24 
10 3 $6 41 
9 «+ 36 57 


B. 


i«32 
33 
34 
3! 


8 21 24 4 
1 47 7 
5 10 10 11 
'9 33 15 


8 27 36 36 

10 8 i8 28 

11 18 56 1? 
29 j8 8 


4 '4 14 41 
3 24 54 58 
3 1 15 '5, 

2 16,15 Ji'. 


B. 1788 
»9 
9° 
91 


6 16 43 40 
10 20 6 43 

3 S 29 4- 

7 14 52 5' 


9 7 16 44 

10 17 !f 34 
M 28 J6 as 
1 9 16 iS 


8 25 14 4 

' i " 'U 
I •« 34 3' 
6 27 14 54 


B. 


1836 
37 
3« 
?? 


2 12 6 S3 
6 2. 29 58 

11 S3 

3 10 16 4 


2 10 22 39 

3 21 2 29 

5 1 42 20 
8 12 22 11 





26 ,2 38 

i^n^a 

28 S3 28 


B. 179J 
93 

94 
95 


7 26 29 
4 16 49 32 
8 26 12 36 
• 5 35 40 


2 20 2 47 

4 042 37 

5 II 22 28 

6 22 2 19 


S 18 J2 18 
4 29 "2 35 


B. 


1840 
41 
42 

43 


8 2 49 42 
12 12 4s 
4 21 35 49 

9 sS S3 


7 23 8 42 
9 3 4f 32 

10 14 28 23 

11 25 8 14 


10 
9 


9 50 35 
20 10 S2 

SI 9 
11 31 25 


B. 1796 
15 


5 28 9 18 
10 7 32 21 

a |« ss a; 

6 26 18 29 


8 2 4S s» 

9 ij 28 40 
■0 24 8 31 

4 48 22 


3 ao 29 s8 
3 I 10 IS 
2 II so 3; 

1 22 30 48 


B. 


1844 

47 


1 23 32 Ji 

I'oi^Jlll 

2 21 4. 4" 


■ 5 54 45 
a 18 34 3S 
3 27 14 26 
S 7 54 17 


8 
I 


22 8 32 
2 48 49 

13 «9 6 

14 9 22. 


<W February, Biflextih Yean Phen art a*VMuJ a 
Dt^iMtiim, inhihShUi, tamhrndm ti ih, mm 
Mu./Ja.aaiy>i,i/ 


i. 


.848 
49 

5' 


7 14 15 "> 
11 23 jS 2J 

4 3 ' '7 

8 12 2431 


6 18 40 48 

7 29 20 38 
9 10 29 

10 20 40 20 


t 

! 
4 
4 


448 29 
IS 26 48 
28 7 3. 

847 19 


B. 


,8„ 


,1. ..»i8-...9 


I26_s, 


i 


17 24 26 








t 


a 













d by Google 



Tbi R 0'!rA L ASTRONOMER 



iK>,B MOTIONS of the moon; lto^W«ic-ni> Old Do^. 




f 

3 
+ 

_s 

6 

1 

9 

lO 

'3 
1 + 
1£ 
i6 
'7 
i8 
'9 

Ti 

32 

*3 
*4 

i6 

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3° 
3' 


:-niY. 


A U D 5 T. 


SEPTEMBER. 




MeanM. D. 


-Ap. 


s mr. 


M.'Bot. J. ' ■ 


Ap. 


5 iti. 


M, Mci. >. 


Ap. 


^»r. 




• / » 


B T H 


/ * 






J If 






» / , 2 




7 28 6 14 

8 11 i6 49 

8 2+ 27 24 

9 7 37 S9 
9 20 48 34 


20 15" 34 
20 23 1? 
20 29 56 
20 36 37 
20 45 18 


9 38 17 
9 4' 27 
9 4+ 38 
9 47 49 
9 so S9 


9 "• 54 20 

9 19 44 Si 
10 11 55 30 

10 26 6 5 

11 9 16 40 


•3 43 4« 
25 5. 29 

23 57 10 
'4 3 SO 

24 10 31 


11 16 47 
11 19 57 
11 23 8 
■ 1 A 18 
1. 2^29 


11 k 2.2627 11 1 
11 18 13 127 17 4j 
I 23 j6 27 H 23 
14 34 1 1 27 Ji 3 
27 44 46 27 37 45 


" 55 1 '7 
12 ,81.7 
ij 1 38 
'3 4 49 
'3 7 59 




10 J S9 9 

10 17 9 44 

11 2o 19 
11 15 30 54 
11 26 41 30 


2o ,9 59 

20 56 41 

21 3 2. 
21 10 3 
21 16 44 


9 !4 10 
9 57 >o 
16 031 

.0 342 

10 6 52 


11 22 27 15 
S 37 SO 

18 ,8 25 

1 1 59 

■ '5 9 3S 


24 17 12 
?4 23 53 
"4 30 35 
24 37 16 
■4 43 57 


II 32 40 

11 35 so 
■■ 39 1 
■ 1 v 12 
11 45 22 


1 105s 21 
.2, 5s» 

■2 7 16 51 

2 20 27 6 

3 3 37 41 


•7 44 "^ 
»7 5' 7 
«7 57 4! 
28 4.9 
»8 II to 


13 11 10 
IS 14 20 
13 IT 3> 
IS «o 40 




9 52 5 

23 2 40 
.1 6 13 15 

1 19 23 so 

2 2 34 25 


21 2J 2S 

21 30 6 

21 36 47 
21 43 29 
21 50 9 


10 10 3 
10 13 14 
(O 16 14 
10 19 35 
lo 22 46 


1 28 20 10 

2 11 30 45 

2 24 41 20 

3 7 SI SS 
3 21 2 30 


24 SO 38 
'4 57 19 
is 4 

25 10 41 
25 17 22 


■■48 33 
" 5' 44 
'■ 54 54 
.1 58 5 
12 1 16 


3 16 4^ 16 

3 n 5» s; 

4 IS 9 26 

4 20 20 1 

5 9 30 36 


28 17 5, 
28 24 32 
28 31 13 
"8 37 54 
28 44 35" 


'5 '7 3 
"5 30 14 
•3 S3 24 
■3 36 35 
■3 39 4fi 




2 IS 4S " 

2 28 S! S! 

3 12 6 10 

i '! 1' 4S 

4 82720 


21 56 SO 

22 3 31 
22 10 13 
22 16 S3 
22 2; 35 


10 25 56 
10 29 7 
10 32 17 
.0 35 .8 
10 38 39 


4 4 '3 S 

4 17 'S 40 

5 34 IS 
S >S 44 SO 

s »« 55,2s 


'S H 3 
'5 30 44 
■S 37 25 
25 44 6 
»S so 47 


12 426 
■" 7 37 
12 10 47 
12 ij 58 


5 22 41 11 
\ 5 51 46 

6 19 t ai 

7 2 u S7 
7 ■? «3 !• 


28 51 16 

»8 57,57 

29 4 38 

2,1. .9 

ig 18 


15 4; i<> 
'3 46 7 
13 49 ■? 
IS 52 2k 




4 21 37 SS 
! 448 30 
! '7 59 S 
6 1 9 40 
6 14 20 15 


22 30 16 

22 j6 S7 

22 ,3 38 
22 SO 19 

2257 


10 41 49 
■ 45 
10 48 11 
10 51 21 
10 54 32 


6 10 6 

6 23 16 35 

7 6 =7 "O 

7 '9 37 4S 

8 . 2 48 20 


'f 57 29 
it 4 10 
26 to 51 
26 17 32 
26 24 13 


12 A) 19 


7 28 34 7 29 «+ 42 

8 II 44 41 29 31 ij 

8 245; 1629 38 4 

9 :» S 5'»9 44 4S 
9 21 16 a61a9 ;i 26 


'3 58 49 
14 2 » 
■4 5 " 
14 8 21 




6 27 30 50 

7 "0 41 25 

7 23 S2 

8 7 2 3S 
8 20 13 10 


23 3 4' 
23 10 22 
23 17 4 
23 23 44 
13 30 26 


■0 57 42 
II 53 
11 4 4 
>■ 7 14 

II 10 25 


8 'S S« 55 

8 .9 9 30 

9 12 20 5 
9 »5 30 40 

10 8 4. .s 


26 30 54 

26 44 i« 
26 50 57 
26 57 38 


12 i 13 

" ♦s +' 
12 4S 5; 


10 17 27 1 29 ;8 7 

10 x^ 37 36I30 4 4» 
1. «48 1130 i< *9 

11 I J 58 46I30 18 10 
II 27 9 " io »4 \i 


'4 14. 4» 
■4 17 SJ 
■4 ", 4 

>4«4n; 
14 27 24 




9 3 *3 45 


'3 37 7 


'1 "3 3S 


to 21 51 51 


27 4 20 


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0. s. Vtn 1700. [6" * s fl rj' 9 27 S7 »* 


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,, Google 



<nii VN A V I G A T O n. 



V MOTIONS or the MOON for MctNTHvand Dati. 



DECE m'^E R. 



if M. Moi. J. 



u U T O i( b R. 



lo 19 51, 


30 31 i' 


«J 30 >• 


3» 5« '3 


6 ,r « 


30 44 54 


19 51 41 


30 S" 3S 



> 'i 



44 3« 
55 ■ 



4 ar 5 46 
.5 5 '* '• 

5 18 26 ;6 
6- . J? ji 



6 27 s8 41 

7 II. 9 16 

7 a+ 19 SI 

8 7 3« 04 



9 3 5' 36 
9 17 2 II 
10 o Tt 46 

10 13 33 21 

10 26 33 ;6 



iS 20 

'5 I 

31 I' 4: 



31 j8 
31 45 4 
Ji SI 45 

31 58 27 

3 2 5 8 



3< 1 



49 

18 30 

• 25 I 

'** 5 

38 33 



32 45 
3" !' .. 

;2 58 36 
33. 5 ': 

- }1 



.14. 3P }b 
■14 33 4* 
14 36 57 
> 4" " 
4.41 



14 40 29 
14 49 39 

14 ;> s» 

14 i6 1 

H <^ ■■ 



S 5 33 
i 8 43 
S " S4i 
lii '■ 



,J 21 i6i 
■5 i4 JS, 
■5 »7 4? 
■5 3° S» 



■5 34 8 
■5 37 "9 
IS 40 29 
ij 43 40 
1S4&S1I 



NOVEMBER. 



28 48 I 
11 s8 36 



5 <* " 42 
5 '7 ^3 17 



6 10 3j s: 

6 23 44 27 

7 ' 55 ' 

7 20 ! 37 

8 3 i6 12 



8 16 26 47 

8 29 37 22 

9 " 4? 57 
9 >5 58-3; 

1° 9 9 7 



22 19 42 

1 s 30 17 
1 IS 40 52 
o 1 51 27 



34 12 « 
34 18 49 
34 25 3° 



34 3' 
34 38 S3 
34 4i 34 
34 52 15 
34 58 s6 



35 



37 



35 18 S9 
35 ^5 4° 
35 32 21 



35 39 2 
35 45 43 
35.52 24 

3^ 5 , 4'' 



36 12 28 

3' '9 9 
36 25 ^1: 

3^ 39 



S 15 27 
S 18 3« 
S 21 48 



4 " 47 51 



S 31 20 1 
334.31 



i« 44 3 
Id 47 13 

la so «4 
■^ 53 35 

16 so 45 
i» S9.S'i 

17 3. 6 
17. S '7 



12 j8 

'5 49 

19 o 

, 22i io 

7 '5'f' 



5 9 58 

I 'i i' 

6 19 30 i 

7 2 40 . 



7 IS Ji ■■ 

7 29 I i 

8 12 12 1 

» 25 23 

9 8 33 . 



">: 4 54 ! 
10 18 s = 
i< 1 i« 

IF 14 26 38 



■7 37 
6 10 47 ^ 
i 23 58 , 



_A£^ 



37 25 5 
37 3« 4 
37 39 ' 
37 4^ 



37 S*. 
39 6 

38 12 



-38 zb 
38 32 

'In 
3846 

38 52 



WI9 
39 « 
39 <« 



39 33 
39 39 ' 
39 46 i 

39 13 

39 39 < 



17 44 25 
'7 47 35 
17- JO 46 
17 53 57 

17 57 



rt 3 28 
18 6 39 
18 9 so 



48 Hi 
18 19 22 
18 22-32 
18 2s 43 
S3 18 28 s^ 



18 3s IJ 
18 38-25 
l8. 41 36 
'8 44 47 



". *' H 
■ 8;. 
iS 54 

■8 57 " 



'I 9 44 3' 

II 22 S 5 O 

o 6 5 41 

19 19 16 

1 2 26 fl 



33 ' 
33 ^5' *° 
33 .3» 2 
33 3843 
33 45 '4 



IS 5° I 

>S S3 12 

ij 56 21 

■5 59 33 

iS 2 44 



'S }7.»7 



3J 4« 



'.'• .'. S4 



, 28 12 ,i 
1 II 23 It 

1 24 33 47 

2 7 44 22 
2 20 54 58 



27 J. 42. ► 

4 34 !J 

'• .- -J'"* 'I 

37-12 37 17 41 13 1 



3J45.53 
3f S" 9+ 
}' S9,-iS 



; fotion oF Moon'r Xpivgee, ii>-t£u 9ige. for Stgnajind'DtgMW' 



I 3 30 . 



40 6 2; 

40 19 47 
40 16 28 

ff,,33 



z 



'9 3 SI 

19 7 » 

[9 10 It 

19 >J « 

■9 '6 3j 



Radical Mb*n Place* and M'A' 



,oT (jTe Moos, from feveral AurDOiriTU 






\. ]x>0 U^oi. -b VI-l^i<Ap.lMl Mot. { 
B Stilel in 100 JulUn B in iCo D ret. in 11 
>_.1I01. Yeift. ' fuirTfir..- Jnl.Vg r,. 



o t «7 14 ii4o 14 J7 i< 



"l Kr />« &'nJM<''» b* E. 



L3L 



'Lt tj[7 y m »» i*> H'a*' 



7 6 JJ 



Utrii, Aft. Afl.R. 

na'j, tinpi hiiTjbT»r 



I 5 e I .7 !» JuU H-J* b •<» 7 4< 4i 



TjhiMi&rnr'iCuoJuK Tabic*. 



*'ft>*wd- 



II 15414 II li 10 J 4 J3[»"f*woT.bte.. 

_ , -■- xVo fitted, indlrfWi H ttf At -rB. 

•■•f'XhAiar villi achu O^tnulMM, ac ^ta Ilit Mlovflni 



d by Google 



40 




rbi 


ROYAL ASTRONOMER 




RADiCin. MflANPtjtcviud Motion* of the Moon, fory«i«»*Nd «-^j«-iN«YiARi. | 


Ju lanSt^lc. 

Years before & 

fin'c Chrift. 


M. Placet D, 


M.Pl.Ap.t. 


M. PI. 0. 


Oiej. 

Si,Ie. 
Y" of 
Chrift. 


.M. Placet i. 


M.Pl.Ap. J. 


M. PI. a. 


» " ' ' 






• ". ' * 


sort 




E. 
B. 
B. 
B. 


loto 
700 


5 4 "> S2 

3 "2 7 '7 
■ 19 !7 ■(2 
1 1 27 4» - 


7 '9 33 25 
II 8 44 40 
' »7 Si Si 
6 .7 7 .0 


6 9 47 58 
1 as 36 43 
9 II 25 28 
4 27 .4 I! 


S. 1600 
1700 
1800 
1900 


3 10 21 52 
1 11 1 42 
II 5 41 32 

9 21 22 


6 7 19 4 
9 a6 as 38 
I ,5 as I. 

$ 4 32 415 


■0 I a? 14 
5 17 19 10 
1 3 11 5 
8 19 S 1 


B. 
B. 
8. 
S. 


6o(. 
500 
+°o 

JOO 


,0 s 3» }• 
8 .3 28 S7 
6 21 19 22 
4 29 9 47 


10 6 18 25 
1 25 29 40 
! '4 40 SS 
9 J S» •<> 


13 2 58 
7 "8 51 43 
3 "4 <," 28 
II 25 ij 


B. 2000 
2100 
2200 
2300 


7 8 II 47 
S a 51 37 
a a7 31 a7 
22 II 17 


82,44 . 
12 48 35 
4 ' 53 9 
7 "O 57 43 


4 4 5" 4' 
1 1 ao +3 42 

7 ' 35 37 
a 2. a7 jj 


S 20O 

B.jnl.fef. lOO 
«-47'3B.Cjo; 


J 7 12 
■ 14 JO 37 
11 22 41 2 
.0 31 27 


23 3 25 
4 '* 14 40 
8 1 25 55 
II 20 37 10 


6 16 17 56 
2 2 643 
9 17 iS 28 
S 3 44 -3 


B. 24Q0 
2500 
a6oo 
2700 


110 I 42 
8 24 41 32 
6 ig 21 2: 
4 14 1 la 


II 10 3 58 

I ;i ;i 'I 
10 7 22 40 


10 8 16 18 
5 a4 8 14 
I to 9 
8 a; ;. 5 


B. 
B. 
B. 
B. 


aoo 
300 
400 
Soo 


8 8 21 52 
6 16 12 17 
4 24 2 42 
3 ■ i! 7 


3 9 48 "5 
6 28 59 40 
10 18 10 55 
2 7 22 10 


19 32 58 
8 5 21 43 

3 21 10 28 

11 6 59 .3 


B. 2800 
2900 
3000 
3100 


2 2, jl 37 
16 31 27 

"■;;;■? 


I 26 33 SS 
S IS 38 29 
9 4 43 3 
23 47 37 


411 40 50 
II a? 3a 4* 
7 13 a* 41 
a 39 ti 37 


B. 

B. 
B. 
B. 


600 


I 9 43 32 
" '7 33 S7 
9 'S «4 " 
8 3 «4 47 


5 26 33 25 
9 '! 44 V 
■ 4 SS 55 
4 24 7 10 


6 22 47 58 

a 8 36 43 
9 H as a8 
! 10 14 13 


B. 3200 6 13 41 32 4 12 58 5; 10 15 5 22 
3300 4 8 21 22 8 2 3 26 6 57 i8 
3400 2 3 1 12 11 zi 8 I 16 49 13 

Billcxiile Yean Places are adTanced a Day') Motion. 


A. 
B. 

S. 


1000 
1100 
1200 
1300 


(> II 5 12 
4 18 Si 37 
3 26 46 2 
, 4 36 27 


8 ,3 .8 25 

2 2940 

J 21 40 SS 

7 10 52 10 


a6 2 58 
8 " 5' 43 
3 '7 40 28 
11 13 29 li 


From Hunandi of Vun Grirriam icduS tbrir Fmrtt (rrjeft- 
ifli Vn&iBBM) iBd llu fftm/MSr «iU b< cqn^ to tbr N°. ofDi** 
thertirc ^> in iny N«. of ffin*^ Ycui tliui ur in tht fiinc 
N*. of ycir. J.Sa, f»ct lioo. Whrnci tbo D,ff. of UMlon 

ElAKFLt). 

Inthc-rcir 1735. lethayuriiij 

9 Doyilefi 5 Doyt left lo 6 WaOai 
[m.lHooJ. YrontJr^. [Vein t;rip,r«. 


B. 
B. 
B 
B. 


1400 

.700 


II 12 >6 52 

9 «» "7 '7 


11 3 25 

a 19 14 40 
6 j 25 55 
9 27 37 "> 


6 29 17 58 
a. 15 « 43 
10 r5 ,8 

.f" 44. '1 


B i!oo 

B. 1900 

& zooo 

BiBextile Yea 


4 '3 48 32 
2 11 38 57 

» '9 "9 2' 
n Plecci ve » 


I 16 48 25 
5 S 59 40 
» 25 10 55 

dnnced > Dey 


1 2 32 ja 
e 18. 21 43 

.t..So'.° " 


JolUnTeOT. 


M.Mot. J. 


Mo. Mot 
Ap. >. 


Srctr. 




n. Mot. I. 


IteiMot. 

Ap.1.. 


Meuitlol.' 
Qietr. 


» « / f 


I / * 










b! 

B. 
B, 


200 
300 
400 


10 7 50 25 
8 IS 40 50 
6 23 31 IS 
S 1 21 40 


3 19 II 'S 

7 8 22 30 

10 "7 33 45 
a 16 45 


1 'J " 's 
8 a8 22 30 

1 la 33 45 
! a6 45 


100 
B. 400 


9 24 39 5° 
7 19 19 40 
5 13 59 30 
3 a. 49 55 


3 19 4 J4 
7898 
10 27 13 4a 
2 16 a4 57 


Jiti? J 
1 la 34 13 
5 a6 35 38 


B. 
B. 
B. 
B. 


JS 

K 


3 9 "» S 
.17 2 30 
1' M S> i$ 
10 2 43 20 


6 5 56 IS 

9 25 7 30 
1 14 18 45 
5 3 30 . » 


10 10 56 15 
a as. 7 30 
r 9 18 45 

11 as 30 


B. too 
B. 1200 
B. i«oo 
B. aooo 


7 13 39 so 
■I 5 "9 45 
a 27 19 40 
6 19 9 35 


5 a 49 54 
7 >9 '4 S" 
10 5 39 48 
22 44; 


II as 10 56 
5 19 46 24 

II 16 at 5a 
S "a 57 ao 


B. 
B. 
B. 


900 

1000 

3CX)0 

3000 


8 10 33 45 

6 18 24 10 
I 6 48 20 

7 25 12 30 


8 2241 .5 
II 52 30 

23 45 

1 s w 30 


4 7 4' 15 
8 21 52 30 

5 IJ 45 " 

a 5 37 30 


B. 3200 
B. 3(100 


10 10 59 30 
a » 49 as 
5 24 39 ao 
9 li 89 .5 


3 8 29 42 
10 27 44 33 


11 9 33 48 
5 6 8 16 

"1 a 43 44 
4 a, 19 ,3 


B. 
B. 
B. 


4000 


2 13 36 40 
9 2 50 

J 20 2J 


I 17 so 

1 29 22 30 

2 II li_0, 


10 27 30 
7 19 aa 30 

A " •! " 


B. 4000 
B. 6000 


■ 8 19 10 

7 «7 M 45 


■ 4 9 30 
1 a« 14, 15 


1° ay 54 40 

4 8 53 a 



,, Google 



mi NAVIGATOR. 



JW«« Motion of the MOON, for 99 7»/;^-i Years. 1 


Julian 
Years. 


MeanMot. J. 


Apogee B. 


a ret. 


S" 


MeuMot. >. 


Apogee t. 


Oi... 


* ° ' « 










..,.,{ 




1 


} ? '1 ' 


I 10 39 so 


19 19 43 




17 56 51 


6 13 ji 21. 


7 






z 


8 18 46 7 


2 21 19 41 


I 8 39 26 




4 27 19 55 


7 24 32 .17 








3 


28 9 11 


4 1 59 3" 


1 27 59 10 




9 42 59 


, 5 I. 8 




26 23 +6 




4 


^toii 49 


5 i« 46 J 


2 17 22 3 




1 29 16 37 


10 15 58 39 


9 






s 


10 % l^ 


6 23 2; 53 


3 6 41 46 




6 8 39 40 


(I 26 38 29 




562: 






i t '*•'' 


8 4 S 44 


3 26 I 29 




10 18 2 44 


1 7 18 20 


10 


H 26 S 




7 


6 .8 s! 


9 "4 4! 3! 


4 'S 21 13 




2 W =! 48 


2 17 58 11 




'3 S5 49 


J. 


» 


11 11 s; 38 


10 1, 3,. (i 


5 4 44 6 




7 19 !9 26 


3 28 44 42 





9 8 42 






3 .0 48 4. 


6 II 56 


S 24 3 49 




II 29 22 29 


S 9 24 32 





21 28 25 




10 


8 11 45 


1 16 SI 47 

2 «7 3" 38 


6 13 23 32 




i l*i" 


020 4 23 


1 


.. 48 8 




11 


9 J* 49 


7 2 43 16 




8 18 8 37 


8 44 14 




1 7 51 


B. 


12 


5 . 8.7, 


4 8 18 9 


7 22 6 9 

8 II 25 52 




1 10 42 15 


9 'I 30 4! 


2 


20 30 4; 






9 11 31 30 


S "8 S7 S9 




5 ao ! 18 


10 22 10 35 


1 


9 S° 2S 




>4 


■ JO 54 34 


6 29 37 so 


9 45 35 




9 29 28 22 


2 50 26 


1 


29 10 11 




W 


6 17 38 


8 10 17 41 


9 20 5 19 






1 13 30 17 


4 


18 29 S5 


J. 


10 !2 51 16 


9 21 4 „ 


10 9 28 12 




7 ■> 2! 4 


2 24 16 48 


5 


_7 s- is 






3 > '4 >9 


11 1 44 2 


10 28 47 55 




II 10 48 7 


+ 4 S6 38 


5 *7 "» 31I 




iS 


7 " 37 '3 


12 23 S3 


11 18 7 38 




3 20 11 11 


S ■! 36 29 




16 32 14 




'9 


II 21 27 


■ 23 3 44 


7 27 22 


67 


7 29 34 15 




7 


S S' s« 


J. 




♦ 13 34 5 


3 3 !» "5 


26 so 15 




22 7 S3 


8 7 2.;i 


7 


25 r4 51 




21 


8 2. !7 8 


4 14 3» S 


1 16 9 58 


6, 


5 I 30 56 


9 '7 42 41 


8 


>4 34 34 




21 


1 2 20 12 


■S 2S 9 56 


2 S 29 41 


70 


9 10 54 


10 28 22 32 


9 


3 54 '? 




2? 


S 11 4. 16 


7 5 49 47 


2 24 49 2; 

3 '4 " iS 


7' 


I 20 17 4 


9 2 23 


9 


^3 "4 ' 
" 36 54 


a. 


24 


10 4 16 54 






6 12 so 42 


I .9 48 54 






*9 


' 13 39 S7 


9 27 16 8 


4 3 32 I 


73 


10 22 13 4s 


3 28 44 


11 


• 56 37 




26 


6 23 J > 


'» 7 SS S9 


4 >« 5" 44 


74 


3 I 36 49 


4 11 8 35 


ti 


21 16 ic 




27 


11 a 26 5 


18 35 so 


5 12 11 28 


7S 


7 "O 59 S3 


5 21 48 26 





10 36 4 


i. 




3 H !9 43 


I 29 22 2, 


(i 1 34 21 




3 33 3' 


7 2 34 57 





^9 58 57 


' 


29 


8 4 22 46 


3 10 2 II 


6 20 S4 4 


77 


4 '2 58 34 


8 "3 14 47 


1 


19 18 4( 






13 4S SO 
4 «3 8 S4 


4 20 42 2 
6 I 21 S3 


7 'O '1 47 


78 


8 22 19 38 


9 23 54 38 


2 


838.3 




3' 


7 29 33 31 


" 


I " 42 42 


11 43429 




27 s8 7 


a. 




9 'S 4= 3' 


7 ,2 82, 


8 18 56 24 




5 24 16 20 




3 


17 II ■( 






•'S S3! 


8 .2 48 14 


9 8 16 7 


81 


10 3 39 23 


I 2*. so 


4 


6+043 




34 


6 4 28 39 


10 3 28 s 


9 27.3! SO 




2 13 2 27 


3 ^ 40 41 


4 








10 13 51 43 


II H 7 s6 


10 16 53.34 


, 'J 


6 22 .S 31 


4 "7 20 32 




IS 20 It 


B. 


16 


3 6 =S •■ 


24 54 27 


II 6 18 27 


B. 84 


II 14 59 9 


! 28 7 3 


6 


4 43 3 




37 


7 'S 4« «4 


2 S 34 >7 


11 25 38 10 


'i 


3 24 22 12 


7 84^53 


6 


24 2 46 




1« 


11 2S 1. 28 


J 16 14 » 


14 S7 S3 




8 3 4S ■' 


8 19 2« 44 


7 


13 23 JC 




39 


4 4 34 3' 


4 26 53 59 


I 4 17 37 




ij 8 10 


10 6 35 




2 41 13 




40 


8 27 8 ,0 


6 7 40 30 


1 23 40 30 




S s 41 38 


11 1053 6 




22 S 6 




4» 


I 6 31 13 


7 18 20 20 


2 13 13 


89 


9 'S S ■ 
1 24 2! 5 


21 32 56 


9 


)i 24 49 




42 


S "S 54 17' 


8 29 II 


3 2 19 56 


90 


2 2 12 47 




44 33 




43 


9 »S '7 >i 


10 9 40 2 


3 21 39 40 


9' 


6 3 51 9 


3 '2 52 38 


lU 


20 4 16 




44 


2 17 ;o 5, 


II 20 26 33 


4 'I 2 33 


B. 92 


10 26 24 47 


4 23 39 9 


11 


9 '7 i 




45 


6 27 14 2 


I . 6 .3 


5 22 16 


93 


3 -5.47 SO 


6 4i8i9 


II 


2846 [2 




46 


1. 6 37 6 


a 11 4^ 14 


6 28 24 38 


94 


7 J! 10 54 


7 14 S8 so 





.8 6,5 




47 


3 16 10 


3 22 26 s 
S 3 "2 38 


9S 


II a4 33 58 


8 25 38 41 




7 «6 19 


B. 


48 8 8 33 48 


B. 96 


4 17 7 3« 


10 6 25 12 


1 


26 49 12 






99 


8 26 30 39 


u 17 S 2 


2 


■* J '1 


dredSfineitherStylc, for theptefent Year'i Placei. 


! "! ■' 47 


2 8 24 44 


-i- 


24 48 22 



,, Google 



Tit ROVAL ASTRONOMER 



Radical M<». PLACES of iht MOON, (bt Tm, lod Mmii,, OU and ifa« %i. 1 


160D 


Julian Style. 1 


t6oo 


Gregoriu Style. | 


Month*. 


Mean PI. ;. 


M.PI. Ap. >. 


M. PI. 9. 


Months. 
D*. 


Viean. PI. ^.M.Pt.Ap. Ji.f M 


■ lei. M. 1 






* " ' ' 


1 1 » 




yaiKBiy I 


7 23 7 41 


6 8 as SS 


,0 OSS a8 


7«..»7 . 


3 16 31 JI 


6 7 19 4 10 


■ 37 14 


Frhruary I 


9 «6 35 48 


6„ 5, 8 


9 29 16 s8 


F^^ I 










9 IS 3i « 


6 IS 18 


9 27 48 9 




S >3 46 li 




38 19 4b 




It 14 14 


6 .8 27 31 


9 a6 9 31 


-♦"■' 9 


7 2 '4 M 


6 17 JO 4c 9 


afi 41 17 


Jt&y 


19 17 45 


6 a. 4* 3 


9 *4 34 11 


U.J 


8 7 3" SS 


6 3o 41 12 9 


2i t ?7 




' 7 »S S" 


6 as IS 17 


9 " SS 4' 


7™ 


9 >6 ( 




7.* 


3 13 3 ai 


6 as 3S 49 


9 21 20 2. 7,/, 


1 1 17 3' 


6 17 28 5t 9 


21 S2 B 


Aj./ 


S I 3" =7 


7 ' 3 = 


9 19 41 S3 Af»^ 


>9 4S 37 


7 56 11 9 


20 13 39 


Stpitmhtr 


6 19 S9 33 


7 5 30 'S 


9 18 3 23 


Siftmitr 


z S 13 43 


7 4 33 24 9 


18 35 9 


Oaoirr 


7 "^ '7 3 


7 8 so 47 


9 16 28 4 




3 13 31 >3 


7 7 43 S^ 9 


16 59 so 




9 13 4S 9 


7 .2 H 


9 H 49 34 




S ' 59 »9 


7 II 11 00 


15 21 30 




ioj9_ . 40 


7 IS 38 S> 


9 '3 H IS 


Dtcemier o 


6 7 16^0 7 [4 31 41' 9 


,,46 . 


1700 


JnUan Style. 


1700 


Gregorian bcyle. | 


J^.,^ 1 


' i 5« 7 


9 27 37 10 


5 '^ 44 '3 


y^rj 


III 1 4Z 


9 26 23 3S s 


1'7 19 10 


>-4™.J I 


7 14 «^ '3 


10 I 4 23 


S '5 5 43 




2 29 29 48 


9 ^9 so S' S 


»s 40 40 


Mar^h 


B 3 '» 33 










10 3 sa ' 5 


14 11 42 


v/jtr,7 


9 11 so 39 


.0 7 38 46 


i ti s« .6 


Jfril 


4 '6 S4 >4 


10 6 as '1 S 


■a 33 '3 


«9 


■ a? 8 .0 


10 10 S9 18 


S 10 22 50 


JW^ 


6 2 11 45 


10 9 4S 4* S 


10 57 S3 


7". 


IS 3<> IS 


10 14 26 ja 


5 « 44 '7 


^T ° 


7 *o 39 JO 


10 13 13 < s 


9 19 »4 


7-* o 


I ao S3 +6 


10 17 47 4 


5 7 9 7 


^•*- ° 


8 2s S7 a" 


to 16 33 31 s 


7 44 4 


-*J«/ 


3 9 ai S" 


lo at 14 17 


5 5 30 38 


^"f^ 


10 14 2J 27 


10 20 4S S 


6 S 3S 


&^,^o 


4 »7 49 S« 
6 3 7 28 


10 24 41 30 


S 3 J' 8 


Stpi.^«-o 


* S3 33 


10 23 27 5i s 


4 a? S 


oa*^ 




5 * 16 4S 




1 8 II 3 


10 26 48 3c s 


a S' ^ 




7 at 3! 34 

8 a6 S3 s 




5 38 '9 




a 26 39 9 


11 ic 43 s 


I i3'« 


Dtttmbtr 


■I 4 49 47' 4 "? 3 


Dtumbtr 


♦ I ^6 4olii 3 36 15I4 19 ,7 57 


1800 


Julian Style. 


iSoo 


Gregorian Style. | 


7«»«7 1 


4 '3 48 %' 
I I 16 38 


I 16 48 as 


I 2 32 jl 


7--^ 


i> S 4' 32 


. IS 2d 13 


1 


3 >i 5 


fiinur, 1 


1 .0 ts 38 


I 54 al 


/■*i««r, 


02+ 9 i8 


I 18 SS as 


I 


' 3* 3S 


M.r,i 


6 .1 ias8 


I 2J 2, 48 


19 as 30 




' 3 S SB 


I 32 J 3S 


1 




^>r,V 


7 '9 41 ■( 


I 26 so I 


ay 47 I 


^/r,V 


a .. 34 . 


1 35 29 48 





38 35 8 


Maj 


9 4 5' 3S 


2 10 33 


26 11 41 


^- 


3 16 51 3S 


I l8 JO 20 





26 49 48 


7«» 


10 23 26 4t) 


' 3 37 47 


'4 33 " 


7«/ 


S IS t9 40 


2 2 17 3^ 





as M '9 


7«* » 


■1 as 44.1 


2 6 s8 Is 


la 57 sa 


7-* 


6 30 37 11 


a S 38 6 





"3 35 S9 


AM» 


I 17 12 17 


2 10 2S 32 


ai 19 23 


Augufi 


8 9 W7 


2951^ 





21 57 30 


Siftimhr 


3 S 40 =J 


» 13 S' 45 


19 40 S3 


S^umbtr 


9 ?7 33 »3 


3 12 33 33 





30 19 


Oi7.*n- 


4 ■» S7 s: 


2 17 13 1; 


18 S3, 


OSahtr 


II f so s; 


a IS S3 < 




"8 43 4' 


M,»™fcrO 


9 '9 'S S< 


a ao 40 30 


16 27 4 




31 18 S5 


z 19 ao 17 





17 5 II 


Drtemiir 


7 4 43 3= 


a 24 1 a 




Dtumhtr 


I 26 36 3<1 


3 33 4« 49 







In Leap Year take out tie Monti Day Motion* for 7«i<flr? and feinwrjr 1 Day fooner, in both Style*. | 


EXAMPLE. 


EXAMPLE. 




r./W«i«Mw*P*«'Il.'*^.^a.>F*»w»Tl?.lT5*> ■ 


IJ, I7fo, 4> 


» n. . <^ J e 


B W. Ap. » 


a 


















,7oeO.S.Frf.i 
» Yn. Met. 


7 a4- •« ij 
1 19 16 37 


10 , 4 ., 
■0 ij s> !» 


! ■! ! 4 


60 Yn. Moc 


1 II I 4 
I 10 41 f 


» «6 »J J» 

» " JO 4S 


t 


17 19 .0 


9 'i 4* 3! 




%o JO *5 


B. D»yi 18. 
I.«.pY**r. 


7 "7 in JO 




57 I" 


B. D«yi 14. 
L«pYe«. 




' 3J 3S 






9 16 4j j< 


1 


11 »« 3 


l,,S..<l.S.M.l 


9 S ao 5J 10 


> ., , ai 


7 as at J3lli76oAf.S.3'ai..i 


■ 16 la 


7 9 »7 S'U 


»« T 7 



,, Google' 



md NAVIGATOR. 





JM>a» MoTioK oF the Moon continaed, for Months, Dayi, 


. 1 




M"". 


M. Mot. B 


M.Mo.-ip. J). 


M. 


Mot. a ret. 


E«. I. Tafimlih, ■«.» P.'««) 0/ r4< J. v*/3j«, aW Q, /.r Mjy[ 






















10th, 9liio"36', P.M. 1759. 
M.Pl. p. 




D'. 


>«. c 


0000 


0000 





000 
















.1 38 30 










S9 

()0 


^pri/ 


I zj 24. 16 

3 •); sz 31 


6 34 23 
10 I lb 


° 


3 728 

4 45 ?7 


Uayi 10 


6 J s8 7 
3 18 8 j7 

3 3] 91 43 


9 27 37 'o 
! « .4 
13 12 K 


S 'S 44 '3 




: J .; ;; 




IJO 


JlAy 


4 2i 10 3 


.3.2Z 8 





6 21 17 




■'i' 


/.«o 


6 9 38 b 


16 49 Z2 





7 S9 46 


Hoorj n 


i ^6 Js 




1 11 




■ Hi 


>y 


7 '+ SS 39 


ZO 9 S4 





9 35 6 




10 J9 




J 






^«j*/?o 


9 3 23 *^ 


2, 37 7 





II 13 15 


.Serandt ^6 






■ • I! !« 




S,«. 











M.PlictnO.S, 


4 >3 S* '3 


6 ij S9 49 






173 'Off. 




1 24 52 
• 3 52 5 




14 Z7 -Z4 
16 5 54 




4 14 56 a; 


- 1 IJ JI 


+ M 17 




jo+i AW. 


1 15 37 17 





M.PIa.fsN.S. ■, ,S 


. 4^- 


6 U 46 I7t J » . 


! ',■* 




354 ^"- 


2 .0 S4 S8 


I 7 iz 37 


17 4' '3 




M.Mo. U. 


^ 


u. 




M.i\Iu.B. 


Ap. 


a. 




Take ou: i Day fooner fo 


r Jaiimrj and f*A 


»arf, ia 


MiT 


> * m 


T-; 


?— * 




/■■ # ^ 


~i — 5 


r-» 




I^ap 


year. 




Sec. 


' ' \\ 


* iv 


» iv 


Sec. 


' • i. 


• i. 


* ip 




Uu>* 1 


13 10 3i 


6t' 




3 II 


■ I 


03256 


17 


3 8 


31 


17 1 ic 


8 ,8 


4 6 




z 


z6 11 10 


15 2. 




,6 zi 


2 


' i '• 


V 




32 


17 34 7 


»54 


4 14 




3 


■ 9 31 4S 


!0 3 




9 32 


3 


' 3! 4! 


. 50 


> 24 


33 


IS 7 3 


9 II 


4 22 




4 


1 zz 4t zo 


26 4, 




12 43 


4 


> 11 46 


1 7 


J ,2 


34 


■» 39 39 


9 28 


4 30 




5 


2 J iM'i 


33 2? 




'S 53 


i; 


2 44 4^ 


I ^^ 


J 40 


35 


'9 '2 55 


9 45 


4 38 







2 '9 3 30 


40 (J 




19 4 


6 


3 17 39 


1 40 


04S 


36 


'9 45 52 


10 2 


446 




7 


3 z 14 s 


46 47 




Z2 14 


7 


3 SO 35 


' ^7 


,56 


37 


20 ,8 48 


10 ,5 


4 54 






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Tic ROYALASTRONOMER 



I. EQUATION of the MOON, or' Annual Equation, 
c. 


Jr/mil. SUN'. Me.li ANOMALY. 


0-. 

M. 
An. 


S GN o. 


SIGN I. 


SIGN 2. 


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FortheCONSTRUCTIOK, fcetht COMMENT on the MOON*. THKORY. 



,, Google 



md NAVIGATOR. 



I. EQUATIOM of the MOON, or Annual Equation, 
c. 


Argument. S U N'i Rfean ANOMALY. 


O'l 
M. 
An. 


SIGN 3. 


sroN 4. 


SIGN J. 


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FortluCONSTRUCTION, falhe COMMENT im the MOON'. THEORY. 



,, Google 



fhi ROYAL ASTRONOMER 



II. Equation oAhe Moon, or I. SemannuaL 


HI. Equat. Moon, 
c. 


Argumm. 


Su. from MOON-. APOGEE. 




jfr^. San 2 Moon's Node. 


0i 


Sig.o, 


Sig. .. 


Sig. .. 


Sig- 3- 


Sig. 4. 


Sig. ;. 


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pro. 
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Sig. 7. 


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Tot lk« CONS 


TRUCTiON, fa the COMMENT on th< 


MOON'2 THEORY. 



,, Google 



end NAVIGATOR. 



IV. Equat. Moon. 



2O i i'iQ. 



l]^ 



s. 



V. Eq. Moon, 
.c. 



J'g. Mean EvtOitit + 
2 ]) M- Anom. 



S. 



o 5b 



o 57 

058 

o s8 
o 58 
o 58 



sU 



o 38 
o 40 
o 41 



in 



r- 



.iV- 



}^ 



11^ 



VI, Eq. Moon. I VII. Equat. Moon, 
C. B c. 



jtrg. McAB Svtaim H* 
O M. Anom. 



0? + 
6j- 






.i}^ 



U 



5}^ 



i]iii^ 



Jrg. Mttn 

Q M. Anom. 



S. 



o 28 
o 30 
•> 3' 
o 33 

o 37 
039 
o ^ 
o 41 



048 

o 49 



.;}: 



i}^ 



o 54 
o 56 
o S7 
o_£8_ 



S}1 



^!* 



For the CONSTRUCTION, ice the COMMENT on die MOON'a THEORY, 



DigHizcd by Vj009 IC 



48 



Tfo ROY A L. ASTRONOMER. 



VIII. Mean Elliptic Equatiou of the Mooh'i Cintir, according to ,o;;oj tke Mean ficcem^icity of hw Oibi 
y ^ toRailiui I t or of 5;ojo Eccentricity toSem. Tranf. loooooOt ormeaii DiAance a @. 



/irpmat. Moon's coirefted Ahohalt. 



3' 5' 



I J7 s' 

I 43 48 

I 49 45 

1 55 40 

45 



* 7 »4 
2 13 14 
I 19 I 

1 2+ 46 



An. 



2 47 26 



3 ao c * ? 



3 30 3S 
J. 35 +5 

J 40 S 

1 4S JS 



S 4 



4 '» ;? 



♦ '9 34 
42+7 

♦ 18 36 
4 3i 

4 a? « 



4 4" V> 

4 45 47 
4 49 S3 
4 S! !1 
4 i7 i3 



4 SS 
4 S3 
4 49' 
4 45 
4 49 
4 37 
4 33 

4 »' 



h6 gj 

"'9 53 
*3 H 
16 50 
29 41 

.31 48 
3S 48 



4t.5 



ill 



Dif., 



Sig. 10. 



10. 3 
II 4 

'. H . 



Uif. 



%i 9- 



_ 


uiT 


/ « 


' 


6 17 44 




6 IB 8 
6 18 Jt 
6 i3 35 
6 iS 38 
6 ,S 5, 


17 

2J 
■s 4 
II 
18 
24 

3» 
D 39 

° 45 

S3 

1 8 
' "4 

1 29 
» 35 
t 4« 
' 49 
' !7 
' 3 

2 '7 
2 25 


6 18 25 
618 ; 
6 17 41 
6 ,7 9 
6 .630 


6 IS « 
6 14 52 
6 13 52 

6 ,2 44 
6 II 30 


6,0 9 

6 8 40 

6 5 23 
6 3 34 


6 I 37 
S 59 3* 

S S7 '3 
S 55 ' 
5 5241 


S SO 10 
5 47 3; 
5 *i 46 
S 4; S3 

S 3' S4 


''4 

' 4« 
" S! 
» 59 


+. 


Dif. 



5 35 49 
5 32 36 
5 '9 17 



5 18 39 
S 14 53 



S 7 3 

5 ' 57 



4 5846 
4 54 '9 
4 50 S 
4 45 35 

4 40 59 



4 36 
4 3' 31 
4 «« 37 



Sig. 8. 



4 049 
3 55 
3 49 5 



3 44 16 
3 38 36 



» 44 
• 37 48 
2 31 23 



" 4S 
2 ; 6 
I 58 2; 
I SI 41 
' 44 M 



3»; 5 



o s6 31 
o 49 29 



65 54 



§44 



6' 



-J- 



Sig. 6. 



Ex. T»fiiJlheSljiuUi<m'm*iS' i enrrtSeS^ntmaljf' 
ConftniCUon, j Arg. coirc^ed An, . . . 24° o' o' 
B7 Tab. for red. com. Eq. > , . C. Eq. . . + i 23 p. 8». 
.-. . ' ■ Ta' 



Elated i Anomal}'. 



2J 
Cawft. Log- + 



Com. Logi 



9.6490S3J 

9.952r?53 



Setfiirther an. Jot put 
SeUtiox 0/ tit Kep. 



Fromthecor. I Atioin.dedaAi tr. An. si 4.5 4,1 Tan. q.^omBqi 
Difference-^ 2 14 i8=tEqaat. 

Doubled . . 4 z8 jfia.ln; triie£q9;itjo4>re(t. 

N. B. In the J j^^ 6 Signi when the jjS ^"■'"'•- •"'■•l^} theSigaof EqaMbn ii ^— J 



' N. B. 7ht Mton*! tamaid Jmmudj, er ativi Jrgimmt, ii ier whom Jmiafy arrived hj ibt VU. f^tgoimg, tr Fiift 

. IX. 



,y Google 



md NAVIGATOR. 



IX. EVECTION-EQUATION of the MOON : Or Second Equa 
TioN of the MOON'S CENTER. 



Hunt. TnieEve&ion ; Or M. EveAion^^ M. EquatioD of the Mooh's Center, according to its Title. 



-H- 



Sipio 






Uif. 




^ 


o o o 


1 a4 



8 -.9 
9 42 



o 16 }0 
o 17 5 



o as 49 
o 27 



z8 25 

o *9 43 
o 31 o 

o 33 r 



o 37 
038 



%■■ 




- 


Dif. 


• ' ' 


' 


OJ, ,. 


I It 



%. , 



40 s+ 

o 42 
04J li 
o 44 a6 
o 4f 3i 



4' 45 
o 47 s; 
04S 56 
o JO 



o S3 '! 
» 54 "S 

o ;6 



° S7 ■' 
058 



! 48 

! 4" 



6!i 
7 4° 
« M 
_2. 



Slg.. 



Sig- 3' 



10 2; 
20 26 

2D ZJ 
20 22 

zo 18 

20 I^ 



20 6 
19 s8 
■9 4S 
'9 57 
'9 24 



! " 
18 37 
18 18 
'7 S9 
'7 57 
■7 '4 

'>S0 



.6-2, 
■i S7 
1; 28 
■4!» 
H27 
13 54 
'5 20 



. SO 



7 

9 

19 

22 

o 25 

27 

29 

30 

JI 

» 33 

o 34 

o 36 

o 37 

.?» 39 
•> 4> 



Kf. 



S.E. 






Uif. 






. .0 5 




1 9 27 
1 8 44 

■ 7 59 


to 46 


I « 27 


046 


• S 39 




' +-*i 


51 
" 53 
54 


I 3 58 
■ 5 S 
1 2 11 


I I 17 


iit 


59 24 
58 26 

S7 'i 


° S7 


S«-27 




ss 26 


I 2 


• 54 21 








052 ,6 




51 11 


; J 




; ? 


48 5I 


47 St 


■ 9 


4£ 41 


45 31 


1 10 


44 21 




°4S ! 


H 


4" S' 


:!] 


040 4. 


+ 


Ui^. 



' 40 43 



o 39 30 
o 38 ' 
" 37 
o 3S 43 
34 



o 53 9 
o 31 SI 
p 30 J2 
o 29 13 
" '7 53 



o 26 33 
o 2; 
o 23 50 



a 19 44 

o 18 21 

o 16 S7 

= '5 33 

o 14 ID 



o 12 47 

o 11 22 

■■ 9 57 

o 8 3 



o 5 42 
o 4 



Si;. «■ 



N. B. U.Jmm. t,±iM. Sfa^i, > CnAr, (odHlwirc otM i tk« effiptk Eqatties) «rMn«v ttiti^klt, w 
krb ECCENTRIC ANOMALY i/I^Afto. 

.«i/ (^ Eccntric ^Amw^ 2 — 2. O « »*j ..^t^. w»i!f if tbt Arguunt ^ fi« EVECTION EQtTATIOH «/* /. 
Pot die CONST RUCTION, fie tbcCOMMENTontlc MOON'i THEORY. 



dbvGoogle 



so 



«/ R G T A'L ASTRONOMER 



X. COMPOUND VARIATION-EQUATION of the MOON, 
c. 


^«t»». MOOH EquKd Srm tbc SDN'a Tmi rLACE. 


12 


Si|.o. 


Sig. .. 


Sig... 


Sig. 3. 


Sig. 4. 


Si,, s. 


51- 

tnw. 


+ ■ 


Dif. 


+ 


Dif. 


± 


Dif. 


— 


I>tf. 


— 


Dif. 





Dif. 


.0 








' ■ 
















* ' 


IE 

11 

11 
«S 

*4 

Z3 

21 

\t 
\i 

•f 

14 
13 

11 

T 
1 

4 

3 

2 
1 


5? 

enie. 








1 19 
1 19 

:^ 

I 18 

\\i 
1 16 

' 'S 
' "4 
1 ■! 

1 It 

; t 
' 7 
' 5 

' ♦ 

' s 

59 
S7 
OS! 
;z 
so 

s:i 

ts 
*i 
40 


J! 19 


37 
34 

Hi 

z6 
n 

18 
<, 16 
>3 
10 
7 
4 
t 

4 
7 
9 
la 
»4 
17 
lo 
23 

til 
3- 

33 
,6 
03S 
40 


3- " 


og 
o4« 
49 
S." 
S3 
S! 
S7 

S9 

1 1 

■ 3 

; t 

> 7 
» 9 
I II 

I IZ 

> 14 
' 13 
1 14 
1 Ifi 

I 16 
I 17 
I 18 
1 iS 
1 18 
1 19 
I 19 
I 19 
1 19 


s 


1 19 
I 19 

:;i 

■ "7 
t ,6 
I t6 

■ 'S 

■ IS 
' 14 
' "4 
' "3 

I t2 
I 10 

• 9 


34 26 


038 

36 
3} 
30 

z8 
36 

ao 
17 
IS 

ri 

4 

1 
1 
5 
7 
10 
13 

iS 
19 
21 
24 
27 

JO 
33 
3! 
37 
40 


34 3 


42 
45 
47 

JO 

SI 
54 
57 

si 

1 

\l 
> 9 
1 10 
1 12 
' 13 
' '! 
I 17 
I 17 
I 18 
1 iS 
I 19 
I 20 

I ZI 
I 3] 
I 21 

1 22 
1 2J 

I 2J 


1 

3 
4 


J 57 


3. 56 

33 30 

it t 
H '9 
34' SS 


30-29 
■9 43 

IS '1 

«7 >! 


S !7 


3! 4 
3! 40 
}6 ij 
3« 45 
37 11 


nil 

3> 49 
30 59 
30 8 


6 
10 


10 IZ 

I. 38 


3! '9 
3S 40 
3! 58 
3f ■♦ 

30 «7 


26 21 

25 27 
»4 30 
23 ji 
22 JO 


9 4« 
" 4 
12 19 

\ilt 


37 37 

37 59 

38 s. 


29 14 
28 ,7 
27 19 
26 t9 
*! 17 


II 
It 
■'3 

H 
IS 


'+ 7 
16. 3» 

.-5 :s 


3' 37 
30 44 
35 49 
j6 50 

.36 49 


21 27 
20 13 
19 17 
IS to 
17 ■ 


16 12 

\lll 


39 3 
39 i« 
39 18- 
39 " 
39 21 


H 13 
"3 7 
22 
20 SI 
■ 9 41 


.6 
17 
18 
'9 

■ ao 


19 ss 

21 

21. 4 

'\ s 


36 19 
36 17 
3< 3 


13 26 

12 t3 
10 S9 


21 S3 

>2 S» 

H ' 


1 ! 
1 3 
1 > 

I 

S4 
S' 
49 
47 
04s 
42 
4» 


39 » 
39 i| 

39 8 
38 58 
38 45 


in 
'4 .44 
13 '? 


Zl 
IS 

*5 


3 5; 


3S 4; 
35 >6 

" ! 
34 38 
34 'o 


■9 43 

8 27 
7 to 
! !■ 

4 34 


27 4 

28 2 

28 s8 

29 52 

30 43 


38 2, 
38 10 

37 49 

'i \l 


12 9 

to s> 
9 1' 
8 12 
6 ,, 


z6 
'9 


29 J9 

30 IS 
30 58 
3' 39 
!■ 19 


33 39 

H3^ 
31 s= 
31 u 


3 ■« 

41 

1 


3" 32 
32 19 

" J 
33- 40 
34 20 


36 23 
35 !! 
35 " 
34 43 
34 3 


2 46 

■ *3 





Dif. 




Dif. 


5: 


Mf. 


+ 


Uil. 


+ 


bit. 


+ 


on. 


Sis>li> 


Sig. 10. 


sig.,. 


Sig. 8. 


Sig.;. 


Sig. 6. 


; - FortkB CONSTRUCTION, fe.tlieC0MMH)To.llttM00N'iTHEORr. 



* Google 



mi navigator; 



fcQRAk<M^16M of Men Va„at.o», t&«!>.g. 78-) 

By D«iin«I Mnltiplien, 

To be WA/ to, w fiAtrailtd Uota, acewdiitgtolti 'Htle, 

the preceding Cemptiaid faritaitn. 


EXAMPLES of t1i< USE. 


E4.0FM.Vj. I) in Oftor 

ltf.0ir.OuVi.iiiPi. 


Sdii*i Man ANOHALV. 


THE MeximuM of the foregoing Ej«»thB Ji the; 
fameaiiliideterramed byDr.Hartfj, the Sun being 
in Ptrigttn 1 wiK. «' 4*. itfiitraJJi from the A/m« 
fariMhM in ihtFirJl, indft*--/* Quadrature, of the 
Sun*i Anomaly i and «M to it in the 5«w.^antf 
rterf. It i», whentbe Earth i» in JfitUta, i' 54^ 
o»Iy. 

TTie Readinefi or Paciiitf of working by diefo 
Mnltiplier* u equal, mt jM. to that by the Le- 
giftiJlLos^tbm.. 

EXAMPLE r. 
5 i 10' 'S'- 5'"''* Anoro. 0' 0". 

Grft.M.Var. 3s >o- Eq.ofVar.124 — 
Ctrriaiim — t 54 Dee. Xr. ,92 


jirg. J a ©. 
Sigm Mtd lUiritt. 


pro- 
per. 





t 


a 





. 


z 


3 


■ 4 


5 


Arg. 
pro- 
per. 


— 


— 


— 


6 


7 
-r 




Xn 


X,. 


xri 


xn 


Xra 


Xr» 




Dec. 


D.C, 


Dec. 


Dec. 


Dec. 


Ok. 


• 


I 
2 
3 
4 

2 
10 

11 

13 
■4 

■J 


1 
•3 

30 
34 
38 

1 


109 

"4 
116 
117 
119 
no 


107 


.9* 


,!o 


.48 


,02 


.49 


,86 


30 


loS 
103 

lOl 

98 


.9a 
,9' 


,»o 
,79 
.78 

•11 


.47 

■43 
>+' 

.40 


,00 
,OJ 
,0+ 

.OS 

.07 


•S' 
.S2 
-54 


.«7 
,88 
.89 
,89 
,90 


19 

2J 


9» 

83 

80 


.9' 
.9" 
.9' 
.9" 


.75 
>74 
■73 
.72 
.71 


.38 
.36 

>3S 
-34 

.33 


.09 
,10 

."4 

.16 


.38 

.59 
.60 
,6. 
.61 


,9' 
-9' 
.9' 
,9> 

-^3 


"4 
23 

ai 
20 


Pref.Var. 33 16. 


C. 248 

.,.6 &«/.f*-. 

36' 49' 

/«— ii4',o8 = 1 54— 


Q^e& 


''4 

'H 

'?4 
■'4 


77 
74 

11 

.62 


.90 
,90 

il 


,67 

,66 


.3' 

.30 
,a8 

.a I 


,»o 
'.'4 


.70 


,94 
.95 

.96 


17 
16 


Gr.M. Var, ss'io* 
For Sun'* M. Anom. 

Pref. Vat. 33^ i6« 


1310 C«-.r*»-.— 34 ss 
0242. Sti p. 7j. , C. 


2562 . . HaAf. 


« 

'7 

, IB 
'9 


66 
70 
74 

:5J 


"4 
"4 
1'3 

"3 

123 


58 
S4 

4* 


ii 

,88 
,S8 
.87 


,64 
,63 


,10 
,18 


.»7 
,18 
.30 


.7' 
.73 
f7l 


.97 
.97 

:'! 

,98 


'4 
'3 


C*mm*» - I S4 

EXAMPLE II, See Page j*. 
ji 2 <» 25*. San'i Anom. 3' t6«. 


»3' 

30 


S3 
S6 
«9 
9« 
Jl 
98 

103 

107 


119 

"4 

111 
111 

109 
107 


3» 
34 
30 
26 

21 


,86 

;?5 


,60 


,16 
,14 

.09 


it 

.37 
.39 

.4' 


,77 
,7« 

;5I 

,81 


.99 
.99 
.99 
.99 
1,00 


9 

8 


M.Var. i6's6'. Eq.Var. 95* + 
CtmaiM + 40 Dec. X r. ,41 

Pref. Variation 27 36 , . C. 190 


18 

'4 
9 
4 


.»4 

il 

.Si 
,So 


>S4 
•S' 


.07 
.05 
.04 
.03 


»43 
.45 
»47 
.49 


,8s 


1,00 
1,00 

1,00 
1,00 
1,00 


4 
3 

2 


SmP.73, rortt^'t 

litaafarialitH. On 


+ 26'4i' 

»<W#i» + 39*,9o c= 40 -[- 


M. Variation 26' 56' 
For Sitn'i Anom. 

Pref. VariAtioh 27 3; 

CtmSltH + 39 


3479" Cor. V. +29 21 
9896 SnP.Js- C. 

337S..^-/''^- . " 


pro. 
per. 


T 


:4^ 
4 


T 


Xr» 


Xil 


Xr* 


Xn 


xn 


xn 


Arg. 


It 


.0 


9 


8 


7 


6 


per. 


tion ! to D/. io SicWr 
of > Des.«, to tic <^i 
to, er >fcr*9^ frcn. 
theprelnE Mod Vuia- 
. ooa, for the Virutum 

'>t^iar„Sf"oS: 

AiZ», ]]a0:toCor. 
M. ViT. to e An. :: So 
i-.uX'.H.'lly. JiQ 
o'V^q-Ss". ©An. 


•^tiirwjt. jttarjitg i» lit l^iH-tiil Ltgfllbm ftr nrnaiwt HiIJct'i Siva P'trUtao. 
f £' = Minota and Saoondt in IB* £<|ittCMaof meia Viriilion in OOiBU. 
ni»n J S' B tilt SeugtGmal, in MJwM and j'm^i, anCmrini toLa. Log. Sun'tmun Anonily. 
"""* }>' = Ibr little EsuatioDinMiuuln and Stcoadi to be addedtoarrubuaacdfroinE, according to DaQ. 
1. for tbc l^ariacion in Paiirt 01 Apopc, nfpeOlTelT. 
I'm es EqnatioH of CrniOiim, (bugbt, in Mj'uvn and SKmit, to find » F 

kttJijE'X-^ «£'+/-. Kmm, bjT»nrpofiaonairfDitifionI!'X4;>-^'s,» J^j,! ,s* 

EXAMPLE. T.jS^fi<Ml,/ri/fi«->».9. &»'.W«-A-»//f d'bvCjOO 
TowWAAb. P.7». ii'oooil ta'™"f)if.6o'— t'i(''=T('{-^"l''=.S5.*'f' >>«»*"«be«- 






















D 


z 





^le 



4» 



«« ROYAL ASTRONOMER 



XI. Metn ItiDVCTiOK -M- 




E,U"T<o. o^tLetloo.'l 


qiiiATioN of the Moo» 


MOON'. Mem LATITUDE. 


Mean to her Triu Lati- 


to theECLIFTtC. 


At the mean Ikclihatioh of her Orbit. 


TODE, for the prelent In- 


C. 


C. 


dia, of her Orb. C. 


Ar^. J) iQ Orb. i O 1 cV • 


Argknuat. li tn Oro. from the Node 1 eq 


^ry.2 Ja0— lorego Ar.Lat 




o.fi 




2.8 


» i*l 


O.N 




i.N 




2 .N 




O.N 


i.N 


2.K1 


> 


i 








i 
























— 


— 


— 


? 


6.S 




7.S 




8 .S 




6.S 


7.S 


8.S 




' * 




•■ 










1 § 








/ * 


o 





6 I 


6 I 


3" 





000 




2 34 4 


♦'! 

4 36 
4 32 
4 30 
4 2S 
4 24 
4 19 
4 '7 
4 13 
4 9 

4 S 
4 2 


427 2 


2 40 
2 34 
2 30 
2 24 
2 19 
2 H 
2 9 
2 4 
> 59 

■ S4 

■ 47 
•43 
1 38 
t 32 
1 27 


9 


4 =5 


7 40 3o| 




14 


' ■> 


! (I 


29 




s 2. 


S 23 
S " 


2 38 42 


4 29 42 


9 


4 33 


7 45 


*v 


1 


29 
4> 


6.S 

6 31 


S « 


"7 


3 


10 45 
16 7 


2 43 ■* 

2 47 SO 


4 3" '6 
4 34 4^ 


28 


441 
4 49 


7 49 

' 54 


»7 


4 


s» 


6 j; 


S 3° 




4 


21 29 


5 22 

S" 

S 20 


2 ,2 20 


4 57 ro 


37 


4 57 


7 S8 




-1 

7 


I 12 


6,, 
6 37 
6+, 


, 20 


24 
■3 


7 


26 51 




4 39 29 


046 


5 4 




IS 
*4 
11 


1 26 
' 41 


5 10 
5 ■= 


32 12 

37 32 


5 ' ? 
3 S »» 


4 4' 43 
4 43 s; 


SS 
■-4- 


S ■». 
S '9 


8 6 
8 9 




' ^^ 


6« 


4 SO 






42 52 


S '9 


3 9 4S 


•4 4S 56 


' '4 


5 27 


8 13 


22 


"? 


2 Q 


6 4» 


t )9 


21 


9 


048 1, 


3 13 S« 


4 47 i'i 


1 23 


S 34' 




21 




2 23 

3 17 


6 ,1 


+ 2« 


•<7 




S3 29 


S >7 


3 18 7 


4 49 49 


I 32 


5 41 




20 
19 


6 i4 


4 17 


5846 




4 S> 3' 


■ 4" 


S48 


82, 


la 


J (O 


6,1. 


4 5 


18 


12 


' 4 3 




32614 


4 S3 19 


1 JO 


5 55 








^ ? 


«5- 




17 


n 


1 9 .8 


S >4 






4 S4 57 


1 59 




8 2, 


17 


U 


H 16 


O!: 


1 4> 


16 


■4 


1 '^ 32 


3 34 7 




4 S* 29 




6 9 


8 3' 




H 


^ 2q 


17 


3 25 


'4 


^i 


1 "9 4< 


S " 
S 9 
S 7 


3 37 s« 


346 
3 38 


4 S7 S' 


2 17 




8 34 


11 

'4 


i 1" 


*(? 


, ,6 


1 24 SS 


3 4* 44 


4 59 16 


2 26 


6 22 


» 36 


:^ 


rsi 


6 5? 


3 3 


M 


'7 


1 30 4 


3 4S 27 


5 032 




2 35 




8 39 


»3 




6 j6 


2 « 






1 3S 12 




S » 4' 


1 4 
59 


2 44 


6.34 


8 4' 


I2i 






M4 


2 W 


11 


'9 


1 46, If 


S 4 
S 3 

4 58 
4 56 
4 S4 
4 S" 
4 49 
446 
444 
4 4' 


3 S«40 




S 2 4' 


2 S3 


64. 


842 


tl 


ZI 


+ 28 


6,.. 


2 « 


9 


20 


1 45 21 


3 S'lo 


3 2S 


S 3 4! 


3 ' 


' 47 


9 44 


10 r 

9 


+ « 


64S 




> SO. 25 


3 59 3S 


S 4 39 


3 >o 


6 53 


846 


2! 


4 ?o 


6« 


> (S 




^^ 


'M:"> 


4 2 57 


1 ■« 


S 1 27 
S \ 9 


3 "9 


6 59 


s:^ 




*1 


T 


6+1 


1 4' 


7 


^3 


2 23 


4 6 13 




36 

31 
26 






7 


*4 

Zfl 


S 10 

( 20 


63, 
6 11 


1 26 
1 12 
s8 


a 


24 


2 5 '9 
2 10 13 


4 9 26 
4 '2 33 


3' 7 

2 S4 
2 49 
2 44 


S S 4! 

5, 7 16 


3 35 
3 44 


7 10 


^To 


J.-. 
4- 




6 27 




4 'S 37 


S 7 4" 


3.52 


7 21 


85. 


*7 
ztl 

30 


s 39 


6 21 
615 
6 s 
6 J 


Q 4J 
29 
1, 



3 

1 


'7 

28 

»9 


*.»9 S3 

2 24 39 
2 29 <3 

2 14 4 


4 >» 3S 
421 29 
424 18 
427 2 


5 8 2 
5 8 16 
S. 8 24 
( ,8 28 


4 


4 ' 

4- 9 
4 >7 
4,25 


7 26 
7 3; 
7 3' 
7 40 


8 S«, 
8 5' 


3 

2 
I 


1 








.i.i 




lu ..ti 




9.S 




11. S 




9.S 










1 




"rs" 


Dif. 




Dif. 
















9-3 


4.N 


,.N 




S.N 


4-N 


3-N 




ti 1. Art. "=■■ !-«■ 9' • ■ M- J«- !•• »'2«' S. 






Jri. EqoMioii J- : . Rp 


wr.-. 8 s»N. 


Latitude AmlJfrgunu^ ot %-. 






Tnu Latitwlc 2 . . 4 59 36 S. 


qnaiioa bdng 

?«.<? ij ' 5N»N,S&S 
O^i iN*S,S&N 
thefpiflriMwillbe 5^ I 
rejpeaively: coirefponding 
ifl» the /re/r« IntliwHim 
of the Moon'i OrA. 

C^ Increaiing an.d dimi-. 
oilhiDgthe above Eq. inrri- 
tSfU Rati* 01 tiun^ Did. 
willbeneaier,*.a.o'27-± 


to the Table of K«r/«r>«», 


£r. 2, .*•«. M.Ut. 2- io« . . Ktt«. 4*49'49^* 


p. 50, together correfpond- y . -*i. Equation s'S" •• Jf 


"». + 3 44 N. 


titn of the Moon's Or*. 

For, B* mmy 5««i<6 in 
{he true campotmd Variatitn 
are omitted, -utK, i^', ai 
Z)i/. between the Sitan, and 
greaitft or leaft £*((/! a- 


1,^1 

SigDi Aig. 

»», 0. 1.2. N.A. 7 
J. 4. c. N.D, ' 
Sr.A. NontAfcendtai! fs 


•1. » 

eieot 

Sir 


■ ■ 4 S3 
iidin.of B 
i» Aig. 


A. 
D. 

dim-. 


T.I. %.%. 
9.10.11. S. 

A. Sooth Afcen 


™*""'" "* . H N. D. Nurth Defcendmg $ S. D- Sooth Defcending. 


atahlunmum. 



,, Google 



'end N A V I G A T OR. 



lii*0M HoRizoHTAL-PAR-AIXAX of the MOON, 

in Sjxigut. 

Bccentrici^X S$o%a to the middle State of htrOrbil. 

Her Mean Dift fr. Q being locoooo. ~ 



■Jrg. Moon's Mean Anom. tt eq. or eq. by the !i. 
or M. central Equation, only. 



Sig. o Sig. I Sig, 2 



S+ '4 

5+ 'S 



5.5 S 



Sig. 9 



Sig- J 



Sig- 4 



S8 57 



S9 JO 
59 »3 
59 *S 
59 28 
S9 i' 
59 33 
S9 3! 
59 38 
59 40 
59 4^ 
S9 41 
59 46 
59 48 
59 50 
59 S' 
59 54 
59 56 

59 s: 

59 59 



60 15 
60 -' 
60 

60 18 
60 I 



60 1 



60 i 
60 33 

60 2J 
60 24 



Sig.fi 



I. Ef^vATian 
Cf n't hor. 
Parallax. 



The above JUfAi Paj-allax, iaSjieigut, and thai. - 
all Pofitioiu of Che Mood and Sao, oriniDy State of 
the Moon'i Orb, adJi to the apparent for the true Alti- 
tude of the Moon i and coDfeqnently _^^ra^/ from 
the apparent for the true DiSknce from the Ftriix, 
and the ctntraiy. 



Arg. Mcanf- 
•otSian. 



5 4 3- 



II.Eq(JATioi# 
of D'thor. 
Parallax. 



drg. D'liri 
Long, i Q. 



Horizontal Parallax ]) to hu 
horizontal Diameter. 
SS' 40' to 30/ o* i« Gn7/». 
SS o tojo o Moftr, 
60 48 toj^2y Hallrf. 
57 ^o to }i 30 Kmiteu. 



EXAMPLES, 
in and QOLjof ^jfu. 



SJ 



EXAMPLE I. 
Equated AjuDi. o^ ov, 
c» o* trne. 
Mao H. P«r. 54' lo'lMEv.o* 
Equation — 4> I 

TmeH.Pir. jj ig fc. 

J3 19 JHalUj. 
E4.An.e»6e BiOj»l6i>»- 

H.^TEaioai I41 H 

iS- 

MnnR.Par, j4'io«-* 
E^natioii — 18 i ' 

True H. Pu, 5J a fc. 

EXAMPLE II, 
E^.An, 6'. Bio 61 > o" 
M. inOion 61 J^a" 
Mean H. Par. 60' is''\ 
Efloatio,. + +1^ f 

TrutH.Par, 61 7 fc. ■ - 

61 7 J//<%. 

Eq. An. S- B J© 9*ii' o*- 

. M. E«a»no'J 4» - 

Equation lUi''- 
MeanH. P«. eafis"! 
EqoatioB — r 4* [ 

TtujtH. Par. j8 4j fc. 

j8 43 Jh1i%. 



Eq. An. 6i oo. Tr. An. j' 1 

[.os6Ecte 
MeiaH.Par.6o'is''l6o'l7|i' i 



ti. B. J equated Aoom. — Hi© faae ^.= An. Arg. where i Eq. Ap. i only 
> Mean Anom. — ». An. Argament = Mean Eveftioii = a. M. PI. 5 a © -- 
JeqaatedAnom. — An. Arg.= J) i © 1 the B '« PI being the fame equat. 



Tn«H,P«.j9'j6''ljs'ss''^ 

EXAMPtB IV. 

M.Ev«,ji7»«iJ , . , , + o , 
M«n Hot, Ptnlln 57 1 

TnieHof.PariI]«..C, t6 1 
B, Hiir,j , . |6 a- 

t> We tall fliew the K»iufti 
of theft Argument] of ParaUax 
S>ll,fi and HiJi,', to thtfc, h« 
after: Or, taking + f,t tK«e,,h 
»iri — for the mwaj Sign, ■ 
Hhf*"' .>_E™'Bq.Ti4Eq.A 

r-"''A, 

I— Oor'*' 



■ concerned. 
-B'>U..AnoiB«fy< 
with 1 1 Anom. 



,, Google 



tit ROYAL ASTRONOMER 



1" 

§0 



K 



EXAMPLES Q{ii<Hatfi6»t*^'^"* P.LACES^f tfceSUK and MOON. 



r«rdM-SVN') TnM PLAC-E. 



I71J 
M, .7. S. 5j 






A.uM. Tiroel 
- I- !«' I 
For fp/. Time. » abow 



Sun't LtWffwfc. 
♦ »♦ SJ »J 



Jl 



To fiad tha gUlTi true PLACE. 
-RVLC. CUM Ibi WCB1 Longltudb sf «£< Sun, nibU Apo- 
|ta i >J»'aR»j' f£f Litter /n« (it Toriner, /tr fiv 5n'i a<« 
4wiw[{r) (• ^bicb fxi ibi Sjraiai tf tbt Sun't Ctmtr, wbidi 
immfhd viirt tbi Skm'i mtnPlati, aterdiwj; li iti priptr Sign, 
jivuAitlnnPlaa, firhtctrnTme, w^oind. With which PUee 
caiiB£fij]ie^gt..r<;uiIU) thefquatioaaf.A,t<iM.TiiDc>faTO'i 
Plitc, tffamiTimi, required, 

Edition of ■ppurnt-ta 3f«H Time, 
-■ ForthB 

t Or pivportien ibc De|> by the tr. Jtuni. Mot. S7' M-"- I*- '95- 



For the M O O N'l Tme PLACE. 



^!* 



"-^5 



? 



fc 






^1 



M. »7. S- SJ 



^ Anoai. gEqi 
C)Rp. «"-. Equilio 



Eqim.Prectf.t'.3 



Moon't Ltmruiuli. 
U 1' jt 42" 

s Si 43 

IS 18 







Mooa't .^iga, j eg. 



{Mun K. Par. eo* 11' 
Jtr.iQE,.— o 17 

Tne Hor.Pat. J9 4« 
By(P.7g)Ba% 5, 47 



5 Jl 



B^0 



IX. Are,offwAi« 



Arg. 



t .1 

» 9 48 

1 , „ »3 



9 3° 



Iif.IifirliriibC.^^vi 

tf.Jir itr Orbii fita. 



C Orb Long. jj', 

](I.])>mOrb^a.LAig.Lit.> ibjj'iG 
'--)tQ— l.Ar.ll.A.g,Lit.fEq.+g 9 



])'■ tnie Lit. N. 1>. 3 I 3j 



i 39 



JiDAp. 7 I 



I B S O «■ 19" o' 
J.Aig.MJd^ *j 4j 

lI^Arj.Eq.tjt. j jj 1 



tne rrecepi in wi: rit>"* u.i". ...j-^ . ^y. .._■...■ ._ 
the ipp. aboTC ind tnie Semi-Diuncter of the Mdoo, in 
Time, ^ih Refp«a 10 J '• Alt, uiil Ul. 01 Declinitioi 



^A 



tifirtnd iMgini^i than ii totn£tti b; + 14'', iCtardlM *° 
" ' -- '•- BtO^'Mjt/lmmiailTmiliti being tKe Dif. of 

* .1.. .. — =- Leog.oiR. A, eliny I 

a: Ot. He/ltf hiTUig J Sun'i correatd Pltcs : 

deduc«dhii&Hr i'/«ccii^iSobl'enin| either Umb of the (, finiiBhcTir^inflcad DfllcT (rwDiiin.M thoATimetj 
4o'xg''to 31' 17" '"*> tio'to 3 3', for the hocUontBl PmlUl to tb( hor.Diani. of the Moon, bein| u i W|SJ, 
L^, 1596 being >dd<d to the Log. Log, of ihehor. Pat. mil pTCtheL*,Lae,of the Moob'i hor. Diua. Or {, -i 
botiiontd ?ii*Hr\ *= homentel Diuneter of the Moon. 

! ILo.Log. 1 Or, ]) '■ ^o*- 1*"* S9'4'^ ^ SS''7^ 

EXA^I ^, in'ihoiiwnlilPinllu J9'46'l 0017 I — — .35 X'- 

+ »59' 1 , i ■ ■ »9 13 

tB ■ 3 59 ]»'iEfi! 



-1*1 horiiontal Diameter 31'ja'l >6lJ 



f^ ftf i tmt m tffi, laUrigr-t EntHifi in fie Mm* 



MmttPlta » Mr Hfmd, tUi^th 



r, II, IH. ly, T, VI, . 



%t 



DigHizcd by VjOOQ IC 



Md N A' V=I G A T ft. 



5^ 



REM A RRS on Mr. MJrER't Accilbkatiok of the MOON'i Motion. 

Mr. MAYER hiTing {tii, dwt hj cOjnp»riag feieril Piriidi ef BtUpfa together he ii jjcertsined of the Moon*! Modon being fn/cfar 
sDiafbnner Agei) »nd thil in 60 Ye*" it ii t' 9" fajler thsn Hi^/gu or «irTibIe« rqirtfenc j^ I bid therefore ■ Mind to Oy, whether 
_ an fcW Etlipfa (whofe Beginning »nd End are much mwe iccurjteliF determined thin batr Oau ; ind which, if central, or oeuljr fc, the 
Errac of ■ M«n in Latitude wili not mikt any fenlibie Error in Ihe Scinpiei of InddenceJ 1 eonld colleO' an; ^cJvmltm bcj^nd what tlie 
BTclcnt Tibki reprafeDt. 

FrntiutPafffi, I took one PtriV of 54 Veart anJ wrtiff of 71 : The^/i^fitaaxHi to i7ii;i tbeochtr from 1676(0 1748. 

EfatI Time at GnmrUh. 

Xtrtito, iSSi, Hnv/uiobferved theEadof the /<br£clipreatZ>«mac , . nk ifia ii* 

Moon I LoDgitude obfbred . . ep ii<> 4.' ^ 

ffrerof Compqtation . . + S 

d^pr^IJi 17151 Dr-Ea^^aUrrTCd the Beginning of the local /a^ Eclipli . . t^ sa40* 

■ ■ ■— Mood'i Longitude obfenid . . ({ na lo) 17" 

u Yean Diftance. Smr of Coo^tatioa > . — 1" 

ytu U iBjt, Btodiui obferved the End of a folar Eclipfe lo* a.B 30' 

Mooii'i Loo^tude obfeired ■ . n %\a %%' 17* 

Error of Computatioii ■ • ^4' 

Jilj 14, IT4S> Dr. BttJlij oblerrcd, at CiwmnVl, the End of a fpUr EcHpb . • ii^ ij» 4S> 

~ . . Moon'i Longitude obferved • ■ fl, }' s' 17" 

7a YtariDifliBcei firrir of Computation . . -f* H* 



According Id the fam 
But, 

H^ C<in6dering the D'tfUmt of Time, between AivuTiii'i Diji and Out, and the great Difference of the Meridian), the oMr AgTWnebt 
1 Compntalion, >■ well >• NearncTi of Obferration, it furpriiing, after Iqch a long Period of Time ! 

I am fenfible ibac thele ObfeiTBtiani are loo >io Co fpcak with CertuniT opon g but Cher aire one Rafa 10 biqie that the JI 
1 thiiAgedonot moth difler from ihufe let down iatarTMn though the AcceleralJao of the Moon'i Motion, for fonnn- Aget, appeari 
lore erident, ai we have Hiewn, and allowed for, luither on. O. C. 



Ad a c c o-'u n t of the foregoing TABLES. 



to the BegioaiBg of each JtEm 
Placet for the U^Tun. «hkh 
' a Daj'i MolioD ■ -- ' - 



THE XaA'/Mein PLACES of tbe SUN and MOON, (diHinguiOied ^om Mean MOTIONS) are (rtte 
Year, inihe OJtfor iVno Style, ai en-rtOed, anfwenble Coi^HiMiJcr 31, at Noon 1 Except thofe RadicalMeai 
■le idianced by a Daj'i Motion, inlwerable to cht ill Daj of yamtit at Noon { and on which Account ) 

fubdiifled in the Computation for Leap- Yean, or i Dij !elt taken out Tor, in the Monchi oljenntij and Fetraary, u being tKe Dioctcr Method j 
inftead of adding! Day and Day's Uotionfot ill the Month) after F'cjruai'ji, accoidiiigto tbe oldMeChodin all fotnter agronomical Tablet, 

The mean 01 middle Mqtiont, in refpeft of Time (dillinguiAed from tbe radical mean or middle PhicetJ arc erer; where propi 
DifereiHMof iheradica- - "■- -- '- ^'- "- " ' - • "- --:—-' ■^^-- 



11 for both 01 



Time (dininguilhed from the radical mean or mil 
,«■«.», Slgni, Deirai, &r. for dlFFereot Poinll ol 



t the Account of Tin: 
nalce a double Com| 



infciled to f.'ii the Porpofei of Computation for Time back (befori 
>y the New Style, wii etiablillicd. By thii Meant ihc Compoter fir/ 
icion correfponding^lo eiibci St>te, and chcieby find the Agreement in 
Or finding a. DiE^recuent of bo^ Methoda, he may pttKccd to Jilia 



i8s», N.S 

tall, bvoneAddh 

We ban aKo gi 



The laJicgtman Placet and Motio 
ew Style) aa well .1 for Time fi'-B«.rd, fi 
.-ducingtbeDanof on« Style to the other, i 
iheReTultof bothMcihoda, when great Crrft 
bn Eriw, and difcorer Troth in the End. 

The pg^t/iflii Yiirt Motion, fuited to both Slylci, and neiei before conCiJTed, fcrve for aJifinj taor/niri-flfli'igfrom theradical mea 
of tbe SUH or MOON ; according ai the Tiirte for the mean Plicea fought it forward or backward, rifftiliv/[j, of the Time for ti 
RdoCui; being the ^bivlr^ JMiri«f of Coropntation thatcinbe put in Ptaftic*, afpeciall; with iba Muuons fot each Month-Day, ai 
annexed to it; there being only one Addition or SubttaAioa of two Linea, and then one Addition of aooihtrLioe to find the mean Place of the 
SUN or MOON, for any Day at Noon ; whateier oiiybrtheNumbcrof Yeart backward or forward of tbe ptefent Year. 

But WE have giTCn the Jt<iix« from iSji to 1751, O.S. when the Slyie receiiml Altenlion by A£t of Pjiliantnl, and tlfo from 1751 

for determiDtcg the radical mean Placet of the Sun or Mif, fai any Day at Noon, in any Year Old or New Style, of thofe Inler- 
' ' " ' in of tt« Linei, only. 

itL the radicalKitw Plata i:X the .^vr and Mten, it Che Beginningof every Mtaib, or End of the former Month, (eicept giving 
cbemfoT^fMifry f,ii]dF'rin.a>7i,atNo<in.inLcap-yeara)in the Yeart 1600, 1700, and iBoo, O. and N. Style, by which the mean Placet 
•f fan and Moon aiv had, fm any Day at Noon, in any Year of ihofe Centuries, hjr the Addition of three Linei j namely the Radii-Line, 
Lineof the Vear'i Motion, andUneof theDay'tMotioOj intbatYeati wbcieby the Kefultef one Campucacionmiy be proved by the other, 
■onefpondingwich theDateiof the diflecentStjlei. 

Tlie Vorim of the San and31i>nare alfo given to the Beginning of each jllnr£In the Year tobeititftJto the Jt^m, anfweruig to the B_ 
Simiirg of any Year, Old or New Style, and to which the Motion ibr the Number of the Month-Day ia Co be added, for tbe Sake of f>rwry, 
and aotient Coliom . 

Ami EXAMPLES of the USE and PR ACTICE, of all tWc diffinm MttUJt of Compatation, areexMKted at the Botcoim 01 on the 
Kdc* of the Pageiat the Hr^nning of onr Work, to rnike them (/ear, and undoubted. 

There an dilfatnC MtlheJi and latla, for proportiaaing the DifTereuci of Equationi i So that the Computer may take bit Choice of that 
Uetbod which fuiia bim bcA. Thii it a mv Imfr/yvrmar we have made which wai much wanted, Co ficilicate Compntation, 
tlie Attcnlioh, We-find, by Eiperience, ih.-t fince Setegtfinali may be reduced, at Sight, into Decimalt, (fit P. 14.} that muhiplying the 
DiJirtiKtOt EqBation, by the i)i^cr«i'r of AtgumenC (leducedto Deciault} Gndt tbt frcftrirauJ Diffcieact to be added to or fubirafted from 
llie fiifi Efuaiitt, aboutit fooo ai the h^ifiital Logariitin of one of them can be found (tuining over Leavei) and Kieail* eafet Altentinn, 

~ A any other Metbod, But, for thofe who «re not expert or ready at Multiplication, they may ufe the Telia at Paget aj(, 157, ijB, 1 
^59> vrith great Facilityind Quicknefa. 

OoT TcUr. atPagei], ii a JVovi/ry, lirjttboughcaf ; but proportioni not lb (juickM thofe iufl mentioned. 
_ •IUrailatftbtteitimi\\ianPltcitaiiiMMnia - ' •- — ■■■ - 






itvibitbAtftatTimwaiJIit Aa^fnJmi, i* afflyr.f 






»6 



ne ROYAL ASTRONOMER 



PRECEPTS 



Pbk 



r 1. T.H 



COMPUTATION. 



oiJing te 



BtTj«,p.i9.Ti)woattt«B(IiUtion, atonce. Handing UBdec A, 

Jorriittraait, looifromtheapp>KinfonlieM«nTiaie. Orif tne/Uo»7.w<iigiitEn, nwoiUt 
,.nt to I'htSua'i in,.- Plaii. ani iccjrilmg to iti Sign, + Or~, aJJ or _Mlrail it, to oifromtheMci 
the CruMw/i of the formti ■Equation fbrrei)ocingApi«rtnHoMe»n Time. 

Othebwde. BjTj*. (. lO, tike out the /fr/t Bjm/i'm rorrefpondent to theS»«'»Piff, under J 
or W«B Time i« (i»en, to be reductd to the Time it^uiwd, ind fet it down with it* propet Sign, + i 
weribk to the Shb'i M. /iKsmalj, under A or M, coriefoondent to the Aposttnt or Mein 1 
dnctdtoihere^uiredTime, ind fet thii id EquH. down *ith it] proper Si^, under die \fi Ep _ , _. . .. 

Sum or Difference with the proper Sign prefii'd thereto, (adding the Eqmtiooi together, if of lili Sin,, inj puttiog tbeSi/- of Either to the 5. 
or if ofunlikeSigni taking their Di^«-nr«, and putting the Sign of the|»M'ir Equation to that Diffttenrel wlU be the Afdmt £jM(;Mof T 
Kqulred, IBheridedloorfubtrtaedfrom tbeTHiK/rmff, according ai iti Sign « + or — , for reducing it to the17r ' 



Sign, +or- 
EquiticnnandiDS under M, corrcrpan 
foitbe Appuent Time, required I beinj 

R' A, or M, ucordiog Bi either the ./IJt^iTii 
f-or_i then takeout the/«»^£fiiari'ijio 
iTimegiren, in the /r^ Equation, to be re 
J thefetwo Equationtconnefledtogc 






AmoHo the Kaiixa of the Mei 

e Sun'l Mean Place and Apogee, 

the Mamb, Cay, fl™-, Mimn 



, PLACEt/'fi-Sl 

Placet, feek the ttadin to the Year in which the Sun'i true Place irteqoirtd, {if vfmnitrn Dtti) and fet down 
n diftinAColumni for the Arpenrnr of that Year ; then i^i (he Mean Motion of the 5n and hii Aftgu, for 
Day, rimr, Mimti ton S«Win that Yev, theSumof wbich will betheSBn'i Mao Plreitoij^igu to t'btMaa Timirnjmind. 
le Veir i> far back, or forward of the prefeni Date, letdownllieM. PlaceiforiRf ofthe Centorin youwill find inp, 3, and afterwaida 
fetdown under themtheMean Motionof the Sun and hiiApugce fortbeVein fince, and under ihofe the Motioni for the i)jT, HcMr, &e. Cnce 
ofe- the Sum of which (rejeJlingKevoluIioni) will be the Mean Place of the Sw, andof hii y^Mrnfor theMranTmnsn'vi/. 
Or,' if you can find the Onrnr^, in the Meo(i-Page lo, take out the Mean Piicei to the Yeai and Beginiiin| of the Muib, then fubjoin the 
atinni for the Ti*r, D^, Hsur, ftt. Gnct that Centuijj and the Sum ofwhlcli will be the Mean PlaceofUie£iniaiidhii./^»^w, required. 
t Ettn. p. loind ii. 

NOW, fcora the Sun'l Mean Plice or I«ng. deduft IhePltcc of hii Apogee, and the XnuiWrr will betbeSan'iM>aiT.^tniu^ ) with which 
(fnmtahUpi it.) take out the Equation of tlie 5iiViC<»'rr(bT making proper Pn^mrtion for the Dif. of Equation andDi/.of Argamtntjaddinj 
orfubtnaingit, toorfmmtheSun'iMia.W^rt, accordingtotheSignofEqui-^-- ' - - ■ -T - - ' ■ -...--. , _. - . ... 

for the MeenTime, required, Sii ExumpU p. 54.. Y™ maj cotrea hii true PI, , 

PnEC. III. To ampuulbeMa-t ml rbia tit iwMi Ft Jtc%^ lit MooH. 

FROM imoag the Rtilra of the Moon, ■■ ot the Sun, fet down the Mua Place ofthe Mm, bet /^»ga and Niai, in difbnfl Cdnmni, 

awipg a Li'x under the radical Mean Place of the Nait. Then fit down in each of thefe MpcAive Column!, the Mein Motloni of theMw, 

Aptta, and NtA, for Time fine? the radical Time and Plata. Colled the Mean Lon^tnde or Place of th; Moon, and her Apogtt into two dif- 

tinaSumi, in hke Manner ai the MsioLongitade and ..*/!>(« of tbeSun itcoUeded, by the fo.-egoing frn-ipf. But the Mean Motion of the 

beiog.tetrogiade, you muftcollea theMotioniof the A't.^ iniooneSum, fincethe firft radical Time and flace, and fubtrift rhat Sum from 

rhe Node*i tadicil Mean Place, under which > Line wai drawn, and the RigJ^t will be the prefent Mein PUce of the Node ; ai the Sum ofthe ndi- 

al Man Plaeei and Motiom ofthe J W to n and jft»tf, before colleaed, will be the Mean Placet oT the Jlfm and ,^>^g(r for the Mean Tiwreooited. 

Vitc.lX- ?« a>^^fi«J(fBi'' EQUATIONS (e io-JMcM PLACES, 11 jfidbrrmipLAci. 

f.^^. (H«>lngcolnpuledtheO'itiiiePtaceuilheMeanTimefof which the B't true PUceii required) take out I. *fii«im of J), 



EquitioD+or~, and tlie AfJ'.A will be the Sun't It 
le Place, tbna computed, hjTtiU^Pna^, p. jj. 



et and Signs, u 






with which a 



and let down theit relpeOive Q^i 
ill be the Moon's Place, Apogee, anunmr, acq 
aled, and the Jl'i Anonuly i equated will reou 
tc, tfaeXf/ir/rwitt betheMoon'iAnoiiialj7.equi 
ke out (fnmf.^ij tht Man CtniraiEmaiie 
Woon'l Anomaly S equated, 
•fuaitJ itivd 1 1 ])'i Apogee, or twice Ann. Argt. indtheRemiinderwillbetheMuafvcffiM; with which 



tofO'iM..; 

I required, ibeX</uAw 
, from 5'i Place i equ 
andidpeOiyeAtgumei; 
I jfpowuify 7. rqitated t: 



lifl the 6 
which (with it! ptopec Sign) 



I. FROM p. , . , 
Apogee, and O, accordiftj to the Argi 
Motion!, which added and fubtiafted, 
■ 1. DWaflthe ])'i4|*tj«i equat 
lefi Eouatlons. taken fromtheir fever 
J. With the Argmnent ofthe Moo 
(ssmS with the 3i'jAnom.7.eqi -" 

■4. From the J'i.^inn. icji" _ , . _ . 

M;Eieaioii«™fl(withtheproperSi/»)iSumoftheMeanEclipticorcfntralEqu«tHin,andSler.Equation, II, III, IV, V, VI, VII, 
thtRiMi willbelhe.^£4. a/'£<vA'»i, foi reducing the Mean to the true Central Elation. With which Argt. of EvtSian, ttke oat f/r.f.^^) 
the £m>ffw» Eqoitior, andcBwrfl it (in itipraperSign) with J) '■ jCniii. S equated, ind you will hiTC S '< <^:«- 9 cf <^"'- 

From the Moon't Anomly gtjuaifd, dednfl O* ('* Api^ee, or annual Argument, and the Xa«iW«- skill be [he } ) Q, orAig, cf 
X/Eoaaris"; with which ("/r. P. 50) take out (hetim^WiBrf^'an'flriM-fi^inoiBi, andoonsa it, aecordiflg to/fa%'i Correflion of M. Vj ' 
P, 71, at bydedmal Xn, Pa|' 51, canntft which now rarnS ^an'tfiM with tt> pr^er Siga, and Il'i.,4i«a^ a tfMaitJ, 
J "a A»mdfy 10 ifiiatiJ. To which adding the J '1 Apogee i equatwl, (before dedoAed from J "» Plica 1 equated J ■ 
OrUl'Plur, or Longitude in her OfWr. 

6. From the Mooc'i Oriii-PUai dedufi the Place of the Ntit X equated, ind the Umaaiir will be the ]) a J3, or the Arg. fiu- the Ri- 
Mhm of her OrUl-PUei to the Ecliptic ; and alto the Ar[<,miM tat finding her mean Ltiilndi. With which jirnmrat take out the Ridaain- 
£««;«! (from Page »« and conneflit (in the proper Sign) with the S'l Orhit-Plict, (connefting alfo the Equation of Prtt^n fromPigt 
— S. nunc TiwTot at laft, if you like it kellj and yoo will have the Moon'it/n* Pii«in <*(£'c/i#<i ' ' 

Paic.V, rifiadiU MOON'i <r« L ATIT UD E .> 
_ theArgniqeiitof KjJtaitw, or of themean Latitude, before Ibund, takeout O™ Pa/* j») the Moon'i raean Latitude. Then deduft 
thiiJifrr. from <wi« the Moon from the Snn, and the Rtmamdir will be tht<«;. of ijuatiw of Latitude. With which -*j. take 
Eouation oT Latitude from the fame Page, adding or fubtradiag it, lb or from the mm Ltailydt befiire found, (aCEOidiog u it u of the /em 

"Mffma Nanie with *e mean L«itode] and the foM will hetbe (t« LtHiadi of the M<— -— ' 

■" p.,,. VI Vtjlmd tb, KOOif, iru, Buriauud V 



inn'hoiiionial Panllai,' and the Rrfmk will be the 
EXAMPI-iS, Paget t\ and (4. 

' " Paic.VII. T./f-frie MOON'i/«.t«-;»rtfl/DrAMlTER? 

ADDtbecoB*. Lo.Log. segStotbeLo. Log. of the true horii. Parallas, and their Sum will be the Lo. Log. of trot 

Otbtmiji. TaketheHalf of IbetrueboriionTal Parallaii, then take theT(ii/i< of tiat Half, and the Sunt of both will be tbetnwboi^. 
(OBttl IKameter of the Moon, required. Or multiply the horitontal Parallax by ,;; for the borirontal Dlfpetet of tbiMoai, 

r;> The trae boriiontal Paroili^, according tDHgxr, difleti ttom the horizontal ParalUi detenniaed by tbi* uid illb BaUrfi Uttbod, by 
Ja»« Half iJIfwaW of » Degree. ^^ 

' PXIC. Vm. Tf^jMfilMOONtliq^WDlAMITtl/nBtvfnKjwilEMra/OlAMITII? 

By Ttk. 1, P. *(], add the Setoadt, anlwenag to the Mboo'i EKflaan from her Apogee, and according to her Aititode, 
DuMettfi and d>* Swn will be th* apparent Diameter in Altitude, required, 

Paic. IX, 7a fadlhtMoaH'i intmi alft ^fertni'OlAUE.Ttx in LoNGiTDan u^ RicaT AietHtion 
At Cot )'| Latitude wDedisMka i ia to Rad. it fl"'* J| 't borixootal Diameter i tohcitrue Diameter 1 in Long, ot R^, r^^vArwf^ 



Tab, U P. *« J, fcr Equadoo of trtK to ipperent Biametfr in 
g|jpi»«^«/y AgiAWy fMt fiOMyhi en fir ^1"^ *&; 



leier 1 in L 
reTpeBiTely, accordlag CD } '1 Lati a 



SUI^tLEMiNTAL 



end NAVIGATOR. 



57 



SUPPLEMENTAL SOLAR EQUATIONS: 

For deremiining the SUN's troe Place from the mean, according to difierent RaJixe; and Hytathefis of the 
Earth's Orbit. 


EQUATION or the SUN's CENTER, aceording to EctenirUiiy of the Earih'i Ori,/ 1692, and mean DiUazK 
a Sun, looooo. 


Ar^u^M. SUN s Mean ANOMALY. 



M. 
An. 


Sig.o 


Dif. 


Sig. 1 


Dif. 


Sig. 3 


nif, 


' Sig. 3 


Dif. 


S'g- 4 


Dif. 


Sig. 5 


Dif 



M. 
An. 


— 


— 


— . 




— 


— 


— 




• 


a / ff 




• ' » 




" ' * 




• ' " 


' * 


" ' " 


' * 


/ * 


/ # 


- 


3 
4 


000 
I 59 

° 3 5? 
; 58 

7 S7 
9 s6 


> 59 

;59 

■ 59 
' 59 

ii 
1 58 
1 58 
1 58 

III 
• 57 
' 55 
' 55 
' 55 
' 54 
' 54 
' S3 
' S' 
' 5' 
' 51 
1 50 
' 49 
1 48 

iii 

■ 45 


57 7 

58 51 

1 33 
1 2 15 

' 3 55 
' S 35 


I 44 
I 42 
» 4* 
I 40 
I 40 

1 39 

• 11 

* 34 
' 34 
1 32 
1 31 
I 39 
I 39 
1 27 

I 2S 

■ *3 
I 33 
1 It 

1 30 
1 18 
I 16 

> '4 
1 13 

1 8 
' 7 
1 S 
' 3 


I S9 41 
I 40 42 
1 41 41 
' 4» 39 
' 43 3S 
1 44 29 


56 

° 54 
;2 
50 
49 
46 
4S 
42 
40 
39 
37 
° 35 
33 
31 
28 
27 
34 
33 

o°;i 

6 14 

8 
6 

4 


1 56 19 
1 56 .0 
1 56 19 
1 56 16 
1 sf 12 
1 56 5 


1 

3 
4 
° 7 
9 

14 

16 
17 

32 
34 
26 

23 
31 
33 
35 

39 
39 
4r 

42 
45 
4'' 
49 
s> 
S3 
SJ 
o;6 
59 


I 41 48 
1 40 48 
I 39 46 
• 38 4' 

' 36 27 


I 

; 1 

I s 
1 10 

> 13 

' '5 

1 17 
I 19 

1 20 

1 ^4 
I 25 

1 3h 
1 30 

1 3^ 
I 33 
1 34 
. 36 
1 37 
1 39 
I 40 
1 41 
1 42 
1 44 
< 45 
' 47 


S9 '5 

S7 16 
° 55 37 
°53 48 
51 57 
ojo 5 


I 49 
1 49 
I 49 
' 5' 

1 i2 


30 
39 
38 
27 
36 
2? 


6 

I 

9 
10 


11 5S 

=^ '3 55 
ij ;i 
.7 49 
19 47 


• 7 14 
1 8;, 
1 10 27 
I 12 1 
' "3 35 


I 47 ; 
1 47 46 
■ 48 ,1 


> S5 S6 
' Si 45 
■ 55 31 
' 55 15 

1,54 Sa 


' 3S '7 
» 3+ 5 

I 33 S2 

I Ji 37 

I 30 20 


048.3 

46 19 
» 44 25 

42 30 
40 34 


' 54 
' 54 

' SS 
' 5'' 
I S7 
' 57 
I 59 

1 5i, 
' 59 

2 c 

t i 

2 ! 


24 
23 

21 
20 

;? 

"7 

16 
'5 
»4 
'3 


IZ 

'3 
14 


11 45 
»3 4! 
2; 38 
'7 35 
79 30 


■ 15 7 
I 16 33 
1 .8 7 
I 19 36 
1 21 3 


■ 49 13 

" 49 S3 
I SO 32 
1 51 9 
' 51 44 


■ 5438 
1 54 If 

1 S3 26 
1 5258 


I 39 1 

1 37 41 
I 26 19 

_ " *3 30 

; 


= 5837 
3640 

■> 34 4' 
32 42 
03043 
02843 

36 42 

24 41 
31 39 

30 37 


16 
17 
■ 8 
'9 
10 


3< ;; 
33 ao 
35 '« 
37 8 
39 ■ 


1 22 28 
1 23 51 
1 2, 1, 

1 26 35 

' 27 55 


1 52 17 
1 52,8 
1 53 16 
' 53 43 
■ 54 7 


1 52 27 
■ 5' 55 
1 51 20 
1 S" 44 
1 SO- 5 


21 

33 

"4 
3; 


40 53 
42 44 
044 35 
04625 
048 14 


I 29 13 
1 30 29 

1 34 8 


' 54 30 
I 54 50 
' 55 9 
' 55 25 
■ 55 39 


1 49 24 
1 48 42 

1 47 57 

123: 


0,834 
16 31 
14 28 
12 24 
10 21 


^ i 

^ 3 

* 4 

* 4 

2 4 

3 4 
^ 5 

* 4 


1 

5 
4 
3 


36 

27 
38 
29 

JO 


50 « 
51 50 
S3 3' 
55 2! 

57 7 


mil 
1 39 41 


' 55 5' 
.56 1 
1 56 9 
1 56 .5 
1 56 19 


' 45 3' 
' 44 38 
' 43 43 
I 4147 
1 41 48 


i 613 

' 4 3' 

I 3 47 

S9 15 


8-17 
6 13 
049 
024 


M. 

An. 


+ 


Dil. 


+ 


Dif. 


+ 


Dir. 


+ 


Dif. 


+ 


Dif. 


+ 


Dif. 


,1. 

An. 


Sis. 11 


Sig. 10 


Sig. 9 


Sig. 8 


Sig-7 


Sig. 6 


THE »feov= EfM*il«, ii McordiDE to the A>irMB« HjfMMh of the &rlh'i Otbit, and th« H>iS7« Computition, 

Rule. Kok the OifteKiice -f _ Id i T*Ue between the gJTen R»dixa of tan'i Plice lod Apotce far my »««>« gr Lut ndr, uid oor 
Sttfrin (niucti [0 the MeHdiu of GroKiich) for the fjune Ycv, uul coaoea the Eune DiSmocei with the man Ptacet of our Tabln loc 
uy Time requited i and then woik with the«^.£fK.(/« Ttt/r ai with any other, for the pieperMcia AiK«na)y of lh« Swi. 
Apogee AccordiDg to 
1 — 3" . , 0' 0" AnMM, 1 
EXAMPtE. Coonea with Mevi PUcei —to —510 Ho/Zcr, {- Then aCe ths B^tkm abon. 




























1 



SUPPLEMENTAL 



,, Google 



5« 






ne 


ROYAL 


ASTRONOMER, 










SUPPLEME NT AL SOL AR TABLE S. | 


LOGARITHMS of the SUN- 


fowgoingj-roportional Diji^cu from ibe EARTH. » the m«ui DUUmx 1 
00. And Eccmtridlt of the Earlb'i Orbit, 1692. |; 


Agumm. SON'. Mtm AITOMSLT. II 


O 

M 


Sig. 0. 


Dif. 


Sig. I 


Dif. 


Sig. 2 


nif. 


Sig. 5 


Dif. 


Sig.t 


ref 


Sig.s 


m. 


: 
M. 
Ao. • 


An. 


Logar, 


Logar. 


Logar. 




Logar. 


Loi^. 




u^. 




. o 

3 

+ 


5,007286 
5,007285 
5,007282 
5.007277 
5,007269 
5,007260 


\ 


5,006347 
5,00618+ 
5,006220 
5,006154 

5,006087 
5,006018 


6' 
66 

69 
72 
74 
7S 

\l 

80 

82 

89 

9" 

93 
95 
96 

.E 

102 
102 

104 
106 
106 

108 


5,003749 
5,003640 
S,ooj53( 
5,003420 

s. 003 307 

5,003194 


109 
109 

"3 

114 

\\i 
"I 

119 
120 
120 
121 
122 

I2Z 
.23. 
124 
125 
125 

I'd 

126 
127 
.127 
127 

;3 

128 


J.000124 
4.S9999J 
4,999867 

4.999739 
4,999611 

4^99483 


128 
128 
12S 
12S 
128 
128 
128 
127 
127 
127 
127 

\ll 
126 
"t 
123 

"3 

123 

"S 

121 

"9 
119 

iiS 

116 

■'S 

■ 1+ 


4.9961C! 

+.996069 

4>9959S9 
,,995850 


"3 

K19 
108 
106 
105 
10+ 

'98 

96 
93 

9> 
It 
87 

I 
80 

7! 
76 
73 
72 

J8 


+,9936>o 
4.993555 
4.99349' 
4.993429 
4.993369 
4.9933" 


6+ 
62 
60 
5« 
56 
5+ 

JS 

+7 
46 

43 
40 

]1 
34 
32 

*9 
26 

'1 
'i 

■7 
'5 

■3 

8 
6 
3 


30 ! 
?li 
12 

■5 : 

"4 ■ 
»3 

if 
\i 

«4 

•3 
^^ 

T 
I 

4 
3 




6 

I 
9 


5,007249 
S. 007 23 5 
5,007218 
5,007200 
5,007180 


5,005946 
5,005872 

S. 0057 97 
5,oo5;zo 
5,005642 


5,003080 
5,002965 
5,002849 

5,002732 
5,002614 


4.999355 
4,999217 
4,999099 
4.99897 > 
4,998844 


4.995742 
4,995636 
4.99S53' 
4,995427 
4.995325 


4.993255 
4.993"' 
4.99J1S° 
4,99jio2 
4.993055 


", 


5,007158 

S.007134 
5,007107 
5,007079 
5,007048 


5,005562 
5,005480 
5. 005397 
5,005312 
5,005225 
5,005136 
5,005047 
5,004956 
5,004863 
5.004768 


5,002495 

5,002375 
5.002255 
5,002134 
5,002012 


4.9987^7 
4.998590 
4,998463 
4,998336 
4,999»'o 


4.99522* 
4.995126 
4,995028 
4.99493* 
4,994836 


+,993000 
4,992966 
4.992926 
+,992888 
4,99285. 




5,007015 
5,006930 
5,006943 
5,00690s 
5,006864 


5,001890 

5,001767 
5,001643 
S.0Q1518 


+.998084 

4,997960 
4.997837 
4.9977 '4 
4 99759' 


4.994743 
4.994<'5' 
4,99+562 
4.99+47+ 
4,994387 


4,99,8,8 
4.992786 
+.992757 
+.99273" 
4.992706 
4.99 i685 
4.992663 
+.9926+6 
4.992631 
4,992618 
4,992607 
4.99<599 
4.992593 
4.99*590 
+.992589 




5,006821 
5,006776 

5,006630 


5. 004672 
5,004575 
5,004477 

s. 004377 

5.004275 
5,004173 
5,004069 
5.003963 
5,003857 
5,003749 


5.001268 
5,001142 
5,001016 
5,000889 
5.000762 


4.997468 
•t.997347 
4.997*16 
4.997'o6 
4,996987 


4.9943°' 
4.994"9 
+,99+138 
+,99+058 
+,f)9398e 


I26 


5,006577 
5,006522 
5,006466 
5,006408 

S, 006347 


5,000635 
5,000508 
5,000380 
5,000252 
5,000124 


4,99^868 
4 99'J750 
4,996634 
4,996519 
4,996405 


4.993904 
+.993831 
4.99375? 

4,99^620 


jo 
an. 


Logar. 


Dif. 


Logar. 


Dif. 


Logar. 


Dif: 


Logar. 


Dif. 


Log^. 




Logar. 


Dii. 



M 

An 


Sig. 1 1 


Sig. 10 


Sig. 9 


Sig. 8 


Si8-7- 




■ Sig. 6 


1 Tl« »boveT*.i 
Taii.(, fot» dilfti 

flAMTLt, I> 

1 

it.B. Tht Lo 


E-D-iccoidingietfae 
-ent Ecctntiidcv of 
Jiird T*«l«, U the 


Jic Ell 

CuncDc 

Log'. 
00+768 
O047M 

3' 


sua of tlM- 
EcBn.. 


Sob'i mnn A1101MI7, nrf othn-Emotrierty, diflmnt from the two formtr 
Prop. Di(>.T 


AnT 


i. + §of* 


— 7 


— * 


i tfDiS^VKa ukii/rmfrjl Ss^^i'J. 


"^»«-^-,i 


00474! 
an » 


1685 

Plicd. (a t> 


mmflin'ifcot in ih« 6th M««. | 


1: 












- 










SOPPLEMENTAI. 



,, Google 



imd "NAVIGATOR, 



SUPPLEMENTAL SOLAR TABLES. ' 


EQUATION Of the SUN's CEN-raR, iccording to Eccentricity of the Earth's Obit, 1680, and Mean DiAuce 
^. , of the SUN from the Earth' tooooo. 


^gwnmi. SUN s Mean ANOMALY. 



M. 
An. 


Sif. 


t>if 


Slg. . 


ref 


Sig, 2 


Dif. 


%. 3 


Dif. 


Sig. 4 


nif. 


Sig. 5 






M. 
An. 


— 




-_ 




— 


— 


— 




— 




" 


> / # 


' « 


/ » 


' ' 


. ' ' 




. ' * 


' 1 


> / t 


' ' 




/ 1 


° 1 




3 

4 
S 


000 
I 59 

3 Si 

7 54 
9,52 


' 59 
'.It 

'\l 

lis 

' 5? 
' S7 
I 57 

■■'! 

1 16 

' 55, 

■ 55 
' !4 
I 54 

> SJ 
• S3 
' 52 

> S< 
' SI, 
1 so 
' 4> 
1 49 

■ 4» 


S6 43 

58 25 

1 6 

• ' 47 

: vi 


1 42 
1 41 

■ 4" 
1 40 
' 39 
. 38 

1 j6 
'34 
"33 
' 32 

I 30 
1 29 
' 27 
I 26 

• '! 

• n 
'< 20 

:;; 

■ "4 

■ 13 
I II 

;.i 

I ' 6 

• 4 

■ 3 


1 38 s8 
' 39 59 
I 4058 
' 4" 55 
> 42 50 
■ 43 44 


1 I 

S9 
" 57 
!S 
54 
s> 

os; 

::i 

9 H 

42 
40 

III 

' 35 
9 33 
31 
29 
27 
24 
22 
20 
iS 
i« 
ij 
12 
10 
8 
6 
3 


■ Si 29 
I SS 30 


■ 
3 

'3 

l"t 
27 
30 
32 

36 
39 
41 
,3 

»;1 

JO 
S2 

54 
57 
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1 40 4 
1 39 2 
23758 
1 36 S' 
• 35 45 


I 
I 4 
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I 6 

I 7 

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1 18 

I '1 

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I 26 

I 28 
1 29 
I 31 
I 32 

■ 34 
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•■11 
' 39 
I 40 
• 42 

■ 43 
> 44 
I 46 


s8 49 
57 ' 
° SS »4 
S3 *5 
SI JS 
49 45 


' 47 
I 48 
1 49 
I so 
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I 52 
' 13 

1 56 

1 s; 
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' 59 
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2 t 
2 t 

1 I 

2 2 

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16 

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9 
8 

'1 
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4; 

3i 


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■ SS 21 

■ SS '5 


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7 
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9 

ID 


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13 48 
D «S4S 
174* 
« >9 39 


' 9 57 
1 11 31 
I "3 4 


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> 47 44 


■55 6 

" 54 SS 
> S4 4' 
I 54 26 
I S4 8 


' 34 3S 
' 33 24 
1 32 II 
I 30 s6 
I 29 40 


47 S4 
046 2 

04+9 
42 14 
40 18 


It 

'3 

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18 
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J3 32 
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29 iB 


1 14 36 
I 16 6 
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1 I9 2 
.1 20 «« 


I 48 26 
1 49 6 

» 49 44 
I so 20 
' SOSS 


.5348 
1 S3 «6 

I S2 9 


I 28 2: 
1 27 2 
' 25 41 
I 24 18 
I 22 53 


38 22 

36 2S 
03428 
37 30 
030 3: 


til" 
34 59 

jS 44 


1 21 S3 
I 23 16 

1 24 38 

. 2;;8 

1 27 17 


I s, 28 
• S> S9 

. S2 28 

' S' 55 

■ S3 19 


I. SI 39 

' 5' 7 
1 50 33 
■ 49 57 
1 49 18 


I 21 27 

' 19 59 
1 18 30 
I 16 59 
I IS 27 


.0 28 32 

^■0 16 32 
24. 32 
22 31 

20 39 


»3 


40 3s 
42 26 
44 16 
04« S 
■> 47 54 


. .854 
1 29 50 
' 31 4 

1 |2 17 

." 33 28 


' 53 4> 
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1 S4 19 
" 54 35 
1 S4 so 


1 4» 37 
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I 47 10 
I 46 24 
1 45 ,6 


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I 9 3 
I 7 14 


[8 27 

16 2J 

14 23 

12 20 

1.0, ."7 


>6 

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055 
56 43 


> 34 37 
■ 35 45 
. J6s. 
' 37 55 


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■ ii 12 
1 Si '•> 
I is 26 
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1 44 46 
■ 43 54 
I 43 
I 42 3 
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Sig. 8 


Sig. 7 


Sig. 6 


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7/. A Mr; M^fr', lU£x« for Ji<„V ,jo(, , i 
Re£«t to th. McTid. of G«(TO,.'<i . . 


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SUPPLEM 


ENT 


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,, Google 



The ROYAL ASTRONOMER, 



SUPPLEMENTAL SOLAR TABLES. 


sun's PROPO&TIONAI, DISTANCES from tbe £ARTH, according to the foregoiiig Eccentricit}' 1680, 
and meao Dift&Dce looooo. 


- Jrgumtni. SUN', mean ANOMALY. 



.M. 
An. 


sie-o 


Dif. 


Sig. , 


Dif. 


Sig. 2 


Dif. 


Sig. J 


Dif. 


Sig- 4 


Dif. 


Sig. 5 


Dif. 



M. 

Ao. 


o»e 


oie 


oie 


Oiy 


Oie 


Oie 


3 

4 
1 


101680 
101680 
101670 
.0,678 
10,676 
,0,674 




3 

3 

4 
4 
5 

1 

6 

7 
7 
7 
8 
8 
9 

12 

'3 
"3 
'3 
'4 


101462 
10.448 

'o'433 

10.418 

10.402 

IOI385 


•4 

;i 

'7 
•7 
'7 
'7 
.8 
.8 
18 
'9 
'9 
20 

21 

21 

*3 
23 
23 

23 

«3 

»4 
>4 
»5 

as 


100861 
100836 
100811 
10078; 
100759 
100733 


j6 
s6 
26 
'7 
'7 
'7 
»7 
'7 
a? 
18 
18 
28 
28 
28 

28 

'9 
»9 
'9 
'9 
'9 
'9 
'9 
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'9 
»9 
30 


100028 
99998 


30 
30 
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'9 
'9 
>9 
■9 
■9 
'9 
'9 
'9 
'9 
a9 

26 


99182 
99,56 
99'3i 
99106 
9908, 
99056 


16 

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»s 

*4 
*4 
23 
*3 

23 

21 
32 

31 

30 
20 

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,8 
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»7 
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IS 


98553 
98538 
98524 
985,0 
98496 
98483 


1 
8 

I 

6 




99968 
99939 
999,0 
9988, 




6 

I 
9 


,0,67, 
,0,668 
,0,664 
,0,660 

,o,6ss 


101368 

.0135. 
IOI334 
10.316 

101298 


100707 
100680 

100599 


99852 
99823 
9979+ 
997S5 
99736 


9903, 
99007 

^^ 
98937 


98470 

9«435 
9842; 




'3 

'+ 
11 


ioi6j8 
101631 
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101280 

IOI26I 

10.242 

I0122I 
.012OI 


100572 
100545 
100517 
100489 
I 00461 


99707 
99678 
99649 
99620 
99S9' 


',lff7 


9841s 

98379 




16 
'7 
18 
>9 
20 


1BJ617 
101 609 
101601 


1011S2 

lOIltil 

101 140 
101096 


100433' 
100405 
100377 
100348 
1003.9 


995*3 
99S3S 
99S67 
99+79 
994!, 


98806 
98785 
98765 
987+! 
9872; 


98364 
98358 
98352 
98347 




12 
24 


101550 
.0.539 
10.527 


101074 
10105. 

101028 

1 01 005 

100982 


.00290 
.00261 
1D0232 
.00Z03 
100174 


994»3 
9949S 
99,68 
99«' 


9S706 

'if' 


98338 
98334 
98330 
98327 




z6 

18 
29 
10 


10.515 
.01502 
I 01 489 
.01476 
101462 


100959 
.00935 

,00861 


.00145 

.00. .6 

100087 

■00028 


99287 
99260 
99*34 
99208 
99,82 


986.7 
98600 
.98S84 
98568 


98324 
98322 
9832, 
98320 
98320 


I 


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M. 
An. 


oae 


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oie 


Dif. 


Oie 


Dif. 


sie 


Dif. 


Oie 




oie 


Dif. 




M. 
Ad 


Sig. 11 


Sig. ,0 


Sig. 9 


Sig. 8 


Sig. 7 




Sig. 6 


THE .bcmsTAii* iiieoAiioi 

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SUrrUMENTAI, 



,, Google 



md NAVIGATOR. 



SUPPLEMENTAL LUNAR TABLES: 


For determining the Tnie from the MOON's Mean PLACE, according to ditTerent Methodi andTBBORii*. 


I. EQUATION of the MOON, Apooei and Node. 


A-pMmt. SUN'S Mean ANOMALY. 



M. 


%. 1 SiK. . It 


% ' 


M. 


» 


•^ 


Ap. 


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t 


ui 


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+ 


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I 


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10 7 


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114 


17 19 




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29 


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6 9 




10 14 


4 57 


10 20 




17 29 


in 


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104. 


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'7 


5 5 




10 26 




17 39 


9 


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17 48 


3 28 






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5 37 




" 47 




8 40 


as 






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9 


7 9 






5 45 




lU ,2 




iB 24 




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9 


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7 19 




12 31 


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16 


l"o 


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8 


0,6 


18,2 


7 


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10 


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19 12 


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9 7 






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644 


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9 22 






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18 


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9 «7 




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7 35 




11 41 




19 51 


' 








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4 n 


.. 




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4 5 


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12 


741 


I 


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1953 


2 


926 




4 


26 


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8,6 


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19 55 




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7 52 


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3 




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^' Spr I'lAAc NiwTON find! the ireiteft E^uMlon ]) from th« nMO- "^ Cmitr, 11' 49"i bat think*, u the Itrth'tEccentiicitt u Ibnc 
thu.gp«la-thMhef.ppoftdti6jw 1000. Rid. <w Moui DW. Q i ©) *» l6|4 iccwtridtj, the grwleft Eqattao wUJ be ihont 


' * h1 f^od that the Apogee uid Nod.ti ma«d fafter in J-mi. (wliere the Fofce of ©'• AAicn n greKtr) thin in Apbel.— Thit thi< Mo- 


tioaoftheAp.»ndNodeit in ibt rinprtiti irif/ietu Prtfriia of Q'l Dift. fram ©. Th« the greMeft E^uition © Center. genetHtd b. 




be »" 54' jo" by » tedpro£«l /n>/j«/f fnymtl>m of DifUnce of tfie Sua i E«rth. Aai therefore the (ntteft Eqwtioiii genented hy the 

S'eAji, 




— 




' ' 






















■ 










I 



SUrPLEMENTAI. 



,, Google 



rhi R O Y A L A S T R O N OM E R 



SUT>PLEMENTa1. LtJNAR TABLES. 


1. EQUATION «f the MOON, APOGEE and NODE. 


Argumtnt. SUN-. Mean ANOMALY. 


O 1 
M. ■ 


Sig. 3 


Sig. 4 


' - 


as- ;s ... _. 


© 

M. 


D 


-: 1 Ap, 


u: 


Q 


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Ap. 


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Ap. 


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9 30 


^ 


10 21 




17 30 


in 


8 I, 


s 

S 




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10 It 




4 ^0 
















9 30 




10 n 


8 






« 14 




III 


l\\ 


I? 


4 41 






11 4y 








9 30 




10 7 


6 


17 ,9 




8 9 






4 3* 




3 


M 4,K 




"9 59 




9 30 




10 1 


IS 


.t.^« 




8 4 




i^ 


9 IS 


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20 


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+ 


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1, 5a 




9 *9 




9 (1 


8 






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s 

1 






8 56 


4 '4 




5 
6 


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•= 


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19 56 


. 


y 29 




9.47 
i 9 40 


7 


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7 


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7 5« 








8 


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9 £6 




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13 

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7 35 


i 




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9 


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19 « 




25 




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8 


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6 5« 












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11 H 


3 


19 42 

19 38 
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4 


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9 20 

9 .S 




li 


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'4 
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t 




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f 


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1 30 

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26 


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1.0 4g 
lb -43 


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9 
9 

9 


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M 

JO 


M Is 

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17 
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- «E *i - -1 '»*%' t H 


liag. t, —J 


«;. Eqd.ti™'S-. Vfi^wrtmcioui 15. 4-,". Aldgf. E,,^ of M«7n'.SJ.-9' m") *hi<.h D/. Ji« 
£,7(^j«i-Eq>. or Mm Di/onct bctwwa the Mein ind True tmrel Ejutsim. Hcnceatifc uuuui £ 


»c to M. diunuIVat. 0. _ Heaic 


% >airt<lKr»o' UKtsf uT': But D. 
» bem Aiwa, foi amni^ the m4> 
qiOtidiu of thdc tbmMaimi, iiwG^j 








*. Lot 


^oyr'j--'"~l'^-f:rMiii;ii3;i-i 


H!i*--^"-}5^- 







SUPFLEMENTAL 



,, Google 



mi N A V r R * T fy ». 



db, Google 



SUPPLEMENTAL LUNAR TABLES. 

SlconD Equation of the Mooh'sApocee, fiamt'ittNmitaiitiiiiTH^aRi. With Deeimal znd Stxage^iHalMvLTtrtnt.t mm 
the Gr.«/<>? Dif. under or above the Mta, Central E<iyATioii of the Moon, for direaiy finding the Prefent correa Dig. from 
the Mian, antfthence the whole Central Equation of the Moon. AccorJmg to our Nivr. Mbthop of Lompatuig- 



rbt 



ROYAL ASTRONOMER 



JrgHmtHi. t)UN from the MUON't AfOG&K. 



1 I rue Place -— Moon 9 Apogee i Equaled. 




AlGr. EccT 66734: LciftE"^ 4131 

which dcduQed from the fiid Annuil Arg, 

El. TsfindiiEiiMiaitn J Af.feri 



J Jf,[, 



:: Tjh. Arg of O i J Ap. r To T. ^th Aft, 
ivn the id Equit. Jl Ap. (ought. 
1.0 G » J -*/«"' 



•4 To Conf. Log . 
I Add T. I - " 



Com.Lof. 
9.Slioi;o 
T. f 11° Arg. or 51° I io.09i6'jOg+ 
T. 1 8 41' 45" I 9.9036498 

Dif. 11" 18' i^i't^.rtfuirtJ. So fiir the lUfi. 
Coi()T*vcTiDHoflhei)(cind/aDd5uJ2{A>w/MDLTiFLTiiit fnto At Gr. Dif. mitt or Mbentlx llt.CiKlralEjm. Ste P . 66, Sj *ai 63 (Miritiai. 
A« 117j1gr.Dff.Ectl' onder or aboie the Me»n ■. O.D. under or aboK M. Ccnti. E^. ;: Dif. Eccr contfpondenc to the Aig. of £q. : Pnf. Dif. an- 
ta or »bote the M. Cmtel Ejaaiia,. 

Pre . Dif. Eccr fr. Mnn jy^^^, Mnltipr. (=P«m of. Degree of S«l Multipr.) "t«h x^ '"to C- "if. Eq. = Prtf. Dif, frm M. Centr'. 



I17J1 



Eq. req*.— F=i-C>»>.ifl«i../f«™'r. J (J^*. See firther on, 

ExAW. /" 1* 7° 40' »7" G a J)'t Ap.lt JiuIiiiJUMpl'tn It ItiGr. Dif. Ef. in tit fUbinv Ttilti, 
rn:f t:,.,.L .. ._ D. Mu|r. So. MiJi. 

. . . =s ,3678 = ai- 4" 



jn i- 7" 4D' %r 1^ a P • Ap, /eft 
i J'lAp. T.c.Ettj'jh.M. 1173. 



,66, 6jnd6t. 



Bj Log. Log', 

f ! ^-^1 

\ EK.Ar.40' 17" 0.1711 I 
tprolDif.— I 16 ii.6744J- 



Eie. Ai^. 40' 17' 
Pirt> ji4'foT 1°.. 5 14 






14 |'-0S94 r^ 1 



afi4.N AV.lXiJitQK.. 



gtWi&M/MulapHmktttt ttoQw««j>f PJflitMlCT under aliti.^Ave tbcMNB BLLitric ^^jTatimi «f lhtkt««.'i Qxift-iK. 
Forla'citng, dmA^!. ihf pwlBru £Drr«S Difference I^Om fb«"M«U, aa4 AROIK "TKf"w£r& "fiJlLime EUtatiom 



a n f n y i > 



sfw 



4llXtt)['* APOGEB/iot Swn'l Trfie Plipe -— Moon's ifpf,te f (qoktcd. 
H-^-a — . 1 > I ■ ■! L. — -^ — ' AM r:r^ .. " Li - ■ ' u 




£ftrtMl Ectntridtiu froa J 



cCf^TiwlfoefiteSKatiMiaBd^gMAottiMixMirifl^iilLiikK'tji ncoidas. ^ ,„ 

>8c^iW^'<M'9)^ $$s>jp1beMeu, and 4*6*9 ;the Z>*^ BMJ uri aity ; W -w ■ W Aw n«incr conftnfijed. A 
.i ,.- . :.i.. 1. — ^-'- dfirtlwtmi tWthePrine^kiaiybeenMi^iwd OnwfcJ* th'TtfTtblo 



fWFLBMBNtrAX^ 



,y Google 



R o YAtASTRON 6 M E R 



(M nt RO Y A t A STR ON O MER 

IV' MEAlJb^N'lTtAL EQUATION of thcM0O>i^, trom Ae AW/Wicn THBOBY.'-Wifli thjGraa^i: 



llV MEAN C^UITtAC Equation of the moon, tromihe isW/B-ici. Thboby. whb uwGraHflJ Difference 
.'if*QyAT«l***rwid*t««tbe Meam. E(iuATiOK correfpondenttotUt i*./ aild OW/fff EctintMcrrui, 
> I'^yj itjI^MytoioMon Dift-iO rbotaooo- Actording to ourUiw Method ot Qmifi^M g. 

'■^••^- .^;i,»,^f. ^(itJoRa ftquaic-i ANOMALV i Or^.» 3. linuMed — i; Apogee a. Eqnatw. 






Ji 



ireatelt' 
lif.Eq. 



[g yS 



. '3 '7 

ij 50 

.-J7 « 

2SJ1 

a 

'9 



s: 



gTcUeS 
3if.Eq. 



Mean 
CentEq. 



6 M 

f\o (8, ja 
"3° 5' 



,-,■'3' ' 
iB'043-n) 

,« a 49 14- 



7 -J' 
13 43 

jf r->i5-4a 
'' 3' ;q 



■'37 5" 
" +3 4S 
■■ 49 45 
':S5 4<5 
' ' 33 



- 7 '* 
2 13 14 

3P 30 



2 30 1 
■ 41 -49 
2 +7 16 



5 c™e,. 



' 3 
6 i 

« « 

6- 4 
s s» 

J 57 
! S! 
5 S3 

J 5' 
5 5? 
I '47 
5,4S 
5'44 
S*" 
S 3' 
S_3S 
S^« 
I 3" 



Dlf. 



J 2S 

3 39 



39 

'9 4! 



30 JS 
3 



2Mi 



abo^ . 



Sre'at.' 



Great. 
Dif. E 



♦»; 48 
i 



»j SS; 



B7 Tab- »ho»e. M. Cei% E3. i_^ 



48 U' 

<s 

I8- 

16 
5'i 'i- 



59 4S 

60 35 

61 .28 



63 , 
53 .39 



under 



Great. 

Dif. I, 



2 jS so 
.~3S» 

3 9 »4 
3 '♦4'i 
3 20 S 
3'; " 



3 SO 31 
3 SS |4S 
3 40 51 
3 45 S! 
33055 



Mean 
CetitEq 



3 SS SO 

4 o 43 
. S 3» 
♦ 'o •? 
4 '4.37 



4 <9 34 

4"4' 7 
4 28 36 
+ .331 o 
4. 37 1 to 
^4' 36 
;4 +S ^47 
4 49 S3 
4 S3 SS 
4 57 53 
45 



9 >S 
12 52 
16 25 



.Mean 

CentBq 



<hvat: 
DiCE 



''I 
S «> 

I »2 

' 'i 

S "6 
s ■♦ 
5 to 
S « 
S 4 
5 o 
4 5S 
4 S3 
449 
4 45 
440 
♦ 37 
4 33 
4»? 
4 •« 
.20 
«:i6 



SB «4 

j6 31 

>l 3'l, 

S« 4" 

39 4' 

40 S3 



4> 57 

43 ' 

44 3 



S 3 3"' V, 5' • 



•bore 



54 « 
£S_i± 



S' 49 

57 43 

58 37 

59 29 
00 20 



D. 



Dif.£ 



I 



lli^ 



5» 
■> 55 

54 



u ^ 



im>«J»f»f' p-fiT* J '*•!-. j-"' •* >«"'I*'?I«^<*M'' 



■j« ii»^l»*. Aaom.— j°~js' St/'' 

Xgiinft' I' 11" EqiwtedAaoni. : . .■+t" *tn9» 

JncmftftomMeaq. Wtail-T ■_, "^ ^ -«',^V«7- 

lewedlnctielwoitfaiKcPirti I ._1.b^ * .lii'?;i, 

fhMB «i tfflftttrmw, into 
■ ■wbitb the G. Dif. i« fcppoiW 



tlknnd. 



aMeto. to be il-T _ , 
iwoitfttiKcPirti I ^',^ 
fHxtnnK, into J 
, Dif. i« (bppoiW r 

3' Put DOChillg I 



. — 4t',ail O. D. Eq. onder I Or, — 4I' IfMIOaOMl 



47* Xltr». 






N-^ vtmnt ■n«BMin ohbkhb 



' SDIVLBIBMTAL 



Digitized by 



Google 



■ ^anf N A tf »<S AT'ORr 



STTFTX E M^TTT S t r V^K A R " T^^ 



[V.UEAN CENTRAL BlltJATlONW^t^ MOON, from tk« X«^«s>«>Thioky. With tiie Gnat,/ Differeocc 
.oTEjmATigiuwiA f .i nA i i^ i art t h e M>*ii, fi q jr * T io ) i , c mrcf|wn(fanr .tt).tlu; tea/tjpd Qrtat(i^KMKXt.iHJin 
A^t^«nd66y8a toMc« a Dtft- ^ Sua iQ9ij9po, AccWin g t o our Niw Methoo of Cu^tfiaj. i 



■^^p»«CTf, 'mQC IB'»EqiiatcJ^NOMALY,Of, j. - a-Bgaated -j- B J^^j;e»a: Eittiw^ 



Dif.E, 



Dir 



69 29 
$9 la 



^ 



7> 49 



73 36 

74 40 
11 



4? 
77 «* 



77 4« 

,7» --i 

7» 3' 

i7f 's; 



ia 



2^ 

■* «s 

7J 39 
7» S3 



iato. . 



ntatcft 



33 

O JD 

o 30 
o s8 
"7 
o » 
O'S 

83 

o:zz 
o ao 
fl 11 
?"S 
6-19 
o ■♦ 

O If 
O 12 

0-is 



Si^ 



CdUEq^ ' 



i '9iSl 

! =3!"4 
S 2°, 39 
S »9 4« 
;,3';4» 



3 S. 3« *J 
' S +1 Jj 

S 44<! 

! 4^ 53 



^ 4fl *5 
S S' S' 
S S4 " 
S 56 H 



.» 29 



6 10 ^ 
6 " * 



5 
6 
«. 
fi '7 44 



i 



111 

^ 17 



K?S 



«, 46 
67; »« 



7' .4" 

„■ ir 

73 S 



74 S5 



o 4^ 
4' 
»44 
»4i 
0-40 ■ 
o +1 
o 38 
9 35 
o 36 

°'! 
o JS 

■> 33 

0,33 

o si 



'J 

?' 49 



4 
o 57 
o 51 



»3 

78. 1 
7' '«3 

zr 



79 

79 . 

79. 36 

79 5' 



80 ! 17 



8.j 47 
8ff. 50 



gs^t 



8> 




ao 


51 


i9 


51 


io 


51 


80 


47 


la 


4a 


to 


16 


l9 


>■ 


<o 


16 


80 


! 



n 



79:5^ 
79 37 

79 »4 
3 

5 



77 if' 
7f ■<4) ' 



7^ 15 

7S 4* 

75 '" 

74 3» 



sa*. 



CtuLp). 



Sir 



;5''i<>:H 



l> jr 



4J4 
18 if 
■« 5 
'7 4"- 
IJ 9 
16 jo 



^ 



■! 45 
'4 5' 

:"3 53 
'" 44 
■ ' 3° 



10 9 

- « 4fl 

« 7 5 

S'3 

3 34. 



37 



5 59 

s:ss -S 



5 so 
5 47 
J 44 
5 4" 



S3 ' 



Ceac£q. 



3' 
4» 



Tlj-T 



CKMaA 
Bif.E. 

TTT 



So 35 

8*: 4] 



if; 



So' J8 



fo 5S 

So, <! 

Bo! V 
80 ; 40 
80 ■ 



79 55 

79 40 
7i_»! 
79 ,! 
78 43 
78: ,li 
77, l« 

rr J4 

77 7 

76' 48 

7* 9 

fSl 3» 



EoE. 



?■• 



?5 
»3 



Efl ^ 






£fw«iia ttf tb« MooN'l CbvtIi,*(iAc* l4^^E]ofl i^jisf. 



, .(SOKUMSNVAt 



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R O Y A L-. A *1 » «> M Q..M E R 



» U P P fcS M E N T A t L.U N-A^fe-t A-SiSlT 



IV. M£itK.CBN'nUi;>EQ(lATlOHof>W.MOON< &^li( /lipuJlti ttst^T. Villi lilt Shdif ItlF< 
.avi66j^3 to Mmm Pift. I Stin loopooo. ^ccogjigg to onr yiw Mrt^op of C 




«»,<> N-A VI-GA TO *. 



db, Google 



^ nt ROYAL ASTRONOMEK 

.SU^PLEMEtfTAL LUNAR TABLES. 



'. MEAN iiLLIPTIC EQUATION of the MOON i CENTER t«»intiwfl<fT«*»THio»T. With chc (Kat. 
eft DtfftunerotEiyiLrwi^t uaJtr and ojov* the Meah, correfptmilciil to Ac JU^ uttGr-u/r/ft EccEHTKiciTir 
• 4^^iQapd 668S4. to Mean Diftancei O mooooo. AccotditigtoottrNlw Mitwod of CoropntiiiE. 



ArgmmM, MOOtft Etjoatcd AnoMALT, Or J i Eyiated— >M. Ap. Eqpatcd by ad. Eg. Ap. 

Sig- a. . 



^ » 



G. U. 
Eqoat. 



I; -36 

16 at 

68 a9 

-59 H 

7% « 



ia7a 



o 49 

"'I 

4* 

o 40 

o^a 

+S 
3S 
o 3B 
o 38 
o 36 
36 
JS 
3" 



71 47 
7' 37 



■! 7} I ♦* 



H 



»7 



G:D. 



. Mean 
CentBq. 



! '7 '7 
! "> 54 

S >* '7 
S a? 33 
S 3° 47 



? 36 S4 

! 39 49 

5 4* 39 

! 4S '4 

S 4« 



S S" 3S 
S S3 
S Si s; 

S S7 S" 
S S9 44 



3 4" 
S 3 
7 IS 



6 14 U 

6 16 \; 

6 17 I 

6 17 j: 

6 iS a9 

t '« 59 



Catt%. 



G.S. 
Eqnat. 



64 ,8 

65 
68 
66 

67 



o 58 



68 
(8 si 
69 35 



Z2_ll 



js ■■ 

h '38 



?* »9 

f« S3 

77 !'7 

77 3» 

n. 
1> 

1> . 

■?« 49 

79 

Z2. 






+ 
Bqnat. 



79 *9 

79 3! 

7i 44 

79 S" 

79 S'. 
,30 



So 



79 5' 



'2 

7« 53 
78 35 
7» 
77_ii 



77 35 

76 S3 
76 aj 

i_j6 



75 "; 

74 sl 



G. U. 

Eqnu. 



C«at.B). 



6 18 59 

6 ag at 

*'9«'l°'.' 
6 19 50 
4 19 54 
6 >9 5' 



6 19 40 
6 19 >3 
61857 
6 18 ae 
'7 4* 



617 
6 16 8 
6 15 8 
6 14 e 
6 la 46 



6 11 25 

9 5« 
8 ao 

. '37 
6 443 



o 48 

s s; 37 

S S* '9 

Liiii 



5 51 . 

5 4*43 
S 45 S7 
5 43 
S 4» 



C«iK.Bq. 
> 



e.D. 

Eqnat, 



79 '» 

79 »« 

79 V ! 

79 S» 

'9 57 



79 5« 
79 5" 

" ii 



75 S3 



78 17 
S' 
77 3( 

76 4<> 



tSrsT 

)E<i«at 



'9 
21 

o a4 
o a; 
o I7 
o af 
,° *> 
' 3t 
33 



EXAJIPLX U* T*M lit Ejmdiim y (AtlfMit'iCiHTaa 

e'> ■ '" • - 



4«loo 



Tti nhmraUt » »" I j' 

Bf. — 

^ Tlfc. (Um j» j« 44* 

>CMtral 



«>'0J>'*«e--'3*i*«' Jfifwrt^w^ 



m. 



'» a»nai»i6MiTah.j^ia an-r" * 



i.lojS 4. 



,, Google 



mi N A V I O A T O R. 



SUPPLEMENTAL LUNAR TABLES. 



IV. MEAN ELLIPTiq EQUATION of tkc MOON'i CENTER fiom the Brraua Tmiiii. Wok Ike gnu 
C& Difir*»n of &qy AT lOK, widfr-»ad ai«vt AiMxui, CMIcipoiuleilt.tO the £«t lad Gr«<Agf EcciKTKfClTlIt, 
4)619 and 66854, toMetn ]>ilhi)Cei O 1000000. According 10 our Nsw MKTBOBof ConpBtJBg. 



JtpmiMt, MOON'tE^iMMdAMOUALT, Or i rMa^uai — > M.Ap. ^oMod by sd Eq. Ap. 



li. CcntEq. 



5 4» 
S 17 - 

5 33 46 
S 30 '! 

S »' !7 



^ '9 43 
S 'S !« 
S 12 6 
S « 7 

; ♦ 



S S948 
S 55 30 

« 5" 6. 
4-t' 36 



3 s'" ■" 

' '3 i, fo 

3 59 68 'J 

^ 67 ao 

!» " »« 



4 37 . 

♦ 3» 27 

4 '7 3» 

4 »« J3 

_2 4 '7 '» 

8 



4 7 

4i ;;4» 

3 S' '3 

3. 50 40 



73^ , 
7 3 39 20 
7 3 33 34 

7 3,«7 43 
■ 7 32.48 



Mean 

CiJilEq 



I above 



6> 



4s»l!r« 

4 55 '° 5° 
»? '2 
5« 4« 

iZ. 



. 35 

i 21 " "2 

i 27 «4 ■« 
':" 5i_i» 

? V. 46 58 
.±S_±' 



Eqnit 



o 36 
o j6 
» 37 
o 38 
4" 
o 42 
o 46 
047 
o 48 
»47 

O J! 

052 

' 5! 
058, 
o 57 
o 59 

59 

1 o 
■ 4 



♦4 J8 
43/21 

42 2 

40 42 

39 21 

36 32 

,3S . « 

2 3) 43 

8 32 17 

8 29 21 



G. D. 



■adef 
~ P 



»4 54 



5' 

20 19 

1> 47 

•7 "5 

'5 42 

'4 9 

." " 

" 3 

9 28 



' 35 

O ..o 






' ''»■ 5- 



Mean 
CeuE^ 



21 4« 
•548 
9 44 
3 36 
57 24 



44 45 

38 22 

3' 55 
25 24 
"a 



12 13 
5 32 

5849 
5' 5 

US' 
38 26 

3' 33 
H 38 
11 4a 



5642 
04940 

0142 3« 
IS 3° 



Me2ii 

CentEq: 
I 



44 22 

43 

38 



i!_il 



■gts; 

Eqnt. 



3<> 

28 40 

'^ ? • 

■5 j' , 



6 32 
♦ S4 



■gnr 

Bqaat. 



QroilieiMetlmIterialiliistlw£Z2y(u£ftMtf« rftl«Ha«iACaMT2a, Sw/eriftfW 



SDrrUMBNTAI. 



Digitized by VjOOQIC 



'it ROYAL ASTRONOMER 



SUPPLEMENTAL LU N AR TABLES. 



/. EQUATION, or Moon" 

TIOH." 



I Leaft and GreaUft 1 



... T*aiA-* t 

■din g » <tf ^Y****"'* ^^?- • 1 . ^ 

'- MooM equated Trom the Si *" 



iMWiMB 'MvL'na'LifiKitotheGreat 
eft Dif. above the Zt^ Fanatitit. 
ThrPmrtiift tnha ■tiiJarl .cbei«ta .fiu 



Moon'i Greateft Vaii 
ATION ia Oaaaii of 

to Fcijge« 0. 




) /n next Simror«(4)4nEar« 



ibom I-. -S. Qr. IW'atiM iiTIBiMt ~ 

Perigre, teTpeftlfclf i S.tnf.£ji^ _ . ,. . 

<mr. «ai. J jS. 31' 10" ««f 4. ijf 18" H &>. »J© l A. 
EqiuaiimiU Jlf- a^TPirrg. Q. 

Ofi sif IB /' J xut i ' IT 1 ^ i i v ^, ♦ O.P. la w t. ' 

I. (. 7,a4 X iDjr L. £q, = G. D. u iboM, 

And, Jb 3j' 10" e-. Sf. imOSM, J) AQ, «4c)»-/. «^.^9r^ 
E;, in t)di«i } ^ O tNOtdiug lo Q M. Ajl. ii Z>^ £r. &a i«r >■ 
" ml yitrt»iini, tequind. 

rrrlmimrithi-- ' 



N.B. f 



h^HM 



L»— - 



htr. eif. ta U *<U«I n tbe 1^ lEq. Sup b Ap.W 
tot aify0rialiiii RquUat. 

Bnici, I "_, 



D. n out ofOaui^ 

LE^Mtlni. 

E>. Ti ;U (/< AAm'i Prrfl F«-. !*«• 



••as" J *© '••* *S'»4' 

Prop' Eg. + a ii 

} PnL Vir, icq'. 17 35 








U Prer.V»i.i7'44''| jji 
xording to (hit SjfMit/b. 
■crori l toSirl j 

r, in JOS. IOAp-3j''4" 
liaSq-of J'l >©Pw.^7 II 
yn.TCT.dirr, ] VaniDoa. 

tt0Db.Ol& I 

' TanMMO. 



i^iof. J V 



■ . ■ OIK? N A V I G A TOR.: 73- 

-SUPPLEMENTAL' Llil^Att 'tAitik. 



on, V. £<*AT|oii af the U«o)i'i ] 
Vakiatioji. Aco*nl(i)g to the Nbh 

,g in Oftanti, or |lt » -Mety Dift- itQ. - 



LocjsTicAi Ldgarttdms, to be idded to dte L. L,<rf 
the Mean A'ariacion tor hSc '!>. Lag. «f Ac oovcdl 
V*ri«ti«o.r 



^. MooM EfiMttftitfa the Su 




Ou I St II- S. Sig.-;\i<».+: 

M SKjrgr) rivf- Mf*o VuiUion, u abOTs, 
im OAmu, or ai » Mpan Difiance from @. 
' ' Vaw 



Kong im OSMt, or at » M|nii UiHance trc 



S!iil'«lir3m. »»s*-. .. 



Obk-VV- *f^. »^' aq' '^'- 



o*o<i+ 



s^il. 



Coxii 



ftuCTiaM. Ai jTM/^ M. VfriaMoi _, 

OaaMi & €>, and O in OOana oi nt 4 Mean Di&> i Q 
PnI>« M. Variation,© being hi Oaamtt '.: great', Viriarion, 
% in Odanta of O, corrcfpotKicst to the O M. AjtimaJy 
Prefent Vaiifdott reqnired. 

Hence: P-M-Var-^P gvar. OinOfh. ^ ^^ 

tmVaiw Mwi Ifenn +L L, PkC G. Var. is OCtt. 
— L:L. 35't</wL. L. t*b« added M, or ooDoeaed with, 
the L. L. of Uie prefest M. Variation, for L. L. of pnlcnt 



-wmsmfxi: 



,, Google 



7ht ROYAL A' S.TR Q. N O M E R 



SUPPLEMENTAL E-U.NAR TABLES 



\^ EQUATION, or Moom'* Vah*tiok. 
Accmting to Oc UfrutioH Tbrary. 






«uoN trom rlie SUN. 



20 8 

21 IS 

2Z 20 
2J 23 

'* '5 

26 34 

17 J 



sig. 



« 33 
3+ 9 
34 42 

JS '3 
iS_4f 
j6 9 
j6 32 
j6 51 
37 'o 
37 Z5 
37 38 
37 48 
37 SS 
37 S9 
ll_2 
37 59 
37 SS 
37 48 
37 38 



37 10 
36 52 

363^ 
36 9 
3S 4^ 
3! '3 
34 4* 
34 9 
33 33 
1U± 



iiS; 



'0;„ 4 



Sig. 



z6 14. 

23 ^3 



16. 40 
ij 27 
14 14 



^ q- ^ 



©■ 



CONSTRUCTION. 
Aa Rid. I S. DodUc Argunieii^ of _ , 
" E^aUioa at Gmtcft j IVefcnt Equation, rrji 
ExAMrLE, T* /ni lit Epiarhn fir t6° 
IX i(° = sii> . . SioB ,7Sa CO Rad. 
Cr. Es- ji * 
6JO4 
*3*4 

M 5. The aboTE £q*. isd 71^ tomfH, being toontt- 
XdWill fonnininipil. fMatua. jn m- iflai^tdfi 
finrtln I '■'^ Miyei'i tm^mi^ Fer. falhniiu. 

tIw jili. ind Jill. &)ai. (0 the Right are impraied th 
Ea.iftBeft bj mrinc-tJMni unheinviTje Ittth of yi.Q, 
vtHnO)}, tilheMaoa'iHw.PinlJu, liipplied bj' iLc h^ 
TaUu of CantOiDa, 



VI. fW^ATJON of dieMooii,-Orl 
2d Equation of the Center. A 
cording to the HrwUtdm Tlieoty. 



ifriF^ 



Jrx, B i O 4- P Ap. ft O A] 



6t 



3^ 



r 3 



S.I 1-5.05- J !,J_A,g. 






IS 



A. — B -*.. Theaboi'ecorTeaiilieiftEqiw. 
twn D'lCtntcr, andirptoKtlTXr^ic'i ,th. 
(V^f /«. 4> Raj.; I S. Prer. Argumenl 
..xa DCanHSiKjfj 01 SuaA-iinri :• ~' .j- 
EifaitiaiilaC Crcitcft ^ Piticnt Zqna 

ExAMFLi, Ts'fidibiTfua^iiffff jo* 

&i t Had. 1 9'4i6 Gr. E, : ^ 5. jo' 



VII, EQUATION &f the Moaw, 
or, jI M»is yariaiimi.' 'At- 
eordiog to Gr(;*r^/ Jfin^. 



.^ywWB/. Mo ox from the Sum. 



-?{;^.;{^s:s|5 5 



o 29 

o 32 

o 36 



: :i 






I CoK.Ta. A) RiA. 1 S. Aril, or Pr 

For 5 Gr. t. 3).,3i^%' ao'/ 
'■W—iWBe-v^^^V- 

tPofition sf Mooa aoj S)in*a Ap* When 

Htlwy •* <««*»■ 5*" add to, but when 
-"-'--'■■jbtr.fr -' " ■■ -- ^^ 



Which Error t-caSnicr a.ai Dun'taria htyt ^ibS^u' ~ ~ --*"• 

fttttHyfaiotf(tf. "t> ll « .H y .. if p knLl tlii.a^..r But in aw Saa iM«»> a .. 



mi^NAVIGATOR. 

SUPPLEMENTAL LUNAR j'ABLES. 



Farther Cok&ecti»m i 
cofding to the Dif. of the 
Moon's DtHance^on ihi 
Kakvh and Sun. 




^OPFtEiaENTSr 



.,' ' it o;y A t 'AVrg &N o M E rT""'- .; 1 
"sUPPLEMe!nTA,£. JUNAR TABLES. 



^ . Semiannual ^(^tatioh of die MboH't Nddi. AcoKding to the NrwtamM TJbtarj. . 

WTlK JTetimaJ MuJ^Iierr rai- li pgHIUal' ft i gnritfmi to UypfJifld M the graueft £«:^i of X^A^imi m4 laiiiKjiof ), 
fbf fini li n g il w twgfei n Ejn:t^ thereof, refeeatwlr> Aovcdie Ripuctiob apdLATiTtiPXfor dt c iJ ii j tflpditytioBW 
dM ZiM^ Orbit (4' 59' 3 s") Alfa the PrufiulEJccigii oriptTinTiSon aHOTTdie Udfi LuihaiitK, 



igtoth 



ArgiaitM. gt>n frOH> jie Mooh'» Noftih 




A« OBBft. S". 59 (Sum ef t»Sil«. A) . . 



Con Log. 

TflthdrWf. ^jCc=59— 5*3 ""trr"') 
So Ridlu - ^ajeaomaoa 



Co. Liimio 

To Cima. N"- s' t^'if °''^'l I.74"S8« 1 

K, T.B. O i a . SBf poft 46'* (? Sum t>pp. i') i£:2a>i*» l 
To T.^ Ardi [| ESf. iXt **°,jio' lo' " , 9.9)i^f8l f 

'^i^liA'i.^""^ ..? 41 **»'«> *>'*"#*- J 
TIh Udll>>cli**tl«> ]>''^r'i'^">'^ ^'^''F'''°^''K4°- 59'l!r*'M Q'*" 
o IT*. W. When thiy ure \n CoDJnnAioD loJ OjtpoStiai with Q I '< WWnluit 
'rM i< t.FrmtlpU, for CoaAfwAioa and Solution oftke dilincat Indhutioni of , . 
<I£r.i»i'<j,iti> : Pn£ Ix.-theKoft: Gi. EU.urX<tf*A« Itid c^LA^nA 1 pMf. Ei, thereof, icQcaiyelj, 
B .Qihit. /<w tb* Ji«'. uJ !"■ II I letpciliKl)' i^uirad. Hence, PM. ■ Em. ImSt, m t>aJia. 
' ' > "7'4S'' 

U>.LEt.-feribe]t«iAaBdL«f. D ) iiiberc «UiA Kn>u(L*:Lag. «iclbMdi«-«iin*. lUieDqt* 



ImL — L. L. 17' ♦^= 



111 J I 



tut tbx yaidt Exctft of lo^miTioa h .ij'4'f'.. Stt 
of ])'• Orbit vidi Eclrplic^Now, >•!;'■ Af'j Gr. 

ef.;Ei 

t 



bt added to tholi^ ftr' 3>e Leaft 
Anf Lo. loci Prer.;£K>. 



cdbvGoogle 



■ml N A VI,& A T O R. 



_S.UPPL£MENTAL. LUNAR TABLES. 



Mabx&amJitr Orbit to the Ec-' 
Lirx.iJC. '-Pot the Infi and#r«r- 
cft^/iMMa; witli the grenut £x. 



:a 



fflJ^ftwUiftlu fori 

]re4 Ipcl°. |ry IiicT 



iSigi II. s-Sig. io.4..lSig.9. J. 



COWIT 



ira: 



.riiV;; 



LaTitcdb of the Moon for the leafl anU greauft ItlcLi h at ion 
of her £>rbit; (+• ss' 3S't ""^ S° •?' ^o*) with the grcateft Excers 
ef LadhMle. 



■n, 



jfrg*«r»tf of I^lnde, orMooM ffom Node, t. Eqaaie<^, 



6. I Sig. I 



to 17; 
'S 39. 



Red*. Eu i. <■ id [he pnlrat lolt and |n*tcS 
ItclinilfcDi ]) pib. S. dqublc Ari. (t*kin( 
Rid. si) Xd intD6',J«y«f t'ji'', ui4lllft 

,Mj w 7' 10". nl5*«iielj, 

Tt fad rii AbVii'm rs !• ii>. Arg, 

By Tib. foregoing QJO i» 17° -.■ Xt^^jS 
BjT»b.«bo« ., JtajJ t' ll'G.t t.R*. Af 

" - ' *^-'- 1B7B0 



e'M,-. L. bd*. 



+ai',o«6< 



■ef. ini-'W^^ J«rLii.Logi.. i'i7» 

r^ (*< r^- Gr. £1. lUd. 47" 

PrspDrtioiul RcduSioD + »tt 

JVIT.'Two of (he'£rllPigBa <f tluxi 

e fufiicitnt id fiod the Rcduflioa, which mi] 
«jyi b« tikt'ngut n Sight. 



36 >8 
! 46 48 ^ 

■ '-£2 



' i7 



7 '9J 

37 a;: 



^^ 'it 

5616 

; 6 29 
: II 11 

>S S 



I zo 30 
■■ »S ' 
■ ^9 39 



B'sLai 
fot leail 
Inclin. 






4 3' 



IV — 



Sit 



il 
18 1 



D. For teaft Dif. 



33S 



* 4 
J 19 






t «' 57 



33 3« 
3S 43 
37 43 
59 39 
4' '9 



VA 



S3 16 

58 s 



59 3 
59 3t 



S. U.. _N.D. 



C^. Ai R«i. : S. prer. ThcUn. 11 5. pre/. Aigi Lit. ot S. Jl i fj 1 5. pul. Lit. > 
iiieffoadcnt, 

£x. AtRaJ jro.0000000 

To S. leift Int. 4» tg* js" . *-9i96M9 
So S. jo*> Arg. B 1 a - . . a.M»T°° 



' ' jyg ' ' 

By Tab. tboTC 4* a<* .... 
Piopenlaiu) Li 
Lai. I) for Pic&Dtlnclin. nqutred 
■ Tib. roicgoing -. -• — 

pidportioDil Lit. u be'- - 

N. B. Three Fijon 
Ltitode. 



■ Jl J'Q, tbcAi^btetbtcfUtiiaat. . 



Lm. for lout Inc. 



. . •• if^fc < 

if"' »• il H U' «J""©*Si 



I ISO 

77 '7 



I of the MullipUtr «« gerterallj fufficienl h 

' ■" SUPPLEMENTAL 




7h n O Y A L A S TKON OMgR.. 



SUPPLEMEliJTAL LUNAR TABLES, 



Omfiian of the Sub and Moos, 
for die mie Altitade of the Moos ] 



iTbe HoRiMHTAL Paralla;x ol the Moon, in&fl;™a« 

Alb tBi P^t ol P'-r. oat of Six:fg:a. To be aUiJ to the af farm 

or AJtrM ^tJ ffow <be apparent for the tree Dift. of the Moow from Ac Fer irr and the tmtr^^- 
UUriiMtiUl'arJlax 10 the Mi'Mlt Stati «f the Aforfi Orbit, oi Mean Kccentn 

dt» «oco to Mew Dift. O i uwoooo. With the Grtaiifi Dijimct. 

of Paralfax ««&r and aiovt the Mean Parallax correfpordcBt to the Greatel! 

and Lea* Eccentridtie*, A (above) and U (under) ebc Mean Eccentricity 



OrrrtOiii of the &ft P^ 

of the Moom'( Hon- 

conud Pahallaz 

ofCtii/miSitm ud ^ 

f^thn, or Sii^ntt. fii 

Legipicel Ltgarittmt, 




' ■' ' * J An. Hor. P»'. C- D. ' 



ifl Pirt of Hor. P»r» «■ Sy«. "<1" • 59' i^ • ~7"i*oPnf.P^Mtxui]M fab. ftam cbc Mom Puillai. 
If a Bertofc J — B An.= J Apostt.. Thmfore ©— J + J Aa. comA b Q— J Apogtc com^ ; iiui 

^eW^nMooD'rAr..tr« (or p An.S: 6») » AmiuJ A,,', correfl, or © 1 p ■< A,. tr« , chc ftmc of m. DiC. 
Ifcim itlioUec'iU'i i" Synygia, or ConJunAion irul OppoGtion of Sun and Moon, ^u ike ,4rxtmixi nt Moon ttnt 

3 will bclbe rame in Sigpund Depiet u the Artt, for the XrinTdt. of © ■ D'aApog. Ibppofnetbit Aigu- 

^rna (the Dif. *hen ibeAtg'. ii Q i J'lA^ ) Zigiatnt, btiiig.ij Eqiurion of J Ap. with » tontratj Sign, 

, ... , .. , __ h/t armliit, 

a aural mid EvuiUn Ejitniim) mi the Cotreaioa sf ihuallu hj 



iV. a. The Owixmtst Pa-*IU* 
Conft. Lo. Lot. iSS*' ^fl *J*^ 
Oi i + Vb "' tbajofHorPWi 



I [D Ihe ippirCDI Diameter of the Mooa, n ■ Mijf, aru fctt* j^. He*ce (be i**" 

:o tbcLo. Lsg.of Hu. Pu. will ^if the 1^ Log. a( tbi Momi't »pp4i«m DiomeMr. ,U410 

= Api. Diun. Moon. S*'' _ 



Camp' 10 I- jO'45— , 
D. xr«"">i-Lo|.6j. 

Andfiifaiihcnft. 

.Ptja'j6"P» ei.Sj«r[+i9 

J i O 3' • • 1+^ 

P«.oiitofSj«Ts8'44'-H' 

Or 5)f jS"»iS9'.* ^ 



res'. 5* 4+ *!*• 
[tori P«». »3*4 



<»i NAVIGATOR. 



• SUPPLEM^ENTAL LUNAR TABLES. 


/ 


The ECCKNTK.IC1TIES of the MOON, kcd SiSerence of tMe EttitlriHHt, fn>m the Mon Eccentricity 
(5137. t)iKGrtMtft befog 66854, Md LeaJl 4.>6t9; tccoTding-tO Htrru, m FUw^uO. With the Diffiem>c« ol 
Eccemricide. from th« Mean jjoso ; according to Sir I/^ N^m, Rad. or Mean Dlft. J i 9 being loooooo. 


Arppmtnt. SUN fnm the MOON's APOGEE j or Sun's true PI. — m. n. J Ap. 1 Equated. 




© 
k 
I 

Ap. 


Sig. 0. 6 


Sw. .. 7 


%. 2. 8 




4- 




Ecceatr'. 
»Orb. 


from the 
Mnn. 


Diff. B«. 
rr. Mean. 


E™.b..- 
JOib. 


Diff. from 

ihe 
Mcaa. 


Diff. Ecc' 
ft. Mean. 


Ecccnu*. 
.>OH>. 

Homx. 


Uiff.trom 

the 
Mean. 


Diff. Ecc- 
6-. Mean 




" 




above 


' aUe 




above 


above. 




nnder. 


under. 








2 
3 

♦ 


66«s+ 
668^7 

6679. 


..6.7 
1.6.0 
..589 
>>!» 
..504 


.173; 
..7.6 
1170S 
1.679 
■ .638 
■■!»S 


6069. 
S9S»9 


58.8 
5459 
S093 
47>S 
435' 


6708 
6388 
6^ 

Si'' 
5033 


49429 

48741 
48408 
48085 
477«9 


.58.8 

««29 

7'5» 
746B 


4827 
52.3 


30 

'J. 




6 

7 

8 
9 

10 


6650, 

66,54 


1.363 

...67 
1.049 

.09.7 


i.jao 

II2S7 
1 114.6 


S«8'7 
58439 
58047 
57«S» 
S"St 


359a 
3ao. 
.8.0 
'4.5 


4»77 
43'5 
3947 
SS74 
3.95 


47463 

46604 
46337 


777+ 
8070 
«357 
"633 
«99o 


VK 
8058 

8373 


H 
*3 

21 

10 




12 


66008 
6S679 
65.98 


10771 
106,5 
10441 

:°o^! 


11024 
10891 
10746 
I0S90 
>04>3 


56854 
5543. 
S6047 
SS«4' 
S5"37 


16.7 
'"It 


28.. 

»432 
203. 
1636 
—37 


46082 
45838 
45606 
45385 
45.76 


9.55 

iS; 


8678 
■8973 
9253 

9522 

■ 9778 


•9 

18 

:? 




16 
>7 
18 
•9 


65089 
64868 
6,636 
64S9. 

64'!7 


985. 
963. 
9399 


10246 
ioo;8 
9859 
96SO 
94JO 


S483« 
S44a7 
S4;'S 
536.0 
53..0 


20.7 


83s 

792 


44979 
44794 

44320 


.0258 
'0443 
10614 
10771 
109,7 


.0020 

.0659 
1084. 


'J 
10 




23 


63870 
f3S9+ 
63307 
63011 
6.705 


8633 

83S7 
8070 

lilt 


9200 
8960 
8711 


5.8.. 
S»4'7 

s';3s 
3.647 

5.«>4 


»4.5 
2810 
3ao2 
359° 

3973 


1102 

i6it 
2010 

2,.« 
.835 


44.88 
44070 
■ 43965 
43874 
43796 


11441 


..007 
11157 
..2,0 
..406 

.1505 


f 
1 

3 

2 






a6 
»7 
a8 
29 
30 


6llS§ 
61733 
6139. 
61045 


i 


7619 

73»3 
7019 
670a 


50885 
505.1 
S'"44 
497»3 


4352 
47'5 
5"93 

Wot 


3240 
3641 
404; 

443<> 

4827 


4373J 

436.7 
43619 


.1504 

"554 
11589 
li6lo 
..618 


..586 
1.649 

116,4 

11722 

»'7.M 




Ap. 




above 


above 




Li„. 


under. 




under. 


under 




k 

t 

Ap. 




EccenCr*. 
B Orb. 
H„nx. 


DiiF. fra» 


IM. En- 
ft. Mem. 


Eccentt-. 
J Orb. 


Diff from 
Mean. 


Diff. Ecc- 
rr. Mean. 
JVM.ra«. 


t Orb! 
U.nvx. 


DilF.irom 
Mean. 


DW. Ecc' 
fr. Mean. 




Si8. ... 5 1 




to .0. 4 1 


.Sig. 9 3. 




A« S.idE,««tion B Ap. i^Diff. between the gmMI Md taft Etcentridtj ii?]!^ It S. Double uiaiul AriwM«, S't4p. OrS. 

rf tke !*»«■. M«ioB ire .ugmcnud u>i diniiniAcd ia du rf,>/:«« Pmporti-o***' Sim't «PP»«iit DuAM«r. And, m<.m»«r, A. kooa'i 
Va.iatioh ii fiuther «!««<«; or rf«B.>W in Ibe iuplicK Pto^rtion of Ow Time b«w«n the. ^«rf«n.r«.-Th<«^ in Aftrono- 
mialComp»t.li™.thl.l^li.e,uJit,i.««moaljllB««.n „«» ud cDofaiiiiM «lch tbt EqiWioa sf the Moon'i CenMi Am i>r*K<ff'd, 
J'rt^. 11. B. 1. . 





SITPPLIMBNTAJb 



,, Google 



nt ROYAL AS^ -R ■& -N O M E R. 



SUPFTlEMENTAi. l.U^AR TAfeLES? 



Hr- 



iqilATiON of ihc Afr(w '%:/V £jMf/M of the Mooif'i Ci»- 
TER to that Mtan, according to tt'ar.l'i Hipithtjii. 



■jiuaenl. Moo^'f BHuateU"rtnon»l)'. 



%. 



X 


21 


1 


? 


t 








» 


i<i 


I 


« 


A. 


27 


I 


Oi 



Sig. lo 



ig. "I' ^ig. • 3 



Si|. 5 



Sig. 8 



S'g- 4 



' i' 

iJi 



i i6 



%• 7 



%. i 



I-2« -JO- 



Hi 

« 5 

£_52 



" .47 



^ 





n 
II 


III 


II 


i 



^11 



iThirint beca «bl<rt*d ^i fie UWnt Plin cCHu m»^ })t lolrTiic'W4iD'x 
KottalBq. ««»gac m^Wj AwMf, fliiEq. marbciniH^ uaM- 



8il 1 J:t 



£.1" ' 








ITTTTnillirU' III! I II tin nl'irrwitirfMiiililheatj. wJ 
ta^lnaclliuic EanicjoD. ■ - . 

«Kai7lDif. ai* 3V' = «r.S« ^ "• "' 

rt49* 







'J wlllghttbefmptf lUMHoBef ttenna^liftit 



Or t^ aji^ E)(t«Aof A(nif»«rt. 

6.7» >lnlti|lia:far407. pit Ie«abidtT. 



SUPPLEMENTAL 



ly Google 



( 81 ) 



DIFFERENT METHODS 

■ - Of Computing the , .. - . . 

ELLIPTIC EQUATION of th& MOON'S CENTER. 



=?F 



SUPPLEMENTAL LUNAR TABLES. 



CONSTANT LOGARITHMS, CDneTpoadent to the Different Eccentricities of the Mooh'i O^, and 
Sem. Tranfverfe loooooo. For tahing out the E^datioh or Corii«Ctiom lo Half the M9*^i E^utti . 
Ahomaly Xti^t f^bninng Pagit, and thcDce to find the Elliptic EquATion of the Moon'iCbhtb*.. 



Argument. Sun from the Moon's Apogee, or O true PI. — J Ap. i . Eqaated. 




IV*TAL 1 



7fc ROYAL ASTRONOMER 



SUPPLEMENTAL LUNAR TABLES. 


BQUATION, (irCo»skcTio.s of half the Eqaated Anoii^fLLY ot th« MooH, fta haiiug, «t<in«, th« Elliptic 


. Equation of the Moon'% Cshte*. 


ApoMt. Moon's Eqoated ANOiiAi,r i 


or B 1 cgnued — Ap. 2 equtied. | 


A. 
La 


Slg. o. 


Sij. .. 1 


SI,. 2. 


> 

2- 

30 


+ ■ 1 


.__+ 1 


* 1 


9^ 


• «rt7 


9^5« 7-957 


996* 


f-**' 


SW 


■MV2 


^■•K7 


^^6. 


9-H' 


9 94» 


»-95' 9.?57l9.9*2 | 


















' • 








/ * 


' ' 


O t 


c 


e 


w 





> 4' 


> 2^ 


I t 


« 


043 


> !' 


■ 11 


> l! 


I 


4i 


I 


t 


3 


1 


2 


2 


■ 4< 


« *5 


1 11 


• n 


<'44 


■ S" 


< 1> 


1 1. 


l\l 


46 


H 


3 






■; 


^ 


3 


" 4' 




1 la 


»,! 


'4S 


' 4^ 


1 1> 


1 1. 


45 




^ 


« It 


10 




« 


« 5 


■ 4« 


1 1« 


■ M 


«fl 


«,« 


* 47 






» r, 


" 44 


S 


+ 


O Ife 


11 


It 


<; 


7 


■ 49 


' !' 


■ ■( 




044 


• 4! 




1 to 


056 


41 


6 


9 20 


16 


n 


II 


8 


■ 5" 


■ 1^ 


1 16 


1 1 


»47 


1 4! 


1 2S 




« 


;f2 


'4 


o 24 


ac 


c,6 


M 


to 


' SS 


' 14 


■ >7 


1 1 


048 


1 40 


1 21 


' 7 


SJ 


41 


7 




21 


It; 


11; 


12 


:{8 


:;i 




1 1 


4a 


1 3» 


1 21 


1 ( 


s' 


40 


2] 




31 


26 


21 


17 


« 13 


1 i< 


» < 


• 49 


i s« 


• « 


■ 4 


■° 5' 


« 39 


t« 


9. 


V 


Z( 


2J 


It 


IS 


:;§ 


1 17 


1 2C 


' < 


49 


• 33 


■ '7 


1 2 


4< 


38 


21 


It 


y. 


3' 


17 


21 


17 


■ I" 


I Z6 




SO 


' 3» 


1 1. 


1 


f! 


,6 


:§ 


oti 


J6 


29 


2J 


iS 


> s? 


' »■) 


1 21 


' 1 


JO 


1 28 


I 12 


o,( 


46 


" K 


II 


)( 


12 


2C 
28 


20 


a c 


■ 4^ 


1 2B 


' 1 


051 


■ «? 


" 1) 


ft 


44 


14 


11^ 


!0 


42 


^ 




2 


' 4= 


1 2B 


• ' 


ji 


1 22 


1 7 


« ^i 


42 


12 


«7 


'4 


,. 


45 


,7 


^ 


23 


B 1 


■ 4' 


I 2a 




c ;i 


\'.l 


■ 1 


^3 


41 


11 




I 


« s; 


48 


,< 


:ia 


24 


2 I 


t.41 


> 21 




SI 


1 2] J< 


J? 


10 


14 


I 1 


51 


42 


^i 


36 


3 3 


1 ♦• 


I 2, 


1 6 


s» 


I 12 


D 5, 


47 


17 


28 


'7 


I ' 


5. 


04- 


V 


27 


a 2 


■ »■ 


1 2. 




!• 


I 3 


os» 


4s 


IS 


27 


•3 






17 


046 


17 


29 


2 2 


' 4' 


1 2! 




SI 


» ^ 


53 


4j 


11 


25 




»V 






o+l 


i?< 


30 


3 1 


■ 41 


1 2! 




51 


I 2 


50 




1' 


24 




*o 


' »4 




^. 


41 


032 


3 3 


" 4' 


1 2! 




SI 


. ,8 


047 


38 


2S 




10 

1 


1 11 




<;i 


04^ 


° 33 


2 I 


> 4' 


1 22 


■ ' 


SO 


SS 


044 


jy 


»7 


20 








?■; 


4- 


IIJ 


2 I 


1 40 


1 22 


■ ( 


50 


" ( 


41 




2S 


19 


*3 


:i 




17 


0,4b 


3 G 


' 4< 


I 21 


1 4 


so 


4: 


o,« 


30 


21 


27 


7 


»+ 




?< 


04: 


° 37 


;{! 


■ SI 


1 21 


1 4 


JO 


4 


IS 




21 






a 


I t. 




1 I 


041 


05a 


■3» 


1 20 


■ ■■ 


049 


4c 


J2 


2; 


IS 


0.14 


J 
4 


1 3» 




1 1 


,0 


S5 


■ SJ 


■ 37 


1 1; 


' » 


49 


0,6 


28 


32 


17 


12 


B7 






* -■ 


sa 


40 


1 56 


I ,6 


' 'i 


1 2 


04» 


31 


2/ 


30 


IS 


11 


; 




1 r 






1: 


041 


> S! 


' 1! 




1 1 


048 




23 


17 


11 


9 


1 


E4 


I S! 


I I 


> 7 


f. 


042 


■ S4 


' 1- 


> 17 


1 1 


» 47 


2, 


1( 


I- 


lol 7 




An 


1 4: 


» »1 


• ! 


!J 


043 


» S2 


> 3: 


' '! 


t 


46 


2C 


1; 


II 


J S 




Aa 


+ 


+ 


+ 


SiK- ... 


SiK. 10. 


■"■ %.9. 


' COIMT«0«TIOJ. of tlW »!»« U.M> Mid SOLOTIOB <A ttw Xl^M*. 


w«W'j. taiSw.. Conj, tad r:c^ J70 17' 44*/; ^s^ij^. 


Pri»^,p.S«. P«t. = S«l.TrBrf. of 4DdlipticU Orbit, »«£«, 


BSZ.S::— rsEn ' BiSs:£' 


l.ylUd.iS.i»A.!B!*1 




AC X. The &>uU -St"^ * » •1"P of (>» ^« »t> "itl> die ^D>t. 


r, udmpliaeui7 0rbiui]inyfimrtbi4<wUcoril>iti«qut. 












Thenmtfi/AaaBuiTlKhickoOin, hy a* Jfb.Dift. : Ptib. D^. :: T 
WlKBcatbtftnieAiMEulraMtfaejEfiutioB, in ill the Plamfrj Oi jit 


4 «rnffW ^, 1 T. i m. .AmA. 








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N A V 1 G A -T ft 










83 


SyPPLEMENTAL- LUNAR TABLES. 


EQUATION 0[ (iOR)lECT10N of half the EqwUcd A«om*lt of the Moo». for finding, at occe. the EUij- 
tic Eqaaiton of the Moea'a Ckmti*. 


ArgnmM. Moon'i Equated ABoMAty, or J 3. equated — J Ap. 2 equated. 


Z. 


Sis- 3- 


Slg- 4- 


Sis- 5- 


> 


+ 


- 


— 


i.i. 


■! ws 9-947 9 9S' 


9 9(7 


99" 


9-?4' 


9-947 


9.952 


9-917 


9.962 


9-9429-947) 


P?^z 


j.9,7 9.962 ' 


Uf. 




' ' ' ' 


' ' 














' * 


' • ' ■ 






' ' 




I 
z 
3 
4 
% 


20 
16 
12 

s 

4 


ri 


II 

1 1 

3 



8 
6 
' 4 
a 


6 
4 
t 
p I 


I z6 
1 19 
I 30 
I 3« 
' 34 
■ 36 


I 13 

:;i 

I 18 

1 zo 

I 21 


I 
I 2 

' 3 

: 1 

' 7 


45 
!0 
o;i 
s. 
053 
54 


39 
40 
41 

42 
42 
<>f3 


, 36 

■ 35 

■ 33 

1 26 


I l6 
1 14 

1 12 


I 6 
' S 

I 4 

1 1 

059 


° S3 
52 
51 
50 
49 
4> 


42 

4' 
40 
39 
038 

37 


30 

37 


— 


° ! 




— 1 


— 2 


6 

7 
8 

9 
10 


4 
e 8 

16 
10 


o 4 
o 8 

O II 


( 
7 
10 
013 
d 16 


5 
7 
9 
II 
015 


1 J 
8 
10 
II' 


. 38 
I 39 

■ 4' 
I 47 

■ 44 


I 23 
I 24 

' 'I 


1 8 
» 9 
I to 
1 It 

1 12 


° SS 

56 
57 


»44 
<> 44 
45 
" 4S 
046 


I 24 
I 21 
1 iS 

1 16 

■ "3 


1 10 
1 8 
1 6 
1 3 


,6 
054 
52 
,0 


04* 
044 
43 
41 
40 


ojj 
35 
34 
33 


Z4 
23 

21 
20. 


12 
'3 
•4 


M 

" 3! 
,9 


O 21 

o 24 

27 
31 

34 


18 
25 


SIS 

so 
« 
o>4 


13 

16 

0,3 

19 


" 45 

\^ 

• 47 
' 47 


1 li 

I >9 

1 29 

I 30 


' >3 
1 13 
1 13 
' '4 
1 14 


58 

59 

59 

1 
1 


46 
46 
046 
<>47 
04? 


I 10 
' 7 
» 3 
I 

57 


ost 
ji 
13 


4« 
046 
4J 
41 
J9 


j8 
37 
35 
33 
11 


39 
29 

III 

Z4 


'9 

18 

'.i 

'5 


.6 
>9 


043 
4£ 
JO 
» 53 

57 


37 
40 

4^ 
04a 


31 

3i 
41 


o >6 

30 
32 
o|3 


22 

24 
2S 

27 


^1 

■ 47I 


1 30 
1 30 

1 3= 
1 30 
■ 3= 


1 14 
' >5 
' "S 
' '5 
■ 14 


I 


9 47 
9 47 
47 
047 
47 


S! 

JO 

04S 

41 

39 


45 
4» 
039 
36 
33 


37 
34 
32 
29 

27 


29 
27 
25 
23 
21 


'^0 33 

20 
0-18 
17 


14 
'3 

II 

10 - 


22 
Z3 
«4 


; 1 
■ 9 


^' 

059 


= 43 
°4S 
47 
49^ 
,1 


■> IS 
37 
39 
40 
042 


29 
31 
J2 

33 


1*4^ 
' 45 
" 44 
> 4! 


1 3" 
1 «9 

I?. 

' "7 


' »3 

t IZ 
t IZ 


S»| 47 

(8 48 
s« 4s 
57 41 


35 

° K 

« 2^ 

2, 


o'2l 

23 

zo 

16 


24 

21 

e 13 


'9 


1; 

13 

d 1-2 

10 

8 


9 

I 

S 


z6 


t II 


; t 

' 9 
1 13 


S3 
55 
• S7 
S5> 


43 
045 
46 
48 


36 

I?. 
030 


I 4* 
' 4' 

!^ 
■ 3' 


I ii 

> >S 
1 1 

1 3 


1 It 

t 10 

; f 

1 6 


■> 57 o 44 
SO 44 
° 55 ■> 43 
54 43 
0!3 042 


16 
12 

8 

• 4 



1} 

7 
J 



II 
8 
5 

3 



9 
7 
° 4 
2 



7 
S 
3 
2 



4 
3 

1 



J- 
A*3; 


± 


- 


— 




%. B. 


1 a«- 7- 


Sif. «. 


B 


W/».«,«,044i40i^'.44"'-a.o5lo+».Ill»rlrM«rt{;i«t<.Mr.A«*»J. » »» 93 f 
*^ *^ HcDce, A-P(+i:s»<> t> 44" V' the ConvOcd Anomilr, 

Theludf IS" .' w" ij"' T«f. 9.4>S7444 • • I>' »»" »j"' Emotion, " 0™a». 
T,-.u T 'f '}" '^' • • '''*■ 9-*'*i*** 


SO 
CMTca Eqntion . . 3° 13' ji" jo"' hmIh^. & At At ftf. 


t>o»n^«*Bou«fciM. 1 


Rxl... 


• 1. 


?l.. g 




.An. p- 
■ 4I« o* •" 


:-m.Ue»: 


0.040 

0-04S 
0^50 

0.070 


■ 4i 
1 3> 




ComAianOTEqoMwa, . 


'.ȴ,; 


Comasd Anon. T. . . 
Bj- T»*. p. »t CoBfl. t«| 


• 


•"ill 


^6rE,. JCn«, 
afromtq*. Anasulr. 






Tie ^n r.Ui^ 1 
by Mr. lU/ubi: \ 
















> 


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i'Ai^ 



84 



ne ROYAL ASTRONOMER 



SUPPLEMENTAL LUNAR TABLES. 



Ei.U?riC EC^AT1«*I 4;f the Moon's Center in aU Sialnai Her yariabU Orbii: Vmm Excntridty 43319 
to 667S2 ; the JlJTifth-iJf^ancf being iooooqo. According to the NnuionioH Theory. 



Arpaatnl, The Moqn'j Equated Amomaly, Or Moon 3 Eqaated — Moon A p. 2. Eqmtcd. 




I^AMPLE J. Ti find lU Moon'i Central E^oation ttnrffaiJat r* i> 1° Sh« i Mom'i jtf. and i> it° 
ar£^ u ibt Nnaloaiu 7tt»rj t . . ' . - ' 

Ectentridiy ]) Orb. ' £rc. al-ove 45000. 

Bj Ttff. p. St. Argl SuaaMoOD Ap.iE<|iutedgivci47]i9 . . . / . . . ijig doubled =: 46]! 

Equation for tuentiicity 4;oc& . . 
ByTof. F, 15. Aig> i» 11" J E^. An. ■—j" 14' 36" . . . Excc& of Eg", tot 'joco to' 37'^ =iof,ai 
Pr. Equation .4-511 fa* 
^Xeolra) EquMion -> ] »4 9 nmn^, icqurol. See p. E]> 

OrExci. Eccr. ijT lysjV ];!' I igio Xa^. T« L. L. 1436 Confi. lCutliiigo(r4Fig, tp") 4-9',55l9.iS 

ExceriKq* . . . i« j7 4639 I Add L.L. Elceft Ecc7. ^ibc Righl wbenlfae ( .FT.'£q. .3}" 

T416 Cpoft. i andL. L. E»t«fi Eg'. J X'nEDfOreniloff f For 1 0000 1 
I 79JS "q""- ■ -Sjoi L.L. Pre^Ef. n ii ^°' " ' 



Kfaatal ytatmaff, s 



„SS' 



i °°l°= Sj = 



PlOf', E^ leq'. 



5 tJdHlnibtCtiartlEq.fir ihi Exafi ? 

{ ^ Eccnaridijobovtibtlafi,. J 

7 or Moon't Orb. (ia p. 8 1,> idiJ then the Centra] E^Dit^n (it 



•I «f the Moon'i ApO{ce. 



«&«;; ii eafilj' ud reullly pc. 



""sCi^EEMERTHP^ 



md NAVIGATOR. 



85 



SUPPLEMENTAL LUNAR TABLES. 




ELLIPTIC E<iUATION of th« Mooh'iCbmtex, according to the Awv/wuVar Theory.. J 1 


In 
oT 
Dc 

M 

(a, 
+ 


ArfKmaa. The Moon's Equated Anomaly, or ll 1 Equated. — H "Ap. 2 Equated. 






SIGN I. 


In. 


4S00O 


Dif. 


5000 


joooo 
E,.». 


Dif. 


;ooo 


J5000 


Dif. 


D.Eq. 
forD. 

5000 


60000 


Dif. 


D.Eq. 
forD, 

Sooo 


65000 


In.. 




Eq. .. 


Eq. D- 


Eq. B. 


E,. ». 


Dif. 


forD. 

sooo 


— 




— 


— 


— 




• 




' " 




' ' 


/ * 




a ' » 








' * 


/ B 




/ J 


/ fl 


3^1 "9 
29' 10 
23,' 10 


10 

9 


° 


2 j6 ■( 


4 3' 
4 '7 
426 


;i'o^ 

.6 10 


'47 S« 
' S' iS 


4 S9 

+ S7 


15 22 

16 19 


2S8 2. 

3 3 49 
3 9 M 


SzS 
5 25 


IS 12 


3 '3 JJ 
3 '9 30 

3 25 »3 


5 57 
5 53 


'5 3 
'5 3' 


3 '8 j6 
3 35 ■ 
3 4' 22 


62s 

6 21 

6 18 


'4 54 
IS 21 


-I 1 


2 40 SI 


16 ^f 


' S7 41 




.647 


3 '4 36 




.6,7 


3 3» '3 




.627 


3 47 4° 


lb ,7 


27 10 


II 


1 

6 


' 45 '3 
' 49 34 


4 *' 

4 '7 


17 27 

17 M 


3 2 40 
3 7 =" 


4 4& 
4 4S 


'7 >! 

>7 43 


3 19 55 
3 2S " 


5 '3 


>7 S 

17 31 


3 37 

3 42 44 


5 44 
J 40 


16 SS 

17 22 

17 so 


3 53 55 

4 6 


1045 
17 11 


z6 10 

ii — 

24 10 


I. S3 S' 


18 zz 


3 " '3 


in 11 


3 30 24 


j» 


3 48 24 


4 6 14 


5 57 


17 40 


10 


7 




;1 

t 3 


.8 4(, 


I ■<•(( 




IH T9 


J 3S 3^ 


^6 


lU 27 


3 J4 ' 




.8 17 


4 .2 18 


.8 7 


23 I( 




» 


, ZI» 


19 17 


3 " 35 


4 36 

* 33 

429 
4 26 




3 40 40 


18 SS 


3 59 35 


!•? 


.84^ 


4 <3 ,8 


18 31 




12 


q 


J 6 ,^ 


19 44 


, 26 II 




3 45 43 


S 

4 55 


19 21 


4 5 I 


19 11 


4 =4 IS 


ly . 


21 IC 


12 


10 


3 ■» 33 




3 30 44 




3 SP 43 


19 47 


4 10 30 


5 " 


19 M 




548 


ly 27 


20 ic 


17 


11 






3 35 13 




3 S5 38 








4 35 55 






11 




3 "8 36 


3 56 




3 39 3S 




4 3' 


+ 48 


10 40 


4 21 11 




20 ZS 


4 41 3S 




zo 16 


18 1: 


















zi 6 


4262s 






4 47 'S 






17 12 






J :6 26 






3 48 21 
















21 19 


4 5> 51 






16 12 


11 


>! 


3 J=i6 


346 
3 +3 




3 5= 36 


*"n 


22 8 


4 "4 44 


4 37 


21 s6 


4 36 40 


5 ' 
* 58 


21 41; 


45825 


5 27 


21 34 


tS I. 


>; 


16 


3 34 = 


22 46 


3 sO 48 




4 19 21 




4 4» 4* 


22 10 


5 3 5» 


21 sq 


14 11 


■ 4 


17 


3 37 4! 


23 11 


4 56 


4 3 




4 iJ 53 




22 47 


4 46 40 


22 H 


5 9 '3 




22 19 


13 H 




IS 


3 4' 25 


3 36 




4 4 SS 




4 ^8 22 




23 10 


4 5' 32 


iis 


22 Sf 


5 '4 30 




22 4(; 




J, 


'<) 


3 4S > 


Z11 Tf 


4 8 S9 






4 32 46 




23 34 


4 s6 20 


zj 23 


S '9 43 


S ii 


21 IS 


11 [I 


12 




3 48 34 




24 Z2 


4.256 


3 S* 
3 47 

3 44 
3 39 




4 37 6 


4 >S 


^3 5« 


5 I 4 


4 38 


.3+6 


5 34 so 


5 a 


2.1 34 


10 12 


'1 


21 


3 S^ * 


wa 


24 46 


4 1648 


'4 33 


4 41 2' 


24 21 


5 5 4» 


Z4 10 


5 '9 5' 


=3 59 


9 tl 




j; 


3 5S ^7 


v\ 


2^ t 


4 20 3f 




4 45 32 


: 6 


24 44 


S .016 




Z4 35 


5 34 4! 


t^l 


24 22 


8 U 






3 S8 4: 




4 34 '5 




4 49 38 


^S 7 






24 s6 


5 39 41 


446 


24 44 


7 »» 


11 


^4 


4 ' J 






4 27 58 




4 53 40 




25 2< 


5 '9 f 




ZS It 


5 44 27 


ZS 7 






3^ 


4 S -8 


3 9 


261, 


4 31 3; 


liJ 


26 \ 


4 57 37 


3 52 


^5 5" 


,2328 


4 '4 


zs 40 


5 49 8 


436 


2s 29 


1 " 




2fi 


4 « 27 


.fir 




,«„ 




26 1, 




26 2 


5 53 44 




4 >' 




a? 


4 II 32 




7fi rt 


4 38 3= 


76 ifi 


5 S '6 




26 3T 


! 3> S' 




26 2^ 


! S8 H 


4 3" 


zA II 


3 '* 


'3 
11 


18 
29 


4 H 3" 
♦ '7 *9 


2 S7 


27 20 

27 39 


4 4. 52 

4 45 8 


3 .6 
3 '3 


%;, 


! 8 59 
, .236 


3 37 


*6 SS 
27 16 


5 3S 54 
S 39 S* 


3 S8 


2644 


6_6S7 


4 '9 


2633 
26 S4 


) 11 


ii 


*o 


4 20 21 




z8 


4482, 


»7 47 






27 3( 


5 43 44 






27 IS 


-^ 


+ 


+ 




+ 






+ 












+ 






15 


Bq. K.lDil. 
4SOOO 1 


5000 
D.Eq 


E,... 


Dif. 


cooo 
D.Eq 


£<,.». 


Di£ 


^°e5. 


Kq. J. 


Dif. 


l),F.q 


E,. J. 


Dif. 


f) Fn 


D 


foooo 


SSooo 


60000 




65000 




SIGN 10. 


BXAMPLE 11. 1iJ!al ibr Ejiitiifi >/ 'ti Moen'tCaOa aPaurOU ti \' ijo m' &• ^ ]) ..^. «^ 31 5° 44' T, ^^Mui AmaJj t 


B)rr«*.p.l7. Ai|i. i' j» 44' J eq* An. . . ''''.*"*'° — fi" i^'^^^'.EiccflofEqi.Tor- j«>o'. , jV28"=j4'.46j V* 
Propl. Eq». +7 s6 - ■ ■ f-^ 


(CcatnlEiiouiciOMinai; ... — 6 t6 1 mi*. Stcp.gG. 0114 


CM^M I4ie+ -) 1 6918 
A.rf.E^)' igf^j" WSf Th. ftm. R.A, to be ebfc.*U In 1 p^duft r«W */ 4 U^i^, i*. +7',q464,76 


P«.pl. E^. 7 5« -8779 •* J 
































SCfPtEMENl 


fAL • 



,, Google 



«6 



Thi ROYAL ASTRONOMER 



SUPPLEMENTAL LUNAR TABLES. 



IV. HL0?TIC SQ.UATION of riw Maoii'i Omw-. Aceofding to tht Vp 



Tin, 



Argameni, The Mbow'i Equated Anomiiy, Or P 3 Equa. — Ap. a Kyiawd. 



D. Ee. 
IwD. 



Eg. a. 



forP. ^- » 



65000 



65000 



D.Eq, 
for d: 
5000 



;;:i- 



' 7 



t 4« Si 
+ SO 4t 

S * S4 ■' 



4 5! 4» 

58 4i 

5 ■> < 



74 



4 3* 



8 J7 



U» 



4i2 



;S 04 48 21 
:8 1J4 Ji el 

»8 39 4 S4 3: 
'8 S7,4 57 'I 

>9 'SS 



.8 38 s 






30 40 s 13 " 

3° SS S 'S 5° 
}| 105 

S »o '7 



:8 a6s 
i8 45 
■9 



9 36: 
5 e6 13 



»7 3% 43 4< 
»7 SSr 47 3' 



!! 53 5 S! ■» 



. 43 57 
S <* 35 



29 30 6 
ag 476 

fo 561 
lo 20 6 ] 



30 
3« 4 
3» 5 



8)528 ^ 

s 29 49 ; 
5 3 ' 
s 32 57i; 



33 2 5 34 23 



33 '2 5 35 43 



3> 38 
33 46 



■" 



Dif.i,° 



000 



5 24 22 

5 26 17 



5 56 I 
58 '3 



|o 526 19 s» 
- 6 6 22 38 

"a f '' ■' 
,1 36 6 27 4] 

• 4^6 30 



26?!« 



3 59 

S 42 



5 36 57 



S 40 S3 
S 41 37 
5 4" IS 

34 105 42 47 

34 M S 4J 



5«j, 



II 29 
.240 
'3 44 



.653 
17 23 



238 



3 36 



E^TT 



•gjTiT 



SSOOO 



ii; 



SMH7 



27 45 
zB s 

28 24 

28 4: 

29 

9 



5 30 43 



9 36 6 



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5 34 . 

S 37 48 

5 41 
44 27 
47_i7 



5 50 40 
S3 5' 



3° '9 



586 



'56«S;* 



6 3a 16 

4 » 34 a4 

a a6 5 36 a5 

- 6 38 20 

^4° 7 



.3 o 6 41 48 
9 5 4J 21 

:4» 



7 8 45 
7 10 51 
if 



JZJ 



648 25 
6 49 23 

36 50 56 



58 



33 
3! 47 



7 19 30 

7 20 ^ 



4 '06 51 33 



7 23 1, 

r 24 S7 

S 39 



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6 4 

i 

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60000 



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65000 



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b 



m 



al, n. Praafu. •' * 



BlUMPLt III.' TijJiit SfiJiui/tnOrUl 
Ldwi of die Mooo't Ueu MoHdu, tx the 'End of Vol, 

Bl.g. i4. iM*l«» Fw Wi fily «aaoo (lb* Am-m ^ (B i R^d.^ tat qihift jo» on the STde wi find ,• i,/ „1 reaninrf. M 
Jliuiiiibudnlactdit bjrhuHcdiiKl 3° 13' 34'". Bt £ii//raAJ^'i Coneaion of Wif i HwoUi^, ' ' ji i 

6»fc.-U»OitIui». Con.. Losuitbm.. 



tScmaCoij. ^'i.o6x>9« 
To Sem..TnmrTCTfi: ',1 . . . ; • 1 ', 

50 T. M. AiHun. . ]0° 

ToT.aftamatdM.Aii. 30 »' 41" I . . , 
Comajon of M, Aaato, +1/ 41" DiHetMM. 
ConcaioBfM.A^OdL +1 «o{ tbtlulf. Of Eq> 
M. Anom. coRcftcd ij« 1' ko*^ 



Now, Al Af. VA. . 

To Perifa, Dift, 

SoT. »je i'-»0Wi ; 

iM.AiiciE 



-.omtSei. }| »-<''7!°° 



E^Mden-— J i| ]6 duDiSbeacc 



blll'l'LkMfiNTAl. 



,, Google 



MHd N A V I G A TO R. 



SUPPLEMENTAL LUNAR TABLES. 



IV. EtXlrt'IC EQi^Al'lQN of the MOQN'i Ctnur, accowliiig'to the Nn»fmmn Thewy^ 




TB£ tottifaag Ejcuuplc 



iX 



TOBglit out ucofdint to Dr. HtStf't Method, 

CoaA.Lsg. 
■ or 60000 to Rid. loooooo gini g.947g«4 



■ 5 1 ■» Tui(. I M, An. cofTcOed . . 9.4187^74 Log. + 
Tmi. i Tree Aoom. ij* %f i*" 44'" 9.1765614 
Donbled . aS 46 15 iS TrucAo. 
E^tcdM. Adoiii. ^o 



f 5« 14' Sub 1 ) Ap. 



Br AtJMbi . 



+ 1" ai'" Enw. 



SUPFLEMeNTAt. 



,y Google 



7lt ROVAL ASTRONOMER 



SUPPLEMENTAL LUNAR TABLES. 


D, IV. ELLIPTIC EQUATION of die Moon's Ctnur, Accordinj! to the Newtonian Theory. \\U 


ot Artum.Kt. The Moon's Equated Anomaly. Or L i.Equa*.— J Ap. z. Equa-". ipi 


f, ' ' SIGN 4. . llL" 


M I> 45000 


Dif. 


or p. 


^oooo 


Dif. 


D. £q 
foiD, 
sooo 


SSooo 




60000 


Dif. 




6sooo 


Dif. 


?o;Ss". 

sooo + 


fo( V /Eq. B. 


E,. .. 


E,. J. 


Dif-fo^Dl 


Eq. ». 


Km' 


Eq. J. 


— — 


000 




— 


sooo 1 




000 





- "' ' ' " 


' * 


' " 










' * 


/ « 


• 


/ # 




" 


f » ° ° 


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31 31 


6 SS 


^^ 


31 40 


S 1» IS 


. 


■ 52 


6 10 27 


]" 


2 2 


J 42 25 






■ » 4 30 9 ' ^° 


;l iG 


' ♦ 1 


C" 


31 2S 


S 3S 30 




1 16 


6 7 6 


1 48 


>3«S, 






io 5^ 


5 1 8 




11 < 


S 3^ 17 


Wl 


1 21 


i 3 J« 


3 36 
3 +3 


:i 12 


3; 1< 




ji 4328 .1 


-0 34 VH!*^ 
10, 44 H 34; \f^ 


30 42 
30 24 


+ S8 6 
* S4 S8 




30 S2 
30 34 


S 28 s8 

s =s 32 


I 4 

47 


6 2 
5 S' "9 


jt 16 
30 59 


J 31 18 
527 ,8 



8 


31 2827 12 
31 1126 12 


12 54 2> 38 


= '■ 


30 ^ 


4 i. 4! 


3 20 


30 <7 




lis 

4 5 
4 I' 
4 »7 
4 24 
4 29 
4 3l> 
4 4" 
t 47 
4 S3 
4 S» 


19 


s 52 ■( 




10 41 


J2,,.o 


10 S3 25 12 


xz 64 >a 37 


29 46 


4 48 "3 


29 (« 


S .8 2. 


10 


5483; 
5 44 26 




iO 2, 


S 18 S4 


4 *4 
4 3^ 

4 39 
4 +7 

4 SS 


30 3624 13 


"1 7+ 's 3of ,; 


2g 27 


4 44 S7 




2, ,« 


! H 35 


9 S' 


4 12 

4 IS 

5 26 

4 33 


1" ■ 


6 14,0 
6 ,sS 




„ 84 .» ic3 ;j 


29 6 


4 4> =5 




2, ,« 


S >o 43 


.9 ,1 


5 40 ■■( 


29 4< 


29 5122 13 


14 94 9 3 
13 104 S +' 


3 22 


28 44 

2823 


4 37 47 
4 34 4 


3 43 

3 47 


28 58 

28 36 


S 6 45 
S « 40 


29 10 
28 49 

2827 


S 35 S5 
5 !■ 29 


29 24 
29 3 
28 41 


5 5 19 

6 32 


29 3821 14 

29 1720 14 


.3 114 I 14 




28 1 


4 30 15 


28 .4 


4 58 29 






iz 113 S8 4i 
■ 1 133 Si 6 


'3^6 

J 45 
3 S' 
3 SS 


27 39 
27 1.; 


4 22 ZI 


4 
♦ S 
4 i> 

4 16 
4 * 


"7 !■ 
27 27 


* 54 " 
4 49 48 


28 4 
27 4> 


S 2. .6 
5 17 29 


4 47 

4 S3 
I 

5 7 

5 13 


«7 55 


5 50 34 


S 'o 
S '7 


2832,8 1, 
28 ,17 14 


12 143 S» *S 


26 ,. 


4 .a 16 


'7 ! 


4 45 '9 


27 '7 


5 .2 It 


27 31 


5 40 7 


27 4s 16 14 


I J «S3 +7 40 


26 29 


4 H S 




4 40 43 


26 5, 


5 7 36 




5 34 42 


S 3» 

S 39 
S 4<^ 


27 1915 13 


I3J >6 3 43 49 


16 


4 9 49 

4 ! '« 


26 13 


436 2 


2627 
26 I 


S 2 .9 


26 42 
26 16 


S 29 11 


26 s7 '4 '5 


"4 >8 3 3S 54 
1+ "9 3 3' SO 


4 13 

4 <7 

4 22 

+ 25 


IS 7 
24 40 


4 ' 1 
3 s6 30 


» 4 
4 4 


25 2. 
■4 54 


4.622 
4 " M 


25 35 
25 7 


4 5' S7 
4 46 31 


; 26 


25 49 
25 22 


5 '7 46 
5 i> 53 


26 3 12 14 
25 37" "S 


13 M3 27 42 
15 21 J 23 ag 


24 12 


] !■ 5' 


24 2S 


4 16 19 


S 9 




4 40 S9 


S 3 


'4 •,- 


5 5 S3 




■5 '010 M 


23 43 


3 47 1; 


.J ;« 


4 11 10 


2+ 11 


4 35 21 


S 44 
! SO 


24 26 


4 S9 47 


f< It 


24 4' 9 >5 


IS 223 19 12 


23 1. 


J 41 26 


2J 2,, 


4 5 55 


e 20 


23 4^ 


4 29 37 


23 ri 


4 53 31 


f.-l 


24 12 8 1; 




2246 


3 37 3' 


22 sr 


4 3S 




23 12 


4 23 47 


23 27 


4 47 ■< 






15 243 10 2J 


22 I 


3 3* 40 


22 ,0 


3 SS 'o 




22 42 


4 17 52 


22 ,6 


440 48 




»3 10 6 14 


13 253 5 56 


4 34 
4 37 
4 4= 


21 4 


3 '7 41 


s 


21 SB 


! 49 39 






4 1' 51 


22 .S 


4 34 16 




22 ,8 s 13 


13 263 I 22 


21 M 


3 " 3; 


2, 27 


3 44 3 


S 40 
5 4> 


21 41 


4 5 44 


Li 


21 ii 


4 27 39 


6 44 
6 50 
6's6 

7 


22. 7 4 13 


12 272 56 4S 


20 4 


3 '7 =8 


S ' 


»»2 


3 38 23 
3 32 38 


!0 ,6 


3 59 32 


6 iB 
6 21 


20 50 


4 20 S4 
4 14 4 


21 35 3 13 


12 292 47 20 


;:. 


19 1* 


3 6 S8 




., ,c 


} 26 48 


S 54 


20 4 


34652 




4 7 « 


20 28 1 12 


12 3CI 42 32 


"9 


3 ■ 37 




19 1, 


3 !o S. 


19 3C 


3402, 




194; 


4 6 7 


19 56 13 


+ 




Tec 


+ 




n. 


+ 




sooo 
D.£(j 


+ 




JOOO 

b.E, 


+ 




I. 1- 


2 » Eq- B- 


Dif 


E,. I. 


Dif 


Eq. ». 


Di/. 


Eq... 


Dii: 


Eq.H. 


Dif 


Cz A. 45000 


^0000 


SSOOO 


60000 


6fOob 


■ 1 SIGN 7. 1 ir 


T. Jtf<r*.«.i<E9UATio.i afibi Mian nib, 7r.i .1mmalj,iirM>a it Ibitrt, Plati •>. all ii„?Unnay Ortiii ixtift ibai ,J M„a„j,fr 


Rail \J,Ju,i/frpmapr,Jftm iS i^md -U f. 49, FalUdium, 1757.) 

Art. 1. AilUdiu«i.toCofiM of the given MwnADomjly, fc i. tb« rc«i«riH>^ of the O.bilmore iti JtWrt, (R»il.ormeuiDifl. being i.) 




th«Seni.TonrHrfcif(h«M«nADoni.b.B«Ylh.r9oorltlitlMni7o<'. 


3. Thtn U.J, Ax the Smm, in one Cafr, or Dlftraa in (he othtr, ii to doufch the ttxi ErrentricifT, fo J< lb« Siwt of the given Man Aooroily 
to the Fnpm!,^! Si« of »n Arc P. 


4. ThcAfr'jii<MiDr5«>«/.of>no<herAcc, tnfwenlile to w (iM V'r^C*^ of thii propoilima! ftW of M AttP, faeinf Mn JM frem the 


Depm Mfnutei uid Seconds of the faid Pioporiionil Arc, P, the Kcl'ult «II1 be the £«»/><» or.I)^<r»a of AiKiiiiily Sought. 

N.B. rtUylrff DiffitiMiith fub,raa^ /ram ibi Mian Aumthfr tbr irut m fl< >j) .Sm i;j« of tbt jbrumm, t«d u I, tiJtd it^t im 
thlafiSixSif^. - 


























SUPPLEMENTAL 



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mJS- N A V F O A T O «.-^ 




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18 







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33 !f 


21 


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11 48 


14 II 


l6 2B 


18 ,4" 


a, 8 


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1140 


17(4 


30 8 


32 I9 


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12 ( 


14 1* 


16 (1 


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12 za 


14 s^ 


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SUPf-LEMENTAL LUNAR TABLES. 






EQIJATION of the Mbah to the prefcnt Eluftic EaeATiOH of the MOON'a Cimtbr. 






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S I G N J. 






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JrgMmtHt. EquatfdANoiiiALYrof the Moon i Or, £ i.cqnued — Ap. I> a.«(|uu«d. 






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»■ 1 


.' 


4' 


6» 


8" 


iti- 




14° 


i6' 


180 




23° 


24" 


260 


38- 


,0- 






» 


i » + 


+ 


+ 


+ 


+ 


+ 


+ 


+ 


+ 


+ 


+■■ 


+ 


+ 


+■- 


-fc 


+. 






3 


6 ■ ' ' 








' * 














' ' 


' ' 




t .' 


/ i 






5 c 


« o 


80 , 


»OB, 


41 


051 


lo ,7 


56 


10 48 JO 36 


«o 14 


9 13 


79 17 


8 ,a 


77 53 


r? C76 2 


75 9 






1 




71 *7 




26 


o,« 


I04, 


042 


lo V 


lo 20 


79 5» 


9 1» 


79 2 


» 2, 


77 38 


645 


'5 48 


74 46 






% 




79 »° 


79 41 


958 




80 It 


11 


«o ^ 


■9 5« 


79 10 


9 '^ 


783s 


7 56 


77 12 


6 It 


75 22 


74 ^> 






"4 


7« 3! 


'» il 


9 IJ 


6 46 


'9 »5 


9 '7 


;n 


1 ; 


7846 




77 S< 


7 II 


■6 37 


5 35 


'4 18 


73 3< 










77 «6 


77 45 


8 2 


'8 15 


8 17 


7 5S 


77 17 


7 '7 


* 42 


6 1 


75 21 


428 


'3 33 


7» 33 






■c 


10 


76 


761? 




76 50 


64. 


640 


■6 25 


76 9 


5 ^' 


'! 'f 


4 17 


73 5i 


73 3 


.2 ,, 


71 11 






13 


i8 


7+ .8 


74 37 


4 53 


5 ' 


75 6 


5 5 


74 56 


74 46 


74 2'' 


+ 7 


71 34 


2 SJ 


T '5 


I 24 


70 ,1 


69 3. 






\% 




7« H 


■» 32 


2 47 


2 (7 


■1 2 


3 t 


'2 tl 


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■2 : 


'I 30 






S, 3, 


i« 34 


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M 


W « 


•0 If 


28 


34 


■0 3« 


3S 


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19 


70 c 


^9 « 


19 I, 


.8 ,! 


•7 5' 


67 11 




'S ** 






■ i 






»7 « 


746 


18,4 


67 s8 


7 57 


•7 49 


■7 39 


17 21 


l\ 


66 „ 




1,2. 


''4 37 


'3 49 


**'S1 






Z< 


lo 


"l-o 


k4 jO 


i4 49 


>4S7 


65 . 


4 !9 


64 5' 


644: 


6435 


6335 


J, 8 


63,1 


61 47 










Z2 


» 


61 .0 


61 24 


bi ,6 


*:« 


61 47 


246 


61 40 


6,, I 


S, 14 


60 ,8 


60 29 


59 59 


59 24 


5843 


57 59 


57 '1 






36 




(7 411 


;» • 


8 14 


8 20 


;8 22 




!» 6 


18 . 


\7 51 


57 36 


;7 -1 


56 4° 


56 7 


55 »8 


14 47 


54 

,0 2< 






A 


fS (7 


14 I" 


4 18 


4 i> 


;4 "6 


428 


54 '3 


54 1; 


;4 1 


H 45 


13 2C 


5' 51 


52 31 


11 4S 


5" 7 








a 


49 «« 


|0 10 


17 


» 17 


;o 13 


21 


so 23 


1° ■; 


50 I 




W 24 


r« 55 


,827 


17 51 


47 30 


4*4' 






1 < 


T < 


45 47 


I! !7 


.6 1 


t.- 2 


^6 10 


612 


f 7 


* I 


45 47 


f5 •! 


45 i< 


14 5" 


44 *1 


-i f.i 


43 20 


42 44 






7 = 


I, 3E 


4' »3 


4' 32 


4' 41 


41 45 


41 47 


ti 46 


41 41 


4' IS 


41 22 


41 II 


40 51 




40 6 


19 38 




38^ 






; 


36 


J6 (0 


36 57 


37 i 


:7 7 


37 9 


7 5 


37 5 


17 


36 4« 


36 40 


361, 


,6 , 


IS 41 


3! 16 


14 5= 


34 21. 






2^ 


iJ{l 


,2 6 


32 12 


12 M 


,2 16 


2 10 


12 '1 


32 I 


31 47 


31 4' 


11 H 


11 17 


31 57 


|o 3S 


30 12 


29 44 








33 


'7 4 


27 10 


27 IS 


•7 14 


7 M 


2711 


27 7 


2657 


265, 


>6,t 






3548 


25 ,0 


2S It, 






■( 


3C 


" 4S 


" 54 


21 ^, 


22 I 


22 2 






21 (« 


21 45 


21 41 


21 J. 


21 31 


21 7 


20 S! 


.0 j8 


30 u 






' ^8 


.6,6 


16 »9 


16 41 


,liti 


1642 


643 


1641 


16 40 


.6,1 


16,0 


16 ti 


161. 


.6 I 


'5 4S 


■< 19 


14 J, 






lb 


II 14 


II 16 


II 18 




u 17 


1 1; 






II IC 


11 1 


11 I 


40,6 


■64I 


10 41 


'9 34 


"■3 ■ 




»' 


! 4; 


5 4" 


5 45 


5 55 


5 41 


5 45 


5 41 


546 


S 4« 


5 41 


5 38 


5 3' 


! J= 


!'" 


5»4 


5 * 










II 




It 


IC 


■( 






11 








\' 






5 


» F 










± 


± 


± 


± 


±: 


± 


3: 


± 


± 


± 




± 


:t 


± 


±r 






« 


i< 5 ij 


5 '7 


5«a 


5 28 


5 »7 


5 27 


5 5" 


526 


5 *S 


5 10 


5 2c 


% '9 


5 17 


? ■; 


5 8 


s ? 






31 


f II I 


>i 5 


11 6 


II { 


II 6 


II 6 


II 5 


II 4 


11 3 


10 t4 


10 t2 


10 47 


10 43 


10 3, 


10 2, 


10 i 






«4 


, 6 16 16 


16 41 


1644 


16 4& 


.6 4i 


16 45 


1646 


16 40 


16,7 


1627 


,62, 


t\\ 


21 21 


■s 5; 


'5 4>" 


15 ; 






3! 


. < W*^! 


!2 H 


22 IS 


22 2] 


22 2{ 


!2 It 






*3 •; 


" 5' 


=1 4S 




!0 ,. 


20 , 






^s 


2 »7 37 


27 46 


!7 50 


.7 t> 


'7 5' 


■7 50 


«7 4" 


27 41 


^l 3C 


27 24 


27 I,! 


26 ,t 


«6 4 


26 '2] 




•5 » 






1- 1 


4 < 33 « 


33 10 


35 15 


11 17 


33 17 


33 1' 


33 11 


'3 ; 


1*17 


32 v 


12 2^ 




11. 52 


31. ,29 


Jl < 

SS Si 


30 7 

35- 6 






»■■ 


10 si 


18 M 


3«''2, 


,8 ,<J 


38 33 


18 34 


18-,'. 


,8 38 


j8 isha 10 


37 56 


17 18 


37-I; 


36 Si 


36 2g 








21 


41 -1 




43 3] 


41 4' 




41 1I 


43 31 


43 2343 >s 


4' 57 


42 ,« 


4= ■! 


,1 4941 13 
46 04s S5 


10 41 


40 1 






' 


*• 


,8. 


48 2b 


4! ,, 


4» 17 


4837 


4» 3^ 


u 


,8 IS 48 6 


7 47 

S» 22 


47 '\ 


46 57 


« '2 


44 » 
48 4 






■ 


. 33 


!» S 


51 5 


51 " 


51 ■: 


S3 17153 t: 


|2 S4S2 4' 


!■ S> 


,1 28 


,0 (8 




49 3» 








- le 


S7 1 


7 3« 


17 1« 


57 4' 


57 43 57 3! 


57 3' 


S7 "7157 • 


56 42 


,6 n 


5i 4' 


SS 19 


f4 "1 


53-4 


S' 7 






1 






Si 37 


6. '46 
69 59 


«' ' 


6i4,;6i43 


6135 
it 26 


61 21I61' 8 


J? 4! 


io -i 

61 si 


^?-i; 


59 6 

62 41 


,8 3. 

IP! 


g' 


S6 
60 






1 


1^ 


sS,c 


IH, , 


69. "'68 !, 


18 (C 


>8 32^68 15 


67 4887 IS 


66'38[6s s8 


69 2! 68 » 






1 


f3 




71 (C 


!' 19 


J2 


7" i!7' 5 


71 (C 


?i 3' 7' ' 


70 4670 12 


So 3 


68,0 


'7 Si 






I 


IC 


7+ '< 


74 2 


74 17 


74 4 


74 4' 


74 3 


74 = 


'4 8 7j 45 


73 29 72 45 


72 . 


n ". 








3 


: 


76 3 




76* 


765 




764 


76 t 


j6 11 7S S 


'! «6 74 s 
77 10176 3 


74 5 


73 24 


7= 3< 


71 30 70 j2 








1 


7» 


?8 2 


7» 3 


78 1 


78 3- 


78 2 


78 2 


78 77 4t 


75 4" 


75 


74 


73 S 


7i|S9 




'3 


4 


79 ' 


79 34 


79 4 


79 5 


79 48 


79 4- 


79 V 


79 "78 5 


78 2177 4 


77 


76 t 


7S ' 


74 '> 


73"' 






■ 




*«I7 


io:2 


Bo, 


«o ,. 


io 24180 I 


'9 54 79 3 


79 2 78 2 


77 41 


765 


'1' 


74 5' 


73 'S 




1 t 


1 < 


80 1 




80 44'8o 5 


80+8 


80 42I80 3 


lo 12I79 s 


?9 18)78 4 


'M 




7» "bf > 


?t 


i 






■) 


— 


..._, 


— 1 — ■ I — 


-- 1 - 


— 1 — ' 


-\-. 




— 












r^ 


U- 


-.26? -I 2+°:. ai'' 


zo" 1 18" 


16' 1. 14° 


.of 1 ,0' 


8' 


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Jrriamm. hf^tMMi A««mai.v of tiM UoAU { Or, ( 5. cijiuud — Af . S 2. eqiuttd. 


■0- 2" 


♦' 


i' 


s» 


10" 


128 


•f 


^' 


48M — 


I'f 


t' 


ii. 


2*" 


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+ 


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1. 2 






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7S V3 « 


7' *7 


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ii 1 


i4.8 


1I2 22 


00 22 


S« "is S6 


i> 54 


i' 7 


4ll4i 


j6-2 


I 


sS 


74 46 7J 30 


72 1; 


70 S^ 


b,<8 


(17 41 


65 S7 


i4 ■ 




60 10 


58 


5S 4! 


53 31 


|o4»48 12 




J 


>b 


74 21 7j 6 


71 +« 


-0 2j 


iS 53 


"7 'I 


;s 34 

64 S' 


63 Si 




19 49 


S7 40 


5! "' 


" f 


45 37 


«^ 


M 18 


2 2^ 


'I 8 


09 4. 


M 11 


06 ,ll 


6, 8 


11 I. 59 14 


S7 7 


54 55 


32 5( 


5° "1 47 45 


45 11 


i 


13 


72 n 


1 29 


70 5 

68 4b 


M4i 


I17 M 


6S 19 


63 5« 


6z 11 


60 1858 2! 


56 i( 


54 S 


51 49 


49 '^K 2 


14 31 


l< 


IC 


71 M 


a 


07 2 


ss SS 


0427 






19 '157 17 


55 ■; 


!J < 


50 ;c 


t8 2g'46 9 


^3,41 


ti 


"it 


>9 34 


i8 2( 


67 M 


«( (^ 


114 28 


62 s8 


6. ., 


S9 38 


S7 49 S! S" 


5, 57 


51. 51 


49 41 


47 H4S ' 


4»41 


n 


i6 


i? M 


,6,1 


oc 10 


04 , 


,240 


M H 


S9 39 


37 Si 


,61. 


S4"4 


5! 2) 


io25 


:2;i 


16 5 43 5" 


t^\ 


ll 


■ + 


6, 2» 


14 22 


', n 




19 3^ 


19 15 


!7 4< 


i6 7 


S4 21 


52 39 


SO 46 


4»49 


14 37 42 26 


■I 


12 


62,7 


'■ V. 


(.048 


19 3; 


18 H 


[6 ^s 


SS »9 


Si 57 


52 i( so 36 


48 46 


4' 53 


4 57 


1" S'5".47 




K 


lO 




■1 '" 


58 8 


17 ' 


15 43 


,4 27 


S3 ; 


51 31 


SO 048 1} 


♦6 35 ,4 s« 


13 


10 S9 3« 59 


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iz 


8 


(7 12 


(6 14 


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(4 '■ 


S"19 


1' 44 


(o n 


49 


♦7 S»4S"S^^ 


44 19 *• 37 


40,2 


3« 37 37 • 


35 3 






5+ 3 


:3 ' 


t" u 


.1 1' 


;o ; 


1» S) 


47 3° 


40 i> 


H S2 


43 21 


41 S2 


36 16 


383; 


J* 47 34 S9 


SS ; 


tl 


* 


;o 2i 


19 V 


18 4' 


47 45 


lii 41 


ks ,<= 


H 'S 


4, It 


41 SI 


40 21; 


39 1 sr 3S 


,6 2 


34 M 3« SS 


so s, 
28 3! 


zi 


2 


t» 42 


1, S4 


H « 


« H 


11 1' 


4» '4 


3' 9 


40 1 


38 4. 


37 " 




34 47 


33 »! 


31 4<36 ". 


I o 


! ° 


t' + 


12 « 


11 1; 


40 2a 


19 5» 


3« V 


3,7 40 


J" w 


3S ^ 


34 ■« 


!5 5 


}• !' 


?■ Sf 


'9 S'7 35 


261. 


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II s» 


,8,8 


,7 ,>' 


17 i> 


S* r> 


IS 4S 


34 SS 


34 1 


33 3 


32 1 


,0 SI 


■9 S! 


284, 


.7.28 


26-1324 58 


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1 


26 


H " 


I, 4<> 


H 11 


5« 3' 


,1 4» 


31 ! 


10 14 


19 2. 




27 ,2 


26 3423 31 


2425 


23 1822 II 


21 < 


24 


.94. 


29 17 


28 4* 


18 11 


27 ,6 


26 S7 


26 11 


25 2( 


Mt' 


M SI 


'1 4 


22 5 


21 11 


26 1219 15 


18 I, 


t 


" 


If IC 


24 41 


24 1- 


-, 4" 


23 16 


22 41 




21 3C 


20 JC 


10 5 


'9 27 


1841 


17 51 


17 216 IS 


IS .1 


lo 


zo 


10 21 


19 -f. 


19 3^ 


19 IS 


19 4( 


18 21 


7 SS 


17 2. 


1651 


16 l< 


'' ■(! 


'5 7 


4 "7 


'3 47>3 8 


M 'I 


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■ 8 


.4 .1 


■ r 9 


H H 


'4 37 


14 17 


■3 57 


n 34 


1, 11 


n^ 


12 2, 


■• 37 


i*-»^ 


16 57 


16 ,7 ,8 


Hi 


;i 




10 31 


10 1^ 


10 3 


9il 


9 37 


9 '^ 


9 10 


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«37 




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5fi 


7 "3 


7 3 6 44 


M 


( ■> 


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5 I) 


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4 SI 


♦♦! 


4 41 


4 32 


4>1 


4 17 


4 5 


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6 4 d 6 


3. i< 


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4 »< 


4 21 


4.! 


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8 


10 16 


10 7 


9 !4 


9 43 


9 31 


9 "7 


9 1 8 iS 


82, 


8 12 


Tse 


7 4" 


7 "3 


7 4 '19 


tT6 


*• 




'! »7 


li " 


14 (1 


14 3714 "8 
19 ?« 18 . 2 


'I " 


'■iV/.i 


1248 


12 2C 


II ,t 


11 >5 


II II 


16 32 9 55 


,2t 


»t 


■( 


20 ,s 


20 J, 


19 ^1 


18 ,5 


■? ' 


16 27 


'S Si 


■5 '7 


14 4c 


.4 if, ,1 


13 33 


38 


» 


^J« 


!, I. 

JO i 


H+i 


H M 23 4; 


23 « 


:i|i 


21 s: 


21 1: 


26 30 


19 45119 1 


IB .5 


17 25 r6 3< 

20 ^S!i, J, 


'S 7 


I, 


4 o 


3" J 


•9 }'. 




a n 




=S M 


24 27 


23 36 22 42 


2,4; 


18 , 


12 


10" 28 


,!•' 


» (■ 


U"M 


S3 3';j2 47 


3' 59 


31 10 


30 15 


29 19 


28 21 


27 i^^26 17 


2,16 


t.t^i 


", 5 


; 




40 « 


,0 211 


V4^ 


37 S7'37 4 


,6 » 


3S i: 


,4 15 


13 12 


,2 6 


30 55 


29 42 




24'! 


»^ 


44 3« 


u ?■ 


t, ■ 


4» ",41 ■; 


40 II 




,8 . 


,6 5- 


,S 41 


H ■' 


33 1 


31 35 


30 I2'28 4e 


27 i 




22 


4» !1 


4» 


47 " 


t' "!4! 1: 


43 t 


42 51 


M 4' 


40 16 


39 1 


17 31 


36 16 


>4 4« 


S3 531 21 




tc 


" 


S« fj 


!' ■ 


!' 1 


so 3 4» !! 


47 4- 


46 31 


ts 11 


*3 *■ 


42 .5 


3047 


19 V 


17 3" 


J8 2136-25 
40 39'38 34 


3> .5 


11 


- .8 


eo, 10 


" +5 


H4< 


S3 57 5" 23 


51 t 


(9 4« 


,8 2. 


46 51 


« '" 


43 3« 


•■ 't 


*" ■; 


34 ts 


>. 


.1« 


19- « 
S2. 1 


lU 


i' SISS 36 


t4 1. 


S» S> 


;i It 


49 i- 


»» ' 


(6 12 


M2« 


42 38 


\<>t' 




M 


4, 1; 


K5n;n 


!7 i 


:5 ,t 


:3 5» 


52 It 


50 y. 


4" 4P 


,6 46 


44 55 


4* 46,49 31 


t»F' 






H^ • 


Hf 


H42 


i9!2 
61.4 


^ ? 




S« }' 


52 45 


50 47 


4« 35 


49 47 


43 37 


42 29 


W-. 


JO 


" 




17 1 


is ?' 


'4+163 1; 




S4 3< 


(2 37 


56 S< 


4»2B 


t" '! 


4,3 5" 


4» *\ 


33 


'" 8 


70 26 


S9H 


S7f6 


« !s,5r1 


63 2fl 


rt s' 


60 2 


58,, 


f6 16 


54 "> 


S« 1 


49 S* 
56 5* 


{736 


:ii 


42 1(0 


'■ 




7' J5 


70 4 


IX> 21 


S8. 1 


» 3 


^4 S' 


'1 '■ 


Jl ,: 


59 21 


57 31 


SS 21 


S3 u 


48 3< 


43 87 


^ 


73 ' 


?' ^ 


70 3c 




S" 


?II3 


;.+ ., 


62 15 


to.i 


5822 


5611 


S3 5' 


5' 4* 


« 23 


4<.5" 


44*1 




2 


73 4S 


;i 11 


?» 7 


>9 4i 




^♦4S 


62 to 


bos. 


S» V 


,6 40 


54 «7 


5» '• 


39 4I 


47 15 


44 if: 


K? 


). 


74 ■>7»4 


71 32 


>9 s; 




■64, 


** S! 


*3 , 


>. 7 


!9 S 


i' 5; 


S4 4» 


;. 21 


49 ;t 


47 ij 


44 jS* 


i ^0 


-J^^ 





— 


" — 












— 










- -1- 


?i 


(••Af. 


^3+3: 


-26«--24f 


22* 


26* 


is4 


16» 


■f 


12" 


10"" 8» 


6" 


f 


2" 


0. 


I.C 


ii2tJ> 8ION 7. ■ j 



SDFPLEHENTAi. 

,, Google 



Md NAVIGATOR. 



SUPPLEMENTAL LVNAR. TABLES. 



~^^^^^^2!^^^^^^^^_^^^^£^^!^^^iiS^^^^^SNT^^7i»7 



■gtcTT 






q«ued Ahomalt of the Mdoh i Or, g j.equitcd- 



in 



. eqnated. 



♦S SJ 

ka-4» 



to 3* J7 ♦« }4 
- 3t>'3'!7 4'J4 
»• s«^ r« jj 17 14 



41 s; 



J9 S4 37 ' i4 
119 18 ■ - '^- 
>i8 33 



36 

ail 



33 33 



33 

'4 

4430 S* 

30 '7 



is 48 
'i 43 
IS 33 
■S ■) 

«4 S7 

»4 '7 



u 3619 27 16 16 13 4 



'! 57 



4« 41 



4 J' 37 
37 4S 3S »3 



')• JsB* Npi 7 
36 



Lsia-3 



!' 34 3° 



> ■! 

)o Ij 

'S 

*7 S7 



»6 4>3 



>6 



'S 

I 38 



» 34 
8 46 
'3 4]'0 S°[ 7 54 



»5 9 59 7 i" 
44 9 j6 7 s 



» 3» 



J5 3 



33 



'|33 . 
* 3» 54 ■? 
» i» 36 '6 
< t6 10 H 



ij 3< 

31 IC < 

18 13 

5 " 

" as 



JO s«i 
»9 la 17 : 



'5 'S 
1 



lu 33 
■5 3 
■3 «J 

■I 39 

9 4' 



II s^po • 
SI 34'i9 i 
'9 49"7 i 



8 10 40 
6 9 16 



«47 6 
" ■ 6 



■3 is 

I 4« ■•> SV 



- „ 7 

-2 JJ5 



1 33' 
3 je 
10 39 

8 36 



5* s'i; 

• 53 
55 



6 33 
4 45|4»5 



40 t 38 



4 '4 



3' 



i^ ■ 4^ 



1 43 3 3S 

^3 



3 411 3 
I 49 1 



'4 
*7 
39 4* 



;c30 



48 

fS '7 



10 48 
il 



-6 31 

38 23 



33 58 3 

3' '3 ! 

■7 57 



.4 3, 

ao 31 



3 »9 
8 36 



3 33 3 43 



■ 6 38 



4 37 '2 -37 



1 V> 

8 4» 

9 37 
10 30 

33 



36 7 



30 
3« 
33 47 

35 -5 

36 3' 



33 49 
34 



3' 
19 1 
30 16 



■3 47 
S '4 

36 33 

37 40 

;B 40 



31 33 

" 51 

"4 < 



3 13 



37 Si) 

38 35 



llt-l 



39 " 
39 29 



35 

35 4' 

36 ir 
36 31 
36 4S 



39 33 

30. 10 
30 37 
30 53 . 

30J938 



3 SS 

4 "5 

«4 47 

■5 

IS. 



4 36 

5 »» 

6 lb 
*57 

'±J1 



436 

<■ ? 

6 36 

7 4" 

8 >4 



" 4! 

> S7i« 5! 



PS 3' 
5 4«l 
*5 5° 13. 4*f 9- 34 



11 3s 

12 38 



4 37 






10 53 8 



■■} 44 
» 51 

ISL 



Ttn- 



QiiD'sA] 



rs Ap, 



n 



4* 



.N. ^. Whetbei yuu loire ibe Cmral fitqasbra by thit Method, ar foriaei aac «A' bcccnlriatici, jw n^ i» *•£■ ■ 

i«: d„C,oogle 



-sS* 



Tit R O Y A L A S T R O N O M E R 



THB fontdDE EQUATION of tb« Ma«i< t» iht fnfeM biitTJc' 
itjVATiaH ii (be ArVnrwr berwecn the ■»■ ind^/rK EttirTic 
E«.nAtia«i MrfniQHl rmm (he diHiient fK'Hiricioo rf theXnwf 
"' ' ' t»,Ot* refpcahx DituKii of llicSiwiMoMii 



Bf r<i. f. fit. Ag<. 



See p, f ], I4. It^tion af Mooo'i Ceom- ttf aired . . — ] S4 i» 
e 1 > Ap. I Vail An. I Equation. | a£. Ion. 
A(». »• (* I I* 100 I — -jd s8" 



SUPPLE M E!^^ T-AL' -L-try A»!':yA-B LKST 



_ Yt^Mw_ 
rroMrELLIPTIC EQUATION, 
•; fid lit JJm.'( C«m/ iT <^jc £ 
rJ! lUm'i ^pi, —d ■• II* MMt 



. .M.Eq. M«»'tOen«r— ^ jj 50 
E*. An. 

, Eqoitio* — ]« 40 



I + I' »3" (b* «" In»- An* 
for ■' I«r. An. 



E<. A«. - ■ • ' " 

l}f Tdt. ;, 67. Ag(. }■ ;> 44' . . U. Ef. Moav'i CcBUr ^t iS 16 

OiJiAp. Eq-Aa. 

By Til*, p.g J. Aj*, ■ ]• IS" vJ, Doder j« 5* 44' • • Eqo*, + 741 



See p. S5. . . ^tlcai Equdaatf Moon'iCeattrreqairad — 6 t6 
O'B Ap.lUiiil',Alk|Eaiiation.|UBil'-An.|Equcioa. 

■■.l-;f|v.-|t"rh-"lr;';r 

+ »" I W. — ; M Dr. ttf — ; ai D«ct. 

HUf...i. — •44j-3'j»"-«4oi--3'«" 



. + 7« 



«/r'l«, It. .1^ Jhl^^ Tlf's Mf dflfiW Sli^, ' 



VlrfiBj 



Let E~A(di of EiMntrie.AnopiilT, « = ie«.MtnfiI9lpe{Erf. 
Sir) «=Ecc««trtdlyof-UieOibit (T*iJ^ret&= i) aalMmAnti 

31icn, b; the Prap«t j of cbe EDi^li uk) ■ . PUoet'i Motfaa ta id 
Ocbh, B + wsM, AndIl*diuilu>K = AKhi>r.57o;ig;7^Dn. 
E»+ X X « S7°.«95779= "" .t-*»*7- >?*^'-»t5W> * ^ 
Deeree* between *c(KT«t.«;»iidmMftAEOB«li*i.) ^ . 

Va /l-^ lit Exfolric Atmtbr 
Yon nay reidily determine it bj the Pin «nr« TiBle oT Wmrtf Si'« 
fin* the »boie Eijiinlun j effumim two Jiffcrmt 
■ddinEtSe refpafliio pi(6tenc«,- ibJ prafortionief ibe Eiron »W»e» 

unikrtbeDepiesor meu AooauiJ . , £) at to affito a awr en 
Anoouly, wJiiih may be cerrtHlf aeieiaiiat-d by a /kW Ofmmht. 

Or, to foNe lb; fli™' £«««■", jounijyproitel tint. ■ j 

4fliriWcentni.^M<lOri whri^ i» Wi" 



tAf..«VM^tM'. 

^ _, . __ nrjtteatric, devil 



r, «ii '*< Lf. tf Eaittridij t 
theDegrwtBflU- ' ' 

:nd »ffra/mmii a 






ith 7'4<^ 
[abeic 



... ^^ 

lUd.) fw d cooftanc Lag 
ft^ ibmi Oria : ft lotitl aid ti» Li[. Siu if Ibt ifi appRucimatcd ocn 
irii Aimuli, "-rf '■^ '** Nmmitr tf Dcrrm itrrcffrndtm; tU fittrAf. 

nh-kttr. Sim a it ti adiid it iht cuifl. Ln. *i t^tn, 

ifD'P^ M*". -«ti't<l" " icjMUMflSfrtmitt 

ft tTtcuiimr lilt n attaric Apcmaly mJ ibi faUnnni Diftrinci btim 

aJM.Jhtjtiqu^'bttitamjtMmatj, vibtnilit cictBtrii jtmmalj^tlt 

"'^•.'Tira Ay, *. 5f. R«' ■4*- ^'/' ' ^- J*** f '"*■ O^- « 1 
i nma £<Kn(, ^b, i T«. f «• Jtafuh,, vihici duJJti u lU 

JStmfIt TIm AitMuly ttMtrair^ beiiig 70*, and Efceatridly ol 
ihaiPUii«t"tOi*m»S*9 (■* 1 ' 
malj of Alenw7, at tbat Time F 



^ISAp." 



, , - i7/j»"i 

Byr«i.|Ql)Ap.iUad'.Am.[I<vtatioa.|UDd'.Aa.|E<iaatiaii. 

AbM *+ I ♦^ " 1+57 7 i * " I+-54 S* 



l»'3S" 






- An. + *• . 
witJiibotK] . 17 



-^ Si 
— 30I 



-l'U''cau«a«ilb tfi' 11" 



[abovt. 



> CiamAA 4*si*i7'ta"-4-54'4>''E^MtiMi«^iMd: 

t A.. 
ElfrAf.O' Vai'^yW'paetlieM.lv J'aCeiMtr- 



B CmU9 i'nfwMB £« s* <>the» aboM M nadt r -tfa* p 
Ap.wiUnifcMiEnnfi>owd»eiofafnrS«Mdt() 
fetMBrnc Equal, fin Adooi. Is nol propoidoail ta tbe Cknip.of Suq i 
llsM'l.A|««n t i^m^Oaa^al XmtBMilj, aMr rHefied by>K 
4^«wwn^ foraAcrCaaputatkh -TV Remedy fcr aiicfa Eint (<if 
^^fcw SwonJa) ii by » Oiort iMtrfJui- 



So Tan. j Jj' . ( M. An, [ i).a45»ti 
To Tan. ( 14* 43' 17" ■ • I 9.6*3799' 



■. £t. Ao, 59 4S 3] 



Rad, J7*,i9sj79 t.yjIiM? 

Ecy. . . .lojtgo 9'3'3»if;f , 
CoikA. Log. . . 1-0717510 
1.0(. line . . . 9.9164519 + 
l0'.i9O9^ _ [ i.oofaO| jj9 



Cor.Ei.An. S9 4S 14} 



Now, Ai - ^p. Pfr. i.lo^i 



9'91*'*»J + 
I .ooE4iin 



To -^ Pet. DiC 0,79411 
SoT.JEi.An. «9» J4'7"»s"' 
ToT.i'ft.An.15. 1,1 .l» 
DoHbUd . . . JO. ■.t.*4 
WbeiKC 19* S7' jl''ftie. £y 
•v* CiMfaw Ue^vwun 
m^limit«tam/lim >/ Witd' 
: 4t to p. 57.) wMrt tM /mETc 
. .X,^. JfanrErrarlhstiUJ 
ration wW comS It, fTo*in| 



And thciiwaecnaly by Piopor. of Inc. 
of £1. Aa. ud Eirar, Ir. 1 and i Ooen. 
Log.. [S~. 

9.959J46'«*-J N.B. ira,**«*f(. 
9 9499404 1,^^ tuttidi Mil ttttn fit 



{.Myootg Jiy, 

niOD, inline witb Dr. Ir«b)r'a TaUe;. 
Hjfuhffit, lS« bu Afilc. TnOi b. p. 



happen by tbctfineJI&'M tlie 
ttel^MhKUU 



:? 



WnUiMSMl&L 











M 


N A V IG A T 


OR. 












97 . 


bUi-i-LiiMJiNTAL LUNAR "E^UAtldNS ' 1 


IMIILLIIIJU ) •*"°"''"1! •» "' Co.b.aio» of 


Mr 

TIT 


MAVER. 1 


of the MOON'i 
Mc^ MOTION: 
Orfiiiiutionorthe 
H'lMtuiLonfr 


ECiUATION of the Node 


Mean AnoM.iv of the "WOON^ ' 1 


^fitment. Mean Anomaly of the aUN '~~ 1 



M. 

Ai. 


1 he lingle lor the S, and double of which Eqoation for Mean A nom W 




M. 

An. 


Si 




I s 


8- 


2 F 


ff- 


, S. 


. ' 


4 ^'8 


S ^'P-' 


ir"b.& 

atCk 


+ 
/ « 


Dif. 

7-T 


+ 
' a' 


D. 


r 1 


tt 


+ 


D. 


-t- 


D. 


4- 


T 


+ 


D. 


B. 800 


' 948 
I 4 19 
S9 4 


S «9 





.0 II 
ai 


II 


5 ' 

S »o 


9 

9 
9 
9 
9 

1 

1 
8 
8 


M7 




10 13 
lo 18 
lo 18 





fs5 

8 53 


i 
6 
6 
6 
6 

1 

6 

7 

I 

7 


'1 
4 58 




2S 


500 


54 ■ 


44J 
4 IS 
4 21 
4 8 
3 55 

' ♦; 

3 J» 
J '« 

3 1 

' 47 
» 34 




031 


rr> 


s »« 


9 3 


lo iS 




"47 


4 4« 






400 
300 


04440 


-L 


43 
°f3 


10 
10 


i^ 


9 9 
9 14 




10 17 

10 17 




2*' 
8 15 


Vi 




a6 

24 
*3 
22 

II 


S. 100 
Ch-aoo 


40 19 
036 .1 
}t 16 

3S 7 


■ 4 

■ '4 

■ "5 

■ 35 

■ 45 


6 ij 

6.10 
6 28 


9 "9 
9 '3 
9 27 
9 3" 

? 35 


lo 16 
lo IS 
lo 14 
lo 13 

lo 12 


in 
8 16 
8 10 
« 3 


4 18 

3 48 
1 38 


300 


XI 53 


■ 5! 


6,6 


9 39 


U> lO 


7 56 




400 


18 s> 
16 5 




■ 5 




'•44 




,,. 


10 8 


7 4« 


3 "7 




18 


JOO 




a 15 




6 ,1 




,46 


lo 6 




7 4» 


1 6 




I?' 




'3 3' 




• »i 




7 


R 


9 50 


lO 4 




7 34 


8 
8 


256 




16 


700 


II 10 


» 7 

■ 54 
' 41 

■ '7 
' '} 
I I 
= 47 
» 33 
e lo 
5 
2 


-w 


' 3? 


10 


7 » 


8 
7' 


9 53 






7 26 


2 45 




-IL 


Boo 


9 3 


^45 


7 ■<■ 


9 56 


9 59 


7.8 


2 3) 


900 


7 9 




■■ *5 




7 2, 


9 5« 




9 56 




7 "o 




' «4 




>3 


1000 






3 5 




7 3> 


7 

7 

I 


10 I 


9 S3 


7 2 




2 13 




12 


IIOO 


^ns 


-~ 


S '5 

3 "5 


10 
■0 
9 


7 3» 
7 45 
7 52 


10 3 
■».,5 
10 7 




9 56 
9 46 


251 


8 


2 2 

." 5" 




~ 


1300 


• 47 


3 35 


9 43 


'37 


1 40 


1400 






3 44 


7 S« 


7 

I 

6 


10 9 




9 39 


62, 


1 


• 29 






;^ 


00 a; 
7 




3 54 

4 4 


10 
10 
9 


8 12 


10 II 
10 13 




9 35 
9 31 


6 12 


1 7 




^ 


.6,0 


003 


16 


4 '4 


818 


10 If 




9 27 


b: 


6 1 


9 
9 
9 
9 


^6 




~T 


1700 


000 


4 'i 


824 


10 15 


9 23 
q |3 


5 54 


o 45 


'V 




p 5 


«7 


4 J1 


9 


8 ,0 








5 ♦! 

5 36 


= 34 






.SiO 


007 




4 4» 


8,6 




10 17 




9 H 


23 






IS 




^9 


45a 


9 

d: 


i*' 


5 

e: 


10 18 




9 » 


5 27 






1 


190c 


o!7 


^;i 


-Si. 

P)M. 




»+' 




R 


9 4 


5 17 


0: 





5: 




OM. 
An. 


19s 

1000 


48 
010 


— 




— 






— 


An. 


mSk. 


10 Sij. 


_5 Sig. 1 


8 big. 


7 8ig. 


6Sij. 


EUMa <K& 00 Mr. MAVEk'i LuNAK Tablec f,iuhi,I,»«- own Luhak Taxli* ^( n/u/i^ » <i« M,u 


pLACit MTf/ MoTioNi: ^w Exunplu Airri^ n. 

i«w, tni ftitce to bt hoped-for nanr AgnaoeM wllh the Honem. Thit IriHh W tell n>, he hj*. of rk>r Ihu (w> *«-JkJ Ohfer«ti(iii 
rfth.M*>BnMde™tonlxmlki.b«intbepreeedii.gABB, Cwe (-were fo*^ ftomwhich hi. Tibletdiflfer «*««*■«»!. Wf, iimt 


T»«eiliCT«ofore puWiAed perform the iike,. the be« of thenioftuiaring fiwr or fi«MuioM<, he wji the more unwiUing hh TAIei Iketfl. 


It MIX laager iMcnled ; elpeeuJly, « the itiaft «Wrj/a< Afinmma; of ■Imoft ewry Age h«»e ^dend; wilHe4 foi ifrftaTiitij of tb> 


Moon Crt «.*;■(* bii ttUa dr. /«J -™-/, » gffrutb) m AccoonC of i>. /mir t//( i« Krvif^im. 

Hot, indeed, (be r»)ftj do tbey fceoi wortV of Pgbliaiion for the S»ke of thii patlinlat Strvict, in MmpleWing the Theorj «&])■, but 
ilfo on Accoant of th» nfy ind ap«litiim. Method, by wtiich thil pittkulw Servite ftom theei nij be h«d, in compating the Lnpnib (ad 
t*nV«A. For, if yM look into othwTjiAi, you will find, an ComptriloD, thefe liner Ef^aiiiu fe few in Number, ind the Reft oT them;fo 


oe«mi,. H, ku *Ml*r«aiidtbt«Tiblei, he&«, wi(liR<lp.a to the /u^^na of Motion., from that /«.«. TV.rjof the C>x*'t 




Equation, after CMufnltlebBSiiy* byothv HMtaod^ he lutblt (u b« &yi) uponiparticulu Milbod, pretty elcunl and coociTe, mUdt'i' 
wooU bo toe ttiioat for hin u> nplun « ittt» in bii Prefbch For which Reiftn he hu eontJuded only to (lie fiich Hioti » miy ccindu(» t< 


.y oren the Or.;;.', ind C»/« nr ih« iBOfiolltiM cdubited in tiN %Mn«r<>i^> lo f» u » 



tUPFLSMBNTAI, 

D,9itizodbvGO0gIe 



9« 



ffc ROYAL ASTRONOMER 



SUPPLEMENTAlr I, U N A R E Q^U AT I O NS., 


Accordtni; w die-Cooflnaim of Mr. MAYER. | 




1. Ew.,,o» .. 


11. tdyAT. Vi 


III. E<U*i-. J. 


IV.Etty.T.l.. 


V. EquAT. J. 
Argument 5, 


> 


Argument i. 


4rg».i«w a. 


ArgumcDt 3. 


Argument 4. 


f 


Mnn Anomftly 0> 


2.paO+AnE.i. 


j.JaO-Aig.l. 


Are. 2. — M. 
An. J. 


%tT.^^ 


o 


1 


a 


1 


4 


1 


"0 


I 


2 





1 


2 





I 


» 





1 


' 














— 


— 


— 


.— 


— 


— 


+ 


+ 


+ 


+ 


.+ 


+ 














'6 


7 


8 










. b 


7 


8 


k 


7 


8 


+ 


-t- 


+ 


-*- 


+ 


+ 


4- 


-f: 


+ 


+ 


-t- 


+ 


— r 


— 


— 


__■ 


— 


— 


" 


/ t 




/ * 


' ' 


' * 


' " 


' ' 


1 « 


' • 


' ' 


' * 




/ ' 


' ' 


/ ' 






' « 


^ 







^ 1' 


9 40 


II zo 


, ,8 


S 49 





3 i? 


D 47 





3 V 


S4 





3-S4 


' 34 





3 16 


1 2 


1 


la 


f (I 




11 ic 


t ?* 


; 39 


I 


5 »8 


J 47 


I 


3 ^2 


*» ?4 


2 


Mf 


t 35 


1 


> 37 




2C 


2 


o 14 


i !■ 


■) !' 


11 10 


9 4'> 




2 


J »< 


1 48 


2 


3 ,1 


S5' 


'. 


. s- 


I 30 


3 


3 ,8 


> 3 






1? 




, ,« 


II 10 


■> 14 


; '7 


y I 


> 2S 




: 


3 ^1 


" <i^ 




> ?^ 


' ". 


" 4 


J 3<, 


I 4 


25 


4 


' 47 


6 M 


10 1 


II u 


9 1> 


^ 6 


I 


J ,0 


1 49 


^ 


> V 


56 






. i» 


<> 


5 40 


' 4 


2( 


? 


> ^» 


ia, 


,0 5 


II H 




+ ^s 


S 


> 31 


5 49 


b 


>,b 




O-IO 


1 2 


I jy 


b 


> 4» 




!5 

»4 


6 


1, lO 


6 JO 


1014 


11 13 


9 '9 


4 44 


6 


31 


9 50 


7 


> 3? 


56 


o'l2 


> 3 


t 39 


8 


3 42 


; 1 


' 




6,o 


10 11, 


11 17 


J n 


4 11 


y ; 


J 12 


3 SO 




> 3t 


J ^7 


i: 


' S 


I 40 


»s 


D 4, 


21 


)> 


1 11 


6« 


a. 


II lb 


> .( 


4 22 




3 .33 


3 50 


.^ 


>38 


^'! 


15 


I 6 


I 41 


10 


> 41 




73 


< 


I +1 


1. (« 


10 a^ 


11 IS 


a (8 


4 li 


" I 


' 3^ 


J ^l 


10 


J 3< 


17 




1 41 




" 4S 


' 7 


21 








.0 ,j 


II 1 




1 ^9 




' M 


J s^ 


II 


1 40 


' 11* 


i< 


' ^ 


I 42 


i: 


,4b 




Tq 


1 


' 7 


7 ■' 


10 ,7 


11 11 


" 41 


1 48 


11 


3 It 


S> 


12 


5 41 


3,d 


21 


I 10 


I 42 


14 


47 


I ii 


13 


2 IH 


7 as 


10 41 


II < 


«3^ 


3 


12 


J 3b 


> ^2 


1 


J 4a 


5 S9 


2; 




> 43 




348 


I 8 


II 




a z( 


/ i- 


10 45 


u V 


» J7 


3 ■■i^ 


11 


' 37 


J V-' 


I. 


i 4i 


^ itg 


2. 


I I 


» 4+ 


17 


J 4f 


1 9 


12 


'■ 


a 4fl 


7 4a 


10 4, 


" S 


8 1^ 


1 M 


f. 


' 37 


J s^ 


I. 




I 


o.«6 


' 'S 


i 44 




J so 


I 9 


'S 


a 51 




10 ,1 






3 1 


a 1^ 


} 18 


3 Sa 


16 


>44 


I 






' 45 


It 


> {■ 


1 10 


't 


It 


1 1 


7 n 


io ,5 


10 ,q 


1 1 


2 ^o 


n 


3 39 


S2 


17 


4^ 


1 


10 


1 18 


' *i 




3 ^2 


1 lA 


M 




1 I^ 


» 7 


,o,« 


<o ,b 


7 ?^ 


2 ,8 


10 


> 1< 


tj ^i 




4? 


1 


il 


' ", 


1 46 32 


S^ 


I IC 




il 


1 *' 


i H 




10 ^2 


7 4^ 




0. 17 


i +0 


Ti 


It 


4* 


■ i 


V 


1 20 


I 46 02^ 


3 s> 


t II 


It 


'q 


1 U 


« a. 


II : 


10 4( 


7 lt> 


2 14 




' 4' 


n 


20 


47 


1 i, 


3S 


I 32 


1 46 2. 


SI 


I II 


II 




1+6 




11 6 


10 4^ 


7 ^' 




1( 


3 41 


u (3 


'21 


48 


> t 


3; 


I ai 


' 47 


121 
26 


3 56 


Hi 


10 


1 ?7 


8 ,q 


II 8 


10 4 


7 18 


■ <;o 


19 


42 


ti 


22 


D48 




19 


I 24 


' 47 




4 « 


«,t 


II 10 


10 ,; 


7 ^ 


I i« 




) 42 


S3 


-z- 


4g 


1 1 


41 


1 zb 


' +7 




' S6 


I II 


I 


4.8 


8,. 




lU , 


7 




31 


> +^ 


> 53 


I. 


3 jd 


1 1 


42 


1 37 


• 47 


2(> 


> 57 


1 II 


7 


i- 


4 *' 


') ■ 


il 11 


10 2( 


ijo 


I 14 


22 


4- 


« 54 


0,2s 


^d 


1 i 


04. 


I 28 


' 47 


ia 


) S8 


I 12 


t 


'J 


4 4C 


9 » 




10 2. 


6 40-1 1 


l: 


4. 


^ H 


-ab 


D ^1 


I 4 


46 


1 aq 


. 48 


31 


' 5( 


I 11 


-5 

4 


♦ ^0 


* H 


II 17 


10 l<i 


6 30,0 49 


21 


4S 


>4 


27 


SI 


1 .3 


048 


1 10 


• 46 


12 


3 S9 


I 12 


*7 


? 


J, ai 




10 1. 


6 ^00 37 


». 


^ 4^ 


" >+ 


28 


sa 


1 i 


u 4S 


. 11 


. 4H 


V 


I 


1 12 






> " 


9 aa 


11 K 


10 9 


6 9,0 2J 


25 


0,6 


i;4 


3t 


^z 


1 2 


SI 


1 3i 


I 48 


t> H 


1 I 


1 12 




1' 


t ai 


* 31 


11 ao 


10 i 


S 590 '3 




3 4b 


LJ s + 


y. 


° <{'. 


1 2 


ti 


« 33 


I 48 


3S 


1 1 


1 13 


1 


ic 


5 3' 


'/ 4t 


II 2C 


9S« 


i 490 e 


ty 


^ 47 


^54 


31 


f 5-i 


1,2 S-l 


' 3^ 


1 48 


j6 


1 2 


1 12 





3 
1 




— 


— 






-*- 


+ 


+ 


-I-. 


-1- 


H- 




— . — 


__ 


^ 










1 


>i 


10 


9 


II 


10 


9,' 'I 


10 


9 'I 


10 


9 












— 


— 


— 


— 


— 




+ 


+ 


+ + 


+ 


+- 


1 


.. 


10 


9 


8 


7 1 6 


! 


+ 


3 


s 


4' 


3 


! 


4 


3_ S 




3 


"% 


Axgomrnt at above. or 


2. xaO + U 
M. An. 


2. jae— ©■ 

M. An. 


2. jiO+OAa. 
— PAn. 


2. >iG— GAn. 
— J An. 




II. r.tivAj. J. m. £q.OAT. J, 


IV. £0^7.. B.' 


V. EquflT- J. 


0/M^. MAVtR.LHNA. tQ.UA-r.ON. WMc.TJO«.. 


Accoiding to Mr. Miyir, ihi Moon . Motion in i«.;i:.rfr oujhi to bo coictaed by Xlli Esualioni , tbc moO cunCdRible of which in 




lljc fifrtirHil; of lh( Mooo'l Orbit, and ro!io«t (he iT^pAf^w Lmw. . luQ£»inity ii not trct[n.nfll by the 7i«r. itfdf, but muJl t* deter. 


n.«d by icnmediate Obftmlioni } ixd ii the onlj oiw, tac thloki, thUmir otX be ifttfltd by the Sm,". Adioa. 


THe Xir. e«B/iM 11 derived from the Power of the Si» Ufim tbe Dbm, ind iht Eccedtricily of iheL-«rOi*i(, jointly, aod wonl. 




B«//wW«,>ndfoiTieother», tilled lh« £wfiM>>. It ftiifily tbJtowt the JC^/wun Law, b(«pt thilit i* TUiiUe Inun ■ twofold Cufc. The 


fciftit-thtuntswLniftwtECi-Pf the ^M from the gart^i for when the Son » in ,*»«>(, the Evictiom will be lefi, ud when in FcriricM. 
ilmofl umuch greiter. The Ja^ad CioiiTi the mutible'Diftince of the M»« from the «flrrt, which 11 the Moon'. Peripem m.ke. the Eb-j- 


)»Dtrnter, aM4 "1 Ji^W/iw leu. Ihe me«Q Quintity thereof ii indeed thit fet dowikin the following EaiijiionTa*/«i butthenthit Pirt 


iihich it, for the jforementioned Ciofe, »»nible, i< reftored by the IV, V, X, ud «lfn fome P.tT of the XIll. Eqmlion, ham wheiKe lb. 




By tbefet*oE.«./«ii, the XI ind XU, the fime Ii>equilitiei)tt tegobted, which N.wToii, ind thof. who h«e elofely fblloweJ him 


»*e eipUioed by the variable Ecamnaij of tbe Moon'i Orbit, u«) the une^uj Motion of the ^eftir. And tbouth 


th>ijlf.i/W, Mr. m,j,/A 
..Ttri,.l 
































i> 


Utfi-J-IiMENl'-'il. 



W NAVIGATOR, 
r SUl-i-LEMENTAL LUNAR EQJJATIONS. 

According to the Conaru JUan of Mt. MAYER. 



VI. E(y;AT, Jr. 
rument 6. 



v^^■^^:<^nT.l>.^| vin.Eq. ». \ 



O IJ 3 56 



0,17 ' 59 



3 3 48 I 
. J a 491 



o a6 



Ai^umcB 






I'i 



p 21 

p IZ 

D 14 

|o J5 



' ^9 



Arg. As above. 



Vl-EqjAT. J. 



31 o 51 

5' 



17 



180 43 



12 " 



Argmnent 8. 



M. As. 



o 56 



0_^ 



o 3S 
o 36 

36 



40 330 37, 
5 o 1^ o 37 
60 z^o j7 
' - 38 

o J 3 ac o 38 

26 



a 8 



o iS 

038 



O 5 3 27 

9 9 3 28 O ^ 

O ID 3 28 039 



I fj 3^ 40 
I tt 33 40 



e> iijo 34 a 40 



19 39 
o«s(£>39 



M. An. i> — M. 

An. O. 



yn.EquAT.ii. B vin. Eq^jj 



Argnment 9. 



3S 
o irio 4s1o 34 

3=' *i~ " 

o 46 



O'JI 



4' 

'3^ 



46 o 29 
do 47 o 27 

47 



3 46 D If 

o 92 3 4J a 13 
o 84f> +S 
440 



S7 3 43 
(« 43 o s 
393 420 

»♦■• 

° 41 



X. £<ii;ATtaH 1>. 



> ^O — M. Aahb. fi. 



S3 



3 3" 

J 33 

3 )<• 

83 38 

US 



2 I y I 



I i' 3 45 
3 44 
} 4t 
3 43 
3 43 



43 
3 7 1 2S o JS 



ICZ 



2 6 



o|l S^ 

21 46 

}'■ 40 

4!' 35 



3 '2' s lip 



= SS 

«f> S3 

4« 

3 40 

13 



rJ^L 



a? 






lx.Eia^*r. D-i 



X. Eqja' 



I^A&. MAVEK't LuHAi Eiluatiohi anJ Mo -. , , „ 

•flerti, tuiay conefpondt with the Tiaty, yet he tUnlu it it » little the mort difficoh, and not fo wOl aiipttd to » fjiiJa- Compuwtrtn. 
•^ which iUalbn, he fayt, the i.««- j^r-mtm, a higfalr indehttd .to the alehmwd £-/™., who firft elegwitly fubftituted the ^«io(U.r ■ 
ition of iLe Caur together with th.t whish ii railed the EviBipn, in the Room of the yniMbie Etuiuntiiy, anil lo idoined Uui/wA 
Theonr, whiaiwHotherwil«ait»rodyintrit«le, with 1 iwr«J</(f*« Cnrm.«Mi naiirf aJ larft Eqiaiitii yiJOfegu. _ 

TheXIH. Zvi^Tianynifitlt diCwuwHl fcy Twjiw. who pn* it t*>e Nune of tht VamaiI-n , ««4i*/A(t. aad otherf, c»ll it 
..■L.cTios. The TiwfT iifelf plainly enough aeterroiM. in Qjantity, .riling from the ABioB oS the Sun fin^y, Ih that it » 
reniaiB, if the OrhiU bah of ihe Mmb and Eaith h«d Hi *e«a»ici*y. Sorte C.rt 4f it depdrii .on the QawKV of the .Siin« ^-«;*«, 
i»bichMr.««u'airan«d = i."4, which he thinki not wide of Truth. It i. here to be nnteJ, ihtt the BiBWiXiiiMitilj- of thu, 1:40^301 
(which by BHron»f the dLliit«ncDitfu«ei of the Sun and Moon .from (he Earth nuking it variibit like the ftcwM>g)l'-9«",*,''ft^;" 
half rhe£t.^im) which, th™(h n« ab&lutely oteefiry, fo fkr.»m«ybe difct.«f.d frwn the«^o*J_te;^W»ftwid_na^be v-hdUy 
■fcribed lo-Cbanc*. Bm the Changes it onde^On, "ffom the alfftfirtt CTflsJiies or th* Soft, 9 
ihofe which bsp^ta on Account of the Inequality of the Moon' t Diliance from the Earth, arc 






for 



heEarth'i Orbit, 
accelscala the Moon' 
K'stion' 

"sOTHIemEntal" 



«« ROYAL ASTRONOMER 



SUPPLEMENTAL L U N A R EQU ATIONS. 

According to the Canflniflioii of Mr. M A YER. 



MHAN E<aiAT10N of tkc KigarrrCENTEgT" 



liilOON'* Mean Awomaly, correflgd by the ii preceding Eqj* 



Argumi 



5,5. 




- 


Dif. 







O 18 J2 
o 34 A2 
° 3" i' 



o 43 
o 49 19 
o !! 
' ' S4 



6 10 
6 9 
6 8 



I 7 40 
I 'J 45 
1 19 4! 
1 ss S" 
I 3' r 



s S8 33 
J 9 »6 
3 U4« 
3 10 7 
3 =; '4 



3 30 38 
3 3S 4» 
3 V> S! 
3 4S S« 
3_S2J7 



— Dlf. 



S 16 28 

9 SS 

S "3 '7 



S'g- 3- 



5'e. 4- 



— JDif. 



6 1! 41 " " 



6 18 40 



' 37 !• 
' 43 JO 
1 49 47 
> S! 4« 
ii 



6 > 
6 o 

S ss 

5 S7 
! 55 
S 53 
S 5' 
5 49 

S 46 

5 44 
! 4» 

'4. 53,';! 
z 47 19 * ^ 

2 SJ 2 

' 58 ;3 



7 2' 



2 2448 



36 , 



nif. 



;. II. 



3 55 S3 

4 "45 
4 5 34 
4 "> 19 
4 '5 



4 '9 37 
4 »4 I" 
4«S 38 
4 33 
4 37 " 



5 35 54 
5 33 41 
5 4" Jl 
5 44 " 
i 4<^ 5' 



4 4> 38 
4 45 49 
4 49 55 
4 53 57 
4 57 55 



5 5 3« 
5 9 '9 
5 " 5' 



"6 18 11 

2 « f " *' 
2 37 2 '1 A 



5 49 *9 
5 S" 55 
5 54 'S 
5 S» 29 

5 5' 37 



SJE. to. 



9 "3 
6 10 37 
6 II J4 
6 13 

± 



6 IS S9 
6 16 43 
6 17 20 

6 17 5' 



15 5" 
f "4 57 

6 I 



5.39 = 

5 35 53 
5 3= 40 
5 29 20 
5 '5 S3 
5 " 



5 '«42 
5 '4S' 



5' 43 
50 28 



6 I 42 

rs9 38 

5 57 
S SS 

5 5^-47 



S'g. 9- 



S 47 38 
5 44 S3 
5 4= 
5 39 



-jig. 8. 



T78T7 1 ;i 



4 54 29 



4 «4 



♦'° I 4 -9 

4 31 33 4 47 
4 26 39 
4 21 40 
4 10 24 



4 " '3 

♦ ' I 
4 o 46 

3 55 2 



3 38 36 
3 32 S' 
3 27 c 
3 21 ■ 



%■ ■?■ 



I 38 3 

I 31 12 

I 34 18 

I 17 23 

I lO 27 



6 It 
61; 
6,, 
6 22 
6 26 
6 30 
6 33 
6 36 
6 38 

< 47 
6 49 

u 



o 49 *9 
o 35 '3 



_Si£ 



;.6. 



., _ AYEK'iLvHAi E«.iiATioir( ««/M< 

, ind ntinh il, when the Son ii in Ptrigm. It hu p>fled uadrr vuimi Namn both in tUiin^ Aehft 
he l'i»ry]eiWi in foinr Mnliitt douttfut Mr, Mn/frbainflorcd froma^rsl NDmba ofOUcnitioH. 
vhichnD ODE, Wonbifn, ffcaii 10 hiKtaltea duelfo^ice of) i? Reafoo of ibevuiiblcDi&incttaftht ]) Innn llit 
Eirih, htlh*«foref(Hindit'ne«fliiyto»ddllK VIII, Eq^BATion, thoogli thit E^oidon doa not wholly »«<Mnt for tke ChjinjB. Tbtntitei 
Ratt il eiccUcntJi reAortd br that Eqmtitm, which it to be tpplinl Co the rrar AatiBtlj, and which itfo contaiu the locqiulitT of Ch« ~ ~ 

rf die a™,, To f« « th.t v«i«on Accouni of iht p«ttr or lef, Difcn« - ->- ' - ' 

Vll,.ndlX. E<i«rATiow. c«in«t lowfily b. tiphinodin Wo,d.» 



Hation *hcs the Son >• In jlft^f 



cheyuirerronitlic/jKA'uiinof thiMoon'tOrb'rio the Eclrptic, which ■• tfaeCmfB, tbit the Son fDmetiiiiei idaob: 
]o ifftElt in Modon in Lngihidit lirite : Add tb ihii, ihe Eccmirlciiy of the Mooa'i Orbit,' which nuket [he Si 
the Moon i) near lu Aftgui, 4nd kfi, -when in iti frripn. There in, 'til true, ttOnt Other Imripitiitia iScduf 



1 AQioQ 



.^ the Moon'i Motjan I 

lentioned. But then Ibme of theA «re aniced with the Equacioni ibo*e nMatio^ ; othen arc preferwd bj llii 

Anomal* ; and DCher»there ire, which he hat entirely nigleOed. The Reduftion E^uitJon to ^e Edifiic, oi 

li^le, thODgh the fac/f Ml 1 M ^ tbtOr^l, wbence it uiln, ii not ilwiyi the Time, 

linilhcd, ai hu been done, and itqairti NotieeflHiuld betaken therrof, it 

1 It mil KMvcnoa equation had been made variable. Tbii he particulatlj' menlioni, that no ^ 

'pUccaijtrJIj feeli out Errora, of which he nay think the Tablet themlblva mt -jU rbur. He hai formed two Tablea to detmniM the 
I LtiiinJi, one containing iti mtaa Quatitjr,' indepCBdeni of the Snn'l Aftioo; the other conlaialiii the Vmiatitmi if Ltinuiii ariling 

If thi« /(WB/£.flrifm/( Table, i> it maj be named,^be made rariahle in the ntifrtittiTiplitAit K«m of the Sno'iDifbnce froto the^atth, 
'ill lierhapi, come fumewhat ' "' "" -' •>..." .1 ... .1 > ,. •-■ 
^ , ._^^ii __ -f _ii »K«r» 



Eqnation'he applied to the mean Anomaly j and other 
the XIV, Eq^DATiov of LturiiuJt, he hat filed a 
Butif thtVAHATIoN or XllI, Ejiutia be Ibniewhatdii 



,^„„ aawellaiofallthofeyetonkn 
m toon cawfnlly yafannti , he think 



E Truth. But Ailt tbereaieothctlrtegularitiei 
wain Ihe TibRry, U ufeld^ till we gain more 
I byMeani of the more ena Piraltam of 



Modi 



the S'i£<nWr,nol7etdircineteil, thatCorreflkii 
ate Oblemtioni of the Latitude, which ma ' 
ifcertainadattbeEndof ihele f ^aafiaa Taibt. 



SUi>PL£Jw£NTAir 

dby'Googlc 



•nd KAVIGATOR. 



.SU_P.I?LEMENTAL LUNAR EQUAT.IONS. " 

According to the ConArnaioii of Mr. M A Y E R. 




"■ Mt. *<!HA-«ON of ttc MttoH". iVtCTlON. or ScconJ tquiiion of tkc MtboH'. cSNftlt. - 




Arg. iz. Or2. JlOcot'.by J'sPl.atioEq. (not at i itli, of which this Kq. is id. Part) — M. An.coi^. orrtrg.iith 




ion. 


s.g. 0. , 


Sig. .. 


Sig. a. 


S.g. 3. 


Sig.4- 


Si«!- 


evec- 
tion. 




— 


«Dil. 




-Cif. 




.J?,f. 


— 


Dif. 


— 


Dif. 


- I Dif. 






■> 1 » 




/ ff 




/ » 


' ' 








' • 




1 M 




' 5 


d i >4 

a 47 

nil 


1 a4 

< a3 

■ 'S 

> 'i 
' 'i 
1 23 

■ »3 

I 2} 

> 22 

■ 22 

I 22 
1 22 

I ■ 21 
1 21 
1 20 
1 ■2C 
I 19 
1 19 
1 19 
1 18 
1 18 

■ •? 

; \i 

' "s 

' "5 
' '4 

■ "4 
1 13 


39 so 
041 2 
041 14 
'>43 >! 
♦♦ 35 
4f 44 


1 to 

• 9 
t 8 
» 7 

: I 

• s 

■ 4 
' 3 

1 I 

I 
(8 
57 
56 
■> 5! 
54 
" S3 

S2 

SI 
49 

o',48 

0° JS 

° 45 

43 


1 9 22 
1 10 4 
I ic.4s 
1 .1 2S 
I 12 4 
I 12 4. 


.42 

41 
40 

° 37 
36 
34 
O' 33 
3a 
31 

28 
26 

2S 
24 
IZ 

21 

1 \t 
17 

IS 

14 
12 
11 
9 

8 
6 
° 5 
4 

Dif. 


1 20 4a 
I 20 43 
1 ,20 42 
1 20 39 
1 20 3S 
1 20 30 


I 
1 

3 
4 
« 5 
° 7 
8 
10 
11 
13 
I, 
16 
17 
■> '9 

23 
24 
26 
'7 
29 
30 
ji 
33 
34 
36 
37 
» 38 
40 
41 

-BIT 


1 10 24 
1 9 42 

\ III 


42 
44 

III 
47 
48 
so 
SI 
S3 
54 

" '1 
,6 

• 57 

o S8 

59 

1 4 
1 5 
I 6 
I 6 
1 7 
1. 8 
1 9 

1 12 
1 13 
1 13 


40 52 

39 38 
038 aj 

37 7 
35 SO 
34 33 
J3 IS 
31 s7 
30 38 
29 19 
27 59 


1 14 30 

; :ht 
■■€ 

:::^ 
1 23 14 

.1 '3 ij 
>■ "4 ,2 
'■ 24 II 

1- »4 10 

: ?5 ! 
.'- 5^ I 
■H 
■i 

...6 1 




6 

I 
9 
lo 


8., 
9 42 
11 s 
11 27 
■>I3 49 


0-46 52 
» 47 39 
49 
50 12 


I IJ 17 
I 15 SI 
I 14 24 
■ '♦S« 
I 1( 27 


1 . IO as 
I 20 IS 
.20 s 

■ '9 54 

I 19 41 


• 5 52 

• 5 ' 
1 4 11 
1 3 18 

I 2 24 




ta 
•J 
'4 

30 

21 
>3 

»5 


017 54 
19 i| 
20 56 


32 21 

o 53 «4 
S4 2i 


1 is 50 
I 16 24 
1 16 so 
I 17 IS 
> ■» 39 


I 19 27 
1 19 11 
1 1854 
I '8 35 
1 18 IS 


I 1 29 

1 33 

° '2 '! 
s> 38 

" 57 39 


26 38 

2S 17 

" '3 55 
02a 33 




21 56 
023 .6 
24 3( 

n s* 

27 11 


57 28 
e (8 26 

» » 23 

1 e 19 

• ' 14 


t 18 1 

1 18 22 
. 1841 
1 18 S9 
t 19 16 


> '7 S3 
1 17 30 
I 17 
1 16 40 
I 16 13 


s6 39 
•> 55 3! 
S4 3' 
» 53 3a 
sa 27 


19 48 

14 IJ 




18 31 
29 49 

31 6 
32 23 
31 J9 


12 8 

■ 3 I 

■ 3 53 
1 44+ 
' 5 31 


1 19 31 
1 "9 45 


■ 'S 44 
1 IS 14 

1 14 4J 
1 14 10 
1 13 36 


SI 21 

SO IS 
049 8 
048 
p 46 SI 


0'12 48 

I' 'I 




a6 

JO 


« 34 34 
36 9 
37 23 
38 37 
39 JO 


1 6.1 

. 7 8 

■ 7 5-4 

■ 8 39 
I 9 22 


I 10 25 

1 20 40 

1 10 41 


I ij. 
I 12 23 
I 11 4s 
1 11 s 
1 10 24 


« 45 4' 
'>44 30 
043 18 
42 s 

40 J2 


I in 

2 S2 
I 36 
000 




■rec- 
ion. 


+ 


U.t 


+ 


bil. 


+ 


+ 


+ 


Dif. 


+ 1 Dif. 


evec- 




Sig.... 


S,g .0. 


SiR. 9. 


Sig. 8. 


Sig. 7- 


Sir. 0. 




Mimai! but, inZdiV'i, ibe Errar, be lOem, wUI natincvnt toao«. And bowpliio ind atj ifaeJIftifcJ of computing the £«i«.A i> by 
FaUn thai coDtrivcd, (-ifh Hr KM frF«i'A'nJ ind how diacrcnt from lUMahodi hmtofeK laid dovn, ii too 

Id fettt;nEtbcniNnMotioiiDf[l»Jf«n be h>>iDdnv(>urcdto>rim(l feme Degree oFCemmiy, aiweli uA^recmenc with the Obttnudoiii 
'r ancient Tunei. He hiiexunaed the encKeft ObfeivatiDni of the L„ut Etiiffa mxle by ths Btijhf^m, » well >i Hiffarch,, uid 
flda^i though thej ire fb grafi lad tncDTieO, thit he in nio itteraptsd to bring them Colenbly neirthcirTimei, by the TaAii ; butthii 
«11 noi ippeiii Anu^taanj one, who confidert, tbiithe jttiitnii, in obfening the Timet of tbefe P^namna, didootmuth rcgird aOuuter 
.r HilT an Hour. BeBiu »Uch there i> great Re*foa to fufpea, that P„km, from whota we hire the Account! of thefe Eilipfa, bTi too 
oldly altered the Timet of fame, and adapted them to the Number) of hit ova Hytabih. InltaDeei of which are produced by Ifmul 
BuiliM;, io the ^Jlra. Pbihl. B. IH. C. 7. For Ihit Reafoii no Body wUl impute it at a Fault in Mr. Xbwr, if hit Tdta jhould be Lmi 

he Negliget.ce of the Af.™<r, or the Uniythfoinefi of Ptol.-t, thefe Oblerr^tioni h.« concurrently fliewn, .hat the Moon', Motfon 

n the Wonn'l Motion i but the Quantity thereof hai fcucely been well aleertained by any one. In Order there ote to deteimiae it the >««•. 
uara^i^, Mt. JMayw h«, with EieatPwBt and Affiduity, eaamiced the Obferraiioni made between tbofc of P<wi»y and onr Time ; was. thofe 

:ei ittindiog them, ibrSom't M:iK<ltttka ai thir Btrimmgnd Emi, ought, in hit Judgment, to be aerounted moieraluable th« R</J W 
»/Mr. He doci not remember that any of thefe Gmlrmn, whs compiled Tahiti of the Moon'i Motion, having made any ITfe of cbert 
QbfemtioDi J tho«gh probably more AdTaMag* might be reaped from thofe alooe than from all the Obfervationa of PiiUrt,. For wWch 
lealbn, and at tbey an panicalirly ufeful to demonftrate the .iftn&»i»« of the Hoon'i Rfotion, he cboaght Ihetn worthy of a Placr, ,nd 
copied .hea, .1 follow., from the P»t,t«m- of Tyt*.". Hiftwi* Cml^i., where tbey h«K hitheito bin hid among othett of lef. Ac 

'v. A (& r«r rf Mahomet'. FMt ,67, « TharAay ,b. %t,b^ ,h. Umt JMWi Rabla, mt atArM/ at Grand Cahx., ,U MetropoUa ,/ 
" Eppt, lb, Bip^-g wf a EdM, ifiht Son, niicb, at rtarT^W, u« 15'- 4V- ''f*. '1" Sf^'J if tbi OiftwMna, t Digiii ; aiH 
• f!Wif S»-<.4K»ab«aiii>. |. Ti. /«rr«r, m S»aivf Ib4 tqib if ibi M,«b Sriai tbiSKm imat iliffii T 1, D<jpn ; at ibt B,„„- 
























- 


iv?PLS.fAmrKsr 





ni ROYAL ASTRONOMER 



SUPPLEMENTAL LUNAR EqUATIONS. 

Afcordiog tq the Conftrnffion of Mr, .MAT"ER. 



XIII. K Q."U AT I 6 1^ ai the irt O U N' " V A K f A T 1 O ^■ 




Wn of nckoniBi 
Eod 4^. JO"". 14' 



_ 1 tfBrf Mo . . 

Aacihu Ecliple is muitioiKd la iIm lame Plice, but it bciDg of ihe Moc^ ii 

> Oblivion, add! the fallowiiig Rikaiie ; " Tht/i lira Otjimaiiaa vitrt m^ile iy 

tmii/flHan, •iliatTnwKir^ ef Egjpt, JivtUd timfilf n thi Siu^ tf jUnMoa. "' ' 

?r./^., • ■ - ... .^ - - -. -■- . 



U LfOHi, wis cmimunitaNd litft liiifi la mi nt af dxm ) j 






< Albert Tablt) mn in tht BanJi if JunuGoliiu, Pi 

< frvo-aJ akrOiJiiTvttiau kui i/bii eiBi 

ttiy fn the PiM, Mr. jS^dyir bkC wii _ , _ _ -..-.-.. 

K.X)iuit«w, »iieie. thwf ait ifP^iei to ietttzaiae tht jicalireuat of tiiB Moob's Motion j yet be waiiodi to cm/ tuiKeul™ tlic PiSjee hi 
lui quoted, u the ObJerraCioD* ciBDot be too wcU known mong tltc AlIroaOBien. STw TiW i/" tib fonmr £cli^, rtjuad la Jutiaa Ttgn 
I DccontxT );. jfu. Don. 977. Ti^ BBgianjr^ atetrJimgie tti MtUuUt lakin, ii fimiuii %i<. i^. 34'- rbfV )0^- 4S'"- 4^*' Mari' 

fupptfig ibt Ltnauk ef Grand Ciiro %•>"'. 1'. ]0<'. «i tbi Oi^wttimu ef ttt MiJmi malu ii K it. "the otUcr BiUfJc, accoiding to Ml 
of nckoning, lupfcned in rU Tur cf Chilli 978, June t : lit Begiuniiii, Jian tbt sbfmtd Miiadt if tbt ^in, 1^. 30m. i6*. ih, 
' ^oMn ! Wiih thale Timet, puliculaiiy dmCc of the Enili, Mr. Mmu i Laadr lailu ire liii^ to igiec uritbin one 01 
ly one [he Uyt) will bai by Trill. Whenw all ihc Tablei before pabiillud by other AuthRii mike the lima tf itif, 
Scliffafoinir iy elmtfi btlf «■ Bimt ; an infillible Proof, duC (be Msoo'i Moticn ii now fwifier ihin it wu mioy Aget ago | ind llut tb 
?HHr9 of lilt A^dmiitm hu.bnn rightly licertaincd in the Equatisn Table), luoiding to Mr. Mmytr, eihibiud at tint Beginniiig. 
^or, indeed, {he (ay[)i>tliig Acceleration of-thc Jl '■ Motion fofii'ill, but that it may be plainly i2iiirva from ihcOblcrvatJani of thia and th 
laft Age only. He hai found ihs Moon'i mean Motion iji ba'alnm Van (beUit 801 Revo] udoni) to be ■• 10° 43' S4" which yet other Tabl< 
the Authon wkercof having caUc£tt<i the Mean MatiaM ftoiD the eirUeS OKcrvitionj ooty ccmpued wiih the Madura} make to be 
i'i 10<>. 41 '• «>"• orit moO i>. loo. 4a'. 15*. Now, we have a grMC many Obfertationa of Ef/|^>i made ahove 60 Yearia^o, (cd with 
::ai« and DiUlSnw aa Ht thii Oar. Uolt of totte Mr.M^irhu r(duc«dIo Kumbeii, ami aileiu that hi hai a»tfouod one, that {irovet hii 
rablei, conHniatd upOQ the Moon'i acattraiti Miiitn, to err a Minute in Lon^iude ; whereat the Error would fomctimcE hiTe b«ea eq^ 

jiliaatft, bod b« rMained tha Quantity, he 071, 4«aB»nl) aSiuMd fbt iheMooa'a Man Mociaa. He liM «Ua pnclued, atJie^e«t9, 

1 ^rtinilar Method to deCcnBioiv moB aocunlely, the f^anttty sf thli Motion* nMwith Handing th* ImptifiBiim at hit Tabltt, /honld 
:b(ie ba any Mt ill tbein. He ^hofe t^cb Eclipjei, u Mete dlAinl, in Time, taie CbaUUaw Pxried, tlutii, ttiLtmaliau, or, which ii betKi 

;be boa Errmin hit Tablet mull needi retumagain, aiarlf, IftkereloRit be known how much hit Tables differ from OUerralioni, 9 
1m End of one Perioi!, We Oiill alfo know how much they ought to difittee at the Expintion of two or mon fntb Period) j and if tD 
Enoit an fcuod (0 be «>iiyiui^, it is a Sign that the Mean Motion ought to be cureded by fuck ■ Qiuncity aa will rcduca Ibem to a 



scmmsirmr 



mi NAVIGATOR. 



SUPPI^MENTAL LUNAR EQUATIONS. 


AcODrfiHg M the CorAmaion of Mr M A r E R. 


■XlV.'R^Ki^oi.. ^nation 
toriio Ecliptic. ■ 


1 
■5 


I ForllwLwiuideofthe Uoos B"' ^" ^* LatitiKie otj 
n the Moon, 1 


a 


Ai-K. KioOrb.aWcor. 


9 1 


ArpumeBC. » m Orb. i Long 'i correftcd. 


1fE.l J a © — forgoingArg. Ut. | 


0.6 


1 -7 


r.» 


O.N. 


Dif. 


I .N. 


Dif. 


2.N. 




O.N. 
6.S.- 


I.N. 
7.*- 


2.N. 




— 


— - 


— 


b.S. 


7-»- 


8 ^. 




• 




' ' 




• ' ■ 


1 # 




' T ' ' 


/ 


' ' 




° 




14 


6 2 
« 9 


S 5! 


50 ' 

19 





00.0 
s 23 


5 23 
5 23 
5 23 
5 2J 


■ 34 25 
' 39 4 


* 39 
4 3S 

* 33 


4 >7 3- 
4 30 i« 


2 4C 


9 


4 25 

4 33 


7 39 
7 43 


3b 
29 


2 


39 


' ■( 


! 47 




2 


.0 4' 


2 4! 3; 

2 ^i ,2 


« 32 S! 




19 


4 4" 


7 4« 


28 




4J 




( ,W 


^7[ 


3 


16 9 


♦ 35 »« 




2t! 








4 


?« 


6 r, 


5 1" 




4 


b 21. 32 


2 52 4i 


t |°4 37 47 




17 


4 Sb 


7 5b 


115 


-1 

7 


1 12 


6 3> 

6 4. 


S .0 


i5 
24 

*3 


7 


b 2b 54 


5 22 

5 2' 


• 57 S 




4 4b 7 


* '4 
' .9 


« 5 


5 4 
S '9 


8 b 

8 4 
« 7 


24 


1 3.b 
• 4' 


S 10 
S 


32 lb 

37 37 


3 > 33 

3 5 S3 


420 


4 42 21 
4 44 30 
4 4b 34 


8 




' *s 


4 50 




b 42 ss 




3 lb K 


4'. 






I 2b 


8 1. 




<) 


2 q 


4« 


4 39 


21 9 


48 .8 




3 -4 23!? :j 


448 33 




• 23 


5 34 


8 14 




77 


2 aj 


6 54 




20 10 


S3 37 


'1 
5 >6 


3 .8 33 


lb 


4S» 27 




' 3» 


5 41 


8 18 


20 
1I 


I 17 


4 «7 


191 


11 


b i« ss: 


3 22 39 


» 52 '5 






5 48 


u 


2 (O 




4 ! 




12 


1 4 11 


3 26 42 


3 59 
3,55 
3 5' 
3 47 


4 53 58 


1 38 


1 50 


5 55 


8 21 




il ,1 


» 57 


3 5 J 


'7 


11 


■ 9 n 


3 3" 4; 


4 55 3' 


■ 59 


6 -.2 


8 .; 




<♦ 


:, lb 


6 SJ 


3 4' 




"4 


1 14 42 




3 534 36 


4 57 8 


' V 


1 :8 


6 ^ 


8 3b 


Irt 


i6 


1 4' 




, 2} 


^1 


lb 


1 19 5s 


S •> 


3 '38 27 


4(8 35 


2 17 


b .; 


8 32 


'li 


" !7 


3 .6 


■ '' ^ 


J 42 14 


4 59 S' 


I' 16 


2 2b 


6 22 


rij 


■4 




^ ?1 


" !? 


J ) 


'i; 


'7 


I 30 .16 




' « s7i; ";5 ■ i> 


2 55 


6 z8 




i8 


4 ? 


6 56 


1 (» 


13 




' 35 "4 


3 49 3b! "5 ' 22 


1 1,0 


2 44 


b 34 


8 ;8 




'9 


4 '7 


!■ H 


2 37 


II 


19 


I 40 ji 


' ? 3 53 " 


i "S 3 't 


= 59 


* 52 


(S 40 


8 jo 




a7 


^ >8 


6 J, 


" 'f 


"P- 


r 


■ 45 36 


5 3 


3 5b 4> 


3 2b 


5 4 25 


1 ■ 


6 }t 


8 43 


? 


4 39 


6 48 


" » 


1 JO 39 


4 b 7 


5 5.( 


048 


1 10 


b-g 




4 ^0 


o 45 


' 5! 


H 


S2 


I 55 40 


4 59 


4 3 29 


\f.U. 


1 18 


« 57 


8 Jr 


s<1 


S ' 


b 4> 


■ 4' 


7 


«1 


2 0. 39 


4 b 47 


a 36 

31 
z6 


J »7 


7 3 8 46 


? 




? .10 


W 


1 26 


6 


J^ 


2 5 36 


4 54 
4 5' 
4 5° 
4 47 
4 44 


4 9 55 


ri' '" 


3 15 


7 «,« 47 


2i 
±6 


S ao 


6 ,. 

'7 


I 12 
,8 


_£ 


is 
26 


. 10 30 


4 '3 , 7 


3 4 


5 7 57 


' +4 


7 '4 8 »8 


— rt. 




2 15 12 


4 .b '., 


5 8 2, 


3 5" 




8 48 


S 


■S J9 

S 47 


>1 
6 .1 


° 43 
29 


3 
2 


27 
28 


2 20 12 
2 24 19 


4 19 10 

4 22 4 


""S 8 43 
■ijS »S7 

'«5 9 8 


3 14 


4 ' 
4 9 


7 24 

7 29 


8 45 
8 49 


3 


2Q 


1 n 


6 ,q 


14 


1 


21 


2 29 43 


4 24 53 


3 3 


4 '7 


7 34 


8 Jn 




30 

\ 









I 


ID 


■ 34 fS 




4 27 3« 


^ 


7 3b 


8 J„ 





+ 


+ 


+. 


U.S.! 


1, 


.o.S. 


Dif. 


9.b. 


Dif. 


10. S. 


9.S. 
























Q 


zi-s 


10.4. 


9-3 


a 




5.N. 




4.N. 


,.N. 




5 . N. 4 • fj. 


3. N.' prop 




' er Mr. M 






EanilitT, InthitMlimcTbe hu nunined, be f])'!, not one or two Cycilii DiJ^, but ■ gtol nii& thmof; To tbit he furtbcr OfmK tben 
»< wiT few ZilMn, of vbich ObfefV»ioM tit'c b«D mnlt >» ihl* Wch. l:.ft Age, but »bat h|^aiidu,oM tlii. Znm.D«Ma. 

Wiih ( V 1''W'" >¥ *"• »''''' "^owPlf^ ♦"''? Obfcn^tionj o£ tlie Uoon tbu wm: nude a littb orlltr, ty 7>f&>, »«.iii,r, Jt«,«B«f«B, « 


well in th» ^V^/"" " '•'"'O'" ^^\ '"l ''»«' ,»I1 t'fOJ fcnn* U OUT ao AsrMnKM u ctiuld wdl be upeitei feoiB OblhrMiom 




WirhRerp«fl»HijSotAi.MDM»i.t, oftheMiA»tPi.AcmndMoTi«iii dri«iUe*Ti'n<«t-ofa l!»»tf.I«», ind whidi ^ hi» 
«h.l-ittd. w;ih Ibcit E<iii*twn; (p. 59i though he bv! ool I9 much Itft for him lo do' « thfft loing brfore hitD, yet he alTumed ik. 




ihe QoiMity or th* 5./>r IrfieairHt. in*9rM>lc, >Ere«h]e to the ObferratkiiH of Hlpp^fdmi, Maipim, ITaUbtr, .»nJ, in fhwt, 3^ 

ObferTJtiani of the Heiveni ; hot dttermtoed by hit own TMtt, ind the Qumtity of the Sihr Ytar, which he hid teceivwl from Hiffmrdail 
Mr. Hfajir h thetlior* fitmly of Opinion, tram very rubftintiil Reifom, that the Ctnnhgiiaf Order of Time ftom P(rf«.ji dowa lo ui, 
hu not been interrupted by 'be Omiffion of ■ D.t or two. Ljflly, Mr. M^fr bii deduced the mejD ■ppuent Motion of ihe ^incJ SlJrL 


ot the Pratrffibnoftbo Eooiamwt, chiefly fromliiKeiani'i Obferntbna of the Moon') ..^t/ar^n to the rixn/Sidrj, *bich Method I'eawtl 
to him more etrt.in Ih.n if be bid uken the Longitmlr of thofe SUn from Hipfianbv,, and made oft of thera to Ihfc. putpofc. 7 


Who therefbte thinlii be kit ftri«(y enmlned and elofely coofidered every Thmg, thit m=j be jnlfiy required of Liny r>„.^ who tilici, t* 


Subjeft inH«id, (id hii left nothing gol.ied, he thmi-i, thii might condurt to the pcrfcflmg of the M»„-, Tlrsr, ; i Point iir the moil 


intricte of jU in tbt eeleft.al Science. And. if t,<i nu paitf Jo-^x-rrf, hi. T.blei are now brought to almotf ai txta a Dep-cs of Pcifcflioi, 
It the LuM^ OtUrvtihm IhemfeU'e. can bt bro»Bbt by the Metboda hitherto made tife of by the AUroaomen i who fi.nhcr i|lledg<«, [hit 




























VnL 


HAhKi 


'*»•; 



db.GoosIe 



tU ROYAL A ST R O N O M E R 



DigHizcd by VjOOQ IC 



and N A V t G A T O R. 



SUPPLEMENTAL SOLAR AND LUNAR EQUATIONS. 

According to the original Conftroflion of Mr. EULER. and late Improvemert and Correaion of hU Plan. 



Y". 

■ 1700 



EQpATION of the bk^i to tke nrfwfrtV Amomalt of the SUN and MOON. 



Argymiitt. Mean Anomaly of the SUN ami M06i>j, reipedively. 



A,.. An. 



Eq.G 



Eq. O Eq. D Eq. G £q. D 



Sig. 



i-'g- 3- 



%- 4- 



Eq. O Eq. I> 



Sig. 5. 



'I50 O 'I 
EOO Q O 40 

151 O 

300 D 

3St 3 ; 

400 a s 40 

450 3 II 

joo 4. 10 

5S0O s 

Ooc 

6500 7 

700 o 8 

75° => 9 
00 10 40 

850 O I 

9000 13 JO 

950 o t 
1000 I 
iioo o 30 10 
tioo o 24 I 

130a 3 28 H 

140a 32 40 
ijoo 37 30 

lOOC D 42 40 

1700 o 48 10 
iSoo o 54 Q 
1900 » 
2000 I 6 40 
2SOC I 44 
300a z 30 
34003 12 40 
4400 % 22 40 



0000*0 

S9° 

1 59 □ 
a jBo 

3 S7» " 

4 56° 



^8 24 
19 15 

30 6 

y S7 

3' 47 
36 



. 5649 29 

' 37 49 S9 



36 SJ 

38 3 



i 18 16 j3 25 



I 38 : 
' 4' 



4' 37 



57 37 
S7 37 
57 37 
57 36 
57 33 
57. =^9 



48 47 
48 
47 4° 



37 33 
35 49 



> 34 



4 1 36 46 

' 33 S3 

I 30 58 

I as I 



2J J 



° +=u- 

o 48H1 
o 51 



2+ 19 

9 5Q|q 30 22 



36 34 



S3 >e 
» SP 



♦8 34 
*9 49 



37 

38 S 
3» 49 

39 13 
4° '6 



S 380 4S .3 
16 js 



40 jS 
4' 39 



3S4 .! 

6s4 31 

» +7 S4 50 

SS 

» '5 



S7 24 

S7 ir 

57 I 

!7 3 



44 3' 

45 S3 
45 ■' 
44 3 



I 18 57 
' 'S S3 



53 16 

54 10 



43 
43 4° 



']?«!'. 



6 30 }o 18 34 



37 3° O 
45 S« ' 
.*' t «■ 



16 59 
'9 45 
" 1 



44 '9 
M 57 

45 34 
4« 

46 45 



55 5^ 
7 5^ 3S 



S«4« 
IS 5' 



56 
57 "o 



58 S 

59 35 



S' 45 
5' 33 
56. 
S' 1 

55 5' 



! 3843 59 
38 



17 48 16 
■S 33 '5 ' 



SS 39 
55 "3 



S^ S4 
53 39 
5° ') 



38 17 
37 3' 



3 

3 ■> 56 



S3 46 



57 " 
57 '9 



36 44 
35 5; 
35 ' 
34 *' 
33 3° 



i 39 I 



58 3'' 
5' 

S! «3 
so 4^ 



47 *o 

47 S3 

48 16 
z; Mta 58 

' 2, 



270 49 



Eq.© 



Si 



7 57 'S 
S7S7 30 
4657 33 
3" 57 35 

'3 57 37 



32 40 
3> 49 
30 sS 
3" 
2. 



47 S9 
45 'i 
•*" '2 
38 4^ 



Eq.Ol £q. 
An. I An. 



1° 



'2;.^ 



EqTG 



^2..' 



Sig. I 



Sig. 7. 



I EQUATION of the SuN, .cconti^ lo Mr."^ 



47 7 

43 49 

o 40 3 

a 37 12 

33 



6 4S 
3 »4 



Sig. 6. 



RkMAkl^S onthcSu 

Mr. Leimard En/ir, af the Ktyil AcaAaif of Sciatu 9t 34riia, ani 

r.R.S. at iMifc-, 

fiKiT, O/rbSDK'inanMoTretKwf AeOLtkitTIOH. 

BY compiriag f «ir jtuiitr Jaji) 1I1B Oblertiitinai of the fcTCnl Agri, 
U dell tcrcd down la at, it ippeinthit (he appamC Motion of the $■(, 
nufedbythe rei] one of tin £<rti inhei Orbit, ii /wi^ff ihin ibi- 
meily, •ndthitby 1 regaliT Accelentioo, ftttfamt ai rti «/.*r*mi 
Tobi«M«jer, (/Coitingen, bai /nt rtmttluJ ^ iht Mieu'i man Mi 
■■' • -'—-'---'----- fr,^WYtit(oTraibtrof thjt 



f^OON from Ae JuH. 



Lon. Sqn ILon. ISon ILon.) Sun HLoo.! San p.on. i Sul _- 

p. be- o- N e Son. ie-Bs^n.^Q. Sub. b e. nsu. 



annexed with hit com- 
_ cfied with ihe Dift. 1 A 

in 74*. p. Co. Ttiaittiir./Hi MiTt^i, 



a by whic^ 



aal Ejuinaxttjhki giiiaiXly inrrtfti to theprde: 
Ptom whetKe it it obltrrable, {fiepaurjta'bir) chit rhu Dii 
of tbt Quintiiy of the folir Yni bu been oearly «« Satnd tf 
eieh Cenluiy. Hence we miy ob!<;rTe, that the mein Motion of cJi( 
Son, mJJiiivt to the limlled mean Motion, (toeelher addltin 
mited meen Pt^cei] determining the t o i re ft mean Placet for «nj Puioif 
or Yrir befon or dact tht fixtJ Pfritd tf ijoo, fioni whence the /r*D>» 
mMM Flkta and KitiMit trtdnnnn'tnl, muil increifi from the £iid Ptricf 
towirdi j^arifn/'v, and tilcewire increaft Avm thcnre, intbe Cune Order 
towirdf falkriry i (hit the Sdd'i corrcS meaa Plam may ency wLen 
repliriy intreaft *t e^il Diflaneei of Period! 0( Time foimd. — Thi 
it a Point of cotteA {urigment Oiewn by Mr. Mfyfl- in (he Aecel«*(ioj 
of (he Mooa'i mean Motioa, or Incieal* of bw mean Placet at equi 
Interral 



«, ROY AL ASTRONOMER 



io6 -— — - - 

S"trt>PLEMENT AL LUNAR EQUATION'S. 

Accordiog to the Iuprovkueht ind Correftion of the celebrmted Mr. EULER's Pl, 



"EULEfe's 1. EqiiATioN at Mt/iHLonQtTiiDt tmibemiMt Siaft of the Moon'tOthh, 

Maysr's Max 
Difference, Eulei'i Maxinatm too little . . . 6 42 
Hence, War"-'* XI. Ecjuation etivit/eJhj ;6,5J, ami ibe ^tient /MitraaiJJivm that Z^vMion nvili givt H,v\.ei'i 
I. EquaTioh, if you thurtatry it. 

N 3 Youmay perform theDivisioN by Loglflical Logarithm*, Mfliall bo aovn further on. 
.ST For EULER'i I. ufe MAYER's XI. EciyATioN. 

EULER's II. Equation (Argomeat, Sun'j ijrroi/r,r Anomaly) Maximim . . 9*44' 
MAVBR's EtyrATioH Moon'i mean Anomaly, p. 97. (Argoment, Son's mean Anomaly) Maximum . . 10 i8 | 

Difference, Ealer'i Afur/nvn too little . . o 34, 
Hence, MAYER'* Equation of MoonVJ»«Hi. (p. 97) divi^J hj 18,18 anJ tit ^tiM taiea /hm tiatHquttiot 
liUgitie Euler*! U. Ec^uatiom. 

!ir For EULER'i II. ufe MAYER's Equation Moon's Anom. for Longitude (p. 97) v/iA Arg. Sua't tximlric dwM. 
of EULER, or Sub'* mean Anomaly. Or, ufeoux LEquATiON (Arj. 5im> An.} p.6i. 

lAParC I ad Part. 
EULER'* III, Equation (Arg. Moon twice equated a Sim) . . Maxima . . 3j' 27' I 36' 10* 
MAYER'* XIII. (Argoment, Moon equated k Sun) . . Maxim* . . 39 3 \ 
DiFFBLEHCE, EULER'e JMkriMa too little . . 5 36 | 
Hence, Mayer'i /r/ Part XIII. Equation £viM bj 6,97, aaJ tit ^tint takix from that Eqoation ••uiS ifvt 
Euler's III. Equation. 

Alfo, Mayer's latter PaH XIII. Equation £viJeti hj 7,55, and tbt ^ttititl taJux /rem that Equation wZf^t'tu 
Euler's III. Equalion. 
VT For EULER's 111, nfe MAYER's XIII. Equa 



B61844 



"o7 Time ion'ui, in Imitiiion o/ihit /'imc Qontanttt of Judgmcot (hewa by Mr. EuUr'btfaje Lim, in itiftEt of ihe Sun vEarth-^i 

/iicrltraii'e', or jncreilii of Place it equal InlerTiliof Time. And theiefote Ihe farther we go i " ' ' '" " ■ -■ -" •^- 

[ht Correflion of mean Motion or Place, from tbe itileil Period whence th« ComAion beoaa j ■ 
~ iniFtmriy, tbe Correftion of tht limited mean Motion will be endintlr the fuai 



equal D^i 



■d, a fmall Mattvr, bjr Ibe Mooo'i AtUaHiiU, uid theic- 
r hu, in ■ Table, flicwa how mtich the. St^i Plaa, aac 



uiovbiyawpand CirirnCf, toe uorreciion oi ine lunited mean Motion will oe enciniif cue luae, accaroing to toe Hypotbdii of An Accelt- 
ntion of Ibiotion, or Incruie of Bie»n Placei at equal Interrili of Time forward. 

N. B. Mr. £(./«•• 1 limited mean Motion of the Sun in in J»ll*mYan, =sso' o'o" 9' il* =i xa'^3Cio\\mn, S/i. by ^ich dindi,^ 
71(,»D»ninth*«o J'»*'jii Vean, theQwtientwillbe j65<»4«Mi69, »t. =!365's''+J"47" ST"', aCf. hiilimil ' 
cotdine to hit Ilyfcitcfii of Arccleration of tbe Sun's mean MotiDo, Hill diminilbei from that Quuitity, 
Nobody, iti> pielunied. (Tiyi ourAiitiKir) will deny the Earth'i Sitiiatiiw ii varisl ' " ■' - ' -■ -' 
fere knowins the Caifi to which Ihit Viriiiion may be alciibcd, the crJiirMtJ Ealir 
hiiDiHance from the E«nh may be changtd with Regard to eadi bur .,4/jmS. 

' loubiful whether hit Ctrrtahn, which he haa talun fnm the kthmttltt Far^lmx ii{, will not be tomethiog tn St, 
lii rcvertlCorreftioDiwiEhfbnner ObTenationt, he hu difcovercd that the Sun'i btriaaial PgrmSmx W but lo*, 
probably doei not ciucd it above \ a Stead, He ihtrefoie chuiei to abide by bit CoTrtHim of tbe Sun'i limited nam Mmhn and Accricntion 
iccordinc to the Hjfvhtfii he bu Jai3 dowa, till the Quantity of Variaiim en hi m^rc accaraiify dijcmirei frim fnOrtOifirvanM. 

HecoTlefledthePlaceof the Sun't Apogee, and the Eicenlricity of the Orbit from the Obrerrationi of the cdebnted Mamu , . 
with great Study tni Paiu had inHituted for the fame Purpols, and publilhed before that rrmmikabli CrnBim from the Moon'i ttifing. He 
hu made the Mtioi if til 4f't'' ''" Nothing difleient from the Prttiffitn 0/ ibi Eauuai, becaufe (hi fays) the ArguacnU ofad hrj AAr*H««rt 
' ■' ■ ■ • ■'-- - ' ''- ,;^HfDrwinl cf the find Stan, rffariuihn) to be infufficient. For though be aUowi tbe S^finci 

lOibii.tVom whence the Acceleration of Uie Earth') Motion, or i)Hru/<of the Year, ii fuppc^ad to procoad, 
retlKha«faund,fromthri Rififiamu, ihe.Poritionaf(he£ii>Fi/.;;eMnorihe Sua, or Earth in hfr Orbit, not tobcaffeOedthucwith j whcote, 
be would ritber {if aij ytrivina ef tbi J^ga, ^aiih Rigard to ibi fixed Starrcn tt tmfy iam i ^ ttii) »ttribnt« it to th* AOionafaCnrr fome. 
■ nci piflint Teij near the Eerti. 

Of lb, Luna. Numbeii ad Ei.OATi»t.i ff Mr. EULER, 
The Defign of which {U /m) to fei forth at large wauM take up too much Rons in the CompaTt of Ui fluJl Effin: He tbscfore 
ob(rr'e>i that they are taken from the fjine Theirf af /tiirsaitn which the celabrated Sir Isaac Niwtok inuodnced into the Scieve 
of Anconomy with Ijj kappy Succeli. That ihcu^ there are Iciieral Inner T*i/rt, piihliflfi be£ar« hit, founded on tbe fime Htfttiifii, yet he 
aflerti thattheCaltulation to which the Pnuiyc o/'.^r»->aieii ii irlaiive, i] ncecdiog!^ intriole. and thai all thole loj^i widr^ dlA'er Fncn 
iheTtu'i; nor don he fictend to hite Aewnall the » uil Mai«i, in ihefe 7ai>/fi. Neterthelefi, he bai fe[ fbrtb«tf iteffMn'ou (he fay«} 
tcepiible to Obfervation, and which are to be foand after the flrfl telf BHhkIi. 

Thill fjc he offen hi) Calculation to the Public j fhewing the Title end itrpmai of every individaal Inequality Or Eufti 

oft of the rtriain ^aanlUia o' each, according to the aCqielaiit aliinud Tbaiy. Some of -whkh QLiintitiea »mi iffuatta 

» ^certain by Obfervition ^ olhen (hefayi) depend upon the Sunt Dipaiafrmt the Earth, or hii bsritmt*! PartUax, whicb, agteuUc 

die latell Obluvationi, he 6ndi to be ti" \ ; but, aflerwudi, 00 comparing thefe levcral Latr Bfustitmi with foniKi Oifirvaiieti, he fiildi 

■Jtc Sum' 1 P^nUtx cunet probably be reckoned above lo''. 

He farther obfcrvei, that whoerer compaiet bit Tat/a with atben already pubtifted, nuy pialentty difixn ■ vafl Djffinnce boA 

i/ti nd j6^um till of ibi EfMtim. That a> be malut Ufe of ihetecMtriM/ i^mmImoI' the Sum aad Hso«, be ptacc* diem fa; 

both/t/n- and luiair Taila, that thole iixl the other jMmaliiimit/ be the more readily found, 

Thi', though the Number of bit Eijuatiani it largei than imny other TaM" preceding hit, yet he hi) fb coUiItm) tham, th*t thtfConpii- 

tion may he made much fooaer, and with leli Trouble from th«ii than ky fornier Tahlei, 

And laftly, that, fince til Ci./u affcfling theAfiMt'i Pi^« tad her Dittante 6am the Etrtt, ,te fi-otrj vriaUt, he ha) addad thq _.„_ 
TMb, by the Help of which, (hclayij the Diftaoce of the Moan from the Earth) ud fiom tbEOCe bet biriatm«J fartMai a«d afftml 
Diamfr miy be the more corieflly and readily known. 

SiK Lmik Pnfaa f tbi Beilio allroDomlcal Tablet, fnm wbii TMa Mr. Miyet fniaUy dipvid main af tk IMir I^Hvmtim, patrioi/trfy 
■bt AaiiraliM nf lU Mmii mam Msliem, by a* Ey. bad It Mr. Euler'i jtcuUrtlh* firfl-Juff^d of ibt S^t't mm Muhm, aid ScilHai ./ the 
iVf«i'i nnim/ £(|uaiiDn, afiinpardi imtaiii ij Mr. Mtyer. (who lihewilc fbUed the Moon'i ParillaE for the tnia Suta of her Orbit ' 
like Manner . ai hiparify a/kmcvJa^, v/baur bit /wbvuMMfi, *y ttnf^i^ ibai ibi /W ctlrirtttd Enhrni (Author of the iboiremcntiai 
rtblei}3iMi ibtfirfi tail fihnJ Ibi AftM'i Central Eqtutioa, ia tat Parli, wlrknr Eccentricity, (fee p. 99 of out Work.) and " lb adoriied 
" the lunar Thcoir with a neat, and elegant ContraaioD." .it*/ «eie itriilin (fee Remark) at ibc Bottom of Mr. M^w't Equtioa TtUtil 
itwf ibt atrvt-wmaliMd Mr.'E.<i\a-a>at iht firjlvibtrtduad ibiVt-rnXoaitaThtorj ti pmtrai aaaljtical Z^vatMra, vMcb ib, KiJVfitnaatdA 
" L.-. _•_ IB titcml aad umift Miibid if rtfiUimg." • 



■ sonaumtAL 



Mi NAVIGATOR. 



10^ 



SUPPLEMENTAL LUNAR EQUATIONS, 


According to the CoaOniAiM -«f Mr. E U L £ R. 


IV. EQUATUON of the MOON, or EVECTiON. 


-^«»««/. Twice Difi. Moes from 6t.H — ExccWric Anom. MotH.. 


Arg. 
pro. 


«^. 0. 


,„^'?:',: 


Slg.2. 


sig. 3. 


Sig, ,. 


Sig. 5- 


Arg. 
pro. 


— 






Dif. 




D,f. 


. - l*^'*-_ 


— 


Dif. 


_ iDif. 


. 


1 / fl 


' " 


e ' * 




« y B 






/ H 


/ u 


■» 


( 


000 

1 le 

2 34 


1 18 
1 16 


36 S9 
J8 5 
39 1: 


1 6 


' 4 5 
' 4 43 
I s !0 


38 
■> 37 

32 

3^ 

30 


' 4 5 

I 3 21, 

I ' 45 


39 
41 


36 59 
3J 53 
34 +5 


I d 
I 8 


30 
^9 

28 


4 

s. 


D 3 (2 

° I ^ 


I 17 
I Ig 
I i? 
1 17 


040 18 
41 23 
„ .7 


' s 

* 4 

J 3 
J 2 


■ f 55 
1 6 3. 

I 7 3 




4- 
5 


' ' 4 
I oil 


44 
° 44 


33 3& 
32 16 
3. 16 


1 to 
i 10 

I II 


11 

24 


7 


9 J 


43 30 


;?'S 




3 


59 51 


30 6 


8 
9 


II 35 


t 17 


■= 4! J» 
046 34 


. 


. 8 36 
■ 9 4 


28 


1 13 16 
i "3 -i 




osS.S 


48 


27 43 
26 31 




22 






* *7 

I :i 

J 15 
t 15 

1 IS 


1 47 34 


56 


I 9 31 


S5 
25 
24 


I 12 52 


17 


;6 41 


SI 

S2 

SI 


25 18 


' '3 
I 14 

I 14 


2IS 

>9 
i3 
■7 


It 
'3 


0.+ fi 
«6 39 


048 J3 

049 3, 
50 17 


■ 9 57 

1 10 Z2 
I .046 


I .2 38 


s; 50 

S4 58 
S+ 7 


2+ s 

M 51 
21 37 


i6 


17 S4 
ig 9 


51 24 
oj. 19 


o S! 

,55 
S3 
S' 


IIM 


17 
.^ 


■ ■■ z3 


20 
21 


S3 ' + 
j2 19 


'^ S5 
° 55 


20 24 

ig 9 


' '5 


2ll 


20 2+ 


S3 J4 


1 II 4i 


I 11 7 


51 24 


17 54 


'7 
i8 


21 J7 

22 ;, 


I 14 


° 54 7 
S4 !' 


1 11 5 


. W4O 
1 10 21 


24 


50 27 


u 'S 


16 39 


; \i 


13 


19 


24 ; 




js so 


Jl 


I 12 38 




' 9 S7 




048 33 




li I 


' IS 


II 


30 
22 


2S 18 


K '3 
1 12 


^-56 +J 


1 .2 ,2 


13 


1 9 32 


0. 28 
28 


47 14 




12 SI 


Hi 




0.26 31 

27 45 


57 50 
058 ,8 


; ;? ,1 


; 1,1 


46 34 
® 45 34 


11 35 
10 18 


ij 


28 s| 


i 11 


" 59 S 


. .,26 


9 

8 
6 

4 




30 
J3 
31 
36 

35 


44 3* 


1 * 


9 1 




7 


«5 

*7- 


o3' 16 


; ;: 

1 ti 


S9S; 

1 036 


° 45 
»■ 44 
44 
41 


■ '3 35 
• '3 43 


1 7 36 
1 7 3 


43 30 
42 27 


' 3 
4 

? 


7 4+ 
6 27 


I 17 

1 .s 

; \i 

1 16 
1 18 


-L 
4: 

3^ 


32 26 


18 4 


1 13 49 
'3 53 


I 6 3, 
• 5 55 


41 23 

40 Ig 


5 9 

3 Si 




M4S 


1 2 4; 


■3 57; 




I 5 20 


39 13 




' 34 


2 


»9 
30 


3! S3 
36 j9 


I 6 


I 3 !6 

' 4 ! 


39 


'3 59 

I 14 


t 


' 4 43 
> 4 5 


o3« 5 
36 S9 


« 


I 18 





Arg. 
pro. 


+ 


i>if. 


+ 


Dif. 


+ 


Dif- 


+ 


Dif. 


+ Dif 


+ 


Dif. 


Arg. 


Sig.M. 


Sig. 10. 1 


Sig. 9. 1 


Sig. 8. 


Sig. 7. 


big. 6. 


MAYEK.'* AcgoflUU t»ike above Ev«CTioB-E<yiATioii » twice the Moon from Sun — Mean Anom. Moon, 


The above Miur/jBKjw . . , 1014' oV 


MAYER'. U«nm«m of Eveftion or Xli. £<iuatioii . . 


. ■ 20 43 


DSfftrtnet, EULER'i M*tt»««too little 


. . . 6 43 


Heoce, MAYER'S Eveaion-EquatiDn £vUtihj 11,02, endlbt ^utitnt tain frm that Equation, -wiU givt tb> 


««»w Equation {/-EULER, cin-nfponiM. 


ir /«■ r^ -iwEquadoo »/« MAYER'. XII. EqyatioB. if y». utUa tb, ftii^^g V. Equation ./ECILER. 
But, if you »««'>. the Vth. with the «ii>w Evection of EULER, ibey will, cimjux^ly oSeA. come near MAVERt 


EvECTioii or XII. EqwATiON ; and cotnftnfait forfome Errori, or Imjualititi, of the Lunar Oibit. 


and Argument of half the SyHeJuai AvomHy) is fupplied by the eaiier Computation of the E'viSiait-Eqiaitnn 3.bave. 
Which Equation is applied to the fm/ru/ Equation &r the mean Eccentricity, and is therefore equal to about ha'l of 
Stkibt'. E'vtSitm, applied to the centriu (01 cocrefpondeac tcctntrit) Equation, for the Utui licceuiiicny ot die 


Lmh^ Orbit. 



Digilzcd by 



Google 



rol 






thi 


ROYAL 


ASTRONOMER 








SUPPLEMENTAL LUNAR EQUATIONS. r 


AccordiBg 10 the Con«™aioii of Mr. E U I, E R. 1 




VI 


E<iUATlON 
Vice ii^'O ■ 


of the MOON. | 


>rjj. ^J'wice 11 a — T«ice Excen Anom. S J! 


-<'«■ 


-ExceD.Anom. ». , [ 


Arg. 
pre. 


^ 


Sig... 


S,g.., 


S.f.3. 
+ 


^'g-* 


='8!- 


Arg. 
pro. 


Arg. 
pro. 


SiR.O. 


55:7: 


^ 


55^ 


S«4- 


"•R-l- 


Arg 
pro. 


+ 


+ 


-t- 


+ 


+ 


4- 


4- 


+ 


4- 


o 






' * 








"■ 


* 




' ' 




' ' 


' ' 




• 


o 





4 12 


7.6 


8 24 


7 .6 


4 12 


10 








26 


44 


5' 


"44 


26 


30 


I 


<, 


4 20 


7 21 


» 24 


7 '2 


4 4 


29 


5 


% 




26 


32 


t» 


22 




2 




4 27 


7 25 


8 24 


7 7 


3 57 




10 


9 


33 
36 


048 


51 


,9 


17 


20 


1 




4 34 


7 29 


5" 


^5! 


3 49 


27 


■5 


1, 


(0 


50 


V 


n 




4 


n 


4 f 


7 33 


» 2) 


3 4' 






17 


39 


;i 


0+8 


33 


9 


10 


i 


o« 


44» 


7 37 




osi 


3 3J 


^S 


'5 

30 


22 
26 


42 
044 


52 
32 


04b 

44 


30 
26 


» 5 




5 


6 

i 
9 

lO 


1 1 

1 19 

1 38 


456 
S 3 
5 10 
S "7 
! 24 


7 40 
7 44 
7 47 
7 5' 

7 !4 


8 21 

8 20 
8 19 
8 IS 

8 le 


t.48 
643 
\ 37 
6 32 
6 26 


J 25 

3 17 
3 9 
3 1 




Arg. 
pro. 


— 




— 




— 


— 


Aig. 
pro. 


S. 11. S. lo.l 


Sig-9- 


Sig. 8. 


Sig.7. 


Sig.6. 


VII. EQ.UATION of Ike MOON. 


12 

13 


I ,6 
' 4S 
» !5 


S 3> 

S 37 
5 44 


7 57 
1^ 


8 11 


6 20 

6 3 
5 5' 


2 27 
2, 19 

2 2 


-!i_ 


Jrg. Twice J a© — Eicent. Anom. O. 


Arg. 
pro. 


Slj^ 


Sig... 


Slf.2. 


Sig.,. 


Si(!.4. 


Sig.5. 


Arg. 
pro. 










^ 


1 10 


s 56 









49 


57 






1=" 






* < 





29 


49 


29 


>7 
[ft 




fi 


P 11 


3 \ 








5 


" 5 


33 


12 


37 


" 47 


24 


'i 


2 16 


fi H 


« 11 


7 59 


5 37 


» 45 




10 




57 


-! 


36 


'>44 


19 




>9 

30 




6 20 


» H 






. 16 




15 


IS 










2 52 


6 26 


8 16 


7 54 


5 24 


I 28 




20 


u, 


+4 


57 


» 54 
52 


37 

31 










' 37 
6 43 
648 

6 5! 


8. 18 
8,9 
8 20 
3 21 

3 22 


















23 

'4 

'»? 

28 

29 

30, 
Arg 
pro. 


3 9 
3 17 
3 25 
3 !1 


7 47 
7 44 
7 40 

7 37 


5 "■> 

J5I 
4 49 


1 10 
1 I 

sj 
4+ 




Arg. 
pro. 


ag 


49 


57 


_0_« 

4- 


29 




Arg. 
[TO. 


S. .0. 


+ 


+ 


4- 


s. ... 


Sig.,. 


S.g.8. 


Sig.?. 


Sig.6. 


VIII. EQUATION of the MOON. | 


3 4' 
3 49 

3 S7 

4 4 
4 1* 


6 s« 

7 3 
7 7 

r.5 


!"' 
8 24 

8 24 

8 24 


7 33 
7 «9 
7 25 

jj6 


4 4" 


«3S 


.*X. Twice J i0-t^E2CeotricAnom.©.- j 


4 27 18 
4 20 9 


Arg. 


srg.o 


s*. 


Sig.2 


Sig- 3- 


Sif-4 


Si|!.5 


Arg. 
pio. 












2 






" 


— 





o„ 


42 


36 


21 




S.M.IS.IO. 


Sig.Q.ISie.s 


Sig.7- Wilt.6 


pro. 


5 


4 
7 


;0 24 
27 


038 

0.4c 


42 
41 


31 
2. 


e. 13 
14 


■S 




f./ir. » Wawr'.lILEq. whofe jMm. ii i' a"Ln«t»d of 57"; uu 




I 


V 


4 






II 








3 


4 






7 
» 4 




>f «i", ictoriinB to *■*)■.- allowing for the Dif. between the mcar 

iE.Kir.6. But Mr. Af-f<r His not .oj Eauit.jfwVto Mr. E«ir, V. 


25 

IS 


2 


IJJ 


42 


038 


24 
2 


5" 


+ 


Sig. 9 


4- 


4- 


An 

pro. 


S. II 


S. 10 


Sig. 8 


Sig-7 


Sig.6 


ill Anthor* tefnrt him th*t we hrtc Ctta. The Moon'i Plice in her 




Mr. Mayi*, uhI piKlrfnmiMr. Eulir-i i^/». Aflo which OrtiiPUa of the Moan a hkd, Matix'i XlV: i>rJt«hA'«-f ^«r»; fron 


ler of the Moon to bi tixtmtit determiiicd iccotding Co our Tiblei loi fbmi P-fif', » the Be^nmng of thii Work, or eUe'by Mr. Matii'i 


S^tflrmt^ul EfMiua-Tai/a, for the Ibne Purpofe, >nd not bj (he Ha^jitn Method j beciufe Sitlii confiden oo^WEi^v ati.n «/r/« Mw.' 


*>m* fiiT detenuining the ArEum"« of i™* A-m^- ./ /i* »«■> .0 which the P*-.*!^. ind CDD&iiiUDtlir »p|»roM Semj-Diunetti of the 

rtnOD, chitflydependi, «cordiBgtotbetf*ffl!.«G«^-n«iS 


Mr.eu[,iiibuKivcn fin E^uniioni of ibe ai^eoding Kode, foUowng the fongokiig VIII. of the Moon'i Oitut.tiU with the , J Eqution 


,r ihcMoon'! ab>igi>enthcIn.:i;i»tionorhcrOibii, which he correal by two foi lowing Equ Hi oni, with chofe of the Q . And with thi 


■ ,hEqui.ionoltl.«Node. be h.i gi»tn . K.Ji-fl<» of the Orhii-Ptuee of ibe Moonto thU of Lh. Ediplic, «.»«■ ^«nij, which E™. 


Heihend::leiDuiKitb<:DilTa(ictaf ihr Moon from the EutR, bf'Cheralloii>inE>4rH«n(ito TITT, Equitianii t. Jt^tjimtm. 1) ■, 3. Ex- 


uMritM-SyMi 3. MM-tnict.j.MiJfrmSM„i 4. T-«it,MHn iSiai — atnmi A.Mn^; ,, t-u>ke Mi»m i Sui — iv>i» ^,,„,. A, 


T) . 6. 7win >i5n4-«H>«n''^- ) 1 7. Tdi'm ) ■ £■■ — wen, A. £n 1 8. Ttoin ft. /5n + u(«. ..4k. £i>«. Hecorrr^ilhi 
firflDitboceDy the fcwrtl following Eqaiiioni of DilUnas. »ecotding to iheir propel Signi, end hiviagobtained ihecorrea Dilbnce (.ceordim 
■othiiMethodJ httikeJOutthehoriHM«ilP«»«ur, ind appaitnt DioiHffT of die Moon, icconliog to the AtsBmtotof thjitoneO Difttnee. 


H.B. Henwkeithe Moon'i hoiiiontJPirdhu totheippuent Diuneorei 6o'40^tD n'lo'. — B«tihefeMetbod.«ie notibcenua u. 




























u 


U'FMi 


BNT" 



( >69 ) 



IDIFFERENT METHODS! 

OFSOLVINGTHE 

iieplerian problem. 



A. Limited Correction tf^WARDV Hypothdis, hy two Terfm in 
Seconds, to be cotmeSied with the mean Anomaly, for determining the 
true Angle, at the. upper Focus of a Planet, from Aphelion. 

PUT <i = Son. Tnaf. Orbit, ^=:Sein. Conjogate, r = Eccentricity, and defcribiBg a Circle, on tlicniipa 
Anu, wbofc Radina s i, k = Arch next Aplicl. to whci« a LiD« ioterfeCU it drawn from the D^ter Fnw to 
ihe Planet; Sine of that Aidi=_j', Cof. =-- ""■ *— ■* ~. -t — -oxf-e. .i.. » _*■ .. . , ». 



Une, n Kftuwefiom the it^/enu to tha Planet ■ 

4M + M + X 

Diftance from die Snn « — ' . „ ... 
hvta.^itS»m, by Rayi drawn to Ae Sun, ia Ae lower Arw. 



%ence, by PrDpcr» of an Etlipfii, the Length of the interfediDg 

t ■ "^t^T^ "= "T+ftT (l«c«"ft**'*« — «^ tod the Planet'i 

and i hhx + - ■! ar - ss PloJon of Ae Area dercribed br th« Planet^ 



• into '^■—^■~^rfit.Sat%Nur»tft. WhencetheFluion above becomeijJ*K+^^^-^^- 



■ ' • J * , ■wMcb, becanfc ji ss — i, andxxvr, reduce* to ii*i+—- X — ij — — -jt", whofefA«/ii 



(^x+V~rXfK — f jrjF — ■ ""■■^]~ (tbe .ilkM of the ctrcolar Segment next Aphelion, fonaed by the Cnrre k, 

itaSine^t and i — «» Iti vcricd Sine frmn the Vertex next Aphelion, beii^B^x — \mj) which Fluent when 

Arch B= Seini>Cirde = f, and j, iu Sine, si o, become* -~z — I" ~~^ " "^ = ~^ ( fappofing rf = i 

—^1 die Area of the Scnu<Orlrit or EUipfii from Aphelion. Whence, ■>~T~ ^^c* Seini-£Uip£i : -— 

• ■ — ~ry~' Area tUSfiu StOtr from Aphdion :: f Length of an Arch of i8«» : k — ^^— -^y; 

die LMgth «f dw cotrefpoDdent Arch of Mean Anomaly es A. FiomwhicbSqnatioo, '^'^^'^^^'^ 



jX Sin. 2]G + --a^xSin.Kl' (becasfoxy, orCof. x X Sin. x — {S. as). Here, frir « 



■Mow/ 



DigHizcd by VjOOQ IC 



nt ROYAL AST R N O M E R 



'nbifcr^nt' M£VHodA of feiv.ng t'kt RflpLfekUN PkoBp^lvJ. 



X Sin, 2K + 

gfrnall ValueinlUrpKlof tiK AtUiAj udlhen^ore mA^iskiA, b^Dgtrm-lj/i. Wl^ea'ce, % STpe x and btm 

X tjin. A| , nvhcM-K the ArA rooiK 
E^e Upper Fivw, or Angle from Aphelion, i» now not to be confidercd equal to A, but to A+ iti Carrtahs, by the 
tjtuantitiw ' ,^ ' X Sin. 2A + %^j ~ * SiBjjA] j'wIich^flQjKnllEfcsitrerMnot:! to Swwft y'a 2)iyw, by faying 

At 3(4159 &c. (Length of an Arch of i8d', Xoiiw being 1) is 10 6^8000 SeunJi in that Arch, fo it - , . 

it Sin. aA+.- ^^- ;t $in.^J„(th;i.^i:h dfOrrc^ionl. to 51*66 X -^. X S». .eA + (^5t«.K '' ^i ~ = 

Q. A I ^ the Nianhtr »f Sttandi to be oi/r/ri/ to the given Mean Anomaly, for the earrtS JingU sf ib* Plautjhm 
at ( he U pper F nm t i w hi c h C ofwftia w f« r» « » i m *l» .9\K a« »T j <i An u o ( fm a ti B remr i ftt j ,-Stit»ni, y m fi t t t , 



_., _ tOrreflly lUlllt Orttn Of JKarj SiA Tieriiiiyi WUft Dor amvtrfai "Tiule 

correAIy fervet for all Orbits whacloever. 

■miM* iht Valiu ef iht fertgting Centilan ef tht MfonJoBma^ (acetrJing taWaid'iJbfiatiiJti)/^ thmt lit /. 
p tbt Vpptr feau ef <i Piantl't P&ci, from jlfAiUan, vut^ it traJj lht»VM aeeerSng U ttt atfvt kwiUi CtmSitmf 
Lao«aiTHMKALtY, from tbt ftrtgung Ev^^Uni. 

4.7 183654,+ a I»g'~^. — t^g- ^ Log. Sine zAsbLag. iftTirm. 
5.1383343 + 3 Log. "~~ —Log. iH- 3 Log, Sine A»Log: zdTorm. 
iteie a, the Sem. 'Yranf. "being confideted = i, the Log. of — — = Log. e of Eccentricity, and fei+ " ' - 

J=i+ -^^. andWL'Sg.is/HMa, Mid may bf rejeJieii or'jtaken at zmot^^ahyt fer all die i'/iw/^ajr Orbits, 

e^pept thofe.of-J)frarj aad Mtrtiay.. 
Supp^le <!=,o6, then 1^1.0618, whorelx>g.s:o.ooo78io. 
Hencf, 4.71 148 + » Log, f + Log. Sine 2A =Log. \^ TtHa in StconJi. 
3' X i.yt 151 + Log. c + Log. Sine A =; Log. zd Ttrm in Sieeiult, 
In WoRBi. 

t, TflStSfiM e/zbtamA^nt Log. 4.;rii48, and tvjict tht Leg. tf Ecetntridlj in Parts ofVmttj, tbi Seta.TranftMr/i^ 
add ibtheg.Sint tf i9^ct tbi Mtmt Anva^tffnd ibt Sim (rejeuing Sadtiu) inill bt tht J^aritbwi *f tbt ir" " 
Secoais,' tQ Be dddtittt, or fuht'raSiifi^n^ tbt "Mian immely, auarding'tu it it hjmr grt^ir tbttn ya titgrtti. 



Ta ibiSian if tbt conftsnt Ltg. t.yizez, and tbt Lag, ef^ceintridtj, add tbt Lag. Sint ef tht MeaijlMmt^, tbt 

{T^t£^a%8,tiJilu)bii^gmfM,■vlaU6r^itl«g.a/^tbi^ ■■-■■- • ■ 

jtnamaJj. 



Stun {r*}(aiag RIuKih) bUttg OifM, -wiii bt lit Ug. tfibi lecbnd T«rta is Seconds, -; 



fibti 



a. B. Tie Mean Anomaly hliCK always nckoncd fiom and to AplMtion, whercfai die.te«m6 my be onittcd 
ip compnting the Corrcdions ; which bcinr maje, St^, as ihe.jMeXen Diji. i> la tbt Pirib. Dift. fa it tbt Tamgtnt 
if Ba^tbt ettriBrd Mtan 4»a«alj, fr lriaJng!ieftbtPlinrttattbiUfftr^nti,f^tm Jpbtkm, ta ibtfongmt ef iaJflbi 
tnt Auamaif, tr ^gU, <*' tbt iav/ir Foau ef a Pleotit, from AphtUen, n^mrid. 



E X A M P L t I. 
TU itttmnatj ef itt Orh't if Jupitci, Mr 0,04Sll9 (attvUiig 
Dr. flallc]'] and I6i Mug jiMwitlj eflM Fiona J^'f rijiiirti 

lA Tmn. 1 td Term. 

4^7(148 CmA, Lag, I i.7i«;i Conft. Lot. 

7.1W41 t wlct Lo). Ear, I t^jia L og, bcukriciqr. 

S.07791 Sam. 

9.ig897 L eg. S> twlEt An, 

|.776n . . J9",«i+ J o.-iioit 

59.8» + 
Comaiim73,6g + 



RniM cbe^ aTitiensDetactbeC^^/KMa 
jjo ii ,j« 40"' 1*6'. 

i 37 1° J* S* ■ ■ T«ng. . . j.t8<i4ro 
• ' OdBfl. Ii«g.Orb. f.fsSt*^ 



J 14 j» S4-7W EqMi 



*r 



DigHizcd by VjOOQ IC 



«»^ N A V IG A TOR. 



_^pilferent METHQBS of ftilvihg the KEPLERIAN PRO B L E M*. 



By gt 

. At Sub. Cmij. => ^/t.o^Sii^^lh.gitjif, • 

To Son. Tnnf. = i, . . . 

So Tu>p 75" Mc«n AooDi. 

To Tang, 75* 1' j", 45"' ^ "Upper Focw 



J4.0 j»C3o" . . , Ttaj. . 
( (9 45 o Tie tree Anom. ntr^ 

75 00 O M. Anomaly. 



O.OOOS5S4M 

[O.S7I947S 



B X A M P L E II. 

iftTeim. id Term. 

4.7ll4Sconi(.L^. T i.7ltja CMiA. Log. 
7.36643 tw.Log. Err. [ legjai I**. £«;»■. 

3.»779ica.L. fiiri.T, > o-j^jf^ conft.Lo. for i4 Tv> 
9^937jjLo,S.iAn.=l 9,93715 Log. S. Ad.s iiof. 

a,0iS44L.iO3''',6B— J o.i3i»9 

9,95 + » .>.o.99937 Log. 9",9S+ 

— l' J j"+o'''ae9 j,6j^ ConcAioD. 



■ 19. 5S at 30 the MiTca ^ it 111* C/^ Fmu, ftoni Aphd. 
Logi. 
59 S9 13 » • • Tmi9I« . , . io.«j83jaS 
CofUt, Ug. OA. 9.9SUS51 



4° iS' 4°" T!m iwriff Efnailsa, apeting with Dt. fb//gr' 



AiScm.Ca[4au»Dftbe Orbii . . . 

To Stm, TiMif. 1 

So TaagcDl H. Ajidiii. iio" or T. 60O. 


o,ooosss4 M. 


ToTwfciVsS' ("o'eo" I' 54"- 
. u the Upper Iot<u, mfrly, 

S,^ 3ft' 0" . . . Tiag. 
DoaUed li; 4 Tnit Anom. H«r/v 
too MiAaom, 


io.ft39iiSo 

10.1JS1I34 
9-9Siolji> 
10.196365s 


4 j6 E^mtion marly 
4 jj 40 CarTed£i)aation tio 


nibore, 



-Ho" Brm, by BalkaUa. 
EXAMPLE III, 



HtfHfrei ibtCtmeHm 0/140°. 
ii< faemriary itirtt pua^ n 



i^MC^VK*" *9 S* 13 - Tiogent . 
L(^, for Eq. J Cent. 

IJwiMed 134 4s ,4 JO True Anom. 
tfo ' CO 00 00 Mean Ajiom. 



Term.' 

.7114S CooHi Logi 

.64915 twice Log, EcceDtricitj, 



.35408 Log. llG" s: 3' 36"— 



\ Ml Anom. 70" o' 00" 



■lagRdngwithnailfn'tiy- 



—5 '4 45 '» Correa Eqmtion J '« Center.! 

■ M. Eq. J Center. 
4' iifi = 140" Anom. 4"" 16' 34* ' 

For gmteA EccCDtHchy +st 17 Gr. Dif. Bq. 

^ — '■ [aboje. 

5 «4 5' »I- DCenJei 
netrly u attoK, ! 

By B*lBaUut'\ Contftion. - - • 

Log.. 
0009705- CO, 



At Sent. CoBJ, 

To Sem Tiai4VnJe=_. . . . 
So Tingent Mi Aoom.' 140' or T, 



l.o6S77j)i ,933113 



To Taog. 400 J* 47" or 1.90 iV 
QpniL Lo( 



6J Tta.'ia4]it!7C 
.oe.fbrOi^. - 



5^147840 



Cj" it> 3o"Tu.io.jSoeM5 

1J4, 45 o Il« true AjwmJyi nea^y. 



+is" Enoe, \>j BiiWaUn. 
E X A M P L £ IT. 
TcfitiJ lit Aitltallb4Vj,perForu-tt jofi M. jtMrn-h in itt §r. 
(It ,f Man, vhff, EnairUitj, ucmUng- ra Dr. MaJley.Jii 
0,09163936 ? jhdh'tenfi IS iSAmimt lit iru jiaimah, onif tb, 
EjMtilkntf ibeOrtil. "' ™ 

BytbeLoprilhnncEqutioiiiifbrettBDg, ' 
»* Term. id Tenn, 

4.711361I Conft.Log, J (.1383,41 Conft. Log. 

9 Log. B«y, j. 6.9003I7 3 Log. E«r. 

CO. Log. A 3 9.gj)Sj39| CO, L«g. 1/. 

644093 Sum. FttiheOrUi $, 1.036860 Suo, 
+9.808067 Log. S. ft A^no"*. 9-9"957 3 Log, S; A. 



4.711361 C 
7.93IJ91] 9 
9-99«3W o 



9.4 ja 16a Log«l3",«4r— 



i.9SS8»7L<«. 9Q"j3g4 



«"f3g4 
30^13 



">9 3* 47> 99 .^ '"'"Vpyr^opM, 



,y Google 



Tht ROYAL ASTRONOMER 



"'TMferent'MSTHOPg of foMng th e REPLgRIAN PROBLEM." 



fWf J4. c! »J,J . T'ngent I 
'Coaft.log.Orb.l 

49 4S f I* , TasnnC | 
OoMti 99 17 43 Trae AjMEoalj, 
110 DO 00 M. Aa«m, 



Bj BtJIisUti't Congftimi. 






Ai Sem. Conj. ^1.0916 19 X>9<>7]'i 

To Sem. Tnof. ■ I o.ddooooo 

SoTut-U.A^oia. iio°,-ar70*> itsSuppi.l 10.4JI9J41 



[j£, utile Upper Fociu, a<wlr-] 



10.4408057 

IO.IJ4M4S 

9'9'*9*90 



'^t 19 Error, bj BJHaUia, 
By R>Li. P. 18. 

Ai Rid. 

ToCof. M.AB.orS. 10". 
SoEcci' + iui>=>ii579f> • 

To ,039*057— . * . . 



bjDi.Oiny'iTMa. 



M 19601941 

T« Doubletctr. . .ilji?*? 

S*S.M.Aii.iie» WTO" . 

To S. lO" tV 40"! 



Lot. 9. f Cube. 7-*97963* 



[Ou^'i ConeaiOD of tfarJ. 



N. B. This Rib it cbieflr of Ufe foi (he Oibin of tbe fjn^ Ft- 

'HI, yvfiiir xni Sttwrw, lod fometiaiei tbit of tbe Mson, but neret t( 
X depended on for tbe Orbita of Mart mat Miretrj. Tht Tratb «i 
fiilan of tbji, or lar otbet Kulc for the Cune Porpofe, SMf b( 
-rared bj our Uarvaftl *■' Csrnfl ilinb, p. (9, 

SXAHPLS V, 



4.7 II 363 1 Cooft. Lag. 
8.6*7l7o| 1 Log. E«r. 
9.990891! Co. Lof. d. 

).]ioS*4^''''i* ^"^ ^^ 
9.814154 Log. S. 4 Am. 

J 114778 Log. iSj9",7— 



1* 44, S— limited Con»aiaabr a Tfnu. 
"* 47 *S>» /,"«•« Upper '•<". ""'r- 



' 49* S4">* • T«ngnrt , lo.oj 
39 41,4 Tba True AmcdiI;. 
00 00 . M. Anomaljr, 



Dtf. — «] ao (1.6 Equitionbrthe AwWCWiflliV 
At, J»»5^«rli5*— »3 iS 35 Equtioo iaDt. U>^'iTiblei. 



+1 )C.l Error of Ae Ak^n^OfwOwh 
By SuSiMa't CoiKdiaa. 

L.g.. 

0.009405! CO. 



Ai Sem.Conj, ^].*05t9 x>794>i 

To Sen. Trufv. t. 

So T«if. M. Anon. 1150 or 65O 



To 114^ )i'4i''iL U Upper Facial 
For (570 15' 50^,5 . _.^ J"^^. 



■••J 



Enar^bvBt 19'. 



♦4*' 



fin dkii Ofbil, bf SiAnUWi. 

J/. S. Tttfiregtiwg limited Common ef Ward'/ Ifyuihefii ty two Terpii **lf, wU gtvt jit Agb st tbi Uppei 
PocM of m Plmet, fiwt Jpbtlin, tvrta, in tb* OtUti af tbt Earth and Venai (^/m^ll Bccmrici^) ij iJk Ujt 
/ ihi firft ftnt mlf : Tti Tecond Tcnn in Qrhin ^JmaU Etttatrid^, hd%g btu o/finil V^tm, i» r^ftS rf ibt firll 
Ttrm, m^ it tbtn /afilj rgtSti. 



IfflprovciBeiilbung'U macb-the Objed of our Attentiaii ai Tfclae* of original InTcntivii, the Bnuiii ( 
if WW** Hypothcfi*, by twoTcrnu, yon will fiod hat not alwa)'i ui« Rea^nefi of the RvLx, f. 88 : Si 
vUtb, we b(^ to fee tibtr RotEi dUmttd, for fiadioKt diicAly aod trulj', the Bovationi for all Orbit* what- 
itu of this Sort wiH be lela teoKnu and perplexiiig than a mmttr »f Ttrna an fellow, em- 



CarrtBiti 
Similar to 



ha Jtfraxim^i - - . . „ - , - 

plored n find tne true Anile at the qy«r Am, which bajng done, (bjr mocb Laboor and Attention) then there 
nun be a fortber OperacioD todaterauDe the trut ^nvmiif, and coafoqocDtl}' the £<tUATioM of the Orbit 1 which 
B^ATion would be beft awired at by the SnaMttJodtiban propofed. 



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and NAVIGATOR. 



lij 



Diffctent METHODS of felving the K.EPLERIAN PROBLEM. 



Pntdng t 



FbufitM of the tlBftit Stettr, by malting -j- — —5 — V 



Sine A, Cb Sine fijUowing Qoantity, tnd contiDoing the Termi of the formei 



ynd oonfidsriag the 



RtttOMglt »f the Cefiiui ef aKj tvm AngUi (Ra£ui btiag Unity) It h ip4 1» half iht Sam tf th* Cajhitt ^ tht Sum and 
80 X 60 X 60 y 1?f*/ rc*f 

Diff.tfibtJnglti, then, ifter a /rwi* Procefi, 77777:; — ^ i+4«x — /yS' — ~-S'+ifyf.2A+™- 

3''t'59 3 'S 3* 

f. 4 A. will be the Number of Sinndi to be added to the mean Anomaly, that the Angle at the wfftr Foemt, (and 
[hence the Angle at the lower one) may be more correfUy found. Whence are derived the 

FoLi-owiiic Eqjt; A Ti ON I. 

L*t E JiMH iht L^. of Ecimtrititf £vUii hj half iht grtttter Jxii, J thtUg.if half th* hfi Jxii JiviJtJbf half th, 
grtafrr, G tht Ltg. af th Snm if ihi Sjiarti »/ half the grtattr Jxii ami Iwit* tbt Btttitricitf JiviiUd if tbi Sjw 
sf half tht ff'tattr JJeii 

Take P = 1,7.277 + E + i F+ IG 1 Then the Loo*. ofiTenn* \ i-Jj X *»"+ Log. STA "— Log. Rad. 

- Log. Kad. 

• Log. Rad. 

= 4^50824 J L4.|S + Log~ S. 4A — Log.Rad. 

Of •which 4 Ttrm: tht frfi it ahtiayt ta hi adJtJ, tht StCtaJ ahoaji t» he jthtratled : The athtr f*ua It he aJdtd tt 
fiAlratttJ acctrdtMgdi tht Sinti »f itt rejhtctrvt ArgKirenli, z A and^h are pejilivt ir ntgali'vt. 

The two principal of the Terioi (lee p. ^;. of Mifi. TroBs) agree with thofe before exhibited, beii^ like thoTe 
two Ternia or Equations laid down by Sir iaxAc Nbwtoh in ScbtiU to 31 , Prtp. Bati I. of hit Princifia. If a cor- 
re£ier and concilcr Plaent of the Fliudon of an elUftit StSer, formed by Raya drawn from the Carve to the Icwei 
Feaa can be obtained, a farther and more certain Correflion of tfarl'a Hypothe&a will be of Advantage, which 
otherwiie, in nomeroua unconverging Termi, will be intricate and ufeleli. 

Aitbe foregoing CorreAion of frard't Hypotheiii hy fmr Termi \* not perftaiy exaA in all Pana of the Orbii 
of Mtrewj, a faiiaei CorreOton in thi>, and other more excentrical OrbiU, ii u foUowt. 

RULE. 

A> half greater Axii ef the EBiffit li It tht Eeeentritity, Ji ii Stat tf the mean Antmalf tt tit Siiu tf alUlher Angle frj. 
fnmdi fiAtraa tbii firft faund jingle fram tht mean Jhtmalj^ and tt the Ltg. Sine tf the Rtmmaitr (which yon may calflhi 



:e P = 1,7.277 + E + 1 F+ JG "J Then the Log*. of4Tenn» r i-kx FT^^XT^ 
Q= 1,14130 +E + fF Lin Seconds to be conneAed ./ a.l; x Qjt-Log. S. A— 

R=.4,7,2j6+2E + F I with A, wiUbe /s- R+Log. S. lA — 

S = 4jSo8a4 J L4. IS + Log. S. 4A — ! 



Anomaly] addthtSnm af the Lag. if the Ecctntriciiy and the ttnfiaat Lag. 1.7581227 (the lafi being Log. 
of Decreet S7',a9S779 = Rad.) tht Sam (rcjeOing Radioi) vdllhi the Leg. af an Jagit in Dtgrtet and drcimal Parit, 
athichteing jnilreaed fram the jirfi fiund Anglt, the DiSCKB^c vjiH liavt a Carreaian it he added tt the mean Anamafy. 
ffithllni carreHtd Aaamafy, rtfrat th* Optratian (if neceflary) hjabaaji adding the lafi CurrefUon le the gi-vta meat. 



Then f^,. At tht greattr Sem. Axii tf the ElUtfii it ta th* left, ft ii theTaagtattf the com&eA Anomaly, tt tht 
Tangent tf the AagU at th* afftr Foco* ^ th* EUifJa ( vihtaee the Angle at the Inner Foem, er tnu Aaamalj, i) had hf 
^bt ctmmtn Prtfartiaa. 

Theforegomg RuLp istrvcto a StetaJatvas Op*ratimi, in all the Otbita of the PUneta, txccpt thofe of Mar, 
and Mercury \ in the former of the two lafl mentioned Orbitit the grtaiifi Errtr i> about thre* osfaar Stands, and in 
the latter amount* to nearly aa many Minntet, in which laft Orbit tire* nptatid Operatitns will be neccflary for s 
ttoe CoiTcAion. Bat, to avoid tbu Tronble, the following Method of Ctmfntatitn, [not qnite lb frtlix ai the former) 
' tme te half a Secand, even in the Orbit of Merauj, wiUioat repeating the prolix Operation I 

A LBS* PaoLix R01.E. 

Add ttgetber tit Ltg. Ca/, af tht Sam tf tht meam Aaamafy ante earrtffed, aad tht txtentric Antmalf, tht Ltg. Se^ 
rant tf th* Antli frfi ftand (h tht faraur Suit J and twice thi Ltg. af Eccentricitj, (in all of which Angles the 
}econdi may be negleded) the Stun af edl (dtdaSing t^tet th* Radiai] -will he th* ltg. ef a Fraiiion ta it addid A 
'Jaitj, lubtn tht Sum tf tbtfaid Ammaliet ii hetvitin go' and 170", hat atberwi/t ta he fttbtraSed thirrfram. 

Then the Leg. ef ibii Sum, *r Remainder, being fahtraBtd fram the Lag. af tht frfi CtrrtSiaa in Minttei^jaa will 
l»nMlbt.Lai.eftbttntCorrtaiamiaMimilei,iabt-add*dta4h*g>mta U eaa Aa t m mif. - - — ■ -■ 



Difoont 



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^e ROYAL ASTRONOMER 



Pttt>»eitfrMBTHOP&of-Soh4i>g tb« K E.P-1.ER1 AM PfrOfrLB-Nfc 



E r A U P. L E. 



ii mian Aaioulihtirt 70°, inlbtOrbii 1/ Mtrcaif, vihtfcEcann- 
titj bai hiiR ^itL4d^,ia^<i, U dttiTWuptiht tnn Anmalf, aatrd- 



0.0*71 X Log. 



^^Vtl^trlKMi, Lo|. Tu. 70° l%',i% 



The oitabntBd Autbar of the l*te Mfidbfi 

(noEdeT -.. ^ ..— 




^r.rouDd t 



Dif, lO }',$( ComQion *dd to 

+ 70 o It. Anom. 

+ j8 50 EicenU. Aooai. 

— — [Htr*iii0fir^ti4ii-a 

J. trtS" '»9 S3. Cor. 39051' 
AddLng. Sec. ^f. roond llOg' . 
Add rwt'n Log. Eccr ..... 



M«fbcd <u'p.}$. iirtalj-flvV'ltlHja 
mafy, byRoLi p. S8. 

Loniilhini. 

AiRid 

To Cof. M. A()om. oc S. so" 
So the Ecer . + jti ( ^ ,>573ei5 

S.9445969 



ii' 3$*JLoc.5. jO^ 



K. E M A K K. 
■I Tivfft, Mr. T. Su^H, in At flrft M|a of Hi* PToTaO!, btt 



Jigiwd to TdItc tlK Kiplaia RroUtm, uuTMiallh u it ii 4(ibc at p. at. of lliii WoA) "a OmaimtaflfiitJ-i liraUtr Btp^t^." B 
Hypotliefii haijbyill olbtiii bten cooGdend u UlifiiaiHuii natcinv^Jm|uirin|eUipiiaiCDrrcfiioii. And y«t, in uwthu PUoc, at 
im nuubnnatical EJtjs, the fame crlclinted Author hu eiimined the Biror oF ^driTi Hypotbtfii [fi'tt^W Gi Minutci ia the Oibit 



^t. of bii naatHraricjl Bjfkji 
■ fjTi; tad. eoniaed it /or 1 
He lui next ncuninod, (p. 



if then Eonfidering, M ll 



EflajO ■ dilitrent firct/dp HrpotheGi to the intient one, f it SulliaUn' 1 Hypo AtSs : And, __ 

Anticnia di4, ..to lAJvcr ibcii Purpole, Ifa* ci'culn Hjpathefii, 1* ii^g dttU tbo dliplic Ectzntildlf, 
iU eiimineii lao aiumpLCd lo corrcfl th( circular Hypuhrfii, Co called of the Antienci, by fuppoGng it of ijiul EecaUndtjr with fftr^i^ 
dUptiul HTpothelit, which he has {» we bcron obfcrred) denominated lb^ ciraiUr Hjfilit/li. 

[Om ill whJcb NoKlIies, uid MiJuUtmi-i Difcrvtria, in lili late Tr*?(, ifgrebid, fufh at Ibt Praefiim ^ (it Equinoxn, douUi 
the Oiintilr "> '*'"' ^" '•'""^ Nkwtdh found it, from Eiperiencc ; TJx Aikiim"-[i arijlng, hy thani, f,<m taiimg ibi Mean •/ e A'n-* 
irre/'l.ifirvMimit, Sft. int. abort all, iii OfduUm if all ibi left Lutar Bfudiimi, viithtui ibt Centnl, ;^w a mxtviic PrindpJe, and am- 
fmdtJaumfyiiiaiErttttai, mV£ a VDaDH>./n*>>^ m Eututo, Jifimlin Pf^^ t* Dr. fbtlty'i Oiftrvtima) vMmtjtift3 fife 

Oftraim tmgarj It ittfirmiiif tf a complete Iharj of tit Mta'i Mttim, (depending more on phjitd Hrpotfaefei, •"■ 

and Obfnration) aifn ht}M -m Mm ami glfri,,,, Llrti pining n AtraoNOHY I » clf4, by/am MifiAance, ' ' 
Numlur if Oftimtittt {-^' l*imiialhaa Ji^aii)_vtfiall }i^ iht SuijrS .itthiJ. iM,iMfeaarsiJi Darimifi! 



■*>^li,llt 



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( "» ) 



RULES and EXAMPLES 

FORDETER MINING 

Other Requisites of Elliptical Orbits. 



PROPOSITION I. 

T» JtUrluiiu tbt Di^atue ef a Plantt, tr Cmit, frm th 
Smt, Jr»^ fie fna Antaalj aid Eteintrieity «f th Or- 
bit, ffvtnf 

Morcofy's ff* JinmiM^ h'mg 66' ;«' iV*, md BtuMri- 
tityrfiA Oriii ,20589, rifund bit Ayhncr /ram tbt 
SvK ■ 

Rdlb I • Lop&ilbmt, 



Ai S^nare RaJita (talcing it 1) .' . . 
To Sqaare Sine half irtic An. 33" 16' iz* 
So Din. bet", feci, or doable Ecci'. ^41 178 

foFotaitt PrepTwtibnalPss ,1339^34 

Then, AsSam Pcrih.Difi. +P,9ifo334co. 
To Perlh. Dill. . . . ,794110 . 
So Aphcl. Difi. ... 1 .20589 '. 

ro'SUt. e from 9 ■ ■. i>043ic9 . 
■ Rin,B t. 

AsJM'kr (tftkin^it 1)' . * . ■. . 

To CoT, rr6c An. 66" 32' 24* 

So (he EcceMittjty, ,20589 . . . . 



To' Fourth' FhJpdr'. (^,0819666 , '. 

riTO;A«lial^grt*«r-«rfifc*<i4i'9oj54 « 
To Ftrih; ETifl, ■,794110 . ■ . . ' 
So ApSer. Dm; r.205T9" -■ . 



OiObooOdo 

'84880' 
46651 



0.037 141S 
9,3998807. 
0.0813077 



0^183299 



9.6000017 



8.9136370 



o-oj7'4'S 
918998807 
0.0813077 



O.OlfljXM 



ToDift. !f from'd . i.o4jiog ^_ 

}i, B. The 'Fhpttr^ in die bft P r opwoon i» alWayi 
lialf greater Axii ± Q. 

. . . Sig » inif Af^ftTn* . _^ . . , . , 

^ fe t' i". 0' I'o. 5i.}t.^+ *^ gwtter Axi. 
ii the Jh-fi Ttrm. 



PROPOSITION II. 

TV diurmiia th* Etctnlrk A»taitdj tf a Fltuttt, «■ Ctmii^ 
frtmihi tnu-Anttiudy tool EettntntHj ^tvn t 

Mercury'i 4Tiu Anomaly iipvtn 66' 32' 24', tuJ Entn- 
trkitj rfihe Qrbii ,20589, rt^ai tbt EeitnMc A*- 
maljf 



Kvf.* 3. 



Upnabmt, 
0.0500596 
0.0406538 

' 9.8169886 



Vt-p^lDift. ,79»ii : , . CO 
To ^'Aphel.Dift.i. 20589 . 
SoTsng. hilftmeAAom. S ^i' {& tz' 

ToTing.haJfecontric An. If 38''57'2s ,.,_,^_„ 
Doubled . 77 54 soexcentricAnO- 
maly required; 

PROPOSITiONHI. 

Tt dtttrmiiit lot MeoM Anomaly aiJ Ejialion torre/panAnt ^ 
a Piaatt, tr Cemtt, Jrtm tit Exctuiric.Antma^ and St. 
(ttUricity rfibt Oriit givtn f 



Exttntrie Aaamafy »f MerCDr^ « |WA 77" 54' <( 
EtetHtriciij afhtrOrhit ,2ej99,* nqumi' bh tU. 
Old EfMotim ef bit Orhiif 



Rad 



'-•Jl: 



Eccrtirfcity ,205850 



I 9;,3'}t3S3 



«.» 



,, Google 



IlK «* R O T A L A S T R O N O M E R 

RULES foe finding the R E Q.U ISITES of ELLIPTICAL ORBI t'sT 



Rule +. 
Conft. Log. OrUt 
JExcentric Anom. 77* 54' 50* . Log. Sine 

Dif.brt.cor- 7_i.,, ,, e ..o,. 



1.0630231 



Sam, M. Aoom. 89 26 $6 [B7 Dr. A'.tJV* Tablet. 
Tnie Anom. . 66 32 24— [Eq«. Si" S4' 3°' 



OurEquatton tf 22 54 32 agredng with Dr. Hallo' 

PROPOSITION IV. 

Tp Jtttmint tot l>ifia»ci tf a Plaiut, »r Comet, frtm fht 
Sun, yf«M iht txciKtric J]i«matf, Mu Jiumat^, lad Sc- 
ttmlridlj *ftht Ofiit pwM f 

Tbt tnu Jnemafy ef Mercary i«»f 66° jt' 14'j Ixetntric 
jfnem^lf 77" jj' 50', aad Ecetmridly tf ih* Orhit 



1.0717580 
9.9902651+ 



RULB 5. 

As Sine trne An. 66<> 32' 24' . 
To Sine Exc. An. 77 5450 . 
S o Sem. ConJBgate = . 
'Ap.Dift. X PM.Dift.=^i.»589X,794U 



To Dift. S fiom O . ■ 1.043109 . 

Othbrwii*. Rvli 6- 

A) Sine half true Anom. 33" 16' 1 »' . co. 
To Sine j Excent. An. 38 57 15 . 
So^Peiib.Dilt. ,79411 . . j 



tbt SvN I 

tagaitbmt. 
0.0374705 
0.990265 1 



9.9905943 



0.2607560 
9.7984685 

9-94»4«4 



To*^ Dift. ff from © ; . . 0.0091649 

ThcDift. tf fiomOreq'. 1.043109 donblea 0.0183298 
Tbt/tm M itfirt. 

Sidei A ia fame Radot. 

98913 t= O 9, from Sun to Mercmy *J 

41 178 B3 O Pt irom Sob to Upper Focni > 
101077 = tl F, from Mercnry to Upper Focni J 

lulf 141178 «■ San 

1*0589 >s H = Half : . . : 

(9512 K H — B P (oppofiteto Z. requited) 7 
, 7941 1 H H — O F . . . i 

31666 a H— OS ; ' ; ~ ' 



N. B. V^ tht DifioKti/hm tht Sm art JtltrmtntJ hj 
thefmgdnl Ridti in any ef tbt plautarj OthiH, aJablt^ 
LogaHtbai mej be ta^fiJ la tbt/t DifimHcti, ml Sigbl, fim 
Gardiner's Tailu, tafig Platti of figm-u. 

PROPOSITION V. 

Tt Jtlenmui ibt ereateft Eqaadon ^ a Planet, cr Come^ 
*r grtalift Diffirtnct hitviim in mtoM aiut true Jm 
litif 



Tbt Sem. Trai^ftr/i af lAttzwrft Oriii it'mg i, and £[• 
timtridtj ,10589, rt^rtd ihi grtmtfi tfietitKf 

Role 7. 

From the lower Pocot, as a Center with Radioa, a 
awn Prtptrtinud between the Stm, Trm^tierft and Sem. 
Caigugate of the Orbic, dcfcribe an Arch to interfed the 
elliptical Cnrve, and the Feini of that Interfcdion will 
be the Flanet't /rw FUict, at the Time of the pteatft 
Efuaiii ' 



Hence, ^Ap. Dift. x Perih. DJft. i.20589 X,794ii 
= ,9785754 = Semi Conjngate, -^.gjSpf^Xi ■•,98923 
a mum Fr^trtitaal betwixt both Axti, bang the Difimut 
ef Meraayfrtm the Sun, at the Time of hit greatcfi E- 
quationi Double Eccentricity = ,41178 Dift. /'en ■ and 
1.01077, the Diftance from the Planet to the upper FttMi 
(by the Nature of an SUiyU, the two Diftancei of a 
Planet from the upper and lower Taaa, being always 
equal to the Tranfverfe Axii of its Orbit) whence, from 
thefe three Sides of a given Triangle, the An^le of trm 
Jiamfdj, at the Son, or lower ¥»au, is detenained to be 
8it 4'6',a, xfbUowi. 



r «89>3 

: \ ,41178 

: Li-0'077 



lod*. 



CO. Log. 
CO. Log. 
. Log. 



4.9186923 
5.7096982 
4.8998807 
4-3357787 



1 2^.1178 



1.20589 

,19512 



r^ Tti^inmmtmJaiUtf^n ftagivm T 
&A in tmj rigbt-Oud Triaagit, vib^ < Doablcd 81 
ibmSUmmrt pvmt ' L 



Half 19.8640499 129 deduaRad.fr. 
40° %%' 3'r4 • ■ "Pi's;- 9.9320249 I L*''^ ludicet. 
" 4 6,8 . • tV /. at O, oppofite B F, bcjag the £. 
[of tme Anomaly, remand. 



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Mi NAVIGATOR. 



R U L i S for findii^ the REQUISITES of EL LIFT 1 C A I. O fe fe'l t'^. 



w>inii.y, (b}> RuJt 8, prececdingl then the Kcimtrit Ado- 
maly, andlafilythenMn Aooniftly, corrcfponding i from 
whence the gnauft EjmUm will be determined, ^Swn^ 
/lif hiffertHci btttiaia tht true and mian Jmtmaliei) nearly, 
~ ^cording to the ajjiurid Eccentricity. 
N O W, Siy, m the computed greatefl Eqaation, 
to thj greatell Equation given, foisHie oiGuDed Eccen- 
tricity to the true Eccentricity rt^idrti. 

N. B. The gnaicjl Eqmlimi and Ecemtricitiii, near]/ 
aJTumedj are in a ■very mar Proportion to one another. 

OTHBKWISB.forl^ V/rjiEccBNTKIC OkBIT) e^Coi 
UBTl. 

RCLB TO. 

MAKE two AJTiunptiona of Ecceiitridtrti, one k/i and 
the other griettr than the troe, [which yon may eafily do 
by h aring Regard to the natural Sine of | greateft Equa- 
tion) and compute the greatefl Eqaatiops. by the firt- 
gdiig SuUi, to both Eccentricitiei iiramed. Then take 
their Exctfi, and' Dtftff, by comparing them with the 
greateft Eqaation given ; taking alfo the DiffimeuofEc- 
centricities aflbmnl- 

Tim /ay. At the Sum of Extffi and Defia of the 
ptiied greateft Eqaation, above and nnder the [^ 
greateft Eqaation, it it the Difference of Eccentricitici 
afliiBied, J* ii theDefefl of the computed giejteft Equa 
tion under the given greateft E[]uation, to a correrpondent 
Difference of Eccentricity, to be n^i/f^ to the dcfefli 
Eccentricity, for the true Eccentricity nqvirtd, 

N. S. IP BOTH the cBrnpultJ griattfl EquatioMi (bo\Ai 
happen to come out tm liitU, or fefr ttian the giinn 
greateft Equation; yon mnft fabnafi their DtfiBi from 
one another, ind^, 

Ji the Difference of Difias ot Equations, h f» the 
Difference of airamed£rrMrnrj/(»,y»iJ thegreuer DiftH 
of Equation, le the Diffirtnct of Eccentricity to be aiJeii 
to the lefs or greater defeOive Eccentricity, rtfp*Sively 
affiantd, tor the true Ecccntrici^, rtquirtd. According ' 
tbbMitkod of TaiALandEaaoK. 

•,• NOW, \ greateft Eqaation given of B'* Orbii 
= lio5i'i8'{, whofe natural ^(Mii ,205438 (by Ta- 
BLi of^SiKEt) for the Eccentricity of S'l Orbit, where- 
of you may obfcrve that the 3 firfl Figures ,30; arc cor- 
rect (in Refpca of the Semi-Tranfverfe = 1} by what 
has been given and determined t but ,;o6 too much. 
7bfnfirt, Let the Eeuniriciiy be afumid ,205 j about one 
tcn-lbaM/andt/r Part greater than the Sine of f. greateft E^ 
qaation. In which j|^Hinfriw, from } greateft Equation, 
you may foraetinici T^eStSrcmA, and tAe ike Sine ef tie 
niKt aui«i Mimtei greater, as of 1 1" el', when the Or- 
bit, a* at prefent, is mach excentric, which Sine would be 
^ ,2056349, or ,2056 at four Places. 

E ectittricity affBmed= ,205 5. w hence * 1 ,305 ^ x ,7945 
^•^ Aph. Dift- X Perih. Dift. = Sem. Conjugacej and 
*^ *' I -2055 X ,7945 " ' (*^' ' ^^ Sem .Tf wifverfe) = 
772055X^7945'* the tium Prtptrlienal between the Axes 
= ^802? 1 =dtrefi Dift. 9 ft. O, hence, 1,0107291 
3= Dift. 9 fr. npper Focai. P ; and Dift. Foci = doub. 



*.* Add the three Sides together, and take 4 )^e ^^iri} 
and all the Di&rences betwixt that half Sum and each 
of the 3 Sides, according to the foregoing Order. Then 
fet down under each other, the arilhmilical CempUmenli 
ef tie Itgarllimi of the ia//' S„m, and of that Diftrtmt 
between the half Stan and the Side oppoUte to the An 
^efsugbli then fet down (under diafe Co. Log*.] the 
Lugaritbtu of the D/^AifM betwixt the faid. half Sum 
and the other two Sides ; the half Sam of which will 
be the Tangent of ha]f the Angle reqaired. 



N ow(byjea/f 3.] 

Perih. Dift. .79411 . . . . co. 

^Aphel. Dift. 1,20(89 

So Tang. | trae An. (juft fanndj 4o'*32'3',, 

To Tang- | excentric An. 9 at the Tim 

of grratefi Equaii«n . . . 46^29' 57',z 



Log*- 
a 0500596 
0-0,^065 38 
9.9320249 



1227383 



mbled ... 92 59 54,4 the 
XAnom. at the Time of tbegnaiejl EpwiiM. 
{SfRK/t^.) Conft Log.fbrOrbit . . . 1.0717580 
Cor. tx. An. 92^59' 54*^1 . Lo£. Sine 

Supplement 87 o 5 ,6 J *^ • " 9.9994050 + 
Dif. bet. M- and excent.J 



An. . +11 46 49 ,7 . >i<',78o48 ..I1.0711630 



S,f J 4» 



37 ,3 reqaired, agreeing with Dr. 



DifAeGt.. 

"quATiOH 523, 42 37 .^ . - - - 

Ha/le/i Taiiii ; oor Equation being greateft but by a 



PROPOSITION VI. 
Tt ditermiu ih* Ecctatridly and cthir Dimtajmit »fa Plaut"! 
ar Cemil'i Orbit frem the grtaltft Eqaaiian gii/tm f 
EXAUFLB. 

7h* greateft Equation (/"Mercury V Orbit itimg zj'^z'jy', 
Ttquiridtii StttKlriciljT 

RULB 9. 

By a Table of natural Sines, the Sine of half the 
^eateft Equation of a Planetary Orbit (Ra£ia tr Semi- 
'ramjv. hiing Unity) will be vctj marly equal to the Ec- 
centricity, in Orbiu not much excentric j but in Orbits 
more or very excentric, as in that of Mtrtuij, and the 
Orbits of Crnuti, the natural Sine of half the greUeft 
Equationwillbefomewhatlefi than the true Eccentricity. 
So that the Eccentricity thus determined, for very eccen- 
tric Orbiti, muftbe aumented, to compute the grtattft 
Efmaitn from thence, by the preceding ExamfU, to cor- 
Tcfpond with the greateft Equation given. For the 

?Ttateft Equation computed alwayi augments with the 
Qcreafe of Eccentricity. 
NOW, from the near Eccentricity, fimnd by a Taile 
of natural Sines ( cem/fajiding l» iht Stm-tranjvtrfi ~ - ' 



determine the lefs Semi-.«w*, it being "^ Af. Dift. X Pirih. 
Difi. I and then detmnine the huom Pnfrtinai betwixt 
die two Semi-/£wi, which ii the Diftance of the Plamtt 
[ot Camtt) at that Time, of the greateft Equation, from 
the SUN. 

THEN, Three Sides of a plain Triangle being given, 
(ih* Diftaui tf lb* Plasul fiam lb* Sun amd i^ptr Fbcui, 
ami OiftoKc* ef tht Fad) determine the An^c of triu A. 



Eccentricity = ,41.10, being the three Sidei of a giveq 
Triangle \q fmd ih, J_ tfu/utf B F, or.^ 2 O F "' 
/ntr Anamatf af '^ at that Tim* T 



,, Google 



u8 



Th ROYAL ASTRONOMER 



RULES for finding the REQ^UISITES of ELLIPTICAL ORBITS. 



SidM A. 
<By Sxh9.) ^«9*?» = ® tfT fr- Soq to Jlfowij 

^iiooo ^ O F >fr. San to upper A^w 
1^107x9 ™ S F J fr. MeicDTy to upper Aflv. . 



M>" 



■ Sum. 



1,205500 » Half !«»! H T . T . . . " ; i 
,194771 = H — 9 F (oppofite » Angle rc<{aired) 

,794500 = H — OP 

,»i6i29»H— ©9 



CO. Log. 
CO. Log. 

. Log. 

. Log- 



Log-. 
9.918S318 
o.7ro47<;7 
9.9000959 
9-33t9'39 



, „, - „ i9-8643'63 
^ ., . 4° 3* 34'^ ■ • ■ T911. .9.9311581 
DoQDted 81 5 9,2 tlM^atO, ot Irm Jatmalf. 



NOW (by X^i 3.; As ' ^Perih.Dift.,7g45 • ■- • «>■ 

To*'Aph.Ditt. i,ioss . : . 

So Tan. h true An. (bmtd 40°37' 34',6 . . > . 
ToTu. f eccwi. An. S UT, ~- 

Time of gr. Equation 3 46'29'47'' 



O.0+99JJO 
0.0405 S 36 
9.9321581 



- .. 126947 

Doubled 9a 59 34, Eccent. An. atTimeof greatellBtiuatiaiu 



{By*«/» 4.) Sm£m 57°,*957779 
Eccentricity ,1055 



Cm^. Log. for the Orii/ . . . \ 
CorrcA eccentric An. 92''s9'34'l, 



Sttf. 96. 

forrett ,_ 

Sapplemcnt 87 

Dif. bet. M. tnd Ecc. Anomalie* + it 4; 29,6 ^ 11 



. Log. Sine 



1. 7581217 
9.31Z8118 



'■070934s 
9.9994073 + 



1.0703418 



3.6 



Dif, Tlie MM^nto/ gr. Eqoatkm . . 23 39 54,4 fr. 4^mk^ Eccentricity. 
Tn* gr. Eqaation . . 23 42 37,3 fr. (mttA Eccentricity. 



NOW, Ai 23039' 54* : 
Or 85194' : 



'^"^ 



«3' -. 
81357* 



Defed 2' 43' of Equation fr. «^Sm(/ Eccentricity. 
1 <^ii>Mi Eccentricity ,205; : ,20589 the troeEccentrid^, na*. 



'.* Jbiu*, itiierident, that byacarefal and near Atrnrnption of the Eccentricity, from a Tails of »a/wr«/ 
Sim/, a very great Aecuracy, from Computation, will refult in determiniBg ttie tni$ Egcentricity of the Orbit from the 
^rtattft EfMofiMt given ; and the Trouble of a Second Afliimption and Operation, foi'any of the planetary Orbits, 
will be thereby avoided. 



REMARKS. 
KsuAiK I. EofncofthcPrKiri Atniu]>*sufcethEpniiAJtfi4n»QrMe[cuirtobe aMlcfrriua*4#. tnHleai, DtitCm/U^ ftniai 
[ly, in one PUcs of bii Element! (rf Aftronom)', p. ti, niiltrt i[ to be 14°. t'. jH. witb Eccenlticitj 111165 *" IOII176 the fitUaSan'- 
III, bting •" .10*81 Eccentricity to 1 the SeniL-trinfverfe."- Simii icaicei the Eccentricity of J 797* t« 38710 tb« Semt-Uafrcrle, ilk 
DW u ,Ki5t) (a t, iccoidisg to Dr. HaUg j Slnii'i Mvmrialj^ltaiKnaj bring roclcan^d vKy cornft. 

7> Jntrmiai tUpTiaafalDumair, nfihi Oriii, t/FUitu f 

Ther*"*^^*^"* "nt'»«Ai*/?(f">'ft«"(M 5 '"'"'") P™pwiM '^ '!>« Periodic Timei (by i>«p. ij. B. !, Nrutm'tn Tritifia) utf 

itKti te be lin«nllf wgmenied in iht Pi^Minian of Ai Sam a! cb«Miffii of Mxcer in ttw siiB indtaeb Pluet uibcFIrfof Two Mtu. 

Praportionilt betwiM th«t Sum tnd tbe (^Mity of Mictar in tbc Stin, \>j Fnf, te. iUtJ. Frm^im. "Umj MfvhcltfPlrioAt'I^ns 

[hit irt io the SHijoipliote Propottion of their Difljnca from lhePria«7. 



HUL£s 



,, Google 



end NAVIGATOR, 



119 



RULB3 for finding the RBCiUISITES of ELLIPTICAL ORBITS.- 



That it 






The Eceatvidiia mi jlp^hsKi of the OAiH of Plineti ire dctttmiaeil \>y 2r«f. 1%. B. I. Nmn 
lit priiuipti jIbi gnmit di^crib4 eOifiie'rrtjtSitiiivibici Pill pefi tirnrb rivtn Feiaii, end nmb rigbi Limltiva ly Ftjiim. 

RiwaikII, The roTcening McdiDiJ of coTnputlng tbc Eccentiiclty of a Planet from thcEinceA Eijuilion.tWindireaiy, ii tctkoncd bittel 

foi dncnuiciog The UimcnrisD! of the Orbiti cf /"/dMIi, thia thcMtlhod by known DiftancM and true angylaiVelocitia ; hgciuje ibe Diriin> 

1 4(dac*4 will be m«M effcAed hy Erren tn&nf in obrtrring the ttae anplar Vflocrlin chin ihc Eccrntricilv will be by the Enon raidi 

the Gceitdl E<|iii<ion. For [Ki:OTa\n%v,Mon(. DikCallli) ihtRcWtaa ol Mtrcioy't Aphrlian lod Perihelion Dinincei ii detcrn-.init 

by a Cotnfnron af an Aich of 1°. 3'. 3;". { taanother Aich of 17'. ij" whereof one Arch U litJe more thin deiiUe the Dtlwr. Where- 

II thofe Diltmcei nay be deteimiaed from the ComjnrJfon of in Anjle of !4°. the Sum of Inrqnalitin, down to no Angle or Inequality 

u ill 1 Jftrniry'i Eccentricity caufing ill thn Vaiiation of Inequality from ihe Mem M*lion, fium Aphelion or Periheliin (where iht 

Meaaaod ciae Motioa is njuil] to the Pwart of the two Mean IXltaoce* (in refpcQ of the two Stmi-axa) wbkh loeqnlily, nor any Vi> 

ftcnn [be luiiform Motion could ha[^>ni, but by di: Ciufiof the fiid Ecteotriciiy of the Orhit, 

itAax 111. Todeduee, from OUervatloD, tht^nv:^ Efgecivi of Mtrcmrj, (he Time ma/t he deiennined when Maairy ii in thoft 

Poini. of hie Oibit, where the DiAjnce (ii tin been ab.emcd) of that Planet trom the Sun i* ■ hmj> Pnftrtiaul between the ~ " " 

ri, both berortaad after the PilTige tS lUtiary throu|h the AifiiUi. 

Thii Time being when the Inn and jMan Velocitiei are equal, iv/i Injliats, at the Diftinceof 14 Honri, molt be found whei 

M have paOeil through 4°> 5'. 31". {, by teal diurnal Motion j being equal to the mean diurnal Motion of that PUnet, accotdine tt 

MonEeur Di la Cailli. 

,17aw, according to Monf.DiAiCi/^i'aObfervatioat, ijta, toi Parit, {| 'itiuediurnal Motion about icth ^a^, and 4th J'f/iaxAn'.ii found 

> be 4». j'. thcmAire inHTptbthrf hit Diftetence), 4" 14' 3j''i 4" 6* »!" > 3' s'' 44" i hetween his ObierTarioni of ij, 14, 1; and 

i6tn ifyufy, the Time vitaif." 5' ji" J ii piUed ago by jUvfi^ will be feimd to be between ^u^ i+d ik 49* and Jiify t^' 1^ 45" 1 

[he MiiUh of which Time, will be Jnlj 14* T4I1 49", for the kjlant when Mimrft true and mean V jocitiei were in Equality ; ot wh« 

It Planet wai tt hit Bean Difc et the 5atii'-«n, frod the Snn : > iht o^Ki Biean Dili, commonly fo called, being the Length of the Saa. 

aaverfafiom tfaeSun, a) the End of ibe Conjugate) Now interpolatine Mcniry'i true Plica on the 14, 15 and i6th of Jt^ (according 

MonC£>a/tfCiiiA'aObltmtioai) JMfrnyi truePlace at the Ji^bMof Equahty of mean and tne Velocity, y<.fy n* I4''49''> wiU h( 

»»" S7' *?''• 

AUb iuterpolatigg the DiQereocei between the Obfemtion of Mtretr 
-vationi of the lame Authot) aiid *ou wiUlind£^, 3' , ] 

hit true and mean Vatncitiu aic Cf nal, (the Velocitisa being leaft and'gfntell at Aphelion and Perihelion,) and hii true Place at ih^ 
4° 49* 10". Now, the DiSeience betvietn tbcb two Plaeea 51 i»a ^yT ^^n 

aod II 4 49 lo 



Mtmrfi true Placet, j, 4, 5 and ( of Stpiimiir, (according to the 
141a f for the Time of hii mean Diit. (of the Stta-MttJ from Q, < 



will be the true Motion. onSumofMircarn'i'WVeloeltiet during the/«n>»i/ofhkFairage be- > ru, 

(ween bit faU mta- OMlnc S 

ThjiTimeof which afoier«dfiirtnu/ii , , ... S^** 7^ 35» }- 

During which Time Mtrcurj would hare delctibed by uniform Motion (allowii^ ia> io I . . . 



5 «' S' 4J , 

S " S' 4J 



C JO 



%^* 13b IS" 31' 

The DlfftrnKi between theft two Motjoni . . . • 1 

TheBalfat whi^ ii (heJiwof all Uercarj't LufmMilia, and conftqaendy it hit rrro ^ £oiiM«i . , , , ^ 

Diflering from the greateft Equation, inanotber Place o'mr Antnor, by -f- iq" 
Iwlrrftlatim it not neceOaty for determining the /a^« when a Planet ii in iti mno DiOance (of the Smi-Mia) if the Oibi 

a eccentric} it being then fuHicient'to compare iti true Motion, at the Time when an Equality of iti red' and mean Velodtiei neatly hafpen, 
the JUot Motioa conefponding to that hta-aal. 

r4|^of^atNoon, {^'a tiw Place ma , , . ;* f ^ 44' 43' 



ID Ibe I4tb of Sfftimitr at Noon, bif Mean Pla« W 



which it the^ruf^'£f lU] 



4- *4 



J 



il 



M rnalifi EfuMi— • • 24 a 40 

1 lEe true Motion, ii caafed by the Inequality of Mercury') Velocity from the 



Which Difiraei, from the ii&ptalefi Equaiiai, derived fiom 
r4tb to ijih of >^. 

But, in ihe planetary Oihitiofyiw££««(Mri(*, the Inequality from Day to Day ii hardly perceptibli 

RiuAiE IV. The two PoinU of mean Motion in Che former Interval, givet Ihe PoGtion of the Line of Af^ia, thofc Polntt being 
Kjai'diftajit fma tkuLinfc 

TherndtUcWaybelwlsB • • > 5' la," 57' *?'' 






4» ' 



Sm» 16 i,^ 4fi 37 
Will b«the'Place of Afffcutyi Aphelion, Vtif . > 8 13 S3 19 
BnttfaePi^MBoftheLineof jfgiUb, in general, may be'bad by deierminiag two Pointi in the Orbit that have equal Vek)«itin,wlHekH*ihoJ 
)iowe*er it cmly it for very scnun'e Oibiti, wherein lixliuptliiia of Velodty, -iiam Day to Day, ate conCderable enough to determine. 
■rith a Degree of Acentaey, tbe Tiw and Pilin, at wiiich the Velocity wooM be ftal it » ma tfwanliij i wjtbout being mnchafieaed by tht 
Erran of OWerraticn. Bst, in Orbita of Imall Bceencricity, where tbe Vdocitiet from Day to Day are nearly unifom, thii Method will 
benftlefl. ' . - ^_^ 



,y Google 



7bt ROYAL ASTRONOMER 

'PKitiClfLR& of Ac frLAWETS PLACES md MOTIONS. 



The SUN'i Mem RADICAL PLACES i 



,.J,,«,iO.S. 



i 7 41 »9 



Our PUca \ 






BrgJiiy't wanting. 

A, J. Majir-t Farii 
Placu *ie but •3''l(l> 
than Ihofi coireTpi Plica it 



M A. TIk £^<. fbccfo- 
ia| bcini conncAtd wttt 
cholt of Modoa belair, in^ 



Mnn Metion Q An. 



M«n Mellon Q Apog. 



Mf«n Motion i1fi<r. 



. . . + I »3 



. Our Motioni in loo Ju' C 

■ liin Ycui, reduce, fianij 

i6qo and 1700, to J 

Equalion of Motion. 



br . . — I' 3«« 



Mitttr't . + 14 4° 



i^ 



Deeiniili. Decimili, 

iQlT + 1'49" i6'''4gi» tMflly— a' 16" 41'" i 



Com. Vear,r 0»r 



iCom. Vear,r 



CfMnmon Vein 
Aftir BiOeiti[( 



:li: 



D«inuli. 
+ "'-99"39»J74 , 

11' OB" it'io'' 14"'i 



— m" 39 3' 



Wn7 
s/g"..,"V45iv 



Sign. 
+ ,ooM77777T 



+ .'»"4T037'>J7 

4'»"4c/'*.tSi* exafll) 



+ iOOOcei]74rsfi 
■ '°*]7"'4»iv' 



Siin. 



Sign. 
-|~i00044i65sS 
+4^ 57" 0-- 



+ JO 1 o- so" »!" 
+ 1 40 >! 40 S5 



Ko,igs]i64 
„^ gft 9/" 47ii. 



Sign. 
+.00136IS, 
at %7" jo"' fee. 



0'( Apogee -^ hi« A 

EX hit Longituile. Thcte- 

fon, LoBgiCiida ^ kii 

Ap. •& fail Anomaly. 



-^ .0000003 ^s( 

' '7i' 5°T, ftc_ 



+rO00O0O3'oS4 
j/" a7iv 50T <ci! 



W.fl.Tlie«*f.Pl'.forthi 
Begin nl. of Leap-V" « 
ced a Day'i Mot. -f 



he Month! of 7n. in 
Being the A'fw and Ihortei 
ComputxCien : the Lp<- Vr, 
WE taking Place till fjCH 

if FebniiTj. 



!^ 



^650' .S4I jootoi T 

';<S''4K"34'46«*J9'<' 
Mean Solar 'Vcar. 



'X 



j«5D«.»j97i7i(i7 
i6H6*i4"o'»S'''i9'* 
Anomaliftical Yeir. 



}6jD'.*4tI9ffi6a7 
i6s'5''43m^4.4.|.hi 



j(sD«.»M»!i(i 



Jul. Yii. Deo, 

11073,1707117 
The rime » « ReralBtion 
f'"'ti G"' *"■ 



[*» g>i4>>6<)>33r< 
jBi''.»S*19"'47 

[jli ga ,^< m h&, 



4 Yeate SoUr,' us, f "■"■ 

nuUHital, ot Siir.l 

r^l, rrtird at advic) 
■ tl 4 Julian Ym.«, L WW. 



— .030797591 

44">o'i4'»4«'' 
Day. 
^,0308013493 

SeahM go bieic , in 4 



+.037S'H'<4 



Dr. Hi^'t Sjjmal Seller 

thin hit Selar bj 10" IJ' 

30»> fct. 



Dly. 
+,»i6i]>(a4 

-'- -5' 4W> to'' 



Dix. 
+,0*5164111 

3«"4Jt44if>*t. 



+ It J7 49 
+ 17 *6 44 
Seifwu go fiirwirJ e«chYr. 



CMi-Vetn 

Aftct BifTeitite 



li: 



Mar.g* »» it" 44', 1700 
Mar.t M 54 10, O.S 
Or f 9. lfXHaay [ im 



Our AwmtlijHctJf' greVt- 
er than oat JiJir b) «j4 



Dr. HtUtf'*A>«mmi*i 
gittttr thin hit M«r V<" 
^ «4" J7» '9'^ •*'" *'■ 





iw-; N A V !G ATOk. 


121 :. 


pklNfttLSs^iElEMENTSiofthcPLANETS PLACES »dMOTIONS, aca.,di.B to J»» I-«ovu,t,r.i 




T.«.S.~.rt. . 




Mm» Mot. Bun An. 


M..0M0D..S.0.A,. 


MeiaMot. i*V. 


AxOHALtlTICAL Y«A». 
j6jd fill ,41a o«-| 


Dtcimah. 


+ ... 


fr,Pt"i'- 


S:f^.f'.fri?.. 




Dedn»h. 
«• .0005617737 


+ 11" 


Sit.. 
+ioeoj6l77i7l 
fo"40"'i7lt «f. 


1™ ,**■■ 


LOKAT.OK. D«C 7 

«D..noS90!5»'9 J-"- 


Sigh. 


;?s".',!.'Ks 




J''°,r,C'i^ 




Sign. 


r^r:?si'Z. 


Si,.. ■ ■ 

+..oooo4s4i<4 
4«,4-.**- 




Tke MOON'» Mwn RADICAL PLACES and M JTiONS. in 1^.E^ olutiods. Sioh! ai;d Dicimals. J. 


OMindNnrStyte. 


Mgon'i a«n PJicH frwn 
the Zquinmi. 


M PI, Moon', m-.n Ano- 


M. 4'i. Moon'i Anogn, llll. PJ. Moon'i .fccn.mri 
fr.lquiom. f Node A-. Efiinox. ' ^ 


T«. 1.5.600? O.S. 


7. »8- 7'4»- 


>' '9" 4''' 47" 


'• ••■Cir 


... 0. „i ii>/ 

" ■ '7 -» 


?«.i.Ji7™(O.S. 


6. J. j6' J- 
1 11 I 4» 


S '4 3* 4 . 


ra-^rr 


(. 160 44/ .jff 
S >7 .> lo 


Ouf Pb«l i 


n.%-«. . --1 10 
JHlmi*. ,,00 

N.B. Ma^r'tPati,.V\t09 


.•.•.?t" 
.•,-+,tn 




1, . ~,^ „' 

■.■.• + 4-V ' ' 
. . . + « JO 


riHi biwud. 






M«.M«l«l|-.Aw. 




100 Juliin Yarfc 


,j36r.o.7-jo',s" 


„.S' <•.!.„.. 0- 


..,,.„.;v.5" 


S'4' 14' ..'■!" 


OurMotion.il. 100 Ju-\ 
lian Van (nm iW 
ind 1700 ledoct «9 % J 

&»-«„■« of fflWrt. 


Nenun-t -. ■ ■0' 0^ 
«<.%'. ..00 


'• [• ■; ■+? S| 


by . , .«' 6- . 




wIU be lb<^ »bok Ef^ai. if M^lia, acid caniMOcd with V*<- efPlim ibore wiil be the MoXaa Eqn. of our Frcjent PIko to, tholi of othcri | 


4jnlU«Ve« . . . 


+S1' J'.*9°4537°37_, 


+jj» 01.16487037057 


+j'-+»SS3i3i33 *<■ 


—a' IT- It' 3- ei.ftl)'. 


^^^3* 


+IJ' 4'.St»»ltil3»4 


+;i;::.'iJV?.,... 


♦■I'.J5J+674Ji4 


—,6443878735 
.9=.,'4,''r.-*e. 


c..v«.. II 


+0 rt 9 "> 




t " ""■ 39' SO' 
+ » It J9 +1 
+ 4 1 W 1» 


-0. i9»;'9'4l' 

— I » 39 16 

— I »7 S9 1= 


Pv. 


+?,i':in?.t,-... 


^m«.'^. 


+,ooj7,j6o94 
6' 41* 4' *<;■ 


Sign. 
— ,0017*5 '7«> 

y .o«i8-*.. .■ . 


Hir. ' 


+?:'!."%'".».. 


-K018145&1J 

3*" 39" 44'* *'■ 


+■^^■"5473+ 


7* j6- 3s.r . 




*^T.i?1,... 


+,«cx>30»4j 


t??Ti;"' 


— ,oooooi»»5! 


Second. , 


,." ,ii. ic. 


+,»00005040J 

1'"' ifi!' *«■ 


^«7,..- 


— ,00000001043 
;i. 56T 


Pa^WmTRe V 1 V T I ov . 


»7D';J"S«4S7» - ^ 


^i^ji,4....> 


Di. Decinisli. 
3lli.3S7filii77 
Ap.B.-l-8^,4"S7'36^ 


ti. D«im.l.. 
679«^D33«>73 
O- +4''S»'»!i* ""• 


s^^R"?-.j.a,- 




.sD'.aio.Mlooj 
Aa.-Fi3fcjl-34t5i"'*«- 


♦u.7«w69>6i *«■ 
Ap.+tgbs.»i8'4t'''&<. 


14M'970*«'9ia fa. 


LuHATrtH. 

TTot. 


t":T.-t'!'f,.^-.c. 


i-.-:-»s^',J'i.. 


■■ ' Sign. ' 


■ ■ Sign. ■■ 
—,051116578 *c 
p. .•«'49'40'*c. 


ANOMALMTtCAL TtAK, 


+;i:y-S'?' 


*iQ\ri?" 


-n;r-vitr-i 


-i;r.n??.^*-. 


>i0 
■ in An. Y«7. 


-^;:5y^'?:'i.. 


\ .^ts^ ] 


iLOHJi 114049 

+ e"> 40" n' <«' 








n 







Ic. 



Tit ROYAL A STiR ON OM E R 



■■£LfeMENTS'of the HAMfets Hac^s and MoTloKS j 



j according to late iMFKOTBMERTf. 
InRavomTiom, Sichj, and DgciMAi(i. _ - 



..^ Man NEV lioA^ln 'jAJJUARY, &t. 



n PLACE5 ind MO llONS of rhe MOON fiom II 



n Dili. Moon i Sun. 



M»n New Mm 



T"h so IN^S 



9« 1+" 44"! 4a'.O.S. 
19 14 44 41 N.S. 



Mun Mot. Moon i 



49'S»io°4o'59''4]''i; 



49''S'-^'?44'7»g4 



■Common Yn. J a 

After Bifleitile. ' 



■9° 37' »r IS 
■(- ! 19 14 46 JO 
.8 S» 9 4J 



f 46 30 



+ ,4t>£l<Si76} 



Majtr. Snn't Mot. 



Majir. Moon'i Moc. 
lYean. [53' 5' io« 41' 



S'^V'^ . ^. 



'1 MdHod, 
J»j43i09»7 



Decinuls. ^y 

3fi5^,i4"S9»6!M /* 



being conrKit- 
ed with ear J 
i 0, willta.. 
rttprmd wilh 

ler)- iie»ilr. 



tf^.JUj,tt7^t Ptrf.Rei 



2U1I a Moan't Apogee. 
,!SqSSOJ9I7+ 

IjO .,' o" 16*, && 

H.lfey. 






Sua t Mdoii'i NCKta. 

I*.0ti]5ii5il99 H In 3^; Dijri , 

i' o« 40- ij» 56^ W 4jul.r 



, Ii.}toofi4i4: 
49-«4'">il 



Moon'i » 
.•.63S3«7iift» 



TJie' JMua Placis and Motiovj of Mermry, Ftfou, Mars, and filler. 



H. i>l>. nJi f. 



M.PI>cc«^.g.M.Vl'.Ai£ 1;'. ri KtonPfini f, ' |U.PlM«4»i. ^ 



isi^ 



-sn? 



1^ 



T ;:' r 



M. Mot. Af . g ■ M. Mot. Node g 



■ Wain Mminn j . |M. Mot. Ap. g . 



° .»7' )r * 






4]uli,»V«r,. 

See Phil. Trinraft. 

Wo. 386. 



f V>" jf ^iU 



tjf 



+'9t'-''9'7' 59159* 



+ 78'-'"5;S70i?°l 



+ 49'-79CS75847» 



After BLffrttile, 



.7 .« J X, 



t « 40 

+ a JO 



Sit". 
+ ,1364115361 
r ;* 31" 3r t4h 



SiKii. 
,0O56S}t5i7 



+ >°sa4°5fci 

1° 38' 7* 48" 



Vui 



Sign. 

+ ,ooii»s»j369 

4' ■>* 19' " " 



-h,oo6^5S]], &c, 



- ,o6<>037oS7». 
« o* 19JT, Ac 



P. IM). i4Cd. OM. Motn. 

ri..— 14' i9^4S'7 

^..,-J 39 3> f 



SMENDATIOHS t. 



X. For TreirUia* 

I. For, where then, ud trae Mttimttrt 
n«l, where tlu m, ud tnie ^tiimtlia * 



■ anJ fi AV IG AT on. 

"ELEMENTS of the PLAV^fcTS FLACKS and MOTIONS, accorfing w our iaie Juraovfi 
JiiREvoLDTioBi, Signs and Dec- - 



itie M«n i* L A C E S~^ 
Man Plicn , 



I MARS i, i J uHVE'tt . 



Radical V(aii. 



H. Pl>. Aph. II . M. PI>. Nad« %. 



M.Mot.N<>d< J- 



M.Mat. A p. U- 



-Hs'-i"*74°7407 



^5 P*? ":. 



Dccimilt* 



er BiflnCilt. 



li: 



The Wmb places tnii MOTIOMS of SATITRT?r~ 



loJO.i 
■ojM,! 



^6; D»T». 



Com. yeui. 
4frcr Bifleitite. 



n; 



o» ii» 11' ll'l?" 
3 %t »i 41 j4 



Sign. 



Node b-lM-PI'-^"^ ^- 



»g 31 s* 1 li S' 4S 



■f i' 10" 
■f- » 40 
^-4 o 



-1- S4 



w a, sit. t/'t'PU^tiurtm 

Diy< >iid Di 
T'mt of tbe Pi»« gi«n, b/th* Time of th( PUaeC. *in-iM 



- . - •.*)>f«F«™i 

4.i*i.«rf'li«P/4«;j««>-/"«t»f3^in* Before B- Afr.. 

RoL«. Ditiiethf T™*, in Diyi «iid Dwimilj; .<fl«f or *(/lrt the rmilKi,/ 

Timeofth( PUaeCi /.^iirfiW Revolution; la 



Dtj, and TimwA, -n^ 'be Qyotieot *ill be the «■■*«■ 0/ RtWJiioni pen 
wru, fcc. (otBltnim whole Rewtliitionj] jtid iJded or fubtrafled to ot fion 
fcmhlwifterorbefbrethelimeof ihePhee»i«B, and irou vrill ha»e the rna 
bya rablegf Logarithnu ta man? Placq. Sri Bxamfl'i fir finJ'tg IbiMmF^. 







b. OecioJ.. 


-■b. h « . -fc 




? 




87 *3 '4 34 »7 




ssljsssi; 






if 








4jjo.3 576B6ojS 








.O7<o.,,.8,fii3= 




Th. 


Pi 


ANiTi Mew Sym 





!o 



0. i( 



18.45)1706^00 
»7-49 30595*46 



I44.»66i497937 
115.8775019497 
loo.g3gi4]6o36 



779.917016 qj95 
398.8861976130 
378.oS75SH7»o.. 



r.iiT»S34»»i(: ' 



^1^ 

»tbat lamiai, wnicn ton 
— Kdiwl Pl3«, accordini 
,„.rifuini, Which Operat 
frm tbijt tivOt fi^ihtr w. 



I S3 » 



89 19 I i» jS 



IS3 11 6 5 J. 17 
J3J la 7 16 45 
116 11 49 16 54 
"9 ^' 4» J4 4T 



7 «t 



7^5.1 3- »3 »♦ >7 



iP/Mi 



EU^MENTS 



<rte ROYAL ASTRONOMER 



ELEMENTS of the PtANET's PLACES and MOTIONSj accordilhg » \m ltirt.i»iUn^u 
~ In RsvoitiTioNt, StcDB uid Deciuali. 



naboiu of thdt Oririti, vidi theii A^n> 



Mr. St»««t'> T»Mm. 



Aph.ii*r. a>>*r- 



,o4l?*3 



,0069811 



THE FiKED Sta«« *n"w « *j?, i*» frMicTrnti «/ 



r n^r frirfliy PUntW, iini/ •/■!*» fiarfi, afoirl riiSan, (Jrfiri 
if x=| P-wt 1 1 Pr<,]vnKn cflbiir mran Difimi/rm ihe Sus. F 



The PirioMe Tim 



, inRff^flof [heFixuiS 



To JTff ?«■ 

To BullialJin 

To periodic TimM 



The Me»n Diftin 



h Ijom Ihc Sun. 



gfTOOa 
95419! 
954006 



511650 



Pa<t«, 

1513 JO 
I5»350 



3BS0G 
385*1 

38710 



The MEAN PLACES knd MOTIONS of the Foor Satellites of Jupitsh. 



7«.i. J160070.5. 



*4 3° 



7 » »4 M 



Mnn Motion j 



iliilssL. 



tnr4iiB°34'io' 



•hg»5^ 9 '-9' n3»3 
+io6t3i.7Ji5,iB}; 



■i-iia'^.snl3i°i* 



-4-»o4T_»M^7'^73 



Com. r«rtj ^ 

After Biflextil'. 



+ jt jj" «S' 40* 



+« ..» 48' 
+* .J 36 
++ 5 »* 



+ 05° 56' 9" 
+ o I j. il 
17 45 -*J- 



-H>>t8«9<» 

' ^° *V "^ '9* 



+.00005479 

5' if' 



tAv%^\.•'^.. 



+.1407981*5 , , 
4» ly 16* 13* t 



+.MMS9ST6 

„» ;5T* 4pi7 



■{-,000008 311 



Tmt, conpste fbi .1 
'. PatapdDtj'iModilD 
ie&lhiatheginalii' 

ft. 7«r. i.loduft. 



ot .K«*w.«. j^ ,i1»j«33,,5.>. 3*«h.,}m4,. 4s.k 7* J? 4»"' 3J' l''' i«* jfiS 31- (■ 3°"' 



,y Google 



fifid N A V I G A T R. 



r,mntf DtfiriflfmJ arrm lie fcfqiiirlica 



I U C I T K K 



numioviil Siteihttt, er Moain (dtf'ril<irg ^rrii riamljai'\tt 






From till Ot.f«rTa-'«M cfScr'H! 

•IrmiJtj, by Microi 

Co^ni, by thf Tclefcnpe 

Caff,K, byEclipfetof Satellin 



5 •*»*■■« 



If ptriajic Tim 



REM 



I (,667 
R K S. 



3 4- 3' . 



4-18* 



^^"^9 



n<£J*fiiir, ind IheKi-nFitionof hiiSiit(l!it», tlmt. 
whT, .n i 1 s Font T-lef.- pe, ind, a t mtin Dift. of 7i 1 g. 
3d^*r(//i>(wa9 lakcn wicli 1 JlfiVrMir/rini Tclffcop: M ii] Fret, it die fame Dinincc 
Thfp-tartfi EbagaiiMol the other SaltlUia, it (bcCgme Dilt. ot "H iQ, ire determirted, 






I. PoDRD determined, by the 

The piatefi heliacintTi<; Elong>rl< 
o.-H found about g' (6". Tbe Ettngaiim o 
torn tnr Eirth, ind wu lound 4' 
ruAe Tmw, to be 1' 56" 47" ir> 
TheDiimeter of J-fS'tr, l>Ua *.-iil^ t\vf M,'cr,m,ui , jn in 113 Foot Telefcepe, ft« 
Trom tbe Eaith, provrd alwij! iefi tlun 4c", ne»tr l-^fs Thin jS", gmmlly 39". Thii 

it a little AVain/ by llie unequal Refrangihilitvn*' the Ray t, which DiliUlion bein ■ 
re perfef) Telefcojiei than in Ihofe which are ihortir and lefi perfeA. 

in which die ift ind jd Sitrllitn pallid over ynpiiir't Body, wen obfened from the Begin ing of the h-nfi to ihe TIej!nnin; 

nf ihe F.grrji, and from Ihe complete hgrrfi to ifae con^lete Egrcfi, with the long Tele&ope. And fr. m the Trmfi nf the frfi SjtcJlite, 

-■-- "^^ — trof jBfiirr, >t it> mean Diftinci from the £*iYi, cimeont n\", and from the TVaiifr of lie TAirrf 37!". Thtre wH -'-'■- — ' 

'• ■— ■■.taththt ShuHrai of ^t frp Sttilhit fiiTei oter Jufii'irr't BoAy, and thence the Diam -i cr nf yir^w''"-. nt it] mean 

■ineout about 57". It' we fuppofe iti Diameter to be 37}", wij nearly, (hfn the ptejt (I ElaigarUn of tbe 



&indm 

The Time 

rfihefr«/5 

the. niimclci 

riOmtHitu 



, ind -^oced to y^fi 
r infhi tw Telefeopn i 
- ' - * lotheDiiDir 



r of 7V"' 



• 5.965 ■ ■ ■ 9.494 ■ 
Ihe HeaienE. l» c 



■ 3 



.tjfrffl 



,6.63 




R»i.i 


V- 




K9 cf lb 


S«T 


LMTE 


. ./JUPITER. 












rdihe 


bls-^ 




the DiAxtc 


< nl 


loniof 


he/Ar 


■ffr/r,. 




eipe 



r ^,U'i. 



f will berefpefliirely eqiul to . 

Sir Prinri^B, S. III. Ph^mmrnm t. 

Ofibt itlitrafi Dr. BRADLEY'i Oifirvaiit-i, mtirmKw lb. Situatioki mi Mot 
THIS inilefaligihle and icennte Obfrmtor of Ihe HraienE, lai comparrd Ibe aided and mc 
bit own modern Obfet*itioni of Jufkir't Sitelliles t ken at trmJLi. Who bat likewife con 
roh ot iJirrr Reroliiiiont of yiij>:irr, and fometimei found rcty rnurktilt Di4erencet in the i 

Me doobti w^eihei thefc hrfvthiUi do not partly, irifc from the Eccenlricitict of tbe Orbi . ,, - . 

nbu he MB ootka from tbe Motinni of the Stciri SjiM'ir, he thinkt it probible that the ftid hrauaHria may proceed from the irs(<ij.' jirJ-.n-. 
"/ifaeSaid ' metlinri fir /o^; th: Motion of tht Sntni Stielliu nria fi mMt, in fe fmall i Time, from if j«<i. 

QoMlfSt*, J itill not accoonc for ii ; while the Reft of the ObCeTdlioni will not admit of a lir^e Eccentricity — He 

• "ilh^t 4 leatly intwcrt M tnc Time ihe /*-« i-,firitr Saiilliia lake up in refirning to the fin:e Situation, in refpeQ 

fa otj PiiiT'i Shadow ; wM h Ptnod ii performed In 417 Days, or in 113 Rerolntioni of \ht Hmni limtlliii. 

ftr iHJ Author liji, that Ih^ like Erron leturn nuily in tba fame Order, Bat, in the intermediaie Time, afti 

B|oia^ will detiaie )o, io> jo, and fomAimei 40 ji^iiiira t/Timi from itt common Rite of Motion, darin„ 

Wforit lonthi. That, bccaufe tbe Saiilb'ia if Jufiur lie not found in ibe fur.ePlare Irt the HeiTtni after 

W-.plei •/, it it polTiblc (mrH frohatli} thefe Emn miy vary fomewhit on ihit Account. That if the Orbit 

nf thft Sm :c«ntric, 19 lale Obfervatiom pctfnade that it it, the fwiu/i.-iciatiCnE ftom both Ciufei muft be.vc 

int(i<-'nt'-, 1, lilliEd by Obferntion only. 

Tht F.rr _ iHiu lie not To |ieat u thole of the 1>/, but appeal to atife from the fime Cmfei with thofe Errsrt 1 n 

whiAly depending on the Eicainrl'j. 

Oi)r iudiciou; Author hwltkewifeabfetved a fenfibleDilTertnce between the Dutalioni of tht EiUpfii ef the iff.Tjrrffi'lemide it the diTrti: 
f/pJa, whi. h (/H fayij were fayr and Jhtrrir ilternalely. Tint Is, th: Duraiiopi of tb« Ecliprei of the ifl Saielliri, at the defccn4i»g NixJi, 
in Ltt, in the Yeari 16S1-J, 1694-5, "^ 'Th *«*> *t leift ab lo"; whereo, il the ifceadinf IMr, in itjuariui, in (he Vein 1677, 
j6tg, tbe Length of ibofe Zciiplei, of the ij! Satdlili, did not eicecd i>i 14B | which wit confirincd by comparing (ogeihe,- at manv 
ObflnTitiani f fuch /anmrjCgH and Emfrfitm, ai could be procured, and fuch u were near together. Hrnce it it mini^lt, thi< Dijimci 
of Length of Time in thcEclipfeiof tht ijISfUBili, iiittotvMIj atife from the fcctMriWr/ of the Otbit, if it hii any ; but to nhat other 
'anfe il miy he ilSgned Dr. Bradly pretendi not 10 determine. 

•,* jfndbmi vt may Afnvt, &m> fmtriaa <r wcrrtain ii lit MiileJ cf Jifirmimg ittLoig. a/ Plaaifivr^ lU Ecllrfej if 'U't Siteilile). 
Dr. Brtdin, however, wilbei, till we can get nirr Light \n thi' Miitei fiom fiiture Obfervitioni, thil fame f reit G imntr, f fuch a 
Ihe celebratcl p . r i 1 1 «, Mr. T. S 1 x r 3 o N ) in Imitadnn of the G » 1 a t NEWTON, would =rp'r h'mfelf ^ 
mifiigan thefe Ittegnliiitiet, or hrputjiiia, from the certain and demontlratlve Principles of Graviij : which, howeier, we will fuppofe, depend 
in pby6cilCaiife4an*Hypothifci,ai weilaion the AfnJJio/aMiJB*fr»/'0««(™ii in which we arc the more confirmed, by he 1 u f.:iiM(f ; 
Arf&ir of the liie m!f:r'larit*i Traf!: 

f Tcm t\ie ObifTtMoru ot Oin^itSaufliu, itt Orbit i»confiniMd to bs elUpiicali And ill Dt, SreJtr/i lite ObfcrvatioDI of the Motiri 
of (bat .W<//'»willbecOTr^ly TCprtrcDted by fuppoliog thtgiea^ell Equation of that-^dicZ/ifcequitto that of the Plairt ''rrvt, 4$': That sti 
higliei./^waii«X !" o*"! the Beginnmgof tbe r«r 1717. Though by comparing'thii Hr^fcA with the sU<r Ohfcrtaiiont of the Year 
1671, 1076, and i6y7, theCompaladoot wen found lodilTcr gteitiy fTotntheObfereaiiont ; yet pulling back the ,*i/i ro c: H* o', aiihi 
Re;inning of the Yiar 1677, tbofc Diliettncei mififf Tanilhed. AiWing therefore id rjnaili Motion to thii 4't Satrilitt of Jnfiif, of fit 
orward in itn Yean, the Hyftibtfii aforefiid wii found to igree with the inlirmrSati Obfer»ation!. The Numbers on that Ptiaciplr, were 
oond every wbeieto^greewiih the f^eaveni (eieeptingonly two Obfetvatipai, both JoAly to befufpeded) within 10' of a Degree. 

Ai to the IjuiiaJr- of the SMclHin of Ji^iirr, itwiilbund, from Obleiraiiont, thai the Nodei of the 4/i fair/AVf « ere, in tbe Year 171I 
.n^and£),no|, tbe f/aJit of tbe jd SaiiBi'it, lying then very near them. Tbe /on P/ini are therefore afligii'*d bj Dr. HraJii/ to it 
NtiUs of the two inferior Sdre//iM,' at Obrenaiion hu not yet dlfcDrcRd any Thing to the contran. Who titces Notice that iftheJ^iAi 
of the Satellitei were, 40 Vean before that Time, in r and J^ 1 50, according to CajB^/. {whofc Auihotiiy it of great WeiEhrl that they 
will appear Id have gone back about 1° in each of Jepiio't Revolutioni, by which the prefent Plate of their NuJci may be nearly iliiDned. 

Co^/jti'i Inclination of IhoOtlritt of the i mfirnr Saii/lira to the Plinc of ?H^irr'i Orbit being i<> ss'< '• Oil retained g but tbe Inctinati 
of the Oibil of the 4r^ Satitlile, 1° 41', Dr. Bradly his confldeicd fomcw'hat left than Cefiri't. And aa it il 1 very diffinll Mitler 
determine, with jl^curay, the Siiuaijon of Circlej (o extremely fmaJl, fo Dr. BraJliy it of Opinion ihit it ought not to be undertaken I 
with m-!t excikntrcUlnfr,. Mr. Stiri, a -"--'■ ■ ■ - ... ■ - 



iia^ 



e^menV^'"^ 



_ I _.. J 




■r^:^ R V A L A 


S T 


H N M K K 




ihEMENTS of the PLANETS PLACES and MOTIONS, according toour bte Improviment.. 
Id Rbvolutions, Sii^tis and Decimals. 


The Me»n PLACES »*b MOTIONS of the Five Satilliti. of Satu.b. 


itAPIGAl. VlAll. 


f^nn Plice i, 
frcm Eqo.noi. 


Mein Plice 1, 


Meia fbce 3, 
from Equjnoi. 


Me.nPUce4, 


Me.n 1-Uce j. 




!• 11= 4i' 


J* iB» Si' 
» 1 -.4 


i'lnr 


).' 7" 11' 


D> 130 45' 






T .4- iS- 

1 7 4; 


i. ,0" J.' 

i 4 > 


3' ij- iB' 
7 >5 7 


6. 5" .' 
4 IS S 


f ikF InrwirJ. 


MeanMudun i. 


M«n Motion 1. 


Mci 


Moaon 3. 
.ij-14' 


M^-.n Motion 4. 


M..n Motions. 


lOO ]<i.u« Vuil. 


i>;347r ,o> t." 11' 


■3345' 3- 'S- 44' 


8085' 


1190' 7' 16° 17' 


46or 5. 90 ,5' 


4 JulLin Yciri. 


77l'i0'»9<'i'(O"24"' 


(3iro'"<'i3'4;"lt>* 


3i,r4<i,=iq,45"36* 


,.r 7. ,y. 3I 4.' 


.8. 5. o" 11' ,1" 


+9.^0../6S„4444 


+64= s'- 74097777 


+ 3bao..q.6<3(3i3 


+ ,09.,'.,o.7037O37 




,S,- b..s 


+ '"'♦* ■S"'^"*" 


'33'4'-3a9'H75S 


+80' 9..5650476K4 


n.io..6S7i8j9so 


4r 7'-»M»646s8 


Common Y«ri | t 
After Bifliitll!. 


+*. 4" 31- '4" 51- 

+i 9 <■= 19 4» 
+a 13 45 44 5J 


+4-10.'lO'lj'' 5" 

+8 10 so JO iS 
+1 31 15 17 


+9' ''° 57' S" 9" 
+7 J 54 10 18 
+4 ao s> 15 17 


+.0.10=37' 6" 40" 

XVW'.Tt 


+7' 6" 17' 18" 35* 
+1 II 54 57 10 
+., 19 11 IS 45 


Day 


+6'. 35658311,5 
6» 100 41' 51" 


j*;-,i'ti?T 


+!•, 656 ,41596 

f 19"4.'*S" 


+,7515679°' 
ii» 34' 37" 10' . 


+,151174697 


Hour 


+.16485763* 

7' 56' 44' 17" ae. 


+.181687114 

;■> 18' 50" II" be. 


+,110680941 

3- 19' 13" 31" «c. 


+,031356996 

,6' 16" 3,- 4c. 


?;'i^n^:iUc. 


Minute 


+,0044141939 
7' j6" 44" te. 


plUTA. 


+,001 344681 J 
3' ,9- ,3-fcc. 


+.0005116.66 
56- 16" 3jiv *c. 


+,00010505187 

..''io-'44l. &c. 


Second 


+??^i^;.,. 


?T.°-^^50^^r. 


+,0000307447 
3" (9* 1311- ic. 


56- i6iv ,3V *c. 


+.00000175086 


rime of a RevolutioD 
of Ij-iSildlites. 


11' 

I <I.SS7 3066058 
1*1. his..,*, ijtb 

i5f» 40" 


1-.7J69 199068 
id 17" 41"' 9- Sl'l' 
47'" 43" 


4d. 5 1748957 99 

4* „i .JM „. j,h 

4gf. s,ri 


'S''-94S405«3»9 
4lf" 16" 


11' 

794.3158898076 
75* 7I. 40a ift.ji.l. 
45?. 4,fl 


The Mein MotIomi nf the Vive SATiLtJTU of Satokh, iiJjcnJ from the PtriiJic Tima, » given, ind not tB,tof«/ from the Mo- 
tion, (Di rj>ulti Sattlhium Salurgi K>U 3, H»lliy'. 4fir«»mi{tl T-Un) ihiwihci the flifffi.,rt from the Trui AfM«» lui T/™ »y 
SimUkri deduced from th»I Moiion, al^t—Hcna ihe coma Kevolutioo. [•■ ibore} Ibould be liwujt dtdutd from ctae Motion, for a 
Length of Time, ind not the Motion from the Re»olutioni, in » limited fliort Time, >• Below. 


['■HI lo.».rd. 'Mem Motion i. 


Mem Motion i. 


Mean Motion 3. 


Mean Motion 4. 


Mean Motion 5. 


,o.J.»..V»,.. 




'1344' 7' 9" JO* 11" 


Hoiq' 1> 100 41' 10" 


1190- T 11- 51' 31" 


46or ,. ,,0 33' 3B" 


,>li„y..,.. 


77,r ,0. igo.o.,,'. 


„3r ^. ,10 11' 4S" 


3i3'4'i7".3'38" 


91' 7" '5° iS's." 


481 5» o- 3o» f 


+7 7 J., 0.93,1^3+63 


+533'9'4It674s47! 


+3i3r4i.,07;Si6i6 


+9i'7*.5J0478s99i 


+ !»' 5'. 016747, 5<;a 


l6< D*)s. 


I93r4'-i4i67ii36 
+4' 4» 11' 11" 
+S 8 44 14 
+0 13 6 16 


+ i3)'4'. 157101117 


+Bo'9'-s6i8iii884 


+iiriu>689476i7i5 


+4'7"ll63674oS4 


Aftir BifliiitUe. 


+ 4- 7° 41' 47" 


+ 9- .6" i,' 3" 
+ 7 3 46 6 
+ 4 10 39 9 


H-i . J s 


+ 7" 6- ij* '7- 

+ 1 11 sl Si 

+ 9 '9 »8 »» 


D.y, 


+ 6..3,656j482 


+4«.334l66o354 
4- M» ,i'4o"&c. 


+i'.«56,3647j 

i«.9"4i'^i4"io-'ie. 


ti^^S-*. 


Sign. ■ 
+.1511777116 

40 ,,' jy" 5y» 


Hour 


Sipn. 
+,164356811 

;u 51;/ 441' ji»' &c. 


Sign. 
+,181677751 
5° **' «■' "* «=' 


S.gn. 
+,iio6So6S6 

3" '9' "1" 3=' *c 


S:°;;.",'.-s'.=. 


Tr.W'^^u. 


Minuie 


+,0044141! 

7' S6" 44" 


?^.C""' 


+,001844678 
3' 19" .,- *e. 


+.0005116107 

56" 16" 34iv *c. 


+o°'4:t^v. 


Second 


7" 56"' 44iv Ac. 


+,0000507438 

S" 18- 49iv 


+.000030744 
3" 19* ijivtc. 


+,00000871034 

56- i6iv 34V 


+J00000 17509 


Time of » Berolu. 
lion. 


1* Sign.. 
iJ n" li- 17' = 
.'.887B115 


11 Signi. 
1* 176 4i>ii 11" =: 
iD<.7j7o6oi85 


d ,i"i^i^;. - 

4b'-S«7S* 


11 Sigot. 
Ijd ni 41a «• s 

i5D'.94si 77777 


1. Signs. 
79' 7" 47- f = 
79U'.3»41°5!!^5 


Of JUF1T>«'1 SATILLITli. || Of SaTDIN'I SaTILIITCI. | 


Rid. li'. OtbiC 10 
R*). Sit-. Orb. 


Revolution 8>«. 


Veloeitie.of5«.. 
■0 Velocity T(. 


Rid. b Orb. to 
Kad. Sal>. 0<b. 


Revolution i} 10 Velocitie.of Sal-. 

Revolution Sati. to Velocity ^,, 


i 


778 to I 
443 " I 


3449 ID I 

606 10 I 
160 to I 


1449 ^^ -964 
.110 to ,ljS 

606 to 778 
160 to 443 




19OJ (0 I 
ia9» to I 

.719 to 1 

ijS to I 

D, la CeilU. 


S7f* to I 5,01 10 IOCS 
3931 to 1 j,sx .0 »i9i 
»3^i to I ijii to 1719 

675 to I 675 to 717 


J 1 »7i » 1 


111 to I 


"ito I7i 


i3S to I 1 


13510 ,,8 



and N A V I G A TO R. 



127 



OfSATURNstlVE SA t"EX 1 1 T fe S. 



it£ 



Accotdiog to Sir //doi Nrtein 
To &#«(■ ind IJul/c^ 



Atcording lo Sir //»H T^'m./w . . . iJ»Rid.Rins| i|,kid.Kin| 

To |»riodIc TimM 1,93 i,47 

HBiTKn'j Tdtfcofe, re- 7 Recited ilto br Dr.) 1,007 - '"' 



Ti by'ih'i/:': 



7 43 



S,T(4R>d-^ 



8,693 



'S.H» 



ifcovBfcd by ^|I. 



E M A R K S, 

Tbt firll of the fotesoing Motions, ir! ellttiucd lie/j/ impiuvtrtwnii, prt'eriibiir'to 
■ i tbc Pl»tei of ibc Xoi!f/,i,i of ^■;a/,r», Jn Relpcit of ihat Piimuj. From wli 
■ of ih* Motions of iliefc Sitellitcs, tin only bi i^ipiited. 

N.B. Ttt Ftrm iimlifg It itt Cenir tf Satan anruipntally /b (A( i&ffficfl" (or Square) PiiJtriitK if ibt Di/iaMei. yM lit CiJxff tl- 
ViStuB ,f ibt S»i./I'l», fnm Itt CfUir ./ SaCurn. <i lii t^parn ./ (A. «^;W« '/!««. 

rbi cefebrated Mr. PusJfmind the Amw of (he fiiiri^, ot Uuypmim StitlUii, (ite bigieft pf all the 5) toiheDiun. of San 
i< 374 to 41, or II 3,7 10 1 Mtr/y. And like wife foE lid th» Ba/id of the Di»n>o[« of tlie Rinp to ilie Diamtiei of ^, — ■■- - 
'lence.by thefortgoir'-Eftfe^tiM.theDiftancei iboK ire computed from ihe Diftjnceind Pmorfof the Fourth Sateltiie, a: 
jkJ, by f^Joiof thtRoy-lSociety'iTeltrcopt 0/ iijFcetlang, fitted with » curious JWit-mrttr. 

jtnt 1719, JMvigd to" }u\im Style, Mr. PwnJ obferied, vfiih the fame Jnftrument, in tr*ite« eiAcrl; Digrettlon, 3' 7" froi 
Center of ^dfura, whafe Place wis iben m 7a 41'. From wbence, by Computilion, the Saihot the Dill, of ' chit 4(h £iHii/i» I'rgm S4.11 
K At Dift. of tbe StB/rvm lit Earrb, u S,ic to 1000 j whence the Dittancei (^ the othci Ssiillita may be eDimateil. 

TkeDiam.of^atvii'i A'l^ by the runeTelercopewu found [it the Time ifbreftid I to be 43", confequeDtly, when ^ "at hii mean Dill. 
i it 4^", and Diim. of I7 iS". Theft Appeirancci ice in vet; lunE ind excellent Tckfcopei, becjure in fuch Telercopei, the i\-fin 
Magnitude) of the heavenly BuJiei bear i greater Proportion to the Dilitatioa of Liglit, in the Eilcemiries of itiofe Bodiei, tlim in fnort 
relefcopci. If ill theJ>wiWi Light be rtjefled, the apparent Diameter of Sbibm v\\\ not amount (o more than 16*. C.#ii fuppoCd 1 
iogr inferior Satillitei to mo»e in the P!eK of tbe Rii,g, or that thar Otbiti arc inclned to tlie Plane of &»»■': Oibit, in in Angle of 30' 
For&«»rj.beinBabgut the middle of C.mW ani Sipiiarim, the gieiter Axis of tlic RiVf (then of the greainl Width) is found to Le mm 
iooble the Lenjth of the hfi Aiis; and thrfe Satellitej fecm to defcribe (/(r/tf/c Oibili, always limilar to the riV/nc Aji:^. In thci grcm 
DigHnioDi from StivK, tbty arc alwa^i found in the ginlrr ^n of the Ring produced. Theic /'inAnnu coulj not haii^icn utilcfs the U 
!iitt of the Satellites had nearly the fame Situa-ion uiih th: Plioe of bii Ring. 

Thcfamceiiccllent AfttoBomer fince difcovered that the jlh and outward SitflJite ii carried round Sa/urn in in Orbit verj' diflVtcBt ftc 
iJie Reft; For iti afcending /fa£r wai found to be Vfl 5° o*. and ihc inc.VM'i'tito chc Ecliptic an Angle of i3<> only, or half of tiit iKUctutn 
[he former SiteULtes. Therefore, a Table of lutlintiiio and Rtduaim a accommodated to the 5ih Salellite, among out Tablet further on. 

The/jmmi Aftronomer, Mi'sldiii, hii (lioee the Difcoveriei of Caffini) by Means of the beft Ttlefcopes, and pitrcing Eyes, fought 1 
NoJit of SafBi-ii'iRing (Sa Mat. Rrt. jbai. ef Patii fimit «»/ 1716). He dnermines from fubiil Obfcrvationi, that the Pi.ine oft 
raid Ring, in (he Year 1715. imerfaaed the Plane of 5.i(iini'i Orbit, in tijt aad H i?" 4S' i """i B^anling the Ani^e of loclinaiion of tb. 
faidRing to be 30", (he fame Plane of the Jtm; interfefled the Earth't Orbit, inI)Kand>( ibo^. with an Inclination lo the Plane of tiial 
Orbit in an Angfe of 3 1" 10'. Therefore, at any given Tinie, to deteimioe, ixaflfy, die Pcfiiin, Sfttin and Poinii of the Apogee and ["er 
gee, both of the Eltipfet of the Ring, and of the EUipft* defcribcd by the SaUililii, an oblique-iDgfcd Sfbtrkal Triicele n-.ult be cefolvcd, j 
iifliewoinourpMit^jfortompuiinB I'm Lsiitiiiii, of the Satellites ot Jufhir. 

The Earth's Latitude, in Relpeft of the Orbit of Svurm, fcareely ever eiceeding ij', it may (at this Affjit ii not fufBcicntlj knoarn) b< 
neglefltd, as if Saii^m and the Earth moved in the lam* Orbit. Therefore, fnHD the gixtni'-ic Place of fj , dcdufl 5" 190 45', md tbe Ri- 
minJir will bethe^^raciM tf Uiii^i ; with which, in cbt TbUi if LainnJi tf itt Saiilluii if Saio.n, 1, 1, j, 4, take the 
which i( the j1r.gU that a vifael Ray, from the Earth to SatHn, it indiaed to the lnnUiii-Oiiiiu. The Sim of which Ai^glt 



iFatds the li'prii, 1 






ia leliitun fiiSigna; bar lice t 



tin of t.'ie Planet of the SatelUlei, that we mij know their 

Lv of otik Flawetaky System. 

and Motion, and other Auibsiiiiti, 



■eriodical (rather Synodicil) R<- ' 
vnAuinTi through their Otbiti, ! 
to the fame fixed S[ar. 



n of their JWn 
:anZ)i/-fiomEqul- 
ico fr, noi 1760, 
! ias. Beginning 
M.S. 



onTno! 
»;a7h ^jm 



!7.9«9» 
ii4,fii7« 
365,1563 
a7.3»'« 
6S6,97S5 
4331.5140 
>C759.»7iO 



1, 51369 
2; 5^006 



JI16 54 16 



V. B. When the Saiilliln hive gnftr Veloeiriet than their Pnmariti, they muft be n 
irfupetiot. The Velocity of ^tj^Vcr'i fecond Satellite (>ting nearly equal to (hat ofi 
ijunftion. When the Velotuy of the PtiiDary ii the gcrater, the SalclHu appcart 



dinO, Sm SilliK J 



nt ROYAL ASTRONOMER 





A General VIEW continued' of .he ELEMENTS of the TrffeORY of ouk fi-AN.TAiir Svstem. \ 










«-„;£*, on 
^heir Sur- 




,« of -heir Ma 




Vata of theii 


1 


s«->«. 


MtiKlsJtS. 


of 






EquaUrial Dia 


EaaHrtdtUi of 


AtUlli, from E- 




BoJif,. 








Deafitiet. 


ATettW. 


SnrfMH, nttew, 
A'WM. A'mfeit, 


mtiy. 


quinoT, 17to.Br. 
Bin. H. S. 
JMIry. 




ATnu/M. 


M,M«: 




Svv 


A..,.Di.n,. 


4< cub. Uiim. 


Ai 


A) 


Ai ■ 


Al 


Aa 


icm. Triiir. 1. 


1 / » 




■4'6.7963 




t65»8i. 


O.IJ 


».9<^ 












MtKCOty 


0,1347 


0.C494 








6.6737 




o,io5S9 
6.0069* r J 


/ »» 35 JS 




Vtsv. 


1.0(57 












I9S730OO 






F.AI1T1 






















MOOK 


0,0751 


0.0106 


0,01513 


t.lllS 


=-3313 


..± ^ 




J f'. 066777 J 


ni 7 50 41 




MAtf 


o,37!o 


0,197s 


jnkntiwn 


iinknoivn 


unknown 


0,43iS6 




0,0916393 


"B t 43 '8 




JUFITI. 


E3,66j9 


65.1574 


tsS,6sl 






0,03696 


. 11 to 13 


0:0481191 


a to 45 4« 






S..756. 


j!„6^.4 


s6,o„o 


0..67, 


i,ii6;o 






0,0=70^,11. 


X »9 51 iK 






Pniodidi Rivdu. 


Pfrfviiia •f 


■?■ 


DiimcteK. 




Dijmeien 


M.in Djl«. 


;Jf*v^ 


Rotary Fr^ 




fi*.^>>. 


r<m. 








MtgiaiMin. 


'm1?^ 


Mil«.^ 


Mtngtelo 

heiraria. 


ar."'' 






Strf^,. 




f 

1 


ii''0P»t'. 








SVf 

Mercvkt 


d h m • 


5f™«. 


K«l. 


K<tl. 






Mile.. 


M,l„. 






o,i8;io" 






763460 
4140 


33,000,000 


•f^' 


^.. 




VrwD! 


114 iS 49 »4 


''.7»!3J 








59.OQO.000 


"iS 


0.71 




Eaiti 










7935 








Mooi 




1. ±.i:oj 




0,1740 


0.0105 


117S 


± 8i,iscc,ooo 


31 


o..sl 




Ma»: 


ess ij 17 30 


«.S»l69 




csooo 


'.>S 


^44+4 


113,000.000 


779 


9.»6 


















414,000.00= 










,07S9 6 3* »6 9.S3»=o 








67B70 777,ooo,oco' ^n 1 unknown, | 






-ffsinr-^ 


-i nmeot their Paaijethto' 


^;*(/« IV. 






«,Pi.i. 


3r. PaTiT 


M. I'ari 


Leitt !•„ 


MS, 




S^a. 


defcend to < 


K Aphelion. 


1*^. 


TOI". to *.. 


la- 


»■ 


I- 


»■ 


1. 


©V 




5 Mnnficut lie l> 


Cjille. 








67' 7" 


57' -b;; 






Sox 








' «7 ij ijt 


MS 


57 .6 Diatn. p .Id..i«. J 
" ;i 31' 37" I 3'' 3>" 


Diam. J 


ly 




19-1^ 




ViKO 


If 

"' 1 


1 '74] y-'"- »3 "S »4 i" 
! 1744 D«. »9 1 51 4c 

; 174S y"'- " 5 1" 4« 

_ .74t 4«-. 9 11 50 40 
r .713 Sfp: 4 13 10 40 


9 7 49 » 


,14 .6 4» 
165 6 g! 














Moo 
Mai 




eo 


S7 « 


«,W.Ring;Di™r..„„4 


="? 




4 ' 49 S 


= es6 1, 30! 


; 90 


57 4 


HS?hiH™K" 


O" 




7 >9 16 is'iorss « 


I StcoNDAiiF.v <ir MnoHS. | 
















ernl 


ipcfiioni of iheSa- e 
-of U. 


nOigieflion. of thaSi- 
lliieiof ft. 
















„.. 1 mde.. 










. 8i 




B-i;«. 




Can^dMtdit 


Grtattft. 


Lull. 


Lioni on Orl^iu 10 chr fim 
their PoiotoftheEilip 


^ 


^' /Di.m««.. 


1 11 ( Dnmeteti. 
3 's ■ h- 












Axa. 110. iftCom. Yr 


V 


4 36 

5 .oS J 




SfK 


li'.p. 


>.p.f<i. 


3. Ocub.jSem.D.G 


Sem.D.e 










lOOOO 




67i4 ■ 


ijJ ..». ' 








*'7 


10174 


I7 ij 14 J 






^«W.S>.el1ite5. 


















N". 






Earth 

Moon 


1 + 




tV 


^i'^^^e 


>.6a6 

«ft-e 


,jh 56m I s 48 J 

17* ,1 • »7 7 43 










t 


t iS ig 36 


I 11 i! 17 




Mai) 




\ 


i 


366,0 


,04.6 


14(1 40" I 111 11 il I 


) * 


J »S •» 5» 


■ 17 4" " 




^Sa'"" 


10+ 








idSooo 


911 56" 11 313 8 35 


3 


7 1 ?9 40 
16 il 5 6 








99 


9S0 111870 hjito*. 


U«k»r 19 'i*/^,J,;,* 


' t 


iq 7 4S 








I>«t« f-tide.it") v,Wch>.LIlbtt™lyd(«rmirH. to.sooP..tortl«whol., <.nAfo^i6, 1761, whtn Fo... will fr«> the S^/^Difl. 
T^D!f'»Z '/ ^"*»'"" in 'he B^;i«»« of '.!.= sJ. Bodi«, theirPW. .ni f./.S, of P.Jig.. in R.fprft of Tim.. >. o-mg to , 
Ix^^fXZcLZ^t Inftrnm-nt., .Bd .Ifo Dilipn« «vd Ability of .he Obfr.ve,., Much 1 ™ pro «me« herein » .xpefled ftoc th. .«»r.t. 
Oblervitlonof theOifcovcrerof ibeAbtmtionof Ligfct, ourprrfent ^«™wjl«j«/. Dr. Brd^, ^ ,. „ . _ ^ u 














volutlAi muft he JiflmRuiftrf imnng ihtm 1 the one ttriidUtI, being the Time the Satellite taktt in iiefcribin» jfio", feen from the Frimiirj .1 
Sn * Jile o.h.; J::^ Tbeing the Tin.^ the SatrSe «kc. ir, ref^.^i^e ,. the f.n,e Pi.yi, or Afpea. in RdVefl of the S»a, The .WV»/| 
theiefoK e«eed5 the *fl-tW/«/ Revoi- tinn by ihe Time tne Satellite fpend. in ™nnin| ovei .n Arc of it, Otbit bmUti to th« run Over by the. 








Priflurf in the Time of the SiwHite'i periodical Revolution. | 



















































,, Google 



Md NAVIGATOR. 



i%9 



yCjOogle 



W/RQTAL ASTRONOMER 



Sjdirtai gTcaier 
ud lets than &' 
»■ Tear*. 
Our. 

o° 29*40''' 16*^° 



Days. 



4333 

7305 



E(iUA rioN 
of jnlian Years. 
S''48*°i4'4-'''^' 



.36s.r 
'o?S7S 



*S567S 
191200 



2000 

3000 



365250' 
730500 
1095750; 

146.000: 

iSz62i;o 



6000 
.7000 
8000 



2191500 
2556750 
291Z000: 

3287250 
3652500 



— 76 



48 
37 49 



Solar Ybai 



EQUATION 
of Julian Years. 



Dayi 



346 
5IJ2L 
4256 



I "i^y^- 



Gregorii 



Days new 

' I forward 

of old 

Style. 



Hundrsd 
Yht> 

of them. 



6'' 9"" 24.' 26"" 35'' 



SyJerealYB*a« 



EQUATION 
of Julian Year*. 



+ 58 
+ 6s 



61 9 
12 tS 



35 



+ Gr. -- left. 



3136 



Btanplt. 

Ti JSmllir KumiiT if. 
11/ Tar iu*t Llap- 



The (boTC Equation (o b« ippliid 
Daji sf Juliao Yeiri in ad Coliunn, /or 
ibe Difi in the fame Kuabcr of SoUi 
Ytaii. 

I-lmpl.. • 
Tj fiti Ibt NuwAer if Ctj, im &jtSt^ 
r,arif -" ' 

yrj. Ju, D^. Eq«. d h 
A|'. 600 . . »i9i5a . , — 4 i^ jj ,^ 

i9»S « It s «4 



Tcart 



KY" 



D» 



Ag'. &>a . . 115151 



X 



a tj s 
5 4* 5S 



tobei|wlicdl«lhED«] 

inJlI.Yr.f„D« 

(une No of Sydeil 

^'■f.S'^'" *73A- 
ife-fff nan, 

Yn-Jo.Eiid 

Agi.6eo+i3 aa 4 »6 

fc+o 9 14 17 

M+O I ji sj 

i-ho ' 

f.Y..7j+4 



V>.Ju.673--»4s''t-.— S * 



'.«?).. 34580! I *S ., 

[lAyiRDniieir. 

And tfatfiMaMetbodfbrJIff^'i Equ- 

JV. £. The aboTtEqaitiou being madt 
fiomtbeidCDlumaof Day> when ilT, id,' 
Kjd Year ii Bifaiili, and i Day addi 
J^B Vcaii, and rubtiafiilnan Biguttion 
yov may find the Da^ 9 to an^ Number 
Solar Yean (Van the Equation!, ai tli< 
ftand for a Diy Itfi of Julian Yeart ; . 
ilioE both Way) n the fame. 



the Stlar and 
rafpea 



Vein nfpe^ii. 



Sjiiirul 



Month-daTi of the Yti, 
>/!«; Or — and + 
Oirm how. math' the 
Month-ilay byeacfaAi 
countii firtvarj arimck 
of the Month-day by the 
•ulian Accognt. 



na trtva uO 
Gretorian »ad Sour 

Y.Gr. h m 1 
100+11 1 34 
40 — 7 1, aj 

8 — I li 41 

» + II 37 49 



S.Vri,d h m 
3000— J n 59 15 



reqiuTrdft. 
Safirli€Blfi, 



db, Google ' 



md N A V IG A TO R; 



0/ /4« PRECESSION 0/ ri* ECLUINO-XES. 

Silt IiAiK KiWTOH (Prop. 39. B. 3. of the PrhKifi'a) bj 1 Dcduaion from tbe Prioclpla of Grnily, {entOntj to the Sim&nin Ht- 
potheGi) Jemonftnlei, thit the mma/Rigreli of the Efmmxa, would be 9" jfi* (oiv, »t a mejn R»M, in 1 nm^r Orbit, if Ae PUne of 
the Eaiuur, taiEiIifiieemnaiai. Bat, becaafe they an iiKUned lo oae anodwr man Anfle of aboilt 93° 30', ihli RecelSun of Motion 
-luft ha dinuniAeit in tlie Pioportioa of the &'» Cmolnma of 1 j<>I to RtJimi, a ai 91706 m loood^ ledociog it to 9' 7* loil, which it 
if the ffii'nm uiing from the AOion of the Sim onlr. 

(anil confeigiunlty EfnimxaJ lo that Force of the Ban ii proved (Frf. 37. B. j.J to be ai 
f ""r ?*' i*''' '^'^ Preceffion of the Mfuiimin from the Aflion of the Moon ; and the 



the Aonaal Pi 

, tJuForct of the. 
, , i toil whence 1 14,4815 11 
9gCD of chii and lh« othu Prccellioi 



the Earth, to moK the £f uWri j fuppoGog the Height of the Eaich at the E^utoi to erceed the Height at the Polet by 17^ Mitei 
aaif. If (he Height of the Earth at the Equitor CKxtiti the Height at the Polai by moie than 17 J. Mils, the teitiftrii I Matter will be tnon 
dwSuF^ce, than at the Center of the Earth ; and the Pnaffitm at the Efmiumti will ^ incraftdhj the greater Excela of Keiiht, 
and J lm imfi i t bj the greater Riiity of Matter. 

" — Long. flHtJa. Vetr tong, i m AUtl 



'• loi) Diflaocc. o 1% 16 $8 Dif. Motion. Ynrt 99 Dfnance. i 11 jc 

Wbmti siy li^ 4ti* Mta„ jtnmal PrKuJffm, ^ mxutt, jo* aaatj Mm A-nast P 

Bat the celebnteit Dr. Btvilhy, our ji/triHum- Rtfl, hit, with gnat Diligence and JadgnKnt, accorately det 
thii oriaUa Preceffion through an intlre Revolution of the Moon'i Node, rperfanoed tn iK Yein, 11 Dip, 7 Houri 



lined the Quantitj of 
. , ., 45Minuta)on which 

ia Vtritiiat, aiotll at tbai of (he Eclifiii OUijmly dnendi; Bring both it a Mean inj' Longiude of the AW«, and at their greitelt and 
leiH Quaittiliia i> o aod A* Loaptude thereof, -rcfpeflivdir. SitTaili, p- zj. 

-ThefiBianlft.i£mr,DfCMrfifpi,ln hit j^AinmiM/ ?*j/a, decenninetfcem theP«i7'i Oblrrvition), themeiD Eoiiinafliat Pricc^tWtobe 
<> 14' t<y for 100 JiSm Van, whidi It at the /tfwn Rate of jo* 36* a Year. But from Dr. Bradln't tnorg acconte Obler*aciam «t 
'find it to be 10 14' ">" ""^y. '"> "» >*"" ^'«h "' Jo" !■>". » Year that the FixU Star, go forward of the EfmiHx, at a Mean Rate. 
OtwhichcooKt to thefameThiag, that the f^amu reccdei from the find SM'I, inthofcTiinei, rerprfliwly, 

runud T. Simf/in phyGcally findt, on aitti'imBUtlan Principlci, the Qiiintitj of Precefiion (Aippofing nnifotm Denfity of the Earth) 
.. . J* bf the Sun'i Force only, (inihad of 9" 7' loiv) which he attificially dcduai from jo", the PieccITion, from A>nu«(w Priaciptei, 
by the San and Moon's Force, and fo determinet the Pieccflian by the Moon'i Force, to iiji MiAiJte, explode A'nuimiu, and ebbliA Sii^- 
/Mua Reiiuiing. Sap, 33. MiJi.TrtSi. 



9"?- 



Iliv for t. 



lul Prier^H of the Ejvim 



', by the jnnt A 



e Moon and 



Year 



,( 170 jC jo» lyti, Brahi, 



19 ■• 



Tjibt Brah. 

Plan^tfd. 

Dif. Motion. 



Of tbt Pnoa&iigioK af tht ApheliODi «(^ Node* tf ibt Orhiii tf tin Planets, In JtttptS »f iht FixiD Staki, 
' '{/'fJfProgtclBon af tht ApBELiON tf tht Eaiih'j Qrhit. v 

,t the Apbelioni of Planatatr Orfiiit a; 



r PlanatatT ( 

H the Ntia) txifi fo far 
n iMl Reaohwioaa, npton one another : whkh, how- 



Sm ItAAG NtwTOH (Pn^. 14. B. 3.} froeea (from Prop. ri. B, i.] tl 
likewife the Plam of thofe Oibitt, by Prpf. 1, fame Boole, (That ff the P/ji 
dittnrbed and fnffer Ibme Imfatliiict bj (he mntual Aflioni of (he Plsmti and < 
CI, prolate bat IiMll MotioM and loequalitin. 

Thai the PiiiiJ Stttn ace imaiOTeable, becaufe they keip the iame Pofitiont to the jifitliini and JVhIh of the Planeta, 

Thai Gnca theA Stva an liable to no ieafiUs PartUm, from the annual Motion of the Earth } tbej can have no fttt on oar Sjfim ; be- 

vfe of tkeir iwrnuJi DilbiiM> 

That, iflbej bad any Efi*a upon the Bodiet of our ^jgftai, yet, by their being di^erfed emy wbua rvond the Hcannt, t^r contiar; Jl 
trafbioiu wonld JeArn their Mntval Aftiont, by Pre/. 70. B. 1. 

XhU(fiM*the.niMnnsaitheS«ir, (U»tmj, num. thmK^rtt, laiitanj are fa JaMtt, that they cannot aft bnt with little Force 
each other, theiefon their /fki<£aH and tftJii muft remain Gacd, ixaf€ fo far at (bey are diihirbed by the Adioai vSyaftitr, (the greatellof 
all the PUncta) Stlmn, and the higher Bodiei. Whence, we find, I7 the Thnrj </ Grainy, that the Afhthm of the lower Plaaeta ntST* 
little in Cnfifiiimia, or accotdiog to 1 following Order of Sjgai, in refpcft of the Fix/J Sun. 



That thit Uotim of the Apbelioot of the Plaaeta ii in the Sr/fnifiitu Raiit, 
Raim) of (heir fneral DilHncei from the Smt. 

That, if the .Ipbtlim of tUn, in an 100 JiJiaw Veara, Itcircieil 33' 10" forwitd ir 
of fenu, and of Mtrcirj, accoriing Co the [aid Sifjuiftican Proportion, will, in an i< 
' \i", TefpeQiveJy. 

4ow, to 1° 14' 10' ^ 



and half Power (betwuC the £mple and daplici 



^ Mlyrr' I Motion of the Fixid Start bevond the Equinox, 



Add 



4> « Motion of thcEtitli'aApniee, beyiwd' tha Aaiaev, 
D 3^,> lo^ Dt.^M^'BSyiJateaLMoiioo,.bqiond thi AfHnwr, 
17 40 Sit Ifaac Siwua'a Apogeoo Pr^rffmi beyona the Starr, 

41 50 Motion of tbe@ or Q 'a Apogee beyond the Eqaiaoc^ 
• aj' so* Dr. Hnitg't Hotioo of )|ti forward 

If 40 Sir Jfaac Nfaun'i Apogeon Ptogrc^n beyond them. 



n 100 yMBm Tan, 



San I 41 o Motionofihe0or O 'a Apogeon from ^Dinox, J 

I 41 7 ao" Dr. Ib/V Motion of Apiece for the lame Tine. SitUi^MK, 
BM, Mnaithar of iheTe't^anlitieiare found to agree i^icb Obfervation, we hare fettled the mean Motion of Q'l Apogee it !■> 4s' to" from 
tbeffnaarin 100 Yeart; being40» mote than by the r^sTjc/GreviIy, which Sit ^««:alw))>ircfert to Obler»tion, M the Proof of Throry. 
InthrTtaie-of Wp/iart*ar, T40 Yeanbefbre-Ctriff, the-Stin*« jJ^t^ei wiiin j" ji/ n, 1884 Yeitr, fince whirh Time In 1744, it hind- 
Tanted 33* to the Calnrit, which ii at the mean Rite of 1' 3" yearly ; ts the Interval) of fame other Obferraiioni, loofely taken, ifcertain. 
Bot a Mean being taken of the Quintltiet deduced from feretil remote ObferTationi Ihewi the Motion of the Sur't jfy^t 10 he, ai we have 
before determined it, 61" 30', a Year: lb fmall a Motion of the Eirlh'i Aphelion, in lefpca of (he Start, difli aguiihed fiom the PritrJ^ 
I Sfihmi, beipg hard to determJiK by the pbtfital Lavi of Gruity only. 

Sa 



Th ROYAL ASTRONOMER 



O/liv iKItlpALtTIBI ;^/J# EaKTH'i MoTIOKI, M^ ^ /^ Ot AVITATIpX c/ ibt MOOH. 
iV^fjKi an frtiiKii lU Frtu^ tj lit tjulmiB, Nulalhi, '»d JiftrnU AAn'H ^ tbt Etrth'i Mit ; tad *lfi amp aftU Ecliftir 01- 



11 ritllHIJ to 11 

din like H«ui 



le IiHjtadltm bciog Icen frooi the Eattlu For, 



ti\j lovardiihi Sum and Egrth, would tb«a appor not abort 3 c', Ttr)r difliciilt to be obfnTCd. BcGdu, the lBCi<ulftit*, 

]) , in the 3'< Motion, cinnot be neir lo conGderaU* aa the Ineiiaaliliet of the Mwto'a Motion ; becauic Ibe Eartb it about jo . 

[han the ]) ; and iheiefore ihe Iniqualjtiei ciafed in the Q't Motiont, by the Gravitation of the Moon, will be almoft i mf ti-a f i i Ut withic- 
rd 10 the Sun, and cenlequentljr the ncifrtcal GnvilMioaa tS the Earth and Moon, can no moR afTcA the Computitiou ii the int flact ij 
lEarih, r«en frnm the Sun, (or of the Wi live f^ia. fan rfom the Earth] than if theEiidi had no ]), or SattUile. 

NcTertbeiefr, TbeMoon'i Gnvitation toiracrfi the Einh, aOingon theElrth'i^>ieni'dSi/FI(uae, piadoca two verr ieafiblc Effieaa. The one 
c ctbii'g tTkifineingcf ibtTiJt ; the other ^yarittiut tf tht PUim tf ibt Ediftic ati Ejiuitri caofini the iDto&aioni of thoft Plaaet, 
id cotiftqurntly Ptinli ■/" 1^ Ejaiiuxti, It mm ritn^ndt. 

For, tlir Moon's Otbit being inclined aboDt c° ^ to the Ec]i:>tic, and ili afcending Q nuking a Rerolution in about il Vem, tbtaagb 
the Si^i of the Ecliptic, it foliawi, that the Inclination of the Moon'i Orbit ii contlnuallT changing iti Pofition with the itrr^bUI Epattr. 
When the Moon'i ifcendine Q itimiiei with the firft Point of Aria, which ii the ifcending Node of the Equator, then the Inclicalion of tbc 
ifoDo'i (Jtbit tu the Plane of the Equator will be the Sum of j°J, and xi^\ :s %%" ) but when the afceaduig Nod* nteeti with the CtA 
>aint of Liin, or drfcending Node of the Equator, then the Moon'i Orbit will be iaclined to the Earth'* Equator by ooly the Otfimn of 
.3°! and j°J ^|g^. Thenfbratht Inclinatiod of the Moon') Orbit to the Plane of the Ecliptic, iDcrcalea, inalioot j V^ara, jiam ■!"] 
ii)|, ; and dttteafea fioiD 18°* to it-j in <bout 9 Yeart, more j when a Rerolution of the Moon't Node i* compteated. 

Were The Earth an bBmtgnan Sfbiri, jti central Force towards the Sun and MtK would cauli: no Change in the Politioa of ib Jbat, . 
ihich it revolveti Bat ilt Figure Being a^nrnf Sphere next ita Poles [refembling a Spheroid generated by the Rotation of an EUipBs on 
let) Alii) ita Matter it raifed or ucmalaiid about the Equator, whenon the Sun and Moon affing obliqnely, iti Eniuuti are nude to 1. 
Rogmde, and iti Ecliptic Obllquitj drawn to ancarer and neirei Cmnddcntc with the Equator: bcUea harini ■ periodical VafbtiDa with the 
Moon'a Node. 

For, fuppofe the Excefs of the Spheroidil Matter, abira the Spherical, to be colleSed aboDt the Etrth'a Equator Into a SiV, adboiat to tha 
Plane of the globular Eatib, infcribed in the Spheroidal one, the two Pointi where tbu Ki'itf ioterfeOi the Plane of the Ecliptic ot the two 
terreftrial NbAi, are the Pbinti of Ana and Lltra. Let all the Pariitln of Matter, of which the faid fmaiimi R'mr ii rompored, be conlider- 
ed ai foouny littlf Moons, (Sa NnetsnitM Prinif, B. 1. Pup, liei. Cor. 10. J tcrolving about the Eaith. in tlw fame Space of TJBie u tba 
Point] of it! Surface retolvcs, via. in ijli 56111 ^i j then the fuppofcd Ring of Moons will be affiled by 3 Cbum/ Fbrcei of Cranty, 
Tie tfi in/aiiilj grtai it ttJfiA tf iht alitr Pat, h itt Crtm'ty MmeriA tbi Eartb'i Caatr, 
7U id il lirir CravUaliai nntrdi Itt rial Mm, in itt HerBtiu. 
Tbt id ibtK. Chniiiaiit uaardi lit Sm*, tit mak^ sf lit lira Fma ; the Sun bein| Taftly fludier from the Earth than the Earth ii frsoi 



iheMooi 

By conibinine the rR of thde Force* with each 
ef lit Ring mtfi ahoajl ttmd 

IM of the £r/iftir._ 
the Quantity of xhe PnctfficH nf tit Ejamta, refultiog from the combined GnriMtion 
anditeGnvitation towards the Son, is apptrenth t«w/'atnch of the Q"* periodical Renlabonsi Sit J 
Gng from the Force of the Sun only. 

But thelncliaatioaof the I|.'s OtU t to tbc Plineof the Cqoator, being IbmMimcs iV\, and at other Tlma' bI*^ the- Batfaya^ ffl irw om 
o Nodd of the liild Ring, or Preceffioa of the EquiiM»ei, from the Ring's comtuned Gnnty nrwards the Earth anf' Moon, nuft vary 
<)*iinrify:- beioR greate fl when the £_ of Inclination is greateR, and tbe tootritT. Hence, Tbc Piw^n tf lit BjainKti, fiwn theft n 
~ ' " ' 'of about )S Yeaia: being greateit, m aboot ct' ia 1 Year, when the S'a afcending Q is in f, and lad, or 
~ - 'inia about - ■ " 



M Other, it fbllowa, 
III nrrtpadi \ and liirHi*! tit Umt vbirt lit Flam tf ita lirrt/lnal Ejmmir ntXtSflil 



at MwfM making it j* 7* soi*) k 



Dcc, it appears, that the Int/iwaiitw of the laid Ri 
jtQ to a ftriidiial^uiriSm i Their VariatiOB from the 



tf'iv, and 
leSun'l i 



[oon't Node is la Q or frp. 
onfeqBently of ttie Plane of the Ecliptic to ihat-of the Equatot, moft be fu 
AAion beiag too finalf for Obfemtion. But the Vitiations from the Mooi 



Rvtliyw- dtltrmimng tht QuAHTtTT ^ pKSCaitlOM, NuTATIOH, mU CHAt^tlll, litnfy, tf SlCLiaATlOM, 

aai RiCBT AiCEKsiON, iurtj^tf ib* Stau. AMVF£ng t» 7tihk, p. 33, 

r<i>J lit priffii tfuiha ./ Pkicissioh ? 

jfi Rad. il It Sim Q^s DiAanoe from the atar^ Equlnoaial PMat, fi 11 tit {nMfff EfaaHta */ PTec^br t* lii pR&Dt Efaation, ^iiFir. 
To bearded to the Mcaa Pleceflion when-the alcending Q ]| ia ia ur of 3w fi SoQChcra Signa, but' to-bȣtbtiaaed therefrani, wWht 
ny of the S Notthern Sign*. 

I/.B. Tbc Decreift of IncliMtiiw of tbe E^Bai«r to the EcUptk, fnm the Q iotbeBegiiuiiiiBof tr* is propatiawMD tteMtfidKBttf 
theNodc'sprefcoiDlllance, from T- 

Whence, the faid InclinatiBn will be in its asm ^aaaiiif when the Q i* la the Sol)lki of aserVf. Cnfi^iHllft the Diffeiencc betwcea 
ibcMean »d me Inctinatioa will be, aa the Difference between the Mrfed Sine of the S'> prelent IMftance from <¥■( ud the tctM She of 
Ibal it. Ai CoSne of Node'i Diflante fram "y. Therefiirf, 



,, Google 



and NAVIGATOR. 



m 



RULES/w i^tnmmmg tht QIUANTITY j^ PRECESSION, NUTATION, lie. 



Ti find lit MfMiM al ay Timi t 

jb llMdi„htstbta,J!m,,/ib,NtdftDifimmfimith,-^Bj«iai^Fi3»l,fi i. At pimt^ NM4htm (ir XfMiim if EtSftii OUipaf^} 
tht f»Sr« NtiaiiH. 

Tabe«!Arfta the Mm* Obn^uh; oTlh* Ediatlc when tb* Nnk ii in tny af the 6 ifctBdlnt SigM U, ST, K> *r> tt> 11, 1 
le fnhraBti thmfntni, wbea the Npdt ia uj of tbc 6 ddctndiog Si|iu SI, (l,> lu ^ '■b f ■ 

•Tiifndtbt Ckahgi i/tf J'Mr'i DiCLiHATiOH «W Riglit ATcciifian, erifimg ptm lit tfmttitaa^ tbt Xmtli'i AxiiT 

^ guJiiu it n lit Sitae/ lit Siar'i Kigti ^fcaifim, ft h tbt Numiim (ot ^TCa Chaatc of the E<iuatot'i InclinMion lo the Ecliptic) ta tit 

Chnritfii* Si*r'i Dttbutiim mafiJ tr that NuiMimi. And, At Cetatr. tf tbt Star'i Dabiutita ii It ibi Ctjhu tf in KitU jffaAm, h it 

fit IfaMitmii 'In TMt, a lit Cia^ ^ tit Siar', Xlght jifit<^ aoftBttaUt. 



Inna which tl . 

fr.B. WhcD thePnccflian, inlhcrecODdrorceoiBgCtfe, unoontt to fmu Mimtu, the Mean Ki^t Aftnifiaa mnft be olid M the Mid 
of tbe lotetial to make tbe Coaclslian enA. Tt,i though the given Right ATcenfioD of the Inteml najr be ruffidcDt fbi the Piupole io eoi 
f^Ca, without the Trouble of a Compntation for the miiMle Time, yet where the grtateft AccDracjr it reqaire^ the Opetitioa moft 
ropated t eritrmiaii Kijiiiiialifitf at/amitrrf Ofmiitmi. Sec Mile. TmS). 

^ jtfmtll MMin t/Stiatit, etJ FhciJ^ (fee the bid I'reai) arUafnm Iht hitm't Dtt&tttit*. "Tht ptaufi Kf^^ilJ ^ ^MA it n 
frtM^ Sjimitief tf that dtfading it lit Suk, in a Ratio umftmiii^ if ihi Ratio a/ Ibt Dttjiiii t^ At tmit Btdia, that ff tiiirfBit£c 7m 
and that if ibt Stna if lit IncUxailin tf ibtir ri/ftaivt Ortiii It tin Timu if lit Ematar, aeulj | ammii^ in n Gtit^ima n mmil 
} ^ d Stttmi. Ai^, then ii another Natatiia and Pnaffim aiiiini from mote thia aU that £nc heeo coilfidered bf the iime iMitltd ^ 
riv) ititg ttt mtanXifiii tf a Hhmiti- tf Oftnuitmi, to be explained bitbrr on. 



OBLIQ.UITY tf tit ECLIPTIC. 



RULE I. ni DiflereBce takin JiMitn ibi 5n'j Meridian jtbimJi, n tirhtr Drj tf lit StVia, «*i lit tltiglt tf lit tm^al EfUUtt m 
lit Pitt tf Otfmmlltii, niUiiMvhf 'Jm/ it lit Sm'i putifi DitSagli—, trOUijiiitf if ttt Etliflii, njuinii 



StSftie Otlipay, t*iiuinl. 



aiOtftramltm. Tb* Sns'a Mmliu Aldtnd^ 



Or, lAMeridiaaMlitad* 17*40' 7*~' 



■ JJjtM* if imh Tnfw >na tit £juar. 



EXAMPLE S. 

t the Wiater Silfiitt, 174 j, oUentd at ftrii .... * 
', at Parii, (Ut. belDg 4!° 50^ Io*) . . , t . . 

Seliftic Obllipiilr. iMrJ^ Tb DiAceac* 

tbeSoMBMt&jMc^ 1744, oUaittd txPmii • . * « 
Height of the Equates at Farii, a« bdoie • • ■ » , 



rf*^ 7*-1 
''4 IT '7 i 
46 ST ID J 



ZcGptU OhUstltr, ttar)f. The DV. 



41 


9 50 


41 


* so 


»1 


»7 "7 
•» 4) 



^ TbaZde.Obr, *) xt 35, ftmff^, atMorc. 



Mean Icliptic Obliqnit]', itrrlBfy, 



F>M) die Mtan of tWo Opentioiu 011I7. 



H. B.' nil MiM J^ii*K/9 
ttitK if if, '■ a Jtn-f&Xra 

UmJkt.ttiam^i'Ufily 



tfiii MiEftii OiCtiarr ii/imil It Jiiriafihfitiai, I MSii, if a D^ntia a CoMirj, f(&ttiiM«iy« perioabi r 
m if ttt It^'i Q 1 varj-i^ fivmili pt»ttA Oiliamlj S3<> if 39', <i« ^'iQMlX^Vi <* 3}' sf »'« 



DigHizcd by VjOOQ IC 



»J4 



Tht ROTAt ASTRONOMER 



0/ ri* MEASURE -/TIME. 

Tit SydemaI' <W Solak Day. 

THE RotMioti of tke Eiuth, oa iu own Jms to tkc Lefr, or EafUHy, bnis iii^Vi>i^*(«iaADgta . , 
$itvolution of tiie /xeJ St4a-i, about the Eatd^ cotha Right, arWeflerly) U tki j^ao/ Mr«^ «/* 7'(m. 

For, the Diwneter of the Earth's Orbit bting but x Paixt in Proportion to the immenfc Diftaoce of the fixtdStan, 
ihw Pfifitioii cannot be ahered to us. by any other Motion of the Earth than that of its Rotation on iu own Jmi, 
except a fmall offarnt Change canfed by the progreflive Motion of Light, and of the Exrth in it* Orbit. 
And therefore the nai Rotation Eaileriy of the fame Poiu, or MeridiaN of the Earth, W the fane fixed Point in the 
Heaven;, (or the apparent Revolution, Wcfterly, of the fame /xn/ Star, to the fame Spot, or Meridian, of the 
Earth) trough an entire RevolntioB, iiakeajjti'tijiiittlffta/artii/iifliatifcalliif'iinSydcreuD^. 

But, the &rtb having an aceibrated ax ntariti Motion, through its Orbit, to the Left, round the Su», and a 
Rotation Ike fame Way, or to the Left. oniti^V, cauCn an apparent Motioa ofthe SuntothcJJijiii/. TVvt Litirvitl 
if tMetwfiMationif'raa/er^t^dtvM/ MtlicSun'i next Rctnrato thefatn* Mct«di«i, is what At ^Jhmaimri lathht 
dfirammtal, trmtm Seiaf Daj, which they make to begin and end at JV«*i, For if they reckoned it to beein and 
;nd from and to any other Time of the T>ay, [m from and to Merniig or S'oningJ the IntaiuUUitt of tit feiar Dajw 
nueald l* i^ri grtain-t on Account of the hcrtafi and Dtcra^ of art'^<iai Dmy*. And ue Svn being the ii^^ 
\Light, and theSiau revolving in Succeflion through the Year, the foIarDiqr, ftir that Reafon, U found Borefonve- 
nlent than the fjdireml, for the tammtm iii^krttf Time. 

If the Sun had no other apparent Motion than that of iti tto'iitd Itevolation round the Earth, it wonld, every Day^ 
appear to defcribe the fame Parallel, thxangh the Heavens, (from Rifing to Setting) and be accompanied witht^e 
fame fixed Stars at its Return to the fame Meridian. Bn^ by the Earth's Progreffion in its Orbit, ei htf^irt dt^ibtd\ 
the Snn, every Day, appears to be removed ai much to the Left, orEaftward, of the j'm'j />/iic/ on the former Day, 
nieEarth'haiManyai[SVed'ihe;;ta!W lfi^,"in the ftfpoflte Part of theOrbit or EcITpticI" And thereibre, apparatdj; 
.ueSunretumi to the fame Meridian eaohDay.abeDa 59' S'- (the Eirtli'* mean dinraal Motion in right Afccnfian) later 
than 00 the former Cay, or Return of the fame fixed Star to the fame Meridian. For the Stan appear to advance, 
each Day, about 59' 8', (or -jjy Part of a Revotntion) of the San. 

Hence i mean aftronomical or folar Day ii meafnrcd by the S»m of 1 Rerolotion of the Earth on tti Jieh, and 
jii Part of another RcvolotioD, = 36s' + 59' 8', OR 

Jn ASTRONOMICAL er SOLAR DAY, at ah Tikh. 

k aeewahb mti(/iirtd h tit Smt <>f^'^il>tS^m',MtdMjlte.»flhtBri,ti»rtmrt^»iid>mt>tkiJM»fllmtlUftii 
Orbit, di/<Tibed by the Evrth\oi Snn apparently) imihat Dmy, i. e. 360* + Di_f. R. A. intitirDif, 

Pot, whenthe Earth hatdefcribcd a Revolution of 360° to the /W £/an, on iuovraJxit, it mnft ftill rwolve ._ 
AeLe/i, thatDay, asmoch as its msWDeparturein R. A. the /•»»#% in it> Orbit, to briog the Meridian of the 
Earth lutder the Son t ihen affttrtntlf removed to th« Left, or Eaftward, &> much as the Earth Jus advanced in. die 
contrary Part of her elliptic Orbit. 

Tb* liki it alfa evidm if:li* tltfurm Mtio* tf tbt Sm and Sun exhibited on tht calrfiiaJGlahej 

ThemfoDBi if a.jSm'J^iM comes t» the JUtt^Em witk the &», U NwM, ^^iknt Jbred Star, KfterflncMonth^r 
, ^- of n YtVt, will come tO'the fsne Meridian cxafily f\ of 1^ Honn, or 2 Hoots, Jtwer, and fo, in Proportion, 
for'anyTTumberof Monthsafttr. In6Mooths, oiHalf aYear, it will come to the Meridian at Mrii>t|i/, izHoars 
preceding the Sui^ an j in 365 Dj^ia, being almofl a foIar Year, it will coine ts th« Metidian ahoncWM D19 fMnef, 
or «Mr4y FMam to it «;iuit with the Sun j in which \^ Interval, the fame ybiv/^Mr will have tMnn]*d t« the 
Meridian ahvut 366 Timet, or made nearly that'Nnmber of Revoludons \» 365 RetOtni to tbc Meridian, or, 
ReTttlutiont, of: the Sun. 
46 c Days 

*^""» .(rtRe^'L —^3" 56° J* Sfi* j''" 56". CsTr. =TiBW of » R«KiJati«n •fth* Ufthnfixmlhan 

'being nearly the Quantity of the Sjiireed Dm}, ia jmw. firiar Tint. 1>U aot convOty, Sm St^mU ^fratakf 
(P. 95, 96) enoneoufly making366 Syderial Revolution!, exactly, in 36; folar Days. 

tr The abavi Csmpatatian docs not confider the Earth's Modon (or bun's apparently) through the whole Orbit, or 

Ecliptic in right Afcenfion ; but only provides for 36; Days of a Revoludon. Therefore the compleat Year nuft be 

divided by itfelf -t- i , the Revolution gained in that Time, for the correAer Length of the j^direalDay. 

36^.3423006021 Days. 

Hence, 366.i+a3oo6oai Rev. "= •997»^s6'7 Day «= '3* S^" 4' s" »6S ift. cwrefter Timt of the 
Std«r»*».D*y. — . — — — — — 



,y Google 



•frf- N A V IG AT OR. 



MBASURS ^ TIM£. 



Or. At3|65l>>.a4}OQ6oii : j^o" pidfad««ttin R.A. n iJX : $y,i^t)lS, iSt, 

. Sun'f mean dioraal MMi<M bt K. A. ^ 59' S^ 19' 4$!*, iSt.. 
Now, A>36o'*+59',i388236 = 36o'.98s647o6«ppar?iitdioraalMot.O : 14 Ho.? . ,, !,--.,,*-< fj., 

:; 3600 apparent dinraal Mot. * ; . S' 3 •9i1-<»g'»i '^f- 

The Sydekeal Day,, inmeanf'ii/ar Time, as before, 23" 56* 4' 5"" a6^",itfr. 

Nigbt, fooQcrtbaaoDtheforiHer Nig4t 5 " ' ■ ' " S+ J+ 

N, B. Ai a Turn af thiEarlh units Jxitmi^KrtitirrfiJenai Day, thtri ma/l bt oat Taro, ar fydtrial Day more, .iv 
#W Camje^tf-tht B artbt tn m^ iier Otttl; lifM tit tfambtr efplar Dayi in lulSch thai Coitrji ii cam^ltatid, Sibatever 
Nwnbtr ihoji Daji maj it, Jad lb* fame hoUi viith TtfftS to awf atber Plmiut rivalvin£ m itf Axit t» tb* Start, aitd ibt 
Narahtr »/ Days in luhiehitgtts ibnugk its Orbit. 

Tit Stdikbal Dat JtduuJ etrrtalj, 

A ^JertaHTiar, sr RctoIauib oTtkc S«a with Ae^mSte-, orOi 4<, u wttill36sD'.as6s3Z9o6 (Ucaire 
the Stan go forward ^o* 30' a Year) coofcqaently, the Number of fydcieal tStmai- Revoiotioiis of dam Surto tlie 
fame Mercian, in tbatTioie-^ 366^5^5^33906^ 



-1»"^97»*9^733D»y- 



365 f;6;3a9o6 Dayi 
Whence,, 566.256532906 Re»' 

The Stdehal Day, in mean Solar Time, = 13* 56" 4" 5'* 59'* 10",. tff. Mrr«J^ 
Hence, any Ar^i)'5'/<w comes to flie fame Meridian each? ._ ._ ,.. _,,! -_*-,.,« --^ . ,^ ^ 

Night,./oonerthanonthefoxm«Nlgh., cor^aiy. J ' ^ ^j Z- °^* '^ * '^ ^ " '^^ 

*,* Ow apparenl Seoalutin of the Sm It tit 24triJiita taili hi M by a PlaflSt mtving roioidbim i in tilt fa 

thai a TrieotUtr •would loft a Daf going round lit Earth tie famt Way luitb th* affarmi Motion 0/ tbt Sja, ffia miakiJ 

:ha one Day itfi at -bit Return than tht Jniaiilaots.rtmainiMg at tbt PUut ff bit Sitting tat ; •wbativtr Ifumbtr of Dagi 

Tim, be took t9 go rouiidthi Earth, 

HencCathcNamber of^/iJar Days thataDyFIancetakesto^roandtheSnn in its Orbit, willbealways 1 lebthan 
the Number tA fjJtnid Days, or Revolutions, of that Planet to thelamc fixed Stir, in that Time. And if the Earth 
tm-ned but once round its Jixii in a Year, the fam* Wig that it goes round the San in its Orbit, there woaU be 
tmtinaai Day on thai Side of the Earth next the Son at its Setting out, and ceniinuai Night on the oppofite Side ; 'As 
the Moon' keep the/im/ Fan towards as by turning once round her Jlxii while Ihe goes once round the Earth. '■ 
-'.Tbb TabH, Page 21, iiufid/or tht Rtgulatien cf Clocks and Jfatcbei, it ftiews tho pijirrnee in Sncc^ffipn, 
between a Number offiilar and fyJtreal Dayt, The DiiEerence between i fa/ar and 1 J/dettai Day is Ihewn to {be 
ai aforegoing, that the JlJre4 Start daily aeetinaii,.at. come to. the MeiidiaB- iboaer' each Nitht 

Ta TtguU^iit Clock v Watoh- 

If, tbiowli a fMall Mole, ii a Window-Shnttar, tn* in a Piece of Metal' fixed to s Winddw,- yon obfervri at wjuu 
Time any Star difappean or vaniAet behind a Chimntf, or CorAer of a Honfe, at a Ihort Dillaoce, and you fnit^ 
obferve die fame Star vanifh or difappeai the Night following 3 Minutes, 56 Seconds, Iboner, by the Clock) or 
IWatch,. andon the 5f<vn/ Night 7 Minutes, 52 Seconds, >m«- ; the Third Night 11 Minutes, 48 Seconds, /ea»tr, 
mnd fo OB every Nighty iboner, in that Proportion, for fevcral Days, according to the Tai/i, in Page 2 1 . of tbtStun 
JcceUration, then the Ciixk or Watch will be found to co true, aretrJing to mean or uniforat Time. OthcTwife, 
be altered to go by that RuU, and may be regulated by it ta half a Sec^ of Tim*. 
- The Timt-mta/if^tr being thus welt regulated according to the uniform Motion of the Earthon its Axis, or eqsal 
Meafure of the fydtrtat Day, tt will ftiew you the d iffe r en t Intqualiiy of the folar Dtg from Noon to Noon i to Ibe 
fometimet greater and fonetimes lefs than 24 Hours by the Cloclc. The Time by a regulated Clock, and that bf 
ante £i«-Z>>W will nerar be.Ae fam^ except abont^^n'/ 15, ^Wi6, Jngujl ^i, utA Dectmbtr 2^, each Year. Fo 
by the tputi M^vtmtnt of the Machine, all the Year, the unequal Time by the Sun will be found dower than ifie 
Time by the Cloclc, ftam Biembtr 24 to April 1 5 j and, from thence, till ^sne 1 6, falter j ftom thence to Au^jf 
11, iloweri and thence to Dtcttnbir 24, fafterthan die Clock : The Snn'sTime txing the BWfiM/ModoD. 
^ ■ !■■ I [ !■ .. in . 1 '■ J " ' I I II I I I II ■ I— - ..^i r -. . 1 



3* 55' SV^ " afo«goir 
than on toe Night before. 



LK«, 



d by Google 



<3tf 



Tbt ROYAL ASTRONOMER 



MEASURE «/TIME. 



JV, B> The foKgoiDfc I>aj>i tic thoTe, oa which the eqnil and aacqiM] Moremeiitt mut, at flicw the fiuoe Time : 
hat tit mat tit Daft, luhtrttmlbiSmfi *fKal mtJirMtMaliQm ii4dH*,fort^Haariy birt^tr Jbtvai. 

ThcRquATiaN-TABiii. it p. I9 and zo, exa&ly fliew the Oj^TmwirfvxM (ivTi'xw J^^fiMSvir, jWfiw/ j_r «■ 
tjwl m»ving Ckti, fir tb€ Ytar, Efpeciall}' the TaUe at Page 19, giving that Equation mAilj imm.i!atSMM't PUet, 
or LsDgito^ only. 

Tbt I^ngimde of tb* fiired Stan M»g hnvm, lobm mf Star, wb«fiKi!atitm ta tit EcSftit ii inevpii, nmii te tbt 
MeridiaQ «t Midnight, tit Sit^t Piact, er Ungimd*, in th* Eiliftie biiiig tbei tpf»fa* la lit Pdmi if tit £c£ptic emimg 

tbiMtriiitm, mriS ii a(/i intvm. 



EQUATION ^TIME. 
Mbam mi Tairi Datj. 

TO meafare Time by a Cltei two Sorti of Time or Days mnft be neceffiuiljr diftingoifhed. 

The one trar or afparmt, known by the ImNniai between the b^aai of Ae Snn'i Center paffing the Meridian, and 
thatof its out Retorn to the fame Meridian. 

The other, a whom Dttf, or Time, known by the Lutrtml from tw Noon to dM Mxt, fnch as woold be Jiefy 
obferved, if the San'i Motion was mtifirm tike that of the Ejmaitr. 

Mum Tim* u Ihewn by well regulated Clocks ; and tnu Timt U deduced fro^ Obfenrations of the Skm. 

The Mrfand aum. Day are each divided into 14 Hoar*, or 86400 Secoi)ds of Time. TbeMtafirttf liti 

Dbj, is the J'«M of 360* of the Equator, and 59' 8', .d««</ Motion inR. A. pafling under the Meridian; which, 
dinded by 864£Oi ftives 1;' z8'. -pafiing. under the Meridian in each Second of Time. 

The Mtafiirt af tbt tnu Oaf is the Siai of 360' of the Equator, and the Motion or Increafe of right Afcenfion for 
that Day. - , 

When the San is lajfiapi, aboat Jmi/ 30, Leap Year, its Motion inR. A. in a Day, is about 1* t'C; therefore 
jfil* »/ 6' is then the JM^fl/i« of ihetrac Day. Say. As 360* 59*8* i 14* mtOM Time :; ^61" t'6* ; 34*0" I «•, 
frwTime, correfponding ; the tnu Day being then ta^'IongerthiilitbesMM Day. 

Tiit irMt and miai Dof art ef eji/a/ Lingti •wRca Htc San'slncretfc of R, A. is 59' 8' for a Day j happening abont 
Ftimary 10, May I^, Jufy 16, Ntvimter 1. Les^-Vear, N. S. . 

7ic almu Daji ri/ptH mfy lit nieaii Ltngli nf thi filar Days, lahen li* mtax and tnu Mttian »f tbt Sim, fir 24 Hitri 
ii aHit, ar tbt Cintk (gthig famttima befiri and famtlindi aftir tbt SmiJ Marks marly the famt Diff'trtna if Tinu, er iat 
m inrtafr for a Daf I tit Difftrinci betviien thi Clock ai»/ Sun-Dial at 12, hting niarlj tit fami at at all atitr Timtt 
tf lit Daf. Tbifi Daft art diSingui^d fnm ibt Daji lefar* ebftrvtd, an ivbieb tbt Timi maritd hj tit Clack, mg 
thva/i tpat, brfari aiid afitr tot Sun, mtit rwitb N9B»,*r \3tiarlitd ij tbtSiai, mauiagmtjuallj. 

The dbcit and £Kif-£>W on thofeDays (j^fil ij, Juiu 16, Ju^JI 31, and Dteimbrr 24] go nearly together, or 
mark the fame Tine tor 24 Hours. At other Times of the Year there is a con liderable Di^nn between the tne 
Noon, or Inftant, of the Son's Center pafling the Meridian, and the mean Noon, or rnftanc, that die Sun's Center 
would have pafied it, had its Motion in R. A. cantioued uni^rm, from any one of thofe lafl mentioned Days. 

The Difftrtntti of each mean and correfponding tru H^y, fucceffively, throueh the Year, from any one Day of Ae 
Year, accBmnlate infen6bly i. yet, at the End of many Days, form a confidetable Variation between the 'T^^e 
of the Day, by the Clock, (going equally from the fame Time of the Day or Noon by the Sun) and Time of the 
Day, bv tneMnW Motion of die Sun. This Dijertnet, or Efaaiitn, from whatever £^^, at Noon, or Time 
of the Day by the Sun. the mean Movement begins its Reckoning, ii at all Times, facccffirely, equal to the Dif! 
ietwtin til Sni^i mean Plate, and in true rigbl AJeenJian, reduced la Timt. For the Sun's mean Place wonld be adva..^.^ 
at far in the £;iui/«r, as in the Ecliptic, by uniform Motion, and confeqaently the Diffrrtntt between that Diftance, 
and the true R. fi.'. in the Eqna[or, u the Arc of Sjuatian between mean and true Time 1 being the veiy PriatipU on 
which the Dil&rence between the mean and true Time depends. But if the Sun's mean Progrei* in R. A. or the 
Earth's Rotation on its Axis, be not uniform, this Equa:ion of natural Days muft be defe&ive. 

The afordaid Ako£ Ejnatian ^ 7iW is reducible to two Arcs j one cf which is the Dijftrtatr af tit mt PUce 
tf tbt Sun and itt R. A. and the Other is the Difertiui af tit tnu and mean Place af ibf Sun, and thereioK die Sam or 
DlftreMet, of which Arcs, converted into Time, will produce the Equation of Time, on its firfi PriBci|dea. 

Tyiia had a Sufpicion of the Acceleration or Retardation of the Earth's Modon on iti Axis, and was for faallancing 
[he Part of the forementioncd Eqaauon of the Diftereocc between the. Sun's tme and mean Place, (depending on the 
Snn's mean Anomaly) by only ufing the odier Part of tlte Equation or Difiereace be t w uii the Sun's true Place and 
right Afcenfion, (depending on the edipric Obliquity) which he called the Emfpin becaofe it ferved him to £nd, 
^ Calculation, the Eclip/ei he had obfejved. 

Strm 



,y Google 



fl^/ N A V I G A T O R. 



i;7 



E Q.U ATION of T I M E. 



5r/-r// imagined that this fuppoled /sffWi^of the Earth's Roiation, or lirlt Mover, was coirpeorated, by mate J 
Ule of the Part of Equation negkdted by Tycfra, under a coairarj Tiiif, or Sign, ai he has given it in his Uftrmai 
Camlma ; though we find no Reifon for any Inequality of the Earth's Rotation. 

Betides the tcmmon Equation of Tint, giving the Hour by the Clock when it is Noon hy the Sun, for each Day 
of the Year, there is annually publiftied, (in an excellent Ephemcris, Incitled the Cannaijaiict dcs Teat', by Monfin 
Miraldi, of France, fent for into England for Want of Aflronomy being more encouraged among us) another Equatio 
ofC/oi-ir/w.correfpondenttO the Increafeof Time by the Sun. This tajl Efiatien begins its Ji/itia wi:h the Time by 
the Sun, Ntvimber z, when the equal and true Motion of the Sun for a Day is nlike : and not from the common 
flpoihai, of Afril |j, Junt lb, Anguft 31, or Decemier 24, when the Sun and Clock mark the fame Time, itfliewa 
Increafe, or Difference, of CIoii.Tiim from Ntrvemhir z, for each. Day of the Year, correfpondent to the Time 
by the Sun. The Difference of any two of which Incrtafe,, for any two Days of the Year, fiiews the locreate or 
Decreifeqf C&ri-TiW.correflly, correfpondent to the Increafe or Dccieal'e of Time by the Sun in that Interval. 
Tikis Equation is exa3lj can/ermabii la tht other common Equation 0/ 'Time, and iti Increafe and Deciecfi in the fame 
Jalarvai. 

EXAMPLE. 0» November 2, (the Epecha of cheinereajing C/oci-Timi Ejiiatisn) Noon hy tin Sut, necarJlngiii thi 
common Equation of Time, " al \\^ 43'° ;l' iy aCUd, tuell regnlateH ; and thcrefare ihii Clock biingft at iz, cii tht 
f.imt Oaj, vibtn itii.tzor Noon by the San i it ivill continue to go i6'^ g' fir-warii of correfl mear,Tii!ie, each Day roana 

Rtqvrid the Incrtaft of Clock-Timi, cortrfpandenl to the Suni Time, from tiovetabn iz, (lO after Leap Year) to 
December 10 felUviing, and tie corrt^Tieus by a regulated dicli, iiibtn it ii Noon by the Sua, on each of tb ft Days? 

lucr. of Clock- Time CorrtflM " 






9 17 



8 5; Dif. Ameas , 



I 41 • Noon by Clock, frODi ibovc. 



■' S3 '7 ( By.'J'e 

. . 8 5+Dif. y^'i'^t'- 



II 44 33 cornft man N»n, br 1 rtgnlaled Clock. 
II a 37 Noon by the Clock, nomibove. - 
— 16 9 '90 fift. 



11 53 18 conej) mtan Nmn, b; a regulated Clock. 
Ss fir the Rf/i. 

r? A ClocJt may be regulated hy making it go from its Time of ii by the Sun, with the Increafe or Decrea& 
of Time, in a Day, or for a. longer Interval, according to the Equation-Tables of Time filLiaing, fir latb 
Dirt of tkf Tear. 

The other Method of regulating a Clock, is by making it meafurr 23^ 56^ 4* from the hfiant of any Star'; 
PafTagc through the Meridian, to its next Return to the fame Meridian^ as brfort obfer-ved. What its Return exceedi 
that Time it goes too fait, what it want;, it goes too flow, of fsrrfiS mean Time. 

To find tht trutTime, or Noon, by a rigulaledCbck Br Watch? 

RULE. Obfervc the Time marked by a Clock, when the Sun 'a Center is on the Meridian, being the lafianl thai 
the Sub ceafes to rife any higher, and is going to defcend. Or, you m^y ohfen/e the fA-o < istei maiked by tht 
regulated Clock, when the Sun has an equal Altitude in the Fore and -After Noon; the A/io'ii'/r of which two hfiant. 
will be the true Noon marked by the Clock. Whatever the Time, marked by the Cl'ick. is ftinrt of or e^CL-eds. 
12, at the tTue Noon, niuil be added to, or fubtra^ed from, the Hours, Minutes and Seconds, marked by the Clock 
at all other Times of the Day, for the apparent or true Time, by tht Sun, required. 

EXAMPLE. LetlhtTimeofobfer^ngagi'viHjlitiluJtoftbtSun, marked by the Clotk, in the Fsrenoon, be<^ ao™ 34' 
and iheTimt of obftr-uino the fami Altitude in the JfttmBon be i^ 55" 36', required, from ibeace, tht Time marked by the 
Clock luien it itHooa, lytheSun? 

Time iH ObfcTvatioQ . . , . jli iqib j^,. _ 



%(,H 



r."- 



2 Jurirval. 

: iH Obrervitiaii. 
ne 2d Obfcrvatien, 
le Clock, 
M the Time tpparrM by the Sn. 



S + Time. 

i-fr.Ti, 

< af.fr 1 ■ 

ock, for M 



,, Google 



lie ROYAL ASTRONOMER. 



1 - 



E Q. U A T I O N (/TIME. 



Thu Inftani of the Paffsge of a Star, or Plaact, over die iUriJiea, is d«terinifl«d by tKe like Hbtmob of 

,'oRReiPONniNt; Altitudes. The farther the 5i« or Siariihota ihc'Meridian, t!a.c /after it afcends or <li:lceDds, 
Hid is ihercfote ihc filter for Obfervation, if equal Altitudes can be obferved.' 

This Mt:hiid is of moll ofe for oblerving ihe Stars, or Sun in his Selficis, having no Change of Declination in the IitKr- 
valoi the two Obfeivations. For, when the Sun has a Change of Dudination, whereby it approaches the elevated 
'oip, and increa/ei the Meridian Altitude «ith the Lfigih cf Days, and confequently makes the Afternoon Arc great- 
er thr.n tile Forenoon Arc, defcribed between the fame Altitude, ihtn the Mean, between the two obiervcd 
inftantE, wil! be hier than it really happened. And the ennirary follows in 'i'ae. Dtcreafe of D^ys: For then the 
Chanj^e of the Eun's Declination being towards the deprefled Pole, the Mean of the two obferved InflanU will be 
fj-.nir than it reaily was. 

The greateft Error in the trge Time, thos computed, occafioned by the Sun's Change of Declination, docs not 
exceed ic'. Eot, to compenfate for that Inaccuracy, we have given a •Tahle far the diffenm Laiiiudei and intervals 
)2Wci-n'ihe two Obfervacions. cxhibiti"g the Mta« hjtanl, or Noon of the Sub, marked bv the Clocks, as correctly 
13 if no Change of the Sun's Declination ever happened. Ste ibit Table fariha- en. 



Of lb, NATURE ef,<i DIVISION cj TIME. 

Time 'is the SuarJJim sf Durai'im, meafured by the Motion, or Change of Place, of the Ctle/- 
Time meafuriJ hj /lu/ Bodies, in their refpeflive Revolutiors through their Orbtsj particularly, by the apparent 
AleiiBa. Motion of the Sun, or the real Motion of the Earth in its Orbit. And the SianJerd M>a/ure of 

Time to which all other Meafure thereof refers by Comparifon, is the Mean Setar Year (fubdi- 
vided into Month, Wctii, Daji, Ilauri, Minutts, iadSeeenilsJ during one Revolution of the Earth {or Sun appa- 
rently) through its Orbit. 

The Mean iclar Dy, and its Parts, differ from the •variaiU Solar Day (from Noon to Noon) and its Parts, as hai 
been fliewn before. * 

The Mean Solar Year ii determined by dividiHg the Number of Days by the Number of the 
jif.'dn Solar Tear. Revolutions apparent, or real, of the Sun or Earth, in that Time, as derived from the Sun's 
Mean Motion. 

Thus, ^3^j;|^ Days in 100 Julian Years =^i^,^^^o^bQ2.i. or 365' S* 48™ 5+' 46"' 19^ i6«. f^c 

100,00110802469, in 100 Julian Years 
Length of the Mian Solar Year. Set p. 7. 

The Length of the Year between other Hie Painti of the Ecliptic differs by many Secmi/i of Titne imrr or left, ac- 
cording to the following Computations from Dt. Ha/lt/s TaHei, (See Faltadium far ij^6J where the Equation of 
Time, and Dtcrta/e of the Sun's Mean Anomaly, for a Revolution to different Points of the Ecliptic are 
fidercd. 



Kll-wtoS^rrur. lar 



: llally; mean St- 
■'«". 16s* i*' 48'" 
"'7^1 E^^^] 



Apptrn, 
•y March \^* : 
8 yipril 19 
n Miy so 

m7-« " 
Sl7-'y " 

to.) 1IJ Aug. li 
*• .a Sept. 11 

m oa. 11 

f-AW. 1. 
^ Drc. la 



— *3 

— 49 

— 61 

— 76 



r. Imp* rur 



4» 


55' 1 


15 


'i 


47 


w 


47 


<7 


* 


"4 I 






¥1 


4 


*q 


35 


4t 


31 


49 


"9 J 



A"s°£l 



N. B. Though the Length of the above Mean Ajlrmnmica} Year is fometimes determined by 
JtfntJ*. AftroBomical the Number of Revolutiom betwixt a given Number of Solftirci, containing a certain Number 
or Solar Tear, idled of Days, on which account the meau Year is commonly called the Tropical Year; yet t'u 
ibi TropicelTear. Length of the Year fo determined il properly the Diflance of Time betiveen the next 'verna. 

Equinoxei, Or Mean Year, before afcertained, /u^^ diflmguijbed by the Name of Tropical 
For, according to the foregoing Computation, therrflpiVfl/Year of Ca»rw is feen to be lefs than the Mea'i Year, by 6j 
Seconds of Time ; and the Trtpitcl Year of CapAcant more by 40 Secendi of Time than the Mean Year ; at the Yeai 
of the A/Bmnn/ Equinox is feen to be lifi than the Year of the ^/rW Equinox, by about 16 Seeeadi of Time i 
wing to the progreffive Motion of the Sun's Afrgtt, and regrcffircone {or Preccflion} of the Efiiimx, in refpeft of 
\t fixed Siari, each Julian Year; making together i' 1* 50*, in a Julian Year, that the Son's ^^n* goes forward 
of the Efniiuue. 

Hence, 



yGooglc 



mi NAVIGATOR. 



DIVISION e/TIME. 


l^ta, SjiUruiriar. 

Sj.iiZ'l rtar. 

A. Dif. 

A. Dif. 


Hence, To \ic* 
AH . . . 


jh 48" 54- 46th the S^^r Mean Vc.ir. 
. io a9 41J, anrweiing 50" 30" Mot. jffi in < Year fMr.Ji. 


Again, To j6s* 


6 9 14. igj, the V™^Y"''< "'Tltne io«hichtlicSuntsturi! tolf,ef.ni«f/ai-, 

jh 4gn 541 46"fc, the M^ar Yeir. 
. as 5 41. »rriWerLng to 61" 50^ nr.rJj Mot. © Apog. in 1 Me»n Yeir. 


But ctrrlfllj, 
it & .7" ,5* 

— jo 30 


6 14 .7, tiieyiiuM/ifl/M/YMr, jKi^r/,, or limt in which the Sun rttu™ to Ihe 

[f,n.c^./,. 

I2il e»aalT= Q'lMcin Motion 1 • „ ,■ v 
00 = M Motion f,„rf5M« f '" ' >''■"■ Y"^- 


1 >9 S9 3* 49 

1 17 i» 
— I ( 50 


11 : 365,15 :: ij. : 36s,*s6S3»9=6 = 16;^ fit. 9m ij. ,6.* ij'o jf i /„,, the Lenph 
[of the XjJar^/ Y.ar, or Revolution © a #, 


I 39 59 tj Z) 


Jt 1 365,15 :: If i 365,159717107, 4c. = 365'' fi'' i*™ c< is^S .tofo nH ic. tl.e 



CnrriH N. B. Ti* >i^« tarreS FroporiioKi artne'-M ; then hiag m Injlanet, thai tit ha-vtfcti, in any fa. 

AnamaKJIical Ttar. AfireB9mj,'whirt ibtS^direel and AnamnUfiitai t ear are eerrtilij deduced en their true Piimil-L-i. 

The Time of a Mean Luniv Year is meafured by tit>tlve Lunathns, or Rivoluihm, of the 
Moon to the San, from any SvaeJica/ Conjnn&ion, to the next, of the Mean and Sua. 
Mow, a Mean Laaaiioa, or one mean Lunar Month, is thus detfiiDincd, 



= E't M. Motion? . _ .^ 
: O'^ M. Motion J '" ' J"™ 



40 14 55 4I! ! 365,15 ! : ii< ! 19,53059015119, *c. = »9* 11" 
TwrfwTijBi which s= 354 D«. 36709011418, m 354^ SI" 48" ^B* 35''' 



1eLent;!liof tliiMn 



iii! or paluical Year confiH of a certain Number of Days, according to the Ufage or Cufiom of any particu 
n; of l^'Cickfomo reckon according to the Days in the Lunar, but inoft according to the Days in the ^.ifl\ 



lar Nal 

The civil Solar Year with U) contains 365 Days for three Years together, and every /iurib Year, commonly calltd 
Leaf Tear, or BiftxttU, contain! j66 Days. Thi* Account of Time, or reckoning, by the Year, is cilled il e 
Julian Account, from Julius Cxfar, who firft inftituted it, as a Menn! to make the t ff/and carrea f.l.ir Yiar. ai d 
its SeafoQS keep Pace together. Ho ordered, in each Leap-Ycar, thz htercaliryYia.y, to b • added to the 2jd 1 f r.-- 
braary, and for the Jjd and 34th of that Month to be reckoned as aiie Day, which 23d b.irg the 6ih of the C,.lt,.ds 
of March, and tv.ice reckoned, called Biife'xtui Die,, gave the Name of SiJextHe to that Ynr. In our Enp'ifh :\1. 
tnanacE this Inttreaiaiy Day is added at the End of Fihr-ary, making the 2r)th Day of that Month, in each ErJ-xti/e 
or Leap. Year. 

, -dffmee; a Mean Julian Tear confifc of 365* fi^ O" O' o"" O^" o" 
1' But'kAf/fiit J'l/arT'far conftfls of 365 5 48 54 46 19 16 &c. 



fertnce, a mean Jalian Year is greater than a mean Salar, 7 
Or, Time that the Sea^ go back each "Julian Year 5 " ' 

rOr. 36S-.IS . ?«/.-» Tear. 

1 Day — ^" Dec* 1 365,2423006021 Selarlear, 



5' ij"" 4of" 4+" 



,0076993979 



"119,997178091 &c. 



f Or, 36S-.1 
\ 30S'^' 

I' ,ot 

at about 131 



Years, m 



m which the Seafons, or Eqainoxes, fall back, 



Or, iiqy 21^ 55™ 56' II''' 13'° a;" Sec. 

or happen earlier by 1 Day in the Juliem Account. 

T*iis fal.ing back of Seafons caofing great Confufion in fettling the Time of Eafier, according to it; original Tn^ 
ftinition, Pope Grtg^ry XIU. took in Hand to reform the Calendar, in 1582 ; whole Examjle was folTowtd ii 
1751, ty the f.riV//« Patliament. 

In the Time of [hu Ntce^t Council. Anno Chrilll 315, the Tfr/r-)/ Equinox is faid to have happened (but was ra 
ther crroncu'idy dcte mined) On the zifl of March: For, by Hal.'r/i A/mamical Tahh, it happened on Mar<.b the 
zri-T. 11^ 2^"" in thi^ Forenoon j which, among Aftronomers, is on A/jft the 19 th 23'' 25" P. M. and not op ihi 
z\'}t oS r.-T'b, according to fin-er //ai/i^fy. Bcfides, we find the *'(r»a/£jiHiic*. accorcling to fffl/Zy, fell on AWc. 
the i9ih, 15'' 54" 30' apparent Time, in the Year 17^6 (See Falladiam far that r^a-) which corref|:onds with 



T a 



yLiOogle 



ne ROYAL ASTRONOMER 



DIVISION e/TIME. 



W<jrfA rhe 20th, 3'' 54"" 30', Morning; and fell about 44'" ii*, later in 1751, that Year forwhich theO/iS///.-wa» 
correfted to correfpond with the new one, or foreign Aoconnt of Time, and likewife adapted to the Errer at iht 
Eifaimx, fallingiinihixift, infiiadBfmthtzotbef March, a j it fell at the NUrvi Qiuxcil, 4nd falU at this Time, 
(hough the Alteration of our Stile to correfpond with the foreign Account was the principal View. Pope 
GrrgnryXin. firft fetlkd the JVctu S'/'A I jS2, who called ^\h Oaobtr l\iK \^\\t forlhat Year, thereby ftriking 10 Days 
out of the Calindar. For, dividing 1 257 Years fince the JV/rnK CsMndl, by 1 30 Years, in which the Seafons fall back 
a Day, the Qu^tieM will be above gi Days, the Seafons were then fallen back. From hence, 1 257 Solar Years, 
fince the hicme CwRfiV appear to have been compleated, belides^l Days, in 12^7 Yeais of the Julian Reckoning ; 
for which Reafon 10 Days loft in the folar Account of Time, were firft ftruck out of the ^n/fa* Caiiwlir, fince 
Diadi: to correfpond with folar Time. 

And to prevent [as much as pe^iblt) the falling Back of the Sealbns in the Month Days for 

AluratUn tf Style, the future, and to keep a ■Conformity between the Grc^n-ian and Jo/ar Accounf of Time, (the 

one in whole Days, and the other in Days and Parts, to ihe Year) Pope Gregory farther oidfr- 

ed, \\tzxvitxy Fourth Hundrid Tear, from 1600, ihould confiH of 366 Days, Mufual; but that every Thru Hundred 

"arj or Centuries, in Succeffion from fi/M Hundreds, Ihould confift of 365 Days only (fimilar la three fuctejjivt Ttan 

'iir taihB:pxiili) and not contain 366 Days each, as formerly. Thus he provided for 3 Da}t,-that the Seafons 

il i-ack in every 400 (inftead of 390) Years. Step. 30, 31. 

In this Niw Account of Time, called the Grecohiah Or New Stilb, from Pope Grigary'vCi Author, the 
al'ons fall Lack but one Daj in 5200 Years. 

5200 
For, they fall back id j 200 Yeari by Julian Accoant = '~r~' = 40 Days. 

5100 
They go forward in 5200 Years, by the Gregeriem Account = ' ' X 3= 39 — 



Difermce, they fall back in ; 200 Years Gregorian Account ... 1 Day. 
Or, becaafe in 400 Gngorian Aatunt, but i Day of the Seafon's falling back in the Julian Account n confidered, 
and provided for, which happens in 39a Years, 10 Yeari* inevery 400 Gregorian, are unprovided for, in which the 

leafonsfjll Back t and therefore — — = 13, Timet 400 Years = 5200 Years Gregirian, as before, in which the 

Seafons fall bsck 1 D^, JnneChr. 

The Old^/i/rwai correAedinft^/iinyto the Vnv, for . . 17^1 

The Year of the iV»«r< CoBjK// 325 



The Years from Hicene Ceimcilto our Alteration of Stile . 

30 "" " " ''" 

len the Stile was altered in England, 

Which 1 1 Days loA in the folar Account of Time, were fufplied in the Gregtriai^ Account, in our Calendar, by 
calling the 3d of 5(/«Mi(r 1752, the i ^h b/ ihu Month. This Alteration of Style reduced the 5*ii/oin ^wi/iFiyiwi/rt 
the Msnih Dan ) as they flood at the Council of ^('cr ,* For 1 ^zj/oiar Years and 1 1 Day* over are nearfy eompleaied in 
that Time inltead of 1427 Years only, reckoned by the yn/Zan ^ci-o«i>f. 

Hence it appears, that reducing the fame Number of Days into different Years of any Kind, does not give a dif- 
ferent Value to ihofe Years in either Account of the fame 1 ime ; which is antrary to cammtn Opinion that thofe Days 
are loft. For, whether we reckon the fame Number of Shillings, in Guineas, at Twenty 'ihiUings and Six Pence, 
or at 21 ;ihillings each Guinea, the afr^f mi/ Number of Guineas by either Accou't, in the fame Number of Shilling 
Piecei, will have but the fam^ Valne, fimilar tothe fame Numbcrot Days inadiiFerent.Niimber of Solar, Juuan, 
and GregerianMeass, 

Of Years. 
The (ivilor common Tear, u of difierent Length, according to the Cuffom among different 
Civil Tea'. Nationi, Some Nations reckon this Year by the^s/arand fome by the Licwr Motion. 

The Cr'i'iV Yiar, in moll Parts of Europe, contains 3b; Days for three Yean fucceflive!)', 
iVar. Lioror. called common Years, and every 4th Year contains 366 Days, called Leap Year, 

Bip^iHe. 
Thefe Civil Years aie called alfo Julian Years, from Juliui C<rJ^r, who added a Day everj 4th Year to m 
;as he cxpedled 1 the Civil and Solar Account of Time keep Pace together ; and keep the Seafons, hy that Meant, 
marly to (he fame Days of the Month. 

The f;V7 or common lunar Tear is like wife Cgra^/t'/, or Vacant. TheCfl»r«/(«confiftt of 354 
Cawipiett. Vatant. Da^-s, al the Eiid of which the Year begins again. The Vacant, or EwAoUmie Yenr, i) chat 
wherein a Month is added to make the Luxar correfpond with the folar Account_ of Time. By 
thi& MethoJ, the JeiMi kept theii' Account of Time, according to the Lunar Motion. Hut,, by adding no more than 
a Month of 30 Days, called Ve-Adea; every tbird Year,, in their Acconnt, it fell SboK cf the>jW Reckoning, in 
that Time, by about 3 J Days. 

ST 



W NAVIGATOR. 



DIVISION fl/ T I M E. 



The At&IUmaMi ukd the L«iar, Facant, oiEmbolimic, Year, u icwas fettled \yy Romulus Ac 

Stmen Trar. lirft King, aod Pounder of Rtmt, who made it conftft of ten Lunar Months, or Lunations, and 

therefore terminated 61 Day) fhort of the folar Year j by which the Seafons in the Roman Year 

Vatottl, Lunar, were anfixed, and wanderingi in the Month days on which chcy fell : Whence they had a Table 

publiflied by their High Priefl to appoint the Time of their Spring aod other Seafoai. Juliei 

Ca/ar, confideriag this Difficult, reibrmedtheGi/jrBi/«r(a!aforefaidJ by making the Year confift of 36; Daya and 

Six Hours, reckoning the Hoois every fourth Year only, confifting of j66 Days. But the JuLan Account of Time, 

dated, requited a ftill farther Correction, by the Equinoxii failing back about a Daj' in 130 Years, and unfixing 

the Times of the Seafona, and the Fall of Eapr, and confequently of the other Ftajii ihereon depending, Thore 

fore Pope GREGORY Xtll, took the Ca/^Mlir in Hand, an J, in the Yean 582, ordered (as before obferved) the 

jthof OQubtr to be called the icth. By this Means he reftored 10 Days the Seafons had retreated, fince the i^kent 

■tl, AnttoCbrifii 315, and reduced the JuHbhXo the Gr^^or/mi Account of Time, Who, by reckoning 3 Dayi 

n |oo Gregorian Years, for the Time to come, made the civiJ or feSrical, nearly to keep Pace with the Stdar 

Years. 

Cy MOHTHl. 

Meo/i. The Momths are of two Sorts, afi'anmnical a\A ciiiiL 

Jfirmmnkal. The aflnnondcal Month is the T"ime in which the Moon gtKi through the ZtJiar, and beyond 

Chiif. and is either ftrhJUal o\ finorlUa!. 

The Ptrieiital Month is the Time in which the Moon makes a complete RevolatioD from any 
PeriBdical. ■ Point in the Eclipik to the fame again, which, at a Mean Rate of Motion, is in 27'' 7" ^y 5^ 
as hiis b>:i.n computed, 

The S'ynvJicai Month, called alfo a Lunaiim, is the Interval of Time between two next 

SfnoJimf. Conjonaiona of the Moon and Sun, being zg* 12" 44" 3", at a mean Rate of Motion, as has 

becti computed. 

Gvil. The Gi-;/ Moiihi arc limited for die Purnofe of civil Life ; and differ in their Namts, Numhtr 

of Days, alfo Beginning and Ending, according to the Cuftom in different N; 
The frfi Month of [he Jpwijb Year happened according to the Moon, 
Scftimhtr i the Second Jwi/A Month in Stpitmbtr and Oaebir, i£u O. S. 
jfntifnt. The Firfi Month of the Egyptian Year b^gan on the 29ih of our Juguji, O. S. 

The Ffji Month of the jS^abU and 7urki}i Year began the i6th of oar Jufy, O. S. 
The fiV/J Month of the Grfoan Year happened, according to the Moon, in ou( 7<MKand7«^i ±t Sicondmjuly 
mAjiugiifi, y^. O.S. aifetdown inthe lolIowingTaii, ufcful in an/w/if Aftronomy. 



n our Aup^ and 



■ -fay the 




The Ji 
jJewiA) MoQthi. 



3W 



^Sbiiat . . 
SMv . . 



uEpifbi . 
■.J,M/feri . 



March] 

May 9 



JRiUiia II, . 
Jtmadah 
Jmaia II. 



""Tlity fl^JiiD=ys»iihcEnrt 
of tach y«rto keep 'the fame 
Monthi w ib< lame SmfiM. 



N.B. . - 

td the Nimrj dF W 
iifcd by eac^ Nation \ ' 
cd good Authority. 



Common. A cmman Month is divided into 4 Weeks; of which Kind of Months there arc 13, o 

Weeks, in a Julian Year j befides i Day over, or a in BipxIiU. 
H'lik^ A Wevk is divided into 7 Days, whofe Names are known. The antientCM/ZAigare Names 

to the Days of the Week, from the Names of the P/aneti, which they fuppofed to prelide over 
hem The i ft Day of the Week they denominated Sun, the zd Mem, the 3d Man, 4th Mtrcnry, 5th 7*//»r, 
6tb Saturn. 



,, Google 



nt ROYAL ASTRONOMER 



DIVISION (/TIME. 



Dot. 

flalural. 
Arlifdal. 



0/J3AYt. 

A Day U either natural or artificial, in Propriety of Diftinflion,' 
The Natiira/Da.y is divided into 24. Hours, from the fame to the fame Time. 
The Artifaal Qny is the Time from the Sun Rifing to the Sun Setting of that Time, 
TheNatnral Day ia Afir«,c^kal or Ci-v,l. 

The AJIrommUal Day begins at Noon and ends the Noon following, Allronomers find th 
Limit, of Beginning and Ending Day, fitteft for their Purpole of Computation, by the diuri'; 
Sevolution of the Sun from Meridian to Meiidian. For the Days would be much more a.-iryaa/ [as wai obferved) 
f they be_;uii and tetminated at Sun Rifing or Setting, or any other Time of the Sun's diurnal Revolutions, except 
a; M.idi:ighi i which yei would not, fo well as Noon to begin Time it, anfwer the Purp^fe of Calculation. 

The fir/({/&, French, Datch, Germant, Spanijh, Parluguifi, uniEiypliani, in common Reckoning, begin their Day 
at Midnight, The ancient Grtiki, Jewi, Bahtmianf, SUtJiam, and modern Itqiaai and Chi/ufi, did, and now bcgii- 
Day at Sun Setting. 

The aniient BabyUnimi, Ptrfiam, Sjriaai, ind modem Gruh, did, and now begin Day at Son Rifing, according 
to the civil Cuflom of each Nation. . 

N.B. Tlie//a/ii«ureckon thenaturalDay by 14 Hours of the Clock. Other Natioai, by reckoning twice tweWe 
of the Clock, prereni their Clocks ftriking 24, [like the haBaB Clocks/ at one Time. 

0/ Hours. 
HuMr. An Hour is divided into 60 Pans called Minutti. 

The Hour is either equal or unequal. 
Eevei. An ^fso/Hour is the 24th Part of a mean Day, meafurcd by a well rrgulaled Clock, 

Watch. 

Vniqual, ha wujmdI Hour of a natural Day, Is roeafured by the San'iuBtjual Motion in the frliftir, 

inclined to the Equator in an Angle of zy 28' {, while ij", and the ^'j of the lacreafe of R. 
A. for a Day, counted on the EnulnoAial, fuccelTivcIy p^flet the JlfciWion. 

An uKiqual Hoot is otherwife the ,'j Part of \Me Ariff-dal Day fioni Sun Rifmg ro Setting j and is alfo the .'^ Part 
of the Night, from Sun Setting to Rlfine, as reckoned by the Jevjs. Thcfe une;|ual or 'Jt^ifli Haun, imrtafi and 
dccrtajt with the Length of Days and Nights. For Length tf lv«\^ »r uniqtial Uauri, /ii Ladiii Diary far forma 
Yean, b^ ihi lati JWr. Henry Brighton, F, R. S. 



0/ M I 



e s and S e c 



SirxfUi. 



T, 



AMiNUTE of Time is dividedinto 60 equal Parts, ciWed SfceiiA, and each 5'/^i»:</ is divided 
nto 60 equal Parts called Thirdi, and fo on, in a Sexagifimal Subordination. 

The ')ruii, Cb-ildtani, mi Arabiani divide the HiHir into io3o equal Pftrts, oj Scrufki. 
;oniaining 1 8 Times 60 ; whereby one Minute contains 1 3 Semfiti, 

0/ C-rchis, tr Pekiods. 

A Cydi, or Period, is a Revolution of Time. 
Cyriri The Cycle of theSsw, or Damiitita/-Lttter-Cyc\t, is a Revolution of i8 Years, in whici; 

Inltrtial oi lime, the Days of the Week in the Julian Account rctnrn to the fame Da; 
Month, And the Sun's Place nrver varies every 7 Timet 4, or 18 Years, above 7 Times I'j/^ij' 

Month-day, not 50' in 100 yuliaaVan, accatdingto Firgu/onsA&ronomy. After the Ctmpletien of thisCyu 
the Week" days begin the lame Order orer again, with refpcA to the fame MoKii- ,yi of the Jiliat, Reckoning, whi.:' 
is only interrupted by the common Hundredth Gng-rrioa Year, coming between See "a.'lei further tu, of tbii CjcL 
fsr fiuaiag the Daminkal Lttur at Si^h, ai-echKg I1 koih Stiln, far any Tear befre and jince Chr'tft. 

Tt-e Cy<k of tl e 'Mmrt, commonly called the Golden Number, is a Kevolution of 19 Vchf. 
Maaa't Cycle, in which Taterva'of "^ime, according co the fu laa Account, (inciuding the 6 o>M Hours yeany 
the ConjunAions, Oppofuiona, and other Afpefisof the .Moon with the Sun, are within an Hour 
and a Half of the fame Situation as thry were on the fame Month-days in the preceding Cycle. But. this Cycle 
int^tci^pMl a Day, l.ketheSun's Cycle, by the common Hundredth Gtr^or/iur Year coming between. Seep t 
Ar ab.e, far iljtr o«, fir f tiding the Goldea Number at Sight, according ta both Sliiei, fir anj Tear before and fitiet 
arifi. 

The Ihdiction-Cycle is a Revolution of 15 Yrars, onlyj uied by the R^mant fo- de- 
bdinian. termining the Times of particular Payments by the Subjcilsto the Rep.btic : Wttich Cycle w: , 
founded by Corflantine, In the Year of Chrift 3 1 2, 
Stc Rulf! fir dtitrmining the Number) of each of tbefe Cytlti, arithmetically, farther sn. 

Of 



,y Google 



NAVIGATOR. 



0/ ^ F I X E D S T A R S. 

They ire fo called, bccaureof the Fixtd DiJIatta (hey are genenlly oblerveJ to krep rmm one mother : Their 

jifftar liggrr Is pirent i:Ariid/Rei(ilution io the Heaveni to (be Right acifing only fiom the Earth'i Rutation to the Left on iti A 

lit saiiJ Sigil tbaa They appeir of difiiretit Utagnruda from their dillerent, but immeDfe, Diftineei, at which they are placed, in 

ib'tmgbaliLJuft. hjlmtt Spaci, from our Sight, ind art fetn much bieger by the nakeil Eye (hao thiough i T(i(™,-f, maenifyi.ij : 

Timei, taking off the fcjttored Rayj, cauGng a SaJiMihn or &iMi.:'aiicn lo oor Sight; aei tbertb< i 

rs their tnie Appearance fo many diilinft Pciinrt'-of native Ligh-. ■ If the Stars flwne with oDr«,wed ai..l not (^r tkiy Jo) with na 

Lii^ht, thi:y would be ai invifible isiihovt the UTe of Tdcfcapo, a* the Satellite] of Jafitrr, any one •!' whicli appeal bigger, when viewed 

1 feleftope, lh«n the En:ateftof the f/mrf J(ari. 

T}ie Miimberof Fix.-ii Sian dilcovcrablc by the naked Cye, in either x\it Nirtbitrt or 5oBlirrfl Hemifphcre, ei:ee4s not tthtajesd, v 
they appear, at fntt Sigiit, to be im.umrakh ; but the Dcception'ii in looking a»f^fedly, and not Jifiintify, upon them. 

ilieBiiTisiiCATALacui, (ooClting ofa Wge Number of Stars, which cannol be fcea without the Help of the Ti/>/»^, counti not ibovt 
]O0O io bath flvmirphces. 

The Light of the M«< to thii Earth in the Night-Time, b^ing much foperioi tothe faintglimmeringLightof 
I madr KH It Stan, itfoilowi from thenre, (hit the S'an were not defigned for giving Light ia-the Night only ; becaufe many ji 
,isbr in ibi than irevifible to the naked Eyeieijuire the Help of aTi/c/cipt lo dtfcnfertbem. And, ai our .^un ii Airroim'^ed v 
l^igBl islj, a SjOtmnl PleiHli and Cw^ri, which wouU be inviliblc' from iht nrtiffjiirj Sttr,- it it probable that every Star i) a Sri 

a rcniate 9vltein of fltniiary Bodie), ihaugh Inviiible-to us at this DiHanee. This Plurality of innutnerable World) ouitt 
mfift.wiIhtheiDfinkef™tr, »yj«. and (?™i«r/i of the Cbiaio. oi- AtL w. BiHot.D ! - 

■J he S/ari on accouit of their ditfwent Appearance, hii-e been Jiilributed into SwC/jJrt, at Ma^nhudn ; the 6lh be- 
SimnifSixMag- ing the lead Megnituie »ifiWe- to the naked Eye. TWn Di/hibuiitn beinj made long before (he Invention of T.V"^t 
ittJariiertfi^A- thofc Stars which cannot be feen without iheHeipof that Ififlrameot atodiHingulfced by tht Name of Ttbftrfic Sicn. 

"'^' ""' 0/ C O N S T E L L A T I O N S.- 

The Amunit, to diftinguilh the Stan, divided the Jwr^y Sfhfi Into different Cmfietlatina, ai Colleflioni of Stan, 

Scar! riadily *ir«m. CtuilcJ next one inoibet, in (he Huveni, by drawing about them the Out- '-.lirs of di^errtil THir.g) and Aniaiali, a(- 

ct>tdin^ a; they fiippoftd 1 Collection of Start to tefrefeD(. Thofc Stan, wliich could not be brought uiid<^r any deft ^n- 

ed Forma, were drtitniin.itcj t-'/crwiJ Slant 

Thofc CnHfidlailtra, inihk^i'imxfumdSrdri, are now rcprtfented on a Cr^^id/C/sk, by which any parti^ilar Star, and iti Situatii 
Refpea of another, is rradlly ktwun and diAinguilhed, by giving the mell remarkable Stars'the dioft rimirkjble Places. 

" : Number of ihcdrriVir Confletlaiiona if 4E, and the Number on our imJfrn Globes about 70.' Co Maitin'i (7/9^1, iritg an Im- 
iM/mSiKEi'i. Vfinfrint Bayei't litiir$. Tbifii&Latm of tbi Creek Alphabet art fat « i/mc(i ii» Magnitodei tf ibi Sun m la. 
CmfiilLuiit, t:t3'k actirditgll lit Ordir of MigialnJi/rai a, Jinaliag ihiSur 1/ lit frfi itigmituJi ; & litmolinf thai of ibt ftanJ, Itc. vbcn 
iy tbitatuaiiar M-irmuiii, and N^mn tf ibt Stan are ei irtly dtfmd a^yd dijligguijhca, at if ibrj loirt firwn ui m ibi Hiaveas. See Mai 
tin's GlOBIS, mFlKI-firvr, Umlon. 

The Starry Utavim are divided into ttra Parii, iH, tlie Zodiai, of t6 Degreei Breadth, quite roond the Heavens, taking all the planetary 
Otbiti, and Orbit of the Moon : Containing 11 Oonllelletions; A'Ut, Taurui, Cimi«i, Cancel, Lit, l^irjo. Libra, Scerpi,, Sariilaria ~ 
triarf^Ajuarw, and P;/fri, In the middle of chii Ziuu, or Belt, is the Edipiit, or Circle which the Earth annually defcribea, ai feen 
[be Son ; and which the Sun appears to itefctibe, as feen from' our Earth, ad, The Righ* of the He»vcni on the Nerib Side of AtXjy- 
diac, containing at CmftAnfoa. 3d, All the Region on the 5wri Siifr', containing 15 Cgn^f/W/ni. 

The jlniiatt divided lite Zodiac into fvj^vt Pane by the equal Droppiogof twelve Parti of Water, {tXtach of which Parti dropped out, thty 
noted a particular Star's Riling) the whole 11 1'atts having firit dropped thiough t Jmall Vegel iaOt t Rtcemr, from the obferved riCng of ibe 
fame Star to i« obferved RiHng the Night following. 

The Niinea of the CsafiiHaiiom, and different Stari, obferved in each Hemlfpbere, by different AArODomeii, llace the Improvement of A(. 
ttonomy begun, »ie as follow. 



ANTIENT CONSTELLATIONf 



CtpbrM, 

fioolts, Ji^efbilal 
Corifa Borialii ' 



Cyzmii, GaUiaa 

Per/.,. 

Serpttnanm, Opbiuduu 
Serfiai 

jfjaila, Vnltnr 

Delpliaai 

EgMula, Eqaifcflia 
P^afur, Equu. 
Andromeda ■ , 



CepL^-ui 
Northern 



Eafle 



Dolphin 
Horfe'i Head 
flying Horfe 
Andromeda 



:| 



AM^JSKT , 
yClOOgle 



nt ROYAL ASTRONOMER 



^ I X E D S T A I 



JTIBNT CONSTELLATIONS cowioawl, 



Ctprittn 



Eridtmia, Ftuvini 
Ut<., 

Catii Mtjtr > 

^£1 Nmih • 



The River 
Hire 

Greit Dob 
Little Dog 



Phlrmy. 


Tjct,. 


Hrv'Hut. 


I8 




*7 






S' 


»3 




19 


3S 






3» 




SO 


»4 




it 






19 








38 




19 








3* 




17 


19 




»' 


4S 




4 


7 




10 


7 






37 
'9 

7 







f *« 

.^la, Avi( Indie* . 
j^fii, Mul'ca . ■ . 
Ct^mi/an . . . . 
Tiiaogitlum jUgraUi . 
Pifdi nUM$, Filler . 
Dvedt, Xiphiai . . 

wy™. '. '.'. . . 



Ngjh'tCovi; , , . 
Th« Royil Oak . . 

Crane . . . . 

Plixnix . . . 

Indian . . . 

Peacock . . . 

Bird of Piradife 

Gee or Fly 

Chameleon 

SiHich TrUn|le 

Pljinj Fiih 

S^vnl Fflh 

American Coole 

Wiler Snake 



Camilcfardiii 
Monceertt , 



SoSiclki'i Shield . 
Liiard ... 
Camelopird . . 



mUtftfgj. 



The Luminiia Tnik. lound the Heaveni, appearing fingie in fome Placet, and dc 
}fay, ftum i 1 Whittoeri, is ciufcd b, lhe«™,M« Swm fcaiterrd ihertin, C/kW<hJ« 
or which cm be giUia^iy Icen but b^ Che Meani of good Ttir/tc/m. 



, called the KiHy 



Of LOCID am/ ( 



I SpOTi 



« fbf Hbavbhs. 



Seteril limn-m Sftti, ia the Heavens, appnr Inagnilied, and more luminaui, being Teen (hroagh good Trir/nfti f 

•trti LaiiJ Sftti. but a.' viHd of Stan. Ore of which SpoU ii Teen In AndnmiJa' i G\rdlt, lirii oblcrved in the Y<.ar 1611, by Sh'. n 
A'anai, wiili wUri^ Rtyt near In Middle. Thit Awngui -^/of it lubje^t Co fevenl Cbatga. .in.' is fomeilmei iatilit>|. . 
Inotherof ibr(i Sfati i> fern near th. £i/,^(c, fcetwecn the HtaJanJ Krw <f Sa^iiiMj ; bung Qiui], lui -v rj ..jt r-wi, A 7Hrd ii 
heBickol CJMir, hrin^ too south to ce ^iCble in£sj^^W. A Ft-rib, of a li..)llcr Siv. ii feen befoie ^Mi>b.r> Riiht Fooli 
Star in it, ■by whicii It s[.|Kan Uie htiElitcr.' A Fifib n\tta in the Corftellalion of I erc-l.i, betnieii tue Sl-is or I ay r, ^, and ,, 
»i ■ 1 1-- \ i, liioiiEii appe«inE but fmall, cothc nalicJ Eye, when the Skf iickar, and the Mn'on abfent. 

Titere 



,y Google 



crJ NAVIGATOR. 



FIXED STARS. 



Thtte tre(btfid««thiApp«Taiica Tpoke of ) f/w^i 5r*n in tha Hrtnin, fo c»tW from (!i«r ipptirioj of • dim >nd miflr 
ClaiJj Slen, Light to the rgktd Ejre ; but appear tbiDueh i Telefcopr, la be bmii li/ymiuitrt Ptrti of ibi Sly, c^ntiinineonF, or mot; Stirs. 
• Fitxoflht{echM,fySianmmcatioattbyI'ic/tmt. i. Osj, utthe EntmnityoftheRigfit-hjriaof Pfr/™i. %. Ow, in the rinafl 

of the Crat, 3, Out, unforOKd, sear the Sting of th> Sarfiu. 4. The Eyt tf Sanitary. 5. Oir, in the Held of Orhn, In tht frjl of 
liitierDore Stuiippeir, tbrough the TeleCcfnw, than io isy of the n&t though 11 taut been reclconed in Orim't Htai ; end abave 40 in 
the Oat. Tve are vifible in the Ejt tf Stgritiny, without ■ TeieTcope } bit fenni more appear bf the Vft of that Inltrnmenl. Pla^JIcni. 
obfnved > c^w^ Star in Che Bow of Sap'uary, conuiaiag many fmill Stira, C^ni and Flamjhrd obfirred ona between the Crnit and Uii'J. 
Dig. appearing fulJ M State, only lifibU by ike Teleftope. The two viti'ifi! Sfttt near tlie South Pole, called the 
MagiHaaicClo^. Magtlfimc Qaid!, bySiilon, refcmbliBe theM//*y T^y, to the naked Eye, appear through Teleftopei to 1^ a Mittntt 0^ 



ic Cloudi. 

naU Cloudi 
, th- moflrttnlrkableof all the[/(wrfj> ^ron li inlhe inrddle of Onuf'tS'jatJ; where Awn Stan (ihm o! which are c'oretngether) [cem 
IC throngli a Clnud, lery lucid near the middle : but faint and imptifta about the SUrll : looking lik« a 6ap in the Sky, ihtoueh whicli 
I Part of 1 irigtiir Rrgicr. Though molt of the c/mi^ f/^rri are but a few Minutei of a D^ree In Breadth, yet, ai they are amoni) 
tht Fix/d Srari, they muft be enty OBC largei Spacei than out 5«jiir 5^ni ouu[net{ U in which theie IceitW to be a, jurfttual agimtrruptca 
Daj, among iiuiuinerable Woildt. 

0/ New Periodicai, Star*. 

everal Stan aft dcfeiibcti by m/iiM AAionomeri not now to befoondi and othen are now viGUe to 



iiinble. 



It difcOTfrnl bj Cinirlliii Cirmu, 
II fern for 16 Monihi in Sucnlt 
vardl it dec lyed [raJtaUj 



Luft. 



he %ib ef NtvnJ^, i;7a, \aCafn^'\ 
It appeared, at lirft, bifjct than7i;;i'B 
rand Magnitude, till March 1573, whei 



rriiJical Siari. 



and Mapiila 



(n»U, at made i 
»n decayed in hot:. 


eriH, fo b 


Uh,..- 


.gnitnde, 
aOaOtr 


which < 
.6oja* 



n the Keck of the Sui/, which be jndgedwai not v 



n Tjtba't Time, not yet wh«i 



• tbt titt <f Avtoft-, 1594!, Oavld Fatntim obrerved the SliHa Mir 

mall, lino-difapptjiing and appearing, ftritditallj, fcrenTimeiin fix Yei 

I>aya logrthtr, which ii never ijgite eitin^uilheo. 

■f Tar t6oo, Willmja-^mu, i.it.oitni nbng^i^U Star in the Neck of the S«M, wbi. 

1 to haTedifjppeared III! the Years iSsTi 1658, 10111650, vibail rrnvtridiuJariBirLafii 

now of the jtHllfft &1B. 

It Tiar 1604, K^rr, and leTerai of hi) Ftieodi, fiw a una Star near the Heel of the Ri^ht Foot of 
fpaiklinj, that it exceeded any Thing of the Kiwi they before hitl lien, who obfened that it wai every Moment 
Colouu of the Riinbcw, eitept when it wai itiar iti Htriter, and generally afptared white. It eiceeiled Jkfi 
ivai near during the Month of Oflaitr, hot diftinguilbed from Jnfinr by liit fttadiet Light. This Stir difappean 
Fckrvarf following,, and haa not finee appeared. 

l» tht Tiar 1670, Jul) the ijth, /irve!'*! difcoTcred a iw Star, which, in CV?ri(r following wat fo decayed la to be hardly percep<[hl , 
In Afril follDwing, it regained it] former Laftit; bat wholly difappeared in Au^uft, In Mxrch %6-]% it appeared again Terf fmal', dil'ap. 
ptaring tver fince. 

In Iht Tar 16SS, XMviSttTt 
1% ibt Tiar i$7t, O^,; ob&ri 
Bayir made hii Catalogue, 

Of Cbahce* in the Heavihi, 

Afiiay Stan, lelidet thofe before -irMntianed, baee been ohferred to change their Magiiitiidei and Appearancei ; bnt a- 
Ptriadiial Stan none of them were ever obfuued to have T«7i, 'til concluded they cooM none of them' beCiaiMii having do Pardllat 
eaaaaiifit. in their greateftLDflre and MagnitBdei. It appcirt probable, that thefe ^'oi^'ni/ 5t««, hating nfl Cinftera of dark Sftfs, 

make tlow Rotation! on their own jjm i by which Man they i£faf pear when the Side covered with Spsti i> turner 
toward) ui. And thofe Stari, breaking outof » fudden, witbfuch refplendent Brightncfi, are probably Sum •/ tthtr Siiiimi, whole Fir/ be- 
ing much eihanlled, acquire their Blaze and Splendor, continuing for fome Time by (he AcceiTian of the Cornell of that Syilem, lodging 
on their Surface, fir, tbii ^aeeotding to Sir Tfatc Nivion) ctbttn ti hi ibi grtaicj! Ufa and End cf iht Ctmaarj Pan ff a Sjflai. 

And M.Maifimii, in hit DlOertationof the Figutea of the Cdijliai BoiEa (p. fii to £3) ii of Opinion, that /sim Stan, by their pro- 
digiou) fwifl Rouiion on their Axa, affume not only the Figuia of^ flatted Gltha next their Axef, hot, ty the great cmriftgal Tone, ari- 
Oog from fach fwift Rotirioni, may become of the Figtire of MiU-Sonn, or even be reduced to jEn tirailar Plena, lb chiq, 11 to be mvto 
iaviliblewben theirEdgei sre'tomed towatda ut : AtSttarn'i Ring itinviiible in fuck Pofilionl. That. wB«i vetj nteentrie "' 
mm, go round iny/rJrSrji- in OrWti much, inclined to Itt EqSator, the Atttaftion of Ihe Plineti or CoiMt), in the' 
the Inlinelia -f iht Star ; on which Account, it wilJ appear more or leli large and Iwninout, aj its Bioulfide il tn«. 
u(. And thui he thinki we may account for the mffartnt Cbairgu ef ibt Magniudi and Lufiri ef thtje Stan; ai likewift for theii appeari 

Some of the Stan, particularly Ara„rai, have been obfcroed to change their Placei, in the Heavens, above a MIntti of a Degree, in H 
fpeaof the Situation of other Stati. Bnt whether ihit ia owing to any ru/ Motion of thC 3(ai«theBi(elvei 11 the Biifiiifclk (tf mai^Apilidi- 

cm charge) Its Place, with Regard to ahjtItitSpan, it mull, in Time, oecafioo »n aff<irt«t Qunge IB the DiOancn of the 
I'her, And, in fuch a Cafe, the Placet of the neareft Stan tone being more affefted than ihofc. at a greater Diftance, theii 
'ill feem to al'.cr, though tlie Start theoifelvei were really iismivtsUk On the Aher.hand, if our Syfltm lemiins at ReH, 
iri of other Syflcmt, hive rial Motion, in tf ipeit of Infinite ^paee, their Pofitions will be changed thereby, and appanni 
"t, pccording at tliofe Start »ie neater or farther fIo^^ oi ; and tb« f*iftti or ilowex thofe Motions are, and Ihejt DlreftioB' 
to our Perception. And the fame will happen from rral and difftma Motions in tlie Sjftemj ihcmfelvet. 

— - - ■■ ■ ■■ " ■ — ■■ -prefent. abaunwrtiWrart'Of aJJegree IcfithanP/eiriiyJ-— 



Plaant 
or lela turned tnwardi 



and any of tl 



Placet, I 



it left Tuited 



The fhUjtity of the Ecliptic to the Sfinflial 
(lined it. For moll of the Aftrono " ■ ■ 

it beobje^ed thatwec4nnoCd;p<nd 
their Infttumentt, it may be urged, 1 
cliptic Obliquity abont i{ Min. of a Degree lefi than Tycii difl. 



Etfiplle Ohliqaily mined it. For moll of the Aftronomers after bin found ihii Obliquity to deeteafe-graduaily down to lycba't Time. II 

-'- - ^ . - -• -. Obfervitioni of the JnTiarr AIliDnonieti, on Account of the InairtBvJi ii 

" - ■ on, jnrt vet ilamjlitd mikes the \ 

in hatJly arif* from ibe diBerenrCor. 



u 



d by Google 



146 



rit ROYAL ASTRONOMER 



FIXED STARS. 



t&tirkot tht IiHInnuati with wbicb tbcfobCTtd, Par, Vtitmy IlMd IJ14 VtHl b«fm 7j«bg inJ tbe (rnAa/ Dccmie of Ecliptic 
Qhliquity. nrarlj coircfpowti To the DtStttatt of Time betnWii tWe three CfhT '^vamm, Thn^ the VarttiwD i>f tht Ohltqirit; li 
hewn \n Dr. BtaAUj, to depend on the Pl«e of ih* Mm'i M^ lliiough in R»r*lati<>n, f^ Tdi. f. 3J.} Vet, if *» conjidcr that the 
'Jitih ii KAmf-rfia, hut X fitiuj Sfhtri, whole Ihvita jOit it [tfuhtn iti Eqntoiiil Diioetn, nd that the So end Mum itf toiRlmallr 
ibtiqucly lOinc upon the (niier Mili of Miller ibmit tJie EquHor, and >ttnaiii| it to ■ netnr and imrer CoinciilaK* with (Iw Ecliptic, 
I wilt 'ppeu in lane Deptt piobeble, Ibil the Atn»€tiaet [onAtatly diintniA tht Aigk betveea the Plioei of tha EilifHt and Eftiuti-^ 
Star iiit Wptobible, (ai the WotMIs to bedeArD^ed, or rome t» > Ptiiod, ttaaiiitfloxhaSiTifiiirn} that t^c aMbW ArtraAisni of aH tbo' 
'lanclibam Tciukncy lo biing the P/«imi of all thiir Orhita to » AatkCvmiJaiai 1 Tboufh tllr EAd be b teaU MMt MpredKC * ' 



• l&O itMffr .^, 1 



A> f riw fimJlJktiriA im immrul 
V^tl tmi^ lb, Ihr y EiMat, 
7h, IfHdtM ^ MfOm mithiCn, 



hmfHT 
YMb, 



: Ktnatkable RMdixa of Tune ii 
ffw, the Dnih af .^^Hub-the Gnat, Ibc Birth of Ch>i _ 
e determiBed according to the 711/iM Period, Ap of ihc ^vM, and Yea: 



called MfMbmi, ot Radical Pli. 
r RalilM of TiflK. Tht 
""" e of Rtm, of Kit. 



remark:; 

According to the Year 



I L E jE 
f the J-lU 



RAS <i»^ EVENTS. 
> PtrieJ, 0( Crealitti, and of Chrifl, 



RemitkaUc Xrai, or fmiiR. 



T H ^ ii - _ i ■ ■> .. 
Cteadoii of the World, by StroHlnia , . 
Delate, or JVo^'i Flood , . , ', . . 
jll^ritK MoBircfaf, b]r ti'mnd .... 

fiiith of ^H-thtm 

BegiEDJiq of the Kingdom of .,4^'vm , . 
firginningofthc Ruiedomof.A£riii, ^fCaiif\ 
Dtptitmt of I/rat/ila (tarn Sgjf I , , . , 
Their Enttuict in C^iuM, of JiiiUm , • 

Dedinaton of Trg 

Be^nninjof KingDtfvnTiIltlpi , . . 
Foundation of fg^BM't Temple . , , . 

jlrmtmU Eipcdition 

jiritm, the I. Kiai of ihe lUtJu . . . 

Mwbmvithcll. 

StfarmmnU 

JfticmiV 

(UrJicMV. ; . . 

PtrMHaVt, 

Cuwu VH. 

BieiRHiKo of the (7ri-ri Ot 

Calmiam JKmt of buiMiDg R< 

M%A of NjttOKilltA> , . 

DMtulTIan of Satiht . . 
D^SllbMl of MWm'* Ti3npk 



«*(* 


'497 


:sr, 


n« 


ikit. 


loto 


ion 


917 


%07A 


84I 

79! 


I'U 


-,.«l 


76E 






11*11 


6,6 


11«^ 




1174 




1»7« 


7(> 


330* 





Remarkibl; ySnu 



THE 
Pfr^a Monireh; /bunded by Cftwi , . 

ttahtf Mfrdlim . , 

Be^flninfi of the Htitn of j^i. Lt*ti»atiiiit 
Rejianinc of Dtmlttt 70 Weeki , . , 
B<ciniBn( of the Pfhftwrju* War . , 
DXATNof ALMAHDea iheOaiAT . . 

RMIonlian of the Jrm ' 

CamaiM of tht I^AMlir V JUh C^» 
Bepnolni of the Reign af Hmi , . , 

SfiwipMn 

Battirat.4flm> 

Talcing of Mxatdrit 

.CEr* of tbtTitle of ./£wiiAm .... 
TauT^aAof Caaiil'-aBii'M . . 

Death cf hmJ 

Stpuiid X.jia!CR*.iiT, bjDitiij^ixi£*itt 

7,v,Vt±r ot C»niT;VtATa . . , 

flf/rrif;« of TW"''" 

D:^/r/M PaCtaiwn ...*... 
^f»of CK/fli:f/«lheC«IAT . . . 

dmUeff/'ii 

iViAofHtciaA 

.^tA of yilDXJXtD 

■yaMtC3lMra 

Mra of tbe Refoimition 



0/ ^ R A 8, C Y C L E S. «^ P B R I O J> S. 

. IB StlmmAtmtr Cydei ti xtuii 19 Yoan, i»d Xmmo liaAWai of ijVMt*, mnltipljed together, prodote the great ^n/ui,, 
of 79toY'eani hmingiti Beginning pSAVeari bdbte the fiippofeA yfrw of Crrdnin, when all the three C^/<i began tofxthei. Aid 
&M JWIM Pmai ii not yet cmnideated,. it tbcrefoie eomprebtsdi all Mhcr Cjtki, Mri, and Paitit. And ai there i: but tmi Year in (ha.- 
i>hoM^fi«rPttiod, haTJng the Jamn WamLiti or Patta w the ihrm whole Ijfih, of which the faid Pn-nrf ii coinFoled, therefore, if ii'^7vwu 
■^-id marked, in their Writiaga, the Nawbcrt of t^ three (^dca for iha Yur io which any rtmulcable £>enc, or cumoraUi: Tram: ' 

ipfiened, there eoold have been M /li^nM about the Tine of i It happening. 

Itfiadib, rimri/rhiJaanP^riidJ^tttCt^J Tbe DUiiJJtmf, or reputed, Mt» of Chrift'i Bitthi fceing kbaat tbc Ead of the 4711 
Year of the ytbaa Period. *- 

RULE. TtiitCumnnti-i/aa/I^Ji^ji'i, lbeSiimwilttllr]ayuaPmi>J, 

Tt fad ibt Tcfr tf tht Tiliaa faitd hffirt lit reputed CnEiif tf CbriD * 

RULE. StiirMa liit/iimtrt/tliiinirmrtriifinairia^^jlj, andittRmtiiiitfirilHtib-lvt:,<aPirisd. 



yGooglc 



Md NAVIGATOtt. 



^ERAS. CYCLES. «^ PERIODS. 



fXJMiS.it. 17S9 VMBbefottta^iff, 

471] Y M I Jd^i'd* F mod It Cti^f Comifl;. 

Sun. £471 Voief 7»^> Period t7fgYi*fiac*(^iiA. PIf. agj^ Tear 7"'- '^'^ 1759 Vein befctcOrjf. 

Tt ffiit, Numiat^ lh,lbruCytUt4 *t4Saa, Uaaa. ^mdJaiUHoa fir t gitiareir 4f tti JMta Firi«l. 
■■■"' " '>iTMtth* gmn Ytarljr*^ lo, ud r ~ -'--"'-■ --....--.--"- ^. .._ ,1 , _ .l_ ., ■ 
luic j^mmri wil] bt AeCfcIeitoinpIejlt''--- ■" 

Yr.Per. iir.fn. 

£iIlMg»£(r, i») 4713 (ie> Cfcltafiiur. i9V4Ti] (HSC^dcifii 



Sen. t [>;Ic of £*i% 



-t- 



0/ ih€ BIRTH mid DEATH »/ CHRIST. 

THE cammon &w rf Cin/h4Van(tfetthan Ac tnu.Cn. for On* wu bom bdbre the Deitb of ffnWttic Cmt, wfwAvthtU 
kill him » torn ii he hnid if bit Bbth, And *cco[>lin| to the T'ftiMonjr d yij'^lv fB. X ;■ Ct. 8 J th«n w» hi EcKpfc of (he Macn la 
-'^ TimeoF HrmetiittiiaoKb, * JItile Mnre his Bnih. Which BtH pit Ihnc .^fremxi4<ii/ TsMi Ikcw t« hiH bippcncd in the 47111 V^u 



b( ibi Julim Vcnki, Mith ii<f ]k !!■> »Ftrr MUidght, at ytnfiihtt. How, Cn/ mult biTt Wen kiri^uH Monlbi bcfare fTm^i 

" -*, tvciure inthilMfTM/ fb«twiit fall £irth iBd ^KniTa TruhJ be wM nniti Into iEgpe, fbt PrelernBon oT hiiLif*. The liMft 

thenfbrcMvfaicb tbetracfrsc^ihe fiinbcMbEEied It lliODt tfar £aJ oT ((« 47»9«k Ymt •f-cha yjuSiaPetiod, wliich i " 



I>si]l, tvcii 



CAr / died in tha 4746 Ycat of the JuKm Peiiad op ^Vpf, ^il j, 1b the jjil Yaf of til AfC, ■ccordbiE b> the rqititcd An, 

r 37111 Ve*t>«ordiiig to the tne JEn, diftonnd b|> tb« EtWi el' the Momi hipftnlngi tittle bAre tbeTiniEtf //fi-a/i Deith, He vu 
[hcCiaft, ix'jtn-^dtm, it it o'clock (u wt jRclum Tiinel aad rapind ahott time in thf jUtanwMi dwwliala Kci^bowibood 

en the 41 

lei, >ad c«n(rq°eD'l)' therf eould be no Eclipfe of tke Sa*. 
Fv anir^/i .««s<i« ef ibt l>r.i ^ Chrifi 0^{:f*in ami Jgi, Bt Hi Dittit, tet f, 41. F*!U^¥m \^m. 
I'he litfatii M" of Cb'if% Biiih v.*s ncict fettled UU the Veit of C^ifi a.^ : when Dim^tJlnExipna, * Jta«n AWa*( Itt/i it at tbclsd 
r tht47'Mh Year of the >/Ma Pnied ; beia; four Yran loo Uv. for the Kcifo* lersre ^en. 
TheBitlfaof Cmir, •ctcrdlos to A'lWi/di Man, Bfq) iahiiUrmA^, |i proved to ba juft £ Taarl brfote th( laid nlsiri or t«]) 
En; (hcEclipfeof the Mwn, a little bclaie /joVtDe)ith, hippr]iin|on JHdrci the ijth, at 1 in the M*min|. 
Bot, that the AaAi or CaaOHOLcCT nuy b« eutnlnH aid fettled on the ToDnditian ot Tiuih) we here gl** the Reader Sir li 
[iWToti'i AiTnaMoMiCAtPaincir^n or CiiaoKaLOOT ) b; which be diteminaa the CaAKD AaA of the ArfMdmii Erf/Jbif M 
ihefounditiooof ill hii atonolaor, 

HaohrerrM, ihit XaAwt, in hie Arcwnt of the Spbcm tf th« Aacienti, placH the SMitn tt^ EjuSimti in ti'MltfAof thtCaafleHi' 
tionsof jiri'a, C^Mcrr, Cl^aLr■nd Cafrinra ; and ttuctha SfhcR or Olobe wu fiiS nude ij Htufim, and the .^R^i/iu ddioeiied apon it k)r 
Ctirrtf lira 'Prttom of th< j^jtrmi. 

It bit keen AiewD, by the Prrr)^ of the fpnairn, coslTi>7 l«thcOi4nof Sifu, that the fixed Stan ^pcar to fo fbfward. In tbc SEgnt, 



■aYear. AndbBclufbal (baEod of lh« Yor )6lo, tht EfniirtllnttCt^n, p&Gd| tliicu^ the mWdk Poinl, bn««eB tbe AiA andJaA 
r of Aria, ihendk) cultheErltptlein K B° 44'. itla then««vldent, that die JTftCrais bad dien ^ne bicfc }<' 44'j ■>>' Ihertfore, Ai jo* 
II Year, fo 36a 44', to ft64; Von, ferthtTicKlhtathe jJT—aaffegiyratiVtMfto tbeBeginningof the Teat 1690, "951 bt^nCirfp. 
Sat, Sir Ifsar Netittm Ra otdn to detmnine the Tine more eoncair) Guk the wtin Plata of the Colare df the ifviaam, and St/piat, 
bf confidnjni tht femal Stan thaj palled throu^k MnOOB the diftereBt CsnflelhiTlant, anordini to &AkbI| ta tbUom. 
IntbeBM&of AhiIii Awof tbeMiMlfnitudo, nuikedy, byfiirrn-^itialliiduf theYa^riM;! itfL«B(iti4ew4i fj g* jf 4j't 
id IheEqulDoOiila&npaCDg tbreo^, mt the EcUpttc, mnribig Id Zviau, in U fi* E^' 57*. 

In the Had of Ctni uc two Stan of the 4t]i Mainttade, tailed i aad ( bj Sii^r Enftxai'a Colntepafing in the Middle bui««M tb«)i| 
It the Ecliptic io H C jC Jt'. •< the End of the Year 1M9. 

In the eaCrenic pfcmR af fridtmn, there wu fsimnly a Scar of tht 4t}i Magidtnde, fof hw trferrel to 4ie Bicaft of OuiJ be!a| tV «pl j 
Star InEorfuB, throoghwhJehtle Colore nil paA. Iti 1.0Eg1tdde uwi, afie End of tfai Yar tHji ^msaMt* lo*, -and tie OUare 
of the EfmBMc pafling cbioiitb it cut tbe EJiplic in tf jv la' 40". 

In the Head of Frrfm, lifhilj deli oca ted, ia a A*- of the 4tli Ifapiilude, callti riyBtjr; Itt Lon^tade waa y »|" ij* JO*, at the 
End of the Ytar |6!9 j and tfae Colure of (he Efui-mi, pafliog through it, cm the Ecliptic in 8 6" it' 57*' 

U the Right HiDd of Ptrfm, riebtly delineated, ii a 9iat of the 4th Magnitude, wht><i Lon^tude, at the Eiid of tbe YMt iVIf, wif 
\f •4»»s'i7*, "od tht ijuiuBM Ctittrt, paflinj throaglt4t, cut the Hdiptic ia ij 4" j6'40*. 

The Su af aH theft \ 
Ftrt Placet of the ^ 
Ciiin 



Therth'Pirtofwbkh . . . tj < m 1*, IidwreforethenKo P;b«,iairlBch theCoIen inthcEnl oTAa VAfflto, 
a cut the Ecliptic I Ttli^ Ii, Mm >/ m Kinwitr ,/ OtfirmH^. 
After thli Manna Sir Iftic AW'u dcterminei the Mean Place of the St^ititt Cilm to bt in J), '* *'' 4'** w^idi being *ny Mdrif goo 

ThcffWBizB, at diia Time, hiriDg deputed i> 6'. if' Into the CtrJitvl Ptlnu «f dim, Jb*w that s6i8 Yrari hiTeeUpfccti/KV^si 
fan, whkh ia cotrcAei than the former Number of Yean, (thou^ lefi b; 00I7 17] for tbe Time, fiace the Ari:iieuli Mra tothe Tc— * 
O^ tU«) ma'. .DC the .4kzi«arjC'£>-d about 4-S Yean bcfiireCirjif. 

By other finiUtMtihadaSirT/ii'rA'fafHlheHi, ihAtIhii.£r4 cf thcy^veaffaftaught to be placed in that Ago of Ibe WorM, AsdhiTiog 

tennuied thit molt /tialal Mrt, hciraku )(ii Aituie CcmfutitioDi in Chionolpgy wilb Rrftrcoce thcnto. Who, with great Skill and 

_ Maatntirtn, hta fnitrd hit^'*r*''"^"ffT ^t'*- with tha^mri^ af N aturt, t*tf ^Tfir/ft ^f t'^'twrWi ^iih Sa^fd HiJIttyf with Htndanif rhe 

Fttbtnet fn/a—Hifiery, and with Ji/i^. H'bici grrti Auilm inhtrtfsrtmtiitiittwmiiatdbti hy tiii-ViAi.^ injiiilptui, a fiat, ai S:^, 

^i^=Ki . j_ . cilkO^ioLOOItJu. 



oogle 



14S 



ri« ROYAL ASTRONOMER 



CHRONOLOGICAL TABLES. 


DOMINICAL LETTERS for 7a&t« or Old Style, forever. ' 


Y B * m btfore CHRIST. 


Years fmce CHRIST. j 


. 


CENTURIES 




■CEntUriKs. I 





100 


200 


300 


400 


500 


600 





too 


zoo 


300 


+00 


500, 600 


YEARS 


700 


8 CO 


900 


1000 


MOO 


1 100 


1300 


YEARS 


700 


800 


000 


1000 


1100 


i20O,t3OO 


«b<^t 


1400 


1500 


1600 


*70o 


1800 


1900 




aiwe 


1400 


1500 


1600 


1700 


1800 


1900 1000 


Cehtohes 






ijoo 


2400 


2JO0 


i6oo 


2703 


ClNTUkJEI 


210O 


J 200 


1300 


2^0 


2SO0 


2600 2700 


hfire 


2800 


29^0 


3000 


3100 


3 zoo 


3300 


3400 


C HRl S T. 


i8oo 


sgoo 


3000 


'^° 


J200 


3300 3400 


CHRIST. 


3500 


3600 


y7od 


3800 


3900 


4000 


+100 


m 


3600 

FIT 


3700 
FE- 


3»oo 


3900 

AG 


40004100 
B A jC B 


DC 


cT 


BA 


AG 


gT 


PE 


ru 


, 


I9H7 


8S 


E— 


D— 


C 


B 


A 


G 


F 


1 


29 


57 


85 


f~" 


c~ 


ET— 


E~ 


r- 


5— 


A^ 


2 


50 


S^ 


86 


F 


R 


D 


c 


B 


A 


G 


2 


30 


58 


86 


A 


B 


C 


D 


E 


f 


G 


3 


3' 


59 


87 


G 


F 


E 


D 


C 


B 


A 


3 


3' 


59 


87 


G 


A 


B 


C 


D 


E 


F 


_4 


1£ 


go 


88 


BA 


AG 


GF 


FE 


ED 


DC 


CB 


__4 


3i 




88 


FE 


GF 


AG 


B A 


CB 


DC 


ED 


s 


33 


61 


89 


C 


B~ 


A 


G~ 


r~ 


K 


D~ 


S 


33 


6? 


89 


D 


E 


F~ 


G~ 


A 


a 


c— 


6 


34 


02 


90 


D 


C • 


B 


A 


G 


F 


E 


6. 


34 


6a 


90 


C 


D , 


E 


F 


G 


A 


B 


7 


3S 


63 


91 


E 


D 


C 


B 


A 


G 


F 




35 


63 


91 


B 


C 


D 


E 


F 


G 


A 


8 
9 


i7 


64 

6s 


9£ 
93 


GF 


FE 


ED 


DC 


CB 


BA 


AG 


9 


37 


^ 


9£ 
93 


AG 


BA 
G 


CB 
A— 


D C 


ED 
C 


FE 
D 


GF 
E 


A ■ 


G~~ 


F 


E~ 


D 


C 


B~ 




38 


66 


94 


B 


A. 


G 


F 


E 


D 


C 




38 




94 


£ 


F 





A , 


B 


C 


D 


' II 


39 


67 


95 


C 


B 


A 


G 


F 


E 


D . 


ti 


J9 


67 


95 


D 


E 


F 


G 


A 


B 


C 


^ 


40 
4' 


6S 
69 


96 
97 


FD 


DC 


CB 


BA 


AG 


GF 


FE 


■3 


40 
41 


68 
6^ 


J6 
97 


CB 
A 


DC 


ED 

C 


FE 
D— 


GF 

E— 


AG 


B A 
g— 


^- 


E 


D— 


C 


B 


A 


G~ 


'4 


41 


70 


98 


G 


F 


E 


D 


C 


B 


A 


14 


4' 


70 


98 


G 


A 


B 


C 


D 


E 


F 


15 


43 


7' 


99 


A 


G 


F 


E 


D 


C 


B 


'5 


43 


7' 


99 


F 


G 


A 


B 


C 


D 


E 


»7 


1+ 
45 


73 




CB 


BA 


AG 


GF 


FE 


ED 


DC 


16 
'7 


1+ 
45 


11 
73 




ED 
C 


FE 
D- 


GF 
E 


AG 

F 


B A 
5— 


CB 
A 


DC 
B— 




D- 


C 


r~ 


A— 


G- 


F~ 


£ 


18 


46 


74 




E 


D 


c 


B 


A 


G 


F 


18 


46 


74 




B 


C 


D 


E 


F 


G 


A 


'9 


47 


7S 




F 


E 


D 


C 


B 


A 


G 


■9 


47 


75 




A 


B 


C 


D 


E 


F 


G 


10 


£ 


76 




AG 


GF 


FE 


ED 


DC 


CB 


BA 




48 


76 




GF 


AG 


BA 


CB 


DC 


ED FE 


21 


49 


77 




B~ 


A 


G~ 


F~ 


E~ 


D~ 


C 


77 


49 


77 




e~ 


F~ 


G~ 


A 


B 


c- b 


z* 


SO 


78 




C 


B 


A 


G 


F 


E 


D 


22 


JO 


78 




D 


E 


F 


G 


A 


B C 


23 


51 


79 




D 


C 


B 


A 


G 


F 


E 


»3 


SI 


79 




C 


D 


E 


F 


G 


A B 


51 


Ii 
53 


80 
81 


- 


FE 


ED 


DC 


CB 


BA 


AG 


GF 


it 

2? 


53 


80 
81 


_ 


B A 
5— 


CB 
A 


DC 

B— 


ED 
C 


FE 
5— 


GF AG 


G 


F 


E 


D~ 


C~ 


B 


A— 


26 


54 


S2 




A 


G 


F 


E 


D 


C 


B 


26 


54 


82 




F 


G 


A 


B 


C 


D !e 


*7 


5S 


83 




B 


A - 


G 


F 


B 





C 


'7 


5S 


83 




E 


F 


G 


A 


B 


c ;d 


z8 


1 


84 


DC 


CB 


BA 


AG 


GF 


FE 


ED 


23 


ii 


A 




DC 


ED 


FE 


GF 


AG 


BA CB 


USE. The DominiCTl L«tt«r ftindi un/<r the Column ef Centn- 


USE. The Dmu'aiai/ L,il,r ftindionder the Column of Ctnitr-ri, 


rie., ot whole Hundred., ud ay.-V the Year (on ihe Left) ibore 


and .gunft the Year (on the left) above Cent»ries, /«, arlfi, for the 


Centuri-, *(/i"a.i», f««J>c liter ^,.,V^. 


Utt«r;*f !">«/■ 


anfirnaicn. There being » Revolution of the Ja/in Dominic.l 




Letter in evnj 700 >/(«Yem, inyNumW a{ JmliaVanMu, 


of >/mi Van fin, OhA »!» t»ve the [»mtJ,li»M Dominical Lec- 


Chrifi, will have Ihe £une 7>A^ Dominicil Letter » the CMt^nut 


of thofc Yean to any Number of 700 Yeart, viU have im Yeari 
Yn. Dom,Let. 


will bare for Yean h^, Orifi. 


Yn. Dom.i.«t. 


(■jHondrtdi . . 3500 


f7 Hondredi .... 1600 


IiimpIe.j«.>r»Chrifl . . —1563 ; . A. 


Eiample.! Since Chrift . . — 1M6 . . F. 


lcon.pi>«Cbr. 937 ..A. 


lcomp.bef.Cbr. ,534 . . F. 


K.B. BreocreafinBtheColomniofHunaKdi bj Smn., the Dominical Utter mij be found for my Kumbet of >//m Yean fe^r, or 


/fK*CB»l.Ti though never fogTMt. 


il,i«p-r«irti(ij9Domini«lirf««-/„wi (e ti< 14/i y FdmBty, «f/.i,fm, (-14/* Wwtv«ic. ™*»«rf, er 14 tarf j 5 f i* /aw W«/*-d«, 
/■ (£> Ron..o Cili'iUrii Bifliitile, i^^ ibt fm, LtiltrJ It, Stc«ui Dominical i<«ff fin^ifi- lb, R,fi of lb, Tar. But in our E,ig!ijb Cal^r 


ihil eittaordinirj Daj ii added on the 19th of Fibntary, 



CHRONOLOGICAL 

od by Google 



and NAVIGATOR. 



d by Google 



ni ROYAL ASTRONOMER 



C H R O N O L O G I C A L T A fi t B 6. 


Tk. GOLDEN NUMBS k, •^%i^ fo. .., v.*. !»%•« 6m. &■•<.». 


K B. Tbt tt.Ur. K,-ir- fct OU wd V«i 
fityl* it tlHfMi«, aMltklMtPlMa, « tlM B«eii)w>iz 
of tht Ytap. «ilh Ht Z)M«t.; bfxr for ocE 


y.AR, ^t^VC madli^j:^ Wfi>K't'H«(*T. 


» 


9^97)9^ 


95 34 93 
76 7J 74 


9"h. 

!4S3 


90 
7' 


89 

70 


88 ^'7 W^ 
6g 6B 67 66 

jc 49 48147 


84 83j8» 8< 
6c 64 6| 62 

+6 4Sl4t 43 


8b 


797877 
60S9S8 
t' 40 39 


36 


3736 


3S 34 


33 


3J 


J' 3 


329Z8 


'I 


>« 


^5 


'4 


43 


22 21 10 




t9l'!!|i7 


.6 1, 


14 


'3 




i.U 


'7 


6 


5 


4 


3 3 I 


S./nt Chuiit. 


^wlw,;..f. ^ 


YsARs abjve HunJrjJj im« •JaaUT, | 






c 


( 


• 


J 


* 


S 


6 


7 fa 9 


10 


~ 


,x 


'3 


'4 


'S 


T6 


F 


rt 






1? 


lo 


" 


12 


»J 


»4 


«S 


2617 iS 


»9 


i- 


!■ 


J« 


JJ 


34 


3f 


3637 


Hiadtgdi 


Hundreas 


3« 


3940 


t 


t' 


Jl 


i* 


4! 46)47 


48 


49 


SO 


5' 


it 


S3 


54 


sib* 


of 


of 


S? 


(8 


^? 


61 


63 


64l6[ 66(67 


ft 


^ 


70 


7< 


72 


7J^ 


74l7S 


Yi<ii. 


YSAKS. 


76 


77 


7« 


;§ 


3a 


81 


32 


8.3 84 a? 


86 


»7p«9 


9<'9ii9*iPiWt1 






?' 


96 


^ 


9? 








_ 






. 




. 


. 






Gt)i.DBN NuMBBRj before ?nd fince Christ. | 


J700 


3800 


1900 





1900 


3^00 




1 


3 


4 


i 


6 


7 


a 


? '° 


11 




IJ 


■4 


15 


76 


17 


18 


■9 


i<ioo 


3700 


18D0 


IDO 


2000 


3900 


( 


3 


8 


9 


10 


[| 


12 


13 T 


'S 


16 




iS 


«9 


t 


3 




-4 


s 


JSOO 


3600 


1700 


100 


ZIOO 


40C0 


1 


12 


'3 


'4 


M 


16 


'7 


13 1 


' ; 


X 




4 


5 


6 


7 




9 




SJOD 


J500 


1600 


300 


2200 


4100 


it 


"7 


18 


■9 


I 


2 


3 


4 


S 6 


7 




9 


(O 


II 


12 


13 


M 


■1 


J300 
fzoo 


MOO_ 


isoo 


^00 


1300 


4J00 


„ 


J 
8 


9 


J 


6 


_7 


8 
"3 


•4 ' 


5^ 


■7 




'9 


\2 


lb 


11 

3 


18 

4 


12 

S 


"j 


3300 


1400 


^ 


2400 


4300 


(*oo 


3*00 


1300 


i6co 


4400 


1 


'1 


H 


15 


16 


'7 


18 


'9 


I 2 


3 




i 


6 


7 


S 


9 


10 


II 


5DOO 


J 100 


laoo 


700 


4500 




18 


>9 




z 


J 


4 


S 


6 7 


S 




10 




IS 


'3 




'S 


16 


4900 


JOOO 


IIOO 


SDO 


2700 


4000 




+ 


S 


6 


7 


8 


9 


jc 1 


1 i2 


>3 




■S 


16 


'7 


18 


<9 




3 


+800 


.'9°° 


1000 


900 


2800 


470* 




1+ 


10 
'S 


(t 
16 


IZ. 


18 


'9 


iil 


617 

* i 


iF 

4 




■fc 


2 
7 


J 


_4 
"9 


lO 


6 


_7 


4700 


2800 


900 


1000 


apQO 


+800' 


4<io<, 


3700 


800 


IIOO 


3000 


490B 


1 


'9 


1 




3 


4 


$ 


6 


7 " 


9 


.il,, 


11 


'J 


'4 


■S 


>6 


17 


4S0O 


2600 


700 


lioo 


3100 


5000 




S 


6 


; 


8 


S 




II I 


J 13 


'4 




16 


17 


lE 


'S 


1 


2 


3 


4400 


2JOO 


600 


JJOO 


3100 


Sioo 




re 


1 1 




'3 


'4 


'S 


16 I 


718 


'9 




2 


3 


4 


5 


6 


7 


S 


4300 


3400 


(OO 


1400 


3300 


;200 


L 


ii 

1 


16 


(7 
1 


IB 

4- 


13 

s 


"6 


1 sl'^o 




12 


8 
'3 




~S 


II 

It 


12 
•7 




4>oo 


3300 


40a 


ICOO 


3400 


Sjoo 


4100 


saoo 


300 


1600 


3|oo 

3600 


S40O 


■ 


6 


7 


9 




II 


12 I 


3 '+ 


'S 




17 


tb 


'9 






1 


4 


4000 


aroo 


200 


1700 


5500 




11 


12 


'3 


'4 


'S 


i6[i7]i 






j 


4 


t 


( 


7 


9 


1900 


30OO 


too 


i3ao 


3700 


5600 


' 


■ 6 


'7 


18 


'9 


1 


2I3I 


6 




9 




'> 




') 


»4 


CONSTRUCTION. Tbe FiiJI Obm. of tfa< OM. Na.f 1, contiiM .XL'O.J, for Ci-C'n of Ymc* kfirtmiJnaClrill t i^ jtel 




for y.m .ben C«.| 


nitiQ wfuic Cwrpa 


By wkitl. C<.nll™ai« of ih« d«M T^, mt No«h«T of T»b i^i« Cl^. .ad tteir Cw^ltrnmi to ny Nonbtr -(rf ig Cotuiti, 


roc V««J flKe Chrifi. «iH h>TC the fun. Cddtn lflIlri>e^ »i dx! «-n^. , 


BXAMPLB. r,J^lt.GMi» KMmttrfir tjtf r.MnJmaChritH uJ^ fir l«n r«n *./« Chriftf 


■^'-'» i^;^--^ -^ — ^ U'-sr -i 


OM* O.N« 




A«iTaH*Tic4i.Lr. 


T./W«i. CM, Mp-irr WWthtift » 
bHit taka from »o. «d k.» the lAiUn. NamlMr forfMVw. 


RUtZ .«M 1 to the re>n nnce CS»/. in] Jjnde (!» Sm h; 


>..wb>trenun>«nt be the C^^ Hooker twtkiTw. And 
!?« WDM* ib« 0*Um tfambcr it u. 

1 


If Kotliias luniiu the GoU«n Nwpbcc it 1. 






;; ,• 


i9li7»o(» 








■0 

7« 






r««Ue»N«nkinqRirN. 










' 






^^ 




















CHMHOUXHCU. ■ 



y Google 



md NATIGATOR. 



J51 



CHRONOLOGICAL TABLES. 



A TABLE, taSndtiM f^tt ttr tig» of tbe Mooir, ma'-fy, \,y the G«/^m ATvin^ and 
Kays «r the Mofilb, tiH 1899) wkieh will fervcfbr em-, by aMing the X>ayi the M—dt 
{• lifnvarAinthe M«Ah-D>>*, for a given Pciiod, beyond that lime. 



Atcordlng'te Ae GrtpHm or Nmu StjU. 



I,e»A» MrriJian. 




E X A M P L E of die U S E. N. B. Evtry Srg* : 

Ttjbd Ai PUu V Sip ^ th. Moon, /tr Julj lo, 1764, iht GMa Ntmiir fctVf 17 1 Dau.fom ly K 

A^nA y»^ fl»nd> i, unrtir or «l<ne wfuch, Hindi the Diy of th« Month, *i«. »», epuHl irhidii on th* L*ft, ftindi », . 
fitfi, md rht OoMoi Wa m bt i haof 17, i^nft wtiTcb Amd) j, to the Tipbt Hand, nnttns o( abofv^ vhidi, Audi tki j4JMait'.(K^, «dt. 
t7) ifiinft which, Eo tju Rifhf, Hindi the Arft Pxit of Stgiiittius, tar At PlMti or Sign thiMooaviU he Ib, n^ircd. 

St th' Rtvrft Atuhd ik' D^j tfiht Mmb km; hifani tt, art Sign. 

Y«JhiirbtFlmtl^SifQflbi'hhBT>,f-rAj/Aia, 176^, ibi CtlJn T7a»hir ttlit iS' 

ApinA AfrHfUait t, dhJct which Hinds x, (grthe iglh Diy, (the tA being dwiyi 18, idi^n theDi; of tfaeMonth il atwreiT) apllA 
«h'ch, lothe Left, Audi to, for the Alvgvti-Diju But igiinll the Ooldtti Number lE, ftandi i, undtc, ot ibove irbicb^ fiaml lh»r« 
!4iBt 10 Mimte-Oofi, asunA which, to the Ught, Aaiuii the litter Pvrt of £« for Anfwer. And the like 'oral! other CtAi, 
COKSTRUCTION. 

AwT Ooyga Musber ii ehoftn to Aind >|uaA ibj Month, (to begin with Jtumtn it be^] lb *i the Nombv of /Uvtua-Dtjif ftwdteg to 
the Left, ({linA iht Daf oF that Month, bdn;; found mnder t, plicH >pinA the Golden Nnmbtr, Ihall Oiew the An or ilnMr Part ef the 
Sitn the Moon u in, (o the Rirti Hand of that Number of A-kwmt.Bajt j which beinf dnennined for an; nu Dtj 'f"3 AAmi, the &eft of 
the Moatha moA be placed /rtMV of Uehmri, in fuch Order of Socceflion, or RetroptlWon, ibMtbtiAD*^ ti«i( to a? Di^ be tee- 
hoMd it t thesd, the 191(1, and fo an, to the prefrnt Month'i End 1 obferTing, that ■) but ai Diye are Tt<biMd firf the Mora'i foinj 
lbna«ha11lhcS%u,iiilt«dafa7Dirt, 7 Hoeca. aiMl>bont4] Mieotei, thai each third CiceMding Maath bethu aDaflaler, •ruSftDajri 
End, b« MoMinf firirarJ : othPtwire the Sl(n will go on t«o f>ft bv 7 Haunand 41 Miontei eriry (7 Dip, or inabout aMoDth. 

WbtntbeM™n'« Plact .1 «/t,T(«W lothe Gnfeen Numfc« (or ary Year, and the Moon'a Mean Place bdn, lw>o»a t» (O fonwrd br 13 
Oar* >n *ach Lri^ TVr, or tn 10 Djyi in each Omhm Vrj'-, tnrf Colini Number advanced by 4, or t, nnS be pbnd i^ or loDafifoi 



=aaii 



fYf^r 



•4 Mtnb-DJi, ri 



willal 



, (bytitr/ing the^Ad'ance-Dajv t» BiwK fMWfd) '**'•*« 



I,: dnCoogle 



151 ?i^ R O Y A L A S T R O N O M E R. 



DigHizcd by VjOOQ IC 



end NAVIGATOR. 



CHRONOLOGICAL Tables. | 


A TABLE of tlie SwV Placi throughout the Year; by which the Mson's.PlaeA 


For Rnding -JFoiflnd.l 1 i 


may be found, and her Rijing and Setting neuly, for Umdm, or any Fart 


the Moon'i tng I 't 1 „- , 


N". 


of the known World. According to Nrui Sijh. \ 


Place. 


r>r.&fetl 


Water 

London, 


of 
Ihe 
Sign. 

T 




J.«. 


Feb. 


March, 


April. 


May. 


June. 


1 

July. 


Au(. 


Sept. 


oa. 


Not. 


Dec. 


z. 


Decree. 
S " 
IJ 


si,. 


, 


Gltf 


13" 


OX 


'or' 


W 


on 


?- 


P4 


QBE 


S? 


0^ 


w 


iiA^g 


3^43 


% 


"13 


"14 


''■3 


.7, J 

>4 


* M 


■♦" 


J 1+11 


J 10 


10 


9 


■»IO 


• II 


J 


□ ai 
I 9 


. j6 


4 ao 
4 5> 


-1 




* "5 


16 


14 
' IS 


;.u 


>4 


s 14 
•s 


•■■J 


"'3 


'Ull 

* '3 


« !' 


.8,3 


■«" 


4 


n 


3 '» 

4 


S ji 

S 5» 


» 


"T 


•*i6 


.g 


.6 


J 17 


I 16 






14 


'4 




"4 


' '4 


T" 


1 19 


4 4» 


6 j6 


I 


.;i 


;,'9 


'•"7/ 


'■tS 
'9 


18 


"9.7 
. 'i 


"ii 


'.'d 


i»,j 


14, 


! 's 


■ U 


1 


3 » 

3 '! 


1" 

6 X4 


7 55 


'^ 


9 


..'' 




""9 


•Ho 


a'"' 


■ iS 


'7 


"7 




16 


"7 


'7 




J jS 












'»!» 








"9 


'«iS 




.i,S 




' Ii 




-If 




8 


9 S! 
10 j9 


3 


"•wTr 


i^j 


11 


».! 


It 


"jo 


'9 


'9 


'9 


iF 


'9 


'-19 


4*5 


8 48 






.1,4 




»3 




















5 8 


936 




Si 


n 


»j 


"5 


^'J 


ie»4 


13 




'Jii 






to JO 






'3 


5 " 


10 14 


iMS 




'4 


■«»4 


! 16 


'«14 


» 1; 


! '* 


•.'I13 
















6 4 




1 5 


~^ 


_I1 


-JU. 


a? 


*J 


16 


".4 


S4 


».j 




'»ii 




t3 
■ S14 
' »5 


■'ij 








3 


5 


16 

'7 


I X6 


<3lS 

» 19 


s 16 
tj»7 


"U 


^11 


.0:1 


.Oj. 


13 
'»i4 


»4 


T IJ 

'»4 


»4 


"75" 

17 


7 
7 '3 


«M4l 
I 3^ 


3 43 


A 


iS 


%i 


. JO 


it 


» »9 




.'I 


7.-16 


I •? 


'»S 


.'d 


*6 


"16 


.8 


I f 


1 14 


4 5> 


6 


'9 


' »9 


'•X' 


* »9 


"•30 


'"iB 


i»ig 


'I 


■S16 




'»17 




'9 








"l 




■OjO 


• > 1 


30 


» 1 


■"a? 


7 19 


»lg 


»7 




■»17 


iB 


" 18 




il° 








"iT" 


— I 


1 


.™, 


^TT 


'ul 


■>10 


19 


* iS 


'•ig 


at 


' 19 


»9 


~r 


9 * 


44S 


6 m 


T 


11 




' 4 


>t t 






SB I 


« JO 


"19 


B9 


' »9 


JO 


*y. 




9 '9 


S 3* 




*3 


3 


i 


' 3 


'' 3 






ill 


30 


' 3" 


30 


i ' 




»j 




614 






»♦ 


^ 4 


'i « 


" 4 




* 3 


" 3 




tnn, 


BAl 


>^^ 




3 


»4 


10 n 


7 H 


gf^ 


ly 


,^ 


" 5 


• 7 


5 


* s 


4 


4 










.3 




16 


10 lE 


8 


9 51 


9 


i6 


♦ 6 


■» 8 


* 6 


6 


" i 


' 1 


' 3 


» 1 


" J 


1*4 


,-i 


11 (1 


g48 


10 j9 


»7 


9 


, 9 


7 


'* 7 


6 


• 4 


" 4 


4 


'4 '♦5 


I* 6 


*7 


11 n 


9 36 


11 4 




»9 




^ 9 


9 


' 7 


' 7 


"1 


•J 


'-1 


...1 ■ 1 


;.i 


»9 


8 




1 S 

' s 


H 


1" 
1' 








■ri 


6 8 


7 
< g 


1 


T 


'.■I "' 


9 


30 


■ *. 


11 


J " 






f,jirj,l. Moon'. P/.« W *;%, 


U.i. The i'm'i P/a« ii mrrfid in Sijni tnd Degrtei uaJer each Month. Oa the left Hjwl 


July 16. 1760? The GoMrnN". be.ng 


of thei^i-ni Of [he ^k"'' P^ui fl'Od the GWiiii ^wxkri, [cfpeAiTelf >a(«reriiig ta the D>yi bT 
Iha AfHii, whereon the Nnii Mnen happen ; when the Mwi't P/nu ii the finie with the Sun'i. 


13, iUndi againH ijrh y„fy « New 


Moon, when the Snn and Moon'r Place 


From whence, tht Diyi of her jlp muH be retkoned fbrwiH to the Month Dijr, whereon Ihe 
MrM't Fltti H nauirati Aditiog the £ifii ami Dtirm gotw foiwird, b; the Metm, icroiding to the 


will 
For 


be , 




Day. of the Moon add x 


a.o 


Nwnbn of Dayi of her Age, in the innued TibU. When the Sign and Degree of the Mt.,', FUei 




■re fbuad, obfene igimft what Z>« c/ (& Mntb the foot SmiC, fUn fludi in the fatU, ind the 


Sum 5 


Moon-i W/TTiK ibove the Hoiiion, will be the fime ■■ th» Mf Daj , known -bv the netnfl 
Month-D^r iaTiblep. 156, of Sin '■ Setting, which muft be .JiJtAf,/ from tlie Time of the Mooa'i 


OrnEoo, to whichanf-erj Af. J,, 
vrben the H»lf-D»y, (e;ual the half Con- 


Soathing for her Rifiog, or added thereto for her Setting, at L»ii«, oe in £»f:.*f. 


tinuance of Moon aboTC the Hori.on) 11 


In other Putt of the World, ufe the S-w-Dw-tim A'c, icrording ta the Plia't Latihiie, and 


yh j>» which taken from t* 14» J*t 


Mocn-i Place or Ded», coafidend without Lititode. fl« Tb*. •/ 5«i|-.Db«»« .,«■« farther an. 


Soutliing, lea*ei 711 iib Morning ber 


"Rifing. And fo for other Cafei. ' | 


HIGH WATER, it the followipg Plach, In Van and Mmin, before or after the Time of High W»t« at iuiA.. 


K<A,, a ilindt for «/(*r, and 1, for *</br,. 


Amftcrdam, a o'ljo' Powey, a % 10 Harwich, h % to Ollend, j 3 Sptthexd, b > 


BrcD. a i □ Flulhiog, h i ]o Hallingr, h t, Otfordneb, * 4 -Shortham, » 4 o 


Bidliafton Pia-, tf « Oourie. Gut, io 5 St. Helent, f 5 jo Plymouth, • 3 10 TinmouthHavetja 30 


Btidgewater, ' 4 40 Cravefcnd, t i to Havre -de- G raw, ( 5 jo Portland, ' } jo Tinmouih, a ] 40 


Buoy of Noit, * I JO Gunfleetj i 4 Loo, a % \<t Portfmouib, i a a Tur^ay, ■> 3 40 


Calair, h 3 Hwtlepool, < JO Lime, ■ ' ] 50 Roehefter. h 1 10 TopOumi, - J jo 


Dartmouth, < J Jo Humber, a % a Leigh, 4 < Bamm'l'hu, b ■ «o Teiel, ' 4 40 


Dover. b j Hull, . " J JO' MountlUy, a i t« Bedfand, 4 1 O Wcymtuih, 4 4 IJ 


n»>pr', «4 Harborough < , ,0 M.at, Jo C SciJIy, d ■ 4; 'Yarmouth Pier, i I 4S 


Exmooth, *.j JO Haiflew, < 5 50. Needlei, 1446 Shot Bacon i» 


£ X A M P 1. E. Tk find lb* Tim tf Rigb-trtlir at Roehefter, m ri> tor£ i)« ./ rie Moon'i Age. 


At L»U, oix that Day, it i> high Water - ob cja 


fabtraa 1 *o '« 


High Water at JI«iMW — 8 jj 
And the like fw othtr Namr hy xldTng or fobCnOIng to or froth High Water ttL^A>a. 



CHRONOLOGICAL ~ 



the ROYAL ASTRONOMER 



CHRONOLOGICAL TABLES. 


A Table, to find (he Time of the /><j/iiw/or £»/?«■ Foil Moon, and confeqaently ia/w, /or rvtr, by ihe Golden 


Numbers, and Days the Lunar Cyclt of 19 Years goes forward in any given Penod, Nev> StjU. 




Pafchal 


Dom. / Golden Numberi. 






Letter. '"," 


ii 1 iii 


ir 1 V 


« |vii [Yiii 


ix 


X 


xi 


xii 


xiii 


xiv 


XV 


XVI 


xvu 


xviii 


XIX 


Mar.2i|C 


8 






11 


22 




' + 




6 


17 


23 


■ 9 


20 


I 


iz 




4 




26 


»P 


9 






iz 


23 


4 




26 


7 




29 


10 


21 


2 


"1 




s 






^i 










'1 


*4 


« 


16 


*7 




iQ 




It 


12 


* 


>4 






'7 




^1 


t 








'4 


21 




17 




9 


20 




IZ 


21 


4 


M 




7 






25 


A 




23 


4 >S 




7 




29 




ZI 




'1 


24. 






V 




'9 










9 


16 


27 


8 


19 




11 


22 




'4 


21 


A 


»7 




9 






27 








6 






9 




I 


iz 


23 




'? 




7 






10 


21 






D 1 






7 




zy 




21 


2 


'1 


24 


1 




^7 




'9 




11 


22 




»5 












II 


22 


1 


'+ 


a? 




'7 




9 






12 


23 




10 


f" t' 






9 




1 


IS 


2J 


4 






7 




29 


10 


21 




•3 


24 


% 


. 3' 






10 




2 


M 


*4 


? 


i& 


27 


8 


■9 




II 


22 




'4 


fl 




Apr. I 


^ T" 






II 




1 


'4 


U 




«7 




9 


20 


1 


12 


23 




'S 
















4 


'^ 


7 




29 


10 




2 


«1 


24 


S 




27 




3 


« .5 




2 


'1 




■ 1 




27 


» 


•9 




II 


22 


1 


'4 


2S 




'7 






^ 


" 1 




1 




2S 




»7 


28 9 


20 


1 


IZ 


23 


+ 






7 




29 




S 




4 


K 


26 


7 


18 


2q 




II 


2 


>1 


24 


I 


16 


27 


8 


»9 












1 








'9 







22 


1 


'4 


a? 




17 




9 








; 


* s 




'7 




9 


20 


t 




H 


4 


'? 




7 




29 


10 


21 






t 


" f» 


7 








21 


2 




24 






27 




19 





11 


2Z 









* V. 


27 




19 




II 


22 


3 








17 




9 




I 


12 


aj 






10 


n 

n 
I ^ 




9 20 




12 


2^ 


4 




26 


7 


18 


»9 




ZI 


2 


n 


24 


1 




II 




JO 21 




M 


«4 


^ 




:^ 


8 


'9 





II 


22 


1 


'4 


3? 






11 




II 


22 




'4 


»? 






9 


20 


1 


IZ 


n 


4 


■s 




7 




'■ 




12 


ai 




'? 




7 


18 


29 


10 


21 


2 


'3 


^4 


1 




27 






I' 




13 


*4 


5 




»7 




■9 




II 


Z2 




'4 


21 


'7 




9 




»s 




'4 


»? 


6 


17 


>8 


9 






12 


21 


4 


M 


26 


7 


18 


29 










K 








29 


10 










I 




27 




»9 





II 




i; 


» ft- 






27 




'9 











'4 


2? 


17 




9 






12 




>; 




r 




27 




'9 





II 






'4 


'I 


7 


18 


29 


10 


21 


2 


'1 




i3 


c 


6 


'7 


z8 


9 


3& 


1 


12 










7 




29 


10 


ZI 


z 


•3 




1^ 


7 


,8 2, 




21 


2 


13 


Hi . 


16 


27 


8 


.9 


II 


zz 


1 ■ 14 


ff 


EXAMPLE. 7i-^«rf >b Full Afyin kfprt Emfi^-S.,^, in ih K* 1765 f 
AEiinfl tbtPtiinA 1700, in Taih brio* Btodi i, and (he Golden NuroSei ibr 1765 beug ig. ig«i(ift i. At Diji fWie fan 






thtt Periol, unJer the Golden {Nqmber niii, in th>i T»ble Sindi AnV (, in the fiift Column for Anfwer. And tte DomuuciJ tetter for| 


176-, being F, icckoning 00 from ^pril b, to T, Jfr. 7 ii K4>/Ut-S-«ulrf. ih) fo for other dro. 




NoTi. TheDijitbeCyde » ^ne forwud, fluding onder the gj no Golden Ntmiber, ud inuifl ■ certiin Month-dif, fetye fcr 








A T A B L E of Ihe Number of Oty,, the Km, F-II, or Sjunttr Mooni U the Grtnri'm AccouD% go forward in the Montbi, 


or (bi 


Lwwr Cycle, (af 19 Vein, or 13; Synaficil Monthi) idvincn of the Cycle in the BcEinning of 1600. 




BilleitUe 


Crep» 


Lo. Cyc. 


Gregor. 


*. Cjc, 


Gregor. 


La. Cyt. 


Gregor. 


Lu. Cyc. 


Cregor. 


Ln. Cyc. 


Gregor. 


Lu 


Cyt. 


y«»ri. 




go forw. 






Yean 








Year. 














Day.. 




liaj.. 


of Chr. 


D,y,. 


of Chr. 


Dayi. 




Day.. 


of Chr. 


Day.. 1 


b 






























;c 




ISOO 




4100 




S30O 


iS 


11:: 




7700 




ifi 






3000 




4>oo 




S40O 


»T 








»7 




1900 




3100 


7 


43=0 




S 


17 




»J 


5s: 












3«oo 


7 


440a 
















1100 






i 


JS 






It 


6y>o 








>S 




**oo 








i8oo 




7000 










B 


3JO0 

»4oo 




;s 


8 


s^ 


*4 


22^ 


■ »9 


7100 


»♦ 


S]oo 
!4«> 




»9 




X 




!K 


9 
10 


4900 


14 

Ii 


61M 


'9 


7,00 


:i 


ftc. 








•TOO 




3900 




CIOO 






;i2 
















'5 


4oo 


*9 


>6 








See lb< Rwfon, Page jo, why the Uut Cycle rn fonrud in the Months Mcoidiag to * certiia Nomber of Diyi, «• here Xiiaac^. \ 



CaftONQLOOICAL. 



mi NAVIGATOR. 



CHRONOLOGICAL 


TABLES. 




A TABLE, Ihewing the Movbaxlb Fbasti, by the Dominica 


L Let- 


A Tabli, Ihewing the Jtfjw- 




TBK and GoLDiH MuuBEx, from 1700 to 1890. Bccordine to the Greearian 


«i/f 'Ftrm, ftom 1700 to 




ot New Style. 




.899- 








Fiom 




















1 






D. 


GoLDBIf 


Xiub. 


Shtor. 


Ealer 


Ron. 


Afc. 


Whit. 


Trin. 


Adv. 


Eafier 


End>. 


b-tinity 


Ends. 




L. 


NOHBBBB. 


toSb. 


Snirf. 


Snadiy 


Snol. 


Day. 


Sand. 


Sund. 


Sund. 


Term 


Tetm' 








Sniiil. 
















begin,. 




Ibegin.. 








1.11.14 


6- 0' 


'■• il 


m;,.26 


Ap. 30 


May^t 


May 14 


May3i 


dec. 3 


Ap. 12 


bi4y 8 May 26 


)". 14 






;.8.t3.t6.I9 


7 




Ap. 2 


M.y 7 






2S 


3 


»9 


IS Jun. 2 






A 


1.7.10.18. 


8 




9 


14 


lE 


2E 


Jun. 1 


3 


s6 


33 9 


28 






1.4.512.1s 


9 


■ 16 


16 


21 


Y *S 


!•">. 4 




3 


May 3 


29 i6!July s 
?un. s. 23r .2 






S.17 


10 


Mar. 5 


'3 


28 


Jon. I 


•■ 


l£ 


3 


10 






S.11.14.19 


6 1 


Feb, 6 


M».27 


M., 1 


May 5 


May IS 


.Way 21 


No. 27 


Ap. 13 


May 9May27jo. is 






z.;.S. 1^.16 


7 ■ 


'3 


Apt. 3 


8 


12 




29 


»7 




.6Juo. 3 


22 




B 


7 10.15.18 


8 1 


20 




■S 


»9 


39 


I«». s 


*7 


37 


23 10 


»9 






14.9.12 


9 ■ 


a? 


17 




26 


Jan. s 


12 


27 


May 4 


30 17 


Jul, 6 






6.17 




Uar, 6 


•4 


•9 


Jon. 2 


12 


'9 


37 




Jon. el 24 
May tolvjaysS 

17JUD. 4 


13 






3.8.11.14.19 


6 2 


Feb. 7 


Mar.l8 


M.y 2 


May 6 


May 16 


May 33 


38 


Ap. .4 


Jo. 16 






2S.i).i6 


7 ' 


M 


Apt. 4 


? 


'3 


23 


30 


2S 




23 




C 


4.7.10.15.19 


8 1 


31 


11 


16 


20 


'30 


Jon. e 


28 


28 


24 II 


3° 






1.9.12.17 


9 " 


28 


18 


^3 


27 


Jan. 6 


. '3 


38 


May 5 


31 18 


July 7 






6. 




Mar. 7 


'i 


30 


Jun. 3 


13 




28 


13 


Jun. 7 2s 


14 




"" 


14. 


tt 


Feb. I 


Mb,.., 


Ap. 26 


Ap. 30 


May 10 


May 17 


*9 


Ap. 8 


May 4 May 22 


Jn. ,0 






j.8.11.19 


8 


29 


May 3 


May 7 


'7 


"4 


29 


"S 


11 


. '9 


17 




D 


2.5.10.13.16 


7 3 


'S 


Apt. 5 


10 


14 


24 


, 3' 


29 


23 


18 


'°°'il 


24 






4.7.15.18 


8 i 


22 


12 


17 




31 


Jun. 7 


39 


39 


25 




Jnly 1 






1.6.9.12.17 


9 3 


Mar. I 


19 


24 


2S 




'4 


»9 


May 6 Jon. 1 


"9 


' 8 






314 , 


5 4 


F«b. 2 


M.,.23 


if- '' 


I 


A^x 


.May 18 


30 


Ap. 9 May s;May33 


).. 1. 






8.11.16.19 


6 4 


9 


30 


M»r 4 


8 


18 


»5 


30 


16 


12 


3« 


18 




E 


2.5.10.13 


7 + 


16 


Ap. 6 


11 


'S 


. *s 


Jun. 1 


30 


n 


'? 


loo. 6 


25 






4.7.12.15.18 


8 4 


-. ^3 


■S 


18 


22 


Jon. 1 


8 


30 


JO 


36 


IJ 


Jul, a 






1.69.17 


9 4 


Mar. 2 


20 


»s 


19 


8 


»i 


30 


May 7 


Jnn. 2 


2C 


9 






3.14. 


5 5 


Feb. J 


MB1-.Z4 


Ap. 28 
l/ny 5 




May .3 


May 19 


Deo. 1 


Ap, 10 


Mb, 6 


Ma, 24 


.. ,; 






S.8.11.16.19 


' s 


10 


3" 


9 


19 


36 


I 


'7 


13 


. 31 


;i 




F 


2..0..3.18 


7 5 


17 


Apr. 7 


12 


16 


26 


jou. 2 




«4 


20 


H. 7 






1.4.7.12.15 


« s 


24 


■4 


'? 


«3 


Jon. 3 


9 




M«y 1 


27 


■4 


July 3 






6.9.17 


9 ! 


Mat. 1 




86 


30 


9 


16 




8 


Jon. 3 


21 








3.11.14 


1 « 
8 6 


Feb. 4 


iH^i 


Ap. 29 


3 


May 13 


Mayso 




Ap. 11 


May 7 


May 2; 


11. li 






e. 8.16.19 


11 


Apr. 1 


Uay 6 


10 


30 


a? 




18 


14 


Jo.. 1 






G 


2.7.10.IJ.18 


' f 


18 


8 


•3 


•7 


*" 


Jon. 3 




H 




8 


27 






I.4.12.15 


8 6 


.. '5 


■S 




«4 


Jon. ^3 


10 




May 2 


28 


'! 


July 4 






69.17 


6 


M.r. 4 •« 


27 


Ji 




>7 




9 


to. a 


22 










EaM'i-t.u, bec^n. ^^r.i ^i, end. 




EXAMPLE. Wb«tT<^i*lU1>b«MU,Fuf,f^i,ijtA}TUDmi,U^LMt, 


bdngC, 


M» 14. Trijnfj Teim hegiiu 7ii« 






i«i -«- 


II, end. Tn. 30, &t the Time Y«t 




AbMfar 


■ 76.. ^' 




■1 i fi> fat Mhu Yewt. 




Wei, Eaflrr Term bsgioi 17 Diyi, 
■Dd cadi 41 Dm ifter £«tir-. ^nitiH 

Term begfn. s D.y.. )u>d eod. 14 




Nm. The .bo« T.We iriU ferve rmn igoe Ki ei», ocept when the fi(»» Moon 


Mil 00 




e &.i4ltj then £V<^ filii » Week ifter the Thne, by the Tibto. 




Diya after ?Vi'«>. Thtnfaie ft^' 
Terra continoei 17, and TV/mVj »o 
D.7,, incIuGTe. 




Stm^JtiH. P.leJ. FotF, C«»un84Ve«e«™»lin«(air.O.S.qnto70o) nukeFlwiihthePen, Sinie Pi. To. f D (lEiinU II 




In. bef. Cbi. 0. S. uaifei 70a) ouke ED. 






r> la the Deoi. Letter lad Golden Ni, TiUei, 0. ind H. Style, the Yri. &«, Orifi 


were firftroEfii!cred«rt,i^/«(«<, or i, a, j. St. 




Yeuiof Cbi.techenediiieitanipleKte, (iulteid of eurreet) he which the e Yeit »u co, 


fiicni BilTeitiJe, fr. tht BciintUDg to [|u Sod of (he 




J Ye« £Dte the Bifih of (Sifill ) the ift Yeir front thente to thi Terf of id, fifr. whereby ift Yeir *</(r( OriJI wil confidettd ijl e>r 






o«, to Sad the 0. Let. or CoUen N-. for aoj Yr. 




before Chi. 1 mod be dtdofttd from the tree Yeir, ^Arr t^r,;^, inO then find ihtm, in tb 






Were Chr. ftoold ftiod in the Plire of 0. Veil 1 , io the Plice of i, Y«r j j in 


P]«e of 1 Vein, &c. io the ^M>ifirY,»r,b,f„i 




C»rtf>-Wbilethelimi!wT.bie., fro Ynrr (ince Chrift, ue ofed » they Ifind. 







CilKOMOIdOCICAi 



pigilizcd 



b, Google 



>5« 



Thi ROYAL ASTRONOMER 



CHRONOLOGICAL TABLES. 


A T A B L E, fliewiDg, at Sight, the Movsabu Fbasts, and TxAUi, for tter, by the DommcAL Lettbr, 


iDdGoLDEK NuMBEK, according to Old Style. 


Of Ufe in H I S T 6 R y and CHRONOLOGY. 






From 
























D. 


GOLDEH 


Xmas 


Shrove 


Ealler 


Rog. 


Afcen. 


Whit- 


Trio. 


Advent 


Eafter 


Endt, 


Trinity 


Ends. 


L. 


Numbers. 


toSh. 
Sand. 


Sund. 


Sunday 


Sana ay 


Day. 


Sunday 


Sunday 


Sunday 


Term 
begins. 


Terra 
begin.. 


2.S..3.16 


6- o-' 


fco.^S 


Mar.26 


Apr. 30 


May 4 


May 14 


May 21 


Dec. 3 


Apr.. 2 


May 8 


Mayzb 


Jun. 14 




7.10.. J.. S 


7 




Apr. 2 


May 7 


II 


21 


28 






>5 


jun. 2 


21 


A 


1.4.9.12 


8 


'9 


9 


'4 


iS 


28 


fod. 4 








9 


aS 




3.6.11. 14.17 


9 


26 


16 




. '5 


Jun. 4 






May 3 


29 


16 


July 5 


- 


8.19 




Mar. ^ 


23 


28 


Jon. 1 


11 


18 




10 


nn. 5 


,^3 


12 


a.,- 13,10 


6 I 


Pel). 6 


Mar. 27 


May 1 


May s 


Mayij 


May 12 


No. 17 


Apr. 13 


May 9 


May 27 


jun. .5 




4.7.1015.18 


7 '■ 


13 


Apr. ^3 


8 




22 


29 






16 


Jun. 3 




B 


1.9.12.17 


8 1 






«; 


>9 


'9 


Jun. s 




27 


. ,23 




29 




3.6.11.14 


9 > 


27 


17 


22 


26 


Jun. 5 


12 




May 4 


30 


>7 


July 6 


- 


8.-9 




Mar. 6 


24 


29 


Jun. 2 


12 


• 19 






Jun. 6 


24 


'3 


2.S.io.is-'6 


6 2 


Feb. 7 


Mar.aS 


May 2 


May 6 


May 16 


May 23 




Apr. 14 


May 10 


May 2 a 


Jun. .6 




4.7.1S--8 


7 2 


'4 


Apr. ^ 


9 


"3 


23 


, 30 




21 


17 


Jun- 4 


'3 


C 


1. 6.9. 1 3. 1 7 


8 2 




I 


16 




30 


Jun. 6 




28 


24 


■ 1 


30 




3.11. 14.19 


9 2 


28 


18 


13 


, 'y 


fun. 6 


'3 




May 5 


3' 


18 


J.iy 7 


- 


8 


10 2 


Mar. 7 


* 


30 


Jun. 3 


'3 






12 


JUB. 7 


25 


'4 


16 


5 3 


Feb. I 


Mar.2 


Apr. 26 


Apr. 30 


May.o 


May 17 




Apr. 8 


May "4 


May 22 


Ju„. 10 




Z.J.IO.IJ 


6 3 


8 


A '5 


May 3 


May 7 


'7 


2^ 




'5 


11 


29 


17 


D 


4,7.12.15.18 


7 3 


>S 


Apr. 


10 


>4 


24 


3 






18 


jLn. i 


2+ 




1. 6.9.17 


8 3 


22 




'7 




3' 


J-?". 7 




29 






Jdy I 


_ 


3.8.11. .4.19 


9 3 


Mar. I 


IS 


>4 


26 


Jun. 7 


■ "4 




Mnv,6 


lun. 1 


19 


8 


S.16 


S 4 


F«b. z 


Mar.23 


Apr. 27 


1 


May 11 


May t8 




ri[,.. 9 


May s 


May 23 


JU..11 




2.10.13.18 


6 4 


■ t 


. 3^ 


May 4 


8 


18 


, ^s 




.6 


12 


30 


18 


E 


1.4.7.1 2. IS 


7 4 


U 


Apr. i 


11 


'S 


, 'S 


Jon. I 




*3 


19 Jun. 6 


*S 




6.9 14.17 


8.4 


23 


1 


18 




Jun. , 


8 




30 


26 


13 


jBl, X 


- 


3.8.11..9 


9 4 


Mar. 2 


2C 


2S 


29 




'S 




May 7 


Jun. 2 


20 


9 


S..6 


S S 


Feb. 3Mar.i^ 


Apr. 28 




Way. 2 


May 19 


Dec. 1 


Apr.io 


May 6 


May 24 


J0«..2 




2.7.10.13.18 


6 S 


IQ 3 


May 5 


9 


>9 


26 




'7 




-.31 


•9 


F 


1.4.12.IS 


7 S 


17 Apr. - 


12 


16 


26 


|un. 2 




24 


20 


Jun. 7 


>6 




3.6.9.14.17 


8 S 


24 1 


'9 


»3 


Jun. 1 


S 




May I 


27 


'4 


!''y ,3 


- 


ii....i9 


9 ? 


Mar. 3I 2 




s-^ 


9 


It 




8 


Jun. 3 






5.13.16 


S 6 


F.b. +Mar.2 


Apr. 29 


3 


May 13 


Mayic 




Apr. 11 


May 7|Mayzj 


JBI.. 13 




2.7.10.18 


6 6 


11 


Apr. 


May 6 






, *' 




18 


H 


JM. I 




G 


1.4.9.12.15 


7* 6 


■ 18 




>3 


•7 


2? 


Jun. 3 




^S 




8 


27 




3.6.14.17 


8 6 


- ='5 


' 1 




H 


^""'.c 






May I 


28 


15 


Jul, 4 




a. U.I 9. 


9 6 


MaY. 4 


2 


27 


V 




t 




9 


Juo. 4 


22 


11 


AG«ira/TABJ,Eof iheSvN-iRi*.fio.!S.m.g, /or£,f/a^indWa-,^, NktStyli. To be uftd with T«W-, !'af= ui- | 




J,n..ry. 


Ftbru^y. 


Miteh. 1 


April. 


Miy. 


,1— 


IM. 


flu^u;. 


^epremher 


Urti.hcr. 


.■^ov.mbcr,Dccenibt.. ( 


D 


ayi 


,ife..| 


foT 


rif» 


cts. 


Hfes. 


fcM^ 


fe< 


fen. 


riles. 


(cK. 


riH 


i;-t. 


rifej. fe 


±. 


rifr^. 


(t<i. 


rif». 


(e». 


,-n^ 


i-r?. 


.jffs.ireH.iriff-, 


'Pk 






h m 


r;;; 


h a 


b n> 


1 m 


irsh m 






rsii, «, 




U~li 


li m 


h m 


h m 




iri; 


Il D> 


h mh mh n> 


J 


S 3 


3 57 




4 17 


6 a. 


5 31 5 17 


434 


4 Ji 


7 19 1 5" 




03468 




4 11 




5 '7 


641 


616 


5 4; 


7 is'4 44^7 59 




e 


8 i 


) i7 


7 > 


4 43 


6 a 


S jSj.i 


640 


4 «7 


7 34^3 47 


i I 


3 1+»t 




* «7 


7 3» 


5 "3 


i6,6 


6« 




7 3o;4 J?-!* » 


I !« 


9 


7 J8 


1 1 


7 1 


44S 


6 17 


S 44,5 '6 


6 454 »x 


7 39 1 4li 


3 I 


4J5I8 


9 


4 3; 


7 i*l! ipS jD'SiH 




7 »j'4 148 4 


li' 




7 S5 


+ S 


7 


+ 'S3 


6 1 iji SOS " 


6 5'4 =77 44'3 45 
574 »3i7 4*3 44 


a I 


5 ) 54 S 6 


i 36 


7 I! 


S 356 »4 6 ^3 


J 16 


7 514^88 6 


3 5+ 


'S 


7 !■ 




7 


* J9 


» S ! i*! 4 


B I 


63 57* 3 


4 4i 




5 4,^6 ,8 6 39 




7364^' 7 


J SI 




7 4^ 


4 '» 


't * 


S S 


; I9V»|4.58 


7 3+ Hi? S3'3 43 


i I 


74 ai 


4 47 




5 47,6 ,16^5 


S '4 


7 4>,4 "9 9 ! 


J S» 




7 41 


J 16 


6 50 s 10 


i 5).^ 8,4 51 


7 84 47 57 J 43 
7 "3^ >S 1 3 43 


S 1 


7 4 4 7 56 


4 S3 


7 6 


5 J' 6 7 6 5 


5 * 


7 45 4 .SS 8 


i 5» 


»+ 


7 39 


4 >' 


6 4JS i& 


5 47 f '4^4 4^ 


3 1 


74 »7 5* 


4 5i 




5 5S 6 > 6 s 


5 » 


7 494 >: B 8 


3 5» 


»7 


7 3+ 


t lO 


6 39 5" 


; 4i 6 lo^t 41 


7 '93 S7 * 4 1 44 


« 


6 4 » 7 43 


S 4 


6 55 


4 5 55 7 1 


4 i^ 


7 S^\i 8 « 7 


J SI 


■1« 


7_3i 






; -,dS l6lt i-- 


7 ^4h 54'i! 7 J 45i8 > 


5 4 '7 7 4J 


5_S 


b so 


i.ol. .,7 - 




75644 S 5 


1 ss 


N. B. ■jX'TiWs/''"' *-■!■' ='='""£• """'iltT.l.k, ifin^ lioubltd, -uill fiicvi Ibi Lag:h tf 'km Hay. U .« r«/'. | 



REMARKS 



ooglc 



md NAVIGATOR. 



137 



' REMARKS«/i#XRAS, w Pmwtr 5/^ T I M E. 

THE Dwft Cunou) Jire it IhM of J'f"! Cbriji, bediming at [be KJJauli of Jamary, imniediriCcly fallowing the Birth- 

Th^ufh [his £rau genenliy received byOin^iflni, jet the £ii|{/^ ■») /ri^ulnl aa ^rn liter by ■ wboJe Yeu la di public and KrJrAKni/ 
Wiitiiig., iKiof: ^e ji&i'a'iiM of tbi Style. They did i»[ begin the Year wi[h the ift ef Jaiuiarj fullowtng the ^oAv/fy, bu[ with the i<t 
of tMC.'c-f:i:it. ox InciiDation, oblerved on [he 15th of A£mi>j *D<i Iheccfore the £af;/j3> reckfned from the Fiajt of Laifday, 174S, itiil 
theie wc.T .-oai^iejtid t^^^ Yeirj. But, from the Firih of oar Loni to the Fuifi irf the N«tiricy) in the Yeir 1747, they numboed only 
1746 Yeir. ...I//.J i «hcre« jU the Rf H of the Ch,ifi,aa ffa-U rcckotied 1747. 

DirryfiiiiUiar, AuUwr ti ii\K Cbnlliia Mra, awde the CuMtfiiim of Chrift to be on the S/i of the XTa/dii/i of ^nV, on the firft Yc»r 
of this Ai'a, and born the Winter toU'owing, it ibe End of the ^Sth Year nf the Riformiilian of the Calendar by JhHi^i Cajar. 

Iiis Wiy of Ctmfulaim wu uojireifiljyii'ceptid, al 61O1, but nowrr/ifTy rereded fiom byDegrect j and did not take Place in EtgleaJ, and 
: nther Hlaoi, bctoie the End of the cIdSxjIt. 

heciiMMON Opiaion it, lharClinjfwai born the Winter precediif the Ti toe in vhich ZJ/oiy^ii reckoned the- Conception ; y«i the EngHfii 
thcAcltof the Cii-rjiiM World, agreed about the Time fince hii Birth for the gieMei Put of the Year; but fur three Montbi, fioin tJ;e 
£a/£wf> of Jainarj to the Sch of the Kalad, of jlfril, they w.oie one Year leli. 

CONTROVERSIES atnl ^ R A S. 
There iie many Ca^nvirfia about the jEra of Ckiatioh,' among the Cbmnbgifli, (ani akofyt viill) fome iDimilng the Weild- to be 
I ^aco Veanbefoie C^irf; Dthrrt affiim loS^. The (Trnt-Church, and fqbrji Emperon i£rd of Creation wji ccoq Yean before 

•'n. ^- . y*i- .r. T*^.- ^t -|__ itT Ij r_ ^..A _IJ^^ . J i*..^!. _i r.--.rr\:r'^^ in _^..__L- r^^l^i ^'^ 



ie C&'jw/f Date of the World iHSuchoUer ; and fueh chrsmltgical Difputei wilfnever be fettled. 
s . _c .i__ ni. — -_j. 1. "rt before Cirjit, odiIk Xalmdi if yiily, *ccatiling toibme j 



The C7«ri-Ch'. 

arij). 

The aniieot .&a of Ihe Olymfiaii begun 775 Yi 
Gr'iki, who yet make the Year of the Jtlian Period ]9]3. 

The ^1-0 of the B|ildin)i of figmii either the Kdrmutt, ^jiYean, oi the dtjrg/ifn, beff'npiag ^tr.Ysi, 751 VeanbefrMvCM;^. 

The Aia of Nahjtjfar, fimoui iniong Aftionbinen, began the tiih 1/ ^liriidr^ of thf Juliax Ye:ii, teckoned backward to 746 befcte 
Ci'i/].' That Day being the lit of the £j;^ruii Year, iislaiy, and, after him, Cnfcrmcai, computed the P/jhi of the u-^ij/Bodieifron 

The y«rfl of AltxanJtr begins 314 Veart before CbriJI, NrvrmUr 11, being on a Sai^ay, and accor 
the ift Day of Che Ef^filan Vat. Between ihe vffra of Naiaiujjir anS A'txardir, there ate 414 Eiyft 
the ^rd of Afonyn, a\lei Dmiejia*, beginning ^i>^it;S ig, in the Year of CbriJI xl^. 

The lurh and jlrskian JEra, call'd Iligira; tikes iti Beginning from Jltii«m«'i Flight, 7b/)i 16, jlaai Cbrifii 61I. 

TheP.ry?-„.>ffrdiicalleJ7-/,/fr,Wbesin^7''«l*, A«r.i,Ch.lJI! f,%%. 

Tw JWiff* Pew/, containinsa(lotherj«ffli, bis been defcribed. Page 146; which .«r«, when ceioced to it, diTer, accorJing lo diffettM 

The ji'iititi diftinguilhed their 7imi by other Revolotioni ; fuch a< the yubilii of 49 or 50 Year) ; an Age of 
Years, among [lie fiiwli, beg.nning at the Wm Ms-n, ne it after the Sammer Solrtice, 775 Yean btdneCbr fl. 

The Ptrjiant obferTc the ^fy/c/ai Account of 365 Dayi in a Year to thii Day. In which Reckoning the Eqmacxa and Seifo 
- ■ rough the Year in thr Sp.ce-of Icofi E[ypt'a-, Tar,, + ffsuri,' 17 MiiMH. 8 S/^oitdu accordioK to Ihe N'-uit^'iai Mean 
lefaraeS-afon begin) a^ain. Thii Year is eitremely convenient for ^' 
intircalai Days in the Redtoningi there being none of thofc Days taking Place 

TheDiyfrtBCfof aYear, or more, between fomr of thefe ,¥.rai, and Ihole we have pven, at Rige 146, (■abicb v)i fudjifpntehh} we leate 
tohcfiirlidbjCbm?l->Ei,l!, makingthi) Subjcfl [heir chief StuJvj as there is do Likelihoodfoi ^sff/'SciMO to agree exactly id thefe Matter- 
nu lafaUi «/ DamonfirMitn. 

Ibe H'tit-daj currcfpondeot tothe Mimt-ilaj, for the reputed Yeat, many Yean beforeCir^, ii another OJ;fiif/<t lying in the Road to Tnrt, 
chranologicjl Computation. For, before the Time of 'Julim CitSa', the Form of the Year, or Ytar if Om/iJUf,, wai ne*er ixtS/j and ttga- 
larly fcukd, by which it will be hard to know the Week-day. on which every fucccDin Year, Gnce Creation, began ; as like^iire the ^cri- 
Jay, contrpondent to the JUiaib-c'aj af any Yiar, Gncc Crcai on : The fatne depending on the fettled Form, 01 known Changes, of ifae 
Year, fiom feme fviicular Da{t. The Anrient ffak and MuHb-Diyt, before Ctrifl, the moft certainty kno^vn, ate icduced [u the ^iiAaii 
Form of Reckoning, whereby Ihry becomi; intelligible. 

WiHH ^W/« Qt/a'- reformed thcOilrndar in the 4;th Year before Cbrlfl, he ordered that the 1 Day of the;'i«i« Year, ihould begin on >r, 
1, immediaiely after tht old Jtsuun Yeat of Ca-fujta, wliith happened, according to Chronology, ontFndaj, Haw [iy 1'ai. f. 148.) the 
D0m.Ut.f0r4, Years before Chrift, Ido-uflins i frrm'4; to find it) was D, old Style, Whence (by Ta4. >. 149.) the iftof yas. in thai 
Yearvi-aaona Friday, agreeing with Chroaolnp, Llfccwilc, we find, on Rrtri/p./?;™, thatigthA^, in the 585 Year before &^, beina 
Leap- Year, wa> on ^Ifidntfday and no' on a M^-Ja;. whe': the Battle between [he'jMMwand Lydiani was decided. Our Afi*flt! again II Firriifia'a 
Afltonomy, it p. 145, wetnerM"ore_/>(r/f ^/weHf ra Triifi aad ^tfiitt. At [be fame Time we obferve, if hit ^ra, 44 Years btf. Chr. fe Irai, 
when [heCd/cW'T was corrected, that Jan. ift happened, by our and hisTuj/n, art \ Sunday, and not on a Frid^, according lo Chronology, 
That the a4ih, andnoti^d Fih. [fttf. id, Fergufoa'i .^/wiii*) li on the 6th of the Aiijtniii of Mok^— and »4 and ijtb of FiK (not ij 



[ 776 according ti 



. and an Olyw-piad of 4 



o be added for 



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rtraj rics apa mib tbi fftik-Dayi it iiibicb tbiy art fixid j (^ 



REMARKS m th* NATURE aa^ MEASURE j^TIME. 

TIME, by our &iK<pl:'9>f, proceeds with a conflante^oable Flux, or uniform Shrx^h. The Meafure of which mull therefore be icTerred 
10 Morion ; and that of the app:ent unitoim Motion of the fxtd Start h belt. But the lariible Motion of the 5» and Mxh hare, by the 
Confentof allAgcs, (19 mote confpituous and obfecvable than that of the P/daci and Srvi; been made Choice of for this Furpole; which Bo- 
lies fecm to have been intended by the iliviM /jrcii'f tfi, be£det their other Ufes, fw ptrfetuaJ Cbrottmiitti, lo diltingulh and niaik out i^i 
Ew/™, Dayi, and Yiari, ai tbeyue. , 

jfflranamcr, obferve that the Dafi, and therefore die Honrj, and JtSnUi, are aatfta/, end [hat by the Earth Jltiki<ti>:g hei Pace, and fome- 
times qi.itkrnia^ it again in her Orbit j belides her uniibnn Rotation from Wtfl to Ea)l, th* fame Way, on her Ann, in a Day's Time. Tiiii 
they ioi'er I'rOm the Sun's diffrcent apparent Motion, through tlie rame Length of Veal, nearly. 

Therefore, to meafure Tinic, orrefcrit 10 mi S/jMbrJof i.ji(/«T«MciiiM, (as they imagine) they hue fiaed the Length of the >/ar I «r 
[or that Time wherein the Sun and Earth finiOi their feveial FoatioDs with eatbotbei, ,aua begin again) to the conftant Period of 365'! jl> 4^ 
S7' 19'N fcc- accorjina to.Sir /fjjeTI/fgim; but different b; others. 

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moring fbnnrd 



I Wit or the othar, thii Loigtk of the Yetr I> aamorttrrtiiBerpenBtiBtnttiiiB^itmitiiLtngiis/aDiif. Since, InthisCom- 
putadoD, they divide the DifhiDCB of l^me between aaji two diftant Ejninua, or SdJHai, oMerTed, hf the Number of Rerolulioni becweea 
thole OUemdonii wbonby ibej but datuininc the mm t-enpb of the vari»bU filar feriod, whieii tbef •ftennidi foppolc pmouieat i 

To do which, ■> Sir^wMnm went aotuthnbuk than 10 Vc*n, betwlit the UrttandhS ObCcmtioD, he coold net detennine t) 
Length of the mean Year to fo great In ExaBiaJs, ii if he had gone aa fat back into Anciiiartr, ■• Ptihmy't Time, ot befbte, for his frfl 
Obfirvitiu, ForIheiK«rolar YearthiiWay detennined, bjr the gnat Diftance of Time divided by the ^ac Number of RcToluiiaiu, woHld 
hiTC romefouur the Truth (tac^ im jiaitirriia tf tht mam Maiiiiif ibt SimarBtrtHiJi^ffi) thai i/ there had beeaa conSdenble: 
fominittcd ia the Time of the tfiOtfavmia, or elftwbae, -ja, it' woald bar* became infigDJGcant for one Year, bj in DhriGoa ii 
t great Number of Parti or Remlutioai. 

Htnce, ]fi5d.i4i34oi7 i ifijd :i iii i iii.i)aio]8i4, tfi, ax ii* 19<> 45' 40" 7*, Vt. Son'i MotioD in ]6( Darlt accordhtgro 
Sir IJiuc Nnotm, From whence the mean diurnal Motion in the Ecliptic ^ 59' t", (St. (at before obferved in the TaUri) whereas the 
■ppaient ot ml MoCiaD amount) to 6 1' fometunei, and at ocbar Tlau* fiarcd j to 57' i The bm* and trin Time beiag proportional 

id Ina Motion! I 

But, confidcrins the antti Preceffion of the mltuQitl Pointi at die mean Rate of co', according to Ibme, but dillerent by othen, the 
Variation of the Ecliftic'i OUifairj, the diAereiu Diltancn of the tkfmtd Eju'itxa, or Sslfiica, by which the Solar Year la difterentlf deter- 
mined, AiTaONOUiCAK TailII, fanned accordini to thefe diffirai Priicifia [aihaibceu the CuDom) mull vary awt or jkfi from tbe 
Truth in Computation i verifying Dr. Haffn'a OUbrration to hii PriW ihit " all jlfiimimcal'tiibla art tudt lo ta mradid," Andtheprefenl 
Hiptrior Actmrttf wc pnWnd to, in oar Tablei, ii bf ■ Conrparifan with, and lii^co*emeaI of, th* latatt and ie/l jtuilmiia. 

Of REST «/ MOnON ^ BODIES, tmi •/ ANTIENT W MODERN HYPOTHESES. 

RZLATITE J^f we obterre daily in iheHafleattf inenimctedjllamraboat tta{ but AitoiitTt Rmt in any Thint we obloTe, iiaibard 
to diftingDiSi, uan«if(ih((^»» in infiniteSpace. 

Dr. BrtJlij, by hia more diligent and coneA Obftrraliona of the Heareni, wla fbe firS who difcovered the jtbaratia af tht fiad Stan, 
(raufed by the Uoticin of Light and of the Earth in ita Orbit) who hai alfo made a Dilcnery of another apparent Motion among the JlxiJ 
St»n, hi hia Letter to tUe Etal if MaitlafiiU. And it baa been the Opinion of the anriair, a> well ai itii now of theaaei/cri, AAroocmcrj, 
that diflerCDt Woiida, or dilfant SjHimi, bave a relatire Motion among one another, at the fame Time they are relatiTclj 
ffrb^ ia Orka mad a eatral ffarld) in infinite Space. Thii Notion of a Pinralilj of Worlda hal prevailed ever Ra/x 
hitunan, who maintained (at n* anv dt} the Probability of the fiviral Flanai being inhabited by a particular Kind of Biii^i, Tu. 
tbo&Regiona. Wholiknife maintained that Jhe Plineti were reUined in their Orbitt by the Power of Crarity. rhai iiih Plaan 
rmaJitiOrUi IHe a Sitat ni^rtid rumd ai ibt End tf a Sin'mg, iy Centripetal and Centrifugal Ftrcti, Ani Lucmiiii, taught by Cnu 
foppofed WorUi without Number, In iheinfinite Space, counterpoi ling each other, by fome general Ldvi «^Crdviidfi«. That if Bodietwere 
bounded, tbofe, within the LnwV, would, by the AttiaSion of one another, in Time, unite in the middle Spas. 

And bctdnit ia obfenable, that tiwd of Space appear at im/Hfiiltta Conceptioni aitheLi'auVi of Time, or ^ Eaifter 
Tbooghtcanima^itew' "•■-'■'■-' ... 

IMJitmmcni except ^ , 

Inunenfiiy of fii^oKf, in their fereial luw 3fa^. Therefore, anETiavAL andlm 
TT. But the i«fimf Sact^intf Timi, and the Pu'tii of it, from whence all ana Frwu of T&'af. Bdi^i, and theii allooilhing Cia^, take 
rbdr Place and EJIea, who but anlnrmiTi GiiAT BiiHO, (tttnu/^ ai;Siir; <^<n «!' f^°rU} can compiebend I 

The Ancient .^nwwri Itril Inugiiwd, that the Cdi/fjiu/Bodiethad a circular and equal Motion round the Body which they fu^ofed at R«II, 
It not finAng (hia Cimbr Htfetbifiito agree with their Obfetvation (the Sonfpeoding near tight Dayimorcin the Northern, than in (he Soath- 
B Stmi-CinJc of tteEcIiptic) to reconcUe Appearance better to Obferratian, Gied the Sun, or Earth, at Kelt, 34joAich Patti from the Center 
nfdwHippofedCircuIar Orbit, » the Radius of it it looooo, which Dillance from the Center it calted£[c«rr»i'r;, whence they readily calcubted 
(hcSaa'i Plate, at any Time, This 32«ry, though agreeing pntty welJ for the Place of the Snn, the Motion of other Piancti could 
KCoaBttdfbr i^iti Therefore it was changed by A^^^trr, for the Elliptical Theory { which foppofcs the Sun in the lower F«vi commoi] 
Ell^leal Oiblla of aJ the Planets, with a rotary Motion only about hit own jixii, they circuliiing roand hin, and defcribing confimtty ryu/ 
jlnai m tnal Tima (tr Anai frtfxiiiaal U Iti Tiam) fy Sijt drmia fnm tit Smt, I* tacb rifftOivi Plaaa. By the fame Hypothefes are 
raprelenttd thcMotionaofaU the SecondafyPlaoettrowid their Primary onei, placed in the lower Finvi of each Secondary's Orbit; And thia ^*«- 
tigtt anfwert to the Appeanncet in Ae Heireitt beyond all othert hitfaeito inrentcd ; though Kiflrr himfelf at Jirft doubted whether fome (frM 
Tary from true EZ^a ; Thinking it it not improbable that Ibme might have a Form like the SeSioD of laEa, by theForce of Giantjdi. 
lating one Part of the Orbit snore than another. But thii Theory fbllowt the Track of the firft DrtirEr •Tbrcry, whid) CtppolM the 
Son at Reft In the Center of the planetary Orbiti, and Planeta moring circularly round Him, whereby they muft detcribe equal Ait» ■> 
oil Timet ) aa they ate now foand to do in the Elliptical fi-aj, by Ob&mtion. 

The Sun'i hg* apparent Diameter in J^%u hai been obferred ji' sg*, and hit girateft in PrnfM 3a' Jj'. by which it ftoold icfnll, tbal 
e Sun't greatefl and leaft Diftanco an at ijej to 1SK9, aa 101661 to 98110 (vii. KtiTi ^rim. f, 177} and the Eccencricity,oBlr iW: 
fiach Pacta, a) the Radiot of the O'm&r Orbit, Sem. Tranf. (ornean Dift.) °f the Elliptical Orbit iaiooooot But the antient Becen 
trkky Mjoia^ove double ilSCi, ftom wbcncetheCiKa&rninjwat long ago coodnded to be fille. For, admittiDg but 1735, one half of 
tbcanduit Ecceotifcity, it would better agree with the Son'i ^parent Dtamcten obferved 1 But then would not, b weB aa Chetwdt, accooot 
for liic Appearancea ei Aa Snn'i nneqaal Motion roond the Yeu. And (ai the Aadrali did) making the Center of the CircBlar QrU^ the 
Centerofequd Motion, 1715 Eccentricity will not account fcr die dinoM/ Ineqoalitiet, For the trJUfhanJa, or Differeocea between the 
San'a tnean andtrvePlacei arethuatwicc ai much at what they will amount to with thli half of ancient Eeceotricity. Thia Ji<fia of 
EtHmrititf of the Circular Orbit «ai afterwardt neariy eompanlated for, by placing half of it eack Way from the OrUt\ Cealer, and nuking 
dw Center of e^ai Motion at the contrary Eitnata to that where it placed tha Sao, in the elliptical Orbit, whliA U fuppoTed, by 
WxrittABaliMUt, fimilatto the Center of equal Motion in the Circular Theory, Mr. 5mi('t Eccentricity 10 tbit Vhnrf of the Earth't 
Motieali 17]!, Mr. Fiba^ba^t liqi, Mfyir't ifiSo, Menis't 16S1, Onr't 16S5, whidi make a fmall Diftnence In finding the Si ' 

Place from kit Mwn | aotit ibHDttfaeBce likely to be adjuiled, while different OtfirvtU -' ' ~ 

flmeGiMTLBMAIt't EiTATi, vary, in thdt Quantitiet, frtMn one another. 



I of the Reavent, lika different Stavijirt of the 



X^^ barinf obferred. That th* Sparf ^ 't* tcntdical Trma 1/ teoMai Ba^a, mimtlh Caha >/ tka Dijtaata fnm iht Calm tf lia 
lOiii^ thai irtict Arj art ffftfid u ftrfirm tbtir Hiidl Mtititm, (i.e. airhCaia tf ttt airam D^t»ttifmtt» Piidj einat ^bitt ittf 
\nvlaa,'} TbiiDVTvaaidtLTjiwjof Moriowjciuiiiaed andcoiLBnwd \] &i Ifaai Nneita, asd Tcrified by OUcrraclao itftlf, iionlycon- 
J aaJIfled by faffiAe% the Son'a Motion, and the Earth at Rdt. 



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PRACTICAL QUESTIONS 

in', 
CHRONOLOGY anfwered. 
Of USE in HISTORY. 



Q^VESTIOHI. 

ANY nor, MtMh, mnd D4f */ tl4 Maui, iitug rim. n Jtmd lit Dn */ tin Wmk. nrt^MJnl f 
J^ EXAMPLE . Whic T)%y of the W«k wu tfae nth of March, \o the 4(h Vni Wore the npottd Tor of CMT, tbt Dtj olMn. 
In tfac£r;i>/f ortheMoanhippcDcd, ■ liltle before the Deitfa of King ^osi^ it then»/Birtb.of Or^. 

B7 To*, p. 14S, Che Demimical Ltttoi, for the Veir, ire found, at Sight, to U BA, which lift LetNr, A, it alad tftn dies4th of Fdraa- 
r^ CoaTeijuciitl)' b]' 7*f. p. 1491 Mirtb laCh, tlut Yeii, wu on ■ Siaidtj, nquind* 

0^0 E S T I O H n. 

t/ tbt Math f , 

Tlui being the Remfe of tbe former Queftion ii uiiweitd from the fuoe T<tMi, diteOlf, at Sifbti 

q. U £ S T I O K III. 

72f i\fr rfilt Maubibat'SAtri fallieii, it atfYiar, Saw* ma, itMimut^Tmn it figll taffim fi tm, w t^fi Mnkffaid 
<u. •■ lU >« Diy tf rh McMtb, «if«- »curdi-t n OM •>- New Scjle t 

EXAMPLE. Let the 15th of AAirci be the Time of Ei^n- bippening, wheoi KcordiDS W the Pio«ib, HtyLttdfiUiiat^ttif'it^T 

Here, Mani the 15th being on i Sumlaj, zht Dmu'mcat Letter, bj7ai, p. 149, will be alwiya G, lot Old 01 KnuSijA. 

Then, byTai. p. ic;, find ^fani ijih for the Time of Kajlr bippening, agunil the Donuiue*! Utter G, Mb Sljit, tai jva will find 

^11. 14, ibrthe GoUenNainbeti, Auiding igilafttheTinie, when £>i^ can poffiblfbtppeat with the i}MDwM/i.mrO, jor thatTime, 

In QlJStjlt, it tuppeoed when the (7i^(* A'miiiin were 5. ij. 16, ind Dtmim'eal Letter G (SaTal, f, Ij6). Now, ■ DoMiimcal 1 
Cicli it iS Vnrt, and i Colden Number Cjde, 19 Vein, (in which PerJodi the Uomialcil Letten ind Colden NDmberi return to tte _ 
Order, O 3.) ihenCbn i3 by 19 produce jji Yrin, called the DitnfiaH Peiiod, being the Cycle after which Ei^, ud til the MtBt^b 
Ftajb, began and followril the fame Order, again. Old S/y/i But, Ih^ Order ii iwtrrrwfted in the Ntv Siyli, by the Day reckoned lift in 
erery fucceeding odd hundredth Year, than it recluinrd by the Qldjalia* AamKi, and there will be iMirmtditt Yeara, in htih Styla, wtxrain 
the Colden Number and Dominicil Letter will happen die fame «a ^ain, bdintthe Ixpiration of Iha Ikid Diin/Mi Piritd i becaufe of tha 
Ilotatian of 7 Lctnn 4 TimM is tl« iS Ve4t-L'ycle. For, by Tai, p> ijOt the Yean when tha Golden Nunbeii an |, 11. and 14< 
afcaifollowi. 

Gtldi* Nmitr 3. GJda Ntmtir 11. GtUaa Ntaihr 14, 

1763 ■ . 1807 , . 19M I ■ •ei6 "1 1777 . . iSij . . 191a i : MOj f 17(0 1 . 1S18 ■ . 191} , . toeS 
88 16 11 0,3, 1 96 3+ a9 a4 1 « j? 3« »7 

I*m^i 'b-fi 4« 40 S4 l-toKrf » 53 4" +1 l.*«'jr 5* G'SI O.46 

rrari hy Dm. 64 59 73 f u ibt ji 67 61 f j<«* 75 70 «( 

La. Tai. fir G.Sj ft 0. 91 ftc. 1 >wr. 91 86 81 [finur. G.94 8g «4 

Jtr. 5. p. 149. 97 J ' ^9 '"'^ "^ 

t3> InibiiMainiirartibtrtaTiiaclmardaatoiiidfirN.S. iy Cnmria. And UcewiTe the Yean backwail BC fbnrari, fbt O, 9, an d 
examined, correfpondeot la tht Golden Numbcn c. 13. 16, I7 the Domiucal Letter Table, Old Sqrle, at p. hfi, far tnjVun (bdiiRoi 
fince I7J9) to which the faid Golden Numben belong. 
AccordiatloN. S. Ladj-Diy/aili enJUmi i^, in tha Yean iB<3, 18941 mu ton, ao^i *ogti ftCtCniB aboifc 

<iJJ E S T I O N IV. 

^Ladt «« tors H M Alh'WednelUay, 13 Febraarri N.S. and nwi nad" ■toTttr^tf.^, '759> "f"^ btrj^f 

Bf FirfUiia/litH'TaiUi, (fee farther on) When j^f'tdmldai iru ta tttb tji tit Fitrran Ei^ Mi wa ..^ri/ tg- *l»>t W^'i' ft *SSt 

the Etmaical LtKtrlt, and Culdrn Numbvi 7, 10. jj. ig. when fo^ir can fo happen. I 

Now, by examining the Z}^^ for thofe Colden Numbtra, ftoD T«li^, p. leo, between 1719 and 1759 [tbeDiffertBC* to Yean, b«lntlhoi«| 

theAfc) and that Dominical Letter for thofe Z>«n, hjTai. p. 144, Vou will find adv the Year 1733, for tht Tune of "her Binh, when thai 

Cold eaMiimberwa«T. and Dominical Letter B ■ Cunftsuently, tbi Lady'i jtgtht^Ttan, rtjalni. ^ J 



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Q.U BSTIONS f» CHRONOLOGY i«jwr,i. 



Q U 1 S T I O.K r. 
XPiiiOB aim 53 ftvt 'f Agit i» ttt T*Mr i^jgi Kui (•"• M a Piidi;, Jalj 14, «lMt tbiYiar 1700, Old M-New^rfAf Hifmnd 

o OW ot iWno 5rt/(, by Tn*. f. 14^1 "u A ( tht von^ Yeir to which 1699, 0. S. or I70j, K, S. 

t both 5n/n, by Tai. p. i^, and Tgi, p. 149. Whucc, hM./ffc, in I759, muflbeCo, according tt 

herefore hit Age ii 60, rrquired. 

'inite'iriar 1/ li* riprntd Birth sf Chnll, ibi GsUa N-wdur vai t, lif CyeU a/ rit St» ^, anJ Rain ItJiSwK 3, Tear tf it, DioD*- 
mPiricJ liiJ, tf Ibt JvhtaPlT'iJ ^ij. HiAce, IheReafoHof theRoiii, p. I^ti. 

q_U E S T I O N TI. 

Ttf Cjclii '/ Itt Son aW Moon fcirij f««(r, n JW tin Tiar cf fit DtonyfiiB Ptn'id, aenrilir " Old S*y< f 
RULE. MgltiplT the Cjtle ot tbt Sun by 57, and the Cycle of th* Moon, or Golden Number, by 476 j divide the A* of 
dufts by 5j», the Remiindtr, ifwr the "Juotkot, will be the Year of the D«ij|^ir Period, rtquired. 

EXAMPLE. The Golden Number it 1, aod Cycle of the Sun j, it the reputed Btith of Cluill, to find the Year of the Dia^fica Period, 

thalTiite? 

I Goldea Numbeit oi Cycle (if the Moon. 9 the Cycle of the Sub, 



if th. Pr, 



47S 



rh,CjtU>ftbt%Ma, Mool 



i's 



Q^c B s T I o w vn. 

n, ■Sn"./ pvn lifni Ibt ¥ar tf lit JuKln PiritJ, amrjini It Old Style ? 



, .„ _ , _.. , . will be the Year of the 7«// , , 

EXAMPLE. To find the Year of the ^Wuii Period, at the rioted Biith of Qbtifi, when ibe Cycle of the j'm wafg, the Cjde of th< 
Mmk, or Golden Number, wu i, and the btHaie* j { 



»07+« 
4360J 



X Kem^det 4713 JuGan Period lefoiftdt 

Q^U E S T I O K vni. 

Tt jfW til Ymr tf thi Konyfitn Pirioi, aranEfg It Old Style, fir mf Tear ttfin trfim Chrift f 

Rln.B I. Add 7j (the Comelement of 4;? to the whole Pntod 5)1) to the Number of Vean before ChtiH, ind dMde that Snm by 
j^i, aud fulitraa what lemaini ^om 5J1, and the tall Jlnuin^will be the Year of the Oinai^ Period, fat the Number of the Year i^ 
Cbria, required ? 

N.B. If lit Sim "/7Sj "•J '*< 1""" V^' C*nj*i ii hft ibam si%, fuhroB that Sam fitm S3«, anJ lU Rmaiaia- ni/lte lit Ttartfiht 
Ptritd, riaylrid. 

RULE If. Add 457 to the Number of Yeara Gnce Chrill, ud divide that Soin Vj jji, and the Remainder wtB be the Year of Oie Dit 
wifan Period, for the Year, /mi Cbrifi, required. 

N.B. If the S<.m -f ^'^, atdtbtYanfitaChrifi, »\tS»lba» ii\, Ibt Sam •aill hi ibi Tiar tf tht (aid PiriiJ T 

EXAMPLE 1.. I0O3 Yean before ChriS, EXAMPLE If. looo Yeara fiace Chiift. 

+75 +457 

S3»)"«75{» i3»)*4S7(4 

1C64 lltS 

— II Reiaaindet ]«g Year ri* Diurtfita Peiiod^ nqnired. 

Rtmaioder jm Year of the Duaj^a Period, reqnind. 

Q_U £■ S T I O N CC. 

thtYiar^lbi VHoaj^taFtritdhaiigpvtattiiUrmitfrtmiliiacttberiarUfintrJlaciChriJIt 

Thia he!^' the RWefli' of IhiTorniir^efflai, letThe Z7iW;,Gm Period be jig, facA Teat lihce'Chrift^ or jii, fobie Tear Mot> ChiiS. 



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QUESTIONS M CHRONOLOGY anf-w^d. 



i YttnEaceCinJItDBeiwiiasofibe i&PcMi, 



^36 Von fiocc Ctrifl, nbcD Period wr 
nniiDuauj. 5JI 

loOD Yart befon Cbrifl, ifheD Period wii jji, 4c. l+fi! Vuit Goce CJnjf, when Period w 

N.B. Ja tbt ftrignwg ExBmpk, before ChriH, i JbnU hi eJd'd n Ibt9.e!a\t, 531 

dli'jn; ;ii, wr^'r i/hnid bruthum fuitraaidfniB, tooa, rbfTr. it/en Ctri/, — 

fir ibi kiftli tf ith OprramH, liiK ^ii, n ap-u vilb Cbrntlagj. StxoaiCbn- ao«o Vein GDceOnj?, when Period w 
~iiltgU*l Seal; fiUheroa. 

Q.ITESTION X. 

Chrift? 

47>4 C'** JVBufer ^ ibt Firiti, n lit til Tar 1/ tbt rrputJ Bint if 
Chrifi> the Remiinder will be the Yeir o\ the julim Period for Ihe Ye»r hifm Chrifi, rehired. 

RULE II. The Number of Yein, >« Chrifi, added to 471J, the Numiier of the Period the Veir before Chrift, the Sum will be the 
Yeit of the Julian Period, for the Ym.fiMtCbrifi, required. 

I ift Vr^bef. Cbrif. 
*955 Year of the Period, rijtirti, 

Q,U E S T I O N XL 

To find ibeYiarhifirt tr^teChrift ttrr^pendnt li tbirniai Tiar if iht Jaliin FiriidT 

ThiiQyiiTiON It t)K Rnirrfi of the tormer. 

RULE I. The given Yeir of the Julita Perioii msft be fsbtnOed from 4714 for the Yeir btfun Cbrlfi. 

RULE II. 4711 muft beiubtiaaed from the giicn Yeu of the ^n/in Period for the Year Cnce On/f . 

EXAMPLE. Thegiirea Yeiriof ihtyu/iaiPmiuf, are 1955 nd 6473, required the Vein of CXrjfr 

fobtrailed 4714 fubtnOed 47I] 



Q^U £ S T I O N XII. 
^P*rfimjaa thtYiar ij^o faiJ, r j«I 49 3Twt lit Yitrt tf til Ap vidi ijKtl It ttt Datt if tti Ttar m vMA bi toti twn ; What Agi n 

PUT X bribe Yoriof the Perjbn'i Age. Then49«^i7jS — «. By Saffijiiiam, Bat49*-l-r^l7i>, or jb— ^35 — Vein of 
bit Age. But thit Age being fabtufled from 17 jl cm leate no whole Number for theiJuMi wlwac* it could not be 175S to which hit Age 

reekoned. Let jr ^ the Diai, then jr ^ -i— { bare 11^1750, ftc For the Tinw to which hii Age WM itckooed, being £vifible by (o. 

5° 
nience — — =35, hii Age, and 1715 wf* the Date of bU Bint, n^it^. 

A GENERAL PROPOSITION; 

r<i ^ « whole A'i^e-, wtichitimgJlviJtJtf mttp'ofn ttbelt Ntmtrt, otH* itliiie Nwmitn JtaB rmaia. 

EXAMPLE. To find aw^u^ Number, which being diyidtd by s, 3, 4, j, and 6 j 1, 1, 3, 4, and j, IhiU lefpcfdnly Rnuin } but bt- 

ig divided b)F 7, Nothing ItuU.rrmaii 
Axiom. -Jby vMt Sumtm bari 

Pat M.ssthe«>iH[r Number, (boghti tkta, " • ■', ^^1, - — ^^Z!, HI*, .' -, will be-tlie6CtM!''''i»< of the QjelUtuij, cipnSqg 
^t fammttli Ngmitr, \ 

Let ifi CondttioD, -^ ^ a. Thai x c= i*4-i. Sabftitol* which Valae of s, ia tdC—^tin. Then - - -.^.,. • vbtk Nniaher. 

IBnt, ^—^, a w&i/r Number. 
Wheare, Jra=e»-f-j. Vbt xfi awi td Cttiliita,. . . . Hut, a= ii+i.(mUw^rimii Bit. . . . J — ^ = J, a viukNutnber. 



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ne ROYAL ASTRONOMER 



Q_D ESTIONS in CHRONOLOGY apf-werid. 



: tbit Vilue at >, in the iiC»*£iin . 



t iiH-ii- The tp, iJ, aid %i Caiitimt. , , . Here j^su+i 
Subllilute thii Value of », ia the ^i Ctadirim, Then 



, OE }^-^' , ■w.Wr Number. 

', a vibtit Number. 

- :s c, ■ leWtNumbei. 

. idW< Number. 

— i^, 1 wici Nuinber, 

ift Dif. . . . -= — ~, I «•£(/( Number. 
5 

i, ■ «Mi Number! 



= it+i. + 



iH-» 



Whence, ]r^6c^+59. The ip,ii,%i,*ni^hCaK. t Id Jim^ Tctm, Here, cs:5/4'4. . • id Dif. - 
Alio jtiCtHbiM, tiirill^pe*r. 
For, fubftitute thu Vilae of >, in the ^ib Caaiiim. Tlica, 7" ** i* i w^t Number b; Csujtfaatt, 



Thetefon, AibSitute the ifore^ Tike of x, ia 6ib Ctmiit'un, Theoi ■ 



Whence, 4iot+itg. The i. 
7i(0iiisiALAri 



7 

J But IHJ., I win/. Number. 

1 7 

,ft Dif, li't* , a toW/ Nnmbei. 



Ti«i Ta>aK«M, /■ (i( ibn^ Timt i tmfanriiig tU iti CnJiiim ef ibi ^^m, la tbiniai ilwill, 
•.SI. n=o, thei) 119 ji.the/ujfwbale Number, 
^ f^i, then 539 ii the tma whole Number. 

rx=i, the«<)j9 (heiwrr, &/, tJitfaiiiim. 
^^ AllotherOgeftioni of thiiNaluie areuirwenil ia tbii Mauner ; the tiif/' BuGneft bang to tcdure the readied CWirim. to FraAioiw 

inthe Ami^Ttnu, lithe Operitioa proceedi, in order that the jSio/tWhi may takein all the Co/ii that can happen; wz. fr ' 

3, 4, ?(• the fuoccfliv* ValnMof the iQiimedwhole Number. And Ihii 72ami will be either d^raa/ivt 01 aijoitw. 

OTHERWISE Miptlvrlj. 

PUTxforthtNumber u before, and Conditiani the lame. 

Lei ^*, \fiCcn£iifn. HeiKe*=:i4+i, it before. Sabftitotcin idCmSmii. Then, , t wiwZt Number. 

J But -J—, a mltb Nuaiber. 
I 1 

. . Dif. .. ...^ilL'sf, >«>&«»•«) 

3 

rhen — ~7^ = ^' -— , •«dM> HsBber. 
4 » 

WK.~l-f4> H i— sr, iv^iifrl'wb 

Be-l4«> + -^ 



SobOitnte thiiVahK, in tbe jdCmSlita. . . . 1 

Whence, xsiw— 1. The z. 1, 3, Cadilitet. . . , Httti^u . • . 

Submtnte thi» ValM of «, in 4(fi Oaiitim. Tbn, — "Z^. 
S 

Wlieace, iin=6o^-i. The i. *. ]. 4 Ct»iith»t. • . . Hen<sj^ . 

Andalfbj 



For, Subftitott thi) Ythie of ;r, in the 5(i Oattim^ Then, — ^ — , t okA Nonber b; Cm/rfMnM, 



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and NAVIGATOR. 



163 



Q.U ESTraNS in CHRONOLOGY anfwtrtd. 



mat iffrmMevtsxnwit. 

= 4>a( + 1 19, at before, f 



of K, in (^ Sri &■<£ 


d». Tlitn , a «>£*& Number, 

7 




m,. !^+i£Zli, ,«,i^ Number. 




iftDif. \ -Zi-, ,o,Wi Number. 




jdDif. i 2£±i, .wi.Ji Number. 
i 7 


H«r,rf=7, + , 


. . , . _fr^ — ,, ivioii Number 



Fromabore. iftDif. . 



Wbeace, ■ ^ 410* — joi. amfoHrim J 

Let c=i, then iig i* 
R=i, then 5J9 ■ 



J±i.=..> 



It litfi whole Namber. 
it the next whole Number. 



es], then 9J9 the oeiC) 9e, ^imjauiu 



<IJJ B S T I O N XIII. 



REQUIRED tbeViAK^CBtiiTTvtflififOoldeaNDnibeT 11 j, ■jn/fifCrr/'g/'ieSun 6 

i-.L- .n.-„j;.i.. .;. .-I. _j._._ .u.-„„. ,j beihiJrtb^ lafortfaeGoMeiiNumbe. _, 

:o be dirided bj at for the Cjde of the Sun fi to remiin. 



'^4 *+l 



CaiUlins I. ) 

Pi>t*=N<>.Tculbutlit: Thea JfT^'""^ , i±! 
T9 * 

Leltlt Conditios— v^-^a, Tben «:= 1}« 4* 4- SabffiMElDg wUdi in id Cocditlon 



Number 5 to 
r the SuD fi t 

will be the tw) Cagdiiims of the Quefllon, cxpielEng the 



'sH-r 




NisATTTiTaaeiiBK. ^ Lei Mho 
Heoc^ M^cji^^jgj. Iiirumed 

Vwhole N< 
ArriKWATi*mTiis«(SM, Ibewbit 

-=SjaH:il7. JitwiU. 



By the iffinBidre 7£fSrni. 
Let *=d. Then 137 the led) Vear of Ctfi>f. 
i=l. Then 669 the next Year of dm/. 



qj} E S T I O N XIV. 

IN what TVorB/'rif DMnyliinFn-Wwin I'll rieVnrir^Cbrifl, v/bnilnGMa Ninaitrviia i, mj CytU a/ the Smn a f 
ThefiitTCni^Vinuof (hit Queftion it to find tke lealt Number, which divided by 19 and a S, lliall lea» i and 9 lefpeftiTelf re 
CWin'mi I. I. 

Fatjt=xthalNiUBber, Then -^^^, -^I^- wiUbe thei&aifrVitiuar theQuefHon, expreffidttheJd■Kw£llA^*ni«-• 
__ '9 »* 



db,Go5^Ie 



««4 



n< ROVAt ASTRONOMER 



(i.U ESTI0N5 in CHRONOLOGY nfmnJ. 



Let III Condition .lf~^-siti. 


H««*asi9.+ I. 




SuMItDtt tlM V«lw la h/CmCow, Thu, 


NiOATivi Thiokiw, 
Whtnce, *=sji* — 75. 





Iji Che No. 
(ATiTE TiKoixUi I comu But Ie& 
= S3»* + 4J7' Jtlmi J31. 



Btri, asaiM — 4 > . . . iSTX£,~ 



«r of the Period, I 

harm. \ 

abet nquind. J 

A'. B. The Dimjat Period limiti the ■) 
Anffffrcothe liajT wbtit Number, or V 
Number in ibai I'tritd, J 



N. 8. The Dimjaf Pei 

N, B. Blrbtr •/ ttr ainn Tbtattmt fad attamj ttniiliaal Namben at jtg fUefi. 
(ly E S T I O N XV. 



Froniboref illDif. 
>d Dif. 






> «Jttb NuBilier> 
• wtnb Nninher. 
1 tcMi Nun^MT. 

, ■«>£•& Nunber. 

^ f > t ivMi Number. 



-, > «iAe& NniLbcr. 
-, K teii/r Number. 



THE GoMen Number hiiiig 
rmro/rjc luliin Period? 



ihtfurbifin CbrlQ, lit Cjib ^ ite Son 9, («f^rr) dii^ (je Romin lodiaion j, mtat teai llet ti* 
1, 9, and 3 OuU rt/ftflniily remain. 



= the Namber firaght. Then 



to 6ai (he Jis«^ whole Number, which beiof divided bj 19, tH, 
Caitdiiim I. a. j. 

* — 9 «— 3 



Two of which Caidiiieti 



re detcitDined iboT^ viz. x^ ^^^<\- ^^ji 

SubfUtuce uhich Take of «, in the jd Condition, Then 



will bi the ] CmJIinia of the QueflioB, eiprclGiig the fam «ig& 
531* + 4 ;» 



ro. j5f + jo+ 



7* +4 



- AmtMATITI TntOlIM. 

Wbeoee. -=79a« + 47i3. 

And whence, thea 4711 liiheN 

of the Julitm Period, njsirtd. 



NiOATiTiTntentM. 

Whence* =: 75g<K— 3*67. 
And when f=; i, [hen47ij ii the Kombcr 7 
of the firiti, u befote. J 



{^- 



Here, Asije + B. 



iRDif. 



Fraa*b«Tt, ill Dif. 
-7. ... sd Dif. 



•S ' 
•5 

"i 



Here, isaije— ; 

N. B. EiibiT tf ibi tttBi'Ditoitna fni ai ma^ t$aJilii^ Nuittri M jtt plafi, 
' <iy B S T I O N XVI. 
THE GviJniNtmirrhiniii, Cfclc 0/ iki Sun t, ai,J t-JlSicn g, rtfaind tbtDut rf lit Tiar, O. S, vtfm ihifi iaffeuJ f 



ntth KwnWer. 
«W( Nomber. 
«£e& Number. 
: t, ■ ciiWf Honber. 
^ttb Nomber. 
ntib Nunber. 
t, ■ vMc Nambci. 



DigHizcd by VjOOQ IC 



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165 



Q.U E8TIONS m CHRONOLOGY gijfa/w/. 



tasYcwftniiht, Thai' 

cipielliDj the /av nMi Niatitr, 
Let ift CwtfiiM, ^ ^— S3 1, 



iS 






> viU be tbc 3 CiMKrrnt vf tht Qs«ftioB, 



•Sit, tbtox^ !$••+ M> 

SabAitott thii Viloa of * 



>»JCn£iiai. Then, 



ArrttMATTTi TBmomif. 
Whence, x ^ 79*«' + rjot. 
Andwheorsd, then 1701 ii thci)a(i«f tLc 
Vearj 0. 5. rtjaircJ. 



Here, < = !» + {. 
Snbftinitc, tbe fbregoisg Vilne 1^ iatbtji CMiiii 




Hai, it^i^^+^ ■ 



idDif. - 



■ vbtli Nomber. 



Miei I 



The GENERAL PROPOSITION (Pige i6t) O T hi ■ w i • i Aorwered. 
LET tbt Sutliai of ttt (am -niUh NrnHbtt ■aba Jk>itUd ij aauttt vibtU Htmhr it taOid x, -ahtm iiviiti ij tficnJ nltli t/amitr it itOid 
b, ijalUrJt, ijtfiHrtbi, tjafifibc, hytjalbf, *r 
FotHiK EiAMFLi. To find 1 whole NumbEr, whicl 
but being diTidcd by 7, Halhing IhiU ramiin. 

OmJilian j. J. 3. 4- S- •>• 

Hat, M+i Bi sH->f =: 4H-3 » S<H-4 e= 6r4-5 s: 7^^ vhicb are the tCmditi 

N. B. Tlf ibUfTbing btn It U amJUiriJ h tt fuJibfValiuof tbtdiftrrm&utiau; b, c, t, ttt. tf tU fame whole Namber, vfa* 
JimJiJ6f£firtwfnioliNambtri,fiaNiiibiiigJbaartmaiii, tnrdi^ it lit frvettlBufr^,,., tmiC ' 
' Jiy vbtli Nimitrltim Jnm ibi fimi, ir » difftrat vibolt Niaiitr, a-uMi ^lamltr, tr 



X, ], 4, and 5 Dull, reipcftiraly, rei 

of the Qseftion, expreffing the ftmxpMt 



Inthe i^ao^K/Conditioni. u+i = jU.: 

SubtnQ I from each Side, m s 3^" 

Subtraa li . . 



t/aiim[, /laJlriatit, 

I, a w W( N« . fiai[bt \ t and h cooditiDnil w 
I, a coDditional n^giVNumbei, diiifiblc bj t. 
. I vAtU Number, diyiSble by 1, 






/ntnti, ii-^is=l, theiJItiuttdCtiiJimin. . . . Here J=i, luifl. i+i, a tdMi Nomber, dinfible by a. 
HOW, 6 being the litfi JHnbifk, divifible by 1, 3, the Divifiri lefpeOing the 1 firll CmJilim, 



Thrifirt, t , . 4^*3 ea 6iH"Jj 

SobtraQ I from each Side ... 41 ^ 6a-t-i, 

Subtrafi 4d . , 



X «£•/( Nuinbei Jmgbl, t and < miali Nnmben, rtfmriJ, 
1 foig/r Number, divifible bj 4. 
a iaba& Number, diiifible by 4. 



aii+t, a«'W<Namb<r, divi£bleby4. 
. Hered=>i. IctJI . . a+l, a a>hJ^ Number, diTi&bleby4. 
, 3, 4, AtDi-uifin rcfpeQing the 3 Jirft Cmdiaaa, ■ " 

rr, . . . ;j4-4 3= 110+11,' 1 ^iI/( Number /imx^, iJ and « wWc Numi 
h Side ... 5</ = izH- 7, a u^«^ Number, divifible by 5. 
Subtȣt icd+ ;, iivJa/rNuniber, divLlibleby^ 



m may bedirco>cted = 4. 



■ X, au^i^fNudibet, divilihleby 5. 
;a . . . a uMc Number, dirifible by 5. 
3^^ — 1, at;j£./e Nuinber, divjQble by 5. ' 
j;a4, ili^ fl — 4, a ^bA<A Number, divifible by <. 



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i66 «( R O Y A L A S T R O N O M E R 



(QUESTIONS (8 CHROKOLOGY m/kmrtJ: 



NOW, 6abciai iht liajl ASMfli, diTilisleby t, j, 4, j, tbe Z'nn/sj'i rcfpcaias the 4 jTr^ Csm/iuW, 

71<n^Y, . . . 6i+^rs to/i+i9,'iii!M,Hamhtr fi„[br, .ind « whoUNuabm. 
Gubtnfl ; from etch Sidc> 6t = eiM+;4, iwio/f Number, diviGble by£. 
V^Kf. 6aa+;9xi59. Tha I. 1. 3- 4. J. CtrJiliimi, . , . Heiea^o, lafi , , yVich ua/rwJj iivirMchy 6. 
NOW, 60 being ibc &«|l Mahifli, SmOAt ty i, 3, 4, j, 6, the pivifcn lerpcftingths firft ; rWi'fiiwit 

- - 5, OindliH 



fln»H, 6(M-f J9=;ti9, The i. i. J.+'S- '■ Ch. Herea=i, « leift a+ ^, »tiii«/(Number, diiifihle by 7, 
; NOW, 410 being ihe/utfAfit/ii^dliTiEblcbr*, j, 4, j, 6, 7, the Z>(vi/«ttBfpeay)gthe 6Crwalo«i, 



"'"■'*"i li ^ '^'l' ' " w ^'""^'/''slf.ii^'^[M' hj 7,/"* ««hol. Number.. 
SubtTia 560+56, i™i«/( Number, divifibleby?. 



4-1+ I, • mio/i Numbtr, dmfibleby7, 
7fl . .* . 1 w&i/c fcmbei, dinnUe hj 7. 
wi«/<Niimbtr, diviTible by 7. 



■ .?; .♦■ s- ; 



Tferr/^-,, 4100+ M, will bewArriiHATiY. Oibj. al T»io»r«. by whicb T«o nuy determine « miny Numtem « yon pl^e, 
(living the »foref«id 6 CssJi/ioii, whenaaso, i, a, 3, 4, &(. affunid al Pkafitrc. J r- > 

(^TfeLrA,TMiTLTi..LI, A».ya/riy feve. J *.»i,M, i, bad by a auinual MMltiplUali^ >f ,l„ U^ Par,,, >»i la,fl M-hMu of lUU 
■umi^,. ,ba, ^ill compofe .// ib, rf#«« Whole, ; vii. M«t. .^ « «*y ./ ,bi folJowing C™>,- „ ,„ „,, ,ii ,/" <i,TecedXo™ 3 
«> M.A,V„. /I, -'«™-.™ ,*. 1«^ M.;«*/. ./■ -z: ikf— 1«. i^i^nOII^. ■' / . ™ y '^ preceding Pm and 



, 5, tk^^mMKombcti multiplied, takiof la the RooM, iX3X»X5=:So, the leafi 

,.-,-..,,. ^ , .. »•> S' (»> j) ""Jtiplied, the I 

eluding (maitt Simiiiiiu/ri, 1x3X^X5^60, ihc Itafi MulllfU of a, 3, 4, 5, 6. 

And, if *, 3, 4, s, 6, 7, g, 9, were the ««/«". then », j, »», e, U, j) y, il, ji, willbe tberfi/wM Numben ofthemmultiplled 
hgethtr, t.kir.g in their Roots, «s. ,X3X»X SX7XIX 3=iS»o, the le*ft mnuDon niu!iipl,*{ themill. "^ 

5ri fir tibtr Ca/ii, 

QJJ E\7 I ON XVll. 

THE G<Jdn NaAit iti*i 1%, Cfcl,iflUiiM\,a^ Roman ludiOioa 7, t> Jttirm!» lit Tur tf li, Jviitn PmoJ, atdBk^ifi HtYtet 

Lets, *, (, bethej^wA'dUiifteidividingtbe Yearof thefffftJ, by ij, »g, and ij, for w, 4, and 7, refpefliTely, loremaia. 

!• 2- q. Cntf/rHffJ, 

Therefore, I9a+i> = i8*+4 = nH-7. 
Subtrifl II. , 19^=3 i8i— g, a™&/*Numberdi.ifib1eby 10, ataihniilt limbir, 
Sublraa i()i . . a.H.M(Niimberditi6blc'by 19. 

Remiinder 9i— g, a leWe Number diTilihle hy 19. 
iftDif. ioi-\-:t, i-MjM&NuniberdlvJibUby 19. 
"<«. *=J> tliei,^. idDif. i+16, ,»W(Ho.di«fihlebyi9. Whena!a8H-4=M. I.&1.CW!/ 
NOW, s3*W.^/fcfc»ftMuUl^e, ./™4i<ii9«*/»gflr,I]^M/«, nliKmngthefirtliCWi(:i«i. "T*— - ». L«nr. 

ThtrefoM, jjH-7 = S3»*+-SS 

Suhtraa7 , , 15c =; 5]3«-t-Si, 1 wiiA Ksinber, divifible by 1 ^, e tai a v/btU UntLhtn. 
iJXlS-'+SXiS- Snberifl 5*S'+75. » wioi Number, divifibleby 15. 



iS<r4-i;, a «>Wi Number, diviGUe by ij. 
* ^kr± »■ * ''^'', N-""!^'. di'ifible by ij. fY,. of Jul. Period, r., 

.dD.f.«^ j,,,^,N..*,ifibUbyis. . . . WWejiiH-ilfa:647,. 
Year 0/ Julian Period id Yf. bef. Or. —4713 

Year of CbriS, rehired 
i} hi irtaghi na aprmaiiiH, 

Oolden Number 19? y1-,d rrfuir^wlfi rbiDiu cf ,b, Ynr, anJ D,y ^/ ibi Wtdc, ■aia lit Cam Firfamaii^r 

GoI.N". 19. Dom.Lelien. ' fine* Chr 

iTj. rj-i. /.. ijo. f'7°9 ■..■'(■ B -JBy H.n«, the P^/« wa.A™io tbelW ,709, O. S, 

lltheDaKibeiweeo^ ig wjih J GE S-Tat. Th.^f™. — m...i » nc lieo 



lit Dif. j 
Hoc a=n, the ibffi, 

N. B, Tb, Ufi SluaMiy Jiv:yii/i fy a mbt/t f!tmba Jbmfd (fir JMi^ rlv la/t Niiitbir fnigitj ii irZ'gbiM'^'i,^^™ ' ' 

Q_U E S T I O N XVIII. ' 
'*^?^'?,^''m'' ^l'""'; \^J " ?*S™>", <U •'«■ A', y. fa™ March g, (Co« 1700) in ,lt r«r er£a (& Domimeal i«/n- 



ijoi. n". 19. LTom. Leiten. 

wisveeo^ ig with J CE J-Tb*. 

9. t 47 ■ . ■ i D ip. 14B. 



AlltheDate.benveef.J ig wiih J CE J-Tb*. Therefore, 00 Wa I, O. S. 

1700 ana 1759. » .- / ^ 1 ~ 



_ „ , „ . . The Ysar of the Pofik-t Age «lli be EHf. Yean jo 
Bot, Duemhir^, 17^5, N.S. anr*m to Ntvn^tir 21, 1759, O, S. 

, t .^,, p B ByT-i/r, Pageji. The Dfffercn«Bf Day. fcr«„« ^i,Vi 77«„,'.are Mi + H = .60 Day., 

Per byr-iA, Page ,29, F™m>.--r,,o W*,^*.,,,. . . 3^7 Da,.. . . To M,«* 8. . . 67 Day.; . . 6iK '(„ ^' 
SothmhePf.OK'iAottinl] be CQ Vfjii, andi6oD»yi, riftind. 



AHlTHMliTiCAL 



«W N A V I G A T O Ri iSy 





ARITHMETICAL OPERATIONS. 




RULE, rail 
Plaa I* A. Rfgk 


Ha-d of wmth of -vbicb Sum., » f/.//i i>^», e^ yeu will bru< ibt Degm.. Ml 
fg tiiltaiJ-Kiilitlbi atsitti mi Purtl of ibiEjualar, riquroi. 


rtuiei, «if Second, tf * Dtgra an/timing 


4 HODT* 

Sina fiHooris 


EXAMPLES. 


HM 

Su 


H 

n 11.67499 


i.-U 4. .3.5 l-.^js 

=6oa. Sum 7.JBS7S.. Sum 10. 5=105 <- „. ., . ''VS='''li' , 


' 


WleflfdSuti. ii6 4sD.8r«i«idMiiiate.,wj.;«i 




-'lytw... 


13 Hoiin . 
i . . 6., 




19 Mil.UK. 

9-5 


. . 17 Second. 
j. . 13.S 

^^.. 6-45* 


■> +5- 2 4S* 


Sum I9.50'9|' 


COSflfSnOO]* 


>7'4S' «1'^«J- Col/^^S„ ,j9- s.'4j'. 




Or, 13 33 ji 








i .. 5.7S.0BJ 








so.346i4^ia]*.46i4, . . fap. 14* 
u before, a7'.74?4 
ite«],. 44».9l4 






RULE. &/ .ffa Fir^l»lb,RizitH^»J,fr^,i,Thtrtt,, MLnuto, «»JS««od., Ww*<<««,W-o«f/>-«Mr*»5><fl.V.%«ri«. 
,--//«■ /«i a W-/XW. /Integer., -W <i. /W*/ >f .^,b ,c ,I» Right Hud) -,^1 rmaiM, ■u,il! it Himi,, Mlnuto, wrf Second. ./YjMi, 




EXAMPLES. 






Hoon. Hoar.. Hin>. 

SbI*^ J . . 6,J Sobtraa 1 . . ,i7S Subuaa f . . .4*5 




Sect. 

j6" or S.6 
Sobtnft j . . i,iet6 


RauiDderijHv, Kanalode. ,5; Hr. Remuiuler. MiiX. ,85 


""^'•«"T",V4'?.',t. 










&.btna i . , 4,6jjii Sub. i .,7 Sob. i . . i.S i . . 6,786" 

Rittt. Houi. 9,i6S67 Ren. H.j^ Ron. } Sec, )]>53;33 
9» i£ii> oooi ft4> iji> 3i>ii 
3 »4« » *>• 
+ 1 3 


8»b.J._^ 

, a«m7" 

■qflUti. 


,9 S«l.i...,s 
,Spi<> 4!* Kern. ] Stt: 


QOaJSMM ,!> 


.J- .7'> «q<J«J. CWW«(«« ,3" 31- 5''- " 




Mini. 








Remvnder. Mia'. i.Sco 
5.. «b^. 







A 

DigHizcd by 



Google 



. I«S 



Tht ROYAL ASTRONOMER 



A 1 ABLE tor finding the NuMBEt ef Day* advanced and retreated by the Epacti and Luhationi, in the 
Month. Dave, (from 6000 Yeara befor« to 6000 Years after Cirjf) from Oii to Neat SijU, from 1(00, and the 
contrar]'. For determining che Epact, and Fall of Easter, accoiding to Nru> Slyh, a) fettled by Pope Gr/- 
gcry! See Tai. p. 30.' Alfotofind thcEpaa, O. S. for the fame Centuricj. 




1, 


'■ 


4- 


<■ 


6. , 7. |. ,. 


a. 


V 


4. 


ind 
Ep.. 
Adv, 

and 

fr.O, 

toW. 
Style 


6. 


7. 


t. 


1. 


q. 


4. 


c;. 


6. 


7. 


CenWriu 

before 

N.S. 


Old 

New 
Styl, 


Ctc. 
nO 
St,U 


D.X. 

and 

■rf'j 
Cyc. 

iSco 


JA. 

and 
Ep.. 
Adv. 
fiom 
Old 

New 


Col- 
den 
No>. 


Epa- 
N.S. 


Centurif. 

before »i.d 

N.S. 


Uifl, 
froin 
Old 

New 
S.yl. 


"of" 

Cycle 

Old 

Style 


Adv. 
»nd 
tett. 
of r 

?,S. 

I Sot 


Gol- 

No'. 


N..S. 


Centnriei 
fince 

Ck.iit. 
N.S. 


D,y, 
Diff. 
from 
Old 

Nev. 

Sryl, 


it,l. 


Oayl 
Adir. 
ind 

!• 

from 
1800 


E'pa. 

ftorii 
UW 

Stri. 


Gol- 
den 
No>. 


Epa. 

N.S. 




— 




+ 


+ 








^: 


_;_ ± 


± 








+ 










b.toco 

5900 

S700 


46 
4S 


*' 


»4 
»4 
>4 


»3 


16 


»9 
»3 

17 


B...OO 

1700 


14 




JJ 


S 

4 
4 


16 


»7 
■6 


'"E 


'4 
"S 

16- 






'3 


6 
16 


14 
•9 


B.jtKK) 

S300 


44 
43 

41 


« 


13 
13 




7 
'7 


S 
»7 


B.,6oo 

1500 

1400 


>4 
•3 


i 


9 




4 
3 
3 


I? 

i 


'« 


B.1400 

»70O 


16 


i 


3 

3 
3 
4 


'3 
'A 
'S 


•7 
1 


i 


5.00 

JOOO 

<50o 


4" 

40 

It 


J 


I 


'9 

17 


3 


6 


B.I20O 


1 





1 

S 
S 


+t 


in 

9 


16 


3000 
3100 


'.% 


I 


5 


>6 

>7 


S 

;i 

"4 


'3 

7 

*7 


B.4S00 
4700 
4600 
4 jog 


3" 
36 
3f 


• 




>6 


9 

'4 

>9 


'5 


B. Soo 

III 


I 


*i 


s 


t 


'9 


»9 
* 


B.jaoo 
330D 
3400 
35"° 


»3 


\ 


1 

6 


'7 


9 
'4 

■9 

1 


>7 


lt.44^0 

4J0O 
4»t>o 


35 
34 
33 


I 


'9 

;i 


16 


'S 
6 


6 
* 


B. 400 

. 300 


s 

3 


t 


6 
6 
6 


3 
1 


6 

16 


J3 


B.3600 
3700 
3300 
3^00 




I 


7 
7 
7 
I 


19 


e 


16 
16 


11.4000 

IIS 

aroo 


■3» 
3' 

4; 


I 


17 

>7 


14 
14 


Is 

7 


s 
19 


B. 
3CO 


^^o 


I 


S 

s 

4 


J 

4 


6 

16 


S 


B.40.C. 
4300 


19 
30 


in 


g 
S 


I 


16 

7 


'i 


B.]6do 

3400 
3J0O 


:i 
.1 


I 


16 
16 
16 


•3 


17 

1 


'9 

't 


1 B. ^oo 

IS 


3 


' 1 3 
1 3 
■ J 


1 

7' 


7 




IC 


3' 

33 

U 


* 


9 
9 


»3 

S4 


17 

1 


»4 


B.3MKI 
310Q 

, JOOO 

1900 


>b 

H 
»3 


*' 


"S 
'S 
■J 


9 


9 




B. «o« 
900 


1 


' * 


6 
7 
S 
g 
8 
9 
9 


1 

'4 
S 


t 

»9 


B.4»ov 
4900 
5000 
5100 


34 


; 


11 


»4 


4 




19 
14 
'9 


1500 


»J 


6 


'4 

>3 
•3 


1 

S 


"4 

>9 

S 


'3 
7 
3 

17 


B.,,00 
1300 
1400 

IJOO 


B 
9 

'3 


*" 


j4 


Bi^oo 
5300 
5400 
.??oo 


37 
3> 
39 
40 





n 


a? 
»7 


>4 
'9 

S 


9 

.1 


1300 


3 

»7 


I 


'3 


7 
* 


6 


6 


;ss 

1900 


S7O0 
jBoo 
S9»o 


4a 


t 


13 

'4 


iS 


6 


j8 

'1 


> 


6000 




' 1 14 


IQ 


16 


17 


N.B. A. fignifiei th«jf^ Y«r current Ufore C*fjS, fo 100, mo, 300, &c. lignity the 101, 101, joi Yeuj cuneni beltre Ci,rt j 
btioE ill Bil&itile. So thic 1 muft be idded to ill Yeu> berore Cbrill in the TMi for the emrrtti YtMo. The Tibnlu Vffn Uing the 
Vaiumplttti. TheYcandAtfCirul wfcCdcwncuirent^>Mc»At(<<j; It lhey«,^,>/mChrDD0W. ' 
For .be ME M O R Y. 
CONSTRUCTION. Ron I. a,ftr, Chrift. .-fa (i. F«fl-<i /«■ ri. ««*«/, ftf, «,, 
Titm tidtw! e^ tl» Difference fl/ifjA v)IU he t»u.*. 

£1. fsjoo hi/TiChM. . Iliri.t II. fn* Ibi HmnitiA fince Chrift. Ufa ibiir Fourth, aotf mm two* 
-I ^^ib. D^i -uiU rmgin tmfixt OU %i W Am.. 

i 54 

^,+tt^3,«,Urubt..aed from the Old Style J j9|oo>«Chr. 

iS DiritobeaU./totbeNU:f<7&, fortbeHew. 
N.B. Tke It'iAge ind Ep»fl. retr. (— ) tbeftme Na. of Diy. th.t the Lnnuioni ad*. (+j from O. to N, S, »Bd the eontrur, ex- 

■Umiag 5. Col. beioKtheDif. orSumof :d.Bd4. ColumM, iccnrdinK loSiEni. 



W NAVIGATO&> 



159 



r*>Uft*llet»tt ^(jt LourCjPtk, v Mom'* Age, !w lU Math-D^ ^ iht OldSifb, acnrAj n ki^Mfi^M^ •/' AotidntioD 
•^ I ^ !■ M>^ joo roTf j'fir xmW Ntmim) tr I i>«|u amah id moy ajoo fiKn /ric «nu Am <n^ i Jjtj in 110,7 riwn^ Aw 
wtoKt ih Xuna «r jUvm if tit LowtiMM /h* W M Mw &f*, xwl n^fifaMji ^ »■ Gtt|niut EpaOi, «■ fmU h th Pap«'i A^ 
IborilJ, *» "i*^ ^tnnrmrf. 

RuLi I. ftibtrta 17 from the Csnliriei^u* CSr^f. lad <I*U« the Riaunte bf ■;, mddplr ttw Qjiollait b^ t, uJ mSth iIm Pro- 
lA.— Kride the Uft Remiiato b; j, a^ add the Qnotieat to the fwhW r ^v^ if tb«n « anr «D ftcmiWct, it mil b« tht Kc- 
UMI )Crd(, if thac ill RcmiindeitlutSiuirmon I will bath* Cjde'* Remit, njaindbvui iloo. 



Y««. Dv« 




Yean 


I* S7l~ >«Chria. I 41 Mt. N. S. 


E* 


n. ]l|og iKt Chrift. 


17 { -ij R«t». J C7C 




17 












■5)'4[« 


Is^ [f« thit FtM. 










j)itC4.+W"S "tr. 


1)'S(S . ■ ' +i 












'. Sun 13 P* Retreat ofdi* > Cjde, tobe MDeedfi«nit)ieM<. ef 




s RMuinder, tdd 


Da^i advanctd fmn Old ta New Stvle, ibr the ]) 't Age 






and Epadntnated that DIf. tram tfaolcarOldStjle, irott l!oo. 





TfjCa/ iff jtftwx •/' tl( Lonar Cjde, (r Mo«n'> A|e, 



ItTtB.lI. nMcedanAlvMia thajSiBB-Rai.1. 
aa Vmt tnan the Refult of the {ame tptrrrim \ tik]ii| the DiAi 
lleul of (he Diftaoce of CnWri'iu htwaid Aotn the laaw 1 jlli Ccntuiy, 



S5}74(*> >n (k>6 PmAA r^firwtf, 

Sam S4i aatlwftnBtrq^erj ri ««. 



ibcRetrait of Lanatioiu rmn itoo to the Year 6000 Jati CtrMi onlr dednA 

if*.. ^. ■ . l^^L r -L- .-L y*^^^._. :- -tT- *__! J ft.' t'. . T_ 



Vtara 

Xc n. i|oo fiotcCbrift. 

17 Centuiiet GnceChrift. . 

•s)i4(<.br««<i 

S)'4(4 ♦ 

SiaUl* Sum;, bj^ t> ^alt. 



Dap 4 Adnaee of the Mooa'i Cfde, ii 
Old Stjie, to wblch I bong added, the AdTioca frog) Old Strie cd 
bdDiAfrwntftherefrein, »i Da« «iU nmalo that the i'lAf* New, the Sam will be 5 Diti retreiled by the )'i^ or Efat 

aadEfsiritntdBKHiJ, or to be <idM to the OldStjle*! }'« A|e in the Old Stjle, or (C bt lobtiafled fram thole of the Old for the 

and Epadi, for tbolt of the New StfLe, frsm itcct New, 

t^ The DiAnnce between the Adinnce of the Dejl Iroai Old u 

y the two roTccoiBg RdIci) that Difference *■"-- "'■- *• * 

'—Vtjudjnk ibim* lit Bftcli fir M. S.f 



Role. MMbithliiGMmKiimiir (iriitretr. 
oKt U dtimctiitOHntifi} -oAat rmmm nill 4f fl 
Temnfau, Chrif it itAOidfiwt itt JM FnAB 
■ifmnJX**S. 

YriGateChr. O.N. 
Xi. I. *ioo .... a . 

yrtch, G,N. D". . 

n . . 'iS . . iS E.Rct,') *a 



orfell, amiJtdmetlitUd nirttttf yt^ttrEfttltfiml 
lit £tma fir ibM rtr rtpini.'-Ot, «>ba /eMtW n^ic 
t/tttCtUaKMrnttrifii. btiiiXtmmAr Itii^M Ij y>, . 



fit* til ProdaA, (adStg jo, if . 

jo) lit ftid Epaa Kurttfir 

dUiw vtiU it lit 



ll+J*e=4l_ 

DM. J) Epaft, N, S. 



30)ig»(« 
RetD. 1 Epaa, N.S. 



CiWONOLOGICAL 
DigHizcd by VjOOQ IC 



'V 



th KOTAL ASTRONOMER 



1 b* D«Mnl (^uuiitiai, o, loc^ soo, joo, tfr. Yexn cnitMt, 
faaCbrif, m foaai to npidk 

ii 101, aoif 301, Bft. Yeiri cunenl. 
ltfiriCir0, tai therefbn 

RtTLEI. imtfi it UUflh, mimif I Vtmo, loO, aoo, 100, 

c. Ufir,a>TiJI, it mr Aftrannmieal Ttblci, » wit ibim nrMjf^ 

ilbi, 101, lai, joi, ftc. Tmfi BilTeiCile, i<ftnCki^, it Ck*- 

"Mlirii ( Or, wiici 11 tbt (em, nv bv^ Ukt em fjw Plicci Aw thi 

Aftiaooaucil Tihlu ^artfriJ./' "-iVtu M-ibeMajTmrcurr-t 

tfit, Majir'* Afirtnmett 7*Uti icqajrc the like ConeAiaq in 
itir lire, vrilh ouf TaUa^ tOBwIcc *11 the filtr tai bmtr PUcei, for 
1)' Number of Van he hai eiprcaed, before Cbrift, to coricfpond 
lib tbe »w Tari, curtest btfore Chiift, WGOtdiDg to CimaUgj. 



CHRONOLOGICAL RULES «W REMARKS. 



ItnUKK, ntfam mmind ^tm 



I, ixfrtfl*[ Wf f/n^tf 



Kucc, \t ii Jtuiifil, if Mr. Af<jw did not firfl nuke ttit i 
.jfliTT Corrcaion, ii rai/i-; mi bsi Campfaatint, whether the Pr 
tifia be caned oa whicb h: roandi bii ^umiila tf Aalneiim of 
Mtcm'i Mlit*. For wbeo he eumined ud compareil the l;inii Pli- 
ca In lili 7Mii wich Ihofe recorded of iDtiinl £(&>/» ind (U/e 
riM, for Ycui current before Chrifl, thrj niieLl Deitly lErec, 
yet in Error In Chronaloijr EU|hc compenfate fot aaother Va tbe 
Sjgamiria tf jltalniim f 1' tbi) fhoold happen to be the Cafe, 

Mr. FtrpAm, In fail Aflrooomy, bit meatiaoe^ tbe fore^nt 
FatmitK \iBfibmt u^aini it) bf delnauniDs the itth tf Mnj {Ss 
Vcari cotreot belne Cbrift [when Peace enTued at the Ecliple, pntiing 
an End to tbe Battle betviit the Miia and hjiieai) to be on ■ Wti- 
irfdaj, ai it happca'd, endnotoD aAffwffji, according ts the vn/nr 
Millakx of Cbnuolagcn. Who confidec the o Year for the Be- 
ginning of the ift Yeai ciiiTcnt of Chrift (bcfinouigit o> ii 
of coafidering tbU a Year, to be the lA Year cutreat before ill Year. 
itf Chrifl, u it tmirictl^ dala, vAtt 100 It fa ftr loe Trtn IB 
rttlttftnCbrifi, ibMtfimlJii/fmfiJijloI, Sec. 



CHRONOLBGICAI. SCALE, 



Tabahc Yean bef. Cbr. 



Tabular Yeira 6ncc Cbcill. 



cal Vcara before Cbtlll. 



CbtoBoloiical Yean fiace Chrig. ' 



cluonol^icaJ Yn. 
before Cbrid, by 
Vcat, 



^ffiJaTYeari before Cbife" 



LI Yean fince ChiiA. 



Tl^l^l-M-fHH^H-?K 



ChroBolo^eal Ycera befew Chrift. 



6 1 7 rT 



that I Year lefi muft be ufcd Iban _ 
iij»Affc«/ Year conent, before ChriH, to correTpDod with the TkJa. 
Year, in lixklDg the true AnfWer from AAranomical or Oironol 
il Tables or from Arithmetical Operation! 1 Beli^a Correftioo 
Afljonogiy and Chranolog]! hitherto unknovrn, or Hnoblerted. 



CbroBoleginl 



Year* fiou Chrift. 



Tabular ud cbnuwia* 
pnlYeira fince Chrift, 



From aboTe it ia nldent, that the fiaw ehronological with the tabn- 
Li Year fines Chrift mull be vCti, in Itekiog the use Aofwet from 
1 or chranelogical Tablet, or from arithmeCjcal Operationa. 



31) 101, t^r. Yean chronolo- 
outftnac^ni/T'aNu, Theie- 



Hnmericaliy 
■icallT, otenttent, before Chrift, 

; r'uLXII, Dtiutl ifitnthtchnw/tricslVai; tr N-Airtfltt 

r. , J0„ cta^i Iha, -t^iilbtrttrnmailm, Q.trN.S. 

imittlLtlUr, CiUiii /ttKttr, tr an ttbir SefiJr, frm nr 
Ttiln, ftr viiilt Itn art fmJ n ititrmm ^ aad - HLvifi tfr tiiirt- 
miwiwg Dm; ia triihrnUialOftrtiini timtmin Omtlm. Bat hw 
/WAraa IV add m 1hi<^ u ri< Con, » ttt Of, tf tar^aila, tr «t 

l^~<-<««»«/ Op<r<;rM oiwt OrHalt;, >r r«t r»M>( >M> Chrift. 

Of Ibt LEAP-YEAR, «r YEAR>«. 

DW, /■ w^ rtMrit&rtOript, if it mw Laap-year, trv^t 
'fmit atttriii tt N, S, 
... LB lU. OlTidc Haodredi nmalmM^ by 4, or Yean om^ 

What -t-pnww taka frOBi 4, wili the fttvit-rtar di&Oier, 
* MvuE>mirt4, afar ifiOtrtBidfomibi Halt. 



t4." 



.. 3, yeaniiic«l«ap-Tear> 



ijpo . . 4)ijt| 



i4|6ft WmeChriAi 



Ken. I Year Sm. ■ Yf. fine* Uw-Tcar, 

[fiacaLaap-Year, W.S. * '[N. B. 
When o rtmriaa it i« Leap-Ycar. 



tOjiaJ, ita*tri^h,ftnChrifi,ifitmuLt*p-rMr, w 
Tiar fat; amr£i f 0. S. 

RULE IV. ra*idiag by 4, afier i from the Dafi, 

TheRcmtiaArtcBii, Ihcwi from Leap- Year ina Jltft.* 
■4. I. 1, 3. Yean«lterLeap-Year. 
Yra. Yn. 

Efmfla, 1701 befoieChiift, .756 beforeChrift. 



,, Google 



Mi NAVIGATOR. 



CHRONOLOGICAL RULES 



10 /ad, laof Tim'JimnCbriJI, if it ItLuf-Tctr, trtuhUTtmr 

m, aitatJi*[.liO. S. t 

RULE VI. If theZJanof ^tytajoa^tj^UunHiii^Mt, 

yntU TtmaiM will the Wnahr* fiacc Lf ip-Tcar Jccide. 
•o. t. ■. 3. Vein fince Lop-Vw. 
Vn. fioM Chr. Tn. fincc Chf. 

■■"¥'»• 4)1751(417 4)'8<»(4J 



e/ ri< DOMINICAL tETTER. 

70 fiuf f ft Dtmimal Lottr fir anj Tur htfitt Orit, tutrStg li 
N.S.f 

RULEVir. Hundrtib £</>* qnotc bj 4, and the Lccter'i P/m b*d, 
Bvwlut'ileftllKKtof 4, imbliJi if i 700 (ddi 
Itien idd once and the fooithafiA^ r«n, nude i W», 
Si*itu[ Sntm I WhU Hmtiri will the LetUr cipnA. 

• £«ir ammJrali mflrr 1 fuitraaid fnm Iht Dm. 
"*' '-' tbt Dominicil Letter for icic Yuii cnrrmt 
'U.S.! 

JS oddTewd 



at. Foti7f» . 4)17(4 



. . 5) Aoirt Haadrtdi. 
»4 

7)73^1 



AteChril 



J]4S[6 

]. .C, fort53j, N.S. 



B.QLE Till. The Ymt Left* iu Fourth lat 4 di«Ue b; 7, 
Pr(«Bwl«tr«M«>«"'ll'""' ' " 



J . , A K^ O. S. 4 . . D m]<, O. S. 

K.B. Wluait iiLrii^T'Mr (hiaJtaJXiniU the tit of thiaDomi- 
DicalLettcn. 



TV? jfW lit DammetlLuur fi, 
RULE IX, Dividg HmmJuJi by 4, mnu m » 
0« added, (he Letter for [hit Vi 



rw /nH chrift, ff. J. r 



X.S. Vhea a rmniB* for the Letter** Phct, iftei Sabtnfben, 
tht Letui ii a, BBd Acwi that 7 alfo loulnt. 
•A. B. C. T>. E. f . O. 
I. ». J. 4- 5«*- 7- 



— — 3 Re«. to befab- 

Sbb ] C the Doffi, Let. for 1700. roiAed. 

~j [GaceCbr. N. S. 

e : . ot O, Domhiiei] Letter for 1719 fioct 
[Cbrift, N, S. 
tf. B. When It ii Ltif-Yiar thii JInA fladt the laft of the - 
Doaiiiual Lettert. 

7* fi*d tbt DamiiinlttlUr fir tjTitr fMiCtrip, O.S.r 
RULS X. Tbe Year, io Fourth, and 4, bi 7 dinded, 

Wbal'*LeflaUaAfTDin7, the Letter n^irU.* 
•A. B. C. D. E. P. O. 
J. 4. J. 6, 7. 



Vn. 



Yii. 



r. ( . . i7{g Soce CbtU, { . . 17BC fine* Chiilt. 



Ifitt WEEK-DAY, FoaSTii, O.erK. S. 






■a JCtiMLvv the bfl D17 of och Uaxh I> de- 



JtioMr/. Ftbrwnj, 



oaplet. 



iSartb. April. Mty. Jtim, 
I, A.I. D.I. >. I. 

'tfuwAir. Oiltiir, Nmcaitr. Dittmhr, 



EXAMPLE. TtM Ii, tfnt-DnMfwtrivnMajt^, 
MiCMS, tf.s.r 

ThePomuucal or SuDd ay -Letter for the Year it O. 

Conrequently A denote! Jlfowln; B, "T-fi^ i C, ffidiafJefi 
D, Tbutjdmyi E, fru/c^i F, SMMrdty. ; 

The tft M JMcr hel^ alwayi denoted by B, now on t'f^if- 
iaj, therefor* (ea^mimlfy ^ditft) theSt^i. ijth, apd aid Dijise 
illTiff/iAHf, iDd coBfequcntlf, the ^th Day it oa a TttrMin, re- 

*a^ Mtmtb af ibt Ymr (by Memoiy} evfaiiiir Chronological Tablei, 
f. 149. abikit ai Stgir f fir^i'ttg (like the Mcmoriil Kiile ihvvt) 
fir My Tnr ti/trr or jntt Cbriji, mhtr actriing it Urv tr Oi 
Stfk. 

•m fiMllixGMi^ Ntmta, uPrlmt. be/ore ChrUl, O. »■ N.S. I 
1 and the iWor wilt be ree)| 



,, Google 



«* ROYAL ASTRONOMER 



CHRONOLOGICAL RULES. 



t^ Coap«n ttii lumflt 
with tbitp. ijo, wben i AouM 
' tin b«n itiiiStti Tniai 
Year for tbit Opcntisn. 

Bihg w inn li^rrvmai laulj 

mir Kk/i maifnuiil. 



r Or, UDiinftHj, ttf. Cbr. 

1 J— J Iftbi t>f and f 17, jm tf 10 diviit, 
19 ) W^MmuMi^an If, wS It* Primti 

— L o^'^' fCoBtp. of a to 19. 



O. N». or Pi-W 6 reauirti!. 
N. B. »■*« <i* rw if/w* Oni* " /f/J lb- 
■ ■ ' ■ ■ ■ ■ - Sniir/i 



li tht Golden Number f 



'Take fioc 
Yn, 
Exgmfii, 397 htfactChifl. 



107 



wbil if £^, and the Cjtii appetn. 

N. B. Wbn Ha Nanbar ■/* 
tbt Tar yjkrt CbriS » bfi iham 
to, in/irA iV ihmjrtm, n' ' 
ttofiUir M li( CjtU/ir 



m 



Or, niUTCtrallir, Itf-Ctr. 
Pirn Jt tf ^ Stmt tbt Dattaai -^ it, 
7ab tobai'i kfifnm 4 Smti, Iti Smu'i Qk6 m 

5 itqttued. fCoBpt. of joloitt 



TOjW(*«it<« 
From tbt DltMatt 4, then ^iiide^' /i/hMt 
Wlut rrnuini tike tbocfiODi, mod Ibc Cycle i* fttfli 
Yrt. 

789 bcfanOuift 

4 N.B. VZaffcrHMDberyiii 

I5)7'i(S> diJmS II Jrmn, atJ lit Rmain' 

75 Arhibthiiaimfimairtm. 

30 Or, anivit^Ilr, */. Ctr. 

■ CDnlhh 15. rfcficfffW t "■ 

I j 1 t C«np. of 410 15. 



' fir Jarmimiiii 

4, ri< GoUen 

IndiSioa, /«- r^ i Tur ./ 

[>r{^, t^im'lttrftr/HabiiCemiiVimltttfiblrmcnJfiimtraMaJlt 

aaj Yier itfin Ctrifi, ibt natrtrf Wm n 4bt Stalnf Cfaronoli^, Ir- 

'- aDivifitnb} 19, xl, iCj itmaMfirJntrmtimiiHtr^MmCy- 

fir ibtt Tmr. — Ai botin hmut CbonoloEan hara boco mihJGen 

bcirCompDtatiDBi, by fubtrafiiof oraddinf t, a, 3 InAeid of •, 

and 4, fmin 01 to the Yeai behreClirill, theiiiti* |iTiat Ikcir X(- 

r>Ai for 1 Veai ] Icfi thAD tk^TnM, m iki UthiMri Sah if Onf 

TO finJlbtTrar if iht Dionjeu, <r c^ Miia-, VvntA,fir«*} 
Tnrhgtnt^'A, ^tetJfiigi* ibi fir^n Imf u n r ima't 

r^ OmBtnL RvLi. Sitmn ^^ rabtradaUe) «*( Nnkr 
/ « OcJb, » Iht i3 Year •/ Orf/f, Aw (^ Dale •/ (it Tur kfin 
, . V;- , aW t^mWa ilm Kim^Mjit H ibi Mtambcr •/ tbt wbok O"^, 
BJMT aw rammt diit« htm Ibt Nnolbvr ff lif yijtf whole Cjtit, 
aJtbiltJIRtmaifJirv/ill'itlbtrimraf ibiCjelt, RqaiRd. 






M. B, H^es tbe Date of the Year before Cbtift ii left An tbt 
Nnmb^ of the Peiiod, in tbe 1 Yew of Ctr^fi, dtdoS ttu Date 
tbeiefnim, Uid th« KiattMDdei will b« ^ Number of tlw <^, 
laind, for that Year. 

Yn; 
BtumfU. For looo befotc ChriA, 

Sablnft 4;l the N«. of Dion. Per. | it being 4(7 

injaYr.Cbi.jfot tbeYta. 

Whole Per. 511)541(1 before Cbr. 

■-— — Or, MluTeHallf, i^^uJ tf ftl- 
—10 Inui^tbt Piriidfir i/l Tr, Cbr. 
531 frtm lit Dati, aM in Caaf. 1 

^'/■'■■'<- JM (not s»i. See /. 160.] reqoired. 
t> Far di^ Yetr^fia* CtriJI Ibirt ii no Comaion n Jv^ Rain j 
ourlmproTaDEat in ChroDologr only takint Place for Vean Gnce 
Chrift. 

TO fii2 ritYwMitwCbrifinfwrmbUltaafYttT^fa^Pri,^ 
acEordinit to tbe foregcJB| tmpiofement t 

t:^ GireialRdli, AeHtvrfiaf Ibt firmtrGimral Salt. 

DtJaa lieHuabti *f tbt ftnid fitm tbt ■aibtli Ftritd, aadaJiibi 
Rataadit It 45R, (the Number in the ift Year Gnce Cbrilt) aad ibt 
ill btibt b^lHtt! UfirtCbrtJI, via r^ Number ^ ibi Ptrud 

■ini 
Ex. The Rei>alc of the Ftrmt 



AUb iMobef.Chf. 



E*. For 5S5 befbrs Cbiift. . 

4714 K». of the Per. in ill Chr. gitater ibaa tbe Ya. bef. 

— (Chr. TherefMtlwIHtEMi^tfr««it. 

Dif, 4119 yalumPtriad, n^*. accoriing tC the Cinuni/Jlajji, 

TO find ibi Number ^ Vc^ bfin drifi, anjnm^ W c^ Joliw 



UiAIlaM,UlbeYr. 7)74 before Ckfl& 

The tealrtrj. Yr>. 
IrOMBalRole. 7374 belbre Chrift, . 
— 47H 



If, S. JtKu IFeriod, tc^rirad, 

Tbt Orimttfiml RmIh (lArt Mi CamtiiwJ Imbt PUa I, 
J — .■ — _ t^ (j, Q^i^ tf Af "^^ '-'■ — '•'-■• — '•• 
a|tee«itb Truth. 



xf^iaaiwr ifiit ibt' D*li' t/ At Yt^ btfmtC^ft, 
I ra (t< RefUn, to - ™ -■ 



dbv Google 



■t^ 



lie Domimul Lhiv fv orfTiar, 0,«r K. 5. ^ifrnt'- 

^M it carRfpODdciit to the Sun'i C)clc, in the inoeied Table (or 
O. S. TbCD RckoD the Nnmbn of Diyi between O. ind N. S. or 
tfae Nugtbai of Letten Placa forward, thit the DiSeieaee of Dir' 
from O. to If. S. U above 7, 14, xi, Vt. the Produai of j, 

XEUn*Ie. 'rtfaJtt4Dtmmitaltatir/ir\-}sit H. S. ? 

17J9 fiaMCbrifc 



*t)T76t(6j Nunkr of Orda complotd. 

Rem 4, tba Nnmber of ^prefeiit Cycle <T). • • Heace Don. 
Letter (wmfpoadnt bj the aboee Table it C, fra O. S. To wUcb 
addiaf the 4U] Letter'i Fix* fonxnl (cfaeDiffereact between 11 ui4 
7) G U the Damiiiicjl Letter, rejwirtJ, for N. S. 

f^ The Epoa i* the IXffi»ut of Dip betwten the fblu Yen 
of itic ud loair of ie4Da7i. d h m 1 

For Ibe mean Solar Veer .«j6{ j 4> 54 
The mean Lnui Year s ^64 8 4S 36 



«; NAVIGATOR. 



CHRONOI/OGICAL-RCTLES. 



•73 



rf DoUlVIGAt LlTTIB TAU.S, O. S, 





r.p 




RA 


, 


nr 


ij FE 




AO 




t?H 


1r 


F,n 




K 




«: 








iK 


V 








i: 




1) 




V 






IS c 




K 









B 


J 


c 


t 


K 


.. 


" 




»o 


D 






A 



,, -- -, --r,(for 

the Periedi of Hnklrtd Yetra from 16 to iS.oo) dinde the VrodnA 
hy ]o, the Remainder will be the Epaa for that Vor, O. 5. — 
Whieb Awt i< rednccd to '7i<f for N. S, bj fablraaint from it for 
10 hMbI) the Difi from O. to N. 5. 1 The R«fwnda bcint lb* 
If aa anAnnUe to the Niw. 

Vn. 

£x. For 1759 GDctCtr,O.S. The O.N*. !• 11 



&*Uo.,. 

Dtiiaa II Dt. Djf.fr. O. 

[to: 

Rem. i£pa£tM.S. 

ihia 't* Xfait it g/var 

ToB reckon the Nunbcr tt At Moath fram AUnt, which la 
Jlcd I, Jlfnlx, M4g 3. ttt. to which Nanber, ron add the Day 
of the Mooih, and the N*. of the Epad, rejeainB jo, and the 
'i .14* rtmma, within a Daf . Or job ma; nfa the foUawbg 

I, Mr, t, Jf, l> Htgr %, 



Ot. t, M. io> ih. i( - ~ 



5 H>. MoDib, 



Rem, 1 jliMa*j Ap, 
H. B. The foftCMOt New Moon ii had fay dedufttni the Moan' 
Age from the Day of tbe Month, when it can b* dooe, or ocherwile 
adding the Day* io the former Month befor: tfae DeduSion il made. 
HtBce New Moon will be «a4l£7«^ I7;9, nearly, 

N. B. TtrtbiTliy •fthfun FillMon aiU i^ii tbt Dajifibi 
aunfi Ntu Main. See PiiriTVAL Taili for finding the Nra, 
FmU, and ^uvMi- Mooni, p. 15a, itSight— Which Table ii fupplieit 
bythei'e;^nu/ErAcTTA>Li, p, t68. Shewii^ ibc Nnmber of 
I>rriJt«ni«OT.<Ma(eof theMoontN. S. f<« tJienPeriodt, to b« 
added and fubtraa'cd to and from the Day) the Moooa bappea in that 
Table, hi t^a Ptriidt, FromwhirhErACT-TAiLi, tbe £^ni 
foti^lW ftritdi are ootreOly deterouMd. 

OtmiALMtHOBlAI JiVliE fir fin Jii^ tbt Efta fir tf.i. 

Divide HmiinJi b] 

id tbao tStJdi 

Ibefide, 



JUnbif/f by 17, and tbao 16 tJd ) 
rtn i£m, by that S}nrr, muft bi 
And then 15 the wboTe Sum muft diiide) 
SnbCraa the lal) ^aMr. frnm the Pn'tu by 
RejeAint tba nirtin, yoor Efact U£hk 



Add 17* 
»S)»7i<" 



t EpaS N. &. reft, 
8> fir fillip. 



■ f»A Noon, Time of 



Or rtibtr •■AM »U Mtm'i J^lyt Tocfe,. vihitb viU ihn J— 
htrSmlii*^ im ttrnm. 

"I 



" mitiaSfyifir N. ! 



r ittthyifltt Palck*) r»nil£m, nm 



,, Google 



>M 



fit ROYAt ASTRONOMER 



CHRONOLOGICAL RULES. 



MEMORIAL RVLB. 
To the tftSt wU t, uid rcjea j Tinci th>M, 
Wluit laniioi ttke jrnm jo, ifoar Limit yoa'li (*«, 
If 50 or 49*> Left— when yoa'TCdons, 
And tbe Prime ibvire 11 — Tike, for c*cb, 1«A by ii 



& for 1759< I • £piA 1 ■ 
Hajotor^a . ■ 7— 



O.N». 



tf March, iaclnjrat, arichmetinlly, If. S. F 

MEMORIAL {lULE. 
Take the LcR;r (nd 4, from the Limit Di}'t fall. 
The HenuiD fmn nut Sivaa — Add the Liw>.— Tful^i iIL 
ExtmfU for 17U, Limit . . Diti 4] ■ . O, Den, Let. + 7 
Sab. It— AM..* 



} 12 .^Wr.tluLWt, 



A TABLE for m^i^ GadiDE 
the YEAR ofthe Di'weCoi 
•nd 7a£M PERIODS, cor- 
tdpondent to iJTen Crt'o of 
(ke £n. Mm, taifitUttm. 



"''21 

India* ' 
CTtlg. 



3 



/Wic^ 



1660 



For id, 

at"" 



, Sjie rrfpefl- 
iielr, by the 
t- We. ofewhCi. 
' :le.in itl Col. 
' aking the Re- 
■ .fli 



i.[bivi(ion eflbi 



PlOdurtiby 5^_, 
Colt. butiftrrDi 
r^ii 4th Colamo. 

M £. ;7 it the Yr. D>n. 
Period, when folir Cycle wii 
, «nd Inmr Cycle la. Ami 
476, Yt. Dim. Period, whei 
Mat Cycle wi) sS, lod lunai 
Cyclei. Atfo 6916(1 Yr.>. 
/Itw Peitod Mrfaen t w« ihe In- 
ditliim, lid 19 the /ww C^cl< 
at mrr f< frtvrd. 

St. T* faJ lii Tiar rf it, 

Di<.n,fi.Q J-m./ «/«Y">! 



farnif 17, Oilr a/ lit Sn i ii, q/tk ff iki J^mi 

ltd IJ, Cjdt^ IrJiaim, 



Ren. DitBjfian Period ijj Yr. R^oiied. 

Example. TiJStJiit Tnr tf ttt Julian Period, 
r/^/iX I' 17, CtiU sfiit £n) Ji, Qvitr ^r£( 
EiM i aaJ t]i Qkw ■/" UidiAiaii ■' 



IndlOioa I] L 

Rem, I , . Tab. K*. 691C 4th Cohunn. 

^/m* Period 7aij lequitnL 

Or, from aboT^ lag -^ ij. 
Rtm. *— 1 

laUaion I] I 

Rem. 9 . .Tab.N*. 6jt4 

yuA'n Period 711] u before 



rROMile jCrcLii^fif Sdh, Mmh, mitti- 
_ icTioK, ^nm, MjfHJtk TW^d«DioBySaa«<< 
Juiiao Piritd aritbiBUUallf t 

Sec Role), Paje t6o. ' 

AdDTatl OlHMALlRDtt, 

Suhtnfl the Lunar from the Solar Cycle, (or from 
j,% added, if not othervrift fubtractabli) and multiply 
the Remainder by ;E s To ihii Frtdnct add the Mii 
Cycle, dJTidins the laft Sum by 53s (if peiter thin 
that Number) tod the Remainder will be ihe DnrjfifH 
Period anfirerhii to the Solarind iMioar Cydci. 

From thii Period found, fubtrad tbeNumbcrof the 
IndiAion [or from cj3 added if not olherwile iabtraA- - 
able) diiMing the Remiindei by 151 tbeu multiply 
whit remain! by 10G4, deduftiDg (if poflible) 79(0 
from chat Piodua, add the Year of tha faid tiit^fmm 
Period (□ the Remainder, aod the lafl Sum will Im the 
Komber of the >tfa Period, nplnd. 



-=■ IS • • «>♦ 

JRem. 14 1 

I XIo«4j I4«9« . 

Ditmjfimt Period kam abo*e -I-S97 ' 

Sam, ijio] 
SobttaOing 79>o 

Rem. tbe^M Period 7itj 
Uii ^ihi TASLB n lii LifT. 

Take oat the Kamber of Solar and Lomr Tan 
From the id and \i Columni lafwering to the Humber 
}f the Solar and Lunar Cyda : and add tocether for 
Li._ ..■ 'uPeriod, if Ichthan cji ; but if greaM', 
therefrom, and the Dinyfin* Pkriod will 
Mow divide thii Period by ij, and take the 
Rtmainder From the IndiSion Cycle, (or ftom ,1 ~ 
idifed thereto) and wiih Ihe iail Remainder is the i: 
~olumn, takeout the Number inthe^thColomn cor 
ifpoodent 1 the Sum of which, and Uil Di—iitn Pc 
od, wUl be theJa/iM Period. 



'ide the Sum of the Nnmberi in id and 3d 
by 15, and tbe Remainder taken from the 
lodidion will give a N)iBiber in the 4tb Cohimn, 
[anTwcnUe -to that Remainder in the lA Column' 
whicb being added to the jam of tbe Numbeti in tbi 
lA and jdCol*. will beftie ^nto fetied, nqaii«4. 



yGoogl?* 



■and navigator; 



»7S 



CHRONOLOGICAL RULI 



TABLE for £atfiBs 

EAtTKlf O, S. 



El. 3</W«fcaZ>ACT 



t|w lA Colaeui, iknd) A, 
.puft C, du Oomi- 



KA Thi Diyofths 
Month aidiA tks OoUta 
Koabcr, Mtila, \% 
fEtOwFdlHo 
pKceliii( B^'Samiay. 
If the DoouikMul Letter 
Ouidt ttfintt theGoUen 



7* findlhtttUir iM Ibi Romui CdttJar, r»nfft*Jait Itwif M 

ntticallY ? , 

RULE. Divide the Numbn of Dtyi, coDariof tnai tka Betiiiauig of tlie Yeir, or Jaatarj o, 
Mlh'dij f/oTst. /. xt^-J bj 7, tad whit ■icnuiiM will be the NwobCT of the Letter. njuiW. 



itt Ytar, itfin tr JUn Chrift, uith- 

thepnn 



Reqiuied the Letter ulweriUi M Ae utk of Abmsfcr, Iq ui camnwa « B 
Com. Yr. Bif. Yr. 

7)3f9{4S 7)j»o<4J 



*'lUat. 4 . . LctterD, mfiltti. 



A B C D E F O. 



RULES FOR FIlfDINO THE WEIKrDAVS. 



•nt «lfe the Ceipletnt of the Hiunber of tbe Maath-dajr, from 'ya»,~o. ffi—i Tti. p. itg.J Ic 
01 (uBiTiT&ll]>) to 371, diTide the lift Sam by 7, enJdeJBfl the Rj milnto frow 7, uidwhitk' 
bedieWecfc-^, required, , . Sun. Man. Tu. Wed. Th. Fr. Sit. 

I. *. «■ 4. 5. 6, 7. Ftriti, 

BiMtpk. r*/«ffit9'iil-/9«rf^'»r(«Mar>l, iliTimiiififarifl, O. S. 









!..iSl- 



From Ja, o, to JC^ il. Biff. 149— 



7)'49C« 



. WalBddij:, O.S. Mqnbe4< 



Q Rctkoaii^ biiA^a <A( Aa. £<«. r«^ >an. f* t^t, 



RLILK TothsYeaM, Uh I, befoti Oriif, add their Fovtli ind ;, (bulsfnini 
iriei, not Lp. Yn. N. S.) ud airo the drnplemDit of the N* . of the HaDdi'dij fincc y< 



At, 25 la the End of Cen- 



Ebrr, tdLJag tb> RtdwiBfcr &«■» 7i ud th« lift Remuodet vtU %iir the 






D>. < Di& b«< O. M 
Mot? 

K.Cnp. 



■ >« 

37« 



+fi D>f.Dt.fi.atoH.S 



Ron. 3 . . THlmj, NiS^uMore. (JUh^U^D^ D^trmiff S^HihtWui-Dty-rf O.S. £<riJht 
^j, iAii[ lit Rmutiii^ fir lit ff'tdt-Dtiy, K.S.) ' 



nzcdbyGodgle 



fh ROYAL ASTRONOMER 



CHKONOLOGICAt RULES 



N. B, Tin Wwk-«ar ftir wrrH^adlng Month-^ q/ O. aiul K. 
S, b:in| the bne, when die Dif> of Moath-itaji IbbViOi {ma O. 
TdtN-S. (bvfonOn^JtlwDiabnaiof W<ril-at)>ifRMB O.toN. 
S. * Jdt u adnncci, m nnch ; ar, wbtn (fiace Cirqf J the Oiiieraice 
of Month-dift *<i^ to O. for N, S. the DifitRnu of Week-diyi 
rubtrtOi or ituttu H much I r^fMif lit ftm Kmb^D^ a tmb 
SijUu 

Vt/rd lit tf/tt-Dt/ irithnNtlalty, a^mnUi it tpvim Mamh- 
Dn, i- "7 TimrSia Chrilt, 0. 5. t 

RUI.S. To ibe complete ynn/jM> Cbtif (vi». i left thin the 
y«ti ranent) add their Foanb, — i, ud ilio the Number of the 
Dlfl Goce Che Beginning of the Veil 
diiide the Reouindcr 



lingofthe Ye«r, or %i(, o. {from T«i.^ 119., 
T by J, end what IiA f miuiiu, will bs th 



.7S8 
■ 4J« 

1 ijs (t.Juuo, toHiftj, Mm.Ym. 



t Jt<m.a 



K 7. Satari. O. S. r 



7a Ai/ lit Wai-Dty, irMunetinUr, sttftHtrM I* a gfvn tttmb- 

Day, 'm anj rurfini, Ctr^, O.&f 

RULE. To (he Mmrtelt YeaM Gnce Onfi {vi». t WJ llu 
cart ciMTtnt) tdJ Aiii Ftmnb, — i, and the Nrnnter of the Di]>i 
ictthe Befinning of Ihe Year, 01 jMt. o, (frtm Tti. p. it^J end 

from the Sum of chcle /■foro^ ihc Number of Diyi DiRtmKt-tet- 

:d O, lod N. Style, then divide the Remiiodet by 7, and ibelaA 

miindcrwillbciheNDoibccaf theWMk Dair, nxgeirBl, *N. S. 

£iMi//(, To find the Wttk- day anfwering to -M^ir,- 

• (759, carrMtiMeChitt.'N. S. 



RtB. jlw^.N.S. ■Rem.]. . Ts^Cbf, N. 4, rt^abcd. 

N.B. 7htDtmi«c^':L.Ht,,fiKtChtifl, rMtm, {\n nOK-Haf fai- 
van), aa ihi Dtm, Ltitir Tttk fi>eaa, p. 148. for Yean <in« CMf; 
iW nnfifmmllj tit tf^Hk-Jwj, «i Jan. o, u,b Year, gKiftrwrJv 
lAuncn. Hence Ch^Reaton of addmf the Month -daji Jiong ya*M- 
rj, and nol their Complement to Seveni, ai befbic Cirifl. 



UNIVERSAL and CORRECT RULES for AndEnf the D«Hiiti- 
CALLiTTaii br(r>,t CHRIST, accordingtoK.DodO. Stvl* ; 
deduced from the Pibcipin of the »oMiKicAL I.ittii Taboi, 
PiSei 148 and 149 : Uiig a fMribtr Uhfirii- ^Rulei Til. AVIII. 
p. 171. . 

7t find ihi Dmmaetl Lttur fir an Ytii hifirt CbHJI, O. S. alith- 
telJcaU)! } 
RULE. To Yean current Afi t, tM^facir rart^ and t«4<« 1, 

^ttthfj, iniwktX'ifLfft wiUibeLcmr'tPlMiAu*. 
A. B. C. D. B. F. O. 
t'- •■J- .4. .J- '• .7- 0.3. isfrfOrjI. 



Rem. » Ikw.I.et.B. H.I. 
r,/biiibiDtmilmltMttrfirt»fYttthifirtOira. K. >. with. 

RUtB. Din'de Handled) hf 4, taVe whit*i left Ann twl«e %, 

One»iihtwic«whMrenuitiiW thatyea''iLnnr Aewi' 
Add once aad the Fourth, of the fU% Veaat lefi OM, 
QfMt« b]F 7, md the Lottn br wlut'a lefcU koowr. 
Hund. N.S.MinCiri0. 

Exm^tfirl 4)17(4 
■7S9. J 



3, twkc which •f-eK7, I«tr. O fer 1700. 

V.K.Bt/.CtriJI.nbimiiiiLt^ { 14 

Tmt li« jfi^ £4rMr n ^rtn f/"'!* — 

nu«; t»i 'U ti Lmtrfiffnu Ibi 7)79(11 

Ntmitr if iht f6rmir. —— 

Tvice what tan. +1 makingo, forXeap- a rem. B. Dom, LM. 
TOr Centa, 7 dedaSi, and. the Dom, Let. ii [N, S, iB^uii 

B, anfveriatla 3. 



jnm xtxtJHttufipi 'Bi Lnjjtrtaaw vsMOMWrn u. «■( N. Strle, 
xfHini, ir0jJ,nibtMi-A-Jaj,,fO\i,firihtl4,mh-^rfitBti 
Strle. Aad a'fi-M,uibiFf«iJ^ I,/ tki Dtmiiii^ LtUiT tfdt Old, 
ftrik Kiaiitrtf ibr Dtmimital Liltir ftf tbt New St^e. ^W wtm 
ibt Dtm i mial Lmtr tivm nt (rtthm^ ftr Yean iimhaw/ i<Ar« 
CtnV; (k D(f«iiH y Dmji imma OU m/Ncw Stflc, ntnm, 
DT >*lr«T( .^ ti( Mimi-Jtyi if Old, >- d« Mv»k-imt if Hew 
SiTle. (from 100 Veua fioce CM*-^ -'«•' »^ btu^tu fimm Oi 



both Scylea wen , aafUy alike J u may b« laea bj T<it. /. i6g, 

UNIVERSAL PRACTICAL RUU far flndinc Ac D^r'a Dif' 
riaaiiGi from Oi.B to Niw Sttli, bofatc CuiaT Arlbri 



N. B. Ttt attn Role agrm m'lt lit Difiim 



> m lit 



I to the Centutiet, i 



before Cti-ifl, the riiiT RvLi (at Bottom of the TaUc, b. 
will lerve, nwivrrfal/j. Sot fiddihg^tbe^ Diflctenee of Style foi 
above complete CeDtnin — It then amoanting to no more th 
U«i-Hrfal tUU lift fmn 1 The faid firft Rnle fetving only fo . . 
plite Centuriei, that are nM Leap Yeara, ftom the asth of Fitnarj 
to the End of tboTe CentwiM. 

ntV^i^tfD^t (fwihtpt^ftn tf,Ci1an)iw,reM 
ty ,, fnm aid n Sim Stj]e,dMt ml taU PUct tOl At tjlb ^ U- 
btuary, afliribi SiffauOt-matinihhtfm, 



,,Googl« 



»nd NAVIGATOR. 



'7r 



C H R O NO LOGICAL RULES. 



l:^ InTaUi, p. iGl, theDay'iDifKiGnceof Stjla between O. S. 
Lctp-ycar, and thoTe Ctnturiei, not L(ip-yun, N. S. brfbre Cirifl, 
take Plice only for ihofe conplFit Centuriei, and odIj' rrom Fiimny 
I Ac End of tbob Centwiet, not Leip-yean, N. S. itCpt&in- 
nd the Rett oF the Nambcn likenife tike Plan in (he lime 
Minim, hr the luie Compleat Centaiiei. And therefore, inf 
Datet aboTE ccmpleat Centuiiei before Ctrifi will hiTt the Time Daji 
;nte in tlie id CdIuidii between Old and New Sljle, and llko- 
liF fame Nomben la tlie 4th and jth Coloiuni, ai at the pre- 
ceding compleat CeaCuiiei, and To in Succtl^on. 

Tlia, la find the DiSeience of Day • between Old and Hew Style, 
Rerteal of Lunationt in Old Stjle, ajid Advance and Retreat of La- 
■ and Mdoq'i Age, from Old to New Style, [/■ Col. 1, 4, tt 
ji/rsmTai. p. (68. j for Yeari ibove compleat Centuriea Kfbrc 
Cinj*. 

You mufl take out the Niunbcn for 100 Vein 
J for Yeara abore compleat Centuriea fioce 
rcci/y e^rte wilb ibt fitgnirrPiACTtCAl Rdi! 
Digtrnei tf Siyla far Tart ateot comfkai MaaJnii Ufm drifi. 



Vein preceding, ai yon 
e Cbri/f, mUrb vJI ihm 



TO T. 



<• YaAK • 



, CHRIST. mJ 
at Wkk, Ote 



YeanbeforeCfoi;) reduced to YearifinceOr/H, O.S. 
RULE. Befoie CiriJI, take the Number of Yean left by One, 

From Hundtedt by 7, and flie Year fince u known, 
EnamfU, 585 Yean current befort CiriJI, 



S»4- 



* Hundred! by 7. 

fiui C&r j9, hiring the Ikme Donu- 

, ^ I. S.l and beginning with the fami 

Week-day, [v/s. Tvifl^} at 585 Tan airrtm iefert ChriJI, O. S. 



Veari fince Ctrifi reduced to Yean before Chrifi, O. S. 
RULE. Yean cnmnt lince Ctrifl talce from Kundiedt by SeTCi^ 

Add I towhat'iLeftj Yean before dUvif! ate ^TCo. 
ExnfU. I7S9 Yean current CnceCirjfl. 
iSoo ■ . 4HDadiedi by 7. 



1041 , . Yean eorrent before Ctrifi, having the fame 

. . etier [via. C, O. S.l and bepnoing with the iame 

Week-day. {viK. FriiUj} ai 1759 Tun Jaa Ctri/t, O. S. 

N.S, TtwRciii ABOvtfeniafor N, S. byufiDgHoadreiliby4, 
inftead of Hundred! by 7. ^c. for fJ. S. 

Before Cbrifi tike the Number of Yean left by i. 
From Hundicdi by 4, the Year Tmce Chriji ii done. 

Exofl: {85 Yra. current bef. Ctr, 

Tn. 



5(5 hafanCirifl, 
Dom. Letien GF, 
Year begini on Mta' 
daj, N. S. 



Yn. 

1759 Gnte Or^, 1441 

Dominical LettetG, +1 

Year begina on ■ 

Mtmdaj, N. S. 144J . . Yn earrent bef. Cbrifi, 

Dominical Letter C, Year bnina ou a 
MenJaj, N. S. 

f^ U lU foKt Ma'MT, tbt TartfiiuChrifi, an fnni temffai- 
imt a ibt tiari trfuri Cbrifi, bmng iht fami Coliia Number, Cjili 
»f tbt Shu, or l*£Sii>H ( (j fMaHi^J i /nm larrml T,ar, irfiri 
Cirifl, anj laiinf ibt Rauiiiidir frtm airy f/amier tf Hiimiriiiiy 19, 
»8, a>^l5, mr2 tbt TtartJiiiciCbrip mill, rifftitiydy, rmaii. And, 
on the contnry, taking tbt emrrmt T/an fitiet Cbrijt, ftom arry IVtmAir 
if Hamdrtdt by 19, iI, and ■;, adding i, tt tatb Rimtlmdir, and ibt 
Tlari nrrtnt btf^ CbriJI wiU rijKll, laving ii. Jamt Golden Nnmttr, 
Cjeli ff Iht Sa, and liaiirin,, njftaivtlj, 

Yr.. 

Exan^ L Of the Golden Number 1611 befDreCXr^, 

—ft II 

1900 . . I Handled by 19. 

Yean current ituxCbrifi 1S9 
id itii before, and itj Yean fince Chrifi, haie tha lame Golden 



ftrtU&elarCycUaadlniaiimrtfiMlartt thi Jni- 



Ai the antieat Egypliia, Araiit, Grtcit*, Firfiiin, ytviji, and 
later Accoonti of Time, are reduced, (for aSnnomial and chrono- 
logical Purpofei J to correfpond with the ya/ian Form c 
Year, or Account of Time, long before any fuch Year had Eii Aence, 
Co, in Conformity to the late CorreQion of the y*lian Acconnt of 
Time, we have rrduced the 'Jnlimw to the Gngeritn Styje, *• tar 
backward and forward at remoteS Antiquity, and Futnriiy. for the 
Improvement of Chronology and AJtrDnomy. This ii petfonneil al 
Si^t, in two Paget, 14I and 149, foregoing, with the following 
~ ' to thols Paget. 



Mrtotho 



,y Google 



■7» 



Til ROYAL ASTRONOMER 



^ Table ff Kalends, Ides, anJ Notiii. far iht Koum/ Yba«. 


0/ Use h HISTORY W CHRONOLOGY. 


D.^ 


J.nuaty. 


Febnaiy. 


March. 


April. 


M., 


June. 


J.1,. 


A.,.«. 


Sept. 


oao. 


Nofembei 


December 




Kal. 


Kal. 


Kal. 


Kal. 


Kd. 


Kal. 


161. 


K.I. 


K.1. 


Kal. 




Kal. 




4 No. 


4 No. 


6 No. 




6N. 


4K. 


6N. 


4H. 


4N. 


«N. 


4N. 


4N. 


3 


3 No. 


J No. 


5 No. 


two. 
Prid. 


s 


3 


J 


& 


JN. 


5 


il 


& 


4 


Pr. No. 


Pr. No. 


4 No. 




Pjid. 




I^id. 


4 


5 


Nonie. 


Nonet. 


3 No. 


Non. 


tn. 


Non. 


& 


Won. 


Non, 


- 3N. 


Non. 


Non. 


1 


EIU. 


8 Id. 


PTid. 


8 Id. 


p',ii. 


Sid. 


Sid. 


Sid. 


Piid." 


8 Id. 


SId. 


7 


7 T 


7 ? 


Noo, 


7 


N.O. 


7 T 


Non. 


7 > 


7 


Nan. 


7 


if 


8 
9 
to 


n 


il 


S Id. 


4 ' 


Sid. 

IS 


4 


8 


It 

4 


4 




'J 

4 




3 Id. 


J Id. 


S F 


U 


s 


J Id. 


5 


J Id. 


3 Id. ■ 




3 Id. 


& 




Pr. Id. 


Pr. Id. 




4 


Prid. 




Prid. 


Piid. 




Phd. 




IdUJ. 


ldU9. 


ta 


Idel. 


jU. 


Idui. 


h. 


Jdui. 


Ida.. 


3H. 


idut. 


idoi. 


'4 


Il"- 


16 K. 


Prid. 


Ig K. 


Prid. 


18 K. 


19 K. 


18 K. 


P?id. 


18 K. 


.'1 




IS 


iduj. 


17 


Idu,. 


>7 


Idu.. 


ti 




Idni. 


17 


\l 


\l 


'4 


il"- 


.6 
ij 


;r- 


16 


;;"■ 


"7 


16 


17 
16 


16 
IJ 


r< 


"9 




log- 


n 


ill 


"5 
14 


14 *? 
13 ■? 




IS , 


'+ 


"S 

"4 


'4 ^ 


'4 


V. 


,1 q 


1 


i» 




;;i 


10 


i:t 


" f? 


ii ^ 


7 


10 


"T 


"3 
=4 


1 


7 
6 
S 


1 

7 


"1 
1 


1 

7 


1 
1 


1 

7 


10 ■ 

? 

7 


1 
I 


1 
I 


r 




6 


Ik. 


6 


5 


6 


5 


6 


6 


i 


6 


s 


6 


i8 


5 


Prid. 


S 




5 


Jk 


5 


5 


h: 


S 


tK 


S 

^id. 


*9 

JO 


Prid. 




Prid. 


h. 


hi 


& 


It 


p.iJ. 


Piid. 


J,fd: 




/a Account y' /4* Old a«J New Ecclefiaftical «*/ Civil Calendar. 0/ Use m History and 


Chronoloct. 


CALENDAR, or Aeco-jnt of the Yeir, borrowi ii'i Nime from J&/™f, egnifylDE iLt firft D»y of e»ch Month, r«koniaE tccording to 


bt itoux AcccnM br the' Moon. Kaliml a dirLved From xoWh, «m<, I mU : For the FrirJI, wbofe Bufinefi it w» to obfim the 
Ntw M«o, by vhich the fitfl Day of each Month wu reckoned, give Notice theieoT to the Fr^l of the SictiGcea, who celled the People 


tofcther, indoidiined how the leAof the Diyi, in thit Month, vut to be Tet ipait for reliliaai and other Ufei. Hence it wit, thit an Ao- 


nual Account of divine and human AfTain, came to be kept throughout all the Manthi of the Year; which Accounc (from recltoaing bj the 


KthHli) was therefore called Th Q-limier-TaUi, and confidettd both ai EakSaaicaUai Ciwl. 


The Dar preceding the Kalt^, at firll Day of each Month, wai called ;>r/'rf}( KslipJa^ the preceding Da; to thii the 3d of the KeliaJi, 


the neii preceding Day the 4th of the Kaltiuh, tec. reckoning bictcwanls to the Ida of the preceding Month. 




Month from the firll Day cf Nmki. In the Full Month) of Mvcb, May, J'lj and OBolitr, whernn are fix of the Uma, the firit of the 


«■«« fell upon the 7th Day ; but in all the Monthi called Iftff™ or Cm, wherein there are reckoned but four of the Nonet \ the fitfl of thofe 


N^rnt fell upoD the (Ih D»y. And ihcre being eight-of the IJi, in each Month, throughout the Year, confequently the istb Daj, in the 7*U 


Month., and ijth in the Ho/fow, vfiU be the Diyi of rbe Ida, from whence the reft are reckoned, like the KtlniU, by inTerted Order. The 
Dii- preceding the JVwn, or ;<i>., n o^rA fridii N-ma, or friHi Jd„,, the Mat preceding Dtyitothefe, the »d, 3d, +th, ff(. of the Afwa, 
or of the Ida, according to the foUowing Oblemtion of theScbooli. 


Prima Dia Mafit oih/fMi «! £^a KelmU, 
Six JVtMi, Ma.i, OaU.r, Julm,, a Man ; 
Slfuiar at Stlif^! , dtHi Uu, tmUha o.'Tt, 
l»di Din rilifia «ma dit rff, Kal:du, 
Skti rim Ktmoins, Mra i Ur-U fffiaiiti. 


TVtt «« Ihe asdent 'Wav of reckoning Time in the Lati. Chorchei, and it ufed is the Prntr-ffuN of tb« Church of Etdai at thli Dajr. 


The Eul'fiaftical and Civil Csltaiar, or Almanack, alfo difpofei of all the Dayi of the Year into Mmk,, Wak-Daju Vipb, Ftf-Dni, 
Biff Daji, Lam-Dayi, U«rwf.ij Tirmi, tec. in a fuccelTire Older of reckoning ; which being inHmtfrnd cannot csnllitDte, LtenQy, 


ThelTcrtlyfiarediAingullhedbyreTenLetten, <i, b, c, i. i, f, g. The fiidt Letter a ii placed agakil the iR of Tminpi, « againR the 
«d, (sgainll the jd, ^againfl thedth, and fa oQ to f tEainlt Ihe ytb, then^ tgainfl 8th, iagainftcth, and fo on, inSncce&inaf the feveo 
Lelteii, through the Year : By which Meani -, *, r, d, ., f, g. will alwavt point out the fame ^«* Da}t in any Yar. And a, i, d, g. 




The pTi«iftI Letteiof the fe.en, pointing out the SuUaj, for any Ye«-, it .awiyi made Capi,^, ind cfled the DmWoi/ Lmtr for that 

Di.idini J65 Diyt, in * common Year, by 7, the Quotient !i ji Weekt. *nd one Day over j if there had been bo Remainder, all Yeait 

would begin and end on the fame Day of ihe Week : But the odd Day occafion. each Year to end on the Week-Day with which it begun. 


whereby the neit Year be^n< on the Week-Day fbllowing. And a Year of 366 Dayi divided by 7, ba.ing two Day. remaining, the nat 


Year begini two Week Days after the Week-D.y en which the former Leap- Year begun ! Whence, if a common Year begloion a Sotiaj, pointed 


out by the DmiiiialLnlK A, it will ilfo end on a SvbJs., and the neat, or fecond Year, will begin on k Mmda,. againS which iUodt a; againll 


Tuifdaft; »B»tnft ftAitfd^ c; and fo onto Swfd^, againft which ftandiO, the Doroinicil Letter for that Y-ear. Againfl the Beginning 


Sf the third common feu, on 1 r-ajday, ftandi *, igainft Wtdmjdaj h, tec, to F. (he Dominical Letter againft Sae^jr for that Year. 



mi NAVIGATOR. 





■fit 








i>r 




FF 








<B 








E 




C 




B 




n 




F 




A 




(; 




D 




R 








<: 




V. 




(I 




« 


* 


^. «. 


E 


." 


O 




B 


lO 


D 


14 


y 


it 





And iheicforcE it the Dominkd Lttcer for the fiwrth Ywr, beginning on a Wti^^Jitj, mdfoan, in j ittrograde Ordtr of Dominiejl Let■ 
-rt»for e»ch fa««iiing Ytir. But in tli<i fourth Year, contoining j(6 Diyi, ci\Ui Bigixtile, or Leip-Yeir, the 14th Day of FtLrvaty, an- 
. iwringtothe 6th of tbc Kilemij of Menb, ij twice leckonod, by piicing tit Letiet/ agiinfl the 14th uid »5ih of Fitmary, whitfi intor- 
topts (he nnnoJ RiWogreflion of Dominical Letteit. from E, the Sniiln-'Ltaa to i4lh of Fibruitj, to D, the Sonrfji- Utter fol- 
lowing the 14th of Fdmary, to the Ye»r'i End. And the fifth Year (of^jfi; Days) btginj two Week-Dayi after the Wcck-Diy beunning 
the Lcip-Ycat, w'jf. on » FriJin, when the Doroinicil Lftter i« C ; and fo for the fiilh Year it i) B, the fe^cnth A, and lh= eighth G, and F, 
■nd fo on. Whereby it ii obfttvable, that, ifier (tita Yeari, if each Year confifled but of 563 iJays, the Diyj of the Month would 
again return on the fame Dayi of the Wrclc ! But hy the IntemiptiDn, erety four Yean, to each Letter, it it 7 Times 4, or iS Years, be- 
' the Diyi of the Monrbi relurn eiaflly on the fame Dap of iheWeek| whith Term of Yeart ii called the C^t/t of the Son. But, in 
.._.j SijU, thii Ordir\> now faithtt iniinafiaf, by a Day tifi reckoned, in every odd HmJndtb Year, being lujw made anau», inHeid of 
Biffimilt, at in OldSijlt. 

•liiCjeliiflUSaM-TaliliifiraiiyYttriif lltCjcb, •/Ufr U Ilifiiuy ami Cbreiiii/i,u, O.S. 

THi Taifi agdibcf^llnf 
inr Rnk, art btrt rfp-.alid 

N. B. UlhtpfiYatofChriJI, IhtVar ^f lUCytU iang 10, tbo-tfirt addimt 9 M f ie rajr/im Cbrifi, aiid inidlgg ibi Sim it %%, iki Ke 
maiwJrr will it tbi Tiar of ibt ttifuM Cjtii n aMvi, is v>bicb ibi Dminlull^lcri Brt dnirmiirtd. Sit Pagej foregoijig/w jinrfiW (t» Oli- 
vine/ Ltiitn 0. S. ariibmakallj. 

The FixtdFi^i in O.S. were regulated ty thf Sun'i Motion, but the W«p«Wf onea were governed by the Moon'i Motion, (i the r«n/ 
jnd Moveable reafli A', S, ate now govctned ; efpecially Sapr, on which the rci! depend. Ced ordained that the Feafl of the ynv'^ 
Paffttnr, Siould be kept on the 14th Day of the firft Lunar Month at Even ffrt Levit. Ciaf. liii.) which was at the Time of the tiift fu// 
^iru in the firll Month. Bgt the Ciri^/iuCbiirch ordained theCelebniionofi^d^n' on the iSxidlir following ) bcciufe our Saviour rofe upon 
tiiri Day. The Primitive Fatberi had no Way of detetminiiQ the Time of the New-Moop, but by obfcrving it, emerging out of the Sun's 
Rapat£v«r, which waj a Day after Conjunftion. The Cwncil of ^;a, A« 3as, fettled the Fall of £q/(er by the MiWi Cycle of Moons, 
(fa called from i('i Inventor MutfJ aa in the Ecc/ijSafiical KalaJat ; inferting the Order of their happening there. They fuppaftd that, In 
every SuccelTian of (9 Julian Yean (the Pirici (hey allotted to tiie Liiur-Cycle} the Mooni would return on the fame Diyi of the Month], 
andHounof theDay, ai in die Order of the GtUa, Namltr, poiating out the New-Mooni, in ikt Bibli-Caloular! Which, befldss Anticipa- 
tion, it incompatible, by the odd Houii not reclconed for the la<{ 3 common Yean. Thofe Ecsh^pcat Kew-Moont (reckoned from and to 
Leap- Year) were about five Diyt later thin the Time of the irnt onei, according lo 0. S. before it'i Akentioo to the New. Hereby Eaflir 
came not to be obTeived accordicg to the Time of it's original laliitulion. ITbtnrxl Saaiay afitr ibtjirf Full- Mosa b^ppnlrg nxi afirr the %iS 
(^ March, or r<rni/'£;>"'>ni. tho' ittiieTitne of the JVinnt Council happenihg on the lolh, but before the Stile was altered and the New 
Stylttook Place, in 17H, on (he 9th of Abrci.] If the Celebntioli of £4f»' had been ordcied on the nixi S\iniiy afitt rbt Jir/I irut FkH- 
Mta* itfpcrmi mxl ajtir Ibi 7lmc ef ibi yirnal ^aaintx, it would always have been obferved according to it't ArftloAlIuliDn. 

The jiraicifilai of the ymal .i^quinox O. S. (and of the Srarnni or any Poiati of the Ecliptic) was ^i'a ^i 2 it^i every font Jalian 
Yeati, by reckoning fomoeh more Time than was contained in har Stiar Ttan [each Year, according to Sir jjaac tftmfeii, being about 365* 
jh^gn jji jglbj by whiehinjjLeapYeintocome, the Time of the Vernal /Eyw»x would be ji ol> 17"" 8" fooner. And, in j^S Liafi- 
Vein backwani from 1748, flnce the Lin/- Year 324 (preceding the Year 31J, the Time of the Kiam Council) the Anticipation vnu lod 
''S9" J**' The jCfirWM, Anay>4, being onMarcb ig"" i;'' 19111, and conftquentlyAw jij on Marc* 19th, iih 18™, Alfn, in the 
_ ear befbte Chtifl, being Bi^ftmilt, the Finuil JEnviasi wai March iid ^h 6°> P. M. and therefore yfimt Cbrifli i, it wai ia< Bb jjm, nurly 
agreeing with tbeTime by the OrnAiieTablej of March la, 7* ^^.TbrttrtanafltritbLaf-Ttaf, iht JE^im ani Stafm vtiii finaard, 
ai ibtRaimf ^ti ^if yi* %^*', tec. iMiTiar; the Year of 365 Days, under-tickoning the fol«t- Year till every fourth Year of 366 Dayi, 
hich over-reekonM what Time watlofl, by44n9t, &t. and then brought back, or retrograded the Seifoni again. 

The .,4«i[ii/iruppofed that 135 Lunationi naftly completed the IiMr Cycle of in Yean : But 135 Lunations, allowing x 9 d izl> ^^m 31 
jjtb, ^r. toeach, are Ci^ual 10 6939^ jib 34m ,71. And ig yulien Yeart, of 3631! 61" each, are eaoat to 6939'! ign. Therefore the Dif- 
ference, i''a5"43>, wai (heZmar-Anticipaiionin 19 Tn/Zflu Yean ! Four Timet that Time, 5" 41" ji', «ai the proper Lmar-An- 
ricipition for 19 Lw^-Ynri, Feu it it (o beobftrred, thit every t, x, j common Yean after each £»f>-Year, the Mean New-Moons ami. 
cipatedoi happened fooner bv lo"! ijli ii", ii* fit ai", a* Sli 41", refpeftively, than theNew-Mooni in the fame Mentbi intheLu^-Year 
prececding i The 6 Houn above 565 Daji in achjaliam Year being counted hut once in 4 Yeati, The Mean New-Moont anticipated 14^ ch 
1" in every foor 7a/w» Yearj j therefore in too r £up- Yean, or 16 Julim, the Iimar-Anticipatlon was 56^ 0'' t"" from v»hc nee deducing a 
Laiution=a9<l la'' 44'''> there remain i£< iil> ion, the nearelt Anticipation g to which adding the third cummon Yeat'i Anticipation after 
Lm^- Yeat, m'ai. id gh 4^01, the Sum ii xSd zo'i 9>», AaticiplionattheEndorfoui Z.upand thrte common Yean: The Mean New-Moont 
then happening fo much loonerin the Montht, than in the preceding igch Year. 

Say 1^ is" 41*' t9<'' : )4'<. 319 yaliax Yeati, or 79 Lap, three conition, and iS Houn, when the Lwinr- Anticipation it aDay; con- 
fequenlly, in I4i47a^'ii, or f^6 LiaffYan, fince the Lafjt-Year, preceding the McTH-Conncil to 174S, tiie Amur-AT^iicipation uai about 
fbor Dayi, eleven Houn { if to which one Day be added, the Time when the i^ne-Moani were obrevved, later thin they reallv hapr>cntd, 
iltheA'iKiK-Coancil, will makeahnoft five Day) and a half difference j which account) for the Difference between the J^rc/^T^d/ifa/ and true 
Moon), before the Altention of Stile, and Coireflion of the Calendar. JV. B. The greatefl Ditfetence of Time between a Mcaji and Ttue 
ConjuniElion, or Oppolition, ii, about 14 Hoari. 

In the Viaiin'an, or i)y«aSiii- Period of (ji Yean, the Nra and Fii/Z-Moont were fuppofed by the Antlentt la return on the fjine 
Dayt of the Month, and alfo on the fame Week-Dayt, which Error bai been dewa ; there being a Day Z-nsir-Anticipjiiun in that I'imi : 
Yet the f triad ia Hill retained for ift Ufe in Hijipj aid Cir,reh[j. 

S'n Ifiuc Neaita, in hit Account of the Bin h and PaBion of Cinfl, printed /Imi 17^3, obfcrvei that (he Piimiiivi Chrilliana had Itltle Re- 
gard to the Timet of (he Binb and Paffion of our Saviour, )i being not material to Rtlipin ; (hough there fincc hit been fuch a Striflncfi ob- 
ferved in the Keeping the Timet of the FaJIs and FrllivaU. Thej were firft celebrated on the Cardinal Polnti of the Year. 1 he AcninKijii'ii 
on 15th of »fflrr*, the Time of the Vernal .^quinoa, when y«/i« C*/bi- correaed the Ca/«flii^. The Feall of St. ^oi. on yB«f »4th, rb- 
Timeof the Summer SoIHice. S\. Michail oa StfiaAer iq, the Time of the Autnmnjl jEquip"- ■ --' ii- u;"*. -•■ ^i."A — n- — '- 
then the Day of the Winter Solftice. The Fcajt of St. rttmai on Dramitr 10 ; St. Afeiibiai 1 
00 the Sun"i Entrance into tbedilfaent S^m ; ai maybe read. 

HeSxei the lirfl Pil]b«er inthc i£th Yearof Tibial, in the 47sSlh Year of the ^^M-Peiiod, between the Baptifm of C6ri^. and Impri 
fonment of Jetn. The fecond, fiiur Mentha after St. ytJia's Imprifonment, and Cbrlfi'i beginning to preach >n Galilei. The diiid Pi^n, 
wat the Peafl following that when the Corn wa> eared and ripe. And the Fifth, at (he Time in which Chri!) fuftered. He thence coilSudi 
that the Time of Crucifixion to be in the ]4th Year from the Incarnation, or in J3d Year fi^im the Time of the Biith, 



PERfETOAI, 



the ROYAL ASTRONOMER 



TIME-TABLES: 

o R 

General RULES for Ckroholocists, Hutoriahs, MfiMORAKnvM-BOOK-MiiEts, Travellbe*. and Na. 
i-ATORS. Determmiug, at Sight, the PoisTS of Timi, for any one 5'«>tor Y«ar, /o^, /«/*W, or « <m«(. 
rHV.-Vf^ ufiful foe ill Perfons writing Almaiiacs for the STATIONERS COMPANY. 



PERPETUAL 



WHICHTables (of themfclves) we no more a CA- 
LENDAR, or ALMANAC, ferving for any onc5*<^OT, : 
orTVW.lhan (he Timber cntootin 3, Dod-Tard icr'ZaWd- 
ing. but not united into Form, is a SHIP ; or no mortfi 
than Timber framed for Building, is a Hat^t 1 or than 
Rules for making Almanacs is an Almanac. And 
therefore thefcTABLKS or Rvl e« are not fubjefl to Stamp- 
hty i fince all Ralti tf Art, for making any Firfurmanet, 
arc 'allowable, without ReHrainti For, without Rules to 
make them', there could be n» Almanacs. 

This Truth we think onrfelves obliged to explain, as 
he Sla>rp-0£Ui has a Ri^ht> by Aft of Parliatnent, to 
harge a Duty on what is lilerary and tniljaa Almanac 
or any one Time, or Niimber of Times : or on tuhai 
CbitO^ Z"^-" '^' Purpofi, for any out Time, or NunJnr 
if Jimei, to come : Since cvety printed Figure or Letlir, 
en the Paper of any Book of Chronology, and ef- 
pccialiy all cbnmbgka! Rules, may (ar/^ ferve that Pur- 
Jn which Seofe of Cfjieflg firv'H that Pwpefi 
I ALMA^AC, for any one Time, or particular Num- 
ber of Times, for the Year or Sc;.ron, or Yean or Sea- 
fons. prefent, or to come,, the aft tflfeeS IplBCC, 
,0 further. 

t, onr 7a*/-" confift of ^Mwa/ Rules, rot ferving 
■ki'j.y, or made for any ent 1 inic. or Number of Times, 
or Years, prefent or to come, but generally (and not 
ckieff) fcrve, for all fajt and /ulart Time, and for no 
Yf.'r or Se;-fon, or Years and Stafons, in particular: 
Ard of which Time, in geni;ral, as injixite Duralian, no 
particular Year or Years, teafon or Seafona. can be un- 
Itri'ood. So that our i'^r/z/Kfl/TWi/rt are only fnbfcr- 
.■ient (like all other giieml Riilei) to the leneral, and 
herein particular, Ufes {qt in\i.ic]\ tLey ivere •u.-anted and 

For Tlma, though in Eternity applied 
To Motion, mcafures 4.L . hi ngs durable 

By piefent, pall, and future. 

Milton b. V. I, 580. 



.Es for Chronolooistr, Historians, &c. 
for f/idlng th M-'-eake FEASTi on,/ Holidays 
I Eabtbb, on which the Refldcfendi, is always the i_/ 
Sxndm after the Grft F. M'sov, happening upon, or nex 
after, March a 1 1 and if theJF. M. i) on a ^day, Eafiet 



the Sunjay following. 

Scpt-asfitna? -• 

S/iag./i..a 

■^wrdr.tgrj^me 
/iDjVEHT 1 

3t jidniM. 



9 „ 1 bc- 
%-f |fo« 



Trimly Sanday 



5 Wks-l af- 
40 Da Iter 
7 Wks (Ea- 
8WksJ/ 



Sund. to the Fcaft of 



JU tb* mtvuMt and fiieti FsAtTt thfirwd in tht Church 
tf England. 



All Sunday! 
Circumcifion 
Epiphany 
Conv. St. Paul 
Purificatioa V>M. 
St. Mauhias 
Annun. V. Mary 
St. Mark Evan. 
St. Ph.and Ja.Ap. 
Afcenlion J. Chr. 



Eve f, 
Sr' l" 



St. fiamabai 
Nat. St. J. Bap. 
St. Peter Ap. • 
St. James Ap. 
St.Barth. Ap. 
St. Matth. An, 
St. Mic. & all An. 
St. Luke Ev. 
St. Sim.&Jn. Ap. 
All Saints 

LB and Fasts. 



St. Andrew Ap. 
St, Thomas Ap. 
Nat. of Chrifl 
St. Stephen Mar. 
3t. John Evan. 
Holy Innocents 
Mo. acTn.inEaA. 
Mo.&Ta.inWhit. 



^■ar. Cbr. Pentectfl \St. Jamii St. Aairtw 

Pitrif. St.MaithiasXSt.'Barlhdhm. St.Tbmat 

BafitrDay Sl.JehiiBap.\Sl. Maltbeni AUSainti. 
_AScinfi<,n Sl.Pettr [Sl.Sm.f^Jude 
N. B. When a Ft'ajl-day falls on a Manday, he Vigil or 
call is kept on the fa/itr^agr-^iif preceding, and notou' 
that of the Sunday, which is a Ft^-day. 

Days ^Fastirq on/ Abstihinci. 

L Forty Days in Lent. pi/ Sunday in Lent 

II. The Ember Days, at the J Fea^ of Pntecofi 
4, S E A s o N s, on the WednefdayS September the 14/A 
Friday and Satardaj after the {^Dectaier the 1 ^ib 

III. The 3 RogaiioB-dayi, MinJay, Tue/day, Wtdnc/day, 
before Chrift's Afccnfion or Haly Thurfday. 

IV. AUlhcFrifllyF^inlhe Year, except CA^/wa*.^. 

Solemn Days kept, far lohieh particular ChtiTch- Service it 

appaitileJ. 
I. Navemher 5, In Memory of the Pepiji Pht. 
If. January 30, iit Memory of the Martyrdom of K. 

Charks I. 

IIL JI% xq, in Memory of the Birth and Return of E. 
Charles 11. 



UiLT.h.Jan 
I Return 

J Return 



13, tnisFeh, 

Jast.zo 



F.b.i 



4 Ret. is J 

^ Ret, on Morrow of Afcen. 



Michatlma^.ieg.N^v. 6,tadi 
IN„. ,9 

1 Return ilW, 3 

2 Return 12 

3 Retuis 18 
f Return 3^ 
Tiimly Tirti, 

I Ret, Morrow of Hoi, Tr. 
t Ret. 7 DayiT Fr. Holy 
J Ret. 14 I -- ■ • 

.4 Ret, a 



n\ Fr. Holy 
VTrioity, 
J txebf/ive. 



PERPETUAL 

yGoogle- 



md NAVIGATOR. 



PERPETUAL TIME-TABLES: 

Or GcDCral RULES for Chroholoqibti^ Histokiani, &c 




MOVEABLE FEASTS for ever, according to the FiU of 
Eastbi. N.S. 


MoVBAiLB TiKua for ever, accordine 
totheFaUof EASTEa, N.S. 




Enfter 

Sunday. 


IK- 

Sonday 


Alh. 
Wcdnrf. 


Rogat. 

Sunday. 


Afcen. 

Sunday. 


Whit. 
Sunday. 


Advent 
Sunday. 


Eafisr 
Term 
begins. 


Ends. 


Trinity 
Term 
begioi. 


Ends. 




Mar. 12 


Jan. 18 
•9 

22 


Fd>. ♦ 
1 

1 


Apr. 26 
27 
28 
29 
30 


3 
4 


M.y,o 

»3 
■4 


Nov. 29" 

Dec'° 

2 f 
3 


Apt. 8 
9 

ir 

12 


May 4 

I 
7 
8 


Ma,22 
"3 
24 


June 10 
II 

>3 
' + 




^7 

30 
J' 


23 
34 

'A 

'7 


9 
10 
II 

12 

'3 


May I 

3 

4 
S 


1 

7 
9 


17 
18 

«9 


Nov. 27 
29 


»3 

'4 

11 

17 


9 

'3 


27 
28 
29 
30 
3^ 


W 
•A 

'9 




2 
3 

4 
S 
6 
7 
8 
9 
10 


28 

30 

Feb.'! 


•4 
IS 

16 
>7 
18 


6 

I 

9 
10 


II 

12 

'3 

14 


ap 
21 

23 
24 


Nov. 27 
28 
29 


18 
"9 

20 


\i 

'7 

18 


2 

3 

4 


20 
21 
22 
23 

»4 




t 
J 

4 

1 


»9 
21 

22 
33 


12 
'3 
>4 
■5 


'9 


29 


^«1 • 

Nov. 27 


23 
24 

27 


19 


6 
7 
8 
9 
10 


a7 
28 

29 




II 
tz 

'5 


7 
8 

9 
10 


24 


16 

W 

"9 


21 

22 

:24 


30 

2 
3 


28 
29 

Dec 1 

2 


28 

29 


"4 


II 
12 
J3 


30 

2 

3 
4 


■ 


16 

w 

19 


11 
'3 
'4 


Mt. 1 
3 

s 


2Z 

23 

■ 24 

2S 


27 
28 
29 


4 

7 
8 


Nov. 27 
28 
29 

3Q 


3 
4 

1 

7 


29 
30 

3' 

June I 

2' 


16 
'7 
18 
'9 

20 


1 

7 

. 8 
9 




22 
2J 

2S 


'7 
18 

21 


6 

9 
10 


26 
27 
23 
29 

30 


30 

June 1 

3 


9 
10 
11 

13 


Dec. I 

2 

N„.4 


- 3 

, 9 
10 

J' 


3 

4 

i 

7 


23 
24 

2i 


12 

'3 
"4 




itf^. B. When any fM> fall in Jai«afj or ftirw, in lta».r,ar, 
fuck Feafts msit be taken a Da/ lai*r than by Table. 

Add I to the Date, and divide the Sum by 19, what remant b the 
Golden Nomber reqajred. 
- WbenoKffltim tqis theGolden Number. 


W. B. £a/«r- Term begini 17 Days, 
and end. +3 Dayi after EASTER. 
fritiitj-Ttrm begint 5 Dayi, andendi 24 
Dayi ftfter Trimtj. Therefore Eafttr' 
Term continaes z/andrw'wVjr 20, iaclu- 
five. 





,, Google 



fit ROYAL ASTRONOMER 



PERPETUAL TIME-TABLES: 

Ot Generjl RULES for Chiioboioo.jt., Hi.ro.iin,, ic. 


» MOVEABLE FEASTS fniB 1755 » ,800, ^f.S. 


Yem of 

Chrift. 


Gol. 


Dom. 
Letter. 
N.S. 


Dots. 
Letter. 

0. S, 


Septoa- 
gefima 
SuDdajr 


Afli- 
Wodnef. 


Eafler 
Sunday. 


Rogat. 
Sunlay. 


Afcenf. 
Day. 


Whlt- 
Sanday. 


Adren 
S.oday. 


e. 

paa. 


B. 1760 
1761 
1761 


'J 

1+ 


FE 

D 

C 


BA 
G 

F 


Jan. 18 
Feb.; 


Feb. 28 
4 


Apr.,^ 

Mar.az 
Apr... 


May 20 

Apr. 26 
May 16 


M.,H 


teyaf 

30 


Nor. 30 
2? 


.2 

as 


B. ;5?j 


'7 
18 
19 


AG 

F 
E 
D 


DC 

A 
G 


Jan. 30 
Feb. 19 

i-eb.,, 


M»r. 7 

Fcb.ao 

12 

Mar. 4 


■ 3 
22 

Mar.jo 
Apr.,, 


8 
27 

12 

4 


8 
z8 


21 

Idh. 10 
May 26 

Jan. 7 


Dec. '^ 
Not. 30 


7 
iS 


■769 
1770 

B. 1772 


J 
4 

1 


A 
G 
F 
ED 


D 

C 

AG 


Jan. ji 
Feb. if 
Feb. 16 


8 
38 


Mar.2^ 
Apr. 19 


s 

2+ 


12 

4 
24 
9 


Mayaa 
J.O. 7 


DO. '5 

2 

Not. 2$ 


li 
S 


'773 
'774 

B. 1775 

■ .777 


7 
8 
9 
10 


B 
A 

GF 
E 


D 

CB 

A 


Feb. 12 

4 

Jan. 10 


.eb.2j 

Mar. 1 
Feb. 21 


.1 

M„,J 


16 

8 
21 
12 

4 


20 

12 

? 8 


May 30 


28 

ay 

Dm. 3 

1 
Not. 30 


— 

9 


1778 

B. 1780 
1781 
178s 


'3 


C 

6A 

G 

F 


F 

ED 

C 

B 


feb.,s 
Jai..ji 

Feb.;i 


Mar. 4 
Feb. 17 

2I 
>3 


Apr. 19 
Mar. 26 ' 


24 


28 

'3 
4 

»4 
« 


iS,2? 
Sa-y.'j 


Dec. 3 

2 


1 

12 

n 

4 


B. \?i\ 

- mi 
.787 


15 
■9 


DC 
B 
A 
G 


GF 
E 
D 
C 


1 — ^*- 


Feb. 25 

Mar.? 

Feb. 21 


Apr. 20 

Mar.27 
Apr. 1 6 


2. 

■3 


29 
30 
S 

'S 
•7 


Mvs' 

Si4 


Not. 30 
x8 

Doc.^' 

3 


26 
7 
18 


1790 

1 \iv. 


3. 

4 

1 


<-C 
B 
AG 


G 
F 
B 
DC 


t.'t 
I'm 


Mar.'o 
Feb.ai 


Mar.23 
Apr.. 2 


Apr. 27 

May .7 

9 

»9 

■S 


,8. 

,.00-1 
May, 7 


11 

3' 

May 27 


Dee.'j 


31 

3 

»4 


>79) 

■794 

B. 1796 
1797 


9 

ir 
11 


E 
D 
CB 
A 


A 
G 

FE 
D 


J«o- 24 
Feb. I. 


Mar.'? 

Peb.i§ 

10 

Mar. I 


Apr. 20 

Mir.4 
Apr. 1 6 


S 
to 


9 

• «9 

'4 

S 
25 


k1 
May 24 

ro..-J 


Not. 30 
29 

Dee.-; 


11 

9 


1798 


13 
>4 

If' 


F 

,^ 


B 


Kb. ♦ 
Jan. 20 

'"1 


?l 


. 8 
Mar. 24 
Ap...,^ 


Apr. 28 
May .8 

fo 


'7 


May 27 
12 

Jdd. I . 


""li 


»3 




f/ 


[ • 

1 


K 


• /-* 


A-5 


/9 


}3 


D 


Qilizod by ' 


peJI 


Ic 



mi N A V IG A T O R. 



PERPETUAL TIME-TABLES: 

Or General RULES for Chroholocists, Historians, &c. 



JANUARY xxii Dayi. 



G F E D C B A 



;uMCisiON.DayBr.5''S9",T.c. 
San rifea 8 4, feu 3 56, i.afli/^6h im. 

Sir I/aac Ntvjiaa born, 1643, N. S. 

Old Chriilmas-day. 

gpiPHAtir. 

Sun flow of Clocyj^ra losj 

Prlncef^iaAeth born, 1740. 
Day ffreak ; 22. Tw. ends 6 8. 
Sun rifes 7 56, feti 4 5, 
3t. Hillary, Biihop of Poidiicrs. 
Ox. Se Cam. Terms be£ia. 
Exchequer openi. 

OldTwelfih-day. O fl.ofCI. lo^sfi', 
Prifca. 

enter'd ^, Noon, 175^. 

Agnes. Day Br. c 43, Tw. e. 6 17. 
Vincent. Sun rifts 7 44, fets 4 id- 
Hillary Term begins. 



CONVIRI 



OP St. Paul. 



San flow of Clocks 13m 29S< 



. 1648-9, O. S. 
[12m pall One. 



FEBRUARY txviJi or xxix Da>s. 



G F E D C B A 



O Fixed Fealls, Rtmariaiit Day, 
accorJing ta NrviSljlt. 



in riles 7 16, fcts 4 34, Lenden, 
fftiF.V.MAKT.orCandlcmas.day. 
aize, Biihop. 

Agatha. 

n flow of Clocks 14m 4js. 



Dili ScMapca, at Oxford. 

Day fir. ; \z. Tw. ends 6 4S. 

HilUryT.endb. Sanr. 78. f . 4 s^ 

Old Candlemas -day. 

Vaieniinc, 3 Bifliop of Rome Sc M. 



Sun flow of Clocks, i4tn 291 
Sun in X 21' Noon, 1756. 



Day Br. 4 5;. Twil. ends 7 5. 
Sunrifes6 49, fets 5 ii. ' 



flow of Clocks ijm 4$ 
Hare- Hun ting goes cut. 
Leap' Year. 
~imb. dm. far B. A. ihe Daj afti 

Ajh.Widntfdaj. 



The NEW, FULL, and QUARTER MOONS. 



The NEW, FULL, and QUARTER MOONS. 



L 

Q. 


\ I 


F 


F 
M 


■i 


f ► 


» 





= 7 


1 17 




1 


5 


1 6 


'4 




M 


I 14 


21 


29 


S 


' 3 


11 


18 








7 




'-. " 







tS" Uftir the D««. i«/w ^ O. ar N. Stile, egttinfi the Day 
%f the Menth fiaiiii ibt Weik-Day Ltttir cerri/pomJtnt, 

*•" Ox/erJ and Camiri^ Termi end Thurjday be/nTiWhit/u 
day— Trinity Oilltge EUaian m Trimly Mmilay. 



O Oxfird and Camiridge Terat htgin Widaefdof after Trinilj 
SubJi^ — Trinit/ Cellige EleHiair, Mmdaj after Trimly Saaday. 



,, Google 



I84. 



fbi ROYAL ASTRONOMER 



PERPETUAL TIME-TABLESi 

Or Gcncial RULES foi Chkoholociits, Hutokiani, tec. 



MARCH xxxi Dayi. 



APRIL XXX JJiy: 



th 1 
f .■ 
r i 

S m 


, » 


th t" 
f f 
f S 



D Fijcei^ FcaRs, RtmarkakUDtyi,St<:. 
atcarding to Nnu Stylt, 



<,A<>p.M.b.4.4. 
Cedd<!orChad.B.Suii r.6 34 f.5 27 

flow of Clocks izra 11. 
Priact/i Mary afUiffi b. 1722. 

Perpetua Maurit. Matt. 

" \mb. lallir Ja Ihvf. of, +5. in 

Lint. 
Daybr. 4 19. Twil. eaii 7 42. 
Sun Tifei 6 14, fcu j 47. 
Gregory. 

San flow of Cloclca 9m zis. 
0;t/. y Cam. f/rmj tJi^tbtDof hef. 

Pa/mS. 
St. Patrick, a Bilhop of Ireland. 
Ed. K.of WcftSajc. 
PrlTe Louifa-Ann b, 1 749. Jofeph, 
Cuthbcrt. EquaL Day and Nigbi. 
BenediaAbbot. D.b.j ;7.T,c8 4. 
Sun rifes 5 54, fet* 6 7. 

nT 20'on 20 D. Noon, 1756. 

flow'of Clocks 6m i8s. 
Lady-Dav. Annonciation B. 

[V. M. Pr. Ed-ward b. 1739. 

. B. Aaerding la Gregorian 
Rtciming, tht '■ioUln Ntmhtnto ibt 
Ltfl af all, pe^ thi Timts of tht 
Full Mtaai prcctdiug Eafier-Suttday, 
nil 1900. 



P F/^^Fcafti, Rimarl^it Digi, tec 
aettrdJHg f» New Style, 



All Foob-day. D. b. j 31, T. c. 
San life* ; 32, feta 6 28. [8 ig. 
Richard B. Chich. 
S. Ambrofe. Sun II. of CI. 2m cc>. 
Old Lady day. 

Ox/. Of Cam. Ttrm big. Wid, af. 
x^S.aJi.Eafitr. 



D.br. 3 34. T.e. 8 57. 
Sunrifes ; 13, feu 6 48. 

EafttrTer. beg, 17 Daft of. Eafier, 
tndt in 1 7 Daji. 
14 Snn flow of Clock* om i6s. 
Sun and Clocks togetber. 
Wtftminfitr Eltaitn Da;ef.^S.af. 

{in 20 Dajt. 
Alphege. Tr.T.big.^I}, a/.E4f,ewdi 
Sun in K 46' Noon, 17(6. 
Day Br. 2 37. Tw. enda 9 24. 
Sun rife* 4 S4, f«s 7 7. 
3. Geo. of Cappadocia, Patr.Eng. 
Sun fafl of Clocks am 6», 
St. Mark, Evaogelift. 
Dui[EopCuuB£ai,AHD,b. 172 
Via.of Culioden. 
N.B.JccerditigtttbeGtee. Steian- 
ing, thi GtU. Nei. to tht Left rfall, 
j&qu the Timet of tht Full Meomfi 
'f.iA'nfEaflier Sunday, tiHi^oo. 



The NEW, FULL, and QUARTER MOONS. 



The NEW, FUI.L, and QUARTER MOONS. 



N 


F 


F 


r, 




M 


q! m 


^ 




rt 


PI 


<[ 


















■'s 




19 

7 




21 


fo 




it 


4I 


11 


IQ 




1 


^3 
13 


'2^' 


a 

z8 





fT. 





N 


P 


F 


I, 


CJ 


f 


f? 




M 


tj 


M 


(> 


















=" 









• 


» 





d 




21 


7 


22 


iq 


7 


>4 


'3 




II 


H 


11 


10 




1 






<* 


^O 




«? 




iK 








'<) 


17 


■4 


12 






7 




7 


u 




10 


"7 








^7 


4 


12 


>9 


18 
'9 


2 



. .B. Corfu Chrifi fh. af. 7r. S. — Cam. CemmencemtMt iff 

Tui/d. -Julj. 



N.B. The Rules Ibr variable Days are in the Bndy of the 
Monihi fiom January to April, and then in SocceflioD froi 
January to April at the Bottom. 

I"»* Oxf. AQ. 1 Days fr. Cam. Couarmuenunt. — — Balis. 
Oil. Ehaion 7h. bef. St. JaJrrw. 



DigHizcd by VjOOQ IC 



0»J N A V I G A T O R. 



185 



PERPETUAL TIME-TABLES: 


Or General RULES for Chrokolocmts, Historiahs, Sic. 




MAY xxxi Days. 


JUNE «x Bay.. 


G 


F 


E IdIc 


B 


A 


Fixid Feafls, Ri/nariaiie Dayr, &C. 


G^ 


' E 


D 


C 


B 


A S 


Fw.^ FmOs, Rtmarkails Dayi, ic 


t 


w 


^r.r 


r 


m 


T 


errtritng to Npw Ulyle. 


- ~ 










2. 


tucarriine le Nt^v Sttle. 


bt.PuiL&jAMBi. D. br. a a.T.E. 


r' 




m 


t~ 


w" 


th 


I 


Nicomedes. fso Night. 


w 


[b 




f 


S 


m 


t 


jSunrilMS 36,fc"7 2S- [9 59- 
3 Invention of the Crors. 


f 


n 




w 


th 


f 


z 


■unrifes 3 52, fets 8 8. 


th 


f 


( 








w 


s 


n t 




th 


f 


f 


3 




f 


f 


s 


m 


t 


w 


th 


4Sunfaft of Clocks 3m 3js. 


m 


w 


h 


( 


f- 


s.. 


J^Giirrgt Prmnif Wal„h>r«. 1718. J 


r 


S 


in 


t 




rh 


f 


5| 




V Eh 


f 


f 


S 




s 


Boniface. Sun faft of Clocks am is. 


s 


in 


t 


w 


th 


( 


f 


6 St. John Evang. ante Port. Lat. 


w 


h f 


f 


S 


m 


t 


6 










th 


f 


( 


S 


7 


th 


f 


S 


01 


t 




7 




c 


w 


th 


f 


f 


s 


m 


8 


f 


S 


m 


t 


w 


th 


8 




IV 


th 


f 


f 


s 


m 


t 


9 


f 


m 




w 


th 


f 


9 




[h 


f 


f 


S 


m 


t 


w 


10 


s 




w 


th 


f 


f 




Prfft Amelia b. 1711. 


f 


f 


S 


m 


t 


w 


th 


iiiDaybr. i 24. Twll. end. 10 38. 


m 


w 


h 


f 


f 


s 


II 


St.BARNABA). 


f 


S 


m 




w 


th 


f 


ii;01d May-day. Sun r. 4 19. f. 7 42. 


t 


v th 


f 


r 


S 


m 


12 


Snnrifej 3 4J, fets 8 ij. NoNt. 


S 






w 


th 


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w t 


h f 


f 


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t 


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in 

c 


w 


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lb 
{ 


f 
f 


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7 


unfaftof Clucks 4ni t». 


th 

f 


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w 


th 


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Snn fad of dock* om as. 


w 


th 


f 


f 


S 


ro 


t 


16 




f . 


m 




w 


ch 


f 


'6 


Sun and Clocks together. 


[h 


f 


r 


S' m 




w 


17 




S z 






th 


f 


f 




St. Albu. 


f 


f 


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th 


i8 




m t 


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r 


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f. 


S 


m 




w 


th 


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f 


f 


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Sunin2B22'oB2i D. Noon, i7?6. 


S 


m 




w 


th 


f 


f 


20 San in n 44.' on 11 D. Noon, 17^6- 


w t 


h f 


f 


s 


tn 


t 


20 Tranfl. of Edw. K. Weft Sar. 1 


n 




w 


th 


f 


r 


S 


11 


Day br. la. Twil. ends 11 49. 


th f 




s 


m 


t 


w 


2l 


Sunrife. 342, fetsS 17. No Night. 


t 


w 


th 


f 


f 


s 


m 


22 


San rife* 4 5, fet»7 55. 


f r 


S 


m 




w 


th 


22 


K Gbo. Il'j Inmg. Longed Day. 


w 


th 


t 


r 


S 


m 




tj 




f E 


m 






th 


f 


23 




Eh 


f 


( 


s 


m 


t 


sw 


H 


fr.Fr*d.WilLb.ijiQ. Sun fall of CI. 


S t: 


ti t 


w 


th 


f 


f 


24ST. JoHNBAPT.bom. 1 


r 


r 


3 


m 


t 


w 


th 


11 


[3m 36'- 


m t 


w 


th 


f 


f 


S 


\{ 


Sanfl.ofC1.2mj..St.John'sCol.El. 


f 


s 


m 




w 


th 


f 


Aagultine. No Night. 


t V 


V th 


f 


r 


S 


ra 


s 




t 




th 


f 


f 


ly 


Venerable Bede. 




h f 


f 


s 




t 


'7 










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r 


S 


z9 




th f 


f 


S 


m 


t 


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t 


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f f 


s 


m 


ig 


E:.CBAiti.E3irsNAT,aodRBSToa. 


f I 


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m 


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th 


^9 


St.PsTER. 


w 


th 


t 


f S 


m 


J 


i° 




f S 


m 




w 


tb 


f 


30 


Buck-hunting comes in and continoef 
till Holy Rood. ExeterCol. Elec. 


th 


f 


f 


S m 


It 


w 


31 
















The NEW, FULL, and QJJAJITER MOONS. 


The NEW, FULL, and QUARTER MOONS. 


c j) 


N 





N 


F 1 K L 


C) 


N 


F 


F L 10 


N 


F F 


L 


CD'N 


F 


F 


L 


7 


• 1 
21 4' 





M 


Q |m 


Q. 


9 
2: 


M 


Q. 


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• 


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6 


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1 30 


8 


26 


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8 


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2 


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i 30 


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11 


18 


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1 




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23 


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1 • 1 11 




1 


■ 1911 7 


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22 


^ 


Embhdation* 


P. 171. Right Hand Col. ]. 18. fr.Top. for jfc/ Cbrifl, re^d h,/m Ch-ijl. 




P. 177, Riehi Hand Col. 1.3. fr.Bot: for ^«//j, reidAki-r. 1 
P. 170, LeftHandCol. 1. 16. fr.Top. {otrijmrtJ, mdrti-irt. 



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l8S 



ni ROYAL ASTRONOMER 



PERPETUAL TIME-TABLESi 

Or Geaeral RULES for CHKOHotoeiiTS, HiitokiaK), &c. 



JULY xxxi Day). 



ir 



f.OTdfcalls, RtniarialU Da;s, &c 
(e Nem Slylt. 



Days. 



No Night. 
VifiLolB.V.M. Sunr.3 4;,f.8i5. th 
Diet Coiiiidor. ' 

Traiif. of St. Mart. B. 

Old Mid rummer -day. 

T ham as a Bccket. 

flow of Clocks 4in 30s. 



No Night. Sun rifej 8 52, fets S 7. 



St. S-uiibin, or SwitbuD, B. of Winch. 

[tranf.. 

SuD flow of Clocki 5m 39$. 

Margaret V. and M.' 
No Night. Sun rifea 4. 3, feti 7 56. 
Mary Magdalen. Pr/t Car. Maiiliia 
3nninft,s3'Noon, 1756. [*-l7S 
Magdakn Coll. EkSiim. 

St. J AMIS. 

St. Ann, Mother B. V. M. 

San flow of Clocks 5m 561. 

Dog-days beg. Sirins rifeswith the 
[Si 



F 


E 


D 


C 


B / 


, 


ch 


f 


r 


~ 


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f 
f 


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S 


(I) 


c 


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w 


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t 


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w 


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t 




s 


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!■ 


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t 




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r r 








ch 


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th 


t 


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i 


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1 








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s 


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m 


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[ 


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1 


f 


s 


m 


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3 



(J FealU, Rtmarkabh Deji, &C. 

accarjin^ to Nt-iu Style. 



>. Day br. 1 27. 

, fetip 40. T.endsio 31 



(low of Clocks j 
n; figuration. 
ne of Jefus. 



Lanrencc, Atch deac. Romc.&M. 

Uifi JiigaJiahOTa, 1737. 

w. 25. T. e.3S3, Sun T. 436. 
[f- 7 »3- 

imption of V..M. Sunfl. ofCI. 
[Zta 56s. 



Haafius. D.br. 238. T.e.921. 
rifej 4 54, fets 7 5. 
in HE j8' Noon, 1756. 
Baktholombw. 
flow of Clocks im 3S». 

AuAin B. of Hip. 
eading St. John Bapt. 
and Clocks together. 



The NEW, FULL, and QUARTER MOONS. 



The NEW. FULL, and QUARTER MOONS. 



,y Google 



md NAVIGATOR. 



187 



PERPETUAL TIME-TABLES: 


Or Gcner»l RULES for ChrohologiIts, Historians, &c. 


SEPTEMBER xxx Days. | 


OCTOBEER xxxi Days. 


G 


F ED C 


'5 KcardtMg t» Nrtu Stilt. 


f, f, . D Fi^c^ Fcafts, R.>Hariabl, Urn. &c. 


r 


$ m t w 


th f 1 GilM, Abbot. D.br. 39. T. 6.850. m : w ih 


t 1 3 1 Reroegius, B. ot Kboiurs. 


3 


m I w th 


f f I L(»NDONbnn«i666,O.S.Smir.; 14, t w tb t 


" S m I U.br.4io. T.e. 7 39. Sunr.613, 


n 


t w ch t 


^ m t 3 [f. S 46. 




w th r f 


S ai 4 th 1- 1 i 


m t w 4 Sun fad of Clocks, iim 30s, 


IV 


th f f 3 


rot c ^aDfiftofCloduiin45>. t f S m 


.»,!.; 


th 


r r s m 


t w 6 f 3 m t 


• ih f 6Si.Fuih. V.iM. 


I 


f S m t 


w [h 7 Eunurchus. Smew 


th ( f 7 


f 


.S m t w 


th 1 e Nativity B. V. M, ro t w th 


f f S 8 


S 


m c w th 


f r c Doe-days end. Canit Moj^ t. t M. t w th T 


f 3 m 9 ft. Denis. 




t w th f 


f i to w th f f 


S m t ic JldMichaelmas day.Ox.&Cam.T.bj , 


[ 


w thf f 


S m U DayBr. 33;. Twil. end8 8i+. th f f S 


rot w 11 a. br.+ 40. T. c. 7 19. Solir.653 




th r r s 


m ; 12 jun rifes s 3+, fets6 15. f f S in 


t .. th .1 [r. s J.. 


± 


f . S m 


t # 13 f S ai c 


« th r i3Trinf.K.Ed..Conf. 


f 


f S ni t 


w ,h 14 HoIyCrof»day,orExalt.oftheCrofi. S m t w 


Lh f r 14 iunfaftofClcclti 14m c>. 


r 


S m t w 


Eh f ij >unfaJlofClock> jm ii«. m i w th 


( f i IS 


s 


tn t w th 


1 1 It t wth f 


f S ID 16 




t w th f 


f i 17 Lambert B. w th f f 


> m t ijEtkcWiedVi™. 

mt w IS 3t. LucEibeEvangdiJl. 


I 


w ih f f 


S m IK th r r S 


w 


th f f -- 


m t 19 f r S m 


, » th ,5 


th 


t f S n. 


t * ic D.br. 3 58. Twil. tods 8 I. f S jh t 


•■ th f ao 


r 


f S tn [ 


w th 21 it. Matthew. Sunr. ; 53, f. 6 5. S m t w 


th f f 2[ D.br. 50. T. e. 659. Sanr. 6;i. 
f ( S aaK.Gio,lI.ctown=a,i7a7.[f.j 7. 
f i PJ 23 Son iniiui' Noon, 1756. 


f 


S m t w 


th f aiEqualDayandNt. in«!ltheWorld. m i w tl 




m t w t 


f f 11 iun 10^48' Noon, i7s6. t w th f 


m 


t * th f 


f 3 4 w th f f 


S in t i4$Dnfaft of Clocks 15m 45». 


[ 


w ih f f 


S m z( Siinfaftof Clocks 81037$.' th f f S 


m t |\v aj Ci-i/fiif fatroD of Shoc-maken. ■- 


w 


th f C S 


in t i' St. Cyprian. f f S m 


t * th z6 


[h 


f . S m 


t vv ^7 r S n. c 


IV th f 2; 




1 S m I 


w ih 2b Sheriffs of London fivoru. S m r ■ w 


th f f 21, St. Simon and JuDB. 




S iu t * 


th 1 i<, 'tt. MicHABL. Hare-huDting comes m t w t 


f f S 24 




m t w I 


1 . 3cSt.J»oro. [in and laflt till the End t w th f 


f S m jc 




I 


fof Feb. w tb f f 


S mt J, 




The 


NEW, FULl, and QUARTER MOONS. 


OIINIF 


f L in N 


F 




L 


11 




f L 


PjlM Q 


M 0. ? M 
0, 1 p • 


Q 


M 


S 


n 


^ 


MQ^ 


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a 




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1 aj 30 


8 IS 1 7 '<> 


'3 


1 31 


8 


13 


10 


lb 


»S| 3 


2 la 19 


26 4 8 5 


'3 


>9 


■7 


'4 


«9 




I4|za 


3 30 8 


IS aj 1 9 24 


a 


9 


"7 


'5 


'? 


25 


34c 


^ S 16 


4 12 |io IJ 


21 


z8 


7 


16 


6 




8. S9 


23 1 3i!ii I 31 
12 ao la ao 


>9 


16 


*4 


17 






U 18 




1 r\ ' 


28 


6 


'! 


18 

12. 


'S 


^3 


29 / 





















yGoogle 



nc ROYAL ASTRONOMER 



PERPETUAL TIME-TABLES: 


Or General RULES^for CHuoNOLoctsTi, Historiaks, S:c, 


N V E M B E R xxK Days. | DECEMBER xxxi Dr.j.. 


G 
th 


F 

r 


E D 


c[b 


A 


g)lfMV</feaUs, SMiarkabU Daji, &c. 


G 


f 


E 


D 


C 


B 


A 


■5 


FixeJ Fealts, RtmariabU Dofj, &c. 
atforJiiig to ti'eto Slile. 


m c 


r 




AllSaint.. D.br.,- ia.T.e.641, 


r 


S 


m 


r 


w" 


tiT 


r 


I 


D2.y Ureak 5 44. Twilight endi 6 6. 


f 


f 


S m 


[ w 


I All Souls. Sun r. 7 ij. f. 4 47. 


S 


m 


t 


w 


th 


f 


r 


z 


Sunrifet 7 57, fots 4 3. 


f 


s 




w th 


1 All Souls College EleftioQ. 


m 






th 


f 


r 




j 




5 


m 


t w 


th f 


1 K.WiLL.born. Sanf.ofCl, 1601 13). 


I 


w 


th 


f 


f 


s 


01 


■i 


Barbary. Sttn fall of CL 9m 6.. 




t 


* th 


f f 


! Powder-Plot, 1605, 0.5. 


w 


ih 


f 


f 


S 


m 








t 




th f 


f S 


1 Leonard. Michaelmas Term begins, 
1 ?t. BeiiTj.FritilTic h. 1745- 


th 


f 


f 


S 


m 




w 




WVi.A«. 




(h 


f f 


S CD 


f 


f 


S 


m 


t 


w 


th 


7 




th 


f 


f S 


m c 


1 K.GiF.b.i683.W.S.Ld.Mayor'iday. 


f 


s 




t 




th 


f 




Concept. B. V. M. 


f 


f 


S m 


t w 


S 


en 


t 


w 


th 


f 


f 


9 




r 


S 




IV th 


1 K. Glo. ri. Birth-day kept. [Lond. 


m 


t 


w 


th 


f 


f 


s 


iO 




s 




'• w 


;h f 


1 St. Martin, B. & Conf. 






th 


f 


r 


S 




11 


Day Br. 5 jg, Tw. end» 6 t. 


m 


t 


w th 


f f 


i D. bn.s 33. T.e. 6 27. Sun r. 7 30. 


w 


th 


f 


f 


s 


m 


t 


12 


Sun rifes 8 5, feU 3 jj. 


t 




rhf 


f S 


1 SritiusB. rr. 4 to. 


th 


f 


f 


S 






w 


>3 


CsO-, 


ft 


ch 


f f 


s m 


1 Sunfaftof Clockjicniu. 


f 


f 


S 


m 


t 


w 


th 


14 


Sun faft of C!ock> 401 34J. 


ch 


f 


r S 




< Machniut B. 


f 


S 


m 


t 


w 


th 


f 


"S 




f 


r 


S m 


t w 




S 


m 


t 


w 


th 


f 


f 


ig 


Sapientia. 


f 


s 


m t 


w th 


f 


'7 


Hugh. B. Line. Anniverfary of Q. 


m 


t 


w 


th 


f 


f 


S 


17 


Oxford and CambridM Tenni end. 


S 


m 


t w 


ch f 


r 


18 


[Elizabeth's Procl. 1558. 


t 


w 


th 


f 


f 


S 


m 


1 8|Princefa iwij/a^ Qt of Denn). b. 1 724.I 




t 


W Eh 


r f 


s 


'9 






th 


f 


f 


S 




t 


'9 




c 




th f 


f s 


m 


20 


Edmund, K.&M. 


th 


f 


r 


S 


tn 


t 


w 


20 


Sunin>tf lo'onaiD. Noon, 1756. 




th 


f 1" 


S m 


t 


11 


D.b.j44. T-.e. 6 ifi. Sonr. 7 4S.f. 
Cecilia. Old Martinmas-day. [4 1 4. 


f 


f 


s 


m 


t 


w 


ch 


21 


St. Thomas. Shorteft D«y. 


ch 


f 


f 3 


m [ 






f 


S 


m 


t 


w 


th 


f 


2Z 


Sunrife* 8 7, feu j 53. 


f 


f 


S n 


t w 


th 


*3 


St. CIcmeiit. Sun in / 41'on 22 D. 
Son raft of CI. 1 11046$. [Noon, tjqG. 
Cathtrine. Pr. WiU^-Hcnry-Fred. 


S 


m 


t 


w 


th 


f 


f 


*3 


San and Clocks totether. 


r 


S 


m t 


w th 


f 


24 


m 


c 


w 


th 


f. 


r 


S 


24 Sun flow of ClociM 261. | 


j 




t w 


th f 


f 


*9 


t 


w 


th 


f 


f 


s 


m 


'5 


Ch«i»tmai.dat. 4thQMitar.dayJ 




t .with 

w^h f 


f f 


S 


26 


[b. 1743. 




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afid N A V I G A Y O R. 



189 



R O L E S /tr the S T A R 8.. 
RIGHT ASCENSION «i DECLINATION «/" STARS. 

right Afca/.n if any Star frat the givn right jtjixa^ tf aiy aihir Sl*r. 

ne mirlted by 1 C/m*. going uniformly, wbether regulated or not, during the IntaiTiI of » SUr'i Riro.u,™.., .. .u ji-u-, 

ft ir the Tinw mirted by the Ijrac Clock, btiween the PaOagc of that and any other Slir, t)ircu|h the Meridian, to their Difference of Right 

Tt Jitcrmhr iht Right jtfcti>fin tf ery fArttmJtr Star T 

RULE. When the Sitn ii near the Efainu, where in Chiap in Decliulisa iifunft^, obtttve iti Meiidian Height 'or Dedioation font 
ay at Moon. And by the Afit*(i a/ ccrr,fjKr>iii»g Miiuiti, or otiierwife, otferve the Difference in R, A. between the chofen Stir and tt 
i.\. It ihe fame Inflint of Noon. Wl^en the Sun hat palTcd the following StIjUet, and ii retniiud neuly to the fam* Partly, obfene, fc 
three or four Dayi togKhei, ill Meridian AltlTudes, and iti DiSetence in R. A. with the fame Star, for detenniniog, from tfaefe OUer*a- 
■ n», whentheSuncomeiinto the fame Pataliel, ai in the firA OfcfervitioD, and the Diffetence of R. A. for the fame /j^f^K. 



Till Mubtd gi«i n 



esinto the fame Patallel, 

'aflanti when theSanma a[ eqaal DiAancei from the fame Trtftti becasfe, 

1 — — likewift the torrefjionding Jra of (be Rjuatot. 

'"''" — laAanta, wiUgive (ibeJtor Js'jif jfxfi/JthcArc of the Ef nator, or Sur 



rqual Diitaiicei, on either Skle 



thefei 
in the hiirval of Ihefe t wo Inflanti. • 

1 he iitlptial Ceitn therefore bifefli that Arr, the Compli 
The Sun'i R. A. being (hui detemioed, the R. A, of tl 



It the Ii tit Obfartitioc. 



47 »9 3» 



S. . . . 4« 44 14 55 17 43 WeA 
fM»f 9/a(/>r thefe Oblmalioat, I'l appear! that if the 5» had been in tbxtlHtiJaaSifl, j* gS jo«i J*; H. be would have had eAid Al- 

lode, with hi) AltiCu(ieon.,^74lhat Noon, pteceeding ; vis , 460-58' 41" 

The Difbence between bit R. A. and that of tha Star, bai been . . 54 5J' toWet 
Therefore, fromy^i/4,.toi'ffii».iifcr7* 8>i jooiEteoing, iheSonhad runthrouih, inR. A. , . . ,15a 4549 
Whence, on.4Dn74d Noon, Sun'iDifiaaceiiiR. A.fiom the Trtff'rofcB via '. . 76 » 54} 



5 M 37 

I 97 5» ' 



ThtSfar PrtijimiitdRtA, njnirtd ,', , Sum . 4 li]> 1$' 15'^ 
USES e/<i> RIGHT ASCENSION amd DECLINATION >/(if STARS. 



tbtlUirUitii. 
R. A. of the Sui 
rf of Time from Noon to Noc 



J. To'cmfKit it ■a/hut Tinu ttd Sitrfajii tht Miri 
hi the Noon of the given Day, reduce tiiii DiAerence to Time, byTkj.;, iS, which will be neailjt the /wi 
of the Star'! Paf&ge thiDugh the Meridian. 

The abore CtmpnUiiim givei the 77aM >/ ibt Pajfap but lUarfy { becaafe neither the Sun or Star are fuppoTed to have any Motion in R 

But, tifindihictrj-iaTrmt, compute cheSun and Slat'i R. A . foi the Time oliWii^ found, ud tbeii DiSennce, reduced to Time 
TC the nrrtH lofiant of the Star'i paSing the Meridian. *■ 

EXAMPLE. Siffcf, ih, R. jI. t/Man, «n a ziva Da* at Nm t, it»o il', aiti tht R. A. ^ ttiSnlly ^%; the Btfrae, 7^ 
roLirJ laliiH it ^t^ 4y ^it, Nov/ManiiiiiiiefimiriK/iit Shu, wiji faft tbt Meiiian timt 1^ ^^b^ %it tijwi NfH, limit, 7>> 14 
' ihi lUtraini' 



if th* Stan bj oUerring cheif PaOiigei am thr UtrUin*. 



ThfDifinwct 
XabeiJ n TnM, » tit It/laiit tf ttt Pt^H' 'f Mart tbnugh tit MtriJian 
Thii CartWarinr ia plainlr tlia Ktvirfi of tSe fonner, in Ending the R. . 
By the abore .Computation, the Timet marked by a Cltck may be proved. 
For, obferving at what Irfiiat any Star, whofe R. A. ii krwiwn, paflet the Stiniiiaa, that ii/«( being complied with (he ilbir, fo«nd by 
Smpula'ton, will Ihew whether the C/gci agreei with true Time, or what it «!i/«-i from it, 

4. Another Ufe of the R. A. and Declination of Stan i>, TtJlaJtbi oifi^act tf ariStarfrtmthiMiridiaiiif aPlaaal a gima^imi. Or 
which i) the fame, 

TojinJ ihi Argil at thtPHi, firmiJ hjiit Mtridian if a PUa adthe Circktf DaliiatifH ftfgw ihrta^ tit Star. 

METHOD. Sidua tht hinal tf Ti»a hmaum Nim aai tht nwn> Mtm, iaii Dvrm, ij "VA. p. iS, add tim U lit San'i R. A. al thai 
gtKI; aadfrsmlhtSiai/ukraillhiSlar'i R.A. 
t/. B. WbcD thefiid Sum ia Ida than the Star'tK. A, add ts it ]io°. 

RULBS>r- SUN ot/STAR^J 



,y Google 



<90 ri/ ROYAL ASTRONOMER 

RULES>- SUN on/ STARS. 



EXAMPLE I. 

VhtMiwiJimMltiiiff'biivTfimaSiar, ttdlti Ptb'i Elrvtl!nbBt[ givtii, fjlivltii Svit wSt4r'$Di^n^!mr 
Tbe clEvited Pole, ind Meridian Altitude, oh tke iame Sipt or thi MiEIBlAit. 
PoIt*! Height frmir than the Metidiin Altitade. 
Caii I. •riMSmmtftbtCtmflmiiii^ihtPtU'iHngbtmiii MaiJiam jihitaJt wO 6t ibtiaK tr Star't D^diimivi, fit^i, tf the f*mt 
'amt viii lb" *f ibf P'l'- 
Or, p +'M = D, La th< Pth'i Hiifli d jos If. «W Mm'ilan Aliliaii ^v. Then, 40" + jo" = ^o^, the Sbu'i Dwlioatian N. 

M. B*. Tb Difema^ tit Pali'i Htiibi nJ IMtri£at jStiitdi in tbii Cafi h!,f aiitd ra tti PoU'i Uiiibl mil giw ili MiriJia* MUmJi 4- 
ttvuUPiU, atnidCafi, via. jo" — jo' ^ 10" ; + so^7o» AliituBe abote tbe Psle, 
Pole'i Height lift than the Meildian Attitude. 
Tht S*m 1/ ibtCtm/i/mni ef lii Mi'idian Mirtdr ami Ibt Pek'i Hc^br (being the Reretle of the rotmer Cafe) will if lii Svti r 



Sttr'i DitSnaiioH 1/ ibthmi Name ■aiM thai tfib* PtU, 



Lit til Ptii'i Hti^ it ^a* N. and MtriJian AUituit ^<', litm 50^ -f" i°° ^ Jo"' ^* Stai'a Decliaitian H. 

tbt Ptli'i Hriihi a«i Mniiiai AhiiaJt in 

The elevated Pole int Meiidian Allitade, 
The Hnghi of the £qui 
Ca1« 3. StifaH 'if MtrlJia* Ahitail frm ihl Efwatori i _ _ 
trary Namiteibaitf lit Pell. 

i)t.p—hl^O. Lit lit FtU'i BB[it ie jo" N.aium6riJiii jtll. I J*. Then, loa — 15° = 5°, the Sun or Stu'i Declinalioo S. 

The Height of the Equator U/i dian the Meridian AlHCude, 
Cai« 4. StilraStbt Efifri Hiirii fitm lit hbridian Altilait (being the ReierfE of the fariaa Ci^) a*d lit Rtmaindie viill it lit Di- 
'naiitm 1/ Hit Nam vrilt liat t/ibi Ptii. 

Or, lA—f^O- LillbtFt!i'tUii[tlii $at K,mdiatn£mMilaiU jo°. Then, jo° — 40":= 10°, the San orStu-'i Dcdinatioti, 
N. te^oiied. 

EXAMPLE n. 
Til Pti'tBiirlilaiidSiIli trSurUDn/iaalittilii'nir'w*ttJli^ 'tiSuv tr Siar'i MirlJltn jthin/iii f 

Tit Ptk'i ElevalitaaKd SlT'iDKlitaliat, or thi iame NAMa. 
Caii i. MJiiiDulimtitiiKiibtE^iiaur'i Htigiit awJ if iki Sam it lift ttai go", h will it lit AttfiJtaa ^ImJc fmril, M tbt entra'j 
SiitifibtMtriJia*IHb»iefib.tlrvatidPik, Far hlmfftfitiu efCi& ^. E<im. I. 

D-|-# = M. Ltilit Pelt; Htighi it to" W. amrDiclLatita^fi 10* N. TVn, io<» + 40»=; ja", the Meridian Attitude, S. mnired. 
Caibi. fnti tUftUSia, liatHtisa', ill Safflmta 11 iiga wiU it ihi Miridiat Muadi, ftufii, itiMtn tbi Hniih and Pili. Or 
by TranrjuGcion of Cafe 1. Exam. I. 

D — P=>. Lit tit Pilt I Hiiibl ii icP ff,**dSl»'' I Ditliratiai jo" N. 70," ~f:fi^ Stfi Camp. Merid. All. aad 40° Meridian Al- 
titude N. {.nipht, altei tit Ptii. 

Alfo, 70' Eqiiatot'i Height + 70" !)t'i Declination =: 140°— 
iSo 

Supplement, the Meiid. Alt. 40' N. ai before, 
Caii]. TbtHrigbliflttSfaaiiF/iJHraflidfnmiirDKtMiiiatftbiaxitiir Star wiU givi lit Miridiaii jStiiadi n lit fame Siii if ibt 
MtridlaB wiib Ibt Ptii, by Tnnr(iotilioD of Cale 1. Eiam. I. 
Tbatii, D— ^ = M. Lit ibi Ptiii Hiitbl it ta" N. and Dtclimtli)m ^. Then, 40«— jo»= io». The Meridian Altitude N. rt- 
nredj iilm tbt PoU. 

Utdvirfallfi via ibc Dicliaaiiiii iiifthtfami Namvwiibibi Pilt. The Com. of Declination [or Diflance frottiPolet b^n'g r<ibliiai;i] (i 
paffibleHtom'tbePole'i Height will (in ihrMeiidiifi Ai itude Jv/enrric Po/ij and being added to the Pole'i Altitude will give tlie hhilJ. 31 
Altitude aiHg ibi P'i/i if under 90". 

When the Sum of the Conp. of Dedilution and Pole'* Heighc exceed 90°, then the Sopplemait to tSo<i will be the Meridian AhituJe 01 
M nniriBj Side of the Meridian n that of the l*Dle. 
^bai, inCafi 1, bceiwng, 80° )|c'aDiRaace ftam Fole ^ 50° N. (he Pole') Height =e 130°, whole Sn|<plcmeDt it jo° S. the Metidiii 

U Caft I,- io" ♦'» DIftance ftom Pole 4- vfl Pole't HeUjEi M. = 40°, Meiidiin Altitude N, ifm ibt Ptif, i: befote. 
/■Caft i.'coO *'aOinaoce from Pole from SoOJ'ole'i Height N, nnaini lo". Meridian Alt ttude, iflatv ttt Pili, ai before. 

„ ;_ Tlie Pole'j Elevation and Strti or SHr'i Decimation, hatibo oirrxiiHr Namh. 

Caii 4: Stilra^ tit Dteliiiaiiiafrim itr IJiigbitf ibt Ejiiaitrawi ibtPamaii^r will h ibt Mtridia* AIiIimIi, if a amlraiy Njwi tt rbar 1 
lit Pub, by Tranffatiiaiiof Cale )■ Exaih. 1. 
^■— D^M.- Lh Ibt Ptk'i ilcigbi it 700 if. and ^'j DeiHiuiiin i*. That, aa" — ^^ = 1 5° Meridian Allitade S. le^oited. 

K X A M P L E IIL I'AtTICVLAlLT VltrVl IH NATtGATIOn. 

TW STAa'a IT Snit'i Dulinatim aul Mtridiaa MHuii iang giva fir Jim tat Piatt ^ At Earti, tt/aj Ibt ffAotfiW tf tit Tab , 
thai Piatt. 

When the Meridian Altitude ii between tWPt/tan^ffWssM, and Diclihatiok op thi iahi Nam* wit> Tnt Polk, 
Caii i. /Ud tit Ctrnfleaint if Diilimitmii tbt Mrfidiaa jUlilMde, rnd ibt Sam loiU li lit Wti^ tf tbi Pib. 

Or, ,/-f-M = P. Ltl ibt MiriJiaa MiiaJi 10° aadDttlimuiia jo" N. Then, ao* + lo* = {0°, the Height of the Pole n^niied, < 
I — M s:/> h ^*^ ■• £»»■ 1> Or 70° — 30° = 40° Conp. Pole, whence 500 Pole'i Height, tf. ai before. 
WhCD the Meridian Altitude ii btiwiH lit Fik aad Zaiib. 
Cais 1. SakraS tbiOmf. tf Dniimiiicn (ir DiJIatttfrtm Psli) fraa Ibt Mtridiaa Jltitadt, «ii ibt Rimaindtt vdtl it tbt Pili'iBtigil. 

Or, 

DigHJzedby VjOOQIC 



dHd NAVIGATOR. 



rjil 



R U J. E S >r SUN W S T A R S. 


Ot,U — d = T. Iftthi M.-rlJn A'tilu^t li 40' m:J *'. D^linaiim 70" V. Then, joo — xcfl = 90O, Ibc PoJt's Heifbt N. it- 
quiiH. OrD — »f=!P, by rrinrpofi'-ionofCafci. Eiim. L Or 70* — 50' = loO, Pole'. Hdght N. ..bribrt. 
when the MeriOiin Altitude ini] the Pole, «re on tenfrerj Siria ./ (ii MrriJis*. 
Caib j. Sthirafl iln Datiniifin fret, ibi AlniaJf, tml itt Btmtimdir a itx Hu'gil 1/ rt, Ejiai^, srCunf.mf tie Felt's jtiini/t. 
Or, M~p=/, i./Mo'«/,M JVtW, jot ixd i^U Dulimiu iO". Tlien, 30= — 10" = 400 Comp. Lititade. Whence J"" '''«'»>■' 

Fw, M — U = f. by Ttinrpofiiionof Cfe 4. Ei.m. I. 

Whtn the Dedimtioo »nd Pole i» of DirnniBT Nauii. 
Caifa. .-IdJ lit MtnJIt^ Abiit^ e^ ■^•iDtclintiia, ad ,bi Sum vill it lU Hiifbi >f ibt Ejinu, wMiCam. i, tbt Ftlit Hiigtt. 
M-f Da=^ LettheMeridiin Altitude be 15° and tWr'tDeclitution (" S. 
Thm 1 5' + j' =j io=, the Eqnator-i Altitude, whence 70" Pole"* Hright, N. wbfkZ 
F,tM+D=f, hTTrt-irpofitionDfCare,. Euro.!. 
•,• Tbt/sng^KF an all lit Cifii ilii tai, bafftnfrm lie JiffrrtUDMa ifain iwt «/ tbi Ibrii fintv''r Jrci if gna Circla nf iht Sfktrt, vix. 

lit tih^ Crlumflaacu e/ li, P^un awl P/*™,,™ if lit Stan, im r^fta tf lit grtal Orel., if lb. Sfbtrt, f» «r fartiadar Flaa tf lit 
Eani, an iimpuud h li, Rula tflrigtmrnitrj. 

Aht Thiei of Ibelt Fill Thihci Itiatsiva; lit OhU^mij »/ lit ZcLirrtc, a S(«"» Right AtviHliOK, DiCLrHATioH, 
LonciTCDi. Latitddi, the «h« Two urnJt Jatrwiual. 

IMi art fBi'ally rtimad u li, OUpiitj ,/ ib, F^.fiii, lb, M,abn ,/ Tim, awJairit A'sajim aai Ot^limaiu of tad Star j /«■ vAtnu 
lit iM^iuJiaadLaiiiyditft Star an^ljkatua. 


TABLE of the ,^parai Sihi-Diahitii of the Sdh, Time of h>< PiOinB the Meiidiah, tsA hu Diitakci fiom 
the Earth, fbr eveiy lolh Oif of the Leip-Year, 1756, N. S. By a»Ki^o» dEn T«p(. 


D.7. 


JANUARY. 


FEBRUARY. 


MARCH. 


1 APRIL. 


Diim. 
jpp. 


r. M 


Dift. © 


Di.m. 


'B.. 


Dift.© 


Sem. 
Dlun. 
.pp.0 


Time© 


fiom§ 


Sen,. 
Dilm. 


Time© 
paffing 
Meridim 


Dift. © 
frame 






s.D.,e 






s. D.. e 




M S. 


s.D..e 




M. S. 


s.D..e 


3" 


16 10 


w 


.,618 
,r6s9 

iiiqo 


16 16 


> 14 


11710 
11780 

,.8,6 


iU 


is 


ai8U 
»'9S' 
»oi6 


.6 

■sss 

.S S6 


1 9 


.1083 
..141 


Dt 


MAY. 


JUNE. 


JULY. 


AUGUST. 


10 
JO 


'I S+ 

IJ ^0 




1S4» 

.S4» 
.548 


1 iS 


")49 
1136s 


IS4« 
<S 49 


*|S 

1 I( 
..V 


1136s 

11349 

MJII 


'i J* 

•S S4 

IS s* 


1 11 


.1.8s 
Ills. 

..I9S 


D.J. 


SEPTEMBER. 


OCTOBER. 


HOTEMBER. 


D E C E U B BR. 


JO 


16 J 19 




16 7 


»" |..|49 
. » "Sis 
«14 1 *«K>9 


i< i3 


. .7 "767 

. s 19 »i7i8 
, iJ 1168s 


i« .9 
■6 10 

1 ,6« 


1 » ..6s. 

» « .1635 
. .. .1630 


EQUATION of the Svn'i PiACi.'fiw every 4 >A« YEARS. According to ft^'t MonoM. [ 


D.,.. 


Jan^ry 


teboory. 


M.r«h. 


April. 


M.V. 


June. 


Ht. 


AujuH. 








December. 


+ 


+ 


+ 


+ 


+ 


+ 


-K 


+ ■ 


+ 


+ 


+ 


+ 






. • 




y . 




/ • 


'■ - 










«l 


« 45 
• 4J- 


« 46 
> 46 

I 47 


iii 


1 49 
1 50 


> S' 
I sa 

J s» 


• S3 


' 5J 


• S» 
1 j» 
« 5' 


' 5' 

I JO 

I so 


.48 


i4fi 


1 45 
» 45 
1 44 


EQJJATIOW of Che Sr»". Piaci ftr ewy 4. ?*/'"« VEARS. According xo D, U CailU. \ 


Diy. 


J«.«Aty. 


Febroarr 


Mtrch. 


ApHI. 


M.y. 


June. 


("It. 


Augull. 


Septemb. C 


dober. 


HoTember. 


December.. , 


-*- 


+ 


+ 


-+ 


+ 


+ 


+ 


+ 


+ 


-t- 


+ 


+ 




1 a 








1 m 




' ' 


' ' 


' * 






*j 


• 44 


' 47 
' 47 


■ .7 1 • 4> 


I4S 

I JO 

» 50 


• S" 
I s« 


1 j« 

I so 
' S« 


1 s« 
» SI 
»4» 


I 47 
»45 
»4S 


>44 


I 44 
' 4> 


» 45 



,, Google 



Yhi ROYAL ASTRONOMER 



A'SolarEPHEMERlS, commencing 1756, wd ferving by Meut of E4U)atioh« to the Ew. of tiic prefcnt 


Cbntukt. 


A TABLE oT Ihe Timi of ihe DAV br ■ rWonrf CLOCK When it iiNOON by the Sun. Sbcoinj the EViion 


of nitatnl DAVS, and AJtuct and Retmc of CiocK-Tmi tot the Liaf-Viai. 


J A N. ,5 


CI. Eq. 


FEB. 


a.tq. 


MARCH 


oCI. El. 




1 + 


MATT 5 


CI. E,. 

+ 


JUNE.- , 

f. ci. . 


C.E,. 


1 


an. CI. 


+ 


Q (1. CI. 


~ 


+ 


on.ci, 




+ 


n. ci. - 


Of. u. r 


+ 


b. m. I. 


m I 


b m I 


Rl I 




s 


m 1 


h m 1 


ln> 1 


h in I 


m 1 


h m . 


m t 


, 


.. 4.>; 


R»o 37 


It 14 11 


" 


JO 11 


TZ IZ Jt 


re. 


18 4S 


" 3 4*', 


b1'9 57 


" SS4!" 


1. 56 


11 57 10 ' 


tj z^ 






11 5 


" 14 '! 












>» 3 3"^, 


J'9 39 






II 57 i< , 






» S »2 , 


^;'". 


i» 14 ij 




3" 34 






z8 19 


11 J i: 




" 5* 3: 


11 41 


" 57 3< , 




' 


;: is; 


iz 14 30 




30 39 








" «S3; 




„ 54 ,, 






tiss 






11 14 5, 


A 


30 43 
1047 


IZ II 4> 


'S 


«7 17 








11 30 


'■ 57 i< . 




) 


>i ir. 


6" S» 


1. 14 38 




11 z 1; 




„ j« ,e 


11 i; 


1. 58 9 


14 i3 




i» 7 ,s 




i» 14 41: 




30 49 


II 11 J-. 




17 M 
















I* 7 3' 


, '1 41 


11 .4 4" 




30 S' 






>7 7 


" ' 4; , 


I -7 5» 










9 


;j n^ 


is,: 


11 14 4: 




1° s« 




i6 
16 


>6 35 


11 I s 


>r;;j 


;;5:i 


, » '3 


" t8 54; 


v\ 


,1 


,. 8 41 


>:;fi 


" "4 43 




11 10 10 




" i3 








" S9 ' , 






.1 9 , 


" 14 r- 












II D 37 


*,6 46 






„ S9 ii ; 


■5 -J 






,'H' 








la 9 31 








, 1' 30 




d " 6 






" 


II 9 s! 


'"! ■ 


■1 >4 3; 




,040 


11 9 1. 




1, at 




5.6 IS 




, " s 


>' 59 4i 


1 'SS> 


U 




, »«43 






JO 41 






15 II 


ii»59 51 




11 55 tt 


, '» 5 






11 10 ]f 


11 14 .y 




10,8 


i» E44 


'4 S3 


" S9 3' 


, "5 4S 


" 55 57 


IZ 6 


iz» 1 


' .«.7 


'■ 




!.7 • 


11 14 K 










»4 3S 


tl St 11 


; 's JO 


" SS 5f 


1 " ^ 




.t!" 


>1 


" 11 3° 


7'"? 


itit^ 


t 


30 11 


11 7 JO 


'8 


14 17 

»3 59 


"'«i 


■;r; 


nS; 


J ," I? 


11 y 


|;s!i 




II 11 4: 


'h^ 




30 IS 


IZ 7 31 




t3 4' 




: '4 50 










i» j» 4 


IZ .3 51 










)i 58 .1 




.1 s6 5 


IZ 18 


11. 1 11 




»3 


IX .» 35 
■ 2 u 49 


m 


» .3 5« 
IZ .3 41 

11 33 ]i 


9 
9 


»9 S9 

19 41 


ini 


19 


»3 4. 


II 57 55 


1 '4 *S 


ill!' 


(, " 3' 


11 1 39 


i;ni 




" -1 « 




la 13 2; 
11 13 I 


II 


«9 a> 


.. i^t 


.. 


;i 7 




„■! !» 


" 5* ^' 


^,"'7 




■ .« .4 


'» '3.'S 


zg 14 


19 10 


" S40 


-' 49 


1< S7 3' 


o'J 4» 


i. 5634 


. " -43 


11 1 17 


>ii< 






»9 3! 


11 13 < 




>9 9 








II S7 I 


. >1 i. 








IS ]g 




" 1-3 31 






'Wt 


.11 s 1 


;;! 




11 57 11 


'■!■■ 
1"! " 


I. sj 43 


i '» 57 




; .s|. 


11 


11 13 4" 












'1 


io SI 


«' 57 ; 






II 3. 5 




3" 
1J 


II <4 -i 


»r.4 




" 




;: r^ 


,o 34 
10 IS 


■:?.V' 




"t S7 3 

It 37 11 


.'.U; 


"•M 


; ...4 


C 
9 


Jotk-Time «dviia»i 
a4jiinIti>>Moiitb. 


inthiiMuith. 


'"s?;x"^" 


7- i» in thii 
Uo**i. - . 


©■ 50",adMBce« im 
14>Id thii Month. 


Clock- Time ^vanca 


t?- INnkJngthtXwof (bcDAT, lad a<KJl-7Tw-£,w'n, out of tbe 4bow To^/', you muft tike out fori Diy fooncr tnt)ie'M*ntti< 


or >ii'')'>, >nd /'<i'»dr^', rorUap-Vcir: For oOier Moulhi in IbicYe^ ttkt ,oiH fbr tte D*yi M Tivy flwd. And, fir (he lA. b<I,' ■ id 


EXXWPLES. Ri<iyi»ii. tb. tims. tj tt. CUk, -uia H « l/«, ly,US», J«wiry loth, 1760, Ptbnai, ,j, i7«i, June laA, 




Leq^Yeir. >■ - ■ Com. V«,. h > . 


Com. Year h ■ • 


Com. Yw. b. ■• .1 


Aatittn, rtifAteA 1761, . i* i] .43 


1761. ... II I 47 


fmberis. , . ,■ 
Dayfoonci . . ., 

1769. .; .; ;■ . " 


' SS S! 


.■ f. i' 


•," Om^H tlh^B^i Kilhi'niih tttia^aa't Eq.v A T f n -T a ■ l ■ 1, in hii AtTioKOMT rHtaliJ fir ibnfr^'Jf^, 




TheDiyi, on which Ihc fw', and CiWr) T/-. meet, cr wtMn tbe Tim* by ■ Sa^Dial, iirf thit by ■ regiihted Clock Ii tbl Ihint, rnce in 
»+Hour>, «teobWtdiobeon.,^/lsrt; ywitr*. Aj(i»)iA «ndi)wi(*o-i4(ft (iney*ir «itk»Botqcr. iV. 5. i 

■ ■ - ■ ■ : - L i: 1 ■. I ■ 1 ■ 

































,, Google 



Md NAVIGATOR. 



A Solu EPHEMEJIIS, nxamnsMg 1756, xnd ferving by Mniu of £<iiiatio)is to tlie End of the prcfcD 




Cbhtuky. 




A TABLE of the Tim. of die DAY by . rW*r«( CLOCK when it h NOON by the 5u«. Shewing Uie Evai.cb 




of naturJ DAYS, ud Adnoce *ad Retmt of Clock-Tiw for the LiAr-YiAi. 




JULY 


P 


rf;i. Eq. 


AUG. 


2,C1. Eq. 


SEPT. 


P 


CI. Eq. 


OCT. 


f Cl. E,. 




E CI. i.,. 


b E C. C| Cl. E^. 




^0n.ci. 




+ 






+ 


f.CI 


■ 


+ 




+ 


Of.ci. 


+ 


f. Cl •) + 




»■ b m . 


J 


m > 


h m . 


m > 


h m ■ 


"9 


m I 


h m . 


'. s J' 


h m ■ 


• IK I 


h m • «fm I 




. .1 3 i« 


.d 




" i 44 


"■ 










II 4J JI 


loo 


";."jj|is 








.9 ,t. 






11 49 






'-!" 


1 i" 


II 43 SI 






3 .» 3 3I 










ii 45 


I. ji S; 






1 i • 


" 4J S» 




"Kj;! 


640 








r, ,a 


'» S j: 


( 


21 40 


" if J' 


:^ 




i> 4S 3; 


t ♦•» 


" 43 S3 




7 5 




,11 4, ( 




10 9 


II 5 I. 




II 34 


I. jg .: 






: 4<i 


"I 43 S 


4 


I. 51 »i,a 7 30 










" s 19 




11 ig 


" S7 17 


in 


■4 6 


1.48 < 


) • » 


" 41 Si 


4 ° ' 






s:: :;i 


9 


ID J7 


n J 11 


7 


" M 


M S7 ^ 


10 


;u^ 


" 47 43 
11 47 17 


',*« 


ir4+ 7 


j ifi 


"S^' 


!<» 










'» 4 i\ 












II 47 13 




«" 44 i; 












\ 


"> i5 


« 4 4? 




I" 37 








" 46 s; 


; ! ' 


ti 44 >o 


' 01, 


■> SI 11 .: 


944 




It 11 4 s^ 




11 3 


11 4 ,9 




1048 


I, ,6 ,* 




i» .J 


II 46 4> , 


\'\l 


II 44 17 


; o]fi 


" s* ' iS 






mi S : 










" S5 Si 




'» 4 




" 44 3i 


-044 


""•;■' 


10 40 




>■ " S f 
14 '* S '6 


] 


11 13 

"VI 


;::i 




10 17 


'< SS 3+ 
M S3 'J 


11 


" « 


■1 46 0; 


\ •"' 


"44+4 
«• 44 54 


» jj 
' 3 


i.M 




i,ii 51; 


« 






" 










" 4S s: . 




I. 45 ' 


. i 'J 




.; 








11 37. 


•» 3 M 


■9 S3 




J, 




■' 4S 35, 


1 ' ^* 


., 4S 16 




,. J. „ 


' 


11 3« 




i; '» s 3; 




II 41 


11 3 ji 




.9 4" 








" 45 »1 , 


I ' 5^ 




, ' n 


■■ s' Jf S 


11 S 






4 


11 41 


u 3 » 






" n St 






" 45 i; , 




" 4S 4',;| I so 1 


"V'° 












'4 


19 ij 


" s» ■{ 

II S3 S 




9 ** 


" 4S ; , 






i '-i 






»;» S4( 


3 




11 1 s* 


19 I 


" 


9 >7 


" 44 s: 






.. s!.l 


■ 


'4 15 






iTsS 


1. 1 JS 




'847 


" S* 47 




1! f6 


"I 44 44 


044 




7 * « 


■• S> S' 


>i I 


























, ■ j» 




:ri 








11**" 


i»* i 




.8,7 


wj. i 




sj; 


" 44 «; 


\%t. 


"♦7 \\ 


J 9 


■■ S9 51 


lu 


































H'* '5* 


'« 


ta .5 


.1 .,* 


■7 


'7 4S 


,. s- «* 




7 3S 


u 44 n 


013 


" 47 3; Li J 46 1 




^ 


»7 5 




.6.. SS' 




tl 1 IS 


.718 


<i 51 6 






11 44 9 






Ji ' ' 












' 








r7 11 


II so 4' 




«• ^S 


II 44 A 


" n " . 


3 ♦'! 


U I J( 


















16 M 


II s" X 




*3? 




:i 


" *l 3) 


4 4' 






1I34 








M 3 


IX 31S 




.6-,7 


1. so i 


'9 
>9 




11 43 s: 




)* . 54 


:! 


ig J 


















S 37 


" 43 S! 




" 49 « , 


1 ' "» 


I. 3 11 


19 31 




P.i S4S 




a- 57 


..•S9-5i 


■^6 . 






" 43 S» 




'1 


I. J 5. 






— 


Clock-Time retreit. 






aock- Ime.d- iClock-Time .dniKe. 




CI. T.idv.»»40'. It. 
«■■ ixt ;D<h>t Month. 


• f.n. Month. 


io» 4' in tbi* 
Month. 


=-&•.,?."" 


-r.ffons:"' rr-^'-iSon'ti;: 








^r.. aXpth^, frofn/TK. idiDinrYor, ons of the Dayi in the Yur (the other beiog At. lo, My 15, ud T*-^ 16, U.S.) when the 




SM:lwmB^"-"MotiaUvirjm'htlSiifir%^Hmru Andthe Advioccor Kenat of Clock Time, hooi ■!>]> one Dty to iny other Pit 






'^AMPLEI. r'J«dtb,RMrut<fatk-'rim,fiim^t.i.uO&.i,(«U4:nSr:rpaiahg^f. 




Foi Sept. 1. . . . aotk-Time Eqnitioii. + ij 4« 








Dif. . 10 4 Xttnu, 11 It the Bottom of SipRmber re^tund. 




EXAMPLE n. 7>fi»d,b, M««>«>f Clxi-7!m, frm^tb Jul)., (* %yl, ,f tt.S*m. Mx.ikfJimini. 






Idy4tt. J-D-fo""" • '» 1 40 For4thJalyiD.f«,iH» 19 49 
>l)»9th.tD.fi»«r . •» S M «9.hDit«>iD.foo«r M 3 




Dif. ■ i4*dnKe, ubytheClockE^itiDD. Dif. * 14 ndTWRe, reqakcd. 




It. B. Apioft Nor. id. . . ft« 


^. » +3 SI 


:iDdc-Thae. when 11 by the Son. 

With which ewmeOiBg (he Clock EwMi""* "^ m "» "w" *« EonMionof 






Qit -16 ,. 








+5 19 E^tioh of Toot, which «y«rf to 11 Hour.. 













,, Google 



194 




the ROYAL 


ASTRONOMER 








A Solar Ef HEMERiS, rammencing 1756, and ftmng by Mexni of EqyjiTroin wtbeBuDOf dKprefcntl 
Oebtuby. 1 


I ANU Ak v." ■■" 


FEBRUARY. ( 


DflTJ 


OPl"«ltf. 


Dif." 10'. bee. S. 


-wr 


©•.R.Afc. 


Dif. 


Dtp 


o-.pi -. 


Dif. 


0'» Dec. S. 




O'.IUAfc. 


Dif. 


e I » 


'"!•'- 




■> ' ' 












' " 




3 
4 


"3* 7 

" 39 >7 

13 4° «8 

14 41 3! 

I? 41 4* 


61 la 
61 ti 
61 10 

61 10 
61 10 

v\ 




« iS 

6 S* 

7 4» 

8 IS 
841 

9 * 


.;2 39 » 

183 45 ai 

284 SI 24 
iBj 57 »9 
187 3 9 
^^-^ 
189 1419 
>9Q ig jB 

191 »s 18 

192 30 J7 


Ill 

fi ss 

«J44 
»S J' 

6s 9 
*S J 

«4 >3 
64 ■ 
6] s. 

IIS 
63 IS 
63 4 

Gi 41 
61 30 
61 IG 

IM 

Gl 4" 
Gi iS 

ei .4 


3 

4 
5 


13 •»♦« 

"■!"■■ 
;;;i4t 


11:1 


16 ,8 „ 
>6 iB 

"5 41 59 


17 «9 

:i4 

.. 3' 

;p; 

19 ai 
'9 35 


319 41 »s 


6049 

S- 

V^ 

59 »4 
59 "3 
59 • 

SB 47 

S8,8 
S8 4 
57 55 
57 44 
S7 34 
57 »J 
57 13 
57 S 

111 

lis 


1 

9 


16 43 j8 
rt4^ I? 

19 47 le 

10 43 3-: 


22 16 

u iS 11 
M 9 57 

12 I IS 

11 !i 9 


6 
9 


iS 14 3' 
"9 »5 '3 

■;;ii4* 

»» 17 11 


6=4. 

6=4. 
6040 
60,. 
60 37 
fo,j 


15 »3 >3 
■I 4 3» 
'4 4S tG 
1416 S 
14 6 30 


3*0 41 ifi 

3»" 41 S 

331 40 41 
31340 i 

3*4 39 18 


'J 

"4 


»l 49 43 

M SO Jl 

»1 JI ss 
»+ S3 4 
14 S4 9 


fii s 

61 7 

61 6 

111 

Ei 4 

t\ 

<i 1 

ei 

605. 

60 S7 

fcs« 

605, 
fc J. 
!»S! 
«o J. 


11 41 37 

:Wi?i 


9 5> 

!H! 

,,' ]6 

,1 sa 
1146 

'3 57 
'3 3" 
I, sa 
'4 "5 
'4 35 
'4 59 
15 13 

'5 37 

US! 


19] js 3= 

19440 21 

^9S 45 4 
29G 49 37 
297 54 


■13 

14 


13 17 « 

14 it 14 

15 .8 57 
2G 19 19 
27 .9 S9 


.3464. 
13 16 39 

13 e 23 

" 4S 54 
" »5 "J 


20 1 
10 iG 
»o tg 
1041 


3*5 38 to 
326 37 7 
317 35 44 
328 34 'o 
|29 3a 28 

330 30 3> 

331 28 27 

33. iG r» 
333 >3 45 
3342. % 

335 .8 a. 

336 rs iG 

337 'a »l 
33* 9 7 


'i 

'9 


SHIS 

»8S7" 

19 58 14 


ic 48 ^. 

10 16 44 

K) 14 la 

« I. 36 
19 S* »9 


298 j8 ,3 
300 X 14 

30, 6 s 
]t>i 9 4S 
303 >3 ., 


iG 

;j 

'9 

»3 
14 


18 10 iS 

51 "11 

I 11 43 

1 22 5 
3 22 .5 

41243 


60 a7 


IX 4 11 
ir 43 17 

11 37 

■0 39 " 


" 4 
■ 'S 

I 15 
21 37 
2t 45 

21 SS 

22 4 
12 13 

11 28 
11 35 
»* 34 


33 
»4 


a 17 

i jr. 


'9 44 57 

iS o*K 
1744 " 
17 17 39 
17 io_»6 


1Q4 16 28 
joe ,9 31 
jog 22 24 
307 '5 5 


60 .8 

60 17 
Go ,5 

t^ 
Go .0 
Go 8 


10 17 IS 
9 S5 20 
9 33 " 

i;u 


■6 

iS 
»9 
30 
3> 


i» 9 <o 


309 19 st 
I'O 3" 55 
3" 13 47 
311 35 27 
313 36 55 
1»4 38 9 


iG 


8 1340 

9 13 so 

,o_2i ,!_ 


7 4" »5 


340 1 11 

340 58 33 
141 M 46 


only.— Xn. to. Log, 


. 


&„.i «■ r MAfecH. 




V 


APRIL. 1 


3 

4 


n a4 4 
11 34 9 
13 M " 
H»4 " 


1:1 
So 
59 59 
S9 J6 
39 S4 
59 51 
59 S° 
S9+B 
5946 
59 4S 
59 '43 

l\ 

M 3* 
S9 34 
59 33 
59 1° 
59=8 
S9 »6 
SB "4 
59 »i 

IIS 

59 'S 
59 W 
S9 " 

59 9 
59 7 
59 5 


7 18 6 
6 S5 »o 


»46 
13 ij 
'J S 
•3 >3 
13 19 
13 17 
13 »5 

»J29 

ij ji 


J42 S2 SO 

343 4« 47 

344 4? 3« 

345 3» " 
J4S 33 5' 


ss S7 
SS49 
SS 44 
55 J6 
55 i» 
35*3 
55 '8 

55 5 
5S I 

54.57 

5448 

54 43 
5441 

54 37 
54 34 
54 33 
54 3° 
54 tf 

54 tS 

54 t? 
5417 
54 »7 
54*7 
S4.8 
S4 »8 
54 3° 


3 
4 

s 


12 10 40 

13 a 49 

14 8 42 


59 » 

It 

S! i, 

S'47 

'!« 

i!4» 
584. 
iJ 39 
5» 37 
S. ,6 
58 33 
Si 3. 

St.. 

lis 
tt 
11;; 
111 


1*4 49 19 

S 35 '6 
S 58 9 
6.0S4 


13 a 
11 55 
11 33 

::ti 

» 30 
>i 24 
11 17 
>i 9 
II 59 

21 S« 
21 43 

21 3+ 
21 14 
ii 14 

20 53 

VI 44 
10 30 


13 ji 

'3 55 3' 

14 50 11 

•5 44 54 

16 39 40 

17 34 3' 
.8 »9 15 

19 14 11 


54 J» 
54 35 
54 35 

14 40 
5+ 43 
5446 
54 SI 
54 54 

54 5» 

55 » 
55 6 

1!U 

55 »■ 
S5 »7 
55 3; 
55 36 
55 47 

55 5» 
5J57 

11 U 

56 J7 
56 3» 
5641 
5647 

56 54 

57 » 


G 

* 


,6 m « 
17 »4 
>S >3 5. 
'9 "3 4> 


S 21 JO 

4 59 iJ 

4 35 4* 

;;s3 


347 »9 >7 
34SHS0 

349 »o a 

35° *S " 


6 

i 
9 


>9 3 7 
a» I H 

11 J9 


6 43 3» 
762 

7 18 >6 


'3 

M 


ai ij 16 

»J"44 
14 11 as 


3 15 "i 


'1 37 
»1 3* 
'3 39 
13 41 


35» 5 3' 
3S3 0.8 

353 55 " 

354 SO '° 

355 44 58 


'J 
*4 


iill- 

»4 SS >B 

*S S3 54 


9 .3 16 

9 40 D 
10 1 24 


12 9 39 

«3 4 55 
14 ,6 


.6 
"9 


1* 11 39 

,9 ,0 iS 
T 19 44 


. 26 S7 
I J 14 
39 33 


'3 43 
13 41 
13 41 
13 43 


35* 39 4' 
JS7 34 22 
358 iS S9 


16 

% 
'9 


iG 52 >7 
17 JO S9 
1^49 29 
19 47 57 
» 4612 


ro 22 38 

10 43 41 
>' 4 35 

11 IS 19 
I, 45 49 


»4 55 43 


»3 
>4 


S ■« !4 


J' 3J 

1 4»»S 


»1 39 

»J 37 
2, j6 
n 34 


. >136 
a 7 4 

3 ' 31 
1 5* 

4 50 17 


t3 
t4 

iG 
*7 
iS 
29 
30 


I 44 45 
»43 7 

3 4» »7 

4 39 45 
SJ» ' 
6 36'5 

ni 


i««« Is 
It 4« 'I 
■3 5 Sf 
.3 »S »6 


20 8 
19 55 
'9 43 
■9 30 
19 18 

,835 
.813 


»9 34 a7 

JO 30 29 
J. .6 40 
3» at 58 

33 19 «S 

34 <S S* 

35 " 37 
j6 9 n 

37 fi .8 

38 J .0 


t6 

JO 


6 IS 49 

9 '3 ^4 
10 u 3; 


s 2931 

J 39 43 
Ji^J? 


21 .8 

23 23 

»3 " 


1 54 'S4 
839" 

7 33 4* 

8 il iG 

9 It 44 


13 44 44 

«4 3 4« 
1-4 12 37 

14 41 >» 
14 59 35 


from or idilEd to the Leap-y«r Quantity, Tdt That la (he lame Manth-diT. >, z, 3 Vn 

i.t;, being .erpeaively added Co the Lo. I^g>. of DifH. fai a Day p.eH^ing the Month-d 

to he fubJ. fr. ot aildcd lo the Leap-ytjr Quantity for the Quant, for the fame Month-day i 

See ExamfU, fanbfr t,, ««/ £f ««;«. /or 4 T^n f^^^o-d if lb, ^mi,i,>,«, «■ P/..«j, / 


t46j ,7a«9. wiUsLvetbcC^uiiticytobeiubCtaUed 

y of Leap-year will ^ve the Lo. Log. of 1 Qaanlity 
1, 3YcitiafterLeap-yeai, refoeaively. 



«ii N A V I G A T R. 193 



Co A 

, Digilizcd b 



db, Google 





l^^ 




?:^ 


ROYAL ASTRONOMER 










A SoUr EPHEMERIS, commeDdng 1756. and ferrbg by Mem of E<yjATioii< to the Ekd of the 

CSMTORT. 


prefent 




SEPTEMBER. 


C T B E'R. t 




Dir 


3'.ci.»Ji 




0't Uec. N 








D»y, 


0'.P1.^. 




o-.u=a? 




Q'tM.ATc 






( * 




. ' " 


I * 






/ » 


' " 




/ " 


• ' « 


1 « 




I 

4 


■1 ■> !« 


ilii 

;>;= 
Si!. 

!l» 
if*' 

>!« 
'!*! 

SS4» 
!«!= 
sl i. 
S» S4 
S|S7 
S< !9 
59 • 
59 $ 
59 S 
59 7 


* 4i' 

1^1 ?i 


11 S9 
11 7 

" '3 
H .6 
" 34 
^" 39 
11 44 
11 51 
"55 
» J» 

:s 1 

13 10 


160 JS J 

161 49 s 

16144 1 


54 »» 
54 »i 
54 «7 
S4 tj 
54 » 
54 » 
54 S 
S4 3 
53 59 
S3 S9 
S3 57 
S3 55 
53 S3 
51 S4 
S3 54 
S3 55 
53 54 

'All 

53 58 

(358 

53 59 

54 » 
54 S 
i4 7 
54 9 
54 14 
54 '7 
54 " 


3 

4 


8 40 34 

tt Jl 13 


S9 " 
S9 13 

!9 '5 
S9 "7 
59 "9 
59 " 
S9 »3 
59 15 
59*8 
59 1" 
S9 3» 
59 34 
59 j6 
S9 38 
59 39 

iH 

59 49 
59 5" 
!9 5» 
59 54 
S9S6 
59 S7 

59 59 

60 1 
60 4 
60 5 
60 7 
60 9 


J »6 47 

3 5" 7 

4 '3 *4 

4 3* 38 
45948 

5 »» 54 

63" 5" 

«S4 33 
7 17 10 
7 39 57 

S 47 8 
9 9 '7 
9 Jl 19 
9 53 ■' 

\:;tf, 

,0 s7 j6 
II 19 11 
II 4° 17 

""55 
11 4> 18 
,3 .48 
IJ » s* 
'3 4» 5" 
»4 a 34 
14" 3 


ij so 
13 '7 
.3 14 
13 10 
M 6 
13 4 
11 S9 
" 5] 
11 43 
M 47 
11 37 
i» 31 

ll'i 

11 9 

11 s» 
11 43 
" 35 
11 i^ 

11 16 
11 s 

" 55 
10 43 
^o 33 

to 8 
19 i6 
1941 

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a»i N A V I G A T Ri 



,, Google 



19' 



Tit ROYAtASTH ON O M E R 



L CATALOGUE of femarkable Staks. ccBtiiuie^i acobg^rS ^ Kal^it. 



Nimct of Sun. 



rdiog Wing of CruM » S; .IX S^ 35 

ihCTu WingofSufM j] 11 " "" 

Piet*din|of»iiiT«lo£tlie.Gofl .31 , , , 

AtSciIingonof Cnne'f Tail it 18 iS j] 

Ig Sbouldo A^mriul | 



SlLanstude, 



Following in Tail of O011 



t of the S< 



■a WingofthcSwui 
Mondi of Ptge/ui 

" mint Shoulder of ^VV 



' S7 S 



NuDEi of Stan. 



In Mnath of the FiUi, Fmalbial 

TaiiofthisSivan 

Infctgof A^oirini, ScbttI 

Hstd of Ujin 

At the End of [he River, .Abtr<^ 



BiiEtieit in flcul atPbm/tix 
IntbeShau. of DegaHiiWiog, Mirjb 
InThighofPudjli, SchtBi 
Northern of th« Whak't Tail, 
I Southern of the WhilcNTiil 



■iS^ 


LatitBdt. 
,■ ••) •» 


s 

N 


S: »9 54 11 4 j4 

K 1 iS 3« S9 S6 37 

4 jS 49 ! ■> 17 

7 59 64 1, 

II 14 6 59 "9 V 


s 

N 

S 

s 

s 


II jOi7 
19 14 "3 
IS »7 13 

Vt 38 ^ 


4034 "> 

10 041 

20 46 J, 


s 

N 
N 
S 

s 



II. CATALOGUE of lemarltable i'/xEo. Stah*. their R. Ascenjh 
of the Yeae 1756. OF immediate Uib in Astrohoiiy and Ni^' 
ftJ}Ufi>td, iw FraiKl, ix Order of the Acada^ afScimcti thtrt. 



=F= 



IS and DacfciHATioMs, for the 
CATION. FVom the Gaanaifaact 



Begin DiDg. 
dtt lemfil 



Ijmea of Sti 
Maokitudi, 
ing to Biju. 



J 



O.A9.-i^^.. 



Oaffiifa't Brcift 

inMb-t TaU 

Caffiafet't Girdle 



Girdle 
PitctJing Horn of Sam, 



Foot ofAJnmtJt. Alim 
FolIowiniHornof tbcJtca 
Tm of the inali 

itod of Medufa. j1/gt/ 



Brighten of Pirfiui 
BuU'a Eye, Mii'"-! 

•t. Kigd 



Bjdrat Heart 
Lyon'i Heart, K^uLl 
The Great Bear 



Breilt of the Um 

Thigh of the Gr. 




Nimei or STAia Mni 
Mackitdde, accord' 
log to Bajv. 



1^ 



Wing of the Virgin 
Spike of the Virgin 
id of the Bnaft of G, Beat 
3d of the Br. of Cr. Beu 



Sonthem Scale of Ba/tann 

lUer of little Bear 
Motthera Stai of BalUon 



Btightell of the Crrun 
Biighteflin Serpent' t Ne 
Northern in Front Scorpi 
Sdotpion'a Heart, Aiagt 



Head of Htrcula 
HaAol Strptatar 
PrKeding in H. of Drigta 



Shoulder of Strfmari 
Bright, of theH, of Draigon 
SouthEm Bow of Sapiiarj 
Brigbteft of tin Huf,JKigm 



f ol; Shoulder of Saw 
Brigbteltinthe£d^ 
Folio ving Hom.ofCMt 
Broft of the Sziua 



Pre. Sfaoulder of jtguafi 
Uaath 1^ Piiefii 
Following in BnaH of Ctal 
Schars: 



Southern Fid), Fsm 
Scbtat, Pcgifua 
Markai, Prgifna 
Htad of Aadre^tJa 



Fcl. tht Chair of O^^a 



I 414s sfi : 
° 44,»;S i» \ 
a 46 160 s4 : 



8 J7 

[9 IS 39 

10 1% 59 

'" *9 45 



IS 13 

as S9 



40 »3 

M 4S 13 

II 48 S3 
*3 S' 54 



9> 3' 
9S S 3i 

rgS JO 



17 56 

rii? "■ 



4 4' »J 
SI 3* 31 
J4. iB ij S 



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J q 8 14 J4 ■■ 
9 S 15 1' S9 

° 43 44- *S f 



6 17 S" 
I46 ( 
'7 »1 



341 59 
343 9 
3S» 57 



4a JO 54 Ji 

15 " 41 4! 

' 1 51 5' 

>7 44 1* 



(5- Enquhi -at Jtaaihin't CbflW-HoofeT" 

ibai^i, Lemda*, for the ^^14 AfiroKimtKl laiia. frt 
OhfcrTationi, {3 f tinted She«ta) by Mr. Gait Mim 



?S 9 , 4 'f's? 4* 7IN 



im aa Imfni/aatiu, iktafi 

Naliiit Ibnabibfjanfaii, i^lhilu fiuH'c Mam, 



tbUv!tmaj Ui aadl^xbtTt\ixliif ihaeli^rj. — Oar lau ajhtrnmuial PnfilJtr, Dt. Edm. Hiltey, /aj^Auj a* excellent Ephemerid:!, vitan 
Itld, ft thi VJi ef our Royal Society, vittnljHr j^muiap/ maftbe thcnfrriU^ iinprmcd. Bui (by out prefentalbaoomicai PmUIon nukini 
an impnarabli Sara of their Obfervationi ind Improrementi) ibh Naiin it M^rd m f/iuS it France fir Ephemmdea, fmii/taJ ij M, Dala 



Ciille, Uinldi, tnJ othiit there, far ikeir Acoraci anJ Impnvtaiua j iaaufi 

hoein hy Foieigaen, anjlhtft Sort uf cax\aa% and ufcfui ProduHioni are mna wt euceitrapdaawi^ 

' -n ua by ^ur Nobility, or thefloiAi. Sociitt of thi* Nation, we would undemk* 

■n to come) to imfrrue lit Tbtay. «/ ibi uel^ial Mmaai, ud to iXuU im. Vfipda^ -- 

en ge need not fend our Money abroad fot firiipi MaaafaStirt ; hiTJag fiilBcjent of out a 



il Profeflwa fof&r themlelvH to bt excelled 
Whemaa If piopcr EncooiaptEncnt w 
lu ajBipiiCE ARoTALEratHiaiDia {for many 
OUimtieaa being, at the &m« Time, allowed 



ELATION 

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md NAVIGATOR. 



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the Sun, (m 


ukedbyri. 

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Sum 


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> 31 41 Wore t. 7 b, the &n.e Clock or Watch, ftewo to 
:,. % JS 45 tact iij bcfilierthinlbc Q. bysdDift.being 

. .. 5 JO »6 TiiliebflvtnoObftrv«tioiit. 
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ifLeh ji« 10* 18", «,»of* 7«>. IQ 

MOHi'Timifoaai . . . . 
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. futioD, Equitioo at No«n. . 


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thi ROYAL ASTRONOMER 



foH lindiiifE the Time of KraiHC and bBTTiiio of tbe 'aau and- St* k*. 




tJ.'S. North ot Souili Latitddi of the Pt ac t, rorwfpowlenl to N. S, Dediiutiiin of Svii or Stai, 




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10 4j 


.053 


II IJ I" '9 


'■ 47 


" 1 


12 ij 


12+6 


■3 9 






,ri 


10 SB 




II 14 II 37 


" SJ 


11 6 




.2 39 


.2 jS 


'J "5 


'3 36 


13 jS 


K 


.+ 46 


IJ 11 






I* 17 


11 40 


11 s| 13 10 


13 16 


'3 43 


14 1 


1410 


J4 40 


il ' 


IS 25 'S SO 


'!+! 


17 16 






"3 S4 


■.4_.9 


.4 16 14 43 


'5 ' 




>5 40 


16 1 






17 16 17 44 




i3 46 








ttI 




<5 39 


IJ s7 16 .« 


16 36 


Teir 


17 20 


>7 44 


iS 10 


TslT 


19 7 


,9 jB 


20 11 


*° 47 


21 16 








'!"° 


'2 ' 


17 19 17 JO 


iB 11 


.8 J« 


19 I 


19 27 


19 56 




20 59 


21 31 




22 JI 


IJ 34 






'1 ■ 


.8 ., 


.8 J9 


19 I 19 i4 


1948 


20 14 






11 41 


21 16 


22 s» 


23 30 




2455 


25 42 






h3 


.948 




lo 34 ao J9 


11 2J 


21 i4 


22 14 


22 S6 


2J JO 


24 s 


'446 


2J28 


;lji. 


17 I 


»7 53 






ii^- 


11 17 






'I 3 


'3 3* 




'4 4' 


'S '9 


2! 59 




'9 9 


,0 S 






T5» 


i» 47 


»3 '3 


»3 4«'l»4 10 


\%T. 


\n 


25 5° 


26 2B 


27 8 


»7 5' 


,8 jg >9 18 


30 »i 


31 19 


31 21 






;e 


*♦ 'I 


StI 


»S "S 


»S47 


27 J5 


iS 16 


>8 59 


2946 


3° 3* 31 30 


,. .« 


33 3« 


34 39 






15 4S 


*! '? 


»7 M 


iS I 


zS 39 


aS %a 


30 S 


30 S» 


]i 4» 


3' 36 33 35 


'ri 


IS 46 


37 






''i 


»7 19 


»7 5> 


iS 16 


19 1 


19 4» 


JO 12 


31 7 


3" 55 


3»45 


33 40 


34 38 35 4» 
16 43 37 5' 


i.i 


39 *5 








it s. 


.9 16 


JO 3 


30 4» 


3' *4 


2i_L;31lL 


3147 


34 4' 


35 40 


39 5 


4' 55 






II'- 


JO »J 


ji I 


J. 41 


3» »3 


33 7 


33 55 34 46 


15 V 


36 J9 


17 4> 


18 $0 


40 4 


41 24 


42 5» 


44 29 






"I 


3' S9 


3» 38 


33 " 


'* 5 


34 5» 


35 43 36 38 


37 16 


38 39 


19 47 


41 


4*. 20 


41 47 


45 »3 


47 9 






'31 


33 34 


34 '6 


35 ° 


3548 


J« 39 


37 3J 38 3" 


39 34 


40 42 


4' 55 


43 '4 


4441 


46 .6 


48 


49 57 






14.^ 


3S '0 


35 54 


Jfi4» 


37 3' 


3816 


39 24 40 27 


41 14 


4^ 47 


44 S 


45 3» 


47 6 


4S49 


50 44 


S» SJ 






*i. 


3647 


37 34, 


J8_il 


39 '8 


40 16 


4< 18 41 25 


43 17 


44 56 


4621 


47_S4, 


49 37 


S' 30 


53 37 


56 1 






16, 
17" 


40 S 


39 15 

40 5I 


40 9 

41 S5 


41 7 

4» 57 


■ 41 8 
44 3 


43 '5 44 »6 

45 14 4* 3' 


45 44 

47 S7 


47 8 
4916 


f.'i 


SO 22 

5' 57 


5' '4 
55 ' 


S4»o 


>^'i 


t\", 






29 


4146 


4» 43 


43 44 


44 49 

4«4I 


46 47 16 48 39 


50 9 


S, 48 


" 35 


5S40 


|7 58 


sns 


i',„ 






43 J" 


44 J" 


*' li 


48 49 i> s» 5' 


s» 3; 


5418 


s< .» 


58 34 


i, 9 


64 10 


7..! 






3f 


iLii 


46 19 




48 43 


50 4 S" 3» 51 9 


. iui 


5< 55 


Ji>» 


'■41 


.*lii. 


68 14 


11*L 








^l • 


48 " 


49 »S 


S0 4S 


S» * SJ 48 55 33 


57 3' 


S9 42 6» IJ 


6s 8 


;;;i 


73 9 






3* 


1* 1» 


50 ! 


'fl' '? 


5» i 


if ^S i* 9 S8 5 


So I, 


6243 I65 J5 169 1 












































"I 



yGfitogle 



lot 



rit ROYAL ASTRONOMER 



Jvnaj 1, i7?o. Mid unnxl VuixtioB from dumce. According 


r. Right Afa.llo.,D.cIUi;r& 
» M. Dl La CAILLG. | 


N«. 


No«TlII»ir Staih Nauii, 

And 

PUce. in Ihcir CONSTELLATIONS. 


Iff 


Right Afcen. 
inDcgreei. 


K. Afwi. 
in Time. 


Ann. 
Var. 


Declination 
Noitli, 


Ann. 
Var. 


+ 


+ 




s- 




H.M.S. 


S. 


• / a 


a 


I 
t 
3 
4 
f 


THE 
Extreme oftheWioeof Pti^m 

BreaA of Ca/fufta 
Wai« of C..^M« 


I 


* 


S 53.5 
6 JO 15,0 
6 57 4.8 
10 a; 14,3 

10 40 lifi 


.4 
a« 1 
16 s8 
41 49 
43 43 


3.08 
J.i« 
3.30 
3.49 

10,05 


'3 47 3«.3 
39 39 18,8 
5J 9 37.9 
59 31 19.3 


30,04 
ao,oi 
30,00 

19,69 


6 

I 

9 
lo 


Weill or A.*.«<1. ' " 

Pr««ding of the Ntribtm TriwiU 
Middle of Two, at the Ear of the S^ 




4 


■3 57 3.6 
17 '5 "4.5 
14 10 ae,9 
"4 43 «8,o 
34 57 46,j 


55 48 

1 9 41 

1 36 4a 
> 3«S4 
.' 59 5" 


3.39 
3.71 
4,13 
3.49 

3.37 


34 17 15.7 
S« 55 37.; 
6a aj ao,6 
38 ao S9,3 
18 3 J4.0 


'9-43 
■ 9.07 
i8,a7 


'3 

■4 


Preceding Horn of the Rum 
Fwt of ^nJromt^^ 
Nodcof thefjiJu 
Following Horn of the Sam 
Northern of the Ttimglt 


I 




35 '3 4.7 
•1 9 50.5 

<7 "7 7.0 
38 .7 J,0 
38 41 1 5,6 


14053 
1 48 40 
.49 8 
1 53 S 
1 54 45 


3,38 
3.61 
3.09 

1:U 


■9 34 34.1 
4' 7 o,s 
I 33 so,a 
aa 16 9,6 
33 47 38.a 


18,12 
17,82 

17,80, 
17.63 
17.56 


i6 

IS 

■9 

<o 


Southern of the TriMgU 
FoilowiBgit, the IfjJ^.Citti 
Northero in the/7»Mr d, Ut* 
Soathem in the f/Mur di Luti 
Shoulder of Ptrfnu 




» 


30 33 0,7 

37 35 34.0 

38 16 0,0 
38 49 39.5 
41 4" 5S.« 


3 3 31 
a 30 as 
3 S3 4 
3 35 19 
a 46 ,! 


3.53 
3.' 3 
3.53 
3.50 

4.34 


33 40 37.7 
a 10 lo.s 
38 11 a6,3 

36 la ^^^ 

S3 30 ■!.8 


■ 7,aa 
15.87 
'5.73 
15.6. 
14,96 


33 
»4 


Jaw of the ffkait 
Head of Midufa 
Bright Star of A^rw, 
Thwhof i'Vw 
8ri£hieft of the PtiiaJu 




» 


43 18 3S.« 
43 4.' 
40 J9 33.5 
SI '« 33.3 
53 10 1.6 


3 49 '4 
353 
J « 37 
3 35 14 


4.19 

4.1 7 
3.54 


3 S 3'.6 
39 58 '7.S 
48 5« 46.6 
46 S7 40.0 
33 18 3S.8 


'4.81 
'4.64 
'J.74 
■ 3.Sa 
12,01 


■^6 

■7 

28 

»9 
J^ 

3' 

3' 

33 

34 
. 35 


^trcme of the Foot of Ptrjau 
Knee of Pmiw 
FitftofthettflA/ 
Second of the /ir«A/ 
■Northern Eye of the JaiS- 




J 


54 37 4.6 

55 '7 34,1 
61 2j 56,3 
6. S .7.3 
6! 30 43.4 


3 38 38 

3 41 10 

4 5 36 
4 8 33 
4 14 3 


3.73 
3.94 
3.39 
3.44 
3.48 


31 7 3.6 
38 15 41,6 
15 6,8 
• t j6 a,8 
18 J6 13,7 


tl,6o 
'1,41 
9.59 


Southern Bve of tke >«//. AMetima ' 

Northern Hon bf the BnU 
Weftein Shootdcr of Oritm 
Southern Horn of the Bmll 




J 


65 34 4.0 
74 33 $6.1 
77 37 37.3 
77 S« 3,. 
80 40 41,9 


458 16 

S lo 30 
5 ■■ 4t 
5 *3 43 


3.43 

3.78 
3,3a 
3,58 


■5 59 3.3 
45 43 36.7 
a8 ea 6,a 
6 S 55.7 

30 57 53.7 


8,33 
5.33 
4.39 
4.19 

-2?34 


30 

39 
40 


Shoulder of the Cta^bman 
EafteraSboDlderof Or/M 
Handof theCw^Aw*. 
Pootof Cd/»- 

Foot of Ftlhix, the brighteft 


-r 
t 


85 17 57.8 
8; at 46,3 
8s 40 8.5 

89 s« 36.3 

91 58 35,0 


S 41 la 

5 41 39 
S 4« 41 
5 59 48 

.« 7.54 


4,41 

3,«J 

3.6,1 


44 (3 •« 5 
7 ao 10,6 
37 9 5'.6 
31 33 IS.S 

33 39 59.3 


1,64 
1.60 
1.51 
0,0a 

0*7 


4' 
4< 
43 
44 
45 


Bnghc Star in the ii'oot Ot ft/lux 
Kneeof Cyhr 
Knee of Faih* 
Thigh of ?n7>« 
H^A of ih^lMikD>i 


r 
\ 


3 


95 48 5417 
97 8 9,0 
10a 18 49.4 
106 If a64 
108 aj 46,j 


6 33 16 
'38 33 
«49 15 

7 S 10 
7 13 3! 


3.48 
3.37 


16 3s 16,9 
35 31 9.4 
30 54 45.1 
3. a; 8,; 
8 46 ao,a 


3.03 

3,49 

4.37 
!•'■ 

6.33 


46 

49 
50 


Bright Star in the Head of G,/»- 
Brighteft ia the UtiU D^. ftwyon 

SOBthem Foot of the Crmh 
Northern^ 


e 
e 

r 




109 39 2,7 
HI 33 i,^ 
113 a9 45,6 
"30 44 4.3 
137 il.4a.e 


7 1836 
7 a6 la 

7 39 59 

8 356 
8 37 47 


3.87 
3.31 
3.75 
3.'i 
1.53 


33 34 34.S 
5 50 43,5 

38.36 aa,; 
9 SO 7,0 

32 3o 59,3 


6.73 

5:11 

IO,I| 
12,11 


ji- 


Southen>4/r< 


» 


*. 


137 J6 4J4 


8 JO 37 


3.44 


19 3 3a,o 


12.11 



,, Google 



and NAVIGATOR. 



209 



w 



A catalogue' of Eminent FIXED STARS : With tlidr Namfaer, Right' Afcenfien, ihctiai 
. yMuuvy 1, I750> and un»>l Vwialian frOBi ckeDce. 



NOKTHIRH StaeI NaMBI, 

Ann 
Place* in thoir CONSTELLATIONS. 



TriE I 

Northern in the Foot of the Gnat Biar 
Cbw of the 0-td> 

Southern in the Foot of the Gnat Btat 
Preceding Knee of the Grimt- Bear 
Foot of the lion 



Northern of the Head of the Liai 
Southern in the Neck of the Utm 
Heart of the Liar. Rtguiut 
Nonhem in the Neck of the Lim 



Followine io die Neck of the IJtn 
In the Beilf of the liau 
Sootheni in the □ of the Grtai Btar 
Northern foUowiig in the Grtat Star 
Thigh of the £.»» 



Hick of the Liam 

TulofitKlim 

Northern Wiogoftheftrz/B 

Soathera following io the d of the Gr. Star 

Laftin the D of the Great ^lat 



Right Afcen. 
i« Degrees. 



H. M. b. 



*9 7.9 
36 28,0 



^ 37 *'.o 
' H S3.8 

' 40 t;.o 



S4 S4 20.0 

Si jS 26,5 

61 o +s." 

65 '■ ?7.' 



R. Afcen. 
is Time. 



8 41 57 
8 42,9 

8 46 z6 

9 <S S9 

g '7 y. 



9 J" 36 
9 38 *9 
9 S3 +0 
9 S5 » 



48 S9 58.7 

:' 47 4*'3 
° 40 56,; 



'4 "4 3S>* 
zy 10 8,j 
7 38 18,4 
'3 'o +3.7 
'4 39 4.0 



o iQ 37 
=■ 46 34 
048 3 

' g 46! 



s 49.3 
,s 6,4 
57 4» Si/J 

03 s 33* 

XI $1 a8,6 



16 47 32,5 
IS 58 7.> 
J 10 ao,5 
SS S 0.7 
S8 as 19.3 



13,00 
>3iOl 
'5.30 
iS.ii 
■S.79 
'S.99 



17,61 

18,1 

1 9/11 

19,0s 

■9»37 

I9»j8 

'9.93 

■9.94 

19*8 

30,04 



ioothein Wing of the /'jr^iA 
Firftof theTailoftheCr/.«j JImt 
ForegoJBg in. the Waift of the Vhsim 
The orightcft uqderthe Grtat Star 
Northern Wing of the Virgin 



I 46 48,1 

> 44. S.6 

> 45 18,1 



I 36 '7 
I 37 40 
II 40 32 



Middle of the TaiJoi the Crrvnr ilnir 
Follswing in the Waift ofthe Virpn 
Extremity of the Tail of the Grtmt Star 
preceding Thigh tjf the CovihtrJ, ta CUvm 
Extremity ofthe Dran^sTail 



12 7 7 
1 42 56 



* 44 17 

^ 49 43 



brighteft of the Clrwn. Jr^Mnu 
Preccdbg Shoulder of the C/atvm 
Following Foot of the Oe-um 
Followii^ Thigh of the CItwm 
Preceding in D ofthe LiuU Star 



; 4' 34.' 

) '4 a8.7. 



- 348 
ij 21 58 
13 37 40 
'3 4* 46 
'5 37 38 



'Head of the Cia^a, or CrielMrd 
.Following Sboolder of the C/b«m 
Precadiog in the laft Joint of the Dragam 
Following io d of the LiltU Star 
Preceding in Neck of the Serptnt 



4 '^ 
; ^9 $<>•$ 
f 18 14,6 
I 32 15,8 



4 4 16 

4 32 O 



23' i*.S 



•19 58,5 



Brighteft in the Cmou 
Brighteft in the Neck ofthe Sirftnt 
Soathern in the NeciF of the 5«r/M/ 
Followiigthc brightjca ofthe Serttiu' 
Following of Sondigro mSerfaitt Neck 



14 s: 
'S S 33 

15 19 *4 
'S » 

'S " 53 



Fallowing in the tail Joint of the Dragmi 
Pleading Arm of Ha-cuitt 
Prccediag Shoulder of Hf.cuiu 
LaA Joint of the t>ragii% 
Foregoing in the Side of Htrcwles 



I 40.» 
S9 39-8 
39 S».0 
JS 3o.» 
■3 SM 



S »4 7 

S 3' S9 
5 34-39 

;S3a 
i S 44 S i 



(45 

ill 



a^ 



■ 8 3;, 
« 30.8 

9 4»'9 
ii 



F S7 
6 10 5« 
6 19 30 
6 20 39 
6 31. S' 



o 4) 3>.' 
!7 '9 'S.' 

+ 45 43»z 
39 40 !S,S 
'» '8 34.? 



» 4> 27.! 
SO 34 5>4 
'» 39 4S.O 
65 34 3*.S 



20,0Z 
19,69 
9.6? 

9,66 



20 29 39, 
38 24 19,0 

48 s«,i 

837.0 



19,01 

■8.77 
18,24 
18,06 
'7.4< 



16.31 



4» '3 »5'7 
34-. 'S 40*8 
59 S° IM 

' '3 3?-o 



'3.B2 



2,76 



>7 3+ »8, 
7 13 5fl.S 
6 i^ 16,9 
5 14 56,3 
* «9 ♦■■* 



l2,iSo 
12^ 

■■•87 

ij,6l 



59 >4 '7.i 
'9-4S ^9.6 



O.JJ 



8.S1 
8<41 



II of htrctJtt 



34 ;9-6 



'6 34 



,, Google 



The ROYAL ASTRONOMER 



L CATALOGUE of Eminent FIXED STARS : With their Nomber, Right Afcerfion, Declination for 
Jaaaary I. 17^0. and aonaal Variation fronnhence. 



THE 
Following in the Side of Htrcuks 

Following Shoulder of Htreahi 

\ieadoFOfi>iuebiii 

Eye of the Dragait 



Northern in Shoulder of Ofhlvihus 
Southern in Shoulder mi Qphiucbm 
Elbow of Htraihi 
Knee of HircuLi 
Head of iiic Dragan 



Brighten in the Harp 

Preceding in the Lozange of the Harp 

Preceding in the Ejttremity of SerJ-al'i Tail 

_. _ . jg ia the Lozange of the Harp 
Preceding in the Tail ofthe Eagie 



Following ii 
Following in the Tail ofthe Ea^lt 
Second Joint of the Dragen 
Preceding Wingof lhe£«2& 
Beak of the S-wan 



Pla. 



NoxTHEKK Stabs Names, 
And 
their CONSTELLATrONS. 



Right Afcni. 
in Degieei. 



26Z 46 55,0 

26J so JS.2 

36+ 10 9.5 

266 js 25,6 

267 4.Z 3,c 



177 7 7>"» 
aSo 12 47,3 
280 56 51.2 
"26 36,3 
4 '7.5 



i S4-.3 



13 H'7 
'90 9 '5 '3 



152 40 si.« 

^l *l +?'* 
:;6 26 30,4 

60 SO 5,3 

Z6l 12 6,8 



8 28 28 

8 40 51 

8 43 47 

18 45 46 

8 48 



16 so 43 
>7 3 >S 

17 s 46 

17 23 20 

'7 '4 48 



7 3S " 
17 36 41 
7 47 42 
7 so 48 



8 49 36 

8 S3 55 
g 12 26 

9 '» S4 
9 '° 3» 



1.36 



4 41 40.6 
^ +9 *8,j 
7 53 3-9 
7 '7 5''.4 
5' 3' 37.9 



38 34 0,0 

5 *3-4 

54 6,0 

' 3S 48.6 

_44S6.I 



31 18 41,6 
'4 4' 44.; 



!-2i 49,0 
30 42,5 
■3 17.' 

■ 38 "8.1 



Brightcft of the jirretu 
Preceding in the Neck of the EagA 
Northern Wing of the SiaaM 
Brighteft ofthe f^iiSr 
Following Shoulder of jfniimiu 



Following in Neck of the Eag/e 
BreaS of the S-waii 
Preceding in Tail of the Dtlphin 
Preceding in the Lozange of the Delphin 
Soatherly in the Lozinge ofthe Dclpbin 



292 14 1,0 
*93 35 JO.* 
194 17 28,4 
294 38 46,7 
94 5i 55.0 



9 28 s6 
9 34 *' 

9 37 'o 
9 38 35 
9 39 44 



■ 3' S8'S 
I '3 44.3 



^9S 45 3'.o 

303 18 50,0 

>8 s6.4 

305 54 '7,8 

3°^ *7 34.3 



9 43 = 
20 13 11 



S.4« '0,6 



1 49 S^.2 
. . f4 3'-6 



Northerly in the Lozange of the Dtlphtt 

Southerly following in the Loz, of the Delpbh 

Tail ofthe ^wiw 

La/t in iKizange of Dalpbio 

Brighteft in Southern Winf; of the Sioan 



307 O 22,2 
JO7 56 44.9 

308 13 38,s 
308 46. 3,0 



. 1 1 36,6 

1 23 54.S 



Extremity of Southern Wing of the S4u^ 

Head of the littk Horji 

FiiBL of P/ip/m 

Preceding Shoulder of Ofbtm 

Girdle ofCtpitui 



Mouib of Ptga/iu 

Lower Part of Soothern Wing of the 5«vaa 

Neck of Fegitfiu 

Nonh^ in the Knee of Ptge/Kj 

Ring gfihe Chain of AiJremJa 



3'5 34 *6,4 
3'S 49 3f.o 

317 37 »S.3 

318 8 41,8 
3«' '9 34.4 



n -8 



' 44 S3-7 
I 3' 5S'7 
> «7 54-8 



S8 

323 14 41,1 
337 '4 43.9 
337 49 37.7 

342 36 49,0 



21 31 S3 

21 32 59 

22 28 59 
21 31 18 
" 50 *7 



i 44 !t9.8 
' 37 *4. 



' 55 H.5 

> 59, '=.3 



Thigh of f/jo/W 
Wing of Pnafiu 
Following Pool tiiCtfbnu 
Hcadof^fMtvjMMb 
Chair of Ca^Bpt^ 



342 ss •4.5 

343 4 57.3 
3S» »9 ^'■' 
J58 52 44.1 
3i8 59 41,4 



" S' 41 

22 52 

23 29 17 
H 55 3' 
'3 SS 59 



p 42 32,1 120,041 
' 46 7.o|»o.04l 



,, Google 



mj navigator.- 



l[li. A CATALOGUE of Kminent tlXED ST^ARS: Wttk their iJumt^r, kight AlccDliou. Uecl.n.uon m\ 
)| Jaaaarit, i7?o, snd annual Variation fiom thence. | 




1" 


SooTHsaK SxAas Nambi, 

And 

Pltcei in their CONSTELLATIONS. 


?5 1 


Right Afeen. 
in Degrees. 


n Time. 


Ann. 
Var. 


Declination 


Ann. 
Var. 






N«. 


+ 




— 






•* '" ' 


H.M.b 


S. 


' " 








3 


THE 
Tail of the Male HjJm 
Head of the PioKx 
firightcS in the ma/i4 Tail 
Thigh of the Phmni^ 
Preceding towards the WhaUsteil 


e 3 


3 2 58.3 


12 12 
13 52 
31 2 
» 54 53 
056 , 


2,7* 
3*1 
3.0 ' 
2.73 
3,00 


78 39 SO,J 20,01 

43 39 434 ".oc 
19 21 51.1 19.85 
48 4 42.' >9-4'' 
II 30 48,8 19,44 






6 
7 
8 
9 


Following towards the WhaU's TaU 
PoIIowing Wing of the Pbamx 

iJead of the Male HjA-a 
Variable of the tTbali 




17 S3 9.' 
19 2» 10,7 
2! 5 4»." 
'7 45 ".S 
t 31 40 53.8 


' ".33 
1 17 29 
. 28 23 

' K " 
« 6 .4 


2,26 
'.87 
3,03 


9 28 49.S 
+4 36 '3.8 
58 JO s^,' 

62 47 36.3 
4 7 28,0 


9.07 
856 

7-7; 
7; ■;, 

6.03 
4.8s 

4-<=7 
?.93 






II 
■3 


Preceding in the Cheek of the If bait 
Breaft of the Wbal* - 
Firft Turning of the Rhitr 
TiirJ Turning of the Ri'vrr 
River, before the W'iai 


{ 


3^ 40 3S.4 

36 51 2Z.9 

41 11 52,7 

t 4S '■ S«-« 

J 45 SI 39." 


2 26 42 
J 27 30 

2 ,8 48 

3 1 26 
3 3 4i 


3.08 
2,90 
2.30 
2.54 


45 jo.a 
1= 56 5'.? 
41 19 4.0 
29 59 '3.7 

Ai ^1.3 






16 
17 
18 
>9 


Fallowing, in Ibc Ri'Der 
Following in the Rivtr 
Fourth Turn of the Riitrr 
Middle of the Male Hydra 
Btighteft in the rhomboidal RttktiU 


A 


J SO 17 32.0 
3 s; 49 3».' 

3 56 35 4».3 

4 57 SI 5'.' 
3 6« 49 11.8 


3 2. 10 
3 3' .8 
3 46 23 

3 5' 27 

4 '■ '7 


2?8 
2,79 
,,14 — 

9.74 


10 19 12,0 
10 37 3^0 
14 14 11,6 
74 59 55.9 
63 « 16,3 


2.79 

2,IQ. 
1,01 
10,66 
9."; 






*3 

34 


Tail of the Gold-iilh, or Duradt 
Laft of the Riiier 
Bright Foot of Orim. Rigtl 
Northern in the Sword of Qrioit 
Bellv of the tt,« 




3 "7 9 "9.7 
3 73 53 44." 
1 75 j8 12,1 

3 77 SS 48.0 

4 79 «3 ",3 


4 28 37 

4 55 35 

5 2 33 
! " 55 
5 >7 33 


1.28 
2.95 
2,89 
3.02 

2,58 


5S 34 i*>9 
5 25 49.2 
8 30 37.4 
2 38 S6.s 

20 j8 43.1 


7.78 
5.56 

4.97 
4.-17 
3.69 






id 
»7 

29 


Preceding of OriBi'i iSirdit 

Brightcil of the Hare 

Middle of Orien'i GirdU 

Uft of Orm-'s GirdU 

i'lcceding of the brightefl of the ZW< 




2 79 48 54.4 

3 80 25 49.7 
. 80 55 ,1.. 
2 81 2 33.5 
2 81 39 12.2 


5 .9 It, 
5 2' 43 
5*3 33 
■ S 28 10 
53037 


3,07 

2,65 

3.0s 
3.04 


30 aa.S 
18 I 19,0 

1 23 I,Z 

2 5 48.9 
34 13 ^^.7 


3.54 
3.34 
3.' 7 
*.77 






3> 

3* 
33 

34 
11 


Belly of the Gold-rifh, or D«rad, 

Soothern-In theWwt'jfw/ 

Knee of Orian 

Nunhern in thoffaw'j ¥mt 

Following of the brighteft of the Dmw 




4 8» 52 .7.5 
4 8j 30 43,2 

3 83 58 48.2 

4 Sj 3 46.0 
3 85 32 30.4 


5 3' '9 
S 34 3 
5 35.55 
5 49 3; 
5 42 10 


0,50 (.2 39 20.7 

2,53 =2 32 ^8 7 
2.85 9 4<i 38,3 
2,57 20 55 ,6,, 
'." 35 <2 40,1 


2,4.8 
2,26 

■ !6S 






36 

11 
39 


Preceding Foot of the Gruit Dog ■ 
Knee of the Grtut Dog 
Btightefi of the Ship. Caiiffpiu 
Summit of the Ship') Ruddtr 
Bfighteft of the Gnal Deg. Syrius 


1 


3 92 40 58.9 
3 9» 55 25,3 
1 94 36 7,6 
3 97 3> 44.4 
. 9832 0.3 


6,044 
6 11 41 

6,8.5 

6 30 7 
9 34 8 


2,31 
2,63 


=9 58 .1.8 
17 S' >M 
;2 34 8,:, 
42 S9 at,. 
i6 aj 56,6 


0.94 

1^60 
a.^2 
2.57 
4-?3 

til 






4' 
41 

43 
44 


Thigh of the Qnas Dag 
Back of the Grttit Dig 
Poop or Stern of the Sbip 
Tail of ihe Great Dcg 
Poop of the Ship 




3 102 12 7,2 

2 104 33. 26,8 

3 107 4 44.0 

2 loe 33 3,6 

3 no 19 40,5 


6 48 ,1, 

6 ;8 ,4 

7 8 ,9 
7 "4 "2 
7 2, ,q 


2,3s 
2.4J 
2. '3 
2.39 
'.94 


28 38 S9.6 
z6 56,1 
36 39 14-4 
18 49 59,7 
42 48 2?.6 






46 
47 
48 
49 


Poop of the Ship 
Preceding, in Budy of the Ship 
FollowiDg in Body of jhe Ship 
Brigliteft in Middle oi" iheS//ft 
Sail of the Ship 




2 ..8 42 4,5 

2 120 27 48.0 

3 124 20 10.7 

2 129 27 S.» 

3 '34 42 '7,7 


7 54 4» 

8 ■ 5 
8 ,7 2 
8 37 4i 
8 57 45 


,,6. 


39 >« 39o 
4& 36 34.9 
58 4^ S-o 
S3 48 2. 
4a z6 4.1 


'2,r3 

'4-79 
14. "f 






5> 


Krtghitil about thi; Oars of the Ship 
MaK of the Ship 


a 


, .37 35 26,0 
3 '37 36 3,3 


9 ,0 2 

1 9 •" '.i 


0,75 l'8 4. '-; 
,,6< !;3 ,4 8.3 


J 



,, Google 



Ill ne ROYAL 


ASTRONOMER 






III. A £ATALSt3U£ of KmUnl nXEK'STAKSl With tkolt Mimbti, Kllht A(colio>, Unliutin ferl 
yanmj I. I7S0. ud Mimiil VariRCion from thenco. | 


N'. 


SOWTRIRB StA»I NaHII, 

Akd 
Plic« in their <?ONSTELLATK>NS. 


1! 


; 


Right Aran. 
inDegnei. 


R. Afctn. 
in Tiinc. 


Add. 
Var. 


DedioMion 
Sooth. 


Ann. 


+ 


+ 




H. M. S. 


S. 






53 
S* 

!7 


Brighteft mem Ntribtrlj 
Heart of thHetnkle /M-« 
Oari of the Shit 
SoDiheminS«aionofthc5A.> 
Nortberr in Seaion of the S^f 




■38 3S !"« 
tj8 49 40,0 
14s 11 4i,< 
■S» 31 34« 
IjS SI 29,3' 


9 "4 '4 
9 '5 '9 
9 40 S' 

10 34 6 
10 35 26 


1,66 
»,9< 
>.SO 

2.27 


S3 57 0,1 
7 35 <Z.t 

;3 55 '.7 

'3 5 »4« 
58 32 59,3 


•5^3 
■S.08 

18.64 
.8.68 


S8 

6i 
6i 


Top of the Ship') Scaha 

Poot of the Cup 

Preceding in the Cropper of the Ctnttur 

Beak of the X«w» 

Head of the Rmim, 




-4 


i!9 I 11^ 
1'! 54 13.7 
178 V SM 
178 S3 3'.4 
'79 '9 46.' 


1036 s 
'O 47 37 
'■ 55 '7 
" 55 34 
II 57 19 


MS 
'.95 
3.05 


4! 6 15,0 
16 58 39,0 
49 "9 39.8 
23 20 6,0 
" '3 44.15 


.8,81 
19,05 
20,03 
30,03 
20,04 


<* 

6? 


Preceding Arm of the Crtfi 

Preceding Wing of the Ravtn 

Foot of tbe Crifi 

Preceding in fgllowing Wing of the Amw. 

Head of the Cnfi 




■80 30 34.7 
I»o 44 4t.! 
'83 13 S3.7 
184 14 19,6 
184 3» 35.0 


12 2 S9 
12 IS 56 
12 ,6 s8 
12 17 54 


3.10 
3.09 

3.22 

151 


57 SI 30.0 
><■ 9 3'.S 

01 43 47,4 
■ S 7 18,2 
70 44 54.3 


30,04 
20,04 
20,01 
19.98 
■9.97 


6S 
6, 
70 
71 

7* 


Foot of- the HM>t» 
Preceding of the Fh 
Topof tTieOBf^w-yO^ftw- 
Soothern in the firna'/ G/ra!Ir 
Head of the flf 


f 


18s 19 JO,0 
,8! 38 +1,6 

186 57 S3.8 

187 IS 7,. 
■87 48 S3-t 


IS 21 |8 
12 22 3S 
12 27 52 

IS 29 
.2 3' 16 


3.14 
3.4' 
3.27 
3,08 
3.52 


22 40,0 
67 46 17,2 
47 34 5'.9 


I9«S 
'9.94 
'9.89 
'9.88 
'9.84 


73 
74 

77 


Following Arm of the Gnji 
SoDthern Wing of die Firtm 

Preceding Shoulder of CmIov 
Sfih of tlie Firgin 






188 19 40,1 
.94 '5 «f." 
'9f •" 4«.| 
.96 J9 ij,6 
19B siHt 


■2 33 19 

12 S7 2 

13 12 3 


3.4* 
3.09 
3.'> 
3.34 
3-I5 


58 -9 8.3 
4 ■■ 47.S 
" 5= 43.8 
35 23 6.6 
9 SO 5'.' 


'9.83 
'9.4" 
19.33 
'9.SO 
'9,06 


1* 

V 
8o 

8i 

8z 


Belly of the Cn/ow 
Waift of the Omtatr 
Preceding Leg of the Ctntnr 
Following Shoulder of the Cnt^ 
Robe of aU-^trgin 




3 


101 3 30,4 
305 I 14,6 
106 36 41,8 
'07 59 57.5 
'09 53 57.8 


'3 '4 '4 
'3 40 5 
13 45 S7 
13 ss 
13 59 3« 


1:?6 

4.09 
3.5' 
3.19 


52 10 ss,2 
4' 3 38.3 
59 9 '.8. 
3S 7 34« 
9 5 43.3 


|«,70 

1 ! 
'7I69 
■7.37 


»3 

il 
8? 


Southern Foot of the r,rghi 
Southern in the Shield of the Cmttmr 
Head of tbe C«tja/i, 
firighteft in the Foot of the Cntan- 
Foot of the W0I/ 




III n 18,4 
114 s6 9.1 
"S 39 45.4 
"i +■ 31.1 
»t6 11 48,0 


■4 5 J7 
■4 19 45 
14 ss 39 
14 22 so 

14 2s 27 


3." 

SI 

4.41 

S.89 


03 5' 48.' 
59 47 9.4 
46.17 40,1 


'7,3o 

16,36 
16.14 


88 
8, 
90 
9> 

9' 


Soaihero Scale of the Bmll^rt 
Extreioity of the Foot of the Wc^ 
Following Foot of the Cf»tf«f 
Preceding Claw of the ScT/itm 
Preceding of Soothem Trimigk 




J. 


»i9 16 10^ 
izo 34 6,6 
110 4s i.,7 
SIS SI 28,s 
S24 2,8 


'4 37 5 
14 42 16 
'4 43 ' 
'4 49 30 
I4 5« 


3.30 

3.86 
3,84 
3.48 
5.29 


14 S? 9.7 
4" « "3.9 
4" 4 45.6 
«4 16 53.5 
^7 43 3'.3 


■515° 

■5.23 

'5.'7 
'4.70 
'4*> 


93 
94 

?l 
97 


The Northern Scale of the B«/W» 
Following in ShODldcr of the W»lf 
Fonowiog in Northern ScaU of the Bailtmt* 
Top of the Sonthem Tritaigi* 
Sondiem Qaw of the Scarfh» 




"5 53 SO.« 
119 38 36.S 
«30 23 4S,6 
233 20 42,1 
23s " 4«.5 


■5 I 35 
IS 18 34 
'5 " 35 
'5 33 23 
■5 4" 31 


3.30 
3.94 

i«8 


8 26 jo,s 
40 18 4.0 
13 56 IO,+ 
62 37 34.2 
28 37 36.6 


'3«4 
".97 
'2,77 


9^ 
99 
100 
101 
102 


Soatheni in the Porehead of the Se»^ 
Middle of the Forehead of the St*rfum 
Northern in the Forehead of the StBrfim 
Top of the Forehead of the SkHmx 
Preceding Foot of Ophiu^hu. 


J 


'35 5' 38.8 
■3' "3 S'.2 
'37 4t 7.0 
■39 "5 M 

241= 18 sS,8 


■5 43 47 
■5 45 35 
'5 50 56 

:i '; ii 


3.60 
3.5' 
J.50 
3-t7 
3.14 


35 ss 18,7 
31 S3 17,6 
'9 5 55.2 
18 47 19.6 
3 ' 46.J 


11,32 
11,09 

10,69 
10,34 

9.9' 


. 103 


Following in the fame Foot of Opbiuelmi 


. 


't;.'^.{,''' 


.6 ; 7 


J..6 


4 3 36.0 


9.6? 



,, Google 



und NAVIGATOR.. 



irr 



THE 

Praceding of (he Storfhu't Heart 
BiiebRft in the St»rfii,-i Heart, jhiarti 
Following of the ScarfMi Utarl 
FoUowing of the Sonthem TriawA 
Sonthem in the £w of Ophiuc^, 
Firft Joint ol' the Sitrfie/t Tml ' ""' 
Second Joint of the Sttrfin'i Tail 
Bri^teft in lb« third ^m/ 
Ftarti Joint 
Following Rnee of Ophiiuhmi 



OATAiWiUiioiilmloentPlXilb STARS: Witk their Number. Wgkt 
Jnuary 'i, \^^a, ind »nnn»l Variation ffcm thence, 



213 
A^cenAon. Declination foi- 



SOWTHBRM StaR» NaHS», 

Akd 
PI«cei in their CONSTELIATIONS. 



Following Foot of Qpbiuclm 

Middle of the Mtar 

Little Star in Extrcmitf of Sctrfimt'i Tm/ 

Brigbtefi in Bxtremit^ of die >m Taii 

5th Joint of the &fl>jj«w'i Ta/ 



7tli Joint of the >« Tail 

6A Joint of the fim fmt 

In the laft Joint of the Sirfnt 

Followi at the Point of thc^Arowof 5^/f/«>7 

Top of the Bow of Sagittary 



Foot of Saglttaty 

Southern Extreme «f tfa« Bvw e/SimUmy 

Northern Bxcremeof the Aw qT aoffilarj 

Aztmr of Sa^tuay 

Preceding Sbonlder of Smgjttmy 



Arm of SagiUarf 

Held of Santlarf 

Preceding StonMer of Sagtiiaiy 

Following in the Head ofSagiilay 

Precedaig of z in Foot of Sagitutf 



Leg of Safftlaij 
Side of Aatimna 
Back of the PtaeiKk 



Brightcll preceding ia the Head aiCafrUm-n 
Eya of the Ptanci 



Following in the Head of Ca/rinm 
Zagaye of the I»dia» 
Wing of the Prenei 
Breaft of the Ptaitd 
Preceding Shouldee of Jgaarin 



Preceding in the Tail of the GMt 
Following in the Tail of the Gtat 
Head, of the Cr^* 
Preceding Wing of the Oww 
Following Shoulder of J^aarim 



Beak of the TtMcOK 
Following Arm of Afurim 
Thigh of ^e Croat 
Water of the ffater-Beartr 
Leg of the ffalir.Siartr 



Brighteii of the Southera FifiMi. Ftte^ium 
Water of the ^mtir-Beanr 



t- « <£ Right Afeen. ft. ATceo 
|-g §• in Dcgreei. in Time. 



4 241 30 40,7 

• *43 3" 5".8 

4 HS S 3«,3 

HS 37 S.O 

HS S' '9.0 



!48 30 I +.8 
248 44 S4.6 
*49 'S S'>o 
'SJ 34 34.1 
'54 o S3.9 



2S640 
158 8 17,0 
258 27 0,8 
H9 9 ^9.4 
'59 50 S6.' 



.61 16 ,,., 
262 3. S3.S 
266 49 26,9 
[67 26 21,; 
'69 4» "7 



.6 54 .8 
'fi 56 4 



17 6 2 

17 12 34 

>7 13 48 

7 16 40 

7 '9 '4 



271 14 31,8 
*7' 53 39>7 
*73 8 5,2 
'77 30 26.7 
'79 56 '5^ 



tSi 40 16,6 

282 1; 19,1 
49 38,3 

283 35 45.4 
"•1 



»86 37 43.3 
390 58 30,0 
295 58 SS.O 

300 50 28,9 

301 a; 20,o 



301 44 |,o 

304 57 50.9 

305 31 1 8,6 
316 21 5,2 
3 ^9 35 ,,S3-7 



321 27 

313 l3 t),D 

324 40.33,5 

3»8 S 7-7 

1 i'8 '4 0.6 

3 3JO 16 46,0 

3 332 11 5,6 

3 336 54 3.» 

4 339 S3 *7.8 
3 340 20 14,6 



Jk 



340 56 41,7 



6 ^3 '5 



17 35 13 
17 50 8 
17 47 16 
'7 49 45 
■7 58 49 



8 458 
8 7 3S 

8 12 

'8 JO 
" W4S 



18 46 41 

8 49 4' 

! 5' '9 
8 54 23 

19 4 37 



963 
9 *3 54 

9 43 56 
20 3 46 

S 4' 



20 6 56 
20 19 51 
20 2: 
5 24 



"5 49 
23 13 

: 3842 

52 31 

^ .5' jfi 



22 27 36 

2» 39 34 



" 43 47 

i5_ 



Declination 
Sooth. 



M8 -. 
f 5» 8.4 
7 40 14,7 
i 3" "M 



; 48 4' - 

' 35 '8^ 

54 3.6 

! 52 39,2 

: 23 »8.4 



I- 43 to,6 

} 38 3 '.8 

: 3 5s« 

J S3 28,6 

' 48 '3.' 



i 52 14.6 

> 59 49.0 
\ 38 56-3 

> 23 5t.7 
' 5 50.9 



29 54 18.4 
34 «8 17,4 
*S 3> ^7.4 



30 13 36,0 
23 5 0,8 

28 o 30,6 

21 23 48,8 

44 ^3 4'^- 



3 *i.S 

I 49 13,1 

66 46 50,8 
3 18 «'8 

57 30 »7.4 



15 33 a.7 
4S 8 14,0 
67 4 8,5 
66 28 19,8 
6 39 ".4 



17 46 42,0 
17 "4 48.3 
38 31 28,7 
48 9 21,4 



61 20 34,0 
* 38 »3,S 

48 10 51.0 
8 54 8,2 
" ? . 9-9 



30 56 24,8 
7 g? I 



8,78 
0,30 
">H4 



5^6 

'6.3S 

17.00 



,y Google 



41+ 






76t 


ROYAL 


ASTROKOMER 












Ycsriftcr) to i8eo. N. S. Which will fem, with conlMry Sign, bic 






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+ 1 


1-4 


]1 


















43 


1 Jl 


IS 


53 


I s» 










3t 


















1 47 


» s» 










D-r 


J»l,. 


Augoft. 


St icmbet. ( 




■ Wcv.mb„. 


_ Deccnbrr. ' | 


- + 


-*- 


_ . 


-t- 


+ 1 - 


— 


+ 


— 


— 


+ 


+ 




+ 


+ 


+ 1 + 


+ 










1 sA It 


3' 


' 47 


° J9 


4S 


' 4S 


04. 


43 


> 44 


31 


7 


146 












M 


I 51 as 


3+ 




*• 39 


41 


> 45 




41 




3' 


9 




























41 












iS 












1 V 




1" 


' 4; 


39 






04. 


39 


1 44 


on 


'4 






-L 






















■ 4i 




39 




]i 






". »I 




, ^, 


S 


17 




19 


4J 




o4» 


lK 




a 40 




' 44 


3a 


jS 


I 4t. 






















40 


1» 








> 44 


31 
























"■4' 


40 










> 4! 


31 


19 


> 4fr 
















31 


47 








I 46 






t 44- 


3' 


"9 


I4f 






15 


' t' 


13 






ji 






40 


11 




4] 




' 45 


30 




' 47 




,, 


-io 


1 ^0 




'4 


' SI 


31 


49 


' 4i 


41 


11 


1 46 


41 


11 


■ 45 


JO 


It 


" 47 












M 


I s> 


11 


S» 




41 


11 


;:i 






















IS 




1 sa 




SO 




4» 


4<" 






• 45 


39 












I (i 


c 17 




1 (2 


•0 14 


S' 


J Ji 


43 


4a 


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I 40 












+ f 


J-Jl 


JLii 




41 




















iS 










I 45 


-jj 


4' 


' 45 


3^ 


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17 


11 


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4" 


i 44 


39 


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ii 








4 


' (' 




S' 






4' 


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0. J9 


J3 














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' 4* 




s> 




a 43 


4>- 


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39 






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1 4<> 




11 i6 


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~ 












43 














»1 


' 41 




>1 


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5- 


s* 


> 4* 


I 44 


38 


i 


I 47 < 


=4> 


»3 


t 45 





11 le 


' V 




M 


;s 


37 


S3 




43 


4t 


1 4i 




9 




13 




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1} 14 


» f 




'7 


37 


SI 




44 


i 4. 


36 








H 


• 45 




,14 ij 


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It 


i 44 




SI 


> 4S 43 


4S 


i 4: 


" 35 








^4 


J 45 








a 14 










■4: 


43 


■ 45 


I 4' 


" IS 






"Hr 


»4 


1 4S 




i6 iS 


I f 






. 4* 


39 


J' 


" 45 


43 


41 


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IS 




f46 






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41 




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19 










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Jl 












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0^, 






44 . 41 3il 








17 


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)(t/i«i infir rvtrj 4 (ulina IiAnadJi in 


bii,n-,taJapfr«i,tb.S,,ulmu Ihfiom 


■cii lm.tfiiktrt, 




jifffl™ frcM tU Scljiicii ti rbt Eqmior. —The Eqiniion of rhc Sun'i PI 
TUrJi, fbf every 4 Vein, iddi «ndfublraib, »liern»tdT. From Jm 




.lioaofClOTk.Tinw. in 


irt, itaJM»J*a.-iO;~fi,ii.fr.ibiMi nM 


ji.*JiA/r.ibi.r.i,,e 


A,%. M.f'.tbiK'1'nHow. tJJt fr-lbcf II 10 [.n.— The Signi pr 




gni ftm for Vn. fcirk. 








■ 




























S 


MLL" 



ami NAVIGATOK- 



3MALL EQUATIONS conttaMd, Ac. tcctniint to M. De!aCiUf/i. 



EQUATION of tbe SUN'i Rrthl AftcofiMi in Tknc 

i»™ of the DifhiM io Tinif , of the S«9i»i pf ,<r 
ne iht Ctmfhmiu of the SWJ'i KithlAlccniMn li 
A'. A 



iDck ufe the coolnry Sigiii 



The SUN'i uppircntScmi-Diar 



cv.TTflfthDaj, inDcErecsindTiirc, for 1760, or Ltap Yea: 



>S 59 
"J J* 
'S .'i^ 4° 



'S JS J" I S S" 

ij 54 10 I 6 14 

■S S3 10 1 « jS 

IS s» 10 1 7 4 

ij 51 10 t 7 »| 



S 4f 45 



J'-'y- 



'5 +7 i" 
Ij 48 o 

IS 4E ij 
'5 48 JS 
'5 4» 5S : 
'i 49 '5 1 



3 S7 
3 5* 



16 14 45 
18 It 45 
16 it AS 



i VI 



EVATI 



The Moon'i Aliitude, 



5 


J* 








^» 


9 




•1 


14 


'+ 


** 


»4 


17 


»^ 


V* 







Apparent OBIJQplTlES of thtEt/ifiie 



In the Ynn follovi 



173! 

rt - ''*9 - 

II dcncafini (Stc p. 3]] 13 



be i^ theJMiH* Obliquilri iccocdint to tht Pi 



lUita't tpptrent SaU'Dimmr >■ .MiHrJl, tail tfpama jOtinJt tftbt hbi^t CaitT,fnm ib 

iflS'i ^'d r^VBU AhitmAtf tht Mtn'i ••pptr LiaA, 4;^ ]•/» sMnWr 
ened* Hoiiioatil or Ime $cmi-Diuiietrr i£' 

Under ■6' axfl, ud-ipufi 4;" yf Allicule, 700 find -f- 



GiAwrLi. T«jM li< 



49 IJ 3» Ap. Alt. >'• 



Appueat Semi-DiuMt«r ) ia Altitude 16 it requited. 



DigHizcd by VjOOQ IC 



41 6 



7bi ROYAJL ASTRONOMER 



TABLE of Clock-Tim. ii NOOK by the SUK, 
^/n from the Min'/i'n, !■ Time, 










5 rt.e0 


«. 


> Rigbi |Co.©R.A. CloekTinw. 
rcenfion Dif.lin Time, « ic Norn MD. 
n Time, \r fr. Mer. the © | 


n Time. T fr- Mer. 4e Q f 


in 'Tine. 


CO.QR.A. 

Bif. in Time, ot 

r fr. Mer. 


h. m. 1. 




. m. 1. 


.•■ 


h. m. : 


b. m. ,. ,. 


1. m. •. n. >. 


fa. m. 1. 


fa. m 




n. t 


h. ID. 1. 


I 11 + 17 
1 11 4 SJ 
1 11 51* 


»7 


8 S0 4« 
S S3 » 
S S9 3S 
8 J 59 


14 
13 


S 9 14 
J 4 S» 
S 9»S 

4j6 I 
4 5- 38 


11 14 10 
» <4 «7 I 


11 a 45 

tl 4 49 
" " 5» 
" 14 54 


4 


» S7 IS 
* JJ II 
.49 8 
»4S 7 
>4i 6 


11 11 JJ 11 51 j< 
11 i> ai 1. 55 14 

t> la 7 T»s8 58 
11 II S4 ,^»| » 4" 


44 
44 
43 
4" 


■ 4 4( 

° 37 19 
= 33 3! 


9 11 7 sS 

10 ,1 8 >i 


1« 

»s 
«s 

«4 
«3 

»] 

11 

M 
19 

:i 

17 

"5 
15 

14 
•4 

13 

9 


9 "44 
9 '7 7 
9 »> ^9 

? »S 49 

930 10 


*3 

:: 


447.6 
4 4» 53 
4 3» 3' 

4 34 " 


11 14 36 , 
11 ,4 38 \ 
11 14 40 
11 14 V J 
"14 41 . 


11 M S4 
.1 16 SS 
»i 30 ii 
>i 34 49 
>i 18 46 


i 

57 


» 37 6 
» 33 7 
1 19 9 
1 IS II 
1 11 14 




13 ij 46 


4» 
4' 
4> 
4' 


041 33 
<. 38 51 


■■ " >« 

1. 1. > i 
ij 11 9 10 

14 It 9 s» 

15 11 10 ij 


9 34 3° 
9 3<49 
» 43 9 
19 47 17 


» '9 

(.10 

H8 

1 iS 


41J JO 

4 >6 S' 

4 11 33 
4 > >S 


11 14 4" - 
11 14 40 

" >4 37 
" '4 3S . 


" ♦? ■*! 

ti 46 3* 
" 50 J' 


SS 
SS 
54 
S3 
53 
5' 
SI 
49 
Se 


1 '7 «9 
1 13 14 
s 9 19 
» S 35 


IX 10 7 
" 9 S" 

.1 6 59 : 


13 .11 19 
xj ji 5 
»3 35 4» 
13 39 iS 


4- 
39 
40 

3 IS 
\l 

ill 


]l 31 
017 J. 

»4 i» 

JJlJI 

s s» 

a 19 
»3 sS 4> 


• 33 


10 .] 1 


+ »5 

4 >4 


4 JS8 
3 59 43 
3 5S «7 


I* 14 »7 
11 14 l» 

It 14 >e 
i> 14 10 
» 13 3 


11 1 11 
M « 9 

»» 9 S3 
» "3 4» 
» "7 Ji 


' S7 ♦» 
» 53 S8 


I" S 4" , 

". l-j; 

" 7 48 ; 

" 7 «9 : 


13 46 45 
»3 S0»4 
»3 54 » 

'3 S7 41 
I 19 


u ;: ;: ,i 

tj H 11 33 

14 "» 1» 47 
Ii J» 13 I 


10 17 15 

10 ij j8 

10 19 49 
10 JJ S9 


4 " 

4 II 
4 >I 
4 "o 


3 4*45 
3 1" 33 
S 14»» 


11 >3 s« 
11 13 47 
11 IJ 38 
■1 .J 19 , 
11 13 19 . 


::i;n 


3 4* 


1 3> 39 

I 34 S" 
I 31 4 
I 17 '* 
I 13 30 


11 6 34 , .1 13 

li 's \l '^ ;i ii 


3i; 
3 s! 

3 3« 

11? 


«s Si i 

»3 S« »S 

«3 47 47 
1344 II 
13 40 .31 


.6 .1 IJ .1 
X7 11 .J .8 
■8 l» IJ 3J 
19 '* 'J 4S 
10 I. 11 SS 




1 1744 


■■ " S7 
" » 4S 1 


"T,,l 


145 

3 45 


1 1944 
I IS 59 
I IX 14 


11 s j8 
" 5 >9 , 
11 S 

11 4 41 
" 4 »J , 


I <• 37 37 


in:;?- 


J 9 »9 
3 S »i 


In LapYcirtikcMtfciriDay hootr is 

V«n U«r Lup Yeit takt one for J, (, J, 
«fmDi7fi»Mrin lUihcMoothi (5.^.194) 


J« >» H J 




10 sM. 


* 


J 1 19 


>» 4 S 


4, ,. 




"3 .« 44 1 


D.I A P K. 1 U 




J U N fc. 1 


-■ » 3 46 
1 i» 3^8 

3 » J 10 

4 I» » 5» 
^ " « S4 


1% 
■S 

iS 
"7 
'7 
17 
16 
"7 
16 
16 
■S 
'5 


044 S4 

IS?: 

SS 49 

" J9 »7 


lis 

Hi 


13 IS 6 
ij ,. .8 
ij 7 S" 
aj 4 II 
ij 33 


.■5.4. 


1 Jt, M 

; » 39 s 
6 '43 4 
6 » 47 4 

;■» s> 3 


It! 

1 S 

1 5 


:: u, 1 
11 It 11 

l\ " ta 


11 S7 «4 
II 57 3. 
" i57 4« 

II 57 S» 
" 5* 3 


iti\ 3 

. 4 SS *S 


( 7 

4 7 


■9 ai 
J9 '6 J5 
19 "49 
19 841 

"9 4 3S 


7 I. I 59 

', :-. ;;; 

to tl I ( 
14 11 5 


I 10 »4 
,» 14 4 

' 17 11 


1 3 
3 3 

3 4= 
3 V 


" 56 54 


;;i 1 

II s6 J 


, > SS » 


1 S 
3 SS 
3 W 


ai 4 37 


11-58 , J 
I. 5814 
" S8 35 

" sJ ^^ 

ir 58 S9 


, 4 59 3' 
, 5 3 39 
'574 
, S i» 5 
'.S '6 4 


* 7 

4 ' 
4 8 

4 ! 


19 o»8 
,i j6 ., 
il sa 13 
i>4g 5 
18 43 S6 




3 4 
3 4 

3 4 
3 4 


11 38 17 
"34S6 
11 ji IS 
« 17 34 
11 13 51 


II s6 " 
"I 5! S9 


;l.'tl 
;ini 


is 

3 5 
3 5 


so 37 11 
10 JJ a; 

aoi9iS 


I. 59 "> 
u S9 « 

" 59 IJ 
" S9 47 


i S*8 3 
, S 3i4< 
3 S 3«4' 


4 9 
4 9 
4 « 
4 


i» 39 48, 

ii:n; 


.6 .1 S9 35 
17 11 S» " 
.B It S5 7 
IP ." i! 54 
10 11 s8 40 
1. -xi-i% iB 
« .< 1% .6 
ij 11 s» 4 
M »« S7 SJ 
1? 11 J7 4« 


>4 
•4 
>3 
»4 


■ 39 J 

1 43 a 

1 47 I 
1 JO s 
' 54 4- 


3 4 

1: 


„ 11 46 


iiii 


■lis: 
■is: 


33 


10 ij 30 

1011 3a 
10 17 34 
10 13 34 
fto 9 3S 


la ji 


1 5 40 5 
3 S** 

lili 


* 

4 


)8 19 1 
"8 '4 S3 

18 lO 44 
ig 63+ 

18 1 14- 


I S8» 

« J 5 

* 9 J 


It 

14 


« 1,6 

1. S7 S' 
»« 54 7 

11 so M 

1^463* 


lip 
I, ji .J 
,1 56 ,1 


lilt' 

•iii 


• 


-0 S 3* 
" 1 35 
>9 57 34 
'9 S3 3* 
19 49 19 


11 I 17 
la I 30 
la 143 

"in 


;!H! 


* ■ 

4 I 


IT 58 '* 
'7 S4 4 
1749 54 
■7 45 4S 


»« "1 S7 3> 


i 
S 


1 17 I 
1 10 ] 
» 14 4- 
>18 , 

.3»> 


3 4 

1: 

I 4 


>i 4> so 
»l 39 3 

:;i;;i 

9 11 .7 39 


II S7 6 


, 4 H 3 

' 4»»4 
J ^164 
° 4104 


ii 


.9 45 »6 
19 41 ij 

' '9 37 "9 
■9 33 15 

* .9 19 I. 


la a j3 


"7 37 X7 
17 3j 18 
17 »9 9 
.715 
.7>o5» 


11 












" V " 


" 4 34 S4i' 


^ lU, 6 











d by Google 



and NAVIGATOR. 



TABLE of Clocx-T.«. .t MOON bj ^ SVK, th. SUn'. ki|ht AfenAon, »od hi) C<>i>.p>««« ^ kight Altenfioa. or D.fti;« of 
A;a from Che flft„A«, in Tim^ .ccording to M. D* Z. C„7/r, «do«J to C™.«rf ObfcrviwJy for ,760. 






StFTEMBER. 


r 


« Noon by 


Dif. 


AftuGoD 


Dif. 


Co,OR.A 
r fr. Mcr 


Clock 'riir 

11 Noon b 

thiQ 


D 


ArnnfHmlDif 
InTl™,.. 1 


CO.0R.A 
In Time, 
y (i. Mn 


Clotk Tim 

It Noon b 

the© 


D 


Rinh 
Afcenfion 
n Time. 


Dif 


C0.OR.A, 
in Tim«, 01 
r fr. Mtr. 


b. D. I. 


•• 


h. ni. 1 


en,! 


X *;-..■ 




1 


h. m. 1 


tm.. 


h. m.-,. 




h. m. , 


n. ■ 


h. n,. •. 


3 

4 
5 


'» Jio 
» 3 3* 

11 J 4. 

•» J S3 
11 4 4 


9 

9 
9 

I 

7 
i 
6 
7 
5 
S 

s 

4 
4 
3 

3 


6 43 I* 
<47>3 
« 51 3' 


♦ 8 

4 T 


17 16 44 

»7 i; 37 

17 8 99 
IT 4 at 
17 14 


IS j 47 

>• 5 J* 
" 5 33 
IS J 17 


4 
i 

i 

t 

I 

8 

9 


lilt 

9 3> 
9 7 I 
9 " 
9 '4 5= 
9 " 3' 


3 JI 
J 50 
3 49 
I 49 

!S 

3 47 
346 

J 47 
3 45 
3 45 

3 44 
3 44 
3 44 
343 
3 43 
3 41 
3 4* 
3 4' 
3 40 
3 40 


IS 4 »o 
IS 19 
14 S6 3! 
14 5* 48 
14 48 59 
14 45 «o 
14 41 11 

'm'3-3 4S 
14 JO 
.4 16 IJ 
14 11 »8 
.+ IS 4j 


" 59 33 

"V' 
;; si H 


'9 

'! 

'( 

II 

10 

11 
10 

H 

11 
11 

to 
ti 


'o 43 S3 
.0 47 jc 
10 SI 7 


3 3 
3 3 
3 3 
3 3 
J 3 
3 J 
3 3* 
J Jt 

^ K 

3 3« 

3 J6 

' H 

3 j6 
1 3& 
3 35 
3 35 
3 3" 


13 '6 7 
13 11 JO 
.3 85J 

n s "5 

13 > 38 


I 

9 


" 4 IJ 
11 4*) 
11 4 1» 

11 4 4' 


7 3 S3 

7 7 59 


4 6 
4 6 
4 S 
4 .5 


.656 7 
i£ Jl . 
"6 47 SS 
16 4j JO 
■6 39 45 


IS 5 »« 

ill} 


" S! 53 
" SS 33 
II Si i» 
" 54 S' 


" S 35 
11 9 11 

■ I itf » 

11 ij j4 
II 17 9 
" 304s 

" 41 3" 
" 45 7 
II 4 4S 

.. JS Ii 


.1 54 SJ 

IS SO 49 

IS JS 51 
IS 19 15 


': 

«4 


» 458 
'« J S 
11 J ij 


7 J» »8 
7 36 3' 
740 34 


4 4 

4 4 
4 3 

4 ; 


16 3s 4= 

16 ji 36 

16 17. 31 


" 4 40 
11 4 30 
11 4 10 


;■ 


9 16 14 

9 30 
9 33 47 
9 37 3> 


16 

19 


11 5 41 
w J 4S 
•« J 49 


7 44 36 
748 38 
7 s; 19 

7 SO 19 
B 3, 


4 • 

♦ ' 
4 
4 ° 


WAT. 

IS 59 1' 


11 J 4J 

«» 3 33 

;:!■; 

11 1 5» 


13 
14 
14 


9 45 ' 
9 48 45 
9 S» »9 
9J6 li 

9 59 55 


<4 '4 S9 
'4 "1 15 

14 7 31 
'4 3 48 
14 s 


" 54 JO 
.1 S4 9 
" 53 48 
" 53 *7 
" S3 T 


•AM A 

;: ;i ;i 

11 7 41 


11 
11 


11 5 s» 

'• S S4 

I. 5s8 

>i 5 ;S 


8 438 

8 S ]g 


4 
' *! 

1 sf^ 

3 57 
3 !« 
3 iS 

3 55 
3 54 


'5 55 M 

ij Jl 1* 
>S 47 »4 

's 43 16 

«S 39 18 


IS s j8 

;: I'l 


'5 
\i 

19 


10 J 37 

10 1440 
10 18 «o 


IJ S6>1 
13 S» 4' 
»3 49 ° 
'3 45 «> 


It S.4* 
" 5» »S 
11 SI s 

II SI 44 
II SI S4 


" 55 54 
II J9 JO 

:: 14 

IS to 18 


3 3« 
3 35 
3 37 
3 J6 
3 J7 
3J« 
I 37 

J J8 


11 4 6 
It S3 li 

11 41 '8 
II jB 5s 
" 35 15 
" J" J7 


it 
»9 

1" 


" 5S| 
.1 s S7 
» 5 S5 
»» 5 SJ 


840 9 


'S 3S !• 
'5 3" 35 

'S »7 40 
'S »3 4S 
■S 19 S" 


IS 1 19 

ii li 


17 
17 
iB 


10 ij 39 
10 19 19 

.O Jl 38 

10 36 j7 


3 39 
340 
J J9 
3 J9 

3 37 


1338 
IJ 34 1) 
13 30 41 

ij 17 1 
"3 *J 13 


I. SI 4 
" S° 44 
" so »S 
i> so 6 

" 49 47 


>9 
19 
■9 


■1 'J Si 

WAV, 


L" 


11 ( (O 


8 44 « 


1 Jl 


15 'S S8 


'l_J9 SI 


' 


10 40 14 


.J 19 4« 




■ 














1 
1 
4 


114918 


iS 

i« 

'7 
■6 
16 
ifi 
>i 
•5 
'S 
') 
"4 

'3 

9 
9 

1 

I 

6 


11 39 '7 
.1 4> SS 

"4S 34 


3 J8 
3 39 
3 38 
3 39 


.1.8 

11 14 M 

II 1043 
II 17 1 

» M >6 


11 43 49 
11 43 49 
II 43 50 
" 43 5» 
" 43 53 




I 
1 

4 
6 

7 
8 
9 

'3 
13 
14 


'4*8 J3 
14 ]i 30 
14 36 >7 
1440 •( 
14 44«5 


3 S7 
3 57 

3 59 

'A\ 

4 > 
4 ' 

4 » 
4 J 
4 5 

tt 

4 7 
4 7 


9 3' »7 
9 »7 JO 
9 »1 33 
9 >9 J4 
9 <S 35 


" 49 43 
II 50 6 
II so 31 
11 so SS 


>3 
»5 


.1 ,. 4; 

l< 41 IT 

•.I'd 


4 so 
4 " 
4 11 
4 " 

4 S3 

4 "3 

4 14 

4 »3 

4 IS 


7 17 '4 
7 »» 54 
7 '8 33 

7 14 »i 


i 

\ 
9 




11 50 IJ 
" 53 S3 
" 57 34 
IJ I 14 
M 4 si 


3 4' 
3 41 
3 40 
3 4" 


>l X 16 
ic s8 4i 
'»5S 5 


" 43 S7 
II 44 I 
" 44 i 
II 44 n 
"44 iB 


J44S S4 
«4 5» »S 
.4 jfi «E 
ij oaB 
ij 4 JI 


9.136 
9 7 35 
9 ) 34 
1 S9 J» 
8 55 »9 


I. s' 46 
11 i» l» 
II s» 39 

II S3 6 


16 

17 

:5 


17 J " 

17 7 43 
7 11 S 


7 5 17 

t SI 17 

647 51 


(4 


I. +6 40 
" 4< S! 


IJ 8 37 

jj ti 1$ 
I] 16 1 
•3 '9 45 


3 4» 

3 41 
I 4; 
34- 


10 s> >J 

10 47 41 
10 43 jS 

104015 
w 36 31 


11 44 »5 
"4+ 33 
II44 4« 
" 44 js 
"45 J 


,,'.,6 

IS M 40 

IS i£4£ 
1SS0 53 

IJSJ c 


8 SI .4 
I 47 lO 
1 4) >4 
<!! 7 


11 54 » 
" S4 30 
" 54 59 
II SS »! 
" 55 57 


iB 

»9 
19 

JO 

»9 
30 
!<= 

JO 


17 16 33 
17 »o 57 
17 IS »3 
17 19 49 
'7 34 "4 


416 
4»S 
4 17 
4 15 

417 
4 St 

4 »: 


6 4JS7 
6 jq 3 

6 ,546 


to 


" 45 33 
II 45 i> 

>' 45 '» 
•'j4i 


IJ 17 13 
IJ JO j8 

■J 34 43 

h 38*9 

IJ 41 '6 


J4S 


10 Jl 47 
10 «9 * 
10 «s 17 

1* SI JI 


II 45 '4 
II 4S •? 
" 45 4° 
" 45 S4 

.. 4r, , 


'S»9 8 
»5 33 »8 
IS 17 »« 
'5 4' 18 


4 *0 
4 10 

4 'o 
4 " 


mil 

I Mil 

S .4 II 


II 56 17 
11 56 S* 
II 57 1* 
II S7 56 
II s8 »6 


17 J841 
17 43 ' 
17 47 33 
■7 5j 59 

■7 j6 li 


m 

6 3 j4 


11 
M 


It 4441 

" 44 n 

i"44»S 
"44*8 


13 46 4 
«3 49 51 
IJ 53 40 
■I S7 J' 

14 I SI 


J4* 

'3 


10 6 10 
10 a as 


" 4S ^5 

II 4S4' 
"4*58 
11 47 '6 
" 47 3S 


It 

'.I 
'9 


'5 SO » 
■5 54 >S 
'S S* *9 


4 13 
4 14 
4 14 
4 15 


7 57 >7 


11 sS 56 
II S9 »6 
II 59 S6 
11 sfr 

IS s6 


30 
30 
30 

JO 


.8 OS3 

18 J 10 
,8 94- 
8 14 14 
iS 13 4' 


4 *7 
t 1? 
h 1' 

i'l 

4 st 


S 59 7 

5 54 4" 
S SO '3 
5 45 4* 
S4'.«; 
S 36 54 

■5 »1 15 


*4 


■ ■44 6 
11 44 1 
» 43 37 
" 43 S4 


14 s 11 
>4 9 4 
,41. J« 
.4 16 se 
14 ao 41 


IS 

3 S4 
3 S3 


9 5448 
9 50 56 
9 47 4 
9 43 *o 


" 47 5S 

114157 
II49JO 


11 

SI 

■1 


16 n IS 

16 15 J* 
16 1,44 

23.2 


4 "7 

V.l 

4»9 


74845 
7 44"» 
7 4« " 
7 J5 SJ 


11 I 16 
M I 55 
w 1 SS 
IS * 54 


19 
19 


,8sj * 
18 IT 33 
iS JI 59 
iB j6 ij 

1840 JS 


i» 


"«J2. 




J jj 


_lJS.iL. 










1 ',' } i' 


_ 


18 45 16 




.S'^« 



DigHizcdbvVjOOQlC 



F- I 



rbe ROYAL ASTRONOMER 



Aftronomical QJJ E S T I O N S (applied tg NAVIGATION) mfwcred by the Tables. 



QyiiT. I. Ta find tbt JnfioMt if a Star faffmgtbe Miri- 
£am *■ aghrea Dof T 

RULE, MA Ibe CoTnplmurt of llic Sun'i R. A. in Tyxae, for \ 
giienPlKC, aBdDar>tNoon(bciniIbeDii)inceinTiinEafthF5iF<. 
noDDf AUtUanxht Mcridiin, t^nd in Tiblth p. iiG, 117.) to 
the R. A of the Star, in Time, found in the Citilc^e of Scut] ana 
ihc Sun thereof (tejcQinfi 14 Houn when ibore tbit Nutnber) will 
be the near Timr, fmm Noon, of the Stai'i Paflage through the Mc- 
ridian, lequirtd. 

TtfiutihtTimiati3rtU^. Sobtna from the ^htl'am, tAntij 
fMnd, the ptopoitional D«re»fc, in Time, of the Diftince of the 
Sefliin of Ar:u from Ihc Meridian, to that near Time [the Dili, of 
the faidScaion, or Complement of die R. A. of W San, hiTing hi- 
therto been only reckoned from tlie procoiinE Noon) and the Re- 
mainder will be the nafl Time of the Star'i PaOige, requirrd. 

EXAMPLE. Scjufndibt arnR Timi ef AMtbinn, fmbiij, tr 
f^i^ itt litriiim-tf Gieenvficb Objuvmrf, m Deeonbcr 30, 
1760? 
R. A. tSMAira, Jaa. i, i7Stt tj- Tab. 



7 b m > 

J 4 »' 36 

i>«. 1760J7 

... J +j! 



R. A. of Aliikarm, 1760, l>a. 30^ 4 ix 14 
By 7dt. p. 117. Comp. R. A. of the Sua, ■[ 1 
'Noon, cnlhitDay J-j 19 11 

Near Time of jilMmrti 




me of jViAarti^t Sou- '1 
k OhfcivalMy, ■76a, ^ 9 39 ]t P. M. 
....... i reqoired. 



Hente, the eontfl Timeof ^irJdHn'i Sou- 

thiogi It Grtaviiib 

DHimlir JO 

(ij> if ilii7imi»fttt/aaa Slar'i Sialtiiitwai rifuinJ, f< Antigoa, 
iar^Weltlndiei, tr at awf Ptati tt Sii 60" Weil LiaigiirJt fisw, 
Creenwish Olfimtlerf, lit fillavn'ng Ru/i mwjl ti rrgarJril. 

FIRST, Any fima Siar if obterved, ippirentlf, to iccelenti, or 
returntothe JMfri^i'wTOf the fame Place /Mnr, each Nitht, than on 
the former Night, b* the I'ftaft of the Sun'i R. A, in Time, eaA- 
wird, l/fi the innualor propieute Motion of the Star, in eith iimnal 
RHbtuIion of the Earth, (aflwitd. Tint it, each Star ntarni nearly 
jD jgt fitBiT io the fame Meridian, in about i\* jC" 41 mean Tolar 
Time, (f»f- *9) while 3600 of the Earib'a E^oator ii revclnd to 
Ibe a/liiuird; eiBGag therebw an apparent Motion or ReiolutlDn of 
the wholeHeivena, to the h^ifivMrJ. And, while 36^0, -f- the In- 
ile R. A. Sun for 14 Hoori, it reallj reuttmi Ea/lwrd by the 

361 

e Arr, in 14 Houit, when the.fuii letutr.s to the fame Meridian, 
entheSior, that wai the Day before on ih:! Mcriniin with the j'an, 
llliitM ihtvbtltaprljlMrtafciif rUS:,-',^igh, 4fcf,Jka, \t£tibt 
_/ffA Afm/M 0/ ibiSlar, m ibar Tmc, le lii -jicfi-word „f lit 5«iij 
IbalnSimthailVKii. Confennently, that .'-iir muft paA the Meii- 
IQ, each fucceffite Day, fooner and foonei tinn tSe Sun (pafiing it 
Noon) iccoTding (d the -mfirm diarail, ;>:'>! ^eriaili innoil Mo- 
tion oC iheEatth, afia^; tiJl, a Ijttleaitct the Year'. End, the £m 
and fhar again mta. 

Thii Inttrvil of Time will be proportional to the D-fernu of the 
Sanind Stai't annual Motioni lajliriy, when the £011, thai departed 
from (he Stai, fullawins him ata Dow Rate, again otettaitet thal^Cdr 
in hit annual Circuit, being Gmi tar in (hit laitance, to the Mi-art 
HaaJdepartiagfrom, amt overtalcing the J£»r ifnJ of ■ Watch : 

. ^^ ^-j the f,„t Way, in a Circle, at the bme Time, and al- 

ig after Ihe tune laiuval. 



Eatth't Equttor, tod -^7— '• fnpi^mlj mored e 



, catteity, by 



NOW, Ai the Ln^iiida of the Earth are meafored, is Time, br 
the Sud'i P^fligc from Noon to Noon, from and In the Meridian of 
Ihe Cam Plan, on the Earth'i Surface, which Place it daily adnnced 
to iheu^ttum/, tlie Diiierence of the Sua'i R. A. in Time, aUPU- 
ca to the wetlward thereof ate advanced to the MjhMr/ia thit Pro- 
porlioD. And fioce the Motion of a Star, (he fame Way, or eaft- 
wardly, it iaamfijn-aiit fir m Day, and at all Slin accilmu wi'Ji the 
Increafe of R. A, of the Sun, in 14 Houtt, (while jfioo Wifi Laari- 
ladi it adraoced bv the Eatth't eallerl} Rotalioo, auri laftrlj, by die 
Dif. Sun'i R. A.) therefore, 10 find the ^cccJiriliMof any Sur, or 
ill foooer foulhinj, in any Place of ^0 Leagii.J, from the Firfl Me- 
tidian, we have chit ^ . 

GENERAL RULE. Aj i4l>Wj) Longitude, ^rtAewilutlonoftht 
Einh, I'l rg 4D i;i Sun'i R. A. in Time for a Day ittri Moiion dif 
vanal to (he caititaid, or ibi( Time by which the fame Star foone 
return! la (he fame Meridian, fe it any other 9^ Longitude, or 4 
Wed, Ihe Longitude of yArijva, » Ibe proportioiuJ Time, or 441, h 
which that Star it idraneed Id Che WcAward, or come bonci to tb 
Meridian of (he Srnmi, than to that of the FirJI, Plea. And mul 
be faitreaiJfttm (he Time of ihe Southing ii the firft, for (he Tint 
of SoDtbing in the fecond, Plaa. ' 

The Soothing of jtldtiatam, at Orttmoiieb, 1760, ? h m 

■D*- JO t 9 M 1^ 

At f 0* or 4^ Well Longitude, proportional Incieaft R.A. / 



Vti of Gramtmch, \ 



N. fl If ibt L'ng'iuJi 0/ a Second i, Eaflwaid cf a Stft F/aa, tin. 
taj Star fitlbt, fir thai Lmriludi, frtpsrllimlly later ikai at iki firfi 
Fleci, at ]6ao Eafi Lci,glia£it 11 iti San'i Immajt i^R,A.ffa Day, 
i^Tim, iting tbf Sfiil.ag Utir fr j6o» Eafl iMriiuJr, r a Day. 
mita'grti Rewr/n/ ri* foriMT Rule, ibt fnforlmial Sljaiiiiij mafi 
it added » rir Saabiag in ibt frpFiaa. 

Quest. ir, TsfiiditibaiSlar/mthiiuat-ljat ggiviaTiiTK 
•» a given Dirf ? 

Find (by Tablet, p. 1 1 6 and yf )■* (be P 
' " ■ 'hich add the gp-eo Ti: 

Houn, uheWCthj" 
r nelieS Time t'o ii 
igajnit it you will find the N 



Numbct. — Seek fo 
•f R. yt. ,f Start, and. 
nearly foolhlng repaired r 

EXAMPLE. RrfnirrJ vbar Sii 
Nighi, in December jo, 1760 ? 
ByTirt.f,lI7.R. A, Sun 



•ly fattt, <tf9'4i»»jt, 
Noon on that Day iS 40 49 



QxiflT. III. 7» fiiid^i^imttf RifmgtaiiSttlinj, af 
pvtn Sl«r, fir awf Day and tear, at a giiim P/ace i tht 
Time tf Seutbing ef tbmt Star ftr the fiaiu Piael itiaj frfi 
ftiad, w given t y 

RULE. Subtiaa and add the Star't Semi-Doratioa Arc, anfwera- 
cioittDecJioBtion, and ine Plicc't Lalitode f/Mt^ fy ibt fnttiiag 
Taila) from tad 10 the Time of the Siar't Soathing giien, and tbi 
RmaimJrr and Sam will be the rc^ieOlTC Timn of that Star't, RiGsg 

and Seidsg, n^uircJ, 

EXAMPLE. Lttiihtrtjairidffiiiiibt'IiitutfRiJlitniSiuiwg 
^Aldebarao, H December ]□, 1760, M Giecawich Ohjir^aiirj, 
- " idesiBil'jN. ■n//ilneiye<«Aotigaa, Laritudc 17a j' N. t 



,, Google 



W N A V I G A T O R. 419 

Aftrohomie%V'Q:bBSTIONS (applied ta NAVIGATION] iiifwered by tho Tables. 



AldiiaraM tvathi »t9K<ttJKb^htemxorj, Die. i h m 

JO, 1760, Ibuiidbytlueft. I J 9 39 

tdiiatioa at ^i/ilmm, «t tbitTims, -'*- 

andUt. $1" i V. The Scm. Duratir 
(in Ptia aoi «in/aoj] ii found 



itTinw, i(»T 
eringtovblch/ 
Ihiration Ace r 
d . , , J 7 iS ]o 



jl P. Mi 



AUiiam nkt, ■ 



Ciwtluil 



Gmvii'b, D". jo' 1 II S Afleni. 

Seu7 (7 K 8 

1760, ^c. 5]t* 5 S t Mom. 



at Asifiui, rirond bji Qj^dl. I. ) h m 1 

i>rc. 30'. J g ]S 54 P, M. 
Sun. Duration Arc iDfmiiiit to Lv, 17° N. ? 

vA Decl. 16' H. ('in/, aoo) ii found . . J 6 la « :p 

jlli^rinrifci ■t.iltfilfsa, Z>k. ^o' 3 t6 J4 Aft. 
Sett ? 16 o 34 
ijCot i)«. ji.^ 4 o M- Mora. 

QuEiT. IV. Tt fiidiit TimtafSm RifiBg mnd Sitting 
! aig Flact, fir amj t>aj «f tbi Mextb, tatd Tiar gi ' 

RULE. Snltna tai add ibc Semi'diuml Arc. aafwcnl 
Latitude of ths Place anl Sun'i Declination, for xhr Day and Year 
giTen./na *ai f« la Hourt, or Noon, and the RrmainMr tniSim 
will be the icfpcAire Timet of Sub RUiii| and Setting, required, 

EXAMPLE. r./WtfaTj-.j/Sun-Rifiagfl.J Setting, m Ap, 
ic, IT59> ai Ctaatiiick-Otfirwaitiy, a*d /iitZi/ft nr Antigua, in li 
Vti-ioUa f 

San roDthi, ID all Pbuxi . . » o O 
jifr. 1$, I7S?. 3^ V'- »'"'■ •?■ t'" !*■ '94n 
A'lDecl. (D'y laODer, n found, accord t I 
tftXi.7»69.'*'''«')"'4S' S'*' ''■»'>'^^- f 
^le to which, and Lat ^t" tii.(mPtg., \ 
totai'ia3)theSa(u-diurnalArc,iifaundJ 6 5] jo ±p 

Son rifet at fJi'WimiV*, 1759, 4«r. ijJ j 6 jolillowrroi 

Sett « 53 toj RefraQ' 

N, ^.'Vbt Situ-iHini*! Jlrti» Unn, Ac. hj/cm^i litTimtrfSiii 
St'i'l- ha,. 

Noon 
Anfwenblc to 9" 45* N. Ded. Sub and Ut. 
170 N. (■" P' *°*>) Seoii-diurnal Arc 



In the Tccond bitf Page 10;, under in* "S. Lat. and i|ainft i< 
Declinition, (the iolciior Decl. lefpeOing the fupctioi Lat. right up 
and down in the fame Line) fUndiai° B' Ampliladc Soulherlif from 
E. dtW, required. Tiiii true Amplitude being compand with the 
magnetlcal Amplitude, the DifTennce will be the nagnetkal Vaiiatir~ 
of the Cooipafi, requind. 



In the firfl halfPieezoS, under S. Lat. 44.0 and againn 11° S. 
Declination, flindi 170 xo' Amplitude Southerly fiom E cr W. re- 
quired ; which being compared with the maenrtical Ampliiude, ob- 
fened, the magnetical Variation of the Compalt (bong the DiAcreoce} 
will be known. 

N.B. Thi famt Mitbti li It ti thfirmd i:i ditmsiningibi Jmpliiajt. 
■/ Rijift "^ SiltUg tf rbt /mrf Stan, if livn Dicliealiini, luhiH it, 
LaliarJt if lit P/aci 11 rrvm. By vibicb Sun lit magwaical .^mpli 
may li obflrvtd, and iStmci, lit m/gMtiial Varia ' ' ' ' " ' 
/«.<«/} btiMg,b,Difm,tfftbtfiivnjtmfbl»da. 



n i/fbi Om^fi 



^ 



14 30— Setting T 

>■ B juft 14 Hou'n. 

At jbtipu, 17S9, jlfrili^* 5 4j 30 RIEag. y H f„uwiitHil 



QoisT. V. Tafndtht f««*i Amplitude »/Rlfingaai\ 
Sitting Jnm til Etft or Weft Peiati of iht Ctmpa/,, o(eeriL«g 
ta (wy LalUudt and Dir/inaiian of thi Sua gyvin ; fir diltr. 
imjBg '*' nwgoetical Variation b/. iht Cumfa/i f 



RULE. Under the given Latitude N. or S. from Page :04. to 907, 
at the Top of the Pagei, and agiinll the gJTen Declination of the Sun, 
N. or S. on the Side of a Page, at the Angle of Meeting, you haie, 
It Sight, ibe Number of Digrtti anj lUinuiu of jhiflitrdt Nwiba^ 
from E. or W. Lit, N. but Sarlirlj Ut. South, in the lirll Hall 
Piu. Alfo t\itDigrm ani Minwla tf jbrflinji Stmlhtrfy, from E. 
and W. Lat. N. but IJinhvlj Lat. South, in the iccoad half Page, 
By which true Amplitude of the Tablet compared with the marniiin/ 
Amplitude, found by the ytfn/'m/i-Compiii, at the Sun'i Riling ot 
Settina. (Refraftioa being allowed for in the TableiJ the Difrrrtia, 
or wmK/m' Virijtion will be known 1 the £,c«/ioi pifta of Mlg- 
netiea! Aijiplitode being the f*'ay of Variation. 



Quest. VT, Tt Jtwd ike Length a/tht l^gefi Daj and 
Migif in aiif Laiiltide, -a bi^i Camplimtnt is UJi thorn the ." ' 
grtatffi N. tr S. Dieiinalim f 

WHEN the Complement of the LititiiJe N. or S. ii refpcQinly 
equal to the Sun'i gtealeit Declination N. or S. vix. tf %%' 30" (the 
Lat, being then 660 ]i' 30") mi I'bc Mtiidiaa jUiiiudt alwayi equal 
to the Sum of the Comp. Lat. and Sun'i Oeclinaiion to the Pole 
of the fame Nimr, whiih Altitude ii alwayt equal the Drfrijpn 
Midnight) it ii evident, that tin ttat Day, the Sun doc t mt fn 1 b 
touchet the Edge of lh& Htriaon at the Noith Piit o( ihe Meridia 
oppofits W Noon i and then afcendi to the South Part of the Meridi: 
tt Noon t wh(^ Ahitade, on ihatDay, ii Cta^. Ltt. + ajt ig' 31 
Nwib Dit/lntim, and the longaO Dij tben, ii joS 14 Hourt,. 
Thtrtfon, in all Placai, where theDi^aKM tf Lmladi is U}i ibat 
tbtSn'iptat^ Ditiimah,; on that very Dtj when the Son'i Dcclir, h 
equal to the Complement of the LaiituJr, ihcSun viillm'fn, bnt touch 
the Hotieon in theoppolite Part oF the Meridian to 11 at Nooo, 
M ibi Itmgifi Dn i* LatimdtdS" 11' 30'} and the Day will be 1) 
I. In the Sun alcending from which Uoclinition , 
C*mflrmtwl tf Laiiiadi) to the gteitefl Dedination, 
back to the fame Declination again, the /vj^ Cay in 1 
Latitude will bemejfuied | and may be determined at Siitit fitmrrfa 
by our £riibr ffinur'ifrom p. 194 to 196, anoiding to what 
Sun'i DecUnst'oo ii i bebg of the /«( Nammr.t, ardi^uil r,i^ 
Ctrni-.'naBi if Luiinil,. 



Here the Complement of Latil 
Jorth, aoTwering to Mi^ 13. ■ 
w/ii thelon|en Day in That Labtudr rijn^ 



,, Google 



fhe ROYAL ASTRONOMER 



Altronomical QUESTIONS (.ppUtd to NAVIGATION) rafwaed by SphmatifiiO 

LOOARITHMS. 



I, QoiiTioR. T» JiMd lht%mCj frtfint J>teliMalionfitm 
t PlBCiin iht Eclifiie (U t* Xo» 19' 40") ohJ bil grtalifi 



DuiiMatim{zi'' 28' 30') givrnf 



PROPORTION. 



r L«ng. from f So< 



«• 15' 4 



V. QystTiott. To Jiaitbt Swit tnu JmfBhJt vf Si- 
fiag tr Stttimg, th* Latitadt af tht PUut, Greenwidi, 
ri« 28' jiy. N. and lb* Stm^t Dteliiutim, at Rija^tr 
Sttiingf 23" 5' 18% N. htwgpvtnf 



ToSiDCprtisncDcd. H, Rijuirej . 1 . . 11 7 i> 9.504O4<il 
N. a. In [be ihove Praportion, ar Jinfr, tbe Son'i LarnnJi > il- 
wiyi taluD from the next t^uino£tia! Point, jlria, or iJira, Cob- 
(cqucnllT, if the San'i Place ii under i%o», in 10^ of ihe Grft Gi 
Si(i](, ^^nVi, Tutu, Gnun, Caiicrr, Xm, ^i^ri, LiirtJ the De- 
GlimtionwUlbeKonb. If above i8e<>, iotbclail 61 Sifot {Sarfii, 
Sapin-j, Caprian, jlfrtriai, and FiJcaJ the DediDKian will be 
Smtt. — Tbii Qjieflion u verj' uleful ia Kinption, 

II. QvfisTIOH. Tt fiaJ tbi San^l Ln^Htde Jhm Ariel, 
or Libra, bii fnjtnt DttlinMi«H N. ar S. h*i»g givm f 

LET tlwgfiea DerliNtiim be *]• 7' it" N. 

Connrfe of the former PROPORTION. 
_i Sine ireatefl Dediutioo . . . iy il' ]o* . 
To Sine pctftat Declination N.otS. 13 7 il ■ 
S* Radioi go 00. 



ToSiDe0'«Loii. fir.T>'»'*^"l'-'o »9 ¥> , ,,^, 

l), B. Thli<IgcSiOD it of Ule inAflnmomical Ob&ivitisni. 

in. QunTioii, T»fiultht&MM^s^gbtJ/eit^»m/rtm 
Ml fUat im th* Etbptit, n ie« 1 9' 40*, giWH f 

PROPORTIOH, 



ToTa»|.Swi'iLong.fr. «¥• . . . (00 la' 40*! 10.7(144]} 
So Cof. pcalefl DerlLMtiM < • > • sj ai 30 1 9.9S14S01 



iB Ti t[> Di ibentba^thMpiTtMiM/ATcb, btheSon'i tlfbt Af- 
ccAfioA ftan 'l^. If UiPlaeeii in tb»tA^stdmi, ZE. ^ tqi. 

■ - 141b MMTtioMlAK of tisbt Afeenfon fc'^^"-'^ "- 

rij^t Afc«nfiOB tma Arim. When in the 
ni, /, the 4lfa piDpoitioBal Arc ii the] 
add) to iBo' n>r ri|bt Alcen&iB from Art 

i.yf.=.y.,^ . . . 

light Alccnfion inai Aittt 

IV. QxiBiTiox. 7* f»d th* Smfi Plat* in ti* Btliptii 
frim th* Shm'i light JJifmfiem 79* 38' 25' Jhm J^t, 



o Tan. San • R. A. from •(*, teqain4 70 

C^ When the Seu'i Flue i* bi the iS Su 

iB (|r, >[> Di ibentha^thMpiTtMM/ATcE, 

fiottftooi'l^. If UiPlaeeii in tbtiJJ^ , ,^ _, 

nrbe4lb Mportioaa] Ace of tisbt Afcenfoa fubtnOifreoi ilo, 
the rij^t AletnfiOB iiem ^a. When in the \i t^oJma, a, 
igbt Arccnfian Ron A, and 
1. And wbcn Ihe Sut M in 



p. Dccliutioi 



r PROPORTION. 



To Tung. Snn'i Lon|. fr. ■»«, reqd. go 19 40 10.7614433 

N.B, In the aboie PropoTtioa, the Tangent of rigbt Afceafioa 
tDB<1 be taken (or the Degteei of tight AIceaGoii fiam .^u, or Litrt, 
or nearafl eqainoAIal Point, bj which the coirelpoBilent Lengitadt 
limm citber of tbofe Point) may be eafilj dtterauBcd, u above. 



PROPORTION. 
A* Cofine Lat. 51* iV JO* 



Zagmn'ltmi. 

9-79*j87J 



ToSuw Son') AmpnindeN, leqnired. > . id e 3 9'799^sSi 
N. B. The jhtUiuJ, fi tiwart of the &ma N«BH witb (be San'i 
Dcdioatioo in any Latitude N. or S. 

VI. Q.IIIJTIOK. TtJindtbtTimttftrKt^MMRifingMid 
Stttiag htf»r* and afitr Six, hj th* a/nnficmai Diftrtntt, 
%mlh thi ttngtb tf Da} aad Nigbl, tbt Latitud* »f ibt Flat* 
51'' 28' 30* N. and Sui/m Dtdinafiaa, (at Sifing ar Stt- 
ti^gj 23" 7' l&' N. btiaggivia^ 



PROPORTION. 



90* a* o' 

. SI <■ V 



To Sine AGxnfional Dif, requirad . . 3» ij 5S 9>7494i6£ 

N. B. Tlf Smm njiiiifirt Six, win rif DtUmitiin it if lii Stme 

tdatwiibibt tieuuti Polej lat tfio-Six, nttm tf tit contiaiy 

f/ami, iytbiiAIaaioiuXDiffiraialtnudlM»TirMi tittmrg 15* i» 

a ' * b m a 
3* »S S* = ■ 9 44 kj »•''» 
+ 6 



Semi-diomal Arc I 



9 44 SanAtk 

250 10 Santifei. 
19 s) Length of Daf ; 



Doub. T. Settii^ . __ .^ _. _ .._ ^. 

Comp. to 14, Doub. Riflng . . 7 40 ]i Length of Night. 

A> double the Time of Sun Setting givet the Lcngtb of the Ibj, 
• double tha Tone of Son Rifing girei tbe Length of tbt Ni^t. 

VII. QuilTIOH. t» find tbi fbU^ JfctnfiKi «r Btjiem- 
fiamtf tbt Sm, ^1 DttknatiBn (at Rifing tf Stttilrgf 23* j' 
i8'N. and Latiliid* ef tbt Piatt, ji" 18^30' N. buMg 

FiadtbeR. A.3aafT0m<r> brlll, QueSion . . lo> ta' 4«* 

TbeA&«i*iMalDir.brVI.q5eftion 31 15 5I q: 

U.S. Wkeatbe£armAandSun'>£«//Mrf«aRbotbgf the/aw 
Name, N. or S, the Alizitf onal Diflirence U/ra^i fcon tbe R. A. 
for the liiBpt J^ea^, tat aiUt thereto for tbe Mift D^afit*. 
"it. 

When dw Latitude and Sno'i Dalination are- of a Jiftmt Utat, 
(N.aodS.} tbe A(ccn£onat Difference uEA to the rigbt Afeeofion for 
tix liEfm J^tBifca I tad JaknSi tbeicAnaa fer the. aUifM Oijan' 
/hn. 

If the J0luiflhmt I ttflerenec eiceedi tbe right ArcenlioD, yon unS 
tU |te« to tbe right AfcenGon, and then liibttaa tbe Jgiofimml 

Or, if r^t ArcenEon, and Afitmfim*/ DiRerenca atfirf exceed 



01 tbe ibUowint SAtm* 



yGoogle 



iod NAVIGATOR, 



AflTOMHDkkl Q.UBSTJONS (applied to NAVIGATION} ulwered by$/2mr«/PfcQFOKTioii tui 

LOC AKITHUI. 



Sff.Vmt i****i _ J firib, lMi«D.fitnf4,. 

VIIL QiritTiON. Ta fiid tit Stmi-Mmwti *r Snai- 
aoaumal Jrc tf iht Sun, w Star, tbi haHtmi* of tht Flat* 
^r' 31' 30* N. «w/ Dntnmiitn z^" 7' iS' N. ^ttn/ 
tiviHf 

' PROPORTIOH. Ltftfitim. 

Ai RtdiD) - .- 



Ji» 31' 30H It 



T»Cof. Semi-no^nial Arc required . . 57 j4 a | 9.}iui66 
Tuned iota Tima =£ jk «■ i ji ii benire g 
beiof tbe Time «f Sab-Setting j vhoft Complement to ii>, ait^ 
oB 441 ii ibe Time of true Sun Rifiag. 

^ Ham Itl ifiat/buMl Diffiraa ml ik St^-matnal Arc art 
atiBtyi ibt Ctmflimat ef ai antbir li urfi, (Bin) tht Lmihiit od Di- 
eEtlitm art •/ lit ftrnt Ntmt. Whn ihtt tre tf a £ftr«u Ham,, itt 
fingut Prtftrtim ftJi lU Smi-^mnnd An ef S» v Sitr, miiti 
ttt, ni Itt elUiiMiial Diffiraa art itia Ctmfiimau tf ow atalbtr tt 

IX. QniiTtOH. 7» /mi ibtTimt tf ^parent Ri/mg tout 
Sftlitie tf tht Smtt, *r tftbt lUtrn, a Star, er Plantt, Jnm tin 
lUeriitat, tbiDttUiiMitiirftUhtr, M that Timt, ami Htight 
of tht Polt, hiing ptttm T 

E. Sappofe the Lidtsfc tmim, iV> \i! K. 

o— '-"KlinattooXRiGng vi )» K. 

if.'t Zcoilli Dift. If tl if. ai !;ctrini 

- t. 

And Dift. of Siai or Star tttga the Pok. 

theL , 

, , ■ t ' Nune witb 

Ae Deelimtion N, »iiil S.) 

Tike j Sm nt iheJc j SiAi df * fpherical Trlufje. From vbich 
\a^ take the Camp. Pole'i Hcl^t g celling wtut'i left the )^ ilc 

Frnn the /dw iijr tike the Sua 01 StiTa Difluice fiom the Pole 
nUlog whit'i left the iJ Rumtaititr. , 

Add^» Log. Sinet td xhtU Jfi tad iJ Saimaitn, ind igaJA tba 
Let.orjWi'H. 

Fraa) which Sn>, fabtnfi theXneof tb(Lo(. Sine of theCwnp, 
of Polc't Heifhr, tod Lu. Sine of the Dilhiice of (be f n or Star 
(ran the Pole t — Baff of the left Reminder will ba ibe Log. Sik 
of half IheStuorSiac'iiDEBbrDiflutcfromNoooariheMeiidiu, 
u Rifiof or Setting I which dcwbled, «id nduced into Time, «rill 
iboefbre be die irti hiirBaJ betweca the ^fartut Rifiug end Settiiig 
of the Sen, m Sur, uiAaTmx'iH ^aif^hnlhiMtrHiam, when 
. . .-. _».!._ ™ <a the Jidn Denomin*- 

-' Diacrencebe- 
I HoBn, wili 



IbeDcdin 



in end l^litnde of (be Place ire trf 



rfriW required. 
Sun'i Zenith KSaac* , ; . ao* 11' Siit ip. £_ ria. 
Cmt-Ptlft Blight .,..)* %aXSiiaiKbMBat/.r. 
J}i/.SaMj»mftU . . . . 7« .ij piral. 



tala Citif. Ptli"! Stirti . . !• Rem. 6t it Lot. S. | |.947M]E 

•I*hDif,lJaajT, ftb . . a. Rem. it 17 1^. &.| 9.67j6a45 

Oiakii^.Kai. to.ooi 



Fiaa . • Sam jg,6i>6»St 



N. B. IfaSlar, trPlattt, iadlttf Lag. S. iBOu'l a.iai 

al Arc, H4» ij' S4* "< — — 

-"-'•- ^\T>^... Sam i».77J,3qri 



/inr«/i«B!n»»!,» 



^aai-Dtrat 



FiMrMll lu 

S4* "< 
taArcArt 



RiMm 19.1401076 
Aij6oOiit*thelB- f jj* ix' jj" . . . Wo.jjiiioc 

tetvalofTime.betwLit ] ODub.iif «j 54^'' 37" 44' Sun im. 
CwoneitPiflageiiChio' j n 

the Ome Meridian, lb I — — — _i_ 

'■ lH'»S'i4'">tW 4 « 16 !' 

Sen)i-DuratIaaArc,r«- J rif tiVuf, 

C'rtrf, Which fubtr. I See p. tfij. tar turniag D^eea, 
m, lad added to, | Titne, arilimmicailj, 
the Time of the Stir I. 
or PliDtt'i Starbitg, that Daf, will (i*« the Time of RiSng and 
Setdng, rtpindm 

X. QOMTIOl. Tr fad tht <ttau tf tht Dof, frtrn tit 
Saa't DttSaatiea, bii tnu Aititad*, mad Latiladt af tht 
Placipvta I ■ 

RULE. Ii oMS^thefime u^aBfireria| the pieixdiagQ|idIki)]| 
Ib finding the Time of fffartia Son-Sife, euipi, thit inHcid of 90a 
]]', (the Son'i Zenith DrAancC'tf^rnrJ foa mull u(e the Compl. 
of theSaa'iAltiCDdcoblcrred, afta ReftaOian it allowed for bj 7"^. 
p. II. 

XxnMt, The Son'i Alticnde waa abfemd, at 5m, aaTuhtt, 
i7S7t lull 14'° 9' (or 9" 44B Dir. of Time) eiSward of Griat- 
viicb OiJrva<vj, at about g in the Forenoon, to be 470 4S' 47', the 
R^raBita then bciiq 47*, itducei It to 47a 4!' true Altitude. The 
Suu'i Declisitkn, ibont that Time, waa ai<> C N. by an Sfhrntri- 
in (it being thm about 7.^ 17^ III- ifiit Might, at Cn«wi5j and 



Camp. Sun't Alt. 41O 11' Side op, /. re^ 
Comp. Lat. • . 4a 41 1 Sidaiocluding (be 
San from Che Pole . . 6S 54) ^rei. 

Sam 160 48 
Fram . • . Half So u 



Take Com. Let. l.Jbw. 30 4aLos.S. 
TikeS«n'aDift.lr. Pak>a.£iai. 11 3oLDg.S. 
Diwb.Loc.Rad. 
Otbnvile. r 

Lt/trittaa. I FroM • . . Sam 
- - • ■ 9.70I0J.3' 
9-»W*SSJ 
0.117(64]- 
0.0301400 



8« 41' t 
S4 c 






L^ S. I 
Take . , 



iwi S" ii' •/=;•.; ^.Vt; ».«"«• 



,, Google 



The ROYAL ASTRONOMER 



jtrj ibmfiTi th, DKfiMiim if the Sun, Moon, «■ a Plinet, at ibt Tiat 
and P!«t of Oijirv^dn, ZtrVf,,/ ,ti M Maiiiom, m„JI b, f»rJ 
u tbe nrrifftiJini Tm, bI lit firft i^nJian iy *n Ephemeriikt, frr- 
pariiMidi7 liailnttmli/Timi, itnoixt ibt noi *txi ffma, fir «*(* 
thfi Der/iiaiitn, tre U ibi faid fpbeniendci TiJftBivtlj pvf. 

XI. Q.UESTIOH. Tofindtbt Sun or Star*l tna JltilMjt 
at a gi-vtn Tinu cf tbt Day, 2'' 57' 47' frem NeiM, w ti>i 
MtriMan, an Arc if 44* 26' ^O* i /** i'«a*i Dieiiitation t 
thai Tiat bang 
8'N. 



> 6' N. and tii L^tittiJt tf iht Plan 



PROPORTION. 



So Si 



IE Complemcat Aic Y 
le Complement Are X 
ePole'i Height . , ' 



9.94><i6S 
0..16W.9 

9.810763 



B. fFln tbi tatittdi and DaHnatin an t/' ibtfami t^amr, tbt 
ftrtffimi PnfvTitafiti, tb, jbummtb frsm lie Herlb Paat ef ite Ha 
nim i iul if til halttwtt ttd Dtanatiim an tf natrarj A'jima, lb 
ftrtganiPrtfatiiwfmii lii Aaimab from' lit Sialb PaK tf th* Ha- 
rixea, viiicb Aximub-Uliilti bring taba frvm JO«, wiH Iravt tba jim- 
fliladi n Ibt Ntnbaard ar Scalbmard tf lit Eafi, at Wifi Paitu *f Ibl 
"■rinwaccardiirilj,rifairtd. 

Xllt. QviiTiOH. T»fiMdlheAximutbtfiJ>iSK>i,M»«n, 
waPltaul.frawt ihi Dtelinttipn jo'sc/ N. Jbitudt ^-j" 30', 
andLatiiade c\« 32' ^vtn; tht DrcBnatita Uiug fir tbt 
Tim* a/lhi Mitudi f I 



D.3S 4« 



ToSiDeSun'i AltiMde leqDiitd 47 4X 

N. B. Acy. (ailraat frtm lit Sna'i Dipant fnm Ibt P^i fir 
ibt Art y, wbra lU lima frtm JV™, tr lit Mitidiaa, h bf, tttu el- 
go", hat aJJi « rb. Si,*'. Difia«ct frtm Ibt Pair, fir ibt Ac y, 
ki* lit time frim tbt Meridiaa iignaltr ibanS*' a- ao". 
t^ The above Propottioni find liie Side of any Sfbrrital Tn'aagfi 
Bppofite tOi|iiBR Angle, intloded bcvween two giitaSidu. 

Thni, jti Radim n Sim Om^tmnil £, nclaJtd, 
Sa Taagau hfi iitelaJirgSidi It Taagail A: X. 

Subtraft thii Arc X fiom the o(ber inelailing SiJi, when the in- 
cluded £. !• lefs thiD ao», but add it thereto, when the included ^ ' 
Srwtnthango", tJlii^tb* Arc ofCifdwic/or of the Sn., V. 

Then lay, ^ SiHa Cim^imi*i X h u Siai CaafkmtV V, 
. I II Sim Ctmplimnil lifi ietbiMag Sidi la Ibt Sift Cumf/hmal qJ lit Siit 
efftfilt tbt ialaded Anglt, 

XII. Question, Tt find tbi afferni AmpBtudt of 
ftifiag w Sitting »f th* Sun, Afo#», a Srmr, er Flaiut, tbt 
DicHiuttim tf tilbtr at that Tim*, and tht Latimdr ef tbt 
PUi*, bting given f 

amfli. Sun'i Dtclinationat that Tima ii ija 7' iS' H. and 
Utitnde 5i''iB' st/'itGrmtwfi. 

Here are p«n Q U. Pole 66« 51' 41* Side of. /, rrquiirtJ. 
ZrniifiKaance . , 90 3] o { Sidet inchiiliag 
Comptcment Latitude , .38 ji jo J /, le^d. vije. Aiim. fiift. 



Tak« O Zenkh D. I f 

Take Conp. I^t, » rem. 59 37 6 Log, S.l 
Leg. 3. 900 3j' a co.j 
Log. 3. 18 31 JO CO.] 



Apparent AmpHtade 39 jq 44 fr, the Sift Hoitherl]'. 
TroeAmpl.'by V.Qf. jg j 3 NorCfaerly. 
Oifi bee tiot and app, . 14 41 in diii CaTe, 

The (•/^'■'Aniplitudeecing ib much t^ utDn t/*nttrfy. 



Log. S. eio 
Doubled t*i 



Sun,,s.l)6j7.3 
Half g,B4]il5fi 
JSun'tAiii^ulhfr. 
J North required. 
N. B, ffita Ibt DtiUmaiin ami Laiiiajc err sfdifirim Natia ibi 
JEhA faJi tht Jximali frtm tbt Statb, rtfuind. 

XIV. QyajTiOH. Ta fnd tbt UtifmJt fitm tbtDttS- 
natim ao" 30' N . Aliitiidt 47" 30', and Aximalh *f ib* 
Sun wr aiy Star 111" ^t' I %* frtm ibt ti. gitinf 
PROPORTION. 



AlRadia,,orSine . . . 

To Tan. Zenith Diftance . . 
So Co.. Aunutb from K. . 

To Tin. Art. X . . . . 

Now, AaSiae Altitude . . 
ToCoi. ArcX . . 
So Sioe Declinatioii . 

ToCot.Arcy. . . 
ArcX . 


. 90" o/ o* 

■ . 4» 30 " 
. . IM 4» iX 

. . 36 M *I 

: : Ji i: :;"" 

. ao JO 




9.9«M5li 

9.73»«»«4 


9«M'7»S 


9.9:1396} 
9-S44JISJ 


y.6l90fi; 



=Y-X, 



Complement Latltode , . jS 1 
Latitude PHfi/rf^ ■ '' ■ . cj X 

N. B. If.-te bi/irvalita it >We immai 6 im lit fibrwlaw aaj 
6 1, lit Afltr^n, » Ibt famt Daj, al lb, /ami Tlmt lit jMimali h 
lift ibaa 90" (■a.blcb gtairallj btfpfu vibttubt DtUitnn and Lau~ 
laii an if diffinit Nemt, and ibt AxSmulb li lain fiam ibc Ssaii 
Ibtn Ibl Sam 0/ ih Acba X aadY, viiil itibt Caa^Itmtvi ./ ibtLali. 
laii, ■:Bitfi Cenplimiia will ii'ibi tulfiaJi rtfuirid. Bai if ibt Am- 
malb from Nant ii Iifi tbaa ho", aaJ Dnhaaliaa and Lalintdi tf ibi 
famtNaai, tbt Samt/ XaaHY leiait ibfCmflav*ttf LaiiiaJi. 

N. B. The foregoing PraporliaDi, ufwering Che- XIV (^efljoa, 
find the third Side of anj Spherical Triangle, when the oth:i twc 
Sidei and an Angle Dppolite Co oneofihi^Sidea are given. 
. Tbn, AaRadiui ii tb Jangent of Cbe kli Side, ia ii CoGoe iS ttr 
given Angle, (oppofitt to the greater Side) to Tingeat of an Arc ;|, 
Part of tht Bale wiihout or winiln the Triangle, where a PrrpendkuU) 
fatlf, fmta the End of tbe looget Side apon the remind Side '- - * 



yGoOglf^ 



tnd NAVIGATOR. 



AflronMiieal QUESTIONS {applied to NAVIGATION) BnTwoed by SfhiricAl Pkovdrtioh and 

LoCARITHM). 



jifain. A) Collie left Side i) Co the CdGjii of Che An Z, (wichoiit 

wiihin the Triangle, where a Perpeniticular fxlli, sacrjing u lit 
pvnjtigliippiJiitlilbigriaifr-Siii, I'l mtrtir li/itbmgo'} Se ii 
theCofioc oF the longer Side, Tr the Co&ne of tb* vltJtBafi, sr 
grislir Scgmenc. 

mtrt il nvP ic mliJ lijit Y it ibt mhtli Baft /tmad, ishtn tht gii 
Z.«cra/]goa, a-dlhciX.lht exirrul Silmcwl ihr-nf, (ahiciSt/rtm 
!t, fir the Lrr.ph^f ihi rmulnd Sid,, «■ SrtmrM. Bui if ill A ' 
givi* il hfi iha* go", /itnV ii itt grraitr nJ X Ibe liji SigmM sf 
rtjuinJ Btfc, vAefi Sum ir ibenfirt ihe labeli Baji tr Sitit rtfuirid. 

Thelic Ihiogi are dcmonllnble fiam 5^i<riu/ Trlgonometr;, 
whirh we refer che Ruder if he itrjuirci furtlier Siciifiaion, 
Truth of the Rutei, u here applied to PraAice, being liifficieiit far our 
Porpofe. 

XV. Qy(«TION. Tt find Iht Difiaict, iM Tiau, af tht 
Sim, ar a Star, from tht Meridian, tht .^xinatth fnm the 
North ia»»42' iz', DiclimHim zo" 30' N. aad Jltitxtle 

±•7" 20' at ibat Time, heitg given P 

PROPORTION. I^ariihmt. 

JO* o" CO. □.01S4114 



To Sine ingulu-Dift. froDlihe Metid, 37 i» j 

XVI. Question. T» find tht Aamnihe/ ibt Sum »r a 
Star, /rem tht Latitude ci" 32' H. DecliaatiuM ao'jo' N. 
and Dijianie at tbi/ami Time ef tht Sua w Star/rm tht Mt. 
ridias, j^^zz' ^*, being giiien f 

Take the San and DiftroKi of the Complemeat of the La- 
i Diftance of the Sun, or Stir, from Che Pole, 
jga xV Cornplemenl IdtiCude 

30 San OT Scu'« Ditlute from tht Pole. 



0.130607s 
9-98387SS 
[0.470867^ 




Agiin, A) Sine \ Sum . . . . ■ 5] 59 

ToSineiDifT, IJ Jl 

SoCoCmj. jiDift. fr. Mer. . . l3 41 



X=7g 



..05H341 
..470*67 



Y+X=ii3» 41 tiAiim.fr.N.req«. 
X— Y= ,5 58 jj^op.M. Ut. 

N. B. In the aboTe Proportioiii, uheo \ Sam of Che Comple- 
ment of Liticade tnd Sun or Star't Diftance lioin ihc Pole ttnti, or 
il left chin 90°, then X ii greater or lefi than co". 

Tie Silk tf lU Arts X aiidV it itt Angli if Aximulh frtm ibt 
tftnb, nd lb, DIf tract ifXadV is lit tibtr tr bfs Anglt, lnclMdtd 
ij ibt DifietKt ef ibi Snis tr Star, frtm ibt Zimtb and Diptma if ibt 
film, frtm ibt Ffit, viba ibe Sun ar Star's Ztmib Difara is Ms ibm 
ibiir Polar Diftanit, ibe ubir Side tf lit Sfbtrial •triargit btitg ibt 
Ctmlnstnt if Latiaidt. When the Polar la lefa than the Zenich 
DiAucefiemtheSDnor Star, then the Kffintnce of Z and Y it the 
Aiiniutb,udtbeSBmofXud Y the other ilteraate ^ oppcfite the 
Pole'a Diflance ftom the Zenith. 



O TbeforegDingPmportioiuiindthe^iofaiijrSpheiitalTriiatli 

oppofiCe to Cwo given Sidej, indading a p*en Angle, and therefore 
find the AngleofPofitionin Sailing by the Arch of a great Clrtle, 
continuilly Tarying that Courfe, trofi the Mntdjant, bettrut twt 
Place* ofgiviM Laiimda, and giren Digirma of Longitude 1 The 
Polar Diftances of tliofe Placet, and Angle betwiiC them, being ilfc 
giTCn, SttMr, Ztttt^tav'i I/tviiaiim, p. aE. 

XVII. QjiB.TfOH. To ftti tht LatitvJt tf tht Piatt 
fromthtSuiiDeeUnatsuniltf 18* N. and tit timt tf tht 
Ssus't Rifing thta j^ jO° 16*, bling given, 

III, Tom theTimeof Saa-Rifing before or aFlet Six Inti 
greei (by p. aS] which it called the iiAnf&M/Dillctence, 
Thai, 6I1 oa o> 



■ 9 44=3*' *5' SS* 
Then fay, by this PROPORTION. 



To Tangeotof LitiCuderequitfd . . 51 tS ]o I10.0990059 

XVin. QuEiTiOH. Tt find tht Laiitudt tf tht Place 
from Ibt Smfs Dtdinelin,, 23" 7' 18' N. aaJ AmpliluAt 




To Cofioe Latitude reaolred . . . : 51 aS jo I 9'794lS77 
N. B. IbtSiajifimitf Data 1lbtHtisa»,att tif.fi fir find' - 

ttt Laliudi tf Flaas \ tuaufi tbn cm imdir ibt Fimi if a Rigbl 

gl-d Sfbtriai Triangle : vibirias ^uifiluu tiwtom'ng jUlilaJi if lit ■ 
Star, itnviiH Rifinj in-Stuifg, and lit MiriJitn, ctn'i U anfvMred 
■ibea rtfilvirg at Oilifut aitgltd Sfitricel Trlang/r, ij Itoo tr man 

Prt/arliom ; at^l vihtrl ibai 11 ns DitHeatias, er lit San it Sltr In 

d„,Eafi«W>fi. 

XrX. QuEjTiON. TafnJthtlaiitxdtt/tbtPlactU. 
frem tht DecfinaliBn tf Ibt Sun zoo io' H. J/titudt tf" the 
San^-j° 10', and Tfnu ^ lit Day 9^ 30" 32' in /i# 3&r». 
sag being givtKf 



9 30 3» 



Sa;, At Sioe Zen, Difl. 
To Sun'i Din. fr. Merid. 

Sioe O DiSance from Pole , 

To Sine Acinucb from Sooth 



u sSsi?" ai' s' AngnUr Dift. &. Merid. 
firfi II find lU AniMulb. 

-- - " - O.17OJI67 

9.7851396 

97 'ji; 



30* 0*11 
69 30 a 



Aiimnth from N> reqaired 



ID Ibt Xirth Ss^a M yoUtii Ml ZlXtb ^^n 



,y Google 



ne ROYAL ASTRONOMER 



1 AfliooomHial QUESTIONS (applBd to NAVIGATION) arfwotd hy Sphtrieal PkOFO»Tioii mi 

1 LoflAKlTHMI. 



And fine* in Aximmb by ObTcrrMion twa tantij tm be tnfted 
to, for BndiHgthe Latitude, eirtpt it iaderiird from thfobfmed Al- 
titude of tbe Sn or Slur, the Mtibei of detennining the Lititude 
from Mkrng an Alliti^t, ot repeited Altilurfet, ii ilwiyt the J^ j 
» being the moft ainirait. And the ^elhod b; Miridiar Ahjiniu 
of tha S"' or a 5Mr 1) not only the m^i lajj for dttennininc the Ijti- 
radet, iiut alwiyi tbe mifi ariam, tnd txftJiiifiu 

XX,<iuiiTiON. TijW ihi TinutolmiibtSvitiiii/l 
^^Eaftdr Weft, Asm /^SanV Deciinatioii 2^" zS' 30' 
N. anJ la/itm/t ^i" iV io", bting given f 



AiR«diui * • • go> 

To Cotan. Lat. 51 

So TiD|. Suo'i DcclinMion . . 1 . 1 j 



"ii* 



SudueiEa* . . 7 10 5 j Mora. 7 
Sun due Weft ., 4 JO S Af"- i 
JV, S. In the Summer Che San it orcrtheEaftand Weft Pai 
_.e above Tb^ uid DecllMlioa Northi Bflt tiadcr tbos ia the 
Winter it the rune ChdioitiMi South. 

XXI. Question, fa Jiad th* Aiiitudt af ih* Sun, 
wiM dbf Eafltf«/Wefl, ihi S<am\ Dtclinaiwh ti''^V 30*, 
mdlatilBJi ji" zi' ^o' ieiMg givea ? 



PROPORTION- 

A> Sloe Latitude 

To Radial 

So Sine Dccliiut. If 



« tl* jo" c 
iS JO 



166064 
f.6col6j6 



o>7o6S700 

XXU. QvEiTiON. TefaJ t/u Saii't Jltitu/t at Sue, 
fi-tm the Dtc/inatifM zj' 28' 30* N. and UlitmJt ^t" ii' 
30* N. hting given f 

PROTORTION. 



XXni. Question. 1»f»dtht Sm^, Jzinnab «/ 6, 
fivmtitSmfi DicEnatiam 13" a8' 30'N. andLaHtaJi 5*0 
"'3o"N. being given f 

PROPORTIOK. ■ 



I E, or Wed. 



W, B. When the Son'i Declinifjon and Lititude ue both Nortii, 

:hB Arimuh found by the foregoing i>TDpartiaDi, ii fnm (lie North j 

when the DeclInitiDii i) South, and Liiitude North, rticAiiiDUlhii 

"mm the Sooth. — The contrary fjr (he Southern Litilude. 

^ThB-lgnmaijmarrS!''fli"l ci'ctrmg (*( Altitude, Latitude,' 

lecUnaiion, Aiimulhf Amplitude, &c. t/itiSiin wia h Ibi E<f<ii. 

lofliil, wtiit are fihiJ if bv Prsfenion ^ Spberir»l Trirmautrj! 

wkUh, a.tbij arnf a fingular N«t,.r,, a,i lift ufif^fh Praaia ,L, 
ihefe wi tavi iiftnid, vtitavi imillid, u furnijb Jlmujimeia, v Exit- 
ciff, fir ibt ynng MtiaumB-'t Imtntia. Who itiwr fafpifif mlnadr 
ai^,,iniid-wiibthK>l«a»iDimn^aua of SfhirUal Prc}«ri= - - 



ibjef} htri irrand tn) for hii ready X3ft and Reftrence ... 
ruttheran. Atlikewife the moH ootid or fonoui Ibttrmt, Rala, 
idJ Prtjxnitn in Pnfltce. added, for folring ill the Cafii in Sfbiritai 
and plain trigcmmilrj \ without which, not only jlfinrntutf, but Ntvi- 
gatiM,iai ill tbe ^f depending upon r^Xa/», would heimpeifea. 
Ftr Dtmu/tralim af wbiih infallible Rulei, iiv rifir iht RaJtr It 
Mr, Emetfon'j Mj) trallna ^riaiifi o/" Tri|onotneIry, (ii dear and 
demonllntive ai the Elamtnli of Eadii) fr amfit Saiiifaaiet, SM 
tj Mr. Ridiaidfon, ii Pater-Nofter-Row. 

Of the Natqu tnd Cauk of Twiticnv. 

WHEN 7vnli[bt begtni and endi, the Sua is alviyi ttckoDcd ibou 
iS* below the Htrixan: but eiiQIy begini and endi when the Snu 
beamipafling (aia tt<^nt, allnaiag fir Rtftaaim) by the Earth' 
Surface, chiough tbe furrounding Body of the Ait, or Aunofphtre, 
to the outer or uTrtme Parti thereof, from whence (at the Middle Oi 
the eititine Atmolfhere, or Meeiing of the two Tangent] of IxaitiKi 
and RtftBin) the Ulununatioa or lUaftration there, of J:he Sun'i fiijl 
or laft Rayi tn rcAea i), itriatlalk, to the Eye of an Oiftrvrr. 

Ai foon u which rucidtat Rayi fall Ihjrt of maeiing tbe ttrixtata, 
Tangent, at the extreme Pint of the funounding AttoofphiR, in Ibi 
Evening Twilight ceifei, and total Night or Obfcurity enftua. And; 
in the Morning, ai foon a> tbe Sun'i incident Rayt meet tbe Uristara 
Tangent at the outer Puti of the Etrrh'i Atmofphere, then Twilight 
begint, and eocmles iti Light till open Day ippeari by the gtmra/ II- 
luninatiou of the whole Atmofpheie, every Way refleSing Light; 
befidei whatUght iirefleOed by iheSatth'i Sojfue, andilj terreftria] 
ObjeOi, which the Sun'* Ught direOly Uli upon. 

Tbi: jtam/fiin, *aiying in iti Height and Mipiitnde, (in tbcSom- 
ner eipaoding by Heat, Ughtr, and condenfing in Winter by Cold, 
IraitJ ia mc Cewfi of the Vitittioa of tha Beginmng and End of 
Twili|)itt, It the lame certain Timei of the Year. Another Craft ii 
the variailt Quntity of Matter in the Almofpherc fit for reHeUing 
Light,nat (()onre,ar'taodenfe,in tbii tranfparut Body. Add to which 
a third Caafi cf the Variation of Length, aa well a> of tbe Ciearnefi 
of Twilight, which ii the Variation of the Sun'ictheriil Atmofphare 
fuirounding hi) Body, fbining before the Sun bimfelf rifei, and after 
he leu, with variable LoAie, augmenting (he Cleame(i of Tmlight, 
mote or lefi, and for a longer or (boner Time. Tbe Duration i 
Twilight it likewife reckoned fomewbal (hotter in Morningi (hinc 
die Eveningi of the fame Dayi, cfpediUy in Increafe of 'Twilight 
tbe Morning Twilight iirecLoned to begin when Stare of tbe 5;^ 
Magnitude dilappear by iti fuperior Ludrej and the Evening Twilight 
cnda when tbe £une Stare begin to appear, vrhich the Light of the Ail 
before rendered invifible : Ai tbe brighteS Stan in tbe whole Hsareni 
Twiiib out of Sight in tb« Ptdence of tbe f^ienor Luibt of the 

From tfatie CaafiJmatimi, it will be eify to detamine the Bipairi*i 
mat End vl TwiHrity in >U PUcat, and at all Timn of tbe Ye» ; 
a:ad alfo the Day A tbt /tart^ tvH'^. The Height of the At- 
■Wfpbert may be mcifirRd Aom tbe known DefnlKoii of the S— 
wlien Twilight bc^udcndi. All wbick at« ibcwn henaftet. 



,, Google 



^d NAVIGATOR. 



XXIV. QoitTiOH. Itfinilht Tim* of Daf-Brtak, i> 
lb* Morning, mni End af Jiviligil ia tbt Evmiiig, /rem it* 
S^ni DteliitrntiM lo'N. and LaimA tf tht Plati 51°^' 
N. hiinggivtnt 



KULZ. 
Soa-iZcn. Dift.>tBc|.7 « ' 
wIEndofTwU. . J108 Siieou.Z.rts'- 
Comp. Ut. ■^% il{8Maiocl([U.S.co: 
SunJr. P<d* So o} ^ n^. [tD.S.co. 

Sum ti6 it 

From . . . HJf nj 14 

TdteCrai.Ut.*.i™-..74 4*»*«.Siii» 

Tike Siurr.Palc arm.]] 14 L(>(.Sm* 

Sum 
es« I7'>B*L. Sinc..H>ir 
DouHt y6 34 jS /. from Nmd. 
-In ThM 9k im «,• 


O.oc6fi4»l 

9,9(446^ 

9.73M"! 


19.9361019 
9.J6IOS14 


D.j.Bre»t, ifc S3" 40» MomJng, »;*» 


U. 



Add the locietlc of Sna'i Dcclinatlao for doable the ^ of Dij- 
tak from Ndod, v/c for it^ iiB4iii, to the Ebimer DMlimtion 
!□« N. and r^ur tic Ofiiraimi, with Che &dh Zailh Dijtmtm tni 
Cimfi€mtni if ttiiaidi, ind tbcRefulC will gire the tuft TimeoFTwi- 
[|ghl ending in liw Erenini (vhicb howe*«ini)''bc taken g^tiBio* 
that Nitht, PiA, W Mora. 7wiii^, fromKocRi, u novl]'. 

OPERATION repcaMd. 

i8k «■ ■ 



IncKife oftha Sun'i Ded. 
fSt€^. 194* .*"■/; In< 

mcDcf, Sun'iDed. at 



i6» «* 

bdoi II 14 
of Twil. ... 10" 16' 6" N. 
[fbi that Dij, 
San'iZen.Dill.atBeg. I • ' " 
EndoTTwil. { lot o 
Contf. Lit, }t *1 
Su« ft. ilwf ole 79 43 54 J JL"<i* 



o Side opp. Z. "V 
o > SideiiDcl.U..S.GO. 






S* 



0.1061683 
0.0070111 



6I»«'S0*-L«.S. . . Hi 
'Double 137 7 40 Z, from Noon. 
JnTiaufi.tlMa 9* 801 ji' at Night, Tvril. trii, 
laT.fr.'NooD, 9 i ^o Twil. btpui. 



On/iitiivi 1/ itt Sim. in wy Lailmli, ibt Sm't Zmib DiflMtct 

MlbaiTml, fiiif dAEWjri'loS*. 

N. B. the TwlL'iht Ircna/n frou Mart* s, to it* ptUtA i »m 
dwniiirHfotoOaiitrii.atlwt-r, atainat iti Owiteft. Then It 
increitc* to Sim ia l:ft tbeii dwtealci to Marcii «, tbck luattkt 
bcfoto, tfi. 



WhiD the Sob deftendi jiAP it' below the Hotlion, at Midnight, 
thea there it no Ditimeli or Night, but all Twilight bcgini to take 
Place. Thii heppeoi when the Sun'i Declliutioo it equal to the Dif- 
ferenca hctween the UomplemeMoT Latitude of the Place of the fame 
Name with the S'Jn'iDeciinitioii, aod igo theDemeaianatMIiinighl. 
In the Latitude of ci' 31' N. the Complement of LaHlnde ii 38a it', 
&om which deducing iS*. the Dcprelioo, there remiiiu lo" it' N. 
Declinatioa of the Sun, when Darknefi difappcaii, in that Latitude, 
which i> from the ltd of Af<r to the tiaof >^ (fee P. 195.) N. S. 
when Night i^n retuDi. 

Bat fromtbtSun'iEicnrEon fton, toliiiRetDro to, thii Lieut, 
the Ltdiude, Louden, it ia alt Twilight, ftom Sun-Setting to Sol 
RiGng I bcin; the bng^ Doncio* of Twilight that can bappea 

there. 

when 

bibt 

Horii _ _ 

cc fo the fi»i^ Tv/iligbi alwiyi 

hi i"» Declination (tf ciMnry Nami 

I, nrtti«riiiJsr Dinftion to the Ho- 

ri rffion in any Latitude 1 Suppofing 

it !, ormwrAlb, for the Time be- 

IwiitlUfing inl SctdOb lod it" DepceOion, iKtoir the Hoiizpn. 

Hmtt, wh(»the Sun bai the lime Aimrb at 180 DcpreBioD below 
tbcHoitaoD, that he had at Setting, hia Defceat will be ^rr;^iWinAip 
totheHoiiaon, and theiefore on that Day, and Declination ('1/ fHti-ar; 
Mkm u tkm if ibt ibvaitj P^t) the Twilight will be the pmtifi 
f^tlt. In any given Latitude, . Tbii Con£deration furniihei a Naa 
Miibtd of finding the Time of fiuntfi Txeirubt, » foUewi. 



XXV. QyiiTiOM. Va fiad ib* Daj tf tbt ihortea 
Titiilight, from lb* LatitnJe 54 • ji' bting givn f 



1^ 7b Tiai tf lit Jbmi^ TviSrbt, ii nia 
■riir/ tttt Tnm, iairmja t Atnefa tbt It^ a 




Put II and I s: Sine and Ccf. of ZS » to8«. 

* and < = Sine and Cof. ZP =: Comp. Lai. 

I s Rad. B QZ, 
Aaij B CoCne Q? s SP, Dil. fr. Pvle, 



DigHizcdbvVjOOQlC 



m ROYAL ASTRONOMER. 



Afaonomical QUESTIONS (in PRACTICE) lofwered by Sfhtrha/ ?xorot.Tiou ami 

LOCAKITHMS. 



T!wa(b7«kn(wnTliMrem»)i-=:t:or.iQZP. AU'-^^ 
s Cof. ^ S Z P, Which jtft!" bfioj equji, their Cjftio •« "Ifo 

/cr a^fmri-g all ^iflim tf ibit Naiarf, 

X, «4-i ' * ■■■■ f ■■ J> tiieSinto/ che Snn'l Dttrmali—, if 



autrtry Kafit !• iBt LaiiiuJi, reijuiicd. 
Or, inWoidtitLengifa, 
AitbiSiiMof 7x<>W[Udfn> ad^rJ, 
IitotheSlnEof ilo. 
Soil the Sine of thcLitiCixle, 
To the Sine af the Sun'i D«ct1rUtii,r., 
On the Diy of tJw /«rr^ rviiligtt 



CMI.N 



L^ariitmi- 
$.19)7116 



Ta Titw. } DepnffioD .- 

SoSint Lilitude , . . 



Ta^MSun'iDcclin.req'. . . 7" 7* ij' S, ^ _, 
uitmiiof to AUrrt t, tpA Oa. 11, iibefcrCj between w^ih 

tiSgin increiie j ind Eroia thp btter to the fonwr of which 



ut u W to I 
Stflt^, in tU Latj^nto.— While IbtP^iincmtfe 



i:mfe of 7-aAri[btt} iocTeafe from the Sua u W to hii Arrinl 
jnddetreift fnai oBtflt^, in tU Lati^n to .— While ibtP^iit 
the AAcrooon Hilf-Biri tre the longer : but while llie Diyi decietii 
ih* Fonnoon Hdf-O^ ■>• loaffi Ikia thofc of ^ Alcrfiuon. 
Which Confidemioa fotaiAct ■ XaA (bj Proponioii] fordetrDniniBg 
ihc Difi»Mce tt Tina, bctvMa PotMom «al AAnnoo* ObfiiTa- 
.tioiu. fra^Voo^ in A* Udttai tf ti rA m i mg w fmm ^joid, 
•/" li4 Saa'i b* hiving ths DiSuice, in ^M, of the two OUtm- 
' u of tb* litnw AlihttdMof th«Stui| (in the Fotesoon *nd Aftci- 



XXVI. Qui>Tioti. TtJMtit Bbigh 9fthtS»Mh\ 
Atm^hirt, trtfittfiKTvm^g St<fy ^fJktJnm tht Sum' 



THE -Hen of 

cheBegipDinfOrEod 
of Twili^t being 




Eirth'i SurA(« ■! E, 

id i) lefleAed hj * 

irttcle of ^ii fton 
tk Top of the AC- 
.nuTpbtrt^ (t R> to 
the U^/irsB-'i Eye it 
H, u) k horiioata! Dinfiion RH. And fioce RH leprdentt tht 
Horizon, ths ^ H&S, sstho Sub'tQipieirioii, =:tle. 

Now, jtt^/f SRiJid HR, Me both Tc^pid to the Eulh't S«r> 
fact. It H and E, meetini at the Top of the Atnu>rphen, R, the 
AngicHCE, ■ttbeEirth'eCeuer, uaqual tothe Angle SRH =1 
[g*l wWoHalf, oitbeAagbHCR ii niaai M Half /.SRH, 
= 90 j which would be cortefH^ fa, if the Ray SR paHed ftrtit 
hratvh the Atiaafphaa wiUiaiU RtfrtQioa. But bccaii^tba lun'i 
ItayaaFeTefnAt^uHtbtnt toward* C|L, (aU ikc Way of their PaAfC, 
bf ttu E*rth'i Suifac*. frow OM Put «f the enciwl Atnot^bere I* 
their Aoinl at cba Top of ths aoatrwr Part HmmO tbanfefc ttw 
^r^ of Deprafiioa will ba 9RHBit°, aa4 ths Z, ORS «iU 
be the Sun'a hotiioatal RifnOiao es jo', at leaA | whenaa, the ^ 
SRH=I70 y^i the Soa'i Ravi palEng diraSly in the Arait Line Q 1 
'11 tliej aMet cheoufideof tha AunolphantB r, and then pafi thn 
: in the caned Unc rtV. to R| the oppofita Part thereof, ftoni 
rheacf chcgr ait hoti««iitUlf i«Hea«4 ta Iks (U/oTirit H. 



S/^ A* ^CR,K . . . . . 
To CF^ Buth'i Rad. 4000 
So Radui ,,.;,. 



■i* 15* • • CO, I 0.0050844 



S.90« 



I a-6o7'44» 
B DR, the Heiibt of the AtnoQihaib 



naSiJa, aat Ibi Cajitt tf 1ti iacliiJid jbigU (vlnvSaH ibt iiultAd jUfi ii it&, aaiaiiimvlMit'umtat tinmriwtl JarU) itfaali 
tht Ce&e tf ihaSUa ^fifi" " '^ btlMU AgE. 

FUnce In the ^lirHeaf TVianglc, ABC, when the iafi^ Letter* itUMtbftCt/Cau, and o«t£deLettm denote 
: Siiiti, of 'the giTcn Sidei and Antle, indaded. 




TbeaM±Hts/. Heacea (irtia^AldatkugoB} s 



t at ('phai A ^t l s AJUW***"*"* y") 



s^-^ or 4ai^~~ (whenZ.Ale&th>S90e.] Bifja'^^^, andis-^—!^ i^Z.Aii|m(ettbMya«d 



,y Google 



«Hrf' NAVIGATOR. 



AftftmoiMcai QUE &TIONS (iff PRACTICE) ail(Vci*d by Sfierica/ Phoportioh aud 

LofiAAll'HMI. 



Tliea ibc Z. ^^^ ~ 



WbereToR, 
S», At Z. CRH . ..;■.. Ii< 
To CH, Evch-i Rid. 4000 Milti , 
So Radiu * . . • . . . S, go< 



Jind ^ CRH 

Ltgariibrti. 



XXVir. QjriWios. Tf fiU tht SicRaaiiaH of lit 
9an,.ef a FUntI, trS3ar,finia ih* Ltngiludi (fappofc 

of tbeMoori) ij-fiz, Parii, April 1, at Neea, as ;» zy' 

mi kMitidt 4» 1 1' N-. itfttg.gitm f 






).6]77B35 



XXVni. QjrEiTiOH. 7tf«diht Right JfitMj!»» of ib, 
Mmk, amief aitf Star, or Pliant, frtm tb* hutgitnk. La- 
litiab, Mi/ DfcJiMtion tbtretf, bthgghumf 



jth Ak . . VJm. <i >6 

f^J/iiirt«mLdikidiaidSipi*fiitLeitglKJri U nf ibi faitr 
Natf, tit utt j&t ftitnftl frtm ih CafMlHit tf'ilii givn Lwitvdi 
/W-ftttAfrf if ibt'L^itwir pvtti mUd'Sif'' of tin Lmrghiiil hf if t 
^^irtMiVkM, liunbt^bJttatUitttbiCe^ipimalltfgnitmLtfittJi 

NOW, Ai Cof. 4ih Arc . - . 13* 11' 49* 
TaCor. jC&Arc . . . £> *t 11 
So CoC Ed. OUiq. i . sj aS 30 



T« S. Dttl. K, nqd, »7 31 j» 



AccoidinE to iKt ABOVE-RULS, 
5. 900 



ni Aiccnnon OT nc Mwui, 

Igilude Z5 jO «7' o" ■» 

LatitudE 4 II o N. S- 

eclinttioil *^ 31 34 R. j 



PROPORTION. 

A> Oor DecliBition 17" ji' 

ToCoT. Long. ft. next eq. Paint A S4 3] 

50 Cof. Utitidc 4 II 

To Cof. R. AfceoGbn, (t. it, Kq<<, 83 51 



in the fbngoIHt In- 



LtgMritimi- 
o-0J»»J7* 
t.g77GlSE 
9.9981414 



EXAMPLE n. Ub^tode ]| 

' Latitude . 
Occliitation 



At Col*. Declination iS" 

To Cof. LongI f^. ont eq: Poidt T • • 59 

So Cof. Utitiwl I 

To Cof. K. A. ff. next ei|, Pbint'? 

cyi, reqtiired t cS' 

3>f«- ibt Rifl. 



. . 8 •,<' S.' o* 1 
. . . t •» oS. iV«i 
. . .U 41 >N.i 



9.7007158 
9.9^98577 



I 9;7*4'7S* 



. AQa 8% 31 o ConiF. } 



'ffi 



t:$> The iban QoeffioA' nu)' be ofhWwIfi mfwerid by finding u 
Angle APE of » 5/£mcit/ Tmngle, whole Sidcfi 

AP tHColftp. Dediiltion, ")■ 

AS tb( CbiM. Utit*^, fare 

PE cctnfltnt Dift. of the two Folei of Ecliptic rgi*eii. 
and Egniooflial - — - 
The Sidet in 



liottheRquiicd^-beiacAP, PE. 



XXIX. Q.HESTiON. r^/W th Jiigbr jf/c»>/«t tf 
Star; trPlamt, Jrtiit ibt LmpitiJi mad Lalitiul/ thitttf it- 
ingglvt*? 

Hen, InAAPE, «fc|i«tt Z.E, Sld«i AE idd PE, li 

I LoDvtod« oFtbeMoon . .cr j* 37' o' 7 .._ 

Lldtnde .... 4 II oN. J »™ 
I To find the Right Aftenfita of the Moon urtlut F^itim, 

PROPORTION. 



0.0x86(78 
9.9C94801 



jtb'AR . . . S 

To Oaf. jfltAie 1 . ■ • 

A> Cof. 4th AM 

SoCof.Ecl. ObUqnitf . . . 

ToS. Dedinition N. required. 
9eiBt > Proof of tlM Trath of k 

N.B, The two Euunptd ibote contiin all ihc Cafci Ihaleui 

luFpeoi.iniiDdiiig theDecliutionof the Mki, aflttu, tatbtSifri, 
tUtr-LoA^tddCi and LatibMel^.rtrpcaiTcly,' given. 



hllaCti^tl 



■ N.B 
jluppoi, 
Ifrontk 



SoCotu.Latitud« 
To Tan 4Ut Ara 



47 5+' 



Ectiplic Obliquily - 
lie jtti Arc , . Dif. ta 19 14 



t^ Wita tit fivnr ttiitwA ni Sin ^ ihi jMg'tiit 
/«IK iVoar N. •■ S. jw «j! fthttta tt, EtlifiU OUnilj fi 
far a yb Ac^ Ba if ill LaiilnJi amJ Sign tf ibt Lsfgiiu, 



digirnu DtmtiaMi 



Ijfhmni^ 

.sfgiiui/i art if a 



,y Google 



ftzS 



nt ROTAL ASTRONOMER 



Aftronomical QUESTIONS (in PRACTICE) inrwwed by Sfbmeal pKoroKTiOM mi4 

LOQAKITUHI. 



• >S' «' H" e 

,_ , 6» 19 «4 

T0-TUI.R.A.&.* 





.u 


s» » 


'J 


»"• 





0.001 1696 
9-94T»»9« 
11.010411S 



ft S. JP™* 
By ihe <i«v Sui> 



ToT»n,4th.Arc . . i . . . ■!. iS 15 
EcliplicObli^tr -« — c. 






6S ,3 ,j 
« ,t IS e 



To find ber Liiitude South ind LontitiK^ fiini 
PROPORTION u Ixftui. i , 

taSine . .....< 90^ o' e*" to-ooopooo 



To Tan. Ecliptic OUtquit7 . . . ij 3I jo 
So Sin* R. A. fen V . ^ . •' jl o to 



ToTju^cnt^tli Ak 



+_ji__i6_s»Coi^ Bed. JN, 
FiitUAtc. ..:...... 91 30 1 

Ai Cofnc 4tli Arc . . . . ; >o 13 loco. 00176x3* 

To CoGjk jth Arc . . . ... 91. 30 ■. I.41I0797 

SoCcfi>e£difiticOU>iuitT , . ij si jj --'--i 



T»5isc LiliMdc S. fCfuIred , . i iS o 

NOW, TtJInJ ibi Itmpttiifitm Arici. 

Ai Cofinc Latitude S l^ tV O* Co.| 0.0001413 

Ti>Car.R.A,fr,thsiincEq.Paint<r5S o to I 9.7i4>76o 



o Cofiae Decliution N. 



9.9678314 
«.ooni90i 
10.136119! 



Lit. S. 2 pf** 
ttMOiiicSIsiu. 



Iha, To Sine 5^1 Alc v 
A*^iK4th Arc , . . • 
So Tin. LoofiiDdt from f 

ToTin. R.A. fwm<i(*«qBl'«i ■ S> o >o 

PUo«iDib',S,X>ir.«,n,iUt.N.l left. J 
itlun Saa R. A. la the Ecliptic, beiii| II 

XXX. QviiTiOH. Te find tht LtagUmti md Latitat 
ff m SUv If FiMft, Jhm lit JiigU Jfitajimtmd DKHmtUim 
tbirt^, htimg ^vta t 

\ ') Rl^t Afeenfioa from <V 99° 7' 5S' 1 
Declintion North . . . 17 31 11 ] 
Tf fad bB- Lttlt*iU Mrfi nilmiaiA film j 
PROPORTION. 
JtaRidhuSiiie 90* o' o* 



+ 61 «7 iS c« 
Sim >5 4I 4fi 



jh63V^9 
■"^ fN." 



To TiDseiit 4th Ak . . 

ifth Arc ......... 

'•V, AiCofine^th Alt .. 

ToQtfinejih Aic . > : 

Cofine Ecliptic OUiquitj 

ToSiDeLidtaiieN. reqand . . 4 11 N. S.tfi30SiS 

N. B. »%M i^ Xi{^ jlfaw/bm «W DttrimOitK pwm an ef iti 

tamtNmi,lt.w&.fbtOiKAtmtiatflhtDMli'-'- 
4/t ^ (j6f jifr <^ I Biiim£tw tU Si^ Mafie 
wn pfJiftmtNtmi, lit 41* jirc rubtt«ai/«n(J 
MtiM /Sr lit yi Arti 



"^Srf^ 



rROPORTICN 

AiCoGoeUtitiideN. 4° 11' o* 1 

To CoAnoR. A. Aom wM B(,Put|& t j 5* a 
So Cofine Dediulioii 17 3> 3* 

To Cofiae Loik&on next Eq.Aiiot A S4 33 o 



o.ooiijSti 
9.01S7050 
9.9477611 



Lonthode from if* . 

Beinttbe CoorerJe t 
Queflion. 



tb« Piafoctiuw lolimfa^ 



rBBs*»7'ieqi- 
totbttXZVJII. 



SoCof. Long. fr.funeEq. P^st T 59 51 o | g.7007161 
ar,.tJ 19, u o Rquirad. 
O iMtbiVriaiigtiKPZrf^thtfiritmig ttx'Jb'im, tn pvaitht tm- 
jimr Z>f/lnn g/iii Pt&i af ibt Bfunr P£, ndEe^li >i^ iS* 30', 

ibeiiubUUi^tfRi^ j^ttUn frtm At Signal CtUn tfesryf, 
P.tiMfbtSiJttMaJit itlhtt ^ vi».JA, vttfi Cawflamil It ^ 
It ittLtultuJt i trExcdi ahrvt 900, ihi ctatrmj LatitMU. rmind, 

jUHilJiiiiMthi ^ £. «/ iL PtU tftbt E^Mic, im/iitd tttwt- 
tUUiitpp4nSi4f*S.,Ujif,<ad,(„^riid, tit Uiii*J, ii mtttknJ) 
mltbtai^ Difintt tfibt Ptla (aftr^i) PE i vhicb i_ t.fm»d, 
wiUbilhiLti'pm^rtnmd/rtmaiilmtiSt^titlCtl^afatryf. 

NOW, Til RJwyj^iti^mP, ami LmiilwA at E,fiim SB tt W 
fi!HlkMftm,llnKiiilj^ai^aitiLti^iai2ifitmTa^£t, nil/ it 
'*lft hvat i lit litter itiar lit Cmffmimlitf lit fanner wgoa 

XXX. QuiiTiON. T» find tbt Lcntitmdi »f a Sfar, 
Plaut, tr Ctmtfjjhm ibt lililrndt x' 59' N- m4 DkSw^ 
tioH zo* I'S. bring frvenF 

n. B. Tbli QaeSlaa ii rcfdlVed bj ■ Profeaiaa on tie Si^Hiial 
C^n. IniSphcricilTriingleAFE (AP'being *'>Dift. fromtbc 
N. Pole of ihc World, AE ift'i Dift. from the N. Pole of the Ecliptic, 
PE DiftiDceof the two Polo, and ^ E the Lonfitiule fiwn !3I, and 
y P, the RitJit AfccoGoa ftoni M 
•AP=*-«D.ft.N.l 

Pole World . .ill 
AE=*'iDift.fr.N.- 



0*SUe«ap. ^reqd. 



— 4c-|Dift.fr.N.? rSldn ") 

'ote Ecliptic . ) 87 I o I joclu. I L.S.i 
sDift.of thetwol I Z "- | 

alee ... . J 13 iS ]0 (.qaiI'.J^.S.l 



Tik»PB, I Rem. I 



Double it Z.E 168 39' 7: 
SalHna5Si|iN 150 o o 



0.000JI90 
0.3997364 



US. 



Hilf o'.»7^ls 
BSfbUowi 



i\t " " 



•f lntd.Q5«dr*Btirf'tlie'Ecliftic. 

Or, 16S 39 7 LoagitudC fiotn prKediof. 
>J i»o " " 
Fitt.yf ti so c3[a4tbQudmlortlieCdlptic, 
• ArcfiTCntofiiil ^ Efr. OB. 



,, Google 



and NAVIGATOR. 



329 



Each Ptui being 78' jg' 7* frain tht aeaitlt E^IboOuI Psint 
i& (DJ 'V rerpeaivelj. 

N. B. !nt Pbn ftfiii rvt Bin Jaail mufhi JHirwihni hj iht 
nitr Siaati— 'f ii» VWan tr Comet nhtft LnfifiA it rrjnrM, >■ 
r.ftta ^ftrnt iMvm Slir, vit^t Laiptrndi it {kv>. 

ElAMTLi II. Tn fid lit LnpimJi if OiFltitittia iht t94th 
''arhiftnCittilltfi^ib^Dtiti'Uii* mthat Tew 140 yil it. mud 
.atinii" N. hifl;fn>«r Swfbl ii.SlicrbaiM J f<il< 5fi|Vii)ceiit 
Wint,In(t. ind Pigcie. Street. 

Ir iSpbaical Ck APE, u befDre. 
ArcgircD*') *AP^7;' jo' Q* SiJcop.^ required. Tjferliimi- 



find ^ 



■)»AP^7S" JO* 9* SiJcop.^reqt 
!■ AEsEG o o{Sidaiiiclu.IJ.. 
J PK = lj i> iol^tt^iinaiU 



Pri7w6neeXl.«l6 j 8 R*%. 
SBintoi4Yn- *■ t 4«Iiicm&«fPUcet 

jKmulMtim iftkt Stan iafiOrn'ogOriir. 

XXXI. QnliTIOH. r» find tbt mght Afimjitn, t>f a 
Star, Pltaut, tr Cemtt, fitmlh* LatihJt 2059' N. «»</ 
DttHmttitM 20° I'S, ^'a; jfvn, inthifirm*r tr yith 

In I ^fcrictf/ Tiiugle APE, 
Aregi*eii* J *KY=s 87" 1' o" Side op. Z. required, 
to find ^l AP=iio I (l5Sidciiiu;lu.7L.S,co. 
P framl:fl PE= 13 »? joiirtqniiid JI..S.CO. 



FromHair 11 



Sbsi 18.04.36497 
a' 10* L. S. . . HUf $.0118148 
4 so R. A.imm t:f preccdin|. 



Sun 157 55 4a R.A.troin T> 



SomaSi 4 loR. A.frnnqf fallaviDi. 
H. B. tbiRitbi j^ca/taBt/ lit rattin /mmd,mifi ttAttmimI 
hGramfitma, or fbattomauacufiifi^ itttiftn Data.; iA> Fi- 
imrj </ d Caur nafltM U, a hvaa Star if pvtn Sigil jtfin/m, &c. 
JutbnciDtbeliA^Calc,wbeathe Longitude ii from^or £a, the 
Ri^t Afapfioo 11 ttomtheliineEyjiiwai*! Point. 



ExiMVLi IT. T. fKj itt Riffr .^mjftii */ lit Pleitdei /■ (i. 
■■•■riarU^Cii\^frimt6iitDrdi*aitmmiib»i tlm I4»30'N. 
aiiaJt 4* «. itiagtrm, mi in tbi fwtmrltffi^im T 



•JTi 



In a Sfbeieal Ttiiogle API, 
Ate given" Y*AE=SS» o* o* Side c^. ^ reqnired. Ltrariitm. 
t» find /.f Affe75 30 olSideii«lo.>L.S.a>. 0.0140(84 
Pft.>f,orf PEssij iS 3oI^re,uiiedjL.S.e(h 0.3997164 
'- Supt. J 



n_v. ■ u e J»«4j'n*L.S.- Mdf 919*48041 

'^"_'''™|.'''^J6$ 10 ** R.A.r£;.£>{romi!Spr«edint. 
JUA. 90 o o 0bnai<r. 

L"94«liy"fctf."xt,jH "9 jS fronlfftUciriBirtTiired. 

M- n*SmbmtMtflblimctid,J^I,,lalttCafiat>v,,fi»>J i»- 
ifa,bukM/,,ifil/i a„SimamlSi»,/iliS,ffL^ i, itoo 
Mm- (if Jlwr. TMi DtfilnlKHi wmit It cartfiiS} rmrdbl, Biariimg li 
lUNamrfftbttbruSHatfibi SftmulTrianik giva, thai it maj 
ii htvw /«■ «Jwr ?»r*^ litStShiial Cilnt Vfryj.lbi^ t/Riiil 
J^aafim, or laaplaJi il mvmitiii. 

When 70a would find titf Timei of S^r and Stt'imt of the Moon, 
or Pluiett, or the Time, at anjr AJtitudc, tbdi Amplitndci of RiEng 
and Setting, dec. You mnS fnbftitute tbc Time* of their Paflige 
through the fame JtAriJiam, \n the preceding Calcnlationi, inSead ~ ' 
JVoM, the Tune of theStia') Piflip. 



JubtlaltrvU*/ lUTiauifniiiiiw -uxt Faffm ,/th, lAm 
Plaaa, thnagbib, baiMirHiaau Uj6o*Jt S tit ^ovaUt 
rifpvtwT<mt,aaJlitTiimt/mmr^fafigiiimli ibihtiriii, 
ibtD^TO,Mim»taailSraiJi tf ibtflaata aapOr Dijaaa, ma..,. ._ 
« rb, tml^tial Mfaur, fim lit fam ibri£a, s4» lb, AUaaii oj 
tbtTlanUa rtfuini. 



XXXU. QUIITIOK. TafrJthl JltiUiffMari^ lb, 

i2lhPtb,ijti,atSlxl»tbtMtrmmii bti»i $b* fom ai 

h n ■ 
JT pwaUthiMei1dIut75l,Feh. tijii i< 4o7At JUrii Dt U 
nX.11 ti aoj CWa'aEpbcm, 



i ftom Meriditli o 6 43 <° ^^' 



Feb. 11' iSk 

>!• 5s' o'N.Feb.iid 18b iji%,LatailU. 
48 50 ID N. Height Pole, Parit, 



,, Google 



9i30 



The ROYAL A S 1 K N Q M E 31 



AfoonomicriQ^UBSTJONS (ia PRACTICE) Mfweied by^/U»«/ Pkofobtiohsmi" 

toSAKITHWl. 



Br PROPORTION, Qi»r. XT. 
AiJUdiB* 90* t/ (.• 

ToSneComp. Dift. ^ rr.Mcridiin loi iiio 
So Tan. Comp. Ut. Avifc ... 42 50 w 

To Tui|eiu Arc X . - , . . 9 38 4* 

DilL 1} rromPoIe + ....(% go 

SoSineLititulc . . . . j . 4S' jo )« 


ro.ooooocCT 


9.a8gfi44f 
9.94167 10 


,.5.rt5,6 
0.0.61B44 
,.!,16,6, 



TnSine Altitnd; ^. feguitcd. ... -9 iS bo ■ g-aatttoa 

M. DiStCaiUt mm; it (S« fail EphFtn.) 9118 onlj 
Who roanri ifae Arc X 90 47' [5«f . 16 La Ceilli EpL) inflnd of 
9" 32* 4.j"»' »bo*e. 

Whofindi joi« i»' i5"=:6li ^jiii ^>i. 
in And of loi 11 39 :=19 aborc. 
* minDiJlt-rtfnim.llitA^diaBUiitB« O^ er.ca" aJJ X ts lie 
PltMfl-iDifiaKiJhinPf/ifirY. if Itft, fiAtrm»XfnmPeli,llifiiact 

N. Si The famt BfaM ai Alt tberc ftrvn f«r all otliu PfMOS, 

tadiirathcAfgiHi) if 70U obferreto tikeoutof »n£fti«irrii the tnii 
Inttrral of Time betwiu the two< nut PatTatci. of ctn MiM, or a 
Plaiiti Chnmgb the faniG Mciidiui, fof propaitianin(tb«it.DiHaiicca 
'- Time thcnfrom, rjtbcr before or aiiec tbsir PaAij» u a. Tine 
«n by.theCloeJt. 

XXXni. Question. T> /ml tit Stg/^.^reafim. ef- lit. 
Mul-Heavtn Ecliptic at iht MtriJia^t/rom iht San'i Platt^or 
(ff. Jffcufim, md tbt.Time ef tht, Haj ar Nig^t.6ii^g pvtiif 

Rcu. To tlic Siui;i Right A/cfuGon ia QcgiM^ Ninuti^ A 
und to the Time given, when Rigln A&ea&oa of ^4jd-He■rcB .. 
lUireJ, adl the Deereei, &c, of that Time fiom the former Noon 
aV<Wioi,liape«nM tp ■• n«u] iD^r^tfaei Swi njcAhf ■titf \l 
iboie) will be the R, Arcenfion ef tlMMKUfawva,.-- ->--"--■■ 

baurts. Rcipriird ()M ntgfit A1eetrfi«ii of MU-HtjTca for 
764, Muih 3«ih, lohtoniDtfaeForeitODii^ 
SBfi'i R., A. in Tfme. 
:7&4Mm, i9,Nmiii- 34m. 6! 



ot. Uid>Hbu>w fr. V iwgedug rf S7 S« 

Longitude Mid-Hea«n™n.Sig. . [Tn , .or™hninaUn| 

«. n. Th,Mid.He«e,l*.p«dSb'X:?t^'jf^Tf^- 

B^^P6«tv„*,U.a,rM«.He,.^Rt^^X^^n 

^fgUafjh, Elliptic W JICnrfA,,./^ ,*, MV.fc; 



PROPOXTlftlft 



30, N 



JT 4J 



^mJiAiUiUfiihMnnin. 



Ijht Afcenfion in Tilne 1764,). _ 

^Mar. jotb. loS io» Morn. { 3? " 



R.A. af:(li:>qli 

(Or SfCfj .94.; 
Aiw, »»■ JO? tcduteAio Degnn — jjjO. o* o» 

Light AfcemOoo of Mid^HeiTcn required . . 



3fa 



R.A.of Mid-HeueiL,l7iottofJV* . 



pj- Wh. 

did-HeiTen from 'V' followi 



. . . IS 38 . 

90° It II Right A 



liid-Heayen from ey following: ifabonao? 

raaitfromiJo, forR. Aft«niaofMjd-Hfi .« 

fmort tUa »I9, ■04 Ufi tlum ijo, fuitr«ft. iSo fwa 
fMid-DeaTe» froin.A fbUowuu: Bat if it ii tbattiia" md M. 
ban3So, ftbt"a it frw, jSo^ Right Af^iUloi^of W-H^«n 
' ™p*oe*"iI,»lil th»Era^l.^«,. '*-^'~-- "*> """" 



nf ^A/. Mn-(^a,, w MtJ-Heavai UntituJ,, carrthandnu lA 

thm^.m^„ Ri^iujfi„M ly 38' fUVt^"^- 

, PROPORTIOW. Z-*,,*-, 



r«C(irnM-Utaidkn^ r«fund. . 



*r «6 33 



J-5!jV6 



£cA/'« Oi'''?«>f ij» 28' 30', i,4 ^'W * 5"^ *^ 



90" o" o" 



9.6377835 
9.4305167 



RROPORTIOM. 

To Tao. Idlptlc OblioDitr . 
SoSiit«R.AiMtd-HeaTen . 

ToTaa.IledinationoalIitM<rid.S:imO. e- -, 1/ „„m.. ~ 
•K A When it. Rigb. Af^Bi^Tof tb« Mkl'^i,?; i, .ll" 
i8o«, aa ID the ptefeat Cafe, tlwii the' Mid-Heami IVHrn^C; » 
il«-Eclipti.P«io. i, South. But if th^ Mid-H««rR^*?^ 
i.4.ftZr.8«., then the U^-ll^^Tt^^^C.^^'^^:^ 

XXXVII. QsiiTio».-ToJ!i^ti^Mi,^ ofthtUii. 

If the Latitude arri Mid-Heaten DeellOitteB ue of jtrW™, w_,, 
fahtraathnn^E,.!^ f^ ^ Complemenr of ■ L-CKi 

(J" ji' 30*' N, 



Mid-ffctrerAMndtreiidnd 



:;* 



AAJVVIJI. 

,, Google 



arrJ NAVIGATOR. 



331 



XXXVIII. QuBtTioN. T>/mJfhJtiitmft»/titNiM. 
aiffmal, *r i)albbegrt* ef tbt EcBpticfitm lit Berixm (it- 
inr squtln ti>* ^fngl* ^ til EeHflie tmd Horimm) fotm tht 
AVd-HurviM Aidttidt 510 48' 15^*, Md tht MMrifktm Anglt 
67" *6' i$*Uin££i-vraf 

Ai lUdiDi Sins . ^ ..... t • go" t/ cf 



ToCofiin Ahitiid« gotfaDesree rtqnircd it tj 4a g.Sw^go 
C3* TticDTOu mar piweed to Gad tkc Place of ax 9Mb Otine 
CM Ecliptic, or iti Difiuce from Che Mtd'Hcifea LoaiiCade, 
THUS, J, StJimi I, C<>> AUilMj. Mid-Haven, 
iSi O^Uirii. AgU U Ten. Difi. Mid-Hiavafim tin ^ih D^ra. 
Which Place ii foaaAij iddiog the Diftina to, (irfbbtrtflia|itlnuii 
thcDiftuncr the Mid-Hmnn, iccoidini uiu PlacefoIkH or [Tt- 
.ffide* the Place of the Mid-Heann. 

fT)ij,I/ilwMii-J>f,rr.X. V, ii,U,»ii Jthe DMlanc* of 
Hciveoba b £ OB. £L> "^ ^^ ^Ir /iIubtnQ J Mid-Hea.fr.oo< 
to and <rom the Place ufMid-Heivco, tor the Place of the 9 olh De- 
gree, in North LitilDdci, and do the coanaiy in Souih Latitndei. 

Then (he Point of the j^cnJaa hai been uRullj found, crtbi 
EcHptic Pliccat IlieHoriion, at a fnn Time, for the Purpofe of 
finding the Pdrd/^fi/c Aafk, or thai Angle which a Vertical (paffing 
ihrouthcbcSvii.JIAn, or Sitr}cB>k.n with the Ecliptic, for com- 
puting EcL trail and Occult at ioki. 

But « tbiU MttbeJi gn lidina mi Mil^i, w rfw lit fi/hinMr 

aifiiiALNiwM>TBODi//,«AV.^ti«PARALI.ACTICANGU, 

and ^ amft^ iht MOON'a P/ 



Aftronomical QUESTIONS (in PRACTICE) ufwere4 by S>Afl-,W P»o»oxtiom and 

Loo AR ITHUI. 



Tiffi M fi^iht Mtn't Altiludt Md jhumMih T 



Intlie 



i QP = 98 48 I" 



Comp, Latituje, 

Comp. Mdob'i Declinatiodf 

Moon'i anguUt DiQ. ft. MeridiaDi 



XXXIX. QuiiTioM. T» JmJ /^apparent Pkct »f 
tb* Moon, fitm btr Lmgitmb, tr trm Plui, wd l4iHt»di 

Find It* yiDvOi. tMd R. jt. (bj<l^&.XTVll.*aAXXVin.) 
jwfiperaUi it tit LonjitDde laid Latitude pvn ; fir in t Sfttneai Tri- 
wJiAFB, itm4r* pvn A£ lit Cumf/tmcml ef Lamiidt; PE, tht 
DiJIami iftbiFiia (f Eftmr Bid Edi flic ; end Z.E1 tb^LmtioiJt 
frmSStrlff, lb, Solfiiiial Coin, n fnd AF tti Cimf/fmnl ef DuD' 
'wriM, a«f Z. P, It* Right Afcmjim fro- H> «■ gs f 

Or take out the Dedloatioa and Right AJcufion to the 'Cimt (tven, 
vm Eftamridn, DtUCaH/i't, Ctmm£iaa duTaft, Vt. letoced 
I (7rwinxn(&.Meiidtui. 

EXAMPLE. 7e JSiid tit MttM'i t^triMl PJaa fnm 



Tfae Sun'a Lon^tode then ■.•,,.>;.Xii 
Hii Right AlcenGoncomlpiMident • . . • • . 341 
— -Dedinationcanelpondcnt S. , . . . 7 
kiooa'aLonetcude then, bTThun, . • * X ti 
-LaticudeN. o 

— Dcdjiuttaa coireTpoBdent S. > > ' . 6 

— Right AIrdSou coR^poodcnt, ... . 
Time fnun Noon apparen t , In Degiccf, iSo jjl 

Henca R. A. of Mid-Hearen . . ' 
Mid-HcaicB Dtcii nation comfpoitdentM, . 
Aldtude of Mid-HeuGB at Gmmiici . . . 40 j: 

Mid-Henres Z«a. Dift. Atim (be BdirtK, AltitMl«at> 

the Meridian . . • • * t M *< 

Mid-HeaveaR.A. — Moon'aR.A. It the Moon'a? 

AniHlairDiA. ft,thel<ejidw, paft . . J 3< ■ 

Angle of EcSptioand Meridian, 10 R. A. HU-Henco, \ 

n Mid-Heam Leogitade .' • • • 3 '7 S' 



.,W.y 




H. 8. ni tif, 

tttvtiitllUtrfimtlitf' Xj\ 



PR<H>ORTIOK. 

Ae RadJoe 8. fO» 

To Cof. angtiliT DW. ttom MctUlm ) 

d.9.rz , . . 5 je»ii' 7" 

So Tan. Coup. Lrt. ZP . > . . 3S j) 30 

To Tan. Alh Ai« 
- D«/. « " " 
tfdiff- f 



9.1061486 
'onp, Dec]. 

[S. 

S>im IIS 49 3S»«'4 »» «S 



t 1»* %1' 4»* t 
. H ■• 35 



Ai CaT. 4tli Arc 

ToCof.rthAtc . . ., 

So Cof. Z P ot S. Loin* . . 51 »8 j o 

ToCaf, Alt. QZ «rS. Alt. QO . . . ■] {> 19 



WOW, Aa Cof. Alt. Oq.ot S. q? . M> 7* 41' c 
To S. B Aog. Dift. fr. Mar". dJtF^ j6 »« 7 
S08. Kft.faitaFoUQP ... »( 4> » 



«-e74»74 
9.l9it«i6 



• Z.MZ^ 40 ti 48 



e.o}Sli90 
5.7740*38 



Here, In itt Sflmett Triatgli MZi, (ft* A MZr, Z.tM3; 

fSapplimat ^ i. ^ Mid-Bttvm EcHftk, 0HI Mrfi!a«J tmrt rl« 
ix^^^MfMZ, lb Z«aA D^tJK* tftbt tdid-BMiMi Ktltjtk, m 




rftOPORTIOK, 
jlzcdbvGoOgle 



Tht ROYAL ASTRONOMER 



Aftronomical QUESTIONS (in PRACTICE) anfwered hy SfbtrUai Peoportiou and 

LoOAKITHMf. 



To CnC oTin^viich the Mctut. theiA ^ 
Part ofThe Supplcmeatofihe Mnid. \ 
irMZ, by » Ptip.fr. M. tor Z i 
Supplement Meridi 



"g - 4 SI 

And, Ai S. Firtt Put of the Supplt- J 



w. > 

: i 58 »a II I J.7>7S*" 
^111 8 40 



.-..., 58 19 IS 

To 3, rcmiiaini P*rt of Ac Supple- { 

ment Meridiin ^ . . . . ■ . J JJ )9 - 17- 

SoCof. Aiimuih (^Z) 40 » 4S 



'0.669194.8 
9.lgt99ll 



by the 7 41~«8 •» I 9-M3S3' 

TbiatbtTttmUfiaiijttmiM f^/mfinf (it Altitude n' Lootitnde 

«/ oo* b/ lit £i!.fiie drtgnadiJ. 

OTHERWISE, 
By DEAN COWPER>i cmfaJi^L METHODj lieiBg en 

./ (i< IMPROVEMEMTS (/" j^JInmrnj in ibii Ufijiie. 

Tlie DeiD of Durham procerdi lo find the J| '■ All. by the foimei 

Mtlbod exUbitrd i who rinfteid of finding the Aiimuth QZP) nul 
nde the ^ ZQP, which he cilli the /_ »l the Center, ■' Tbii At- 
gU at tbt CtMir ii lit femt iviih itci ntich ibi Ait »f ibt Eioth 
mtka niib a veittcil CinU dram itra/gi tit Cnntr qf a PUei ' ' ' 
PryiBiitt of tbt Fnptfi t/ ikt Innsr Pmb tntr U>t Etnk'i Di 
PUmi •/ ri( Htrisn : Tbt Qmflmiti tf tbt Sum, tr Difttrenn, 
•/ vitici JlfiU, and- Itt jfngfitfi^ ^o'" '/ >>" Br/iptie ni Emb, 
n tbt fM Pr^iffiM, falcprJvf (i ibf Pole if tbt Echptk, ni V»r- 
iMiH, fa^<i% tbmiib ibtMtaTt Ctnttr, fall m diHircnt &iia, trtn 
tbtbiat *S\ic,i/ibi lUri^i**,* Bart fijliii, rrfftaivil/J ii tit 
Pir.ll»aieAinle." 
£m Pallxlium 1756, p. je.'iaTtlw EipUmtioa of thli nTeTBlOif. 

eo«ij, ),y DeM COWPBR. 

AiCoGiwAlriiudeU,ocS.Zti>.Dift. 660 j' ^f to. o^]8li9Ci 
To»iif. Diftinccfr, Mer, ^'QPZ 36 i< 7 g-J7t''6s^ 

So Sine Pok from Zenith ... ]8 31 30 g>794]877 



[itMid-HeiR 



nploreniii 43 sS tit^^PmU. Z.ttn* 

iRKto D. Cnntv'i lomsendiooi Method, Which ii acairttJ} inie, 
theComp. of the ^ of t/Vric«/, piffiog through the Q or J), 



Compleinent of Ptnl, /_ 

IccnrdinKto 
'hen theO . __ . . _ _ _ _. 

nd ■ Circle of Detlinjtiua ii taken initnd of the ComplenwDt of 
McridtiD Au|le Bt the Mid-Hentn ; when there it bo Laiitudt ; Mid 
ui other Cirei of Anall Lttitade, ii ■ n{j atcTal yiffraimaiin, u 
ippear further on. 

O /( OrAr .-• /wf lit P^illiftic ^ camflli, bf lif ari 
(ml mm MrtboJ, tit iitriJian l_triifl ^ alieajtiaJm attbt AEi-Hiavm 
Feint ^ lit Eitif tic, eaiiM frtm ikiSm tr yiPhd, trLnptmii, 1 
itttn/ta 7iW t/ait Obftrvatim sf aa EtlMi ir Qcnilalim, attir^iig It 
lUTtbk tftbtfJbhiiaa C, itbicb ^iifyrihtSilieiaK'rPr. at t/ett, 
«-»i(JM-»tH<«™LoBg. U'bB'tatag^am^taiaiiuSina-'iUfr^ 
LtaritaJi "in fnm tbt TabU af Miridian c. (p. ij.) aaai_tbai lit 
Scbptii Mta viil a arch efDrtEnUHn at that rim. TlijAnglr 
lai not the Meridiui Angle) i, ihrrtftn itittfiJ vitb licAntti 
iltbiMtt'iCaa^; mUfiDifirauiliibr pinliiftic Angle, arcWi'iv 
M Dtaa Cowpn't mfnttd cafaJiim Mthii. • tt, whcntbe Pnat q[ 



htring fmill IiUicuik) niMiJti with the Pan r in the 'BcltFtic 
it it niiJ^irl thiE the /.MrP of the Elliptic Mr, lod Circli 
of t)eclii«tion rP, willioatain the Sura of the PARALLACTIC 
ANGLE mad the Angle ihit the £uiie Circle of Dedinitioa rP, 
the SvH'Oc Mtvif Bukei with the Vpiical, QZ j Aerdate fi.. . 
which ^ of the Ecliptic end Drcle of Dediuitioo, taking awip the 
^of thtVerticat, pafligg through the Sm ot Mo^n, ind lune Circle 
of DeclinitionZrP, uid the PARALLACTIC ANOLE, UrZ, 
will then tviintlj renuia ; vbicb it tbmfiri V. COWPEK'i ' 
tmtd tafaiiittt Mtibtd effiadinf tbt PaiaSaaic A^b, 

Ibai, the Mnon't Longitode it the afordaid Tine of Oi- • ' 

/(Tvona) of the ECLIPSE beginaing at l7rinRijJci II X Ii M 44 
CoRerpoodent to which the Z. °f Ecliptic and Circle of 

DeciinalionMrP, byTdi./'. I), i 67^9 

From which 'aR /. MrP Cake awa, the ^ ZQP of the 

Vertical and Circle of Declioatioa, at before found — ij ji 54 



Thei) will remain the PARALLAQTIC ^ bjr Deu Cateftr't 

improved eompetkdioui'JtftfM . . 43 46 9 

B7 tlieU>iiv«>(jtL NtwMiTBOD . ~. 4] 48 1 



How linall the Djffirauc! 



(E„„ 



RiHAX. The ^ of the Pole) of the Earth and Ecliptic being 
alwiyithe ComplEmentof ihe^ of the Ecliptic and Circle of Dceli. 
Dutioo, whethetlelioi tnott thinooOj (tvidimitjPrajiSin}. There- 
fore when cither the 5n or Cijf. oFthe ^ of Ih: f Poleiand^ ofthe 
Center, or Verticil >ad Circle o[ Declination, according to D. Cmftri 
compcndioiu Method, it eqoal (a the Complement of the ^ of ihi 
Eciiptic and Vertical, it ii plain from thence, that the Angle of the 
CWrr rfo called] 01 Z. of theVertical and Circle of Declination being 
taken from the Angle of the Ecliptic and faid Circle of Dedirutiu.^ 
[commonly called the BfrriHaa Z.J will Icate the Z. of the Edipti 
andVcKica), tiXiti-Xhe ParalUiHc /.• » afoitljdd, aKordiiic to D 
Cavtftrt improTtd compcndioiii Method. 
For, Let M = Z. of Ecliptic and Circle of Decti nation. 
Then, 90° — M= Z. of the Polei of Ecliptic ind Earth. 
C K Z. >I the Center or Vertical aid Qnle of Dccliuitiao. 
And, C :t 90° ^ M ^ Complement PartilaSic,/^, 
Hence, 90" — C :^ 90" d; M s=BaraUa(Hc Z.- 
i. t. Jn lit Cafe M — C = P araUaific £_. 
Second Cdi «8o<' — M-(-C = P.r*/&Hii Z.- 

Or fince, in the xi- &>/', M ii giuter than 90°'^ which Only iMffCn 
wbcn the Longitode it from OK to 1^) tberefere 
oo* — lSc° .{.M^Z-oflhcPoleigiEiaptiOBdEuth. 
*7«. — goO + M. 

And, C 4- 90° — M = Compt. ParallaSit Z., 
Whetrfbre 90° — C — 90" +. M =; Parallaait £,, .sM—C. 
Henct^ Ualvtr/allj, M — C ;= the Pitallifljc Angle. 
Or, Comp.M — C ^ Comp. Pic. ^ according lo D. Cauftr, 



atlnbiTphca\ 
VfOVrr With theMooo'i mean Aoom. to the TiNie^teu 
Find n>f 7al. p. ;S} D'i HirivfiM Parallati o 54 Js 

Coirefpondentta which theHiri'E.5nn-i7i<iN»r .. > O ^4 56 
By PaOPGRTION. 
■ TwVer^axinJSlitaii. 
Ai Rjrfh* ' . ,,-.,,., ■90* tf o* 



M''S 



'% TmaaaxkB. Altitode 



; *0 1 SB Jt fX ^ ni / J Axit of I Left f af ths 7 f for the ^ of tbtPolet of Ecliptic and Eothf 

^ly>3 SS K f tl nlEclifticJRlghllEuUi'e^ktn.}- jtiDadian»C^Mifr^tMl.«ti'lad,0.ar i msriUEtl^, 

dbyGooglc"' 



Old NAVIGATOR. 



93i 



Aarottomical QUESTIONS (in PRACTICE) anfA-cred iy SfberUal Psoportiom and 



Fer ibi Parallax in Lt*iiliidi. 



To TingctiC Piiallu in TongitddB 
- a » tin E^ l«d fitlrtB m iht Wij. 
Sgaimtt ^EtEfticftT vifiilt Lttg. 

1) w/U/f Longitui 
^rtiPtrtllaaiin 



o* o» 


lO .0000000 


JUS 


9.858353. 


35 40 


S.QlgOllO 



^t^U Latitude UN. ..... ; j ij rrfiir/J. 

t^ In ccmpntlng (he Moon't PiraJlii, by Dnn Crarber'i fieri 

bW, for thathmcof £ci.irsiior iheSvn, the Mvji'iXiglH Ar- 

ECafion my betaken the Time with tke Sus'i, wilhout fenlililc Error, 

And if, inHeid of Ihe ablalute htrimiatl Parallax of the Moon, jou 

he £«-</! of llieMoan'ihDriiontit Piralln, ibon tbit sf the 

»■ mittavi rbt Parallax if thi Mma fnm tbt S<a, in jViiiaJt, 

aJi a*J LaliuJt, 

ft OU MetM.oi finding Che PiraBaP.h ytnjli (from whence the 
PirallHa in Altitude, Lonfitude ud Latitude ire hid) ii thus. 

The AltituiJeiad Loniitnde af the Nonagifinil or ^oDeireeof tha 
Ecliptic fnrm theJiDtimn, being gompatci) by Rulei beTare deiivend, 
touiHl from Takla, on Pnrnore, for a given Latirude, 
Say, Ailtada,ii«C^i^Difl. f fftm iti go' '/ Siliflie, 
I it rtt iatig. Alt. 90* a Tatg. ^th Art. 

Thi) Arc taken ^m the l^>mpleineDt ]) '• Latlmde^ or UUUcce 
&oin Che North Pole of the Ediplic, jearea a jth Arc 

Then, AiC^ ^'k hCcSo. ^ib^rc. 
So ii Cajae jlhtnJt 900 SJifh Ii Sl<a S 'i Mitaii. 
And, AtCiifiii ytjViilaJrfSiaiDiS.Jhm 90° EcSplU, 
' ■ SisryWuj.Ago" te{V'"Pi'«l''"i< Z-'oogl't. 

ttbi9ii/<l^frieditfar exceeded by Dean Cn^'t new and c<nn- 
^ndiooa One, befoK.<lrlivciqii which bvwenr ii here given Place 
toforthe/iriAi'fd/ AflronDTTicT'i SatitraJiioD, thai he may . coDipaie 
the iJ/^rrjfW Jtftf JWi, and choolethe bcli. 

d^ Mr. Daniharwe, in hii Aftionmny, ft. E3, rtcommendt the 
nding the Angle, at the Mooo'i Center, which the finUal inakei 
lib a Circle ofLatitude, ind theste the Moon't PuaUu, in Lti^l- 
tade, and Laliiadt, which he fayi ii the mm »aA. By tbia we ap- 
jinhcod, that Mr. Dmalbarm direflt ui to 6n<l the Angle that the 
I'l OibiC mitet with the JVi/m/ Circle at the Moon'i Center. 
nrethe LongiluJet and Latitude) of the Sua, Mica, and Slari, 
;o, or are compatcd to tha Ecliptic, the ParaJlalhi jbgk and all 
the Patallaaei of LcagiiaJi, LaiiiaJi,icc. derived therefrom, muS ha*e 
alio Reference to the fame Ecliptic, and not to the Laaar Oriit. 
it ij not the Orbit but Ecliptic Place of the Moon we compute fcoi 

And* Solar Ecllpfe iSthFcb. 1737, being campuied by the Operofe 
Method in Uaaiaier'i Uraaefirfia, Iron #, 147 to /. Ijj, vis. for 
finding the Meridian Angle, culminatiag Point of the EcfipticAlte of 
Mid-Heaveji, Nonagefimal Degtee, ftc. in the Lunar Orbit, the fame 
£(1ipfe wai alfo computed with the Jame Requilitci in the Eclipiiej 
the Ecliple by the laft Method was fguod to come aia,^ to Oblerva- 

Likewife in the Eiamplet of the Ulc of Dr.fl^Aji'i Tablet (d, d a) 
.-eNonagrtiinalDegreeandPa/fl/iflicAngleatthe Moon (i.e. cor- 
rcfpooding (0 the Moo»'i Place) ate both taken in the Ecliptic [and 
not ia the Laiiar Orbit) Iho' the Moon had almoft j Degrcet of L*- 
tiwdei vbick QUI aatvtrfal Maiti o( finding the ParaUeaii /^ al- 



a bj th, 

RULES. 

When the Moon i> tb the Eafl of the 90. of the Ecliptic, the Pa 
raUaxinljmiiiaii laa^ be sidtd\.o the true for the vifible Longitode 
but when flie it to the Weftwwd thereof it muft he fJartatd froni 
the true for the yifible or apparent Ltspiujt. 

I. The above Salt holdi good for Sighi Afeiafivn, according at tbt 
Moon it to the Eat) sr WeH of the Ucriiliaa of .the Pin of Ohfer. 

3. Tht PantHax In lar/Wc beiDgaiflU to the true DiHanceof the 
Monn from the Pole if the Ecliptic, which it ata'ifl to the Veitra of 
the Place of Ob&TTat ion ,■ will give the apparent nt vifible Difttnie 
of the Moon from that I'ole, whence it will appear, whether Ibia Pa- 
nllai ii to be aJaWw, or fubttifled from the true Latitude for iht 
apparent. But between tL- Trfin, where the Ecliptic ii verticil onci 
in 14N0UTI, itfuchTimciii ii always to be ojiiM to the due for the 
apparent Latitode. 

4. In like Manner, the Parallax in Dalhaiian bring added to t 
true Dillance of the Moon from that P«le of the E<|aitor, HMr$f 
the Vertex of the Place of Obrrrraticn, will give the appaient or ti 
ble DiHince fnm the Pole. ^Vheoce it will a/^ar whether tbit F 
rallaa ii to be added 01 fuhttaA^ to or fcotn the tnie Sot the apparent 
Declination, But in Placet on the Globe which have no Lati ' 
the Paratiai in DctliaaCion it alwayi o^if iv( to the true for thi 
parent Declination. 



Iht Mcn-i j^ahi It afxtJ Star, «- ilr Difiaat, fiim 3 fixtd Sla 
lyiog-uar ibeParalkl cf UHiaJc-attrt ik.MtiaiUa i,(ita«,\du 

'- ' ha Mum'! lanf Hied Diflata frtm tin Star, r^aliiK 

T t/htr Lalhaii) tr ilj, iy ti. DiJIaaa ,f ,ht Mk 
a Ihi Saa /■ ihrpfi ar Itji ^oarur. Fnm mn tf mhcb Oifrva- 
u, lit Laliladi tf lit Piatt, atdTiaa %f am Oifirvrtita hhg taHva, 



iriae turmd Mt Digrtti (alha-itg 159 ig an Hnr) «;. 
laffi tf Iht ivit Mtridiaai tf ih^t Plata fhm tath ttbtr, rtfaind. 
Wluch MxTBDD, with neceflary Exaa^lf we have eahibiled fur- 
ther on, 

PARALLAXES detennitied from EPHEMERIDES. 
Rt/atiw la ibt Pubcbdibo Quistioh b/ the PARAL- 
LACTIC ANGLE, tmi »lfiia Tabli p. 115, ^tht 
Ei^ATiOM i^ tbi Mtam'i HwiKmUmi Diumtttr 
Mmm"! DiamtW im MittuU. 

XL. Qu«»Tiow. Tafitdlbt tnufrm iht aff»rtnl 
M- vi^i AiiiiuA if lit AfMs r 

ExAMrti I. Soppofe the apparent Altitude of the Moon't Center 

at Parii, fith OBtUr 1761, at gh 5jm Night, to be 17° 31' 4', what 

wUl be the Uoon'i true Altitude at that Time i 

H'tHor, Paialbx. 

,761 (W. 6 Noon 5 55' i-l Dei,c»ille'i^*t«»r.A;. 

llNoonZi44» 5 '^ 

If i Dt. dettnlci »i' 1 1 jh 53» I Deer, i' 49'» " 
SS' ^ 



PROPORTION. 

Digilizcd by 



Google . ^ 



'^34 



rb« ROYAL ASTRONOMER 



Aftronomical QJJ ESTIONS (in PRACT 
Loqaki 



ICE) afafwned by SfbtrUal Propoktion and 

THMI. 



To Sine Pantbi in Alutude .. . • •(* 4S 4^ 
iry ta reducing the (ma M [he *[f Ue ' 
dc, add Pir. in Altitude 



7 S. Haiii. Parallu 



8.15084 



■I 

at btfoK. J 

S, Horii. Pirall. of the Mooa'i apper Limb 41)9 - ■ 

AiitbtPdriUixot Jt'taf/etlAiah to . 17 47 :; ipp' Alt. I) 

" aeAllitude J'l upper Limb . . 18 36 4. 

'< Semi Diimeter ■ it tbit TiDK, cor- ? _ , - - 

t*fledbjTa4ir^,»i5. J * 



XLE. Question. To fi^ ibt UxmU PeraHtx 
t/^oadiMt U ber Irta Allitudt givtn, and U rtiact b*r trmt te 
•tra^pariniMtihidtf 

E>AMFtii tS> ao* JO* ]) '■ b« Altltode to find her AhJtade 
ipBit«nt i 

' PftOPORTIQW. 

AtRadliM ......•• 90« e* «* 



J*7 J* ♦ (Altitude. 



I II. If tbe Alrkude Mood'* upper Limb wat 
be 17° 47' 15" ic that Time. Sine Comp. 
■ ■■ ■ - ■■ oajs'to" 



■94*77 



Which PreficeWntar taka Notice that it bai occaSoKd id Erroi 
in the Plicci of the Tible intiilad Lmt Miri£^iut of 15* j 
butleldorD eiceedinE that Qgan^tf. 

C^ An tnftincc of redacing the appueac or oUerved Placroftha 
Moon froni theEirth'iSurtaie.to hercorrca'Ptace fioni the Earth*' 
Cealer, will be (hewn in the Pmrplt. ■ 

XLH. Qui.TioB. r« fiml t6t Momit DifioKt fin 
tit Culir tf the Earth, at aay Timt^t 



I, *c. 

B7 tha liiDe Rult, the grtti^ Di/ttiut of tht Moon k 

■1 tslltwi. 
Ai Sine lafl Hot, Panltaa . . 0° %f % 
To Cafuie Altitude o> vix^S. 900 sr Radiui . 
LSo the Semi Diameter Earth . . . 



To SlMof certain Parallax 
ComplemcM cme Altituds 
Again, AilUdioe , 

ToSioeof CompitmeAlt,. 

certain Panl. found < 

SoS. Hor, PnL . . 



. J (a »7 J4 
o Si o 

. . o +S 46 



8.xsig4 



RcnMiiu-ll'k apparent AAituJe . a? ]• 4raqai>cd. 

t^ 72*r(i(lfKWif/'C<i^i^(£<Pua!laniygrri<ttue«i appa- 
rent jttiilrda an ttaarelif/ iifiii^fiti j tbtir^fmtitia. ^vim tm- 
IrarjSijni, — and +. 

ft*PaiciPT WiiTi^h Dr. Hallej'i TtHafMt. O. Monial 
afiir tnlj t^t^\»g tkmt ibt Parallax in Misadi h ttmmp at I ' 
Sim tf Iti appan*t Dijiaia frtm rbi Ftrox, HJtytaOfrtmfi ibt ti 
DiJIaia fnm ibi frrtur i» Cat{i, ti p„i tb. PeraUex a-/anrvt!i 
ibt affarni jthimii, nfitad (/ ufinj rir fni Mtthul «Jm. W__ 
fiji fiirther, "JflbttTttDiSanttfnmtbtVtrtatbitalMJir tbtwfr- 
" parni, ndi'n Paiallai i« MitaJ. hifmai]f^m it, ttat tnu Difaau 

*fi»g intTK/id fy itii FarallaMaj it! ' ' 



'CV:^ 



itiahafir tbt affarai ; and 



erfrom, D to | 64,179 



Ltkewile the liafi Dlftance thua. 

Ai Sine fiw(^ Hot. Parallax . • O* Si' 7* 
To Rad. . . . &. }o o o 

So the Semi Dianetsr of the Sartli i 

To the N>. of Earth'i 



J S7jiS* I l-7S7>S«' 
the J^f Dlftance, 
ThtDifiaamtftUSmmtMdPkatti "t 64,919 7 tjieatafl 
tdfrtm tbtir Parallaiui tf lir/aau f- 

Earth'! Sami-Diameien i £0,741 MeanDift.Q 
[from the Moon. 

' XLIII. QirstTiOK. Tifiulfit tnu H)H«amlmJ Dia- 
meter tf tit Mmh f 

, from Obler- 
; the full Mo 
le Mtaidian, on a ^lenCiislerf DecUualion, 

PROPORTIOW. 



Zk 






the foregoing Rtftt froin tha 

accnrtte Dr. Bredbj j freiag, in the fotejoing Inttaoce, that it'i Enoi 
i4 11* of a Degree, a greater Error than the faid Pricrpt and Pnfact 
Wr\itr to Dr. Hilliyt Tiblei, hai detefled in that Author, bf hia 
.ofingtheappaftntinfteadofthet™* Uiametet of tht Moon, for re- 
.dodogthe B'l apparent Right Afcenfion and Lon^tnde obferved to 
'her true Ri^t Afccjiliao and LongitiKle of ha Outer, &^ tbe Baith't 



Ailhe hiHrval.of Ti 
through the fanK Meridian, ii ro the /Mrxva/ of Time cifirvrd.'of 
the PalTage of thcMoon'i whola Diitc, OT.ffiJI mi Eaft Limbi, over 
tbe lame M<Hlfan,/s I'l jSooto theAfisk(a and Staadi of Ejiittti 
pafling tbe Meridian while the Moon palTea it. 

j^aia, Ai Fa£ui ii to Ctfiai at the Moon'l Declination, at thai 
Timo, fi an the Minotea aod Secondi of the Equator palling the Me- 
ridian, while the Mood palTet it, (itfiriJsMai) to the M-mmIu and Si- 
(naAirfthe Moau'itrMHarnOBaU/DijiDeter njnirtJ. 

]) pti&l Faiii Mer. at Night. 
* EraurLa. ITS';, si Od. ( iib ia>7 And fuppofe S in ]• ii 
Dt la CaiOt'i Eptiem, la . f i« 44 1 ftMag the Merid, lift. 

Inteiral ]{ from Meiid.to Merid.a4 41 

Sa;f, Ai 14'' 4*"' a Lunar Dajt lai j»- •• jto* 119' jj'.of tbe 
Eijmtor. 

i Decl. •■ 0£t. Noon| 90 j£j t whence DccEnation laa 15' ai 

SkNoan $14 ji Iiib»a NigbtMiddleofpaffing, 

[iifl Ofl. 



,y Google 



t«i NAVIGATOR. 



Ato^^cl Q.UEST10NS ji. P ^^^„C TI C E) .n,i„,.d by i^.y^ f ..,o„.„ JT 



«ss 



3^ jo" e*! 10.00000DO 



le Horlcontil Dianurer rtquind. 



M. Z>f b GiiYA hai the Stm. DiamclFr of tha Moon, 
14' 4!"iori9' jT^iheDiifntnr. SukiiEtbtm. 
""'- ""■ -- N.S. diSiiinifrotohbownEHmplebyas* 



h 54' 46" 



176J, 0£t. _ 

HoiUonul Puillu £ 

r/ rfaSi,. andofttib of ibi Planm. 

XLIV. Question. To f^ ,ht latlmaiim tr JagU of 
thi Mom's Orb,l md RpanBaU/, from ibt UngituJt tf tht 
Meon'i t^odt iiiMggivta, s 0° c ^ 



Ai Ridioi 



o* o* 



aX 30 



To CoHne Dccliaitlao, romQrantot R 

tht Lonplbdc Rfiom <y of ^ 
So Sine Diff. bcCwiit the Inel. of the U\. 

aB(baCS.5inirof faidlnd. inS Mtrid. 

^fr. a insto 19>)V». in ihnCde &.,%. , . 

(Inclin-H'iOrb.withthcEcliptkbtlDB 4 59 J5) 

To CoCne ^ of the J 'i Otb wiib [he 7 

IqoinoJtial requinrd '{ *3 S' ' 

Liaiaiair ia hit Allran. i vol. mAxt 7 

(TJ,.f. 7,) j »3 *9 



_ f Ecliptic 
, uid Eaui. for 

S'lOrt.AEq. 



To Cofine ^ of <he ^''lOi 
nofiiit Rqaind 
<aAtiur in bii ARrOo. a 
itfT*i.;..7») 



.dEsui.> 



go. 0- 0" 


10.0000000 


•9 44 39 
l> < 51 
S 4 »l 


9.9736**7 

9-99S>73S 


11" 13/ V 


. 9.969 jfioi 






Createftud lciA^of[bc}'iOrfawithEqiiin.QiRcv>ig 4J jo 
A 18 Ji 10 

Tlw two laft I^cKti of ihe Ineliintion of p 'j Orb with the Equi 
ooaikl, ire the only two, wherein LitJiMitr't Table), p, 7i"«Bd 7a 
ite tnie, in lU the rSo Openlioiu j however be cum to be miSakei 
in the lUilCTof fb ejicntiil ■ Pmat of Ctmfataiim, 



, XLV. Qu..i,o,. T.J.J,hTm,fi.„ N... ,j;l,c„. 

PlmtO./r^ ,h, D.f,rn„ ,f Di„d «,/,„ 5^/*, il/„ 
W"/«!T Piano, -irf, Di/I.„, ,f ,h, U,«, /„, ,i 

tit gira D,irm»c= of DioiDjl ModonO imj j,,,« ? 

I764 0a'>l>«>3. lC.Ui.gitud.N«a "^ . . ,p^j^ 

"* _^» 4+ 

S '» Dinriu] Motioa , , , . 14 to 

S '1 Dioriul Mation . ; "T 

Kffcrenee DiuriwI Motion J i 9 , ' „ , 

Difl, J befoteD«3<10aoberNoon 7 , * * 

vi«,fr,botliJDiheruneSig.«iidDegtecI* • * 7 S< 

■~^'»'-d Af,™,„ „ "J^m,r,. f, „ ,b. DiJI.^. ,f i, ;^^ 
^ >^ PhM (or other Afpefl) at N«m, h Dir"' "JMimiu, (left 
.tll« the f«d Difterencc of Dium.J Motioni) tck. H«ir ad Ml,,,, 
fjtvrarJfr^ tbi! Kxw.iebn, ibi OnrwAna (or oUmi AfpeA I ef ,bt 
MnuvihbibatPbiiiibaffm, r- 1 j -^ 

'^"' L..LO,, 



□.66gg 



Toi4Hoiit. . . ; • '4 3B 

So Dituce of J before J n Nooa ijd Oft. 7 "yj 

i7640aober»3. * J 111" 50= 

Oft. »4th jQB Motnini, Par, 
Ai 14" J9't0 14* So 7» jo* to la^ jo" 
= 14.65 «=7.8j|. by 6? 

«4.6jji87.99*(>»''-!j«=i3'' Jo« A-i, paS Noon at 
^46i' ' Plrii, or nft 40a 40' 

4>49 



Km. jie 

K. B. U.DiraCailkiiyiMtteutioa) made (he Coniunflion of 
the D iDii 5 to bippeo on itft Oa. tj6^, inftead of on uth, « 
above. .Sa bU Efbt^iriJaftr ttM Tar ; Col. Da Phenonwnn ft 
Ohiemtiont, p. 155. 

P't Laticade it (fie Time of tke ibon ConjunaioD , i» 
{ Laticade theo , , , , .it. 

Sum 1 6 

CoBfequenfTji the Moon palTei nnder Ftuki in the iii^ Time ef £«■ 
>jia,«i. at the Diftinie of j" «'. For whaCerer PUntt hat bmB 
Northern LatiWde, or ii neareft to oor elevated North Pole, Ii ch( 
ippennoftor ruperior Plinct, when »ny (wo PJjacIi happen in Cos- 
the (jme Sign of the Ecliptic. 



gilzcdbyCjOOgle 



836 



fh royAl astronomer 



ASMiomkal QUE STICKS .ppU.d » PRACTICE. 



OrMATlON if lit LMttudCi. 

Moon'tlsit. ¥ L»t. 



) 41 1 5<> liM JOB to 



•N-ie* J litinrfe. 



D'iLaCi4D. 

Mm*. ' Ai «i/-*«- Afp.a. tf tb, Moon ™irt /W«*«/ Pl'-^h 

SeKil«,«-Oppofi<wn,« A'»,,m«../r«tiaoO, jo', 6o», «■ Wo 
i^^ivt/f^flMlfrtrnm dinthr at UoM. 

urifi ri< Mm* i* Afril 1764 ^ 

Birtn in infc EfbtmcriJafoi Pmrli bjDila C^Ib, 

The firftSign of the Mow htring Oppofi^"" ^T »W»««t, i»tlie J 
in B, ind J in *« oppofile Sign / 
1764.^76, B'tLoiisiWiieitNoo 



Diurrul Motion 

Sai. ytFIatiJfrUb, 

Frm ^'i Plate April 6, 
f,r-MrDifl,/r.Offi/l> 



PlaaJfrile' ij '. 



$ DLoroil Motion , . . . ! O 14 

Difftrence raotoil Motion J » ittf . . . li 54 

DiduKeof Jfromuitif^tffrtmvrtfh J «Naon,4>r,6,7 , Sj 
yia. from»QoppofiEi:9Jg(n*itDesn«. i 

Lo.Log. 

., A. DiBirenee DiutnJ Morion 5 i f jj" S4'"''|9'»974 

Toi4Houn . ' . . • ■ 0-39J9 

So Dift. Imii ft. Ofpofitidn Apr. 6th 1764 i Js M-jlIS 

ToTinKOppofition]) S p»ft Noon 1764 Apr. 6.5* jj" [ i.ooSS 
.tA»-iv"S';43-' 

DBCIMAILTi 

• J4''to«4'' '■oio S5' w S* SJ» 
.,9 ■'"'■9'!^*J = 24 

n».9)<9.9»4(i*.S8=s'' SJ" P»* "oo" »* ''"■''> 

J9J , . jk 4J>° 40* at G « ii i ii n iAi 



(i;^ U tU !*me itaiatr *ta art H freptrIM thi DifiJtkt t/ i£t 
Moon, w fwifirr Msvin; P&wt, fi^ aty Afpefl »/ imifcr Plaiut at 
■ M J Tie ^fl" c/ li. AfiiM, uiii a// ibt Planiii, a-i uuk vUb 
^-.. ancfttr i^ifg difcovf^BU at Sigtt, by tit aintx'd Scbtmt, of Firart i 
nbicb it ftrtlt^larlj niitgirj fir fcdins itt OffafiiUf, if ibt Smn atd 
,ny 1/ ibt Start IT Plaatti. 



O»MATi0«./ifaL.titnie.. 

Moon'iLil. i Lit. 

i764AFa6 4'N-_S»'| l""""^?' 


' 









AiH**^ 
Sos""!!"" 


19 
S 


A"« 14* to 
Sos^SJ"" 


> 


S'l Ut. *t the 


4'N.sT 




0ON.MI 



40N. 



.37' Moonruperkt la J. 
;tIRE ii for diica*eriat 

ASPECTS, of the Cal^ial BODIES, 



I tit TiMii of die 



in| FIGURE 

OPPOSITIONS, or other ., 

PLACES in the ECLIPTIC beinB given, for toy YiAi; 

■nd ill tlie Mvnb-Cijtr 

f^ X "IDiltincelntbcEcIip- 



u 



4 h^utlBtt^iettOM. 



\^Opftfi\M 



•0 Ct^X iWn*. 



Two Bodia bebg in die fiiiK Paint of the Ec%tw i* ctlkd Coo- 
Junftion. SitAi Rgari btlm. 




BiAHFLK rn. ri^HilbtTiimifftbt Mew, Fnlt "/Q^ter 
MooHtfiraiyMtMUmBiyritr-, ibiSvatad Koea't P/aui ti ateb 
Msnib atd Daj m ihl Trar Mm pvtm t 

Ftr the Ctnamaiim, tr Una Mta. 

PJice. D Plict. OlKl^n "b- 
1764 M«eh % lii^Xv' 4'>"|'0°X o'W'.^l' V^ 

3 13 >7 41 IS \^\Dt Li Caittc't\ 

_ phaDcride^ P. 

Oiarnil Motioiu @ Mid J|| i o t jia .13 |rii. 



Dtf.blaiMl Motion ]) iO ... 11 )] 

How, Ai * Dif. DnimlUotioa D tQ • it' ij'co. 

To 14 Ho«r> . ' • 

So DiB. © before J M Noon from CoBJonaion ■ »l fcie 

To Time of their Conjonfllon j* i6»mft Noon, Mudi 1.65; 

i»th. 1764, «tPB™or5'' 7" it Cr««i>if*, teqaired. 
' • mm tht Planet art nmpait tali Itt Sum impad «/ Dj^tri. 
t/D'nmal Main, 



9^717 
J979 
.]tl6o 



EuEHDATiOHi. P. Ill, I Col. 1. ;. Kid V Of A foT tV lad A. p. 131, 1 Col. If. B. SiJ>. ^tbfnm Ct. Drc/iMriM vDijt. from 
N. Poll, fir lib Ac,iohatbf^ from tbtMtridiai i, bfilban go": bia add iba ^b jIn to Ct. DrtlinalUa nr Dlfi.fr<mlltIf.Pelc,ftr ;(* 
Jtrc,v>bm ^ fnm ibi Mtriiiaa iignaiir tban no", P. iji, i CoCl. 17- forOilfcuiM r. f ii« of the Mid.He»»en. 

jif. £, Adding the 4th An to the Co-Dcclinition, when of coninry Uitne to the Pole, and nkiiig the SupplcBKnt of the Som for i jth 
Ate, it the lame u fitbtn£lioe the laid 4ttL fmm the Uft, fion the Pole, fttasthArc, SttExamf, p.kji. 



««/ NAVIGATOR. 



AflroDomicsl QUESTIONS applied to PRACTtCl 



= ,'w? 



14,796 by 41""^ 
II,»i6)S9.'*4(l''.*7=S* iWwlwfote, 




1^4 March ic 
DiutDalMotiouO^ J 



" «6 4i 


^""1 


S» 4J 


" - 




It 11 



Obcfereji i ). 

ire dlftut 3! by 
tbrcf Cling Figure. 



NOW, At Dif. Dlurml Motioa > I Sua 
To 14 Houit 

So Dilt. Sod itfoK ]| « Nooo, from 3*, 1 
Firft<%>*>Ki 



TbtheTime pift NowmlhdiDBhncej.or? k ., 

1« Qoutn « Ptm . . . . J » S» 7" 3" 



(• to »4^ fo 4" ♦o' » 9* 5» " 
=4,666 bjr 6 7 

l"jJS)"'>9*4(9''il6=9'S»'K»"yi "«™e. 






r*. T*( A«ff ittviiig Bidf ./ tji <«w, m,JI ie lift tbta tht Dif- 
firaif 'f the Di-mal M>ii«u, hfin ittfi/ln mrvhg Btdj, 1, Smi lii 
Tim tf*!! it" 4ff^h rf'"^ " ^ <"<'='»> ttmnxt tttim Baiia. 
Ttr lit Oppijfnm, rfill Mttn, 

Jl Flice. Sonbcf. OppB,}) 
-— --U" i 41- 

pppofita by fIk Fi- 



Diu. MotioDi Sun ft D I 59 3' 

Differencg Dimaal Motioo } 1 Soa 

NOW, At Dif. Dtaiul Motion ]l \ Sii» . 

Toi4HoDn 

So Kft. Son bcftor* ]l uMooo fron Orpofitian 

TotheTi»ep»ftNooiiofliefOppofition«tfarH, n" ii»|o.<9zi 
, \ » s «.Cm— 



o.l9.]6j4 
I 0-1979 
10.9189 



DieiMAI.t.T. 

1 1 J* 5;' to 14k lb 7O4' to III) I in 
s Ijijio ^7°,o66 by 6] 

*i,j|6!.)r4j=*4 
Ij,9i6)i69,s84((,i.,,j=,ii.,,»„bifore, 
Ij9i6- 

30414 

.7S3» 



Ron. lyrs 
N. B, Tbt Difftma ef MoiiiMi, a Tbw, ilnttii Crteowiclt 
aJ Puii ii 9B lo', (£ar t^ /am Phanomenon i^fiiu fmtr at 



Sun't PliK. } Plice. Sun bcfon g> 1 ]) 
17fi4Uudit4 U'Vio* 44-^ loyiSli" 51 44" 
15 [j 10 o (ij 5s \Nttt, T " 
— I — — Ij" Diflance by Ei- 

IT Motiow Skin & J|.| j9 iS lij ay IgDre fei^alag. 
~ S9 



DiflcKute Diuroil Motion H I Sua 

KOW, Ai Diff. Dionul Motion S 1 5ui 
Toi4HDDrt ...... 

5a Dift. Sua bcrne ]) ■[ Noon ftooi g> the lift 



:-»j. 



9. J 176 

0.3978 



DlOKALLT. 
11" 18' to H** ^ •' S)' * 3* J*" 

1M66 =i.g8j£y6? 

11,198 by 4 J=7 

17 398 



Rem. 6508 

N. B. WlmaPUKtunlngraJi,lbiSiim,'a^i'fft*Difffrtixi 
if Diurnal Mtim, miifi ituhafirali ibt AjptBt, 

XLVI. QiTEiTiOH. Ttt find ih* Timi if tht MMit\_ 
«iid»lfe a PUuut"! Sntbins, Bifiagmd Stttiag {fta£\ialij) 
fram EpbtmtriJn, atdfrtctdinglabUi, 
FiKT, Far tht Msaa" t Ssalhiai, ir Faffigt thnii ih itaiii 

RoLi. Soblrifl the Son'i BJBhl Afrenlion in Time, from th« 
Mooa't Right Arconlion in Tiox at Haaa, on the Dv/ preccduie ' 
rime when the '])'> Southini iiTc^aited, and the Renuinder uill 
X ihe Time pncalinj Noon, of the Moon't Dillmce from the Me- 
lidiin, '•■i^en the Sna. it Nooo, it then upon it. 

NOW, while tiiei'«i(l>y tbe Earth'i Tcvolvint EaAnly on it' 
jitiij n ippirently deputing ftom tbe Meridiin to The Weltwvd, *i 



viAfabdd, iCol. wbetliertbe HciidiM 



|5> ItmaJirimijiiamitiUfiadiMilbtTaralLaic^'P.iit.hf^. Cetuftr'i imprftmi tt^aJiit 
j_ u f lutet or lelt tbia ao<>. i 

*- * Ecliptic Pi»w. ^f~lO P 

■Jht Meriiko £. ibow and below the Ediruc, aad one Side ud other of the Meridian, beiog Suppkmcou of euJi other to i Eo» nffefti wly. 



■!>S 



Ue R OY A I. AS T R^0 NO M E R 



AatODWiical Q^U B S T I O N S ipraOically aidwMwl, 



r Hourt » the Moon mnced of ccming. to Ac Mrr^aK, the ii 

ncing tDwar^iit, lod would ar^ve rhere, inthe Maonci ori S«<r, 

tbe Mooano Eiftcrly M*wi>>'iii theTimeaf theSuil's piffing 

ihofc Houis la the Weftwiidj deducing the conctary Mption at Ad- 

oribc^un'i Right Afcnifion ia that Time, (« che EaSwan) 

(PtviHj. lit) all the whilc-Bimuig the Star, *rid acccleciting it'i 

' proam to ifae fame Meridian.-' But by ihe Mi>on having a moce 

ifidcrablcEaltcrly Motian of Right AfcMlion in 14H0U11, than Ibe 

I's Eaftirly Motionrf Right AfcinGon in that Time, therefrjie ihc 

Moon'i Approach or ^oming tn tlie Meiidijn la tbeteby retarded or pro- 

lonied i bjf ai muth-a the Increafe 0/ the Moon'i Right Afcenlioq 

- Time Eafterly, from Naon, ecceedt that of the Sun'ain Time the 

■ne Way, during.her Approach, from Noon, to the Meridian. For 

Nile the Sun W ;iung that Time id the WeSnarri, he fpendi thi: 

Diftrna of Increafe of (he iv™ Right Aftenfioni more thin the' 

MuOD'ifirltDinance in Tine, from the MnidUn, while the Moon 

aSl/.arriires there. Hence we bjve thii xavtrfal and -tvrrH 

uii, for datrmm'mg the Time ot PaJ/agi cf the Moon, *Dd of 
I the Plahits through the Mebidiah. 

jfi 14 Htari ii ti lit Diftarenee is Timt. tf ibi Meot'i Iniaff 
if Sisii. ^fanfin ahavc lit Sm'i [at Inciufa of the Sua'* Riglit 
-"'-n Aon above a Pknet'i) in aarTtm,-to ii ibi Difitna 1/ ibt 
I fnm itt Sfn'i Right yljcafiem (w Planet'a Right Afcenlion 
the Sun's Right AIcen£on) in 7imi, m lit Mn fnaJiug ibt 
Timi tf lb* Smibing nfuiriJ, Is tbi proportional ^(tm/i ^ ibt' 
•toai'i Sight .^ctnfta Bbnt ikai bf Ibt Sui't, >> Timt, (ot Svn I 
ight AfceaGon ;t»ut oriels chjm a PJinet'i in Tine) le ii added N 
• Moon's or f/oKi'i D^Mci frm iht Miridian m Nnon [but /ui- 
aaeJ Trvm a Plaoet'i DillaDce at Noon, if the Sun li the Body ot 
lifter Motion)/af iif fut uraceurtuTaiit o/" South injs^rit Moon ar 
lAN.r ftnbi. 

N. B. ffbaibtSi.ii-iSigbl^Bjm it rnixirliM Ibi Mtaiir 
lewft Right Jlfteifaa, ■n Hi^MflwrnJi ht tddcili lb, lailtr, ib*t Sub- 
aBiMmyttmuiditfitiJbJi. Md ■wbtn ibi Plain mntt Riirt 
■a^.ihiiiumtf lb* Diu'tol Right Mffiat afiitSunir Plana, in 
imt,ert 10 bt lakta infitaS »f iHt Ditt'irraDce, in ibt fsrigting- Prr- 



. DLat.S. HDccI.S. 

I i" h''\ ^'i' ii' 



DilTcieiiEe In 44 Hour* 



Decteafe, Decrc 
lay* I O R. A. 
' 7" >S- 14.- 



J'iR. A. loJDlf, Noon . 



+ *i "S 



It. i Tim 



J-sR. A. ujuly. Noon 1761,13 ,g J 
p '1 Diutnal R, Aicenfiun between lo and 11 July 
Sun's Diurnal Right Afceofion ... . . 

DiSbrence of Diunul Right Afeenfion , , , 

Now Jayi At 14'' I 39" 4i< i : ijh ien : icU 
Difference p'l Ri^t Afcenfion and O'aRijBtJ! 
tor [he corteQ Time of Jt'iSoutbingiequiied. 



»5 4" " ^ 
pi Southing lotb 
(nly part Noon, »c- 

if ijli 3a« attrrira- 



N. B. The J'l Right AfcinBonin TioK anfwering ti 

Longittde and Latitude of the Moon, arc more readily found ftoat 

compuiedTablii of Right Aixnfion in Time, uTweiiiig to Lonai. 

tudeandLatiiude at Sight, °^ 

_ Long. Ut, S. B.A. J, 



DTf. DiumiJ R. A. .... . . o 4obw^, 

Or the Mooa'i Right AfcenGon in Dtgreti ii found bw~£ StHCi 
PnoroiTiOHfromcheDATj|{ thna, 

Ligarittiia, 



Ai Cofins Declination _(N> or S..) , 
To Cof. Longitude from rtru E^ulnq 

lial Point hcK precriing , , 
So Cof. Lititude ftoni the Ecliptic ■ , 

ToCof, R, A. from the finte Efoi 



JJ's Right Arcenfion from tip 



i" »i '> 



IS ]4 iS following. 
_, „,„ CotTsaiy and nearly aijbom, 

J^l, A»Cof.Detlination- ... go 50' " 
ToQof, Long, from <V prebeding .' . M ( 
So C»fine Lat. fcom the Edipik 



3 59 , 



To.CoL R. A. from ty* preeediDg 



])'< Right Afcenfion from ly 



9,9885776 
9' 9989496 



9.992709: 
■ R, A. fViMi. 
t> [V preceding. 



r, or Iht D^™. 

(11 3iBK f,r Ibt Aftiw'j SoMibi, 



» ipprotrmatt 

Sunitf^fi ,h, 
-- ■ -,1, 



,P: ™!" '*' ««^ ' Soa,tj„f n ditefily Waccuf.lely dt«™,W 
(Am ^ L„^,n.d. ndl^i. ,f,t M«^gh,n for n^JuttUnt DajtJ 

it.rr>M..fa.^i^nS,.ib.,g/a, ,a.g6.ly%l^i„: '""^' 
LiADBiTTCR III ii, Apronmy (p. 164, i6e, 1 vol J *• „ 

ffiimal, M^btd, fndt th, ^imtu Soi-ibirr fnvi tbt Wwa't A. %<,*. 

ibtn frm iL. Plata and Ladivdn 0/ tbt M», fr n» /««rffc £», 
findi Ibi Motn'i Plait Is lit iBimaii Sctriing ij Prspartia,, and I 

■it Sifbt j^anSim of Mte, llo-ile i ihtn bt AWi lb, Sun', Fit,. 

lial ^imau if*,, .uiboft Difftm 

fimt of Stnlbini f«- ,bt true T 

MmdiaitiM Tiau, wlt/t lit Mtc. 

higtrat. If lb, JMw. /„■ ,b.S 

iht fnta^tit Day, wiiU I'j anrly 

BoT if'tiMj-.nnndS<,a',RitkijtJ,tnfioniu~,~dai!ymaiin-Efhe- 

mer.d« ih, Dg.«t, ./ <V-*7«-A - M».'r iiW^fitaS- 

Sun , Rigbl AJctnfa^ «.,* ataaj, U tbt Mm-tfrtt^w hilant, in 

pwporaonal fl,rf,-^,T;»,, ,U,m.,fir lit E«rf. a/ tuinirtaftsf tb, 
M>» . ««j4r ^i>;Aa akw ,b. Sun', Rirbt . AfcaSm im that Urn, 
j.«(t»tf accurately fl*/ftorlly ^ndibt Mw.', Southing, flr™ £»„' 
*,i*.4»a/^ri*CoiioifanccdqiTem., or ariir Ephtmeridei, w*;™;- ri 

r,,«/A.dd lb, d.:l,Intrtaftsfib,llf«,', Rirt, Aftn^ .*«, ,t. 
Snn, Sight ^ctnfiH ,n I,«, « /*, Tim, of ibtfirmirD^', S^,bi„ ,f 
fie Moon, _,=„ W/ «rr,«i (and not w.rly)i*« tb, 5™, lm,r\di 
later, of the Moon a Soutl.mf, ,n fna^t Day, itrurhmt. H. Tar 
And th. >«< KiltbMtgi^ fir filing lb, Tmn. of lb. Plana, Sowlb- 
•»£, fiic^'tl^. by adding »■ fubtraaSig t, and ftw, lb, Tinm ofil, 
fsnn^D^f, ^oajkng, lb, Dium-l Dijir,«, ofRigt, ^>-™&, ,f a. 
iw Bnd-ii, at^ordinga, ti. Sun (appirentiy) i, lb, firua- a fajhr 
mov,ng Bodj ita, Ibat wbcf^Tlm, ,f &Mii.g i, fong^i. '' ^ 



,y Google 



and N A V I G A T O R. 



839 



AflroMmical Q,U E S T I O N S pnaiclly anfwerod. 



Mt.C»*.i„B.«T (who )n»4oiu: SerTinr w ft.rt«"i"J !■ 
hi^ 4fr««r,, p. 3,3, findi Iht ncir Timr of die Vlf«,-, iW/«r, hi 
t^.i.K tbr B ■. Rigiit Afrrnfioo from T.blu. .. if (U h*i r7uti^ 
(ude ; and then (0 fiml » Dill nsirai Time, he milui Eaamiin foi 
her reil LatitiiJr iccordiat to the Jijii Iht Mooa'i Place ii then iiu 

A.ki. u....^! „j eirj,w»h«H(i»e it >• phmupoffi. 



U hii Methad ii 

with I fmill Impni*ci 

Ih the foKgoiog Eij< 

'167,, July io> 



J « R. A. wirtugt Lit. to joX I' i67». J"Iy 10 > 

ItNoOB . . . ■ t=S*»>' IT" M. 

SontR. A-theCwieTime, WfromTib./. ai7 . 7 ,j 4 

Ne«r Time af Moon*! SouthinftTfii, Jjxly 10 at Pmi 7 
Kdli, Addto wbichnnr SoutfaingiB It ' 

Hoorth^eof bdng iboui ihe Dif. 0" 

Time of D « San is >n Hour it ' ' 



[inglBji fomeir ) 
: Dif. ofMatiouiii t 
-itaMciu . ■ J o 30 , 



/««<-(rTiBie Jl'.SoolWogonlh«Daj,pift Noon. .1. 40 
: E<iu*Tioi. jVt«i(-i]| «»Wj«rtWr.Bretit. 
RoL*. Atgt«a(enLit. i<>iiiag*Dif.or Time,? 
bpieicntUt. 40 3]'3. to 7* i6t<|> ... J + 7 

t'.SootliiB(.MPdritT7S., 7ii^lop.«,Ki»n . i; 47 „ 

l-t.N. . . J - ( Lat.S.' .' .' [ _ 

W. F. Theibi)Te»5FWrttrirf»iriMinthe7«J«««dvenbut yotoo 
much, fretn the trae 1 jme of Ibe Moon'i Soutbing ; md theiefoie if 
.iAthe///)Equat«iaonl7f.«j«,-.^,4,/flj9; „iUbe worth lie- 
coming frequently verj near the Truth, at the fame Time it ii 
teiy reuly for Pra/Ua. 

The mbamcT,uJy,i,itfi„tr, MffiaJ of finding the »eir Time 
of the «™ iStiiihiKg, i) by multiplying the D.y. of her Age by 8 
Tenthi, for the Hoori and decjind Partt of an Hour of her So'jthing 
paft Noon, which are tomed into lUimila, nier.tallv, by multiplv- 
inttholeZh(»u/j>aMf by6. " 

The Moon't Age, 1761, July 10 . . 10 Dayt. 



WwrTimeof 5'.Sojithfoath»tDa,paftNoon i,* .i» 








Oc. 7./.ll«l 5* li" Mom. 










U. awcrately, 










ifi - Pku', mjinf ^s.i,h.z^a 

ex, nJicfiUftaixUgiva. 


a,.i,. 




r/j,firajfi 



EXAMPLE II. T(>i ,bt Thm tfrt, Meon'j Rifing a^ Setting 

Qra!nw|ih OtJh^Aitr,, ,7(1, July ,o, ibi Tim- tf ibt jMrn'. 
5«(fJ-mi«Paiii^,'™w(r_y,i«;i.£*,/(Hi,n^((ra„BJl5b4in,g., 



Ittt Diy ptB H 
Fu,T, /,/r/ 



As (411 1, to the lime oflater Soothing of the Moon on the ftl- 
Wing than on the foimei Day, in the liiae Place (or to the 
DiffeteiKeinTlmeofR.A. of O and 5 ina4Houii) 6 J. the Dif- 
ference in Time between the/jjf Meridian, and any other Meridiln 
iyiOi EafimfTifi therefrom, to the Time of 6»«»r or il«W SoothloR 
ibfrt (refpeftlvcly) than at the fej! tUa 1 Kcfconlnl by Time in the 
famdPlau, 

J South* P«nj, i76», L«Caay»iffa«,l'''>i'^'**.i5''4i" 

Djft IT" 
j7' H* to 4ini fo 5" 10" to i6< Meoa fimit later it Crtmelct ia 



Fo., A. 14b to »4b 4,» J-, later So.thiag at Ftrt., ft. 91- , 
ff™™,i " V'^ "^f '™ '" Ti-M, to ,» jl. the Moon 2 gc 
from P*-« to CnnMHirf Meridian. 
: '^M"* ? * '■'"'tt'.«i'^.inP4™Tim«,J ^j ^^. 

Time.fpent by the J goiia from Pwii to Crus- 7 
OTf.'i Meiidian Weflward of Ptrii ' 

. D fiiulht at Gnanich in P<ni Time 

QeJuft gB xQi^ Time : 



oCna-I 



'rttmaiib than 7 

. . J 9 " 



r7(a>j.io, 5Hinth»atC™»iw(i, in<;™mi.«i7 
Timt . , _ _ . J '^ 

„ ^ * P. M.. a. befote. 

To isDici EpHiifEaiDit from -om Mhidiab to Amo- 

rxia. Ani fait InmpaHiie GrttmaiibMitioiAH. 

_ UmviaijiLLr, ^1411 i, ,,911. io> f,i,itifcl:avif,Oaj'l Dif- 

^•e"'^lt'S.MKM-iPiati,Mm-iUliludtadDlcrirt,r.B,srj4ihDiffi- 
rnti sfLtipmdt, Latiinlt, ifcrfimlicn, tad aifi Jaih Diiinga cfSnii- 

•HfflbtPlntu, n- SU", «f*,rerpeaiw 

lidulli, er'-*^'--" ' '' -• ' ■■ " • -J 

la, tec. « Greenwich f wmftomfcM « fi. rjmi.'p/jr,,. ic. 

na. E,fl*.rt ,/ Cre«n*icUT4. /«« ft&«^ ,/ ji^ .^ 

biUifir «y ar^ Difnrir of MrriJitn, ]«,1,ad cf 5" iq» Weflt 
ward j^Pari.— 8«,xiYAToaY. Arf;/-ti. Afo.AtfB,-, EaHwani.-r- 
^Mrf •/ Weftwird ,f Parii, gr ./ »j, .i<r >^ MiriJia^, ,ha ,„ rnW- 
'w Paria ?/««, r™,. ./Swiiiiy, &c. r« ib>fc /^ a,y abcr b.^ 
MmJiat u amfpnJ -u^b » SaadM'riJi-' (E^flviard of Greenwich, 
" .'f" M Maiiimn) y,u mufl fubtrafl Ibt PnfKtinal Dig. ntn ,bt 
<it,lfD,g. iporafe., fVadd U ■aU^tiiJtilf Dif. deo«.te^r= ib, frS 
%««>«, raIpeai,ely,jV tU ^wi/i„/.<,,ii, r«rr.>»rfi*j w-i-i. 
-iffwrf AttriJiar, 

And, becaulc -S ? *°' 

LT, Any daily DifteicDce in Pdrii Efbfwuwi/n, being multiplied by 
6^ aoS four flgutn cnt off to the Right Hand in the Produa will 
give the noporlloaal Difference 10 be added to or fubtraAedfiom 



Planai, n- Su", n tbi refpefliw ftn#««/orai/ Di/aoHi I, i, 
orfuhflraaidfrm; tiffr^Da/ifima, Phut, fc. «A'™, 
"ll>.dt,lftiiS€rt-cti-rrtmS'aiKrfaJ,^)w Ibt Tmli, PL,. 



B1D065 neaily. Theitfatc, sicimai- 



TimeofSDuthrnfit rrarfitifi. ij 41 i( 
Corrtrpond.toTI/n^ofSoutliinKalPanVis 41 o - 

t>7i( Smibi»[ •ifpltmi and if lit Mton » tS PI*m bitrfy ai lit 
w Tiw ^ lit Day ct Nigii i. tacb Plan, it rming 11 lit Stt Si.li- 
g im all Plata ai 13 ar A'nm, u- ibt femt Tiwu naSlj inaci PI. 
fnm nbici Luminary, (meafuiing Ihe apparent Time la all Placa\ 
the Cialeaiil Bodiei Tary their DilUncci, but a fmall Milter in R, 
. in «4 Houn, or dlonial Circuit ; the Uoon Tarying her Diftuoe 
R. A. in that Time the BioA. 

HiHCi, tiie Moon varia ber,Time of Soothing at Cmnvici anl 
^ligaa in the Wiji-Jniia, \m the S'vtib Part of her (Aanu/Dif- 
fetence later, at the latter thin at the former Place. For, 4 fioci 
Diff. of Mcridiana it cgnat the one Sixth of 14 Houn, in whic 
l^me t^dlutaalDiffereHce of Southing ii performed. Which Vj 
~ 1 of ])'• Rouihing, to an Hour Piiinw/ Difference, «iU be 
1 Minutei of Time reckoned later at vArfVa* ihan'it Onti.- 



,, Google 



n-t H O V A I. ASTRONOMER 



Aftrohomical Q^V £ S T I OH S -praaically wCwtni. 



ipute thi mjiiig ani Stirhg by. 'And, if yot 
fcjjld compute tht Rljiiv and Suiiw of the Planed, in iny Place, 
Che Time of their SoutHing {ini eTpeciilly of the Stan} miy b< 
ikeii, with ftill gteiter Niarittfs tt) Tmili,- fiwn EpbimtriJa ti 
.jtvefMlheTimeofSoothmini inyonePlaw. The Diffeicnct of 
the Su-jftneft o£Pliineti,(Jlf«vBij'idiffeteiilSouthingin 14 Hourr, 01 
uB, being fcldom above vt Minutes) imount not lo above 
of Time Bifterence of EouihinE in half' Hit Globe Dif. 
;b 1*0 Pbtei i and fomelJmM not to » Quarter of -Ihai 
Qmntily. 

Bai, *hatever ihii DijfiTfliM' ii, irhttherof the Moon, or anj-of 
the Pl»nel't Souihing, il it readily hid from cotiffllr compoled Epbt- 
meriJii f by which the Sonihing for any PIic* i) coneflly fbond, 
',e Rifinr and Sali'g of tbcMiM tiii Pit 
followr 

Ut. s. 
■ 33 



had for that 





Ijh 4,n ,61 10^ ,4.' - 

BfbuthiP.M J Deel. S. "' 



lOJ, SmiJurMin Are, coner- J 

34' ]| S. Decl. and Latitude > 

»K'f . . . . i3 

■^ 't SoBchiog 



's 41 



WjjrTimt J'tRifing loj^^ ., lo ji 
Setting . P, M. 10 JO 

a Declinitioni talSiSitr ( ii" 10' J ^j d„ ,■ 

-thofcw«.nTi»ie.t^«4i 9 >» J 1^ P«>I™'"" 
° S' DeiT. DecJ, : - ' _ .- _ . 
'3 53 
" 39 



, 103, Semidnrjlion Are, corref- T 
I* 39' J) S. Decl, Latitude Gnta- J- 

J— S" 4'» o' 

J)'i Soatluag . 15 41 16 



t] 

J) '1 Southing . IS 41 



Otrkwiii, To linl the 1 



e.Rt>iHe of the Pl/ 



O R, A, Noon, fiune Day, Di U Caillt's Ephem. 



'1 

3 »3M 



Near Time of ])'■ Rlfin) «76i, >^ lO . . . 10 a 

Correfpondent to which near Time afRiEng, 

,'< Place toa'Klj' latitudes. 40 iS'obliqueAfcen. jjli j 

0'«TI.A 7 a 



Moon'a tnie 
t«*wici 


Time 
Refr 


of Rifini 
ftioD here 


176. 


CI Jowedforf 
Pad Noon, 


16 
—6 


14 


10 34 


Or 


UK Moof'i Pai 


AtL* 


I AKK RirtACTtON 




..fi-Jz 


Horii 
dingt 


e Rirmg and Setti 


not cooGileitd ; 
; of- the Moon 


the foregoing 
and Ihe^fo.e 



>ic Rula And the Timei of the iiue, and not apparent, Rifiog and 
Setting of the Moon. The foregoing Tai/ii of Sn^idmrad Ara an 
computed by allowing for UifrtBia of the Ci!,fiial Bodiet ; an 
therefore they very well ferve to God the apparent (not the true) Ri 
Gngand Setting of the Planets. 

But, the Mud n having gteat haiixmiel Parallax (and conlidenUe 
ParalUi in Altitude) that Parallax mult alwaj's be con£dertd, toge- 
ther with the Rtfraflia, for determining the Tlmei of the appa- 
not Rilyig and Setting of Ue Sud >nd Moon; and thence to find 
wbeiher an Ecllpf, or Ocsuliafva, will be Tifible.or rvoi, in a ^renPlace : 
which il one confidenble Ufeofiithac ii called tiipittimt. 

TheviGblcAltitudet of the Moon, or other culeftial Bodiea, muft 
be truly augmented by FaralUx, and dccreafed by Refriflion ; becaufe 
thofe Bodiei art apparently depteftd by Parallii, and raifed by Refrac- 
tion i which contrary Appearancri, or Eflifli, muil therefnie " 
way! truly allowed for, (u above) by a contrary Aogmentatioi 
Decreafe of their ipparent, for determining (heir tme Altitude! 
thence the true Time cotiefpoadent. St, likewife, on the ccn 
the vilible or apparent Rifmg and Setting of th; Moon mull t 
termined from her given real PUa, FaraBas >nd Refraaioa, 
given Day, by reducing her real Altitude ^vcn, to her apparent Ri- 
fiiiE, by Meani of her horiinnlil Parallax dipn^uig, and RefnfHon 
raifing, her Body, at the fameTiiqe, 



Or Vu; 



D Tairi 



HiHci, when the Moon'i Parallax in Altitude, and SifiaHita 
« equal or alike, there ii noDiflerence berwecn vifibk and true Time, 
rib between the Time contfpoadcnt to the vilible Altitude of the 
H, Mm or Star, and the Time cotrerponden't to their real Alritndi 
'hich Timei difler, when the Parallax and Refraftion of the Si 
ieu, or Star, vary from Equalicv. Thia Vi/i'iiiiin between vi- 
/lUitni irac'JiiMtherefottiefpeflitbev/J&acdirnPlacei or Alti- 
tude! of Che Sim, Matt or Star, in the Heaveni ; which tiKTime (only 
lefpeaing the ttue Alee, not the vifihle Time celpeaiug the viGbli 
Altitude) il eqnalable to Jlfnu or tjual 7imi. 

Tmairoai theitf/raftgu of the culeHial Bodiei muR, for tbi 
foregoiitg Reafoni, be alwayi taken into Cooliderition, and the Paral^ 
lata alfo, where they areconGdAable, tor dtfcovering the trmiTa 
which o^erwlle, In the Refult of Computation, will be (he rifible 
Time; conlidetnbly diStrtnt/in fome C^lei, from that which i: 
Which true Tune, aa it icicn to the Soo'i Motion, will be ■ 



,, Google 



W N- A V I G A T O R; 



AllTonoraical Q^U E S T I O N S piaOically snfwcred. 



''uiaisi hep- 
,1 and mftli 



otherwre. catltd (he atfamU Tin hy the Sua, to be reduced, (m 

aforefaid) to tf >al oc C/tciTimi, by the BfusiitMi/TimTatlt, p. to. 

Tb! Tim cj 'ibi viffili (k'imaiin af tbi Sai diu/ Mtvl, Juli fftm 
ittEarrb'iSurfaaiahiMfiJifmfitmibi 7uK tf tii tmt dnjia '- 
a^mttd tipptar pam ibi Et'ik' t Catir i Entipi lit Ctrnjuiai 
fHS is til NanagduiMl Ditra tf ibt Eti'iflii, wia . ' 
Ym, tntb^fium. 

HiNci It fdlima. that \f <ht Im CagiialHit h in lit Onentil 
^uaJnntttf rbi Eclifik, tr til-ana fi( NoiugeGmil Digret anJEaflmi 
Barixen, lie Mm'i Plan li lift afperadj ad^aaad Eefitrty ij tur 
Parallax of Lngimit, B«d lit Timi if lit mjiili Cmj-aHiM will lit* 
tiktfiritbiTmit tinntCtnjumaiin. Pn, if Ih ttvt CoajinHion 
ftllin Ocaiauil ^uaJrani of lit Edifiic, or brtvm lit Vonxittaati 
Digrii of xhi Ecliptic a'.dtyeJhrmHiTaaa, tic Motn'l Piacrmillibiitit 
eppamlh aivnccd ffijltrly, fy 41 niiib ai tbt AUnn'i Parallax ii in 
Longitude; ai^ a^ft^aally ibi T,m, cf lit ■vi^l. Cij.i:,fl„n ■a,ll fit- 
lata til Tina ef lit Int Cww-flim. Wh.ck Difiinflipa, tf i-i£blt, 
tnean^iAe equal TiHu, atiof hifaritait laitinvaminlttCimpkiaiitii 
^Eclipfc!, m mil at in altir Pari, ,/ j^nemj. 

THif'recoiBC Account tf tin DiftaBittiMf Timt, inn Aofwci.to 
one of oar Correrpondenii and Subfcribcr^ wriijn; thut. " In 
"altibiMtiiaJ>tffiiuHtrtbtJIia--aftb<<Nii^ijibiSlan,a, mcy- 
•• ihn U null wbnbir ibi tjvaliim cfTmi i, (o b, laiai iaio Canjdtril- 
" lisn ir tttttr vinkir itr Timt fsald it a^rtnl w i^ual ; fmt Pa- 

fle iiiagjila Lcfi in till jlffair." 

N. B- As tbe fiited Sian have no fenllble Panllu, M^ their Ri- 
fraHii* ii to-be coufiikred In Sndi ng the ^mp of the Night, ipfuient 
Iblar Time, by their afpartnl Altitude, 



affaral It1fa[ and Sit- 



Fill 



, fat the Mooh'i ippireat R11 



f Without RegirdrMoan'iDccl.rH 
to PjhIIu. 1 corrtfpondeni CO 
RiGng lo^ j7») iioSjg' < 
SelliBg20 S9 (. 9 aS I i 
Moon below the viGble Horiion at hei ip 

Rilin( by her Ilariiontal KefriaioD. 
Moon' ■ Horiiontal fnallii then .. > . . 

Mddd'i true Altitude iboTC the tnie Hotiioo 
. ippirent Rifing , , 

Mood'i Zenith Dift. So"" 37' e" Side op. ^ required 
Cmnp. Pole's Height ^ " —-■--•--■ -' - - 
^-iDiIl.A.N,PoUi 



[di k Cailh'i 

ss 40 + i 



ji 30 jS)dt.inclu.7L.S.i 
39 oiz.reqniH U.S.i 
ft. Merid.^ 



Som 119 47 30 



TikeComp. 7 ,__^ ,_ „ 



..Us.%. 
. Log.S. 



Ligariiimi. 
o. 1056113 
0.0090401 



9.9875951 



Double 74 10 » ^ Apparent Ril 

Now, At j«o° it CO lit Interol f/Tmi inmiixi mn and Faffa£a 
tf lit Moon, iranvPlina, liio-.'gb ill }amt MiriMan, b i( ihi anp- 
iar Difiaa,f of ibal Otlrpal BtJi, from lit Jami Mtridicm, rilbtr at 
appar/M Xifnt.Sttliig, nr a«y Milndt, to inDifiaaiiia Timtfraa 
ibi Mtridiax.—lt bi Jabiracled froBttraddidlttUI'm of it'i Sovlb- 
ing, aiterditg m jr ii aJvanc'nig tawarib, r bai paffid Ibt Mp-idian, fir 
itriai if Bi^ag, Sitting, er at anjgtviaJiliaidi, 



MoonSouchi 

>6 13 



Dt la CaiOi'* Eph. at P.iv. 



Diflerence 14'' + 41" bifierencc ilfs it 
Kow,- A-i 360" to \i^ 4j» fi> 74" 10' It" to 
761711^10, ]| SouthaucoM'.itCruiRwcfiP.M. ] 



17^1 J!"^ )o. Moon apparciid] 
■wi-b F. M. accurately 



ty rifti at Cm*- 3 



35 »7 



N. B. TiiDiffmiictifibiTimt 1^ ihiMtmtr a Flani'i SmiL- 
ligim lacb 14. Hmti, ii —if the Diffimici if Rigit jtfeafaa of ibt Sua, 
end if Ibal Plana, i-Tiau. Tit cal^ial Bi^ Siaiti^ /imr sr ' 
raft Drf, attriing at if '1 Mitiia ii fitviir ir faficr lidn E^ 
Maliia ia Rigtt Afeafiia. 



NixT, fbithe MaoM'i apparent Settino. 

1b.DifatKiifHirixiMal Parallax alMm't Ri/iig atd Stitiag 
hinf iere iai 4" li/t at Sating ; ibijamr ParalU* may ti ujidal Stiling 
11 fir Rifxg, vji. 5s' 40" i vAiMC, J 1 Inii Mliliidi al afpareal 
idling. Mil' 40"; ir i^> my nia'lj, ai itfin. 



Moon'i Zenith DJ 

" p.Pole'iHeigh 

DiO. h. K.Pole 99 



Sj" JT* o" Side op. ^ itquiied 
Comp. Pole'tHeight 38 11 10) Sideline. I L.S.c 
■ 18 oJ^re,d. JJ..S.C 



Take Comp. 7 , - 

l'„le-sHeiBhti'"«-7S- »«■ " 



Log.S. 

.Loe.s. 



Doable 77 
6x' July ]□, Moon So 



Lagaritimi 
0.105S11] 
0.00595,1 



$.98550 5» 
9- 3918087 



irent Setting fr 
18" to 5h 
* ac-> 
^M.J'S 



19.5908813 
9.79544=6 

fr. Mil ■ • 



f"r " -^' 

' [teijnlttd. 

^ Fi'rdini til aauralt Timi if Ibi Moon'i appaitsi RfJStg and 
Saiing^jidalp'ibcaccuriiiiTinii cfibcNiriHiitihiLh it pafotmtiintht 
lime Manner) :e bn- afpafim Altiiuii, bai . tut iiaa jbeviB irfort by 
— jluibtr ibaivntavi fin. 

VHiKlTia yuo would determine the Time b\ the Afoni'i 

Mi'i Altitude, in any Latitude, to ■ Decree of Acciiraef, the Di- 
aliin of the coileftial Body aC that Tivtc, mttft he fiitt delennir 
u war ai f^iile, by taBfiimaii of the Time'; allowing fot Rcfi-, 
iicn,t.aixlb, Parallax i or the TinM will diHet conlidenibly from the 
Truth ) and anTwer no End in detent) Ining \ii>t Ltagitudi From that 
Obfcrvatioa, Fot which Putpofe, to facUitate the (^taiioo, rorreft 
s of thE Sun and Moon'i Plant, Dalitialim; Rirbl 
jBc/aSixi. ftc. with ibiir Diffirinai, foe each Day of the Yejr, 
■ ^- ' ■ ■ to S«i, ,/ Primtirt ifLiliralari and Scimct » lUt 

' ' ige the coireft Computation of Aicb 

raged in other Nation!, for public Uli- 
CAi. Paoriiioat, who hare n 
ihofe in other Nations) bepie 
WoaK. 

If jaa viOhld ktmit tht Titit lubtit tbt VLoovTi i^ovitr-hiut-afiradt 
lbivifiitBrixca,joarmifladdlbi ^' , iwiwntal SlmiJianuia- u bx - 
Altiladt, al affarail Rtfixg, ai,i pneai ai Ufiri, ftrlxr Cailir. 



fhouM beca 
Natim can it faad, I 
ufifal Bpitaurida, at . 
litj. Or, if our As- 
SccrtI if tbiir Art, < 



DigHizcd by VjOOQ IC 



Th R y A JL ASTRONOMER 



AtlroluMnlnl Q^V E S T I O N S praaicalljr tafwered. 



0^1 ifftuwaddJamtilh'timtniimttitSo^imftrLimhJ^nnJi' 
tvfiiltlbrixm, jm mmJI fibrta htr itrixiMi BmUinmltr Jhm 
V tm jVtitiiJt at tfftrim Saihg, fitt fim dt M RifitzJ ita fnatd 
r (K lit finpi»i Ofrretin. 

Ooe nor Mitbiid to find Ibc Tima of itm Rifiac of the MitK, 

Plamt, orStar, for > given Lititude, ii by takin{ the San'« (UrfiH 

Arcenfion in Time, (for thit Latitude) «t ihe cflinute Tine of tbe 

Moan'i PI»net 0( Scu'i Rifing, from ihelr lefpeflite liLfiu Atcta- 

' ID, in Time, it Rifing ; aiSng thi Time of StH-BiJi ts tbe Re- 

lindrr for the new Time of their- refpeflive ti/lirr th»t Diy, 

Thii M^tad ii rendiitd eortefler by repe>ting the Opcricion to the 

(r Thh fouDd; ind ilfo bf finding tbe Moon, Pluet, or Star'i 

Minf Jlfinjiin lothe Plice ind LitiCiideat thit Time. 

And Ihe tHur Till to the Mood, i Plinet, of Snr*i me Setting, 
ii lifo AiuDd bj taking the oblique DefcenlkiD rf' tbe Sun (nm theii 
:f|>e£ViTe oblique Defceal^op, it tbe i^iauw Time of Settiag ; mUii^ 
ie Time of Sun-fttting, on th(t Dij, ta the Remkiader, foi the 
Time of the lefpeAiTe Setcing, ' 

And, if )nu would be awn orrtB, tent the Opention to the laft 
uodTbne: ObfcrrinttD tike tbe obliqoe DefeenHon of the J4<ni, 
Star, et Flan*, cotiefpondemt to in Latitude at the tneia Time of 

Anotberwur JHffWofpeifoiming the f^eii u followi. 
From tfac oblique Defcenfion in Time of the Jlfm, Plant, eiStar, 
iiraff the Right Afcenfion of the 3un, ia Time, «t the eJUmate 
ine of Setting ) tni, H tbt KaiaiiiJirtiaeJi 6 Heart, ftttmei 6 
Houn thcTcfroiD i but if the Remaindct be J/i than 6 Houn, »dd 6 
Houn thereto) the Difirriia, oi Smm, refpeOiTcIy, mill be the 
TbiKOf thtAlW, PlaiM, ot Star'i Silinig, te^aijeJ. 
N. fi. Tit eilipa Defeenfioni ari talm ml tf TMn tf Mifiu 



EWM»l« of 

,76. 7.>.o 
Db^alDiff. 
Oif.itj.oo6s 


thcRiDi: 
Sdq-i1>1. 

NOOD. 

■9 o 


CTIO« of 

tD AnoT 

.rir 


PiACt. f 

-IT 


Sm,bi.,. 
U'S" 


fniMAN 

Paris 
OWerr.- 


+ S7 


Gr»<wUb 


^ 


+ 41- 

ionlei. 


l 



Il[ la o I IT o 1 S 4! I«* M |Crt(* 
Dioiaal Diffrnaii ai for Poni above. 

N. B, The foregoinc i) ■ Sfttimn of the RedaAion of Place) fnm 
iny Meridian to tay other Mcrldiam Weitward of the firll Place, 
according to Propomon of daily DiifereDCe, or iDcreafc or Decreafr 
" "lofePliecjfromanyDijtotbentitDayforwud, for jSoo Weft- 
, And [hcrefoie, the Proportion of Diffireoce for tajltrlj Lm. 
rituJi from tbe titCl Meridian, muft be rtgulatid according to tb( 
LxTeaft or Cecieafc from any Day to a former Day, fof ]6a> Longi- 
tale Ba/hoaJ: Tbe Difference for uRerly Longitude being coninn 
to that For weftetly Longitude 1 Increife tor I^creafe, inl De 
for Incrcife. 

And the Sun, Moon, or a Planet'i Dedtnatioir, or right AfcenGon, 
Foi any P/aa, Co tbe tffJhtiarJ or Eajhsari of Grttrvncb, it deter- 
nined in tbe fame Manner, by propartioDing for Ilie Diffirma of Mn- 
HliaBiWeftwardorEaJlwiii), accordiog to the Difference of the De- 
■Ihiation, or tight AlcenlioD, for etiy sibtr Stjuifii) for a Day fol- 
lowing or ptecediDi, auTwering to ■ ifi'unu/ Ciicuit of theTCvotting 
Body. 



©•.R.A.rSM-aDec. 


}'aDecL 




M. 


.1. Noon, 








.yS. y.f, .0 7 .8 M 


aa 15 ij 


'JSJS 


11 7 » ig 


" 7 »4 


i s= 


DrtnuiTDm. +45 






5i4>|(04»9" 


.■, ibtheref- Propl.Pl.lPropt.Pt.tPtop'.Pt. 


eSi« Dift toi + 41" 


-I'll' 


-S*'47'l 



.,7jr xr. ' 

I h m il' ' •!• 1 "l 
176> 7'*f «> 7 18 sfiUa M S» 13 » »3 S. 

Ditnal DiBereocei COOW Out, a* before, for Paru 

EiAMPLt. TtfiidtbtiutrTimafanMm'itniStrtBiiifrm 
ihi finfiiig RvLtl. 

D'iLat. 
Noon. 



Correfpondent. 
|ElUi>uteTinie.[Sun'i Pl.l {'■ Pl.lJl'iLit. 
tj6iytlj M|Settiqg »!* o«|igoaBS»'l'S°Xj''| 4* S 4' 
OppoQte Placet, 



xi'YfSi'Us'm^'l i'^*' 

Off^f Hate, I Prom T^ki for 51* ji' Lat. LniM. 
\ I J'tqi] i' Lat.4*N'.4' kUAf K Dtjcafiuh b 

0ii«I^Ss' lOlMfH Xl^f r^, lO 

— *i i6 
N. B. nr /« M^iad, viith >iBfmt ] 
y/«i!«>«, firva fjimltht Mtta'i trm i- 
Rifag. Seep.a40. \ 



Sun lint lotb^ar^ t 



K. B, WZm dkw i»t 



1 ith Day of Jutj In ike Forenoon, 




nt. lotb Jid), HI Hooo ; 

t> 7bifaaHMaIndifin>tttfiaitbi«m Tim tJihttriK KJhu 
daJSalint f not (i» affartnt} of alltbt Plamat j •■/ «*» jta vi t M 
fiai Iba irmt Ttmt if ibt Imi Rifag ttd Saiimr tf 161 Mmm, - - 
tf Itt Plamai, iy litiv Miikal, jtu map repeat lEi ' 



,, Google 



«»rf' N A V r G A T O R. 



Aftronomictl Q.UESTIONS prtaicilly tnTwwed. 



M TiBK will Tcrult aftci the 



tbmc>> B; whkli Moni t arna oi 
Time of the Moon'i 



ASaahoA of 'be Sv from the oblique Arcen£oa lod DelcenfioD 
Tine, of the M<h*, « Pibn*, (by Tabln for tbc (iven Litilnde 
ot the PIum) and A^dl^ or fiiin-aa'u^ i Haun accoidiac » the Ke- 
niunder be lefror Bore ih«n i " 



fraQiof >ad lidiat the ftmidiunul Ai . . .... 

the LititDil* of the Plicc, ud the Mdqb or Pluwt'i Declinalioa tt, 
;Noon, (int titur m SiaUv) fnm utd ID the Tinil of Southing 
of the Moon or Pliwt for thit Diji, (of 14 Hoort) va vhich the 
Kffar Of &nux ■" re^ uind, 

St TmUa fnm f. ioo U 10%, Jtr ttii Frf^l. 



ind Smii^i ■fto'hiiRiidiniberSiHEhini, ubcfbreexhibitedj ubid 
>lcthod (with •wAwiUlKptOTemnK} urn followi. 



F»iTfbctkeMOOtri» 



tobtrtTueTnvof 



Thii !• (botrf w tbe Sta'i DeclioiliH, frosi the DiStmin 7Mi, 
(p. 13.) ufweimUe Co the Moon't Place in the Ecliptic, coDfidntd 
withiNt Lititgde, firft fobtnaiag tiom and addiag to her Place at 
Soathiog, { 1 Dtptt, fbi einy Hour.befon aa4 after h« Sonthin). 
' Next, fi»Mei7 DepMof tfaeMooa'i Latilnde.loallow (' ihrOBgh 
all (kt SigM of cht b '1 Pl«e, in the Ecliptic, according to tkb Ron . 
■ Mnltipl' the Degreee of fn/iu Utituile by ;', And (ajr, ■■ 90" are 
to that Prodnd, fo ire the Nnmber of Detreei of the Uoon'i Place, 
fnai Cmot, (betwixt jlriii and LiirtJ or Samba of Degrece from 
Cfriarm, (betwiit i^wandvirrw; ta t />tfmliimM! ^uniiiy, to be 
tUmKjt faiirmati from the MOos'i Latitude, liir the Sigtmiy to be 
tM^ to or JijM ^t d tnai .ber DecUnaUon. found accordint to h<i 
Place in the Ecliptic, without l.atiiude, fi)E the Mooo'* star Dedioa- 
tisa atSoMhug, nfnini t 



BoT, Whn the Latitude it mtrtr dun the EdipdC'DecllBatikn, 
\bal moll be UvAed frons the Latitude, for the Mooa't Ditla»t»m, 
ri^irtii which will tbea be of tbc/«<t Ham with tS» Mmh' 



IW/toIVns'tJi called the Mooo'i N^. 

TbcHonn of Moon-L]|ht being tbii Way Oftennined, 

Yon will tlwayi luow, bj <be San and 3&»'< Placet, apntMhlng 
tcorbanagpafl". • Ct^iBym, Oi O f f i ^ m, whether it it die 
Xi£^aSmim[tabt foand. 

for the Mcoa moitBg faifiir thaa thcSsa, if JM fobtna hit 
from her Place, ia the Ecliptic, the DiOance, in Sipt, will Oew ran 
dieir 4P«**. Plft. « » -"hi.* tbey »« tpjmebioi, acootdiDi 






fahl 

of gifi^ ind Siuiii£ t 1° which eflimale Tiniei of RiGng 
find the Moon't refpeAtue Dedmation), with which 1 . 
tihe out the tuni-jiumal Arcs for Rijiag and Srtcing, To each 
of which Arct add *i many Timet a« i', [ibout the mean Moiion 
in Time of Moon ) Sun pet Hour) at there ate Houri, and fubtrafi 
and add the Sum thereof itrpeQively, from and to the Time of Sooth- 
ing, and yon will hiTe the tar a«d raTpeOira Tine of the Aftn'i 
RyS^taiSiaitw, rcqnlred, 

Jv. B, The Time sf the ftmi -duration Arc for the Msoo'tffifrf- 
Dulimaim, with i> i> for erery Honi Oorcof, added, aodTimi 
of thoMooB*t Seni-dDraiioD Arc for ber Sitlitf Dicrmaritt, witb 
t" !■ for every Hour thereof tJiliJ, will be the Moon't Tune of Cn- 
rinwa-i aboire the Horiaoo. 

m>iinbiMiim'iSttlii^Dtdh-ram h mtrh f—t H mi ^ tit l»m 
Nmm mti tU Stmi Siaiag DttTmatim, ihi JmHianmt Art^ihtStM^ 
ff^ 7te «/ SuB-Sattinl) mtiMiaaam .Oettf ihtM-m, Mwlta 
marlfijaJ, midittaiict lifTmi 1/ Smttav aaJ fmUMntimSjat- 
trm U At M-n'i Smi<g[ iMiMTm, mi it H fiitit fir tb M-m'\ 
Tmi^SttiAai,tb,nSn, « that C«/i (and no other) <(« Smmifik, 
Tiaw •/ SoBtbing miAtf^ Sam Dwratiii tqmtion, v/i/l ii lii Ikui 
•/ MtaSttfiflw Sn-Stnirr, frim Newo Full Mim. 

la othei Caio, irnnm New ami Pull Mm, jm ma/l fMrtli iht 
nrntt/Sam-Sitnl/itm lit Tarn cf Mtm-Saiiiq, and ibi Saniiutr 
■uUiiiriiHmine/itooB-UftitrfitrSm-Stttiir. 5i iHm-i/i titwiii 
FnU aaJ Nnr Mf, i/r^iala ibtTim, tf Sbta-Ki/ut fim " 
Sijilt, ymtailllavtli, Htmt •/ M-a-UgU, itfin Sma-Rifimi. 



Ikaktli itittlaflmn-M 



Moon't 

Place. 



Uooa'a I Moon 
Lat. S. I SoBtba. 
4»S,j'l ijk,,- 
J 59 16 »» 



Tt/aJOtUtm'i 



Moon't |£d. Declin. 
Place. S. 

S'M*' U" 31' Y 
17 o I J 8 a* 




H(«e,byr<*. 
Ptga 3], ud 
Xtuii faei|oiiit. 



A.9<.»'w»»',7(a4*»3j'X5')''o6i°&I ' * 

M>ta • S— 16 ifilnaliaa. 

4'33 y tlAS. 

2'aL«t,tttlZcnptitDed.of&D)cNaBte +4 16 14 1 e^oad QoaBi 
Ecliptic Decliaaiion g jg tgJS. 

Snn . . Mooa't nair Declination, 7 ,,,,j,,. . 
>h 10, Noon .... i '5 SS^« '• 
AKD, ' ' ' 

At 90° toi*'(^ 4" XsOfcTT* ft* W*"— '7 • Equation. 
3 59 o 11'tUt.S. 



]) 't Lit, and ZcliptkDed. fame Kam* + ] 41 547EfudQgint 
ScUptic OacUnatiM 5 8 aS f S, 



km • ' 
tlDacr, t'tDcd. fii 15 41 to | in 
t« M ID 3 at 



DigHizcdbvVjOOQlC 



T&i ROY AX AST-RON DMER 



Affrononiical Q.U E S T I O N S pnakiiilljr urwered. 



IDDecl.illMnnlem. 
Sonthing. O. Arc. 

Moan Toulhi i; 41 



'Eflimatc Riling ^'^ 10 jia^jia 

Eflimite Sitting tb 50 
Biifg mar iht iTiic. ^ fPiANMn. 

For, A< i4.''ti>3»'s'-dior.l»ew,]|'iDecl: fo 1 
As iktofi>-itxM«n, 1 




And thertfote we h»»e been the 
lag this uf^fnl Sim^ien on thlt Ai 
effartrrt RiGng md Sitting mult be prtriouflj hid, u well u acihi 
r'-Hi RiGng and Setting, btfarc the angular Diltince from tha Meri- 
dian, nTpefthig the apparm and rtal femi -duration Area, can ii 
lightlj found. And fience to dElermine in anf Year, (h mtai Daj 
of ibt MoBib i* ibat Tear, in a pitn Laliindr, rhr p^irfi Diftrmct 
Utmn lh€ McsnSKifiBf indSoatVmi, enrfSoollling aj.rf Setting, wi// 
IfffiH, er Vila lb, Rlfing ami Stlling ftui-dtratisn jirt, vl/i it iroff 
uoojuai, (»■ m-,JI equal if y«, pl.„fi} muld bt a ptl mv JiffinJr 
S^M^ita, uninnim h ptiQicil j^irmvirf 1 And viai rtvtr yit Hjtivtii 
iyil>,fimajb!i«-c/,bilAi(<xnuito<aTnaj axi Phjfical Aftro- 



XLVIL Qdijtiow. 7t jkdiht Point 1/ iht Afetuitnt, 
Dtgrit ef tbi Ecliplii, afctnMng tbt Bafttrn Horium, 
[/?*» /A( Utiludt oflh* Plaei and Tim »f ibt Dey, ar Ni^il 
(paA tke Meridian] ian^ given F 

ExAUrci. In the Year 1764, OfMtr t^,t.t to at Night, wha 
Point of the Ecliptic, at Ladai, will be tben rifing, ot aTfcndiag tb< 
EaitcratfinieM f 



Soa'a Place at that lliiu, Laidam i , , 

San'i R. AfcenGon then, cotTefpoDdeiit . < 

Timi; from Noon lO Houn itiDegrra, tJd , 

Sum, B., AfcBoGon of Mid-Heav«D . , . 



IpJ' Fran Ibt /"^gting rtftetti Oprrsaitia, tit JtfoM'i ftmd-Jai 
An n fttn It tiatf int^iirablf ij 4 Change ef ttr DaruMiai ; rndting 
tbt /ani'dnralif jfrc imgtr tr fi»rt<r, anJ cnfifimlly btr Ri/mg cr 
Srititg fienrr ar/Mrr, acarJrng ai hn Saab DaUnaiim, at SifiKf anJ 
Sitriag, isfftxi It it Itfi and mire, ani marl and lff$, iban at Sotiting j 
»■ b<r Nirih Die/irialiea ar Rifiiig md Striing, man and l/fi, ar lifi and 
mm, Ihanbir Dnlixalisn at Sttrbiiig. 

And ai there ii do^i-M? ^df of coming at the Moon') Declination 
It RiSngandSettiag, hut by repeated Triali and Operitjont, (how- 
ner accurace the ftmi-dnratioa Arc may be found from a grain, or 
^ujip«/iif Declination of the Mood, atRi^ng orSening, hjTrigaMmt' 
try, (at tak'n for that Purpofe) [faiilaft nearMaTHoo, by a mean 
IJeclistlioo It SoatliiDg, will difcover the near Rifing and Setting 
of the Moon /sr all Latittdu, the beft and Iboneft of any Method 
whalfoeTCr : neglcAing the CotrcQioa of the Hiliag and Settingyoii- 
durmitm -A-a, which ia often rompenlated for in t£e bcu Declioa- 
nn, taluo at the Moon'l Southing, 

fiaaer, from what iidoDeaborc, 

I]}'iDeeIin.|McanS, 
at Southing. I Dur. Arc. 
jo 111 I 5'ij7»i^ 
MooafoDthi 16 11 Idfoidr'aEpb. 



Rifei I 
Sctis 



591 



in Aica (from Riling to Southing 



Since the Moon't true I 

; and ftom Southing to Setting) depend _ _ 

of the Moon'f DecUoatios, at Rifinv, Saiibiiir, and SoHar, (loubt- 

-. fully obtajoed within few Minuteiot Ttvth, bccaufe of' t£e Declina- 
tion 1 very vatiaUe Motion) there ii not a more di^lt ^cfiitn, in 

' praAictl AAianoOiy, toiightlyrtblvt, than the foregoing, i)f fiidiiig 
ibtwTtB^mi tf ihtMtaCttnior BfpmutLlfa^ai&aii^t 



■ (lejeQing jSo') the oblique Afcenfioa of the Af- 



NOW, br PROPORTION. 

Aa Radiui S. 90*o'o* 

To Cof. Obi. Afcealion aftendent it.«f 01 

£i (here T) to XI a« 

So Cotas. Lat. Place -, , , 51 ]i o 

To Cotan. of 4th Are . . El 15 10 

'Jar tilijmi Aftt»Jin afcmdMHi U luar^y 
ftllewing , . . . +13 38 )o 



paft .^o. 



)bliqiie -taa 

rcenfino I 

rccndi. J 



Y'\DiftmKiaf TFoT* 
(EclipticOh-i ttb 
f liquity and tjln. 
j4thArc. J 



rcrto T thia^'I^MMof the "JFora 
following / Ecliptic ' 

fOhliau- 



ThtPr^iKiJbmaHiiTrab. Thia Anfmr ii the Solntii 
the 7th Cafe of oblique fpherical Triaagla, where 1 Anglei and an 
'iclDdedSideareglTen toGod tbeSidaoppontctooaeof them. 

PTs. r ^= Co. LatitDde ^ ineladed oblique f to find Dill. Eclip- 
riven 4 £. Obliqoity Idjptic VAfeenGonfrom ttic froo fame E^d. 
t 3 T or <!^ i Point. 

Or KX-^ I-at- 4-90<> 7 included oblique ^ to find Dill. Bclip- 
liMii \ ^ Obli^ity Edipt. >AfcenliOD bom >tic from fane £qu, 
i iV <"<*■' i Point. 

NOW> 
DigHizcd by VjOOQ IC 



#»i NAVIGATOR. 



Aftronominl QUESTIONS praaically anfwued. 



MOW, A. Cor. jth Arc .... j^<- V iof ci 

To Cof, 4th Arc . . . . Ss 15 JO 

So Tan. ObL Afcta. Afcud. So 3 1 16 

Here rTo Tia. of ihcDiOi 



o.;ti44£ig 
g.liojiofi 
10.7697161 



Here rTo Tia. of ihcDiOincc^ 70 34 4 10.4 

jtb I of tht Arccodut frcm the I 

Arc ■ifamtoi caitrarj v\a,VcAax.Ktiota ^ frteidltg, 
icKdllfrom which (he oblique I iQO ijij^'/s^Wir^.tl 
90°, I, ArteaCoa if reckoned . . Jot A!<xaiiBX, rtjiiirtJ. 



I you nckairche Dif- 
InHCquinofiiat Point 
reckoned from j but 



thai the oblique Arcenfion of che Arccndi 

if the jth Arc ii peattr chin 90", yon reckon the Diftince of the 
" Brint from the contnryequinoaiil Point, to thit from wbence 
hiiqqe Afccnfion of the Afctndint 11 rtckoned. For when the 
Ire ii gieiter tbin yiB, ibe DiAince of the ArcemJanC from the 
lame tquinoAial Poiol frcun whence the oblique Arccuiiaa of the 
Aftendint u reckoned, will be alio erealei than po» ; ind the S'ma, 
Tangtmi, •&!. of Arct, and of tbeit Saf^ementt, being the 
ftme, therefon the Anfwer will be from the contrary equinofii^ 
gftt the DiAance from the famt eqaioofiial Point gtala 



Point, 
ihio 



130=. 



the foregoing mm^arj Difimflim the ' Place of the Alcendint 
of tiie Ecliptic, or Sun't Place it RiGng, conerpowienl to the oblique 
Afcenluin or Dcfcenlion, of a Riling or SMtiitg Stir, ii Inlj dtiir- 

\t the Point of the Afccndant it the HariioB (or Arc of the 
Ecliptic between the Meridian and Hotiaoo} were required when the 
Beginning of ^I'u, or Liira,- eulauiuteai or ii 00 the Meridian above 
the Horiion, the forgoing Proportioni, fot detecmining ecnerall]' the 
Point of the Afcenilant, ftom T or ^, fail, and the following Fro- 
<nf, in ihefe nvt li^muti, take Place. 



wa ii then on the iitferitr Part of the Meridian below the Hori- 
it LiKia, and confequenliy ire ^len the Part of the Meridian 
the Hniion. ■{%" iS', ^ Complement of Latitude, the ^ 
of Ecliptic ar.il Meridiin tifia ji' 30", and /. of Meridian and Ho- 
riion 90", to find the Arc of Ecliptic Utwiii the Meridian am) Ho- 
rizon. — Heacc, by fblving * right angled fpherlcal Triangle, of one 
Leg, and an adjaeeal Angle to bod the Bjfabnaje, bring the inferior 
Ate of cbeEdipticbetwiit rbeHoritonand Meijdian, weiiarethia 



Moji'jo* 

90 o o 
it 18 o 



To Tan. Ecliptic between the Hcriion } 

and i& preccdioe. I ^1 > 

Fiom(|rto A . . rto 



•Aia u then 00 the inferid 
tiion, itLm/gH, and conieqi 
diinabotc theHotiion 38' 
S6» Jl' 30" the i of the 



if the Meridian, below the Ho- 
B giTcn, the Part of the Meri- 
: the Complemul of Latitude, 
Ecliptic and Mcri^ao ) ud 90* the ^ 



:□ find the fuperior Ate of the Ecliptl 



of the Meridian and Hctiion g 

between the Meridian and Horii 

By foKiog a right-angled fpherical Triangle of one Leg and an adji 

"/.given, to find the Hypoiheoufe, beingche Tuperior Arc of the 

■ ■ ■ -...^--j: ..,__. . 1, ai before, thi. 



Ecliptic betwixt (he Meridian ami Moiiii 



^()00oS$; 



0.1091*19 
of Afccndant following, 
for $ j» m' 16", required. 

N. B. When 91 or Vf culmlna'ti, the Arc of the Ecliptic betwiii 
the Meridian and Eaftern or WeHern JJoriion ii evidently a Quadrani : 
the Meridian being thi^a the fdpt'ul Ciiart. Theniore, vbea 25 
culminilei, the Place of the AfccndiDl will be (he Ba^nning of ^; 
and that of the Defctndinl the Beginning of IT*. A nd when yf cul- 
minatei, the Place of the Afccndant will ba. the Beginning of y, 
and that of the Delcendant the Beginning of Ai the Piacei of Af- 
ccndant and Defcendant beingalwayi opp^te ) and the Area of the 
Ecliptic between the Meridian and Ealtetn aiid Weflero Horizon are 
the Supplemcnti of each other to i Sos . 

TkePliceiof Ihe vHcflirfnr, at the Beginning of each Sign cuTi 
natjng, i« nearly a< folW" '--'-- ''--- - - ■ 
ihiiRei-I. 



I, by the foiegoing Rila and Fraftrtim 







Ate ot' Ec- 


Mid- 


Place of 


liptic betvT. 
Alerid. and 


Hcayeo. 


Afccndant. 






Eaft. Hori.. 


Besui.'V 


^ ,6^3* 


..6= jlf 


» 




106 JO 






97 XI 








a 


^..-jS 


S. 38 




711: 


73 JO 
«3 M 


"l 


/ »5 »» 


S5 'J 








yf 


r 


90 


zs 


n . 5f 


Jia 50 




3» 4 45 


•14 4S 



HlHCI, 



(owtAffc 



tnd'iuhci Sigr 



e/ritAfcendi 

MndDignt tf 

maiit. wiincir greaiell 

Difiancei af iht EcUfti 

dudtd havim ibt lOiridiait and 



iFibtEcnpi 

itnl II rJgit jffienfiin tf Mid-Htrvn, and (jco/fim 

Cfriaiu, givrn, in an oiliM ffhrnal 'Irim[/t, ttjaj Itc 

of Eclifiit bav'aa tit Miriduli md HinBcn f 

XLVnL QvBiTiON.- Ti fiadiU Daf af tht Tear i 
ntitm LatiltJi, vihta a Slar, W PUwM, vail riji tailb tbt 
Smm, (w riftt CoCmicalljr) frawt tht Mifu J/cinfitM »/ that 
Star tr flmU h^ng given f 

AS erety Stu, or Planet, rilei with (he P«W tf the EcPfrie, hat; 
the fame sMi^^njAa with Ihal Star, or Planet, it fultowi, tl 
when the Sun ii m that Point (^ the Ecliptic, the lune Stir, 
Planet, will rile with tfaeSoii, or a^icaltf. 



,, Google 



24^ 



n^ ROYAL ASTRONOMER 



AflreROEnical Q.U B S T I O N $ pnAicaUr ufwend. 



ZiAMtLt. iUp/nrf til Daf «*» Oi MihtSurin liiZa^ 

^ijti wilb lit Sm, m Loadoo, 17(0 ? , 

ByP. aio, N". ilB. 
Cortefledf • 

101760 J DccIlnicionN. bnehtStMin£i|k ..:!■<> 
Begin. {, Right Aftcurion of tbat Scar .... 194 46 3 
^aofimtimS.ya^itt.'V^Q^^-'Vl.) fubtrta . . lo 31 8 
Oblique ATcenfioa 3)1 firara v> foUowing . . . . st4 14 ;7 
■ — '■ — :!■ I From If. preeeing 75 45 3 

HOW, bf ibi pruidimi ^{7in XL VII. 

Ai tLtin S, 90* oi 0* 

To CoT. obi. Aften. j|c fi. flextequia. ? 

Point (here <T pnctdiog) . . .J 75 45 j 

SoCounB- Lii-PlKC> Ln^ . . . Ji 3a o 

To CotiDg. of 4tli Arc 7^ 56 7 

Obllq. AfMD. G) or :t< iWMft J idd + »» 18 M 
■Tpccedug. J ■ » J 



jdi Arc . . iM 14 37 
Oi . . 77 3S «I ' 
, 4A Am . , 71 5S 7 



W0 . , 



75 45 J 



9.1911673 
Eclip. Obliq. 



ToTinc.ofPl.of Aftend.fr. AfUlowl74 7 3a 
Or mwrwn «, ft. ^. wAdnx !</. ] 

4s™. Uritbmii Imnfiiihl or f n* y jl* 
yftTiiiBsrtiWji 90°. J Snfl't Place, Rqaiitd. 

WUcb Flu> ufwd* to dc b£ {/" D«*nilKr, 1760, N. SL atm 
/if iri^^ Star in ibt Eagli <iii< ihi San n/r i^iif j md wtf ttutimu 
irijitigttimiai-tfmtbiit Dn firm Namiiref Ytmri, larLotidon, «r 
-.ifiFlmeaMtartkilliSUiUifii^LMai, 

XLIX. Question. Ttd^trmm tbt Dtsf tf thTmr, 
1760, «f London, •whm tbt aftrtfiid bright Stmr in tbt 
BagU/tti at tbt TiwmtbtSiai ri/ii, (ar ftti miaaiaiij) 
frtm tbt Mjm Dt/cttifitm tf thai Star, givtn f 



Right Alcmfioii of the Statu Won . . • • 
Afceofieiul Dif, in Degreei u bcfgre, tJJ . . . 
Sku, Obliqoe DelcenGon )|c fr. V foUowinc, |^Ttn • 



•s;t 1 

305 17 9 



Oblique Afctnfion of the Afcendao^ then (r^efting ) 

jSo") hoiB f faUowini { 

SdfflciDcnt— obt. A&en. from Apnceding . . 



lis *7 9 

i4 4» 5> 



S. 9c^ e* e* te.oeooooa 



To Cof. oU. Afc. fir. nnt tq. Pu rfk F>e> $4 4> 5* 



■V, 



thntatm 

10. 1 501 70] 



AeCof. , . . , 5th Arc 

To CoT. 41b Ate , . tf J io 51 

So Tu. oU. Afttan Alccot ^.^pnccJ. 54 4s 51 

ToTeB.ofPI.oftheArcroJ.fir.Apreced. 38 11 

Or fuBC Eqn. Point fioni whence obi, '1 or 
Afos. A(ceid>. ii redconed ) be- I riots' 
<aulethe jlhAic iilclj ibugo^. Jmi. Si 11° tS' 11' 

SuDiPbc^ rcqailtd. 



L. QiriiTioH. T» fad tbt Dty, in tbt Tim- 1760, 
«r London, vobeu tbt afartfmtl bright Star im lb* Eaglt, tvill 
rift, M tbt Sim fill, (ar riji axiuomtaiXj) fram tbt ahB^ 
Afetafiaa ef lb»t Star htiag pvim f 

THE Anfwac ta diia QacAioa It contaiocd in the AnAra todK 
farraet (tatftioa, being only to fiad the Point nf thr f rJiiWwr, <m 
Smmg-Poiotoflbc Ecliptic, oppoiiiefo the RiJ^Pniat tbenof, or PL 
of the ^Cdutut, found Iotbi<t/M»/Rifing at t Stu with tkc Sun. 
Which Piice of the DtfanJtM will be the Sim'i Plict, it Scttiai, 
ufwenblc 10 tbcfuirMnW Rifing of t^t Star. 

Tlmt, the PUce of ^/»ilnt it «/«./ lUfi^ 7 * „» _, ,,, 
«f the briibt Stir loth* EigleiafMsd i*^ ^ ^* 



LI.QoEiTiOH. TtfiadtbtDio, in tbt Ttar 1760, 
at Lcmdon, v/bta tbt c^Jmd irigbl Star in tbt Eaglt •wiH 
ftt M tbt San fiti, (or Jit ■cbrooically) fitm tbt »i£fu 
D^ctafitn *f thai Star itinigivtn f 



The Ame Point «f the tdipit, at Phct of DcTceadiat, dut let* 
with the ifcnjijd Stir, ii the Sun'* Place, it Setting, when thit 
Stir let! (acbnmkaify) u tha Sun feti. Thcreferr, the o^ofite Point 
of the I!clipdc, to that of cbe Afaindin^ when the rame Slir feti 
ttCmitalli, or it Snn-Rifing, will eiidetatly be the Place of the Off- 
or Sus'i Place in the Ecliptic, at hia Scuini when the Stir 



Thai, the Pliee of tbe Afcendurt, or oF Son-Ri- 7 

fing, It (iffait«/Settingoftbeiri{litStiriallw> Jt, *l* ]!' : 
Zaglt, bemgfovnd .<•...•. j 

The ^f^t Plice to Sun-RiSn|, it <i/Ur</ Set- 7 

tloi, ii tfaePlM* of the Eclirtic \\^inmt^\s3 >I* jS* 
Settiagt of the tna* Stn, via, .... J 



nu Star will tmihmi ta fa aOnaiiaA m ihm Dm h m^Plaut 
mardaUiddk^taavA,faraKmiitr ^Tmn. 



yGooQie 



md NAVIGATOR. 



uy 



A TABLE of tlie iJAYS in the YEAR. Npw StjU, when the itfimtal ud atbnm^ai Rifios ud Seitioe of *j 1 
emment Fixed STAKihsppeD at £»Ml».. * '^ ^\ 




JV. J. &/««;RiGnB iDd SettiDK of. A.r i. .t So»-JIi>i, 
^&6r»fH/ Ribnt ud Setting of * 5Mr ii M Su-6t. 


C^micl. 


^.. i 


NO. 


STARS NAMES. 


RiGog It 
SnRife. 


£» Rift! 


5w ^* 


Setting 11 
£|H Set. 


3 


FitA in the Wing of ?<«/», 3{(niwt . . . . 
Right Sboulder of .«^rt» . .... 
Eitranctstbc WiitgofP^^Ai . . * * . 
Lift in the Tiil of the Com . . . . 
Bright 4c in the Head of yfriVt .... 


7—^ " 
■0 

IB 
JMfnc* IS 


0^ 1 




ST' I 


A 

7 
8. 
9 


la the pieccdiDg Hoia of the Sam, or i ^ C(> 

In While'. Tul . . * . . 

Brifhtcft io die PituJi, . . . • 

BrighieA in die A''l<A-. Mwth, MK«r 

Morthrrn Horn of the a.:?, or Foot of Arip. 


11 


at ;; 

OfArf<r at 
Ktumitr ai 






Northern Xte of d«£a// .... 

Bright j)[ in the Bellr of die »2<jfc 

Souiben Eje of the Bull, j€Mmrmm 

SootberiiHon.ofd««.J/ .... 


16 


>■*. 4 


Dmo^ a 
5 

»7 


7™ to 


lb 

I? 

»9 


C.-)^ - . . . . . . 

P^/« . . , . . 
Middle Stat in ()>■.«■• Belt .... 

Uttle Doc, i'nrxn . • . . ~ . 
Bright « in die Hate-i Thi^ 


3» 




IC 

•s 

•9 




"3 
H 

17 
aS 

*9 

1o 


Li-'iKevt . , . . . . 
L».-tBu:k . . .Si. 
»vir4'i Heart . . ... 
Bright 4c in the tJNi'i Tail, Darf 


»,-, K 


Stvmttr )« 

Si. S 

4w; >6 


iw™-, « lit, ,4 
>6 J-.* ag 


/frflirai . ..... 

Bright « In the r^rxhi'iGinUe . . . . 
Bright If in die CrMn .... 
Virgin-. S^i. . . 


"S 


M, .1 


"3 


Abopifcr M 


3' 
J» 

13 

14 


LeftShoalderofHaoMfa .... 

Head of fbnafa . . . ' . . 
5tw.'fBiU . . 


17 

t6 




^ 'I . :; 


J* 
37 
j8 
39 
4° 


Vulture-i ToV ... . . 

Sr«^»'. Heart . . . ' . 

Bright * in die Eafcle . . . . . 


16 




IS Xni 16 

fO W«,r, 8 
11 Ihtmiir IS 


4' 


Bright * io die Thigh of Pye/w. S(i*m 


T««7 j 


0<N1» 7 


?■» "7 


t^ I 


EXPLANATION. 

TU Sox, inhhinnnilM^-MCbMnihtUEcUetic. pu to Uiq.E*8wird of tbc fWf Adn) ihtrdcN, & KtrAUHuA, »/ FIta,, 

^ C From Cyi-WS«.i»i (.i Soa RUe } StM fa be- J rife .Wj ut «J!U., .bov* the H.r>i»H fiW thdt Rifii>t to Stttios doring 
■* { To .4Um"WIUGaR(u Son ^ Jtofc Sua Rife {San-Set 5 dot ZiOrW. 

EiAMTLK I. Si»fi«,', Bopt ■^pU/nm in Kifiig u Stiii^ frm May ifi, '• June i, fiBmii. 

iJ r7rcmAir».(-/Settiii( (rt Son Set J Suit frt b«- pfcTf^tr 7 ii. ,■-»>«., .bo« (In J/*n««, fiom thdi RjBdc (o Srttinf, 
rt«/»V*7TD&Ji"«/Ri6ni (.tSuoRili J fcreSuo Set |Son Rift f dorfaq thit/MB'W. 

■'ziA«»L. II. S«.y.W. M„rt imrifiJ. fnm ii, Rjfit " SatiMg, uO, D^fimSonmhtttT, uDoxmUt 3,Jillmi«t. 

^ cfra».^in>tt/SJ£nt(tfSaslitIStin lUe bblte aftw } m «4CU liU tlM]> apprawh A ae«r tte Jnt, u to bt bU ia Iu> 

** iTo C&«</ Rifing (« Su RiJ>f fbM Son Set JSunRifc] R.;!. 

IaAi»L> lVr7i.PleUdei«j*W.>-N<«emberfi, M Mif 4. >»»>%> ^ "^J^'i? 4r<^* A *«>■ «''&"•«» '' " '• *" «*M 
which ohea * Stw iKom. fram, »>d i< feu in die MomiDg, before Son Rife, >• oUcd it> iU.«M/RiGoi , u the «» An>tD.ch of > 
Stuto the Son, io dw Efeoiiv, I'd u to become incoiifpicuoiu, ii called, du ibfi^nc/SeninfOf diKStuwTliiTime to be detei mined i> 
fnl1o«>.> 















'248 



The ROYAL ASTRONOMER 



Aftronomic^ QUESTIONS praaicallj ■nrwered. 



L!f- QoisTiow. Te find ih Timt of a S/ar't heli«ad 
Rifing, frtm iht LatilMdi ef tit Piatt and Slai'i tilipi* 
'Afifnjim, -mth tbt Sviti DepreSion M»^ iht Harixn, at 
ibt 7imt if tb»t Slat's hcliacil Rjfing (afttr iti n/mital 
^'fivJ tiiKggivenl 

OBSERVATION Oie»i th« the fmallifi Stan »« !n»iflble whi 
ibeuppeiHemifplitrerectiiieiny of theSun'i Riyj) and therefort 
m fitll itt* Ln tht Evening, at tht End of Etenini Twilight, and 
\iR feen in the Morning, at the Beginning of Morning Twilighl, 
when the Sun, at dthet of thofe Time), is iS« Jc/m the Horizon. 
And Sitri ci diffnent Mif nitudei are obCerved to appear firft and UH 
in the Evening and Morning, rcfpffiiTely, when the Snn't DEpnBlon, 
MfUi the Horiion, ii » f<jllawa. 



Si« 



!l T Wflfnimifc appear f " "» 

9 y theEvcDingin'l < ,t }: ''' 
4 I Morning, when ih* 1 i VHtrim*. 

I J Su.i. I " J 



EiAurt*. Thi-.SItut it njaini-in tht. Ytat rfio, vha tbt 
brigbt Star hibi Eaglt (of the id Magnitude] toill rift beliacaUjr, 

N. B. It will HIc btRMaBf when the Smo bai defcribed an Arch 
of the. ScUpCic, further to the Etftwird, from hit Place at ce^al 
Riling, corrcrpondent to 1]° of hit Depremon below the Horiaon, 

the Time of the fanv St»^ RiRnt, CnftinBlfy htlitctl h ajiir 
rsjmiial RiJImi fd '" ^ota tbt Jawu Star firji hipiu Ji tffar, *[u 



hlitg bid urt£r tht St»'l Bfji. 

OiTipn ATcenfian af the bri^t Star ib the Ei^, 1 o ' ' 
before fooni^ ........... { ■S4 14 57 

Subtiadqoo go O o 

' ~ A. of Mid-Heiruat tbeScu'iRIGnB . 194 14 57 

-- . - ^following 14 J4 j7 

Loa^ta4e of Uld'Heaven, cgndpoDJent ft. ^fol- '* 
lo»dng [by ^j!. 34,) .......... 

Meridian 2. cBrrefpondentfij-TiJ. ft. aj, v jj ^i 
Deeliniiiooof Mid-HeaienS.eorrerpoBiicni('^"' ' 



. . .f .^ J7 

?«/; 67 17 it 



S7 18 6 



A>Cor.Mld-Hei>enZeniihDi<lanc« . . j; 3! € 

To C«f. San'i Zenith DiflaiKe ■ • . 77 « o 
Therefore, Sapplemcnt of the > f_ „ . 

Anrwermoflbeutea J - - f" lOJ o o 

SoCoCfthArc . • ji 11 i 

To Cofina of ' 6S jt S 

I U Supplement, jth'Are .... iii i ja 
Dif, between 4th and jth Am ... . 79 4s Jl Eclij 

f^ Becaufe the Meridian Angle, next to which the Petpeadicolir 

filtf, it aborago* fr. Place Mid'Heaien, or left than go«. 

When Mid- "» T >4thBnd;thAr 

Heaven I 05, ij,. "B. ^> "I- f ■ I'^'f- U"' 'he Eclip. 

Longitude f ig^ i;:, K, y, B, n, f Smm f Arc between U 

it in J J jMcrid. andSui 



^ha Si^fjHttmt tf am-Ar( ahovfyi^ i 

'--neni of the Anlwer (but not 

' ji" for ego j8'-!", above. 

iRWiit, to iad ^ EcBpricjirc itimi. tht Btrhica, the fif^i 
citing fmaJ, in lit I-Mgitaili 0/ fie AJcadtia at tbt Star' 
mical Kifing. - 



J.96+947J 



At Sine Sun'i Zenith Diftinee . . 

To S. Mqtidiu) AngI 

So S. Mid-Heaven Zenith Diltance 



To Sine ^ of the Ftnics! and Ecliptic, J. 

bekwtheHonion jSS S S^ 

Ur PataUaflit ^', at the 
Ecliptic. 



if Eclip. btlow the I 

Add f I. 



».63Mjsg 

9-7784834 



10.41 jlig3 
'.PI. at*'. 
cobiicul Kit 



Jftno tbiri art ^km, in an tiPijai fpkirial Triangll, til Mtridiaa 
_, Md-Hravtn Zaitb Difiaaa, at abtai, and tbt Sgg'i Ziiutb- 
Difianemi^, ai tbiTnuef ibtSiar'tb,[,actlRifimr, ttSmd ttt Aek 
t/ til EtHfi'u bitma tbi MtnJian t*d d» Su; n that Tiarn T 

Vix. Two Sidea, (th; Mid-Heann &nith DilUcce. and Son'i 
2>nitb Diftame) with an Angle (thfe Meridian AngteJ oppofiie to 
one of them given (the Sun'i Zenith- DiftuKcJ to find the ibitd Side, 
ilercEpted between the Meridiim and Sna. 



Jo Tang. 4th Arc 31*1 



Or, AlS:^aftbi Htntan and Elliflic, 

7* Sin of ibtSia'tDift'JI'm, at iiiiaial Sifittr SiUinr tf a Stitr, 
tr Plkaa,- 

s= h luidioi, 

TtSimtfEelifiicAehtltntbiHtriaMi, nrriffet^na. 

The forcgoini Place of the San anfiven to the x6th of Dtnmitr 
N. S. 1760, when thEbtigbtSur in the Eagle Hfea beliaialH, leqni^ 
led i the £« being then i3<> below Che Hoiiion. Which Stat wil 
cofltinne to rife bdiaallj on that Day, for a Kumber of Veari, afte 
having role nfmlallf, at the fame Time with Ihc Sun, (and confe. 
quenlly iniiable) on the 6th Day of the fame Month. St ibatoa iL 
itthafDtcxaibatiti-igbtSiatiaibiEagli begiqt 10 appear, afie 
being hid in the Sun'iRayi, from and befoie Diumitr f, at lilini 
with the Sun. .Alter the if/iwa/RiCngJStcai/itrafi, ' 
appear in the Morning before Sun-Rife. 



ItHfitwi,: 

DigilHZcdby VjOOQIC ' 



Md NAVIGATOR; 



«« 



AftronomJcal (QUESTIONS praCUcally anlWered, 



of the Aftenduit fonjeiiii, 1 o ' • 
tbe Star') Riring, p. 24'. . .J 154 7 ]s fr. <(• fcl]owlD|. 
■■'"'■'" . »8 j» ft. IP loUoiriiE' 



Loagitude of Mid-Hcatco, Chen 



Bcliptic Arc frwn Heridlir 
[00, atStar'i Rtfiag ■ • . 

jUJ Ecliptic Are fr. Hariion tc 
Sun depreOed Uil found . . . j 

Xcliptic Arc from the MeridUn to the 7 

Sun, » lirfl foand .... J 

jti/MM-HuTeD Lon^toda . . . 1 



To f^ 9 Situ, Snbtnft 



>7! 9 14 fr. ¥ fbllowinf. 
W S 9 M. 



LLII. QviiTtov. ?«;(«/ «& 7iim »f * Sitr't he- 
liacal Setting, fnm tht LatitxA 0/ th$ PUct, mJ St4B-\ 
tba^at Defceiifiaii nuilh tit Sni^t D*priffica heltnt tit Horixen, 
at the that tfthmt Siar't heliacal itttixg (before iti acbn>> 
Oical Settisg] itinggivaf 



K. B. It will let Mitalff, when the Sun hti jM to drfcrihe w 
An of the Ecliptic fuitber 10 the Eiftwmj, (ill hi comn to hii Phca, 

the Slu'iaririHin/ Setting fcQin hii ptclenc Plaee of ij* belaw tt» 
oriioD, or fo ffiDch more to the Wellwud, than he will-teiTIbe 
:it'i xbrairic*) Setting I Aad Ibetribic lln htbtat 
imt ol the •Kt'UirM/ Setting. 

Tmi firft Mrtbid, in tht fanner Qneflion, deteiminet ibefcTaM/ 
JUfi'g t'd Siriifg at once, indepcodenl of ihe ufmiit! Rifng, «nt 
--' -^itai Sffritg, vhich Methoid ii reputed in ntertnioing thehe< 

Oblique DcfcenGon of the bright Stir in the Etglt, be- 7 * ' ' 

foie found, p. 146. ilSetting, aibmiicalfy . . J 305 t; 9 

jUJ 900 , , : -4* 9a o • 

5«i(rcjeaiog 3(100 R. A. of Wid-H«iveB firwn. v.? ., „ . 

following) J JS '7 9 

LongitudeorMid-Ha»eiiMirifpfa4e«ftot»>V>fal-7. „ ,. ^ 

lowing (by QMcfi. 14.) J 37 19 4 

Meridi)n^coR«l^iulwit(bvT*b.p.i3( orj^QiwA^ 71 
Declination Mid-HeaTCn N, correfpondent (bjr Tab, 7 



And, Ai C«f. MId-H. Zen. Dill. . . j; 27 

ToCor.SuD'tZcD.DUl.atijODepnf, 77 a 

Supjilemcniof Am mull be talcen . . loj o 

SoCaf, 4tbATC ....,.., >3 J9 



Plice 79Sifl>>>ei&'lt i>7SDm,>4lliitkd cth Arci 
Mid-Heaven. J yf, sT, K> T> tf 1 n, J Dif. J tm Weft Side Meti- 
[diu or Setti^. 



Ai S. ^ of HoriMa ind Edipcic . . H'Si' iff 

To S. Sun'i Depreffion 13 o o 

ioRadiui S. 90 o o 

To S, Ecliptic Arc htlea the Horiioa 15 57 34 



Ti>i iht Aic 



: iiltBttB ihr MoUUk and 



A] 3. Z, of BcHpttc tnd Horim • . 54*53' }t*c 
To Cof. Zeu. Di». of Mid-HeaTCn, or > 

S. Alt. of Mid-He»ven . . . JJ7*7 * ■ 
9* EadiM : Slae 90* 

To 6. Arc of Ecliptic between Mfcri 

dla* and HorfOTD- 

An VCm the Hortnn befoM (mat- 



|7< " S\ 

»3 S7 J* 



0.-0S71746 
9.8997379 



Long, of Mid-Henea • . '■ • 

>ghelit«ll; . ». . . . ,p°i^yt 



Bitlaftfr. U-E. Mid.Htiven, 

fiddiag 360". 
■ 17 39 4 fiwnV. 






AogleofieiipticanlHannM . 



To Tut. 4ih Are "J S9 7 






&in'i Place .fS 5 40 37 
n;itarf».;«/fiett>a(,7 -,, ^ i» 
ni. p..«6. , , , J-" J»>» 
Ecliplic below the.Ho-l 
~ Sui/> DeprcliioD, > 13^ J7 34 



bctote abrtnical Setting 



I* !» M S 40 37 ailijiru 



WMch Place n^ratn ta Tuiany 15, 17C0, Kch— tbt hneht Star it 
r^e Eagle Auheliacallj, in tall Plain liom lb, MiJJ/i /England; 
taiwiatmmi-rubt tdiattil^ nfhnt Dm /t m Kamiir rf ri»f: 
'[Sa.Att Dumlv x6 (the Time of tbu Stafi heliic»Uj KiAng] it 
the Time of iti fitft Appearance, in the Morning, after being hid 
under the Sun'i Ray) in the Day Time ; whiehSur, fromtbatTin- - 
continuea to appear in the Morning, heroic Sun-Rire ; aKo appeal 
the Evening, aflcr Sun-fet, till the ijth of ^mury following, wh 
it laft appcan in the Evining, fetiing btrianllj. It thea cornea agi 
IntotbeSun'iRiri, >f be hnher adTancei to the £i^fiMrrf. liicii 
—brmcMU/ with hini, oa Fiinarj gth, and then leu btfaie him. 



,, Google 



250 



rht ROYAL ASTRONOMER 



AflxoDomical QUESTIONS prafUcalty anfwercd.. 



The Times of htTiac^ WfiiB »'"' Seiring of any other fixiJ Star,. 
ly be determined by the fbregoine gmrtl MalsJ, whith e<iti»lly 
rvc. for firtdins the biliacal Rifinj mil Setting of the PUnen, by 
ifcifinglheSao't-DepreffioniiltboftTiaief, u fiUmn. 







Dej. 




1 






belcw 


V 




t 




! 


S«>'> 


5 





Pmital Rifi^ t»i Setting ihtritf ij lit Atti_ 
lod where to L»k for tbem, lo make our Obfeni 
«/Mr. Scnex'iOi.««, fMtj Mr.MAMTiK, h 
tittrdsMF a bh lau Jmfirrotmtmr, vri/l JiBll/j " '■ it<fi, ni maiy 
Hbtr liftfil Enfuiria wiii mfi Eafi axd ExpuHimi ; vbtn rnar 
Aunnef ii mt 'nju'inJ. mgtb Gl-diii »a Jlfirmaur mtlt tt 
tt-aiUma, t, tb^ mB firm t, amfrm ibtTiath, tr.ilJcjiH - ■■—- 
in til Cm^atitfi,, 



OF THE MOON. 

ititrgivnTtm tf SrniUng, m MtfpvaDtj, thi rigit JJiaJbm ^ ih Shu, U Timi, m ttt fntrJSi<t 

RULE. The l^me of the Mooa'i Sonthint added lo right AfceuGiM of the Son, in Time, at the Time of her Sonthini, will b«thea 
equil to the right Arrenfion of the Mid-heavca, or right Afcenlion of the Moon then upon the Meridian. 

. r .r L-iT.. ._<■.. ir.:._ If f^g„ ri|ht Afceofion of the Moon, in Time, on i giren Dir youdedaft thed^ ArooTion of tbt San, In 

' ' ' ~ thifX^ATimeof the MoOB'i Soutking, pif) Noon, on thit Day, 

1^ Hence the RcaToo «f Grit leckiiq the Moon'i cSimate Soudiing, by tlie common Mctbodi of findiDg hv tnv Soutbin^. 

EXAMPLE. Tt findibt Mtm'i ngh J^cmfiK mi tU Ttmaf ttr- Sm^tg, Oftober 1, 1760 ? 



CmlrtaeKth, l>y Traafftfiaai. If from right Afceofion of the Moon 
ime, (bothutbeMoOD'iSaatbiiig) the Remainder wilt be the ix<A 
g^ Hence ^r RcaToo «f Grit feckiiq the Moon'i cSimate Soudiioj 

f»dlU Mnh'i rrj 

R.A.©» ■» 
■» IS 17 H' 

I»f. ] ]1 JN 



How, Ai •4> 



Re|«ain( u He 
I >»» Jl 59: i 



itf (hf7ai. f.ali.) lioa^i«fcillowtn|.. 



34, 4S) in Time 
T0fiaJtb,hlaQa'irigk^a-^Himlliim,fmadhigtb,giMa'I7m»fMmi*iStttU^T 



D louthi. "1 
Dif. S5« J 



-jr 



rRMi.M«oa'«R.A.T7C«. oa, I 

L By T«b. p. it, InDegnei . 



nuraalOU'.R.A. Moon .... 6a rt (ByT«b. p.st,bDegnei 95* !>' 45* 

IJ'ifl*.!- Lit. I DkI. I 
By£aC(i&'iEph. 176a. oa, I. j>oi6'i*H.4'[ss*N.>«'|Wh«Mt,byRRA,<}ucft.>8.p,»7i R.A. f 96* 



H. B. n< £a'aalDifirmitftlarl^Afmf-i/tb, H IQfi^ttttl* It Ht aaSfytit Jnu 



Dif . — I 7 Error. 
tttbi DiffiroM tj iiQfimSmlliMl 



yGoogle 















Ai 


NAVIGATOR. 












MI 


*^ Q U A T 1 O N of the Ecliptic Right ASCENSION, 




tn th« Ri«kt ASCENSION with LATITUDE. 


for the EiiuATiOK of iheEcl.ptic Declin. t» the Dt- 
clin. «ithth.tPU«i'iLAiiTi-t.i. 


Lon- 

tuJe. 


Sicn. 
. , tNorlh f, 8. 11.70 I » 


Sgn. 


... 


South <v. b. n,7o I a 
North ii,ni, x.U 7 « 


^'•S'A '*'■ ».lT,W,Jl.«9!'-^t 


VA. 


.0 ■ 


1" 




70 ,. 


I* 


,. ,. 


7" 


9" 


,0 i» . ,. 


4° 


5" 6" 


tiic: 




— 


— 






— 


+ 


+ 


+ 


+ 


+ 




— 


_ 


_ 




_ 




« 1 


9 ' 


« ' 


' 




. 




<> / 




, 






/ 


' 


' 


/ 


■> 


T^ 


"1 




" S9 


» 47 


3 37 


a4 


1 II 


' (9 


a 47 


3 3S 






,j 


ao 






JO 


! 


0.3 




' S9 


» 47 


3 37 


013 




' 59 




3 35 














a? 








;^^ 


»47 


























>« 


< 








1 3ft 






I ,» 






















li 


on 




1 i» 




3 3! 


oaj 




• S» 


»4S 


} JO 








.<. 






9 


)S 


o«1 


I to 


' 57 


"4ft 


3 14 


013 


1 to 


t « 


»41 


,ag 


J 




14 


;i 


14 




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ut.^|.ft.in./,y,ir,x.}+j^. 


The tbllowlng l;:;iaalcal lauUD, trom whence the abOUe eOUattOtia are dirduced, air nil 


Imitation of the Shortnefs and Ufefulnefs of the 


©ean of Dutoam'tf i^^ethod 


in finding the jparailaOic angle. 




c...,..c..... r"i--}S}i..i-}2:;,^:;;}t ;: Ht,. 


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AiRad. ..... S. 90* lo.ooooQoe 


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SoS.Ut 600 9.0(93346 






A» Ridiiu ; . S, }0« 

SaT«.Ut. . . ..900 




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9.600,636 


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g.oiiGioa 


Tc.a*ilofE.li^^ndM«ridiu.(<r«drf^) . . . 66»3.'3ft* 


9.6ooa«36 


ToTii.r.Dif.Decl.«q. . s joa4 


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The ROYAL ASTRONOMER 



A-TA ILH oi -tr La.c.'T,,, .nd A.oht A.c».,o» 


■irsna 


.-M.Ar« 


VoiLMih 






DictEE of Ihc EcLirric 


^om tbe Htrizm. (ondpondut. 








taflg. 


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rt 


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161 


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10 49 


109 


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140 


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9 14 




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141 


170 








9 S4 


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171 




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10 33 






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144 






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H 37 


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174 


18 40 


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4 19 


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118 


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176 


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177 


I 19 


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90 


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LoogituJt 


ni 




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M>d-H». 




Mid-Hia. 


Ko».Dtg. 


Mid-Hcj. 




M><i-H». 


Won.Dei. 


Mid-Hti. 


H«D.Dtr. 





lUo 


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log 


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1,8 


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3 59 


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333 


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305 


335 


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177 


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118 


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178 




399 


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139 






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310 


'3 '4 


340 


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341 


'J 37 


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190 


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17 46 




14 7 




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344 


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3-7 


so .s8 


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16 


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114 


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187 


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M' O 




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10 43 






34» 






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USJ 




11 14 


Wt 


>9 S> 


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11 4» 


3« 


*3 59 


349 




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«7 


IJ SI 




191 


14 4'> 


3" 




35" 


»» 9 






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19 5> 


11 


"99 


IS 8 


M9' 


•5 37 


160 


7 


193 


il 10 


3>3 


»6 5» 


35« 


10 jj 








IJO 






9 14 


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114 


17 47 


313 


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103 


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10 »7 


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197 


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198 




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156 


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Z«ailh^ 




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mi NAVIGATOR. 



rrsna fcr d«c™ini»g ti.c «. li-., tn «., &.r. wi- tb.' sitN. ij66ti. , Khim, » staR. i. i, tb, bith.ii p«., of th. 








Argument. S.ON'i Pl«t ir Noaa, w PUntfi L^utitnde il SootKim. 




- 


V o» 


a 


n 


2E 3» 


a,. 4" 






Pltce. 


Point of 


in Time. 


Afcrndin 


R.A. 

In Time. 


fointof 

Aftendtm 


inTiw. 


Point of 

Afcendtn 


in Tine. 


Poimof 

AfceDilin 


R.A- 
inTime. 


Poiutof 


R. A. 
in Time. 




" 




b m 




h m 


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h IB 


( 




1 


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5 
6 


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□ 11 








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31 54 






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7 40 


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to 4t 




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40 


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44 








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51 






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9 6 








° Si 


17 14 


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7 ! 












i6 


7 «s 


59 


> S4 


19 17 


5 ° 


11 14 


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4 










15 


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10 49 


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9 ig 


H 4J 








9 '4 






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6 41 




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17 11 












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19 41 


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«♦ 3« 


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1 39 




S 47 




7 i« 


11 39 














« 44 


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3 43 




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6 39 


3 47 


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•I »• 1 


* - . >' 1 , W . . .»« B - «• 


X •!• 






Point of 


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B.A, 


Poteof 


R.A. Point of 


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P«at«f 


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Afcnxbnl 


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Ar«ii^;>Ill 




Af«-l.Unt 


in Time. Aftenduii 


i-Tta*. 


MMKtMM 




Aftendwit in Time. 




■ = 


I 












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/ 


h m" 




« 


3*'9 


11 


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10 15 




M .31. 






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1 -J 


16 16 


13 37 


.> ^ 


9 ?J 
•0 49 


10 *j 

»o 33 


." 1" 




6 


7 »4 


■ 1 11 


0-C14 


"t "i 




■ 7 


J.I 




1 19 


14 »9 






',' '' 


11 J 










11 19 


* IJ 






16 is 


lo js 


'! 3S 


'3 »4 


to 41 




" 39. 






9 li 


'* 33 






II 40 


16 >9 


IJ o 


■J W 


'4 H 


» 4i 










" 37 


4 6 


14 JO 


IJ JO 


jLm. 


»*_»» 




IS 3» 


10 50 


_Ii_Jt 


n so 
11 s4 

" 57. 




11 to Ji 


II 40 




H H 


(J fco 


'(• S« »» 43 


.1 .1 


.* 40 






11 11 15 


11 44 






17 19 








.7 46 

in 








13 » J 


„ 4B , 








,6 46 




,« S7 










M J. 




14 4» 


M 10. 














»5 »1 41 


,1 S5 


9 » 


.4 JO 


IJ JO 


16 ss 




■! ! 


«, s» 




,i Vj 






i6 


t4 »6 


» S9 


10 6 


'.U 




.6 „ 








:; ;i 








'7 


.i 10 


"3 J 


II 9 


'' *5 


'^ 3 




;s:! 


.3 


;; « 












II 14 










'd'^ 










,6 j9 




IJ 11 


IS 6 


4 ji 


17 11 


14 4. 


19 " 










" .7 H 


■J N 
is 'S 
IJ 11 


.4 «9 


1; «, 


17 16 


.6 JI 


.9 17 


'S- S5 


1. 30 










■8 M 


;ij| 


;;» 


7 
9 »4 


17 11 iS 10 
17 »s >o S 


19 JI 

>9 35 


16 s' 


:: s 


10 j3 


13 17 














II S3 


17 »9 »» 5» 


>9 39 


>S 4« 




It j6 






H 






19 It 










19 j6 










*4 


31 14 


11 33 




•5 i» 


16 59 






0CT19 


II 49 


13 ts 






*« 


la I 


n .6 




«5 3S 


19 JO 


>7 43 


. 49 


I 11 




















11 s 








a 14 












ij 16 




14 »4 




14 19 




»9 5+ 


















,3 48 




15 47 


17 10 


17 s6 






3 56 






>3 sS 




,o " >S 


' 51 


17 ic .s S' 


30 




. 50 


10 9 






16 4. 






Cenfiftht-H. 1 he ibovc Table conlaini the rigbt Afcen&ao*, 


1 Time, of the M.J-Heiven, comlpondent to itu levetil Afcen 


"eotP^.. 




>f lh«EtlLptie«theH.-ri«ii, ird the light AfciBfiQn of ihe Mid-Ht.wn, in Depeti, itNoon, «■ Soothing. 





254 ri^ R O Y A L A S T R O N O M E R 

RULES utd EXAMPLES for Jndiag when tke SUN, MOON. PLANETS, and STARS, wiU 
bs ID the Nonagefimal DEGREE. 



_ , _. Ssutbiig, of tht Sun, Mtm, Plami 

Nei^igrfmarOcptt, willbetheTimt fram Ndoo, i 
liigheH Poiotof tbcEcHftic, nj<und. 



EXAMPLE T. Riju-.ridibtfimi-BibnibitviiiwiUUhthi^D'itiitSiatXDrpit, Julf 15, t 



RUtE. tatuambtn^l^UMjlimiiiTimaitiSiia'iPtaaMlifii, tr PUeitf thttXeon, PliMt, «j- Stir, aiSiiUtiv. Tba add t SltaA 
IbiSMM'iP/Mt di JVm>, tr In ihi Main'i PloHti, tr Siar'i PUct tt Saiiiitg, (oicra alfo (aitbe Place of the NoiucefinMl Degree) amJ tiil 
Samv,}/1 ti Ibt PdIkI of lU EcRftic, tr Afia^Mtt M lit Harimai af Loodoa, (fuff(^wg KtCtatgi d/ Pttci from Nm. er SnOtifr, H ibt Ntmi- 
p/aalDegxtt) amfjiuMlnil u vibict ArccaAint lait lit lit riiil ^anfun if ibt MiJ.Hiavm, in Timt, Mwi place it •adir At fsrmir rirbl 
^cnjimef ibi Mii-HiOviti, at Kxn, er Ssulbii^, mud tbt B0irait viill briii Tmt of tbt Na^ifmal Diptt, ftfi w biftn Ntt* fwt tb* Sin 
or fafi sr hiftri Smlbiitg far tbi PlaiHlt, rtfuirtJ. If vii'icbTimtbr aidid latr fuhlraBcd fivm ibtTim of St Kiting tf lit PUmtti, atntSur . 
itUfirt ir afttr Siutking, fu viUl bavt lit Tim af ibnrhingim U« IiTciuge&mtl Dr;[rn, n/filHvify, rtjuini, 

Snn'i nace at Noon 22 i)* IV 41" Kigbt Mctitton Mid-HeiMD comfpondent 7k 4e"40* 
R. A.Mid-IItiTCB<oricrpoiid'. hyUaTMi I 11 44 






hen the Sub 1 
^iptic, foi y 



Noon, K chat Time. ^ IKf . R. ATeeafioD or 

n In the 90 Dej. 1 
tiwtPq', 

y, B. When the right Arctnfion ef Mid.Heana it Koen, or Soothing in TlnK, ii I^ thu the ri|ht Arceafioa of Mid-Heivea to the 
ArceodiDt of the Nani|eCiiii] Degree, thea the-DiSereDce of tifht AToenGoni, or Time of Nonigcfimal Degree n pad N«oa, or SoolhiBg; 
bat if the right Afcenlion of the Mil-Heiven, at Nooa, or Soatbingi in Time, u mote thia the right Alcenfioa of MU'HeiTcn to Ih) 
ATcendant of tte NoiugeEmal Deiree, then the DiSctenct of right Afi:eafioai or Time of Himigefinul Oefret ji btfiife NcMi, or S«utbii^. 

EXAMPLE II. 7t find tbiTimnf tit Smk bang iHittNnugifmalDtgrrt, ijit af /tfiA, 1764? 

7' 54' 14* •'••*•'••'• '• Rigbt AlccafionMid-Heivenconel^ndent ik 43" 3S* 



The Afeendint to the Place of 'Igi 17 J4 19 . . , . Right AlctuBan Mid^HeiTen eorrerpandeat, Iji the Table < 

the Noaag, Degree biTing { — 

Bcirlf the fame Place wiib | Dif. R. Alcenfion*, or Time before Noon, whea the Son it io the 90 Dcg. •— : 

the Sua at Noon J 1; 

fim. Ho« faefete Nooa 
M0. VoumayalmfKlEdaa theR. A.ofMid-Heaveo'). Or Tmk pA ftinniir Noon . . 

«t Noon, &om the R. A, of Mid^eaien to the AT- f by iledoAing the Right Afcer 

cendsot, to (he Nonag. Deg. tu the Time poll the f Heiven it Noon, fr. R. A. to .— 

preloit 01 fbtaMr Day'i N*)n. J -Afeeod. of iLe Noaig. De(. fitft 



■nfion Mid- ( 
iMM-H.of f 



EXAMPLE III. lafitdtbirimiwhiMthtiaMwviUlitinlbtlfiMg^mtl-Bipf, JiinirjS], tj6%} 

,;,,.■>, R, A. Mid'Hu*«a coniipondent tjii £■ jC> 



The Alcesdint to thePlKCof Nonig,1(V> 01534 * ■< . ■ R. Ai Mid^HMTtn eotieTpoDdent iS «5 41 

Dee. being fuppofed the lime then > ■■■" — ' '-'- 

widt the Moon'i Place, J Dif. R. A'ctnfioosof Time bcfbietheMoonfbath* whes IheiiintheKanaeef. Deg. — 40 5] 

Mooalbuihi yn.-*], i;^), Koon . . Is o o 

H. B. TUCht^af th, Mta'i Piatt bffmartfitrlv^SamtUtrntttl 

tfiMgrf.DipufiHJditaUimJfa^'nitKmJUirsiri. I Won ia tbt ttiMltfimtlOtfnn, tttitina. it 19 7 



DigHizcd by VjOOQ IC 



md NAVIGATOR. 



*53 



RULES and EXAMPLES for finding when tbe SUN. MOON. PLANETS, or STARS, wjl, 
be in the NonageOnul D£GREE. 



EXAMPLE ir. ^t J!tdibtTaMmbatb4aboiimB kin atttDniffAttaiDtpv, NoreubeT 19, 1763? 

>. . • 1 ■ lU A. Mid-Heana, c(ifTd*foiidMt ill 440 



TbcAf<ciidanltalhePtueBftlieNo-'1f^4 ij ij . I > .... R. A. Mid-Heinn cantfpondnit o 
lug. Dcf, fuppoTeil the lime with > '- ■'■ 

the Mqod'i Pliceii Neoa. } Dif. R. ATcenfioni, or Time be&re Moon Ibucht, \ __ 

when Ihe ii in Noug, J * 

BnttheMooanot beiof intbe&incPliM, Say, Ail4k 1 11* 7'*) Moon foutbi Ifrv. ig, 17S], Ltmim , . if 
Moon'i dlur. Mot. :i a'' 40 eftimitc Time it Noug. Dog. f ■ - - 

befote Soathing : t> *' Chugi of Mood'i PIkc left thui r Moos iikthe A^m^, Degtee, required , . 9 
It Soutbini. J 

Oxaet, tbeAJcendanECbenwIllbe j^, 4' ij' ij.' 



Time, btfore Moon Gmthi when ffieii In NoniieT. 1 7 

Moon in the NtrngfimtlOn, 9 15 Night. 

EXAMPLE V. 7t ftdibi'nmttBhnHt^tniBhtiMtUKm^fiaatPtfra, SepteabertSv 17(3? 

Plice ^ >t Noon / i]* jt' • . . > i . i R. A. MU-ffaana coRcfpondent 16^ 4t*{ 
Add ]« o 

T1ieAfcei>JuctotliePUeeofNoaig.Deg,l X >} 1' i R. A. Hid-Hnra eontfpondtnt 17 ]« ( 

bnnt ^ fame then fi^pafed with PL ^ . { ..i — 

Dif.R.Aftcnfan^ crTiatpifltoHhi^ when f ii in th« Miwtf Dtgw . > o 43 1 

Add, f £Mthi £^.18, 1761, £««&■ 4 si P.M. 

' i la NoiugeGma] Deg. P. H, 5 ii t 

[requind. 

t^VUfm* Utthdfifvafii/tJbijriit Tinw oiei «]r SVw It Im lit IfMMgt^ui Zhptt } tbtfinpiii Sxtnfla iawg filial /i 



Here foUow 

Sexagefimal Tables : 

Proportioning the 

Difference of EQUATIONS 

At SIGHT. 



db, Google 



«$s 



nt ROYAL Aj5 TK O N O M B R 



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nd Sec^Ddi itf Seoeiwl. produce Fowibi, 


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47' X 44' = 34 »" 






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11 4j 


»1 " 


13 41 


14 ID 


H 39 


15 8 


»J 37 


»6 35 


»7 4 


»7 33- 




19 


3' 


»3 


»3 30 


1^ 


»f 30 


.J 


IS 30 


li 


»i ,0 


»r • 


«7 JO 


ill 


18 30 


ig 


19 30 


30 


^346 


14 17 


H48 


\Vl 


U£ 


■6 11 


itS> 


»7 »3 


»7 54 


18 IS 


18 s» 


19 17 


■f!j 


30 to 


JI 


1» 


•4 J* 


»5 4 


1.36 


IT 11 


»7 44 


a 16 


.> 48 


%% 40 


19 s> 


3'> *4 


3- 5* 


31 .8 


ji 


31 


.S J8 


'J J' 


il>4 


*< S7 


17 30 


1& J 


.8 j6 


19 9 


*9 4» 


30 IJ 


3048 


JI 11 


3> 54 


31 V 


33 


34 


.6 4 


xijs 


17 >* 


1746 


iB 10 


18 S4 


1, iS 


30 ■ 


3"3« 


31 10 


3144 


31 18 


31 s> 


13 »« 


34 


35 


•6 so 


»7 «S 


iS D 


18 3, 


>9 .0 


»9 4S 


J0.0 


10 55 


3' 30 


3» 5 


J. 40 


33 '5 


33 5° 


34*3 


1^ " 


3« 


■J" 


>8 11 


1848 


19 14 


JO 


30 j6 


j> i« 


3' 43 


3* »4 
33 18 


33 


S3 36 


34 i> 


34 48 


35 H 


36 


37 


iS XI 


18 55 


»9 36 


30 '3 


JO so 


11 «7 


3» 4 


3*41 


33 55 


34 3« 


35 9 


31 4( 


36 «J 


37 


38 


*9 8 


z«4S 


30*4 


31 1 


31 40 


1. .8 


11 s6 


33 34 


34 " 


34 S" 


35 »8 


36 i 


3^ 44 


37 M 


3& 


19 


'9 54 


3" 33 


31 11 


31 SI 


ji 30 


33 9 


3348 


34 »7 


35 « 


!5 4S 


J* "4 


'J 8 


37 44 


38 SI 


39 


4° _ 


JO 40 


31 so 


1» 


3».40 


33 » 


34 


,440 


35 " 


1' = 


364° 


37 «o 


,g 


3"40 


39 «o 


40 


4" 


3. *« 


ji 7 


3.48 


33 »9 


34 10 


34 5" 


35 3» 


,6 ij 

37 « 


3' 54 


37 35 


38.6 


■3857 


3>S! 


40 19 


41 


4» 


1» >i 


3> 5* 


33 36 


34 jS 


35 


35 4» 


tt. 


37 4> 


38 JO. 


39 i; 


J9 54 


40 36 


41 >s 


4» 0, 


43 


3. 58 




34 H 


3S 7 


JS JO 


3* 33 


37 J9 


.3"4« 


39 »5 


40 a 


40 SI 


4> 34 


4» "7 


43 


.44 


3144 


34 >8 


111 


3|S« 
384^ 


36 40 


H *♦ 


38 a 


38 S» 


33 3« 


40 M 


41 ♦ 


4.48- 


41 31 


43 16 


44 


,.45, 


34 3° 


35 'S 


37 30 


j8 IS 


39 


39 45 


4" y 


V 'J 




, 4» 4? 


ii-!l 


44 '5 


45 " 


•ir 


jpr 


j6 . 


^ 


37 34 


,810 


39 « 


39 s» 


40 38 


%\% 


4a 10 


•;rr 


4}4» 


*"T 


45 14 


V^'o- 


47 


1* a 


3*49 


37 36 


38 »3 


39 "> 


39 57 


%l 


41 JI 


43 5 


43 5» 


4* 39 
41; S* 


45 16 


46 11 


47 


48 


3648 


3736 


J8.4 


39 " 


|0 D 


♦04B 


4* »4 


43 '» 


44.0 


44 4« 


46 14 


47 W 


,48 « 


49 


37 34 


39 " 


M> 1 


V SO 


fl 39 


41*8 


43 '7 


44 6 


44 55 


4S44 


46.13 


47 " 


48 ,1 


.49 » 


so 


}Sio 


3f 10 


4° " 


1:^ 5° 




4> 30 


43 " 


44 1° 


45 


45 50 


4*i4P 


47 JP. 


48 tfr 


49 10 


5° » 


J' 


J9 6 


3? 57 


jr?- 


S3 


I» 30 


43 »' 


44 >» 


45 3 

11 


US 


4*45 


-51^- 


=48 »7 


49.8 


JO 9 

5* » 


Jl 


- S« 


19 5& 


»o 44 


*i-3« 


t3 "" 


44 11 


45 4 


JStI 


4« 3» 


4«»4 


|» l« 


5* « 


53 


t°S» 


41 31 


41 14 


" 'I 


44 10 


♦5 3' 


n 


811 


4?rf 


■SO«i 


5. '4 


S« 7 


■53 


54 


*i H 


t«iS 


43 " 


H « 


*i ° 


tSJt 




49 30 


50H 


51 18 


S» w 


S3 6 


54 


55 


(» 10 


M 5 


M 


t4 5? 


ts 50 


4740 


««5 


4»3o 


S°«S 


.5' " 


51 IS 


S3 1= 


54 5 


55 


56 


,.j6 


♦J S» 


***S 


H44 


♦*4o 


♦7 36 


48 J. 


S-3- 


50 14 

51 18 


SI »o 


irrr 


S3 " 


" 5 


H ♦ 


55 o' 


S 


(3 4; 


44 39 


ii^ 


tf J3 


B.JO 


(8.7: 


49 X4 


Sb« 


5».»S 


S3 It 


54 9 


ill 


56 1 


57 0: 


4418 


4j>6 


»7 11 


48 10 


♦9-i> 


5016 


J> *4 


S»ii 


S3 " 


54 » 


55 6 


St " 


58 0, 


59 


(S >4 


*SiJ 


47 11 


^8 u 


♦9 10 


so 9 


fi > 


!■ 7 


53 « 


54 5 


\l\ 


S6 3 


n ' 


58 1 


59 o( 


So 4S 0I4T «'4» '49 o'SO oUi 0; 


S« 


W ° 


S4 


55 *> 


57 ° 


S8 


59 


to oJ 


ikAMPLElV. DLf. Elation s.'j7- J f 




<5i's= 


18' 3' - 






if Si 


]i ai 




-•""-^ZJt J 


■ «" 


XSi'= 


41 39 


Jmrii.£icrbiTMAv,. 


Pn)doadi»idodhy6o = i9' 17'I'roportl. 1 




57* « 


47 




[Dif.re,*. L 
















19^ 16* 47" ^ 




F.»> 


Ufc, fcr 




Hi{iia>«i. 
























Ms 














A 



fh ROYAL ASTRONOMER 



A TABLE tf the VISIBLE ECLIPSES of the SUH, fer ai PrijKi^ CITIES of EUROFM. 



CITIES 
NAMES. 






Lifin 



Ntftn 



Rtm$ 

VfSti 



M 






it: 

I 16 



i:i 



5 K 



u\ 



,J3 



:!:i 



biAm. 



I. Of thiMMV, Jl£nia. 
Ba. gl" It- iT ■) NltU 

SmJ g j9 37 tCm 
BwSn 46 o J vriti 



Ell 10 IX iG (Gria, 
Dtr, ■ *7 o J tad. 
^nMTf* cclipfed C Dt^ nf 
la tlw Nort^em Part of dkt 



IV. Ofthefar, Dtt.-;, 
Middle lb tm AftnnooD, 
ian&bla io Etrefi, bntvi- 



tfMo .s 9 l«f" 

Em. Tt II jS fCrcn- 

riirfis 18 38 \m!a. 

Jmt. J 46 s8 -» 



m. Of IbB AAn, »«. 



1. Oftbefa*, jt^tt^, 
[fiUe in thtSoathera Pitt 
of tbcEirtfa. 




fifib]<>intlK»Vj»*'<<- 
£v. il> si> 34' 1 Mara. 

Euf c 16 14 \vKb. 
^S^itf cdipfrd 9! 42' OQ 



m. OfthtSwM, OB. 
rifiUc, H abora, is the t A 

Table. 



IV. Of the 
r, riUte, MG 
5tf. 7b i»n a6> 
MiJ.S 



TlGble at ^oftfK and CfriM. 



rv. Of the &nr, ATtv. 
16. vieUc in the Sonthmi 
Paiti of the Globe, but not 
ri£blcia£iinf(. 



MO a6> 1 
edipfed 6* ,,f , 



the Sfluthem Fait « 



I. OfAe3n,.ArUt3, 
tAft ia .^ria, and to- 
irdi the eitieiiie Southern 

PaiUoffu^. 

II. Of the Smw, Oa. 7, 
GUe ia South jbKrita, 

ud not viliUe in Euvfi, 



SEE 

tim rules 



COMPUTATIOH 



h Of the Mwa, Mml 

e.J I 39 siVraK 
Dura.* .46 4SjwtA. 
^jfofrlf/f eclipled gd ji' i 
the Sontbcni Fart of die 

IL Of thej'ar, Aril%, 
■ifibit It L-im, n ur '^- 

UeaboiB. 

III. Of the BAn, Stft. 

te, tifible in .iAktih. 

fl&.7 1.33 t « 
£«< S ij J? fCnra- 
i)*r. a 11 50 J wkA- 
thumulj K&tU 4448' OB 
the NotAern Part af the 



IV. Oft)ieAur,5^a5, 
TlGble oolr in ibe Southern 
Paiti of tM Earth. 



yGoogie 



tnd N A V r G- A T O R. 



ATABL2 oCtheNiw, FvcE, ina QvAiTiaM OOHS br GnmwVi Oiiiitatoii, from Noob. ' 


MOHTH3. 


^ 


1760. 


1^ 

S 
>3 

!s 
16 


iT«i. 


i 


.781. 


1 1763. 


If 

? .,(4. 


JAMUABiY. 


9 

H 

3' 


4 Jl Fnll. 
17 s6 t»«<l. 
1* ja New. 
la 11 FirAQ, 
>S 14 F«U.^ 


*■ 44 New. 

H 1. FirAQ. 
« 14 Fall. 
II ifi LaAQ. 


3 

,s 

8 

M 




G S »9 L.ft<i; 

3 14 49 New.^ 
I »o 39 PkAQ. 
S ij M Full. 

4 Jl 47 l-«t 

13 49 FirrtQ. 
7 10 10 FulU 


Ii a 
■ » t Ne«. 

ii 9 SI L««<^. 


FEfhUARV. 


S 

le 


I, M L.AQ. 
I 4. New. 


IS !9 New. 
Sj 58 FirAQ. 
17 47 FulL^ 
7 so L*ftQ- 


16 6 RrAQ. 
8 3 Full. I 
S S° Utt Q, I 

10 39 New. 1 


" 11 43 N». 

.? 'J ;j Fi:?.^ 

»1 >E » UAQ. 


MARCH. 


,9 
16 

«3 


■9 >7 Full. 

M 4^ Firt Q. 
I 7 Full. 


'3 

2! 
4 

16 

4 
iS 

9 

g 
16 
14 
li 

7 

'S 

11 

i2 

s 

'1 

3 

'3 

10 
«7 

4 

IS 

iti 

4 
IS 
'5 


6 j9 New. 
4 .4 L.ftQ.. 


3 
S 

il 
1 
'J 

»3 

3f 

7 

•s 

»3 

22 

6 
'4 

>S 

s 

«7 
4 
»9 

3 

17 
2* 

16 
21 

8 
'5 
13 
12 

7 
'4 
»J 
30 


1 jB Fi-flQ. 
ig II Fuil.^ 1 
JO UAQ, . 

3 34 New. 1 
II 1, FirAQ, - 

4 4* Fall. 

.9 9 UAQ, 1 
17 Jl New. 1 
.9 9 FirAQ, 1 


64 9 UAQ. 
4 + 4* New. 
1 3 43 FirAQ, 

B 19 JO Full. 


» S 7 New. 
' 9 4J FirAQ, 
7 11 J Fall.^ 
4 3 18 UAQ. 
r .1 ,0 New.^ ■ 


APRIL. 


t 

'S 


4 lo FirfQ, 
17 »7 FuU. 


19 31 New. 

14 »S FirAQ. 
,9 47 FaU.^ 
M 37 UA Q. 


^ It 16 UAQ. 

. M 13 New. 

' '3 IJ FWQ. 

S »4 F"ll. 


9 I to FirftQ, 
J IS ]S Fall.^ 
» 14 14 l*ft<i. 
IS »9 New. 


MAY, 


7 
14 

«9 


.9 .. I-A4 

13 5 New. 
7 Sf F-rftQ^ 
9 16 Fall. 


S 17 New. 
«( I FirAQ 
10 13 FuU. 
14 L*ftQ, 


16 Ftilt. 
13 17 L.AQ. I 
4 41 New. I 
IS ij FirtiQ. » 


IS 14 LiAQ, 
IJ 13 New. 
1* I FirAQ. , 
ij 40 F«ll. 


8 IS 47 FirAQ. 
J 4 54 Full."^ 
s 3 * I^ftti: 
1 5, New.^, 


JUNE. 


6 
■9 


S 17 L«ft<fc 
10 iS New. 
10 13 FitAQ. 

□ 19 Fall. 


'1 n Si 

> 14 Full. 
1 .6 UA Q. 


4 19 Full. 

5 . SS LiA Q. I 
t\ is New> . 

4 . 3 FirAQ, M 


3 IS UAQ, 
I SJ New!*- 1 
43 Flrfi<i. » 
SJ ij Full. 1 


6 SI ij FirAQ. 
J 1*. 14 Full.^ 
= 18 ,T UA Q. 
i 10 .8 New. 


. JOLV, 


S 
»9 


i> t6 LiSQ. 
J J3 New. 

3 17 Full. 


« 3» N"-. 
14 3» FirAQ. 
iS jS Full.- 
I* ^ L.AQ. 
J 13 New.^ 


18 o Pull. 

»o IS UAQ, It 

10 33 New. 1 

11 40 FiiflQ, n 


.0 ., UA<i. 
tl Jl New. 1 
S 37 FirflQ,* 
lu s» Fall. 1 


63" FirftQ. 
1 » IJ Full. 

884 New.^- 


AUGUST. 


! 
16 


7 so J-^ftQ- 

* 49 New. 
4 37 KfflQ. 

I 3s Full. 


3 »6 RrAQ. 
7 18 Fdl.^ 
19 J7 LiftQ. 
I 17 New, 


S 11 Fall. 
9 41 UAQ^ < 
> 33 New.^ » 
IS >4 FirAQ, 3 


,j 17 UAQ, 
10 ] New. 

■■ >i ?■;!«: ■ 

38 Fnll. 1 
4 !! I^«. . 


1 2 .; ai'^ 
1 .i 11 Jsi'^- ; 


SEPTEMBZR. 


16 
»4 


3 tt L>HQ. 
3 JO New. 


,9 4j Fi.jftQ. 
11 li Full. 

1 48 LiftQj. 
1. 14 New.^ 


S Full. 
« J3 UAQ. . 
II 31 Hew. 1 

» 4S FirAQ, X 


4 10 N.». 

.3 .! ri,iiQ. 
.7 I r.u. 
It « uaq, 


* «3 J' KiAQ; 
9 19 4 FuH. 
7 II 44 IjftQ- 
j s 9 New. 


OCTOBER. 


8 

16 

"3 


1 'I i;f.* 

R 11 FirftQ. 
1> 46 Full. 
14 34 UftQi 


9 31 UAQ. 
la J I New. 


■6 30 Full. 

5 31 UAQ, I 
SI 14 Neif, » 

6 34 FirflQ, » 


I] a Ktw. 
i 9 FirAQ. 
,0 jl t^l. , 


I so JO FirAQ. 
9 .0 s" Full,^ 
7 '4 49 UAQ. 
4 14 43 New. - 
1 6 31 FirftQ,. 


NOVEMBER. 


19 


T s New. 
1. 1, FirAQ. 
9 14 Foil. 
? S9 UAQ, 


10 SI FirAQ, 
13 48 Fall. 
I? *3 l;,ft<l= 


S S3 F"ll. 

I J >i UAQ, 
9/ iS New.^ I 
» 44 FirilQ, 1 

13 45 Full. 1 


It 4j N«. 

,. .0 fHQ., 


6 31 FirilQ., 

8 4 39 Foil. 

J 45 N**' 

9 " 3s Firflq. 


DECEMBER. 


•s 

aS 


a a New. 

* 1] FirtiQ. 
19 »7 F«il. 
1? ; UftQ. 


6 31 FirAQ; 
11 ,0 tM. 

. 33 LaftQ- 
10 S4 New. 


10 sj UAQ;, A 
*' « New . 

9 11 FirtQ. .? 

11 43 Full. 17 


9 3* Nbw. 
4 la FirftQ. 

■■ ■< r.n. 

■ 4= l.«<l, 


7 *3 47. Fall. 
5 .9 IS UA^ 
1 10 SJ- New. 
9 M 43 FiriQ. 


.Ji.USEj/'f-W,,. 
J««t^ 1763 *«■. I, 


64. ■7i™t«/i<M«.'ii'i«>«G™wkht.Antlga.A/r^J'«i 

i -5 PL Grum^Ub, Br tl« Tthb. 
Km* ijo IIS ,1' 1 Agdoa 140 Di«.Dif,ud«r6o«Dif. Lode. 
Nooa >3 ]6 «'.••• 

. Dif. 140 AC' , Eqiutkn of J) '• Pli 


7 Jl' 


Diu 


c . . + » .7 3 

. . »» 13 s- 





N.B. Tfe /*« Mutti Jtrva for 



« Google 



ASTRONOMER 




s^nmsn 



and NAVIGATOR. 



263 



kqyATION of Che true HDiiiontil Diamito of the MOON t 
appirent Horitontjl Dkmitjk, ia Firti ofthc E^dj 



M<!)otJ't b kfiiliJ'AT'i?5iJ." 

Trut Horiioau] biai 






li^30'' [ 3i'o*H'y>*M3'o' 3}^ 30*134' o" 



,6 
4alo 43 

50 51 



li ^: 



j6 J 

55 3 S9 

»4 + 19 

i4l ♦ ]? 



♦ j6 



ri 




T* JSkJ tit EfiidliH 
SifirihcRtJI. 



CONSTRUCTION- 

Smi'Ditm. tf tit Maui ia Parti ^ tbt 
S.,o 



MM 

Cor. DeclinuiDD 

To Ridiui 

So tr» Horu, Diun. } . 



To jfyfarai DUmcter 
Dif, Tlw£qi»lien . 



J4 J9' 



-}■ 4' ji)* required. 



Nut, To find the Time of the Moon'i PiTige thro' the Meridian 

^ 360B11M ]t'"ffarrntbmxeiilalDiam. in Pn-n rftii Efmirir,fiiiltilatm»i 

i/Timi tttToixl lit Mtfa'i two natPaJfagiiiirt' lU fam€ Min£ni, (tr Kf. (f (i. 
Sm flurf Afwii'j " - • — ' ■■ • — -....-- 



'i R. A. it riwu, fir 14 HcwjJ it lb, rim, ,/ th, Mm', Ptfa^, tbn' 



EXAMPLE. r,findih,7M^ib,Nb<»;P-^tptbn'tttMm£m,DumUri, 
1 764. ai Grearancb T 

5 ■« Declination yi Da, ■tNoon, 7' jl'N. Trac Horit. Pirallixthen, 54' %t 
For Horii. Puill. si Da. 16' 51" j' 7" T True Hot. Panllax 7 

iS... SS »S litpiffinjtheMerid.i S4 " 

( J'lHorii Diime-i 

Dif.injDiji I a4i!4ii \' •}" y ter correfpondeiit. J *' '! 
]> PaOei Meiid. Cntcnnci ]o Dh. 1674I 6^ ll> 1 Eqution . . 
3' • • I* S9 ^ „ „. 

— ~- — 3 J epp.Hor.Diim. 29 jo 

Now, Ai 36o« to J9' jo". So t^ 41" to m i». Time of J pUfin( 

the Meiidiia reqtiiicS. 

N. B. De U Caille'i Efiam. bn im HtriM. Duni. 1/ 9}" 7 
TmttfyiPtffip Atf tbtMmSaa , . . . i" i> { 

^ TheMo»B'iHotiieiitil Pir»iLw to p'l Horii. Diameter it 5;' 40" 



EXAMPLE I. 



Dif. M 

Greenwi(h_/w- tbtji Dap, 

Ai^unent, 13s + 5* 3" 

4»' + ° » 
Snm, Eqation •f' J s 
Moo. j ■**•,» I'J'g if 
B '■ Placet It Crwraitb, ten*. 

EXAMPLE IL 



Nooo 



; At ParU 



Snm 30 57 
ra-Hm^ by 7 
T»b.i..«9-S 
3*0" ! 19' 5»' 



FT.b.p 
,j«o. 
41... 



'• Dedimtlon. 
;i76l.O«.4Jia0 44'N 

'" " ^iL^' 

Dir. 6 46 

1?s rfjftr tbift Dicliiatialu It 
OrtcDwicb } 

Aliment. £• •^ t' ic 
46/ - o 11 



jUIj'ZqlM 



N. B. V2< itftm'i ya«.<f;iinur..Ci^ a, ill -idTahi, if lb, Ufi HtMd Pa^i, f, tJJ,Jic ^ futirOitlJ frmlii m 



■ T'W e/ in- Smo^i'i;, atar3i*£ ,- 



ilk 



W» ROYAL ASTRONOMTEH 





A TAEi:i! h»Jine th^ Pftbl'ORtlQWAL &ll^frfift6(Jefe X) be «^ t.r/J^,flJw cr ('rom lU^lriTT W06W,'ot PLAWBT*. *i« 
O^ffiMf/cB, /[.,<. fife, it « /r/S Miridun for the r,f;rf?i« P&rt, Dir!i«ah«, R. A Kc. » . giwn i>i]f«™-r of W** or Aj^ L™*itBde. 






*««./,. DiumJ Bil&renrr nniE or Icli ; ind Uiftmi™ of lawltuit 






Diff, 


10° 




JO" 




■,00" 


60" 


70- 


So* 


9"" 


loqo 


no' 


Iio» 






+ - 


+ - 


+ — 


■\ 


+ ■- 


H 


+ — 


■+■ — 


+ - 


■+■ — 










o 




- - i. 


• - ir 








' ' ir 


" " i» 


" ' i 




' " iv 


" * iy 






' 


. H - 


' " • 




/ * * 


;' * - 


r-«' m 


, 4.'- 


' ' ' 














a 


D 1 " 




a J » 


a / • 


a / * 


^ 1 a 


/ • 


e / M 


a ' « 


g 1 a 




/ • 






3 

4 


I 40 
S 10 




5 
li 


640 

OIJ lO 

o!6 4^ 


i 10 
t. 1646 
ij 
33 to 
4t 40 


30 
40 


If 40 

0,J K, 
]| 
4S 40 


M 10 IJ 

li 4c JO 
040 c 04s 


OIS40 

ojjao 

I.J.O 


,s 10 10 a 
36 40 "40 
SS ''• 
. 13 »o i 10 
' 31 40 I 40 






6" 
7 
S 
9 


II 46 
1] 10 


%i 10 
1640 

30 


30 
0350 
040 
4s 


040 
0-4640 

S3 iQ 

1 640 


■t G40 

I IS 


1 30 
~ S" 

-» 10 


I 11 40 

I 31 10 

1 S ao 

.3140 
1+3 10 
«SS ° 

1 640 
J .iB 10 
3 j3 
3 41 40 


iij:: 

1 13 .0 

.164^ 
» 40 

» S3 M 
3 640 
3 »o 


' 10 
I 45 

* IS 


1 40 
I 56 40. 

:ii3 


11640 

. 45 


14a g 
1 
JIO 






'3 
'4 


□ iS JO 

11 40 
a ij 10 


3640 
40 


' 3 < 


1 Ij 10 

J *6 4^ 
I J3 10 


I J140 

I s* 40 


»4S 
3 
3 'S 

J 10 t 

3 45 < 


3 3 " 
3 3640 

3 SI ».* 


3 11 40 

3 40 

4JS 


340 

4 «o 
440 






■",6" 

"7 
i3 
«9 

11 

>J 

■«4 


16 40 

JO 
31 4'> 


14.1= 

S7 40 

1 640 


1 ij 

' JO .0 
I js 
I 40 


■4640 
I SI io 

> 640 

1 13 »o 

1164^ 
a J3 »o 

J4D 

1 40 40 


» 13 to 
1 11 40 

» 46 40 


1 40 
. JO 

J 
J 10 


400 


4 " < 
4 IS t 

4 JO C 

4 45 <^ 

5 c 


4 «e 40 

4 43»o 

1.1,: 


4 S3 " 

5 w 40 

5 30 
548 10 

6 640 


5 10 

It : 

6 *o a 
640 






Olg«. 

040 

4' 40 


ijii 


'45 
' S« » 
« SS 

1 1 a 


1 5S 
3 3 «o 
3 " 40 


J 30 
J 40 

-3 JO 

400 


4 S ° 

4 16 40 

440 
4 S' 40 


440 

re 

5 10 

I 33 10 


S 'i -^ 

5 JO 


6564* 


6. J c 

6 43 10 
T > 40 


7 
S lo 






19 
30 
J' 
3* 
31 
34 
35 


43 iO 

048.0 


. JO 


1 IS 
1 lO □ 
»iS 

1 30 


» SJ »o 

3 * 40 
3 13 10 
3.0 
3.S40 
3 31 10 
1 40 
J 46 40 
1 S3 »o 


3 3* 40 
3 45 

3 S3" 

4 I 40 


4 10 
4 JO * 
4 40 
4 so 


S 3 10 
S «S 

S »6 40 

S jg »o 


6 It »o 


6 JO 
645 
700 

7 IS 


7 ij .« 

730 

7 4* 40 


1,,.. 

8 S.40 


840 
900 

9 10 
9 40 






Ji 4C 

53 10 


1 50 


» 35 " 

140 
« 4S 
1 JO 
MS 


4.810 
4 16 40 
4 31 
4 43 »o 
45140 


S 1= 
S »o 
S JO 
J 40 
JS- » 


63640 
«48»o 


liii 




S 3640 
g Ji 10 

9 16 40 
9 43 10 


,,S.o 
9 4* 40 
J 
ij 10 
41 40 


10 40 
1 40 






39 
4° 


100 
I 140 
I ] «. 

:i; 


3 

3 _S 

3 >S 

3«> 


4 6 40 
4 13 10 


'1'° 

5 "S 
S 33" 


6 10 
A 10 
6 30 
640 


700 
7 II 4> 
7 .3 10 
7 JS 


S IJ U 

g 1I4C 

It:.? 


9 c 
9 "I 
9 JO 
9 4S 


!oi24^ 
10 33 10 

;;i4 


I 18 ao 

13640 
' SS 


» 10 
1 <o < 
3 
3 10 






4« 
4» 
♦3 
44 


1 8 10 
I 10 
I I) 40 
1 13 m 


1 1640 


31s 
1 30 
3 35 
340 
14S 


4 33 « 

440 
4 4640 
4 51 10 


S4I 40 
S so 


«50 
700 
7 10 © 
7 «o 


l>Mo 
S45 . 


9 64* 

9 ID 

9 J J .0 
9 46 40 


IJ c 

030 

4J 


n 13 M) 

1. 40 
11 s6 40 
11 13 *o 
11 30 


1 3140 
3 1640 


3 40 
400 
4M 
440 
S 

1^ I 
6k> « 
64° 






4i 
49 


I v> a 
1 11 40 
• >3 " 


» 40 


J JO 

3 Si " 

4 « 
4 S « 


S *40 

J IJIO 

S 1640 
S 31 »' 


613.0 
6 J140 
640 
648.0 
65640 


7 40 

V% t 

8 10 
g 10 


I jll40 
9 S 10 
9 10 
9 Ji 4° 
9 4} 10 


040 


I ]0 

I4J e 

s IS 

. 30 


1* 46 40 
'3 3 >o 

13 ]6 40 

13 „ 10 


* 3 " 
4 .1 40 
4+0 






5" 
i» 

SJ 
54 

-If- 

II 


1 il to 

I JO 
I JI40 


» 50 

3 

3 3 «> 


4 "J 
4 JO 

4 IS 


S40 

5 46 4= 

rro° 

6 S40 


Mi 

6 30 
6,Sio 


JUS 

8 JO 
900 

9 .0 


■0 iS .0 
10 30 




» 45 
3 c 
3 »S < 
3 30 
1 4S 


14 10 
■4 16 40 
14 43 «o 


5 JS 

in:: 


700 
T 10 
7 40 
800 
18 to 






I J3 10 
I 3i 

1 40 


1 6 40 
3 10 
3 'J «> 

■J 10 


440 
4 45 
4io 
4 JS 
^ 


61640 
6 33 ao 
640 


64640 


9 10 
9 JO 
940 

9 JO 


10 ij ao 

I 40 


1*640 
1 40 
1 jj .0 

3 6 40 
3 10 oJ 


4 c 
4 «S 

4 10 
4 45 » 
J ol 


IJ 31 10 


7 640 
7 .J < 


1840 

19 D 
I) .0 

9 4« 






CONSTRUCTION. A. 360" to >m A«rW Diffoence, fo io«, 10", «», flfc. Dif. Long, to the propettioiul Dif. M bi «(M to 
r l-diirtBid Stair, the Qointity for the I ft Mtriduo, ucotdiag » the Qomtity Tor »a Diy » mon or lef> tbio the QMntily fat the ift Mtri- 

t.a.-d, whin the DiBiieiiee of LonltiwleueiihalT from the iftMeridiin. Sh B«tem,f p. >6t fir Em^ b>n ml idifllim. 





0ni NAVIGATOR. 



365 



■ SquatWiI J.U btfrafetotl ^tiigb,j^4^, inTiint, « s««. b«v™«. tkesuN. mo<Jn, pUnst'3 -ndffAfirSTi 

the Dcutr Time of their tefpeftiTe Southing tt Gnt^iih. \ 


ILA.K 


>inM. l>i«ft»nxc<>ftWfi-n'ift.A.ia¥i»4.tM<«fl, rrMDlUlUA.uTi»altlMU«»...^Ua««S»^, uUa^ | 


> 


«? 


V 


» 1 « 


e 


* 


CONSTKUCTION of At idJMmit TABLE. 

M. DhTMi Uktfn. D.Mix.TIm,. 
liQ") ■!• II' aC 41' r4B«4fiO Tikcnu 
©45 S7 7 46 3 49 '>«i»«o 

©iJ>'o «7 41 40 < I s' WR. A. of 
$iO 1« 59 19 a 18 ttioTeBwIiei 

©i*J a 59 » «o I 3 S7 J "Ijettivelr 

Time, nken m mein Dia«r«B«t of rigbt AlMnGon, 
the QniiiiitK* of ITfutM to tlic Gift Tine of neat 

RUM. n^/> £p«ri«. «JJ,f^ f»i,raa from ,h 
T™./««-Sn«*Jflf. jtGKOlwich./sr/i.j.Mw'ri,. 

ihm.atariiMgat the Maia pftU emfiflial Badt (m^ri/l 
« tb. Hu-i B/<«AtW™,7 i,fm,f,„ vd>Lrth^ 

EXAMin,E 1: Tb /*jrf I«f MHT'- Twe ,/ fif 
Mun',S<,uihmi,frm dm D\ff-rm> -f ritbt AhnC^r. 

fly p. 338. D R. A. — oR-A.i76a,7 b m t 
J'^Jo.N™, Cr™«.,i . '. t IS 16 3 

.i».... £,«,!«+ 033 


OOO, 


■ + 




— - 


- 1 + 


+ 


— 


h 




m • 


m * 


m . 1 >. . 


m • 


m • 


m 


m ( fh 


1 th 


1 ih 


. *| . U, 






■ 


. thlb 


th fo 


th fo 


th fo 


th fo 


a tc 




s 
1 

4 


s s 


19 


I .1 


" 5 

9 

.0 ;s 


e 

li 
*s 


•3 31 

» 33 
» 4 


JO 

30 
39 

.49 


' 6' 
I 


"4 »J 

O.StJ 

18 17 

6 WI, 


57 
• 7 

1 t6 
■ s6 
« 3S 


• 54 

I 3 

I 30 


>8 

e ja 

37 


37 
4} 
49 
55 


4 9 

4 40 

5 " 


» 59 
' t 
I i» 
1 »9 

I 39 


'3 
«4 


014 »3 
o»6.s 

iS «7 


» 4S 

» 54 

» 14 




51 

55 
* S 

« 9 


I 14 

1 a6 


e 44 

Hi 


1 aS 


■ 6 
19 


ji }■ 


1 33 

. 3 I 


a as 
» 34 
» +3 
* 5» 
3 ' 


I >4 
I ip 

: a 

I 3» 


1 39 
» 45 
» 5' 
» 57 
« 3 


is 

9 '9 
9 S» 

10 ,al 




1} 
14 


041 40 

04846 
504! 


J »o 
J 1) 
1 39 
J 49 
3 59 


152 


» 37 


a 9 
> le 

s 18 

« 34 


10 S3 

11 a4 

;: ii 

ta ST 


3 «7 
3 37 

3 47 

3 S7 

4 7 


■«kb, ,78., 7^^ ,0, P. M. ...\ '5 *' S 

AlV'*%>'«M>'*'»lAf'-. BaiNT't MlTBOD. 

CWsSTimeof p'.JwjW, P.M.itl , 


"9 


5a 50 

• (7 




3 SS 

4 4 
4 13 
4 »« 

4 3' 


« s 

a S 
> M 

I 19 


a 40 
a 46 
* S3 
" S9 
3 5 


ij aS 
ij S9 
"4 3° 
IS 1 
IS 3» 


4 '7 


Zrr^ . . — 511147' 
r> Thu UiTMOD of findiutbc nm Time of tl..- 
Moon'i SoBlhiag never difitn from the Tiuih but 4i n 
/xeMi'nM. A> thefune Meihod findithi SoutHln.. 
oftbeStinwichina Aw£rc«ii of Time: md tik 
the Southing of »11 'be Plmet. fcnxly iifieiiog > Mi- 
nute horn Truth. 

EXAMPLE II. Tf JS-J lb, mtr0' 7 !m if AUcU 

j^/*. &,M fiim right Afcafin ,f Alddwtan, *t M^», 

B* p.atS. R. A. BfAUibam— R. A. 1 
ofiot + Con. R. A. 0. 1760, J- h m . 
^■V. "OM ■ • . J 9 4' "5 


3' 
3» 
3] 
J4 
t$ 


I 1 ;t 
I J * 

• 7 3 
» 9 S 
I II 7 


1^1 

s »I 

5 «4 
S J4 


4 40 


» 33 

* 37 
a 4a 


3 It 
3 >7 

3 "3 
3 30 
3 36 


16 4 
It js 


' i 
' "J 

S 35 
5 45 


36 

li 
19 
40 


1 15 10 

t 17 It 


5 43 

i:i 

6 aa 


5 »S 
5 15 

5 44 

1 n 


a 46 

3 


3 4» 
3 48 

3 S4 

4 " 

4 7 


.< 39 
19 10 
19 41 


11 

6 as 

S 3s 


4> 
4« 
43 
44 
4J 


..3.! 

t »S 10 
I S7 « 

■ 19 14 
1 31 »6 


7 9 


6 ■■ 

Hi 


J w 

3 14 
1 '9 


4 13 
4 '9 
1 '5 
4 !> 

4 37 


ai 45 

ill! 


6 S4 

7 4 
7 »4 

7 i4. 


ByTat.aatteLcftfk , . < ffsMw — i a9 


46 

:i 
49 
JO 


1 33 »< 
I 3S 19 
« 37 J», 
I 39 4 
I 41 6 


5ii 

7 48 
7 57 


i ]e 

7 5 
7 »4 
7 »3 
7 3» 


3 33 
3 37 

3 4* 

3 47 
3 S> 


4 44 


xj so 

44 11 

U 5» 
as 13 


7 34 
7 44 

I 'J 

f 13 


T.tf</E4a>tH>ii — I 36 
R«m. UeerTifK So>thi>i| lSAUd.arc. „ ,„ ^. 

(>«flTiineof.«W*f*.-.Soiuhii.(,h,» , „ ,, 


5' 
S» 
i3 
S4 


14J 8 
145 w 
I 47 " 


i ,1 

8 a, 
! 4! 


7 4» 

7 50 

1 '1 


3 56 

4 ° 
4 5 
4 ■<> 
4 14 


3 H 

I »7 
5 33 


as a< 

»7 *7 
,7 58 
aS JO 




E™ - 11. 
Afl^a 4^ Weft,L»ng. . . . Equilion — 391 

.,«^«.n«.ly fouth. H A>{r» . v . 9 39 >o 
(:«reQJyfculbt»tAwiM,-.6TP,»i! ■ - . 9 3854 


S6 


1 57 »i 

' 59 iJ 


8 54 

9 4 

9 "J 

9 aj 


J ^s 

B 44 
! S! 


4 19 
4 31 


S 45 


»5 I 

•9 .J» 
»9 43 

JO 34 


9 13 

,9 »3 

9 3» 

9 4» 






Tt, «W -.hi. -fti rf«/i fi* &/. »/?i« t. i, .^AJ /. «■ M«fld A-. ,fc 


■K-. .y Stiiibi^ at Ibt firji ii,rl£„», /w /*; tim, of S«tii«p at i^ pla» If ,«a, 
T.m, » i, /.i^^rf WWd«/ fir Eift W Weft . L>„p h rim,, ,b, Sim', ia' J tU 

[ft&UFto. v/Su«ul,, DIffirm,. .f Lmgil^Jf, E.ft,rVeft_/^™,,i(>/ Mrtfia,. 


here follow 
Logistical Logarithms. 














Ui 







2 66 



n« ROYAL ASTRONOMER 



The NATURE and USE of LOGISTICAL LOGARITHMS. 



THE Diftmci httmttn -hi amrnni Legariibm cf j6oo" (being the Secondi i 
tnJt, niUr trabovt ^ao, iitallrJibi Lophid i^tnthta ff 'bai Kumiir b/ Standi, 
nrgfftivtiy under dnd ojgirmaii^e^y shove fiiJ. 

Thepiincipil Ufeof thcrt hgifiical Ltgtriiinu is hi the teidj proportioning Sfxtgtfimiii 
" ■ " " ' ' ' Argument to > ^nn Incteili or Decrofe of Equ»tioo 

iber of SecoDdi is the fiUnuiiii ItUi (p. 167) eiUod. 

tht DETERMINATION »d USE of lU l^fiittl Logarlibmi Jhm tbt (mmu LOGARITHMS. 



Te fiaj til Ejnatiai tf tbi SUK'i Cntr fer 



Eaiiat.G''Cent.T 

1» 6' 57" fAi eo* 0"= 

ii—fTo+i 36 = 

IncT, i' j6* JSo vj 38 c 



Tirft Eqaition 
EquMibn of Sun't Ceotei 



• .j'aS"' 



Com. Logi, 

L. I . . . . 

L. 96— L.] 600 
Bo -T^a I" 165S— 1..3600. 



3600 
i6jg 



To- 



-IS L. 44 — L.j6oo, 



EXAMPLE IL It pii ihthV^'iJligbt Afenific»a^air*hl,UthtSin'iPlM€ f ^T ^y ^V 



■I.S740 
0.3367 
■1.9 107 



R.A. Sun. •x 

i66» 43' 47* Iaj 60' o'^36oc 

1*7 49 II J. 

- ' \ To 65 14 =J9»' 

:. I s *4 JSo 37 ♦' =»»6: 



R. A. Son ^67 34 51 re^'. 



To 



=£ L, 39(4— L.jteo, I 
^ L. 1161— L.3600 



: L. >464— U3G00 



Lo.Lot. 


^ 


— 9.9S«5 


73S 


— O.10»O 


019 


-o.,64S 


7S4 



>,6 



«o' o« 



41. 4 



By theaboTCt/MO^miMuit appesn, that At MJIiial LtgMrittmi, for til Sixsgrfinali, under 60*, comt oat * negBiivt ', and lU lo^llia] 

Loprttbici for Seuj^funale xboie 60' come out «^»ri'vr, or with contrary Siini to one ina^er. So that if the logifticil Logarithm! for 
Qumtitiei under ec/ be conGdetedffjEnufkv (ii thef in confulercd in the LMiracil Tablet in pir(ra/J the logittical Logariiluni fdr Quntitiei 
ibuve 6c' mufibcconGdendaiifefdriw; and therefore we bare giicn their ariainecici] CWip/oniir, to maks lliem torrefpond with ilie logiAical 
LogariEhmi fDrQiiuititie*uni)R'6o'| onlj intaking them out, 70a mnftremeHiberto prefix the Index -{-9 or i to all logiftical Logarithau 
for Namben ibore 61^ j t)M JjkAki for all Mombengnder bo' being given in the roUowing Table^ vis. below 60', down to 6', thtlnJtx'a 
o; and below y down to I*, the/ni'fn areeither i, i. or 3, aieipreOed. So liiu ym bavt Ntibntg u dt iai tfi iti logiJUaU -Tatla likt ibt 
tttatiHTakloef Ltgtrilbmf iwtalihg eul litLepiriitmi,taiti JVunitn, mi fo^ag ibi tiumtv turefftKdiai ti any Ltiariihm. 

70 fiad tit hp/iical L^ariitm ef mjKawAtr af Dtgrat tadMiama, atl ixcSding 90*, tr if Miaiati aird Sittudi, itl eivof 90', tr af ny 
Humter am aenediag 5400 f * 

AT the Top, or Bottom af the 7aik find the Degnei or ttioaln, .and in the (aine Column againft the Minutu or Seconal, nluftlvelf, 
sntheSiilettf tbePagc, jrou will firtd the logiRical Logarithm, required. — la the fimtd Reru, aciofitbe Page, ^m the Top, find the Kam- 
bcrDeitleli than the Number given, ami in the fame Column, againft theOi^mw gieacet than thacNumber, to mike up the Number fonghr, 
on the Side of ihe Page, yea will iind the /^^in/Ltg-drit^ thrreoF, required. 

When twti of the- siven Tetmi ate greitet than 5400, take their Hahm, THrdi, Gf(. being In the fanrie Ratio. ~-r Bat if only one of the 
giTOnTwJW exceed 5400, ttia iti Half , Ikird, fiff. and multiply the 4th Term refuldng, by 1, 3, &c. toconcfpond with iheginn Kafia. 
If Hturtv intheTermaoT the Proportion, their logi Dial Logarilhma may be talieo out of ih^ Table ai 3f intra, tad the lagiftical,f4iga- 
hm to the Minutei of in Honr may be td^ia out a> for Seoondi. 

TheAg. L<ifari(faiuortworiiiallArct(b£gnutlya!their5/ii«OT7'infrjWiJmiybeuledintrieoitametrical Piopottioni, with the common Log. 
Sao, or lavmli, of two of the other Termt, being large Ata ; but then inltcad of the Log. Siaei or Taa[i*tt of thofe lirga Am you mul] 
take their antbmeiiiaj Complementa, and the temrary ; beciufe (pr^ly) the logiflical Logariihnu in «u- laiir are all Migalivi, ^jut ' 
all of one Kind are confidervd Affirmative} and fo in uiingtheni with a^rmrnv nrnsn Lefariitaa the Utter maft be reduced to f/tgaiiva, 

logiflical LogarithRumuftberedaced to jfffnmiivei, y^e noaitnoa Logiritbmi) by taking tbeir arithmetic^ Complernenti, 
when chey~an ufed with nama Lagariibmi, without taking tben"^itffictlcaK:DmplemenU, But thii Proportion may be as Ipcedily rclalved 
nunon Logarithn Jtaa to cvuy ScCMid of bullArei (fet^vingindiffenntly for Log. TangeBtiaf thule Aro) with the Li^ SiaeaorTu- 
of lam Arct. ^ 

^ -' E X A M P L I S. 







zed oy V- 



*»<f N A V I G A T D R. 



i6y 



LOGISTICAL LOGARITHMS. 




o ;. 


o 


-4- 


^ 


5 


4 


S 


6 


7 


8 


9 


.0 


II 


.2 


'S 


'4 




' " 


o 


110 


'l«o 


»4o 


300 


360 


410 


«71. 


540 


600 


660- 


7.0 


780 


B40 


' ".. 


o 




i.ttSi 






...76. 


..0792 


OODO 


82,9 


7781 


7,68 


6«o 


S14. 




^: '' 










..MkO 


1.1743 




998B 






«i3, 




716. 


l.», 


"17 


6,,, 












..a96» 


1.I7JS 


..07*1 


9976 




";ii 


8221 


7767 




»„I 




.,,.9 










i.4b6< 




1.1707 








»-■< 






714II 


6„. 


H., 






4 


1.5;.13 


1.7^01 


..46ig 


'■»9'5 




1.0734 


99 ;i 


,289 


«7„ 




77S3 


734' 


6,1S 




6300 


4 






I -7414 


'■4«4 




...6s4 










8.99 




733! 6960 








6 


i.7'!«S 




1.1S68 


1.0706 


91I» 


9269 


M,7 


8.9. 


77-iB 


7128 




660, 


6.89 


6 










Ki»4S 




1.06,2 








b.Sl 








»lo, 


I.I4 






irz 


■ .7MK 






1..6.9 


i.o<,7K 






U„ 


hJ75 


7714 




.„■ 


1.198 


«79 










1.27Slt 




.,.b6i 


9»91 


9M^ 




8.6, 






l„(, 


1„. 


t.74 






l.^.oi 




1.4424 


'■177S 




1.0649 








«'i9 






6930 


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7100 


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LOGISTICAL LOGARITHMS. 






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64 


^5, 


66 


67 


68 


69 


70 


71 


.71 


7) 


74 







DigHizcd by VjOOQ IC 



4J1 



tl* kOVAL ASTRONOMER 





LOGISTICAL LOGARITHMS. 






75 


76 


77 


78 


79 


80 


81 


81 


83 


'i 


«s 


86 


87 


88 


89 








4S« 


,S6o 


46.0 


^80 


474a 


4800 


♦S60 


49»«> 


4,8. ■ 


f.40 


!•" 


j.6. 


!■" 


,.1. 


;?♦<• 


' ' 




3 

4 

s 


90]i 

90 JO 


>»7J 

p! 




S86t 
8860 

11^ 


884 

SSI! 

asm 

Slor 


s;r. 


8697 

in 

SS'.I 


B6^4 
864J 
864» 
8641 

B640 
8S^ 


;»■ 
IT, 
SlSl 

8?8, 


8,H 


848I 
8487 
84I6 
848! 

I".* 
8484 


84,6 

843, 
8434 

84!! 
84!! 


l!87 
8!l6 
8^8, 
8,4 

VI' 

8,8! 


Sir. 

Slli 

8,14 
8311 


'S1I8 

8187 

8aS« 
8s86 
8i8j 

8rfj 

aai 
8181 

8181 

8aSo 


■ 
3 

4 




I 

9 


90*5 
»«3 


lit; 
IS 


p 

8907 


nil 


38oo 

l?,l 


f744 

f74J 
8741 


sts: 


S638 
8637 

B6]6 
86,, 


8586 
ilfl 

SiSi 


8,14 
8,!! 
8,,. 
8,3. 


848s 

ill, 
848. 
8479 


843. 

SSI 


8!l. 
Bjl. 
8,8. 
8179 
8!79 


8,1. 

a„. 

1„. 

sii; 


8 
9 






90M 

P 

^;5 


g4S9 


190, 
•90, 


SIS 

8847 


;7>! 
879. 


S74" 

8740 

S!ll 

8717 


888, 
8686 
«l8j 
8(84 
8884 


IS" 

86}i 
86,. 


8j8i 
8,8, 
P'- 

S5!l 


8,30 

I'M 
I'M 


8*7, 


«4.« 

84*, 

84.6 
84., 

8«»4 


1,78 
8,77 
8,76 
8,7, 
8!74 


ss 

8„6 
83., 
8,.i 

1 


B.79 
8»78 
|,78 


•3 

•4 




t6 
19 


901J 

901 s 

9014 

301] 
9oi> 


■ „I 
«9SS 




KM 

S844 

!1JJ 


8791 

8,8, 


8„« 
S7SS 

8714 
8711 


863, 

86S1 
868. 
86S0 


S630 
8619 

8617 
Bi.6 


S?^ 

SKI 
8,74 


S« 

8,H 

5S! 


8474 

B47. 
847. 


84.! 
84.3 
I4.. 

s:^ 


"371 
8373 


!.„ 
8.71 

8.,. 


19 




•1 

«4 


9011 
9010 

9007 


•ssi 

I,;. 

i,s. 


S196 

.195 


8lt4i 

8840 

»8i7 


I786 
178s 
•78j 

SI' 
878. 


87!. 
87!. 

s;:i 


S678 
86,7 
8677 
8676 

8671 


864 

se>4 

86>j 


«i7I 

S5i1 


S- 
I'M 

8,,1 


8470 

Sjll 

8,6, 


s;;i 

84.8 

s:;'. 


Sis 
816B 
8167 


83,0 

i;i 
si;j 


8.,. 
8.70 

s:.'i 

8163 


"3 




■ti 


JOOt 

9oOf 

9004 
jaoj 

900. 


.a 

I94J 


IS,: 
IS,. 


ii'' 


87B1 

i;si 


i;ti 


8674 
81,, 
16,. 
867. 
!6,o 


8ti» 
S6ao 
8619 
8618 
86<7 


8568 

8568 

8,6, 


ss:i 
pii 


8466 

8463 
846. 


14., 
:;; 


SIS! 


S316 

5i:i 
ii;i 


3.67 

8x66 
3165 
Bi6| 


3 

>9 




33 
34 


9001 
9O0» 


8«° 


!■>■ 
IES7 


i5n 

S8|o 
S3ig 


8777 

«776 

»7rs 
8774 
I771 


IVd 

87.9 


SSJI 

86i3 

IZ 


S0.7 
8610 
g6jj 
85.4 


S0 

8,6* 
1,6. 
gs6i 


s- 
p" 

8,., 


846. 

Slil 


i 

.4.8 


51?; 
B 


513 


8a6] 
816. 
8161 
8060 
8»6» 


3' 

3» 
33 
34 
35 




16 

15 

39 

l". 

41 

41 

44 

49 


fMl 


111! 
P 

?9J1 
'"• 

"9n 
i„. 

ie 


tBti 
888, 
8880 
8«„ 


mii7 

33,6 

mj 
ail 

BBao 
88,9 
Utt 
«I7 


»77» 

877. 
S771 


87.8 

s;:i 
87.4 
s;;i 

87,1 

8,09 

p 


866, 
86i| 
866, 
8661 
866. 


8611 

8610 
3b]o 
860, 


8,6. 
8,59 
8,S8 

8„6 


1,.. 

S13 

8,0. 
8(0) 


ss 

845J_ 
84,1 
84,. 
84,. 


84.5 


81,7 
l!,4 
8l„ 
81,4 

f!,! 
1„. 
83,1 

SIS 


8,6, 

13 

1:1 
83.4 
83., 
8,0. 

8,6, 

s:',i 


P 

s:ii 


3« 
IS 
39 
40 




ggse 


lis 

817, 

«7S 
SS71 
8870 


8768 
8767 
B76fi 

SSI 
S,1l 

»7fo 


866. 
8660 
86,9 
868 
86 J, 

ss 


36o8 

ss 

S£| 


8,56 
8,5, 
8SS4 

I"' 

8,5. 


8,03 

5g; 


«4., 
14.. 
8401 

St" 


s- 

fir 

a.,0 

S3 

8Mf 


4> 
4» 
41 
44 
45 




860J- 
8601 
S6ot 
8G01 
8600 


pi; 

p 

8», 


8,0. 

SI 

SSI 


8«i_ 

844, 
8444 

|44! 
844. 
144, 


SllS 
Si. 

8!5f 


513 

P 
834, 


t3 




S' 

S3 
S4 


III'. 
s;8 


8911 


8gti( 


ills 

8II0 


;i2 


8704 

8,., 


i 


I'il 

!S97 


8,„ 
8494 
B494 
849! 
849. 


8!94 
|!9! 
8,9. 
l!,. 
B39. 


Bus 

Si:; 
11:: 


s:?i 

8194 


S3 
lis 

8»44 


SI 

S' 
SI 
S4 
SS 








lis 


88t»" 
8I(T 

8m; 

8861 
SSfii 


S3 

IIS2 

»8o, 


879! 

!"* 

I7f. 


87.. 

si 

8S,7 




SSI 

8», 


■i-,V. 

8,4. 
8„. 
8,40 


84,1 

1 


841, 


Sit; 

IISS 

>i8, 


HI 

8!!. 


S191 

>>9i 


8*H 
?>4> 

8.4° 
gs]9 


S6 






7! 


^ 


77 


?8 


79 


80 


Bi 


Sz 


») 


»♦ 


»s 


86 


87 


8S 


■89 


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,, Google 



cid NAVIGATOR. 



.^n 



HERE FOLLOWS 



Seaman's Ready Computer: 

BEING AN 

IMPROVEMENT m Tabular NAVIGATION. 

Whereby any Perfm underftanding Additimy is qualified to keep a 

ship's Reckoning at SEA ; in Latittide^ Departurey 

and LONGITUDE: 

As by which eafy TABLE, the Sbifs Places at any Time, may be Jpeedily taken ou(, 
(likt the SUN's mean Place from jf^ronomical Tables :) 

And all pramcal ^tftions in NAVIGATION and Plane TRIGONOMETRY are readUy 
anfwercd, without Logarithm-£infj, TaHgents^ or other artificial Numbers : 

Of which fee S^ampUs further en. 



for deterinuiiiig 



By this fufEciently ntar Mctbtd ni travelling at Sea, a&Redhy Helps coataiacd in this Work, 
Ute Loi^itudes ftom Gretmvtcby £/^«<3Ei'm/ Navigation is exploded, aaufelefi. 

FOR, s> Mr. EMERSON jadicionfly obfcrves, at P. vi. Pre/ate to his NAVIGATION, (cnnUining the exafl 
Rxki tnd their Demm^Mimi oa the PTiaciflt* ot /fitriia/ Navigation) to which Our Navigatiom \a fafpUruxtal, 
■' Ifa/tuUieoMiJ/tR'SiiemeiitliMiifeaTai/eefttiendionilPiirti/rtmlteSphetoid. That itivtuUrefMirtaHtieParal'tl 
" »/ LatitM^ and Artbti of tbt MtriMtm It ii ailtrtd ace»r£mglf i ertatingan endlifi Otai »/ 7r«AlM /or aa Toi AJvati- 
" t«g*. That, if iix fnfi/er thai n Ship caa fietr true ta a Degree, er barilj It a Qputer Point tf the Cm^afi, urn 
" (a» vuafitre htr Diftamii failed by tbtijo%. It oaf /urb JOegrte c/ Exa&mSi, but that ibtre luiil aliva^i bt aetnfidtrabie 
'• fariatitM from tie fieaCc TrMtb, in Regard tt ibt Ship' i VliXc, fir vihich Rtafin Jbe ii tbligeJ, at often as foffibit, tt 
" correS her LatilnJe a*J Ltngitmde bj Obfervation. 7htrifire (be coneladei) it ivtuld he quite trifling It defceeiJ ti fuch 
■' tninote Digermcti eu ea» have m fenJihU EffeB in Praflice. 7hat, jinte fueb is the Differetue bttvaxt ipherical «m 
" [pheroidicil Navigatita, if <uit mufintedi vvidci frta tie Tmib, we bad belter do it in afHam emdtafy Wof ibaa in 
" Hnd emd digiadt me" 

Mr. EMERSON then i>T0ceeds to lay down Ini Rulei of fpherical Navigation (agreeing with eari) as (hort and 
plain a> poffible ; " DifiKtmabering the Seaman of evety Thing Itng and tedieui, andgi-ving bim at naub Saliifaaion 
' naill ever find, tr earn itnfi} fir." 

7* •which may be added. 1'hat every Perfon'i Experience (having travelled by Sea) will inform him of the Tnitli 
of the foregoing AITertions. And a Perfon we know is perfe^ly convinced thereof, in three Voyages he mule to 
the f^ijl Indies, and one to Cretnland. That the Errwi by Lie fray, and millaken Courfe, and Dlftaoce run by the 
Log, irom their various Ciafica (of (find. Sails fei, high Seat, Curreali, i^e.J are with DoiUit and Di^ulty 
correfled. fint a fphtrtidieal Navigator, having never been a Voyage, if he goes one to keep a Ship's Reckoning, 
will find himfelf involved in greater Erron than tbofe he pretcndi to con-eft ; fince there it always much more 
Difference in Mens Judgmenti abont fettling the Let'ffeefi "Cnrrenii, Ctur/e, and Dijlance, than then u betwixt 
(fherital and j^i^«i^'r<*/ Navigation. 

OUR fi>«rt and eafy Method of etmpuiing a Sbip't Way through the Ocean, it an Improvement from a Table we have 
lately fcen at the End of Sberwint Mathematical Tailei, revifed by Gardiner j but did not fee till we contrived our 
fun Table, Computer N«. I. ftr thai farpufe (conltruAed from natural Sinei) in a more eeneral Way. at lollowa. 
Campuier, N«. I. II. are quite a NEW INVENTION. 



,y Google 



ni ROYAL ASTRONOMER 

r . 




yGoo^te 



09d navigator; 



875 



U S E of the S E A M A N's 



LEADY COMPUTER. 



lOOO 2000 



8000 



9000 [ dentQif. «/■£«/. and Drparl/iri, arB^ 
900 \and PtTftnd. ageitift the OairJiorA., e» 
90 I eni Side aftkt fabli, la hi taktm in mial 
9J •uiUlt Numheri, Tbt/e t» thi Rlgit ef 
the/t ieiHg Dtcimah, 

THEREFORE, tKe 1>ifi;r«aoe oF UlUmit aid Dtparhtri, (or Safe and Petpendicular) anfwerable to tke givefl 
DtftMtee filled for Hypot^entfe of a right angled Triangle) on a given Courfe, or Angle, muA be uken out b^ 
P«ta, »ad added ttgithtr 1 taking out lirtl for the higbeft Number of Tni, then for nexcTeng lefs, and fo down to 
Unilii accoKling to the Number* of Figure) mtheDifiaace/ai/td, (or Hypothenufe of a Triangle) to be ta^en out for. 
PROPOSITION I. T« find thi Diffirnti »f lalitud, and Dtfarturt from the Cantfi and Difiaact livtn t Or te fiird 
ibe Safe md Ptrptudicalar frtm an etult Aigti and the Ujptlhenufi af a Triaaglt being gives f 

EXAMPLE I. Rrfulrtd/ie Dtfftrmu rf Lalitadi Olid Departure, vtbtn a Sf>i fiat failed 8$ Mibit m a S.W, 



iyS..Ca»feiP«Mlif^,rfy 

Di^ 

Agaiait 5J Pokti under 8 



. Tie-Pifianeti fmHtJ, *r Hfptthtmi/et, ml iheftf andSttlim tf tbtf^b, mig figiiijy am if thrNamberrith'm. 
MO loooo 30000 40000 50000 60000 70000 80000 ^')0<X}'\ Under tr «ifui'wbi^hJlaiidthecBrraAait\ 
3000 4000 5000 6000 7000 " ' "■' *' 

300 400 500 600 700 

JO 40 .50 60 7b 

34567 



Mile* 85 



ieiwf; j^ Paiali la the Weft<mard T 



Depart. W. 
S0.7S1 



65.709 



53.923 Anfwer. 



„} 



But two DednuU to the Right of any wholf 
Number will be fufficient in taking out i excefSt 
whc^e Accorac}' 11 re^uiied, ia Trigonoiiieti;. 



EXAMPLE n. A Ship baviwgfajled i 16 Mih, t. 
a Caurfe af 41 l>tgTtei from the Norll>, eafitr/j, regui 
red her Difireatetf Latitude and Defarluref 



A TABLE fiiewing the A»glti that every Paint of the Cat 
jnal^n with the Meridian : For taming l&nmbi, 01 
Conrfc, lleerqd by the $bip, into Dcgreet, and the ai- 



Agaioft 41' Duder 1 



Dif. Lat.N. 
75-+7 



Dep. E. . 
65.61 
6.56 

3-9+ 



87.54 ) 76.11 
Awwer., 



EXAMPLE III. Rtjniredthr Safe and PerfemSca- 
lar af a right angltd Triangle, having an acute Angle 
ejMo/laiy, JSditiHjpalbenufee^uait* 15+3 ? 



Againft >]■ onder 10^ 



rypoth. 


Safe. 


Perp. ' 


I0«O 


9*0.5 


390.70 


500 


460,25 


'95-37 


40 


36,820 


IS. 6*9 


3 


2,76" 


1.172 


IS43 


1420,332 


602.871 



EXAMPLE IV. JUauired ibe Safe and Pei-f(n£- 
cular fif o rigbl aagltd flmn Triangie, homing an aeiiU 
Angle equal 10 66', aad ili Hyfalhtnuft ejtial U 77 i 



Di«. 
AgaBift,66. under 70 

7 


63.948 
6.395 


Pop. 
aa.47« 
..8,7 


Anfwer 77 


70-343 


31.3.9 



North 



Paiatt, 



S.byX 



-*»• 



lUr.Wift 



ir. by K 



D.M. i 



' 48 45' 
5 97 1' 
B a6 i; 



H 3 « 
16 52 30 
19 41 i; 
Ig 30 o 



21 18 4S 
18 7 30 
30 s6 IS 
33 4; 



j6 33 45 
39 " 30 
42 11 IS 



47 48 45 
SO 37 30 
S3 26 IS 
SP IS q 



,19 3 4S 
5i,S2 3" 
64 41 ij 
67 30 o 



70 18 45 
73 7 i" 

75. S« 15 

7* 4S °. 



■■ 33 45 
84 21 30 
87 II .5 
90 o o- 



SMi 



S.ir.byS. 



Sni.E4i/) 



.bjW. 



Sou.W^ 



!.ir.iy,ir. 



ir.byS. 



u a n. 

,, Google 



tjS 



Thi ROYAt ASTRONOMER 



USE of tk< SEAHAN'i READY COHPUTI 



fevnal Ctur/a and liifimuifiultd;, < 
ip £^ M tflut, Br Cewtl/ r 



Courfei. 


o± 


iJuF.t;.tadr- 


Utpmu,. 


iHJii. 


S^k 


»«rf. 


ii^. 


»y. 


N. 8s»W. 
S.S. W.^W. 
S, 4o»W. 
S. STe. } E. 
S.45.E. 
N.l. } E. 


7" 
■i 


06.101 
S4-SS7 


97.096 


37H' 
.11.697 
66.479 


19.011 
SJ.994 




60.658 


16..8S1 
6o.6i8 


"SV7 
1+2.750 


i«1.7SO 


Dif. L.t. 


102.19] 
Mik.. 


71.667 
Man. 


Dcpm. 



PROPOSmON II. T§ find ihi Difertnct tf Latitudt and Dtpm-ttri fm 
WaxiriMShi^tfravtrfti n find ibi Milti ina'Dtptttf l^i-^, artaJuaii 

MAKE a Tramrfi '7alh, ai on the light 
HsDd, and plice tbercjo each Contfe and Dif- 
tance. Then find the DUfcrence of Latitude 
and Departore to elch CouTfe, by the foregoing 
Prtptfitha, placing them in their proper Co- 

NOW, the Eiffereoce of the S^mi of the 
Nertlang and Snithiog, wiU be the whole Mfe- 
rence of Latitude ; aud the Diffieresce of the 
Sums of Eejliiig and H^tfiiig, will be the whole 
Departure. 

EXAMPLE. 7ti tUffiTmui if LrHmA mJ 
Dtparl^t tf a Sbif JMag feiMrsl Oaajt) md 
D'fiantti, luill ht faiptd M tM ibt M§»im*g7abU, 
iX tbt farmir Prtpsfititw. 

■ The above PROPOSITION find) the Milet in a D^ee of LaiitBde, and ii extenlinly ufcful in rurvcyiqg 
Bftatts, CoiaUlti, or large Trtiat of Land. Mr. NtrwotnJ, in ihs Year 163^, made Ufe of it u dcterauDing the 
Difference of Latitude (according to the Method in the foregoing Tiayerfe'Table} between the Parallelt of Z^m/of 
and Tark, of given Laticudei, by coleftial Obfervation ; and <o determineg, -atry mar the Tmtb, the Miles in a De- 
gree of Latitude. (Stt bti SianoM'i PraSice, fi»ei rifrimuJ/trVf. Mount and T. Page, «» Tower-HilL) For, he 
meifuring the fererat Dillancei between all the Turnings of the Road, from Undn to riri, ai the Raad led him, at 
the fame Time he abferved the fcTetal Bearingi betwixt thofe Turnings, by his Cirrum/hwftr, he then determined, 
1^ Trigonometry, the feweral Diftrnrts of Latitude and Departure") (ivbicb ii deni at Sight bj sur Ea^ Cempiutr) 
and thence he determined the Diftance, or Miles, Difference of Latitude, between the Parallels of Unden and 7>i, 
and alfo Diftance of ihofc Meridiana. And confeqoently the Milei in a Degree of Lnitude, by Proportion of the 
Milci in the Degrees, Difierence of Latitude, by ObferTadan. If which Biariiigi and Diftancii were again taken 
acd meafured, more correAIy, eccartUi^ tt tht Ufi imfn^itd Mttbtdt tf Survepng, there is no Donbt, but that the 
Difia»ti between the ParaJleU of Lm^ and 2Vi (on fo targe an Arc of the Meridian] might ba determined with 
as much jlcturaij, u that Difimci (mcafnred by the Fmtb) wai dctcrinitted between the twa Parallels near the 
Polar Grclt. 

In furveying Connties (or even Efiates} b/ the Bearingi and Diftancei of their Circnits, the Ufe of the Hitdk 
(not always heeping Parallel with itfelf ) is not to be tra£dtOi but the feveral Bearings and fiillanccs mu(t be taken 
and meafuied by the tinj3*r Mrtiidi known. And, in //s/aV^ the Survey of a County, hy Crcuit StatitM Lr'tn, 
(though confilling of never fo many] theymay be rcdnced toa/iMtf A'luijfr, for the firll p^ or Cloftug. Andthc 
like Method fbould be parfued in plotting the-iotermacUate Circuit Stations betwixt each two plotted Stadoni in At 
firft Plan, and fo on ; whereby every Circoit Station will be more correAly placed than by any other Method ; and 
the rt/nltitig Out iim Or Pirn, will be a* near the Truth ai pollible. 

At every Bearing taken, each Diftancc between the- fcveral Circuit- Stationi, may be meafured in Cbm'Ms, of 1 00 
Feet, or by any ouer Mcwfhre, (tc bi infirttd in a SiativM *r Trover fi-TaiU^ ai aiivij corrcfpondent to wUch> the 
feveral Differences of Latitadi and Dtparturt, or Nonhings and Sonthinn, aod Eallings and Weftings, will be found 

the fame Meafure, uken outof xiwnadfCamfmltr, lor plotting each Station, and the whole Trad of Land. 



REMARK. Til Miri£n*I Difsmt, md Dtfwtmn (af Zaftinc u>d Wiftini} ortmaaMh Hpnu. I* faSurit 
D^rluri h lU patir, i.raufi b/ iht ww and martr j^n^tb af rfa MaiWIni trifi'd r0r Ij lit fam Ctarft, fir utTi 






tMMnEi tht Pole, lie 
... - . , , . -, T-r. «« I. 

tnot'ii ii< Editor iht DrfOritn I'l/r/i f in dw moMHiul Dinnct j bcomle tM Umduiu cnirid over bj the linie Coarle, fcraiM 
groif wider, orrtcFden.DrenndmcrefroaiuMUothWi TUtiifaranhd^ if » aiUit <isiatitj (ifiirimtlj ik mt CmrfiJ iovmtii Mtri^ 
dhmttD^ttti af rvD Plata, fir ttt FtralU J^trui fitm atd fir lit tmvtdia. Tit Lti^ttit it imuritUt, 6itwaa r^ ivt PlMta, t 
Ftrallt/i, fiiiJ Jigirini film rti MoiJitMl DitMiKt amJ Dfartmn. Til MtriUmU DiUate ii dW^irm h iigirm PtraiUli ; tmlthtDtmnt 

s.A<i.>*«,/l'«finBleCoEirft, *«««-««;«■«&& J Jwrn/ia "' - ' - ■ -" . .~. -■ 

Hoiiiatl DiJImtt, m vikict iti Sum if tin fivtrtlDg^anrm > 
Diy'i Retk oning) en itt pliin Chut. 

V Sfi 



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«W NAVIGATOR. 



USE of the ^.E A M A N't C O M P U T B I 



«77 



PROPOSITION III. 7» fixf th CtKrfi and Difianii, 
frurn tb* Diftrmi gf LaiitaJe md Dtfartnrt givtJt? 



RULE I. Find the given Difftr, 
Departure together, Jnfome of the Ctim 



of Latitade and 
of the Sia- 
READV computer Number I, oi find the 
tft Numinri to them, and even therewith, on the Side 
of the Page, ia found the Churji ; and the Difianet it 
foDiid at »ie Top or Bottom of the Page, in the Ctbam 
of given haiituJitaMdDtfarturt, 

EXAMPLE, To find tbt Cnrfi nd DifioMi aHjwirmg 
ta ;oo Mibt Diffmmtt if LtUilrndt StUlbtrlj, amd 388 
Milti DtfartKft Wtftrrlf t 

In the Colnmo Soooo yoB will find 69970 Milei Dlf- 
ference of Latitude, and 3&7.85 Milc» Departure, the 
nearcA NumberB to thofe given, even with which tahvler 
Nnmben you find itis Cmaf* 5. la' lutfitrij i and, at the 
Top of (he Column of the given Latitude and Deparcnre, 
yon find 8do (taluDg an equaLNumber of Figures) the 
Z)^d»r( coirerpondesi, r-tpunJ. 

RULE IL If the given Difference of Latihu/t and 
DepariKTi cannot be found together or in near Numberi, 
you moll divide the /t/i by the ^mt/t Number [Difference 
of Latitude by Departare, or Departure by Difference 
of Latitude, according aa which happen* to bethe great- 
and afcertaining t/rai Fipa-ei in the Qnottent, find 
__ wor^ Mupi^ Bnfwciins thereto, in the Column un- 
der loooo, of COMPUTER Number II. fiiltnaitg, 
(which, in ail Cafct, you will readily find, without Stop, 
or Difficulty, by calling the Eye along the Column] and 
even with the laid :^W/nrr- Figures ilandi the Camrfi, on 
the Side ; and the DiAance ii found by talcing it ok)t 
of the laid Riadj Camftiitr Number II, aufwcrable to the 
given Difference of Latitude, 

EXAMPLE. In the fotmcr ImBmet, 70o)3SS(,554 
which ^tit is immediately found againft 29", the Coarle 
Sooth- weflerly, as befoK. And againft which Conrfe, 
iUKlei70o, Difference of Latitude, ( in /it Ce/anaj'Xioo) 
will be found 800,45 or 800 Miles for the DifitoKt, 
required. 

Bat. UNIVERSALLY. XtjMirtd fh Ctm-fi amd 
HJUMct wtfowiAlt ta 97 1 Milti, Dtffrrnu bJ Latittidi, 
SMii awd 1117 Mi&j Dtfarha-t, tafiatjt 

Il7)o7i,0oo(,869 which ^«/r ii immediately IboDd 

1^56 againft 49', Column loooo, in the 

^—— StMKMti C»mf»ttr, Number H. fol- 

7740. lowing i which ii the required Osurft, 

6703 Sooth-eafterly. 

10380 
10053 



t^ WHEN (of the Difference of Latitude and De 
parture) tbt DifarUn i, tit greater, t^ Cuafi it mhovt 
4 J" i iai lohtn thi Diffirhti tf tatitud* it tb* greMcr, tht 
Cuaftii Ufi tbaa^^", 

NOW, by the Seaman's ^aij Cm^^ur, Nonber IT. 
following, uways take oat for the greater. 



Conrfe S. 
Againft 49' 



Depart. B. 
Uodenooo 



DiftsRce. 



13,150 



Hence, aUb the 
twoLegsofaplaoe 
right . angled Tri. 
_^angle being given, 
'the acute Angles 
and HyptKhcnufe 
may be found in 
the fame Manner. 



N. B. Vhtn fit greater Side (either Latitude or Depar- 
ture) and M jfasli ii ^ws (or the Conrfe) the kfi Sidt 
[Departure or Latitude) and aJ/i tie Jfyfetbeaa/i [or Oit- 
tance run) tnaj hi feuad b-/ Computer, Number II, B^t 
lbi\t{i AiAt aadaa A*gU betng givm, tie REST canoft b* 
ffundbut bj Computer, Number III. foUdwing, 

PROPOSITION IV. Bavlff tb* greater if litbrr 
Diftrewci tf Latitude tr Dtfartwi, tln4 aija tb* Courfe 
giwn, it fad tbt \eit ^ either, if Difftriact »f Latitiide » 
Defartur*, nd alfa Di^aace Jailid. 

This FrafaJUim is univcrlally anfwered as in the fore- 
going £';rAH^, by the £ra«a4'j CM^B/n-, Number IL 

EXAMPLE II. Caar/e uaAr 4J> [via. N. jg* wefl«r- 
ly) and Di^treatt tf Ltaititdi 349 Afiuln, u fi»d th* Di 
partitre and Diftanft failtdf 



Conrfe. 
Aguoft 36^ 



Dif. Lat. N, 
Under 300 



Depart. W. 

117.96 

39.062 

6.539 



Diftance. 

370-8a 
49-4+3 
ii.i»5 



MiUt 349 853.561 431,388 
Anfwcr. 

Hence, the teft Side and Hypothenafe, of any right, 
angled plane Triangle, are found in the fame Manner, 
from having an acute Angle, and a greater Side, or iteg 
given. 

PRCVOStTION V. Saviag tie le/i ,f ritUr tht 
Differ*wet if Latitade tr Dtparture, and ai/t the Caarft pvm 
la fiad tb* grtaitr tf either tht Digertatt »f Latitadi tr De- 
fartart, and alfa tbt Dijiaact failid f 

This Frgpefitin it folved in all RefpeOs exadly likethe 
former, but by a different Computer, Number III. fbl< 
lowing, by taking out the greater LEG and Diftance to the 
le& LEG ud the given Courfe, inHead of kfg LEG and 
IMftance to the greater LEG, and given Courft^ by 
Cna^tr, Number II. 



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rh ROyAI, A-STUONOMER 



The Seaman sKG&^yCOM.?VTh,R. N^. il. A Kcw Improvement 




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CCnKTRVCTIOH. I, s, Ji 4> 5' ^' 7> 8> 9 Timet the aitunl Tti^ait ind £(Mi>r« to K*diui IQOOO. 



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md N A V I G A "T » R^ 



■279 



The &aM.» »'8 Ready COMPUTER. N°.U1, A New ImproveiSeMT 




C0N6TRUCTI0K. 



nUnnl CotuBcnti ud Cahtuta, to M^ditu loooo* 



D,g .od5'©3t.gle 



Ttt ROY, AL ASTRONOMER 



PROPOSITION 

Digitized b 



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M'f^&ft&A'r<>-'R\' 



. U S E «f ,^the,,S^,E A MA ]N'., QOIA P JJ T E R, 



PROPOSITION Vil. ■ TfjhJthCtm/tanJDifenntt 
^ l^ituJf, Jhtt tit JX/Umi Md'DtflirtJtt^ivh t 

Examplt. The Diftancs being 84 MilM, and fhc De- 
panure $4 Milet, to find the Ccnufe a&d D)fil±retice 
of Latitnde i 

Firfl for iht Onrft. RULE. Divide the lefi by the 
gtuttr NDmbcr, and fecit thb Decimil C^lMStleiit (of «'- 
boot 3 FigofO) In Ae Ctilatnti of-IM^atmro Mitt 
loecx) of the Cooipaier Number I, eren with which 6b 
the Side fltmd* the Conrfe. 

^hui, »4)S4(,643 nearly; Which ^j/f''ii/ou!li! In thi 
Aid ColdblD igkiofl 400, the Ctturfe reqtiif^. 

Navj, with the giren Conrfe, and Diftance, ai above, 
£dcI the DiffercDce of I^todc by the fame Compote 
Nomber I. 



Conrfe. 
AgaioA 40' 



Dif. Lat. 

61.384 

3.664 



Mile$ S4 I 64.348 Dif.Lmt. Tcqnired 

PROPOSITION VIII. ft^th* Jhfirntt f £•«. 
gitrndi p»M iht mitlMi taI'MAimd t>tf&rlw bm^ggivtmf 

ty 7ht CtmpUnunl af mtddU LatltaJt mijfi ir Imin -mt 
tht Cekr/t, eailbt Sijlwici toij-vurahii H lb* givtm Dipar- 
tmrt tn that CamjH v^ittbi Digtrmrt ^Itigiiiidt, 

RULE. . With the ghen Departate, it tbe Trip Or 
Bottom of the Coin|>iiter, (Number XL if the Comple- 
ment of middle Latitude be lefi chaa 4c*, but Number 
III. If pitttt than 4c") f^e oat the Diftinte, a^9 
the Cdurfe (equal to the Compleolciit ef itiiddle Lati- 
tude) Oil the Side theteof ; aaiyoa will have chfa IfiSe. 
rence of Longitude, revoked. 

EXAMPLE I. Our Sfte iei»£ Ttfitrim at N^a /» 
LtuMdi ti" 5' N, ana this Da; m J^mn In Lelitndt 

lbtrt»f 13.*} mr DtpattUte 71 JHi&j Wifiirlj, ri^ridair 
Dtff'tmcw ef LmpiuJi f 

By Computer Number If. the Complement of middle 

Latitude bdngabove 45°, v'm. 53'. 

Courft. Depart. Dift. 

Agaloft jz* Under 70W. 88.831 

or 38 I 1.269 



Milci 71 



90.100 Diff. Long. rcq. 



EXAMPLE 11. Our Ship bting Ytfitrdat ml Ntoo in 
LatitnA 46° 9' N. okJ ihii Dig at Nmh nt 470 Jl' N. 
(tie nadJU Lalititdt heimg 47°, and Cempltaunl tbtnt/'^i*] 
Dw Dtparthrt laftirlf, 1 1 2 MiUt, rtf^rU tbi DifirtMi 
tf LanfilKiii ? , . 

By Computer Nnmber III. the Complement of middle 
Latitude Nfiag i^er f;S ^ne. 43*. 



Conrie. 
Agaiaft 43* 
.".47 



lift. 

16,263 
2,93 a 



16$, 82; Dif. Long. req. |i 



//. B. If the CompTement of middle Latitude it cot 
in wbi^ DegAci', but In begries ind <^d Minutti, yon 
moll find tbfe Longitdde fi>r the Complement of middle 
Latitnde a Decree left, and greater than die Copplement 
given I adding a pro^Ationdl Par^ of 3ie DifcrcDce 
of thofe Longitadei for the odd Minntei to the Ixin^i 
lude for the lefi Degree or Complement of middle Lati 
tiide, >nd yot wHF hove the Di^ere'nce of Longitude, 
r^^iiiled. But the Long, to tbe tuartji whole Dee. oTMid. 
L«.wiIlbefil«dHit. 

PROPOJfmON VIIL ftfatJibt continual ttio// 
bttnct'eit tv.v Flacti, dnJ ittlr Dijlaiitt 6a thit Coar{e,^vm 
tie iMitiuItt end I.9KgitaJtt ef tie/* PUeei heing giveu f 

'k6L£. find (l>yCim^/«rNnmb«r I.) the 
2'nfwenng a Diftancc, equal to the Minute* Di 
o^' La^tfOli glfcB I iheA by the Differtnce of Latitude 
giv«n, and tv DcpA^we. jufl now foutad, find the Cdvfi 
■d Difi^ti by PROPOSITION IIL 

SXAMPLB. The Ihe^J lie* Id LadtiM'e 49° eo' N. 

and 4« u'' W. LoBgiiude fiOm GrmtiUh % Cape Finder 

ih die Drtitode of^43<' lo* ahd 9<> 4«' W, Longitnde, 

ftm GtiitMutdii Required the coalfattt Chutfe, and 

-DiftmKc .theieott^ beitvcen the Lt*ri and C^ Fi- 

nifitrt 

Hmee; tSfc inf. of Latitnde ii 6* 40' or 406 Mmdtei. 

Dtf. of Longttdde 5 6 W, of 300 Mi- 

[ntrtds. 

Middle Latitnde 46* 30* 

Com'plem'ent 43 30 

By Covporer Nunttfer I. 

Comfe.| Dia.| Depart. 



Againft43'> lUodcr 300I 204.60 
AgaiDS44 | 300] 108.40 



Dif. 3.80 
Half 1.9 4. 



Coorie 43° 30' Depar 
Depi 206.J 



206.5 Milea. 



-=,50161 Which ^gwtt. In Com. 
Dif.Lat, 400 
puter II. itandi, in Colomn 10000, tgaiafi sy" CoorCi 
S.wefterly. . . ^ 

By Computer, Number III. 

Cowrie. Dvp. W. Dift. I Dif. Lat. 
Againftzye Under aco 440.54 I 392.52 
3.21 I 11.77 



Milei Z06 4;3.75 |"404.Z9 

* Here it ii MrvaUt that the. DifFerence of Latitode 
cdnffis out Agr^eii^ (fo fiir aitheNearneft of the Conrfe 
H taken ) Wm tUt gtvAi Difference of LxtittidC ; a Pre*/ 
tf the TrtUb §/ the fare^in^ OftratitM. 

And thu* all Caiiu relating to condaAing a Ship orcf 
the Ocean are readily anfwered by the Stammifi Ctrnptiir 
only : being an entire New, eafy, and praAical METHOD 
of NAVIGATION . 

WITH 



The R O Y A L A 3 "y R ON Q M E R 



anfimt Ceur/t that a Ship ftcen betwixt any two Place* on t^cTConvex Surface, beiog on a /fimi lim, or 
To, (as before obferred} ii ia a »>/rar;Dire£Uon failing back, to what it wu in fdlingTorward betwixt thofe 



WITH Regard to the foregoing ( Vllltb.) fnptjbiim, the cwJiiM m continoetl. Coorfe ftc.ered Jw ^.SUp Jbctnixt 
two Placea, mtfll be cjircfilly aifimgu/kid from the iSrtS Staring of one of thofe Places from the Oiner, 

For any Courfe, on tlie-Sar&ce of a Globe, nuking die fame conAut An^e with the feyerat MciUiaiH, ttraOed' 
over bv the Ship's Way, i> it^'rV Tratk (of die Logaridimic Kind] which being condnoed on will terminate ia that 
PolcoftkeEaith towaidi which ^e Ship'iCourreiidireOed: £«fi|;^/ when the two Placei lie nnder the fame Mrii^, 
dircaiy Nonb and South, oi on the Efimuaial direaiy fiaft and Welt of each ■ other, on the Arch of a great 
Circle. 

TYit Jlria Biaringcif any Place from another (genially ^ifunderftood fb; the copdniied or eooftant Conrfe all the 
7'ay betwixt tbofePlacei]ii the ^& ;/" /^'lon op the Arch of a. great Circle, or nearly fadi, that one Place, on 
the Convex Surface of the Globe, direflly bear; fto^ the icb^r. , , . 

The 
nearly 
Placet. 

T\iK Jir*a Staring tm the Arch of a great Circle marks the KMr^Di^du/bctwlxtkny two Placet, on^ globular 
Convexity ; but this Beiriog is continually Viriible all the Way, 

The condnnally TkHsble Angles in faitlne badi arenotcontrary tothoft in failing'fbrward, betwixt AofePlacet. 
at it eafily fliewn by the Rntet of Sfbtritailrignvnittrj. Thii has been propofed at a Partuhxt by fome, though an 
obvious Tmih. 

THEREFORE thii great Cirt-Zr 5«t£a;. in h«epng fa many different CoDrfet, itmuiS bekeptin failingoverthe 
ntarifi l^iJliBKi betwixt any two Placet on the' ConTcxicy, is hardly pnAicable, (efpecially when thofe Placet lie tery 
remote from each other) bccaufe there is not only the Difficulty toovercome, iHCOmpnt»K all the Variety of Coorfn 
DcceiTaiy to be ftecred, bat the Difficulty of pocting tbem in Prafiice againft all Impediments or Acddentt what^ 
foever, of Winds and Weather, that may confpire to prevent '' 

^QTaniliiptUaiSmUng, by the Arch of an Ellipfison theEllipfoid, or flatted Globe nextthe Poles, be better pnt 
in Practice, for failing the kmt^ Z)^«x» betwixt any two Placet, .on. Accoont of the like ObftuJet, tiiatmay prevent 
ihatKindof Sailing t^iogfofnn^f«»>/r~ ""-'^ 

Therefore praCUcal or jpiral SaiMmg, or that which has loiig beeii intJfe, and lately immved. accordingto fome 
conftant Couife and Diftance run on that Courfe, or other Things gnjtn for finding the Rijmjita, at near the Tmth as 
poffible, is here lud down and exemplified, in all ibe Variety of Caftft that can happen, for the Pnrpofe of the 
_ Praaital Navigattr. 



Afier we haveconfidered, from 



R oor own Experience, (in lereral Voy^s at Sea] the many Impediments to pn 
PraAice, witlf all the Advantages to Cfeograplnr, from the late l^ifcoverics i 



tit trot Tbnrj cf NavigA. , , ^-. ^._^.^, 

of the tnu Ftgart and Diinttrfitnt of the Earth at a SfiertiJ, (by the Meafure of^ a Degree of the Earth's Meridian 

' I Ptra and LapUmJ) we would no Ways depreciate thofe Exftrimtnti, at lately pnblilhed by Mr. Mariia, 

1 hit Ftit Work. (Iniitled NEW PRINCIPLES of GEOGRAPHY and NAVIGATION) fo far as they have 

riaJVft and Advantage. 

And as that AUTHOR fays with Regard to the fhtry itfil/, " The beft Way of fetting Ta^bndmi Bmr 

ia a proper Light, is to compare and confront them with 7rj»r^," (the Truth of the A««r«;i/4/7'i«H7 being admitted, 

however falfe the SfieroiJvten) To in Regard to putting fach 7ittry iutt Fraaiet with its fuftrlor M-vantagti to Mtr- 

(otir't aqd Other Sailing, heretofore in Ule, will belt appear by comparing ExoKfUs, computed according to fphe- 

roidal and other Methods of Navigatitn. 

ty The Errar arifing from the Thjhmti [meaforcd by the t«g) and Gurft ((leered by the Camfafi) "being fo doubt' 
fully afcertuned, will be always of far greater Concern to the ^rioh of a Ship's Reckoning than the DifftTtnct be. 
tveta ffhtricai 9.11A J^btnitlai Navigation. —Till which C«vr/^ and J>>/mw can be murecorreftly afccrlained, the 
fmaller CorreOiOn in TAmt^ will have (as we apprehend] but a very fmall Ufein the Niamrfi ef PraBici. And all the 
Correftion that can be expeded of Advantage muft cbiiflj arife from a rtnta ObfirvattBH of the Sun, or other ctelefiial 
Bodies, for afcertaining the true Laiitmlt and LmgitnJt of the Ship. 

See all Vlt.M^tiJi ExamfUs^ SpbtnUal Sating fiUtviin, anfiatnihy t» Seanan't Computer, (wiAout ScaU, 
Compallet, Chai^ orCanon) atUttw^artd^anth tht AH/vitrt^}A<SKaiiat'tSaiHng. 



,, Google 



W N X V f G A'Vo'r. 



»Si- 



OUR NEW ME^}iO&-ai-CmfmamH Troft^^/iScale^ T^mjpaflesi 
Chart, or Cmi<mi) exempKfied! &I ^njwersl tb.i tfie Five CXSES 
of SAILING^ as pVopoicd: hyMr.'M:(i'S:flN m;lus New 
Principles of Navigation, according to failing, by the Spheroid; 
confronted and compared with the Answers to thofe Cases, accord- 
ing to Mbrcator-Saiung, by. .the SPHERE. With REMARKS 
and INFERENCES drawn on thefe different ME TH O D 8 
of SAILING, 

'•C 

Examtlt. A Ship faili.f^m^a IV)i;C'ii|Ltdtade 38°. v)d ju^wi it iDOthcr Port in Ladtnde 5', ind finds hci 
Dt^irnci of longitude 'to be 43'( re^oired from thence her Cmir/i and Diflima f^lsd ? 



AS?. Ttjiid^ Cmufia^pifyKtruBtfrm th* Dijirtatt*/ tnUiSmdt. aaitm^taJt, ffvmf 



Latitude. 
Under 38' 



Dif. 33" *'5+ 
Es 1980' Mer.Dif.L; 



Sfitriiai. 
Mer. Putt. 

1463 



Lat. Mer.Dif.Lat 



By Cot^uitr N*. 

Now, again&50<| I 1000 I ISSS>7* 

900 I 1+00,15 

t 80 >f4>4^ 



Bv JUitrtJi/fr , . 1980 1 .30^0^33 



Dif. Longitude 430 = i58iy 



[whercu k Cmdl, Error ia the Conrfe will canle 1 rally gfMtei 



■ E* IHK in Miftg '^'> liif. Lat 
; a rally groater Diff. in ute DiJlaKii 



nrji. 



3580 



>8.349>agaiDftwhicli, OBdarCoL looooCompQterN'.II.f 

ftuds {0\8' the:<iMD^; (the Dif. LoBgitnde being raccording to >9J«r»raU Sailing. 
' more tWtb|e Dif. Lat|tBde.) "f J 

Or, ■ '' . "'° a ,8401 . . Agaiati whic^ under Col. 10000 fimc Camfii- >accoiding to Mirrai»r-5viivg, 
*5*° r*r, ftand»4^ 58', or nearly so'Cwoyi.. i ■ 



3168 



•f : 



t^ fbi) CASE unvvtrtJuttJtaMtft/fieiM Sailing, tht Cnrfi md Ti^mmt tf laHtuA, pvtm tt fad tbi Difim 

"»•' ■ \ -" 

tat 
Byr«Wf P. J9+. 138? ■ 

s 



Length of Ak*. , 
»*&J.JS 

.2971.76.?.. : 1 



33' 



ipbS'.cp troe Dif. Lat. by the I 



A£niBft5€> 



According to Mr, Muriln 



REMARK. &infi no Shif tm ftt 
I. 11. UI. for each Degree (^ Gnrfti 



Navintion, p. ».. The Ourfi being 50' 8' . 



1000 

900 



1969 
1968,6 



. htr Onrfii 



j - ttf. 
therePiire OOR 



'SSS70 
i+oo.ijl 
.93>34( 
■ M^OoJ ■ 



3<*^3.»» 

307^" 

'j79.' or about 



:6mputbrs 



r exaft for the fraaitai Purfafi of' Navigation, according to 



Cttrji, and Dilli&cc nuir .tl^at oanpoc: Ue kepi or determined to ExaSmfi, or hardly CO a'iVrar^^'wiU ahuuft be f«a> 
I liArahly griattr thin the fr'm- or Di0rvKtrvp&xi% fronj the DIFFERENT MBtHODS of SAILING, . whether 
\>y «U wmn Prmei^ti: . . . ' ; ■,.■■,■■■;:■ 

INFERENCE. That nnleft. Ai;^r«wmM/, can be tnade in iceeping the C««/^ aiid meafiiritig th^ D^oitf/ Kin, 
ro a greater BxaAnefi than hat Kea hitherto fra3icailr, or kygyn by Na?igatotJ. the gusMffr Ja^nveaaa 
>f J^htnUei Navtga/itm «U1 be' fo far an USTRefiuwuia, ['ai*oHfervcd by Mr. Emtrfta in the Preface to hii Naviga- 1 



Digitized by 



Gcft^Ie 



tU 



tbt ROYAL ^^Tf^QNOMER 



ftPHBRieA^ -nd-rPHSROIDAI NAVIGATION compared. 



'T — 3 — zt-rr 



DLfffrMceVjS**??:'K^M''^''?^4*J'*?f'P'^ •>( 'H%^ ^jH b( of no A4vid^ 

lODg 'Runi, UDce the Ixr^r Error,- from' the CoWre aod Uiftabce failed, will M it 9<tf n tuen^J thereby m 

r^r, to'goidc tti)f MailD^. iibSki i SbifU Retie/fire, kept.fromDaj^ to Di]r, bx3(«Y«Mr, or Sfi^^nlf^ ^iae, 
yiiH^hxn^^ain^ff^Sf^ qri8ffj4i')feiI?)i^E»*»in£is£ace^luc«i^e ^ffcrcEceof merMliiNialPtuti, of both&iiKGi 
f^ Uj^i^fu *n lark-^ r*me. ' . ' . . 

: T4^e^6 sRJjiq>rOTeinent of rni/ Advnntage ia Navigation cbltfij confilb In CorreAiOn of the SBii^p Kattf b]f 
afiem»imtai<^lifir^Mitii^ Of ^ Ibme Mf^U>4i » dcccn^c t^C^V tjw £«^t/M|lk^ V^^Q V.^'l^*^ >( % Slw 
be a|>pM wiA the eammt Mttbtis of Nirigatioa in'Priaicc. 

But, we hare given [he mtriMntd Partt of the Earth as a SfBtrmd, in & Tahle mjcoviig,. Msfim*/ vith uothc^ 
Table of the mtridiaiuil FarU Of the Eatth u a Spbtrt, for the Navigaiti^i Otritfilj tad SatiifiiBUm. Who may thcrC' 
b/ make 7>/>t/ of either, and their Differ* ace, in computing the ^^/Vi'ilict, at i^e lun liuereejcemplified, oc^tii 
Prafiice, for hii ]U% in Zgg[ Saw ; whic& feldom or never lUpptB » PRACTICAL NAtlGATION. 

Therefore Mr. Muriath, and Mr. Martin after him, having exemplified AifrWiiVjpr {MCDlative} IfapiMit*, in Jont 
ftuiii, l^C4»rMwr'/«^v>««'"i^^'^''>l>^^i^««^?<^'»^<^tbe I-lTUTILlTY OF'ThAT DQCTRINI 
(except to Gngrifiy) aa mndi ai pbffible. 

II. CASE. TtgMJti!(,iiifnitav^LOSiGSJVS>EMmlI)lSTAiiCK/iiilid_fi^ 
.dCOVViSEpwM/ 



Exmi^i. A5hip;failiQvtjt^Pt|iceM»s^.A'vt££^MAtoaw>theiiii 30* af$Mf^^>a4S^ ■pona<:;>a9iof43', 
10 find Uie Difierenceof ^j?ji'i™_^pA "j/'^'f Jikiidt 

JL'Pa 




ago. 

._,. S^hirieal. 

[errPu^ UiL'Pat^- 



Kf.Lan&M5j> 



B7f^..P*s94. 35< 

' 30 



3438 



ByC*>4«">-Nr.n. 

iMere DU.IDt£ Long ' 

ConrfeJ Lat, [for Depart. 

AgaiBil43" 3000 I 1797,50 

.*»• I J73.0' 

9.3' 

3.73 



ByI!i^r..ll£««ni*aNavi^lJ^n^P. 53^ . '. . 31^4',! 
Ltngth of Aici. %toaf.C*mfmttt, N' 



/tecarjing t» 



[■« 53* 4' »j^ LmgitnA. 



"+89,79 
I788;i6 



Agtinft434 



3S78%oC trtw Dif. LW. 
by the rpWoulal n^ira 



+00 

3<l 



373,01 1 According to 
17,97 \.*^ Sphere, ' 



Saiiiiig, 



.^th^Birtli, "> I 34j8^ 

Iftvi, Tf/MdtifpiJoKt nm^fimtit tnt Djfirmt.tf. LttitsA 3*y», »/hm tbt -mmmii Difftmu syx/pvn 



B 53^ nf tfiC. Long. 



Conrfe. 
A(*ip4,43» 



[Dirlat. 



r«r, Nfimber II> 



Or, Agtinft43» 



44lit,ii J;Dtft.ni|i.. 



I, 32;? 8, 
byMr. MirtA^.-pfaviga. V -g,;,, ,^ ^^ SpheroU. 
tMW^ r.,sJ. . . • • S^. -' f . ( . '.^ - 



bif-Lu 
3000 
-3«o. 



4101,00 I 
419,10 1 



Difluee ra bf cnn. Mi$M. 



4483,11 J-I9 Spheroid. 



Bat 3o',oo Dif. Dift, is ftiliwt IS* 



,y Google 



«d NAVIGATOIW 



$.P0£RIQ4l4 UA 8PHl%0VVA.1i. VAYl^ATHt^ 



»S5 



DISTANCE^'A/, Mmgititmt 



I «r I^NGiTUSe Mn^ (|»^ COURSE fim-iii. Dig m i m ^. l^TIXUMUM 



, £)mm/(. a Ship filled fnun the LKtitnde sj' Norths to Liuknde jo* Soiuli, and.]ier.DiAufwrailed.nealure4 
4482,1 Hileii aiinthe foregoing EzM>pU, to Sad the Cw^ ind Difference of - ■ ■ - 

Given, _3'7,^ -H'l?:,."^,^— gs ,7313,1114 ftaadi in ConpnteT.N*. Tin Cpl. loopo, as«infl43*C«rA n^'l 

Sphetaid Spivere 



fiy Computer, \ 



Coorfc. 
Agiinft43.'* 



Sphevoii 

MOT.Pam. 

3000 

400 



Dt& Lo>g. 

fmt Oep. 

" *797-S 

373-01 

9J*S 

3-73° 



1414 3> 83.565 
B]^ Mr. JUsrrii^i Nkv. P. 54.3184.1 =£53" 4'Dif. 



ccoraineto 

lpheToi& 
Sailing, 



Conrfe. 

Unft43* 



S^ierical 

Mer. Put*, 

300Q 

400 

3D 



Mug. ai berarci 



34J« 



Dif. Long,. 

for Dep. 

1797.501 

J73.01; 

27:971 

7.461 



3105.94 _ 
s ;3° 16' I)i£ Long, u be-- 
[ftre.. 



■ S Diff. 
owing to the fpberatdal meridional Parti,? 
being t&ken 3414, mQcad a£ 3414.6. 5 

IV: CASE! Tcfi,dtb4 Difftraa •/LATITUDE md DISTANCE nm^fimthf COURSE aUmfimk 
af LONGITUDEi givtnt 

Sxamfit, A sup full from a i>«r#ia Latitude 51' 15', fiaering a ConrTe of 35°'3y^k^it- MaridlM, till>ll)c 
findi her Difference o{ Lmptadtx%' i^ ^ t;io JU/rj, tofttdherDiffbcnccof jutfIVMAa»dIMilUO»^Br 



Coarfe. 
«''-3o' 



Dif. I^ng. 

forDep. 

1000 

700 



Mcr. Pam. 
1401,3 
981.58 
i4/» 



■ 1397.80 
Mer.Pamof 
Dif. of Lat. 
N.B. l/M^d. Parti cf tit Hi/: 
t/Lmt. art gnatrr thtu lit Mtr. Fartt 
tf tit Lot. ji'itfn, joM mufl diJaa tit 
lalltr fr*m tbtfarwiif, tmd tit Jltaum^ 
ill toifwtr to tit Lat. *» tit aif 
trary Sidt tf tit Eq»atar. 

If the Ladtudehad been 210 40' (initeadof-Ci*i5') 
Splwrald. MtriJitiiai-Pata 



By Cmfmrt Nonbcr III. 

Spknoidi 

Now, ji» 15' 

Sttbtra£t 



hfcr.hiu. 



SplMiie 



Mer. Parti of Lat. arrired int. . ., . _ 
Mm^'t NaTigation, P. 54, ... 19 ■ zi 



Hewfinalltke DiffitTeBcebyjM(rM«b/ and ]iCerca> 
tw-Sailing, in 3i*-{4' M 3>^'M{.Latitad«. 



1387 . 

239r 



Spfaedc. JlfiHi*M^Futi^» 1397 
»398 



Anfwcnng to Lttitode 16" 44' S. : 



Dif. Lat. . . 39 24 ^tiwvfaU Sailing. 



Dir.Lu/ 39 -7 JjlifMfrWCtltiag. 



tS" How fmall the Difference, oulr W, tUfinmtM, in failing httimxi > Sttmt m fmnMh-uid dercfiwe wh« 
will be the Oddi betwixt fpheicidal and Mercator Sailing for daily Recbmugi f 



yCjOogle 



i86 



Th ROYAL ASTRONOMER 



SPHERICAL Bwl SPHEROIDAL NAVI6ATION atmpmd. 



NOW Ka find the Di^aiut JmM fnn the- Conrfe tnd OiSercnee ni LMittdi given; being a -Caie of //^<i.' 

SaiSng f ■ ' ■ i 

Lat. jLength Arci*l A Mr. Martin'^ N^gttim tht tEgrt^mi£Tr»t'\ < 

ByT«b. P. 194. SI' is' I 3059-81 > Jrei art trrMianJy pvtit, ai< a999-8s \Cimfrant$d 'uitliTnti 

19 21 I 1151.91 J fdlfi" . • . L H7i-a J <mlhetifl. 



'[ 1906.90' 1 ' 

{abont 1907' jWbich jtutbrn" hai taken out ftii 



By Cai^ltr, Namber II. 



Conrie. 
Agunft ss" 30' 



By Mr. Mviiii't N»r, 



1907 
r, JT. ss- 



Dift. 
I2a8'.42 

1105.58 
8.59 

1341.59 Difl. nn. 
2123.. 



172865 
So». i5'5iiifteKl55i« 
»i 20 5 of for 2,19 
fame Ctmfuttr, Number II. 



Coarfe. 
Or, Againft 35" 30' 



Dif. Lat. 

iOOO 

9PO 
10 

4 


Difl. -] 

1228.42 

i.oj.sB 

12.28 

4-9'. 




.1914 


-i3Si.i9 





21^-57 4- Error of Mr. 3£ir^ViNarigatioii. 



V. CASE. Ttfiniiht Diffmmt */ LATITUDE rndtfiffmnct efUiliGyTJJtiE fi-m tbt'Omrft taid Dip 
run, hia^pvaif 

t^ THIS u the moft freqaent aiid nfefnl Cafe occurring in'NaTieotion, tiioagh eonfidered and introdoced lafi 
of allby tbeAttthor-of Wpiu/*r««ff>4js^0«jp^^ WM»»n;f«/i#ir, whafe Qaeltioni arc propofcd all along (like the 
Rtvirmd Mr. MurJicli't, the trigiiuJ Proprietor of this utv/ Impravtuaat) quite •«/ c/^raaUe, or fuch M nevo 
ocaa ia fraSical SaiiMg. — So that if Queftions in thii wmr MiiIkJ, had beeapropofcd to work Traverfct, oTa.Ship' 
ffe)^K(r>>«(iv,-uischcchief Bu6nefiof Navlgatari, (iKpad tf 'o/triing tboii/aiul Mi/i &aii) the IDLE REFINE- 
MENT,^ /Miww Ntmigatlan (obferved by fa able a Judge as Mr. ^IA%P.^0N) •would appiar obviem it tht meaneft 
Capacity in Sdence. And no other Advantage can arifc from conlidering the Earth as a Spheroid bat to Gngraphj, 
Map-ma^ng, and fmall CorrefUon of etrltpeSOli/ir'vatUH ; TJie Advantage thereof to Narigation plainly appearing 
to be none. Therefore, .in'Idiitation' of Mr. Emtr/mi, whofe Jodgmoit and Method in all He writes u 
txtn^lary, we hare giren fuftritr Piaer to the meridional Fartt of the SPHERE, at being rery fufficieqt for aU the 
faipoftt of fra^ieaf NavirMitH : at cbc fame Time they !cSrrefpond with the tha-miiig Eiigauei itA ctrria St^im 
of all QueJlioni of Spherical NAVIGATION, byJ^e Ltgariibm-TaiiMuti «f the half Coqiplemeijts of Ladiodet, 
at demondrated and cxoaaplified by the late Amoiu Dr. HALLEY, In m^/^ T'rda/SU!. -Number 219. ' 

Exof^tn ibt.firfgMi^Cafi. A ^p roni 4482^1 Miles D[nn aCuuyiof 43" from the Meridiaa, SwtktmrJ,' fnap 
a fvr/Iying in Latitade 25° N. to determine from thence her DJfFerence.of £o/]ln«6and£MrnViM'c^ 
FIRST >■ fht Dfftrtnc't »f Latiiudt, by C^puitr NamberL 
" ' ~" Dif. Lm. 



Cokufe. 
Againft 43« 



Dift. 
4000 
400 



4482.1 3277.98 Dif. Lit. J 
By Mr. MwrfiVa N"Wg«i«>j P 55-;; • s 3»78» pif-Lat. according to hi> « 



2925,4 . 

292.54 

58.51 

1.46 

.07 



BttHga Ca/t (^ PLAIN. 
> SAIUNG. . 



u friiuiplti of Navigation. 



DeiiS^the Length of the Arc 3C«, 7 , .„ .„ 1 Or ^ 

b,T.b..pJ34. . . .!. . r<^5-?9 -• 



r j»78' 
iSjoof=as» 



1778 = 29 38'. - 



Remaining Arc *<^ iWht' ^j.^* of the? 1788.ZI 
EgMttww.Sof -. . ...... v 5 

Dif. Lit. . . 55' reqnired. Or ^2 — —54. 38' Dif. Lat. 'ituthtut ttifiutmnf. 



r- NOW 

yCjOogle 



W N A V I G A T R. 



SPHERICAL «Bd SPHEROIDAL NAVIGATION compared. 



■zSy 



ttdW-tt-fiidtieDiftrafi tf Unfftmii, frm tht €hmfi j^%*, and Diffirmt •/ LthaJi ^i* (tr %^' ^t'J iting 



Bjr T«b. P. J«9, «90. 



Lit. 
iS» N. 

30 S. 



Spheroid. 

Mer. Pam. 

JS39 

187s 



Spheric ' 
Mer. Parti, 



By CamfMtir, Nomber II. 



1S88 V 

3+38 
er.D.LatJ 



Coarfc. 
AgiinS 43« 



Mr. Martinet Navigmtiw, P. 5; 



Mtr.D. 


Dif. Lon. T 


Lat. 


foi Dtp. 


3000 


•797-SO 


400 


J7J.01 


13 


9.)! 


♦ 


3-73 


!4'4 

!. Si. . . 


318JS6J 
!■««■ 



AtewrdtHg 

S3- 4' Lon- 
gitude re- ' 
qaired. 



By Tab, 
P. «B9 



19 38 S. 



Spheric. . 
Mer.PirtsjCourfe, 



s+ 38- 



Mend. 

D.Lat. 

3000 

400 



DirLoDg." 

fbrDep. 

2797-50 

373-ot 

a. 79 



tH" HowDcar thi* Anfwer 
refined Anfwer in Mr. Martin'j A'iivifttft'm, and jii dui 
^w>^ bj mtridi»nai Parti of ibi Sphtrt. 

PROM •what it ixta^ftd i 



3182.62 J 
S3' 3' w> tlw") 
bit Ntanu/t it > 




■if. Loitgi req'. 



ftngMHg Paget, It mn it ti/trved, tiat oar COMPUTERS, N». I. II. Iff. a 
MaOffir^fir aU r^ 'METHODS OP NAVIGATION. Ad thai viiim lamplMdiii a«tirmid, tbt mtriditmaJ 
Dijirntt »f Lalihidt imfi bt uftd mfttad ef ttamw Dijtrentt of LalitKdt, mfid >• C^ f/ PUin SaiSag. Tim taif Diff*. 
ren(tbtlvvtin flain aaii_mrrcaler, tr evtn fphtrriiai, Stuliag, it in tvt Jimilar flmaTriaaglti;. tht fLun'/aiUng Triangle 
ieing ctntaintd in tht Mtrealar-fiuBag Triangle. The piaia-Jialing triat^nlar Leg, ff^fi* ta tht C^rjt, mtajitring nohat it 
cal/ed Departure i and tbi Mircatfr trienpjar Xtg, tpf*Jitt te tht Jamt Canrfi, latafnting tht Lin^tndi, in tht EjnatBr, 
or en tht tmlrary Side thereof, ta the firft Plate af givtm Latitude, failed fram. 

. tS" FOR Satisfaction of the Prefortian of the Linti on the convex-Sarface of die Earth, at a Sfbtrt, uftd 10 the 
different Mtthadt of Nofvigatian, and alfo the Froperciei of plain and fphtricalTaKa^t, fee fnribir an, 

WeharealfoOiewn, funheron, the Error of Mr. ,5. Jlfi>rf<«'a METHOD, \v.Yh New Prineiplemf Gt^rapbj and 
Navigatien, of finding the Dimenfiani of the Earth m an ehlaft Sphtrtid, whomakei Ufeof an>jmrr«i? Radiui of Cur- 
Tature (for folving thofe feverat Problems] determined by fuppofing the Earth a ttrrtS Sphere, and then drawi hi:. 
Concluhons relating to thePropertiei of the^rr0ii/<i//i>m or thcKarth. We hare Ihewn the Infnfficiency of his 
Method \ty /merai ExampUi confronted with the Refuli of M. MoKpertuii' (coinciding with Don Juan's) Method 
of determining the Rati* af the Earth'a Dismeteri, from the Meafore of a Degree of Latitude tm the tU^i Mcii- 
dian, at diflerent and remote Places j in Lapland, France, and the at Eqaattr. 

Upon the whole of which it nppean, that the Spheroid followed by B. Martin* New Chart, according to Manper. 
tail and Mardach, it twice ai much from the tme Sphiraid a« that it from the Sphert. So that if Don Jnmf* Spheroid 
(of Diameters 266 to 265) it true, MnrdacVt ox Martin't Chu^ Navigation ai« d»uhlf erraneuutomfuei with the 
Navigation of the Sphere. 

Hence it follows that Mr. B. Martin hat depreciated Mr. EMERSON's Judgment and Spherical Naweatian, without 
Reafon, or anfwering Mr. £'t Reafoni given. Who, with at much Reafoof mieht depreciate the Gbitt, Speffaclei, 
Fifi«n-Glaffii, and Matbematictd Infirumenii not fold by Himfelf, while he boafts the Inventitn or L»frovement of hit 
own. Yet we are informed that Sentx'i Globei were firlt fold to Fergsfaa and then to Hits. And thatG&Jcx, Sfeilatlei, 
yifan-Glafftt, and Mathematical hifirnmtittt fold by Mr. CbU, Cuff, and otheil In ¥kttfintt, are really ai perfefl U 
tboCe fold by B. Martin, 



MEKSSOMAL, 



thi ROYAL ASTRONOMER 



fl 




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MGi(tD10WAL tAKTs'on M.ru»>rt Cha.t. cor»ii.o"admc »ith the £.rth'. C«.c S»f«. of. Spl^. ^^^ | 


" t>.sr«. oi; tA'i-ifu6E. : — \ — r—r\ 


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Md N A V I C5 A T O R. 



29.1 



MERIDIONAL PARTS od Afc«4i<»'iCBAit, tontCfoMint «ith the E»rth-iCoB«< Sorf«eor» SplKrc . | 






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439' 
4395 
4199 
4401 
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3»99 


3384 

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339° 
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3^74 

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3770 


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3790 
3793 


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3074 
3077 


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3609 


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3703 
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39^ 



Tbt ROYAL ASTRONOMER 



MftAimiNAl, PARTS on jMW^', C«a.t, «W|^nJlng •ktiKfel.WK'.TSnvci W.« of . Spl..,,. " 


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md NAVIGATOR. 



»93 





l^^RTS on Mowfw'i Cbaiit, comfponding *iih the E.rth'. Con.ei Surt.ce of 1 Sphnr, 


1 


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•43>7 


.7.87 








^i: 






























>g 














9»« 






109 s* 


"775 








)& 




70.3 


7»t., 


75!» 


jUy 


8i»7 








97*8 




10976 




"JO" 


145" 


.7668 

.7844, 






70]i 


7177 


754' 


78=17 


8137 


»„, 


88,7 


91(1 


976s 


.03»8 






"945 


'ii87 








Tint 




71117 


!■<" 


8,,, 




9»97 


9781 






,1869 




146 s8 






»6 


70*7 




75S9 










93" 




1OJ69 


11051 


1190. 


'3031 


14730 




16 


il 


70 Si 






78 S6 




!<., 


88,7 




9818 


IOJ90 






1307I 




'84,5 






706J 










8„7 






98,; 


.0411 








14H80 


^ 


30 




7071 


7310 


7^87 


7877 


i„. 


•51. 


8914 


91 S3 


98, 


1043a 


Tlli/ 


11999 


13.69 






7079 














9371 




10453 


I1IS3 


IIOJI 


13116 


15036 




»■ 


16 




7337 


7l.;)b 




i,„ 


JSi 


89,. 


918, 


,88, 


10474 


.1.79 




.1164 


'S'"7 


194»4 




709 ( 






79CJ 


!;;j 




9405 


99°7 


"■I9i 






'33'». 


ijiao 


1971J 












79"7 


8,8« 






9<»»4 


"OJS*" 




1-1,4 


.,360 




«0O50 


-iU 




7III 


716t 


76H 


79»7 


■mS 


8600 


8991 


r43S 


9943 


ii,,8 




13410 




8 


7119 


737» 


7t'41 


7937 






9007 


94! t 




10560 




11103 


13460 










7t>51 








9011 








1131a 


11139 




'\%l 






' 4> 


7'T> 


738^ 


766x 


79^8 


8igi 


86,8- 




9481 




10604 






11561 


4.10, 


l> 
















904s 


9490 


10017 


1.6.6 


1.366 


11310 


.3615 


16051 


"411 


50 




7";» 


7407 


768' 


7979 


830+ 


8(6, 


9C&3 


9S'S 


IOOJ5 


10648 


"194 


'>147 


.,66, 




7160 






7989 


8,,, 


!';! 


9077 




<oOj4 


10671 


11411 


«»l83 








!» 






7700 




a,., 




9091 




IOP73 


loOjj 
1071S 


"450 


11^1 


M77l{ 


•i,«l 


J' ■ 


t. 






7710 




8ll« 


l,o. 


9 'OS 


9S''4 


10091 






.,8,4 




.•,,66 


g 


7.1l( 


744» 


77'? 




8„o 


17.1 


91... 


9^80 


joi., .0739 


"S«7 


.14,6 


■18,. 


■•.74 








thtL«: 


:.,/=ii|i. ..i.=ii 




w/ /v 


«vi«(Mr m itidifar uTveitd. 
ANOTHER RULE to find 


Jt«£H 1} ud the «^«t'NiiiDlXr 1437.87, Cf the «M<iMt, of tha Squn of ibe Aco/ DiAwce li 


?»&.? 


of the Sbe of the pKD Lit. (t 




CcDOT of the f^rnhb Id Puti 0: 


>f the Sfihif for the f^iw'if of the fuiw Lalitade. 


lb«lbe 


iKTidiooilPtmlefKlunihore 







































»9+ 



Til ROYAL AST. ROK6MER 



the WSCTH of "T DEGREE, •nd .Ifo uiy 




' 


JflWrf* of DEOR.E8S. Iwt«dliptic^. of Ih* 


LZHGTH of tlM /EEMifiH jtt, af ^ SPHBRB, br tfcc Rnemid Mr. »brJ»A, 




BARTHH MERlDlAH, in MJuutM of tb« 
EiJUATOR, »ii4 fii^iAt JWti. Fot Mj Lati- 






jUAK .nd tnXOA. 




tude. Acco(dhig(oOoB7>>al« 




















Arthet 


Diff. 


d7^ 






U,ff. 








Uogtb 


AKha, 




U-gth 


ATdW 




Ardin 


Sphtroid. 


Sphrt 


Sphd. 


Aicha 


Spheroid. 


5ph«. 


Sph-. 




Ut. 


of> 


•ftho 


Ut. 


of. 


of ita. 


LU. 


of the 


Mi. 


.od 


Ar. Lit. 


of the 


Mr. 


.Od 


Ar- 






Drgm. 

IS 


MnidiiB. 


"?■ 


D.g«.. 


MeridHn. 


__ 


Sphttt. 


Mvi,^. 


'-3 


chei. 


Sphere. 
.760 


»f*A*; 




tha. 




'H. 


' H(iii. 


60 




7—^ 




"T* 


i»-si 


S9-55 


5,.m 


174S-7 


\%.y 


.7.6.4 






S9-5S 


»«-io 
178.65 


Ji 


59.90 


180J.07 


« 




1 17.3 


•-7 


bS 47 


iBio 


1776.. 


41-8 


18.S 




3 


59-5S 


39-9* 


*a64-99 


J 


.8» 


I76.0. 


4.0 


..6 ^ 


.I80 


.835.9 


44- < 


»9.o 




4 


S9-5* 


.ji.« 


+9 


S9-91 


^^■\l 


4 




»34-7 * 


?-9 


5-5 49 


*9to 


.895-1 


44.J 


*94 




-f 


^»-5i 


»97.76 


J' 


^9-94 


1984 .8 ( 


4- 


300 
360 


'9?-f 
151.1 


_fci Ji 


JO60 


'955.1. 


448 


-SI 




59-5 5 


3S7.3' 


J9-9J 


3044-81 


3015.1 




7 


59.56 


4.6.S7 


j» 


39-96 


3l>>+.77 


1 




.4.0.8 


9,1 


J110 


3075.0 


44-' 


19.7 




% 


S9-S7 


476-44 


51 


S9-97 


3.64.74 


■ 480 


499.6 


1Q.4 


•■! 5) 


J. 80 


3135.0 


4S-0 


«9-7 




9 


HJ-S* 


J36.00 


54 


59-99 


3»»4-7J 


9 


S40 


s»s., 


M.7 


7-7 


(4 


J140 


3i94'9 


45-1 


»,.8 






.i9-}7 


_m-v. 


55 


io.oo 


.?''*73 


10 


600 


587.0 




9-1 


5i 


%V^„ 


3'S4-9 


♦J-' 


H.8 




"iT 


S9-S7 


655.14 


ir 


60.01 


3344-74 


tJ 


660 


645.8 


"h^ 


s6 


,360 


33 '4-9 


4S-I 


.9.8 






59-5* 


714*71 


15 


60.01 


3404.76 




710 


70+.5 


^^■^ 




37 


3410 


3375.0 


45-0 


19.7 




.'1 


59.58 




60.03 


3464-79 


IJ 


7 So 


76J.1 


.6.^ 




58 


3480 


3415> 


44-9 


4.6 




'4 


59-SV 


S 


6c«,4 


3S?4.8| 


•4 


840 


Sii.i 


.7.9 


1 1.7 


S9 


3540 


3495-. 


44-8 


.9.6 




: "5 


^9:S9 


'^"S 


-li-, 


900 




.9.1 


"-i 


60^ 


36« 


3i5Vj_ 
3615.5 


44-7 


*9-S 




^rr 


J9-60 


9S3.08 


-iT 


^^ 


3644.94 


16 


960 


9J9'7 


«0.J 


>3 3 


61 


3660 


44-5 


"94 




"7 


S9.6I 


IOI..69 


ea 


60.07 


3705.01 


»7 




998.5 


11.5 


14.1 


6'a 


J7.0 


377 S-7 


44 J 


19.3 




jB 


SS-S' 


io7».3o 


'1 


60.08 


17«St09 




1080 


1057.4 


11.6 


14.9 


6j 


378« 


37j6o 


44.0 


»9-" 




>9 


S9.6. 


1 131.91 
IJ91.54 


? 


60.09 


'h*'i 


•9 


1.40 


.1.6.3 


»3-7 


15.6 64 


3840 


379fi-» 


4J.8 


rf,. 






if 


■If 


60.10 

60. iV 


3885.18 


•TT 


.160 


.175.1 


15.9 


■!-i 


_xl, 


3900 


3856.5 


43-5 


18.7 




»S'-'7 


3945-39 


1134,1 


I7.0 


66 


3960 


39"6'8 


43-. 


.8.5 






S9.64 


(3.0.8. 


'I 


6a.ii 


, 4005.50 




1310 


M93.0 


»7.0 


.7.8 


67 


40«i 


J977.. 


4.-8 


iS.j 




•] 


S'll 


137046 


68 


60.., 


4065.83 


•1 


.380 


.351.0 


ig.o 


.8^ 


63 


40S0 


4037-S 


4»-S 


18.. 




-»4 


Sfl.fii 


r4|o.i» 


69 


tt.,3 


4M5.76 


a4 


*440 


i4.r.o 


.9.0 


19-1 


69 


4140 


4097.9 


41.1 


17-a 




-»i 


l<t*7 


«4l9-79 


y 1 


60.14 


4.85.90 


«5 


, '.Soo 


1470.0 


JO^ 


'9-7 


70 




4.58.4 


41.6 


»7-5 




■6- 


"^ 


Ji;p! 


7< 


60..5 


4146.05 


-IT 


.jfio 


1519.0 


31.0 


10.4 


7t 


"^h^ 


4113.8 


4t.i 


17-1 




17 


S9.69 


■ 7* 


60.16 


4306.= 1 


"7 


i6» 


1,88.1 


!:j 




71 


4310 


4*79-3 


40.7 


16., 




■iB 


jl^69 


.S*i«4 


73 


60.16 


4366.37 


18 


1680 


it+7.« 


at'e 


73 


.4380 


4339-8 


40.1 


.6.5 




»9 


S9.70 


1718.54 


74 


^■■J 


4416,54 


39 


1740 


I706.J 


Ji-7 




74 


4440 


4400.3 


39-7 


16.1 




3' 


S9-7' 


t73S.s6 


76 


60.18 
4o.^ 


44«6.7i 


J2. 

3' 


iSoo 


1765.5 




»3.1 


-11. 


4S90 


+460.8 


39-» 


'i-9 




S9-7» 


t*474< 


4546-90 


iE6» 


ilH-Z 


76 


% 


4511.J 


38.7 


.5-6 




3» 


i9'74 


i907.7» 


?7 


-60.19 


» 


31 




1883.9 


.3.8 


77 


4)81-9 


38.. 


ij.. 




33 


S9-74 
S9.76 


t9<7-4* 


7< 


60.19 


33 


.980 


1943.1 


t% 


H-3 


7» 


4740 


4S4..S 


37.5 


»4'7 




34 


1017.M 


79 


60. JO 


47*7-4« 


34 


1040 


«>01^. 


*4.8 


79 


4703-1 


38.9 


M-J 




IS 


.J9-77 


,086.99 


So 


60.JO 
60.21 


«787." 
4847.89 


_3L 
36 


it6o 


106..7 


39.0 


»S-7 


80 
81 


4*00 
4860 


4761.7 


36-1 

35-7 


»3-i 




IT 


I9-77 


1146.76 


48143 




37 


■S9'79 


.io6,jj 


8a 


66.11 


4908.10 


, '37 




1139.8 


19.6 


16.1 


Si 


4910 


4S84.9 


35-" 


ij.i 




38 


SJ-So 


«6fi.3j 
2316.1* 


Sj 


60.11 


4968-3" 


3« 


1.8* 


40.» 


.6.5 


83 


4980 


'^K 


34-5 
3J-8 


13.B 




19 


S9g> 


84 


6o.» 


5011.53 


39 


*Wo 


*i9a.i 


40.8 


.6.g 


84 


5040 


It. J 




J£- 


59.B. 


»38i.9S 


* 


60^1 

60.M 


,088.75 


4" 


H60 


,351.7 


4' -a 


/7-. 
17.6 


86 


^ 


5o66.!_ 




.1-4 




4" 


S9S4 


"44S-8> 


ji4>.97 


»4tl.. 


5';z-* 




4S 


SS-Bf 


1505.(7 


I7 


6o.i> 


5«C9.19 


^ 


3510 


«477-7 


4»-3 


17.9 


87 


51.0 


5.83.1 


11.8 


»'-9 




43 


^|.s« 


»5<J-53 


88 


6o.>t 


5i6»4> 


43 


1J80 


•JSA 


4'-7 


18.1 


S8 


i.80 


5148.8 


J*.. 


10.6 




44 


jS.Sj 


16.5.40 


89 


60.11 


JlS^l 


44 


.I40 


43-» 


18.6 


89 


J340 


5J09-S 


30.5 






♦( ' S9-!.S 


l6S>t8 


90 


6o.» 


43 


1700 


3656.6 


43-4 


.8.6 


_9?_ 


«oo 


,370.1 > lO.X 


■»A 




tB At itetf TABLE ihe L<^r* of iny A«, fnm 


Bt the ABOVE COMPARISOR of Mr. Muritch't Air. of the Sfb^J with 
th^ of the i>i.r^ ««1 .Ifo with tbe Arc of tbe Spheroid by Do« 7«-. T» "-7 




tbe EQUATOR, ii <^u.l to Ltneth of dl th. D^ 




p» ^LMiCudt •• fir H tbr tirtB Z«y>^. 


/« ti«( >«'. ArciMC .boot two ibJrd. M mwh giriter tbin Mt. MurJ^b; « h.t 

b7 .Aout 1 P«t. of tbe 3 Sun the Arc. of Mt. Vunt^k, by wWt »»t^u/ P.m 
Mr, Mtnin't Nfu Stt-Otn u coDSreaed. 


















DiSf^ct of Arc, tO|i«thebellerIt«orihdr Deftan « rf th« £!<>«. of ihi 




TAf*^ Wff ./Jtw«>f '•l^"*' -^^ :En«r '/« * /f^«- 


Ugbihi^t,mf*nMM/a»houtii«mwMrftt^*tumktMt*tmi. . 





,y Google" 



;m^ N A V I 6 A T O R. 395 



Of die DIMENSIONS of Ac EARTH as a aPHEftOH>. 

KV his fir 4ltHrm»!wt tbi DIMENSIONS tf iht EARTH <r<ffftS(rrfy, «•« AORf 9^HSS}B. Mv/T^ 

P O L B S. 
PUT c ^ tlie Semidiunetcr of the Eutk't Equafr'J Tke ^mi-hwijvtr/i, 
a n tbe SemidiUDCter of the Eanh'i Jxit X The ^aa-tt^Kgalt. 
X A the Put of ihc SemUdiimetei of the Entt'i EqnaiDr from the Center thereof, to where t PtrftHtaUm 

blU on that SemitUametei from die Place of Latitade on the Eanh'« dliptic MeridUa. 
J «r that Perpendicalar. at Semi>oidiB«t«i kt fall Itom the FUe*- of Latkow, cib di« <kA RMi« of thi 

EoMeor, or SeaH'trm^itrfi. ' 

r- ss the Rj^ui of CwvMtrt, ot id » Circle toochiag the ellijitic HerMian of tbe Earth iii tt^ flacc o 



I, t, I, RmSu, r«^fftf. aid &MW of tke Ai^le of LatitiidA. 

!l « «. WHENCE, hf Ike Propenlei of Ae AE%& and of ff^A;///. we have the fbUowIag JUki^ foi 
' deteminii^tha Riftifiiii of the Eartk'i Diawafiou. 
RULB I. _^s«Ksx theZrfAur«;juiori*4rMHMrof thecJI^^kteidtaB. 




1 f'K ' +*Tr ^ j;^ AaoTBBi Latitvpi. 'Whence, 



.lj»«— rt^*# 



COnSTRUCTIOH af BMlSml PARTS teatiMri. 



THUS, 9iM Lm. <o> 
^ X'hrCanK... . „,,,-, ^ ^ - -tj-j r- ■ 

RULE fet ■Mr^t^nivinv On J*m. Multiply a Aw ri|va of ihiHtv^Aw of tbt LMinle fo XdAm ■} bf j I 
tfaic %, wai iht iiift FigBK, with wku ta orriEd, will bo tb* Diffrmci that ths incridiOMl Pntt of tbe Sfiatid uc 1^ 
Sftn, fot the bine latitude, wbsDthc DiSennccar tba DUmcten of the Sf beroid i> JmEI ; atbtnriti tUi XnA ii of ao 

ErnoU. Sine Ltc 6o> =s ,Sfi«, &(■ by | (m ^nacd) s Aj.^g DiS'. Mcrid. PitU A/i, 

1^*1 far S(ioi> Duunetni of tbe Spbctoid u 166 M (6 j, ttaifMi with th* neiidieD*! Pvii 

By M. Jl/di>f<r(irii tbe XaH'a of tl» EiTth'iOiuMtenii u 311,1ft to ]0(,7a{ Iriun wbion tb« (iM uncA {mm/ JUb (laiNe^fM] 
find tbe DifTereiwa of meTidionil Put! 66,49 ^" ^' '*■"* LililsJs, «is. <■}■. ^ 

' BytbBoiher Jloti't of the DiunennaM to 16 j, wt bin ontj iifot DiRtROCV- 

Doa Jthm Gt^gf Juan «nd Don Ammm ii XJIht, mofincd ■ Dipu of tbt Mcridiin oey Ibc Bqulor In &a«A OmmtM, la 1^ ICla(dta> 
>r i^ft, u dwir Book feu forth, (fitft piUibH io Sfu^, *rA then truluad into Fmct^ who AtA iiieiitMk tb* Wotfc In tbt Vmt vj\i, 
tad Stcrwudifvwd 16767,711 7«ftf in I DepM I wbi'iIii>peM«Ttb>Athe Ai»mi(/T.bw7P*n it, b; ahnt«nTHA>) fttf> n nMifU 
lioa dependiat oa the'MnJhn of ■ Def. of ^ Merid. in LflHif ud anxbei Tanvanw Fnm wbicb bit JIAi^irMMn iaAiriid, ~ " 
lenaliKd-the JlMid of lbe,^r««li/K*swtn*of tbcEirth tabc(uberonot>6n«d)i£Stoxej : ■ Jtao>iDDcfc MinvdifstbKMiftaiaibf 
Sr'A^Mw<H(tVamtbcTbeor}af Gn»t7iBdEvtb'iDtBfit]r) thaa aru htfote dcMrmiaed fr«m tbe MMfonttT aDitrtrfal^ibWMd 
wotber in Frota. , 

TbeiMR'^iirw/Pattiriut^nidelae iq the ^^^^wWbjDsn 7Sm*e3 iSiji,?^ ^"- S>ae 1$° ft ,f998j|ai X4 >I ] (<« diifdaDK luy, 
Vr. ^ JO the ireUcR Diff. die meridioul Parti ofihtS/ifnii in left th& (botl! for die 5>ifp(, Wke^fnn 16300 neridisMlRrti 

r Spbttc, dedoa JO, and then remaia) tbe Bkerldional Parti for the fime Latitode^ vhi, 16970, 

Mr. il&nftri'i roe ridienal P«:ti (In «hi<b lit. ULartiw-t Una Ciw/ii cooftru^ed) and Doo^^us'i fbf tbi Spb«rfU, diflhr ftimkimW/" 

lional Parti of tbt Sftvt, for tSe Cum Latitode ^ 60', b; 6E->nd 11 j and thele from one uwdKr by 4a, tbctcfin* liNjawCtarrHd 

M^anV^UAi (pubHAedlbr<^Adtantat«t»'Ifni|adu) differ twice ii nKKti fra'Ai one tnothcr u Jun'tTahtet ti^fnmtM 
Ipbere. That If Twa'i TiUe* art n«ar tht Truth for tha ^ttrtii, (aakinl tht r^aic of the Earth alfooK u nt»x to a Sfiirt at Sr J^ 
UrMMUMdclt) tbcBMtrMa'twwClartfftotnJMn'AciS or' Jlin^onii'i I^HuIpleil !• dtHibfj errontMi, (m ibe Jijfairr befoi* iu« W^ifa* 
^rapoitlMof ^id;.Partifi>rltt,<a"J'dlfletin|THifbriiilndltfBar^iKi), ai JWsdlaVrt uAdn tUSciIwit^ tn'/Ouatot Mttuttr, 

OBSERVATION 
Digilizcd by VjOOQ IC 



z^ 



Thi ROYAL ASTRONOMER 



Of tbe DIMENSIONS «f the EARTH u a SPHEROID. 



From. aboTt «^ « -r- 
Whence. 



— , bySa^*titM9ft*+ I lbr/»i Ucwfc **»—/••;■■*; 



At the ^oj^ (when t and f are » 



1. a«lf<= 



.'(^ 



^:1J^ 



T/GnVrand tpai, and a finite beiag addedWoMtBfikite QfltBlitynMlcet naDiUercBce) 



+^11 — TTtli ~ '*i ' ~ ^' 

Tbiahfvt RULES (of gehaine BXTRACTTO^) ariurrta ttKdi/efkt^4>tn'th»'ka£»t *f Gtre^iH 
itAmrj ntar/f, trtxaR^,fattnd. Bwi Mr. MARTIN bu ^ed tttmit m F»f^, Tnttt, tntdvaah^t.tij fiuBmi 
iM inctrrtS RaJim of Carvaiart «j /tllivii 

PROPOSITION I. 70/»^i:^Radioi«/CvrauiA(n ^'litE^'lhrn'MilM, arr^anJtmt tt HhiMJdlt ^ a Vigrti 
\ta.funi em lit tliiptic MtriJiaa tf (bt Sart/fiSmfaa, 

Extpifli. In Latitnde 66' ix^ ' a Degree of the Earth'* Meridian hai been meafared and fotind to be $7437.9 
Frnth T»ifu, whence the AmStm »/ Oirvmimv r, will be Mt {bond ia Degrcei, for die twiddle of Aat Degree, fay 
thii PROPORTION, actording to Mr. Mm-)iMi At 3,141591, £?f. : i :: 360 "* — 



i8o» 



i.2ss»72s. 



57V9;75 • • • . ■. . . . ■• 1.75^1226 

7'*j&mi-.ares7437.9' • • • • ■ • 4-7S9'98S; 

Log-'ofYi^iiiir -. . . . ■. . ■, ■; 6.5173211 

Tii/ti in.au EifgmUiik.ili,fi^. ... .-. > z^}j9ii4 



EMgltfir Milei in r ts 399iil ■$ 



•5.6014097 



^«* In the ftlne JInvHf-,' fron the'lcngth of a Degi 
.of the Earth'i Meridian, KnPttrii, being meafurcd, and 
found to be 56925,7 Tei/ti, the Length of the AmEm 
of Curvature of the Earth will-be found 3958.4 £«;J^ 
Mill, for the Middle of that Degree. A Degree by 
Don Juan ==56767,79Toife3, at the Efuatar give* Ra- 
dio) of Corvature 3947141 taj^* Mile*. Sal ih'u C*r. 
vMart it meevrJimg It lit fitfp^fid fpherickl mi nt jphe- 
siHAtlf*rm^tiMStirtkfMdtlitr^tftBKMt*Gi. 



OBSERVATION on thelimt Ftn 



0/ th j INTRODUCTION n the Nn, ^riwAflu of 'CMfy^'iltd Mv^^fiw, b; B 
Mi. EMERSON, irid mirTrprcfrntinghli JudixncnC ind tie TRUTH. 



%MlXII(a\,jthtSfhtrKJitMtA'ot bf the Spttn, (dtl the Itrgrr Ernn if ttt a-ffiratd DlJIna can be ttulj cortcSnl) t>J 
mOIdI tbe /iw// E<toiiiau of the Mmo'iOifaii, while Cht br;ir Oku, or Eren ihofe of tlif mun MoUdiu, »Tt\iA lurpfy AfilKvi. 

To whit Pnrpoli then ue the dilfeieatPrrirdpln of MirJeri ind^mn lonndDCRJ lo the fVoA/ci of NivigatMn, *oi aUfi fftn FrimcifJtt 
rfO«(rflfai*BJW«mi«iM, wheiin«ilKr(of thofc^JeJ-raiffntrttPrfaclplei) - ' " ' 

* ' ' "■ ' ' vitat bt did mt, r»ho five hii Rcaron r 

■ride bhn wkh ibc 



And ^Tnie A 



I Stfff/liim, 



KL-MvnVnXL. 



Tu the AOTItOR rf the'H.OyAL ASTRONOMER eni WAYIOATOH. 
REUARKS an a BOOK Utided Kite PHMphi if Gitgrttb, uul ITtmitliO; tnlriiJint ta mon ExaBMift ib»n. TRUTH lad 
' ,PR ACTICABILITr. 
At^OitftlfciSmiKiplaif'riMittiitVh^yntikcni.'iMioinMufitihi Wficn I read tfa cm I found the Reifoning act iVrr/i!^. The 
Table of ■Mn^'nui Pim, the vny E*»mflH add the Krmarii are all AfkrUtA*!, imlclng up the /^ Pirt of thii ww Vtfgtlim. 
.A&inlbci'i Book ii ( ^htM Pimpblet of ]t Figft, befidtl >n Intniduaioaaf » Pi^ei, piinted in 1741, intided Mrrunr'i SmFi^ 1/^'^ 
til »at Fipm ,fihc X^iii \ Book eXccedidf tUIftw Priwdpla if Navigailun but the wilcr Autbor (IbiTe bcud] bM^rdfored 
t«(na hit- fmn. ■ ' 

The^Kt^p*/ Thiap of Now In the »fw fttKBWpi of NaTigation MT thefe. 

to Ftzt IS. the ADthor i) pleihd to ^eII at, from Matpaims lad PiiarJ, that the Eirtb'i Simi-taii to the Xa/iM of the tftaitm U 
]e4,7»teii3,tt) from whence it foirowi, thattbe fw^i of tht Height at £q<utoiiig|s of the RikTmi. Sir ^ate fivmrn ania it ij^ 
oofy, by ISroputation. 

f^-19. The Author of the Kv PrmliJa calli |tie riStta of the Pl»ce (1 Shir airiict at) ftom the MetidJao of the Plue failed from, 

..L.u.-^-r n , i.^..m__. -",aiflDiftinceireof idMmrtKatoMi Whici iewithat thii Ajthor liaowi Nothinjt 

riite ■ Book of NantitMa I 

Ftp 



bf tht Nairis of Diparfirt j tbou|h Depulu.re and a 
of whll Defattuie it ) and therefore ant; fit Ptilc 



PKOFOSJTION 
DglzcdbvCjOOgle 



ojiJ NAVIGATOR. 



«97 



Of the DIMENSIONS of the EARTH at aSPHEROID. 



PROPOSITION II. To dtlirmitii th* Rk^o e/ tit Smi^anuttr e/ th Eauth'i EqyjLToi, tt tbt StmA^auitr 
tf ibe^K^ru't A3^\t,/rMii /if Radius tf CJirvalitrt, amd Lattliult, firfwc Fiacii, en f hi Earth" i Surf act biing pvrwt 

'txi perform which, the Value of a inuft be firft detennined by Ruxi V. foregoing. 
Com. Logarithmi, By Laplandajid Fraua. 

rTir'-^fJi* I rJa*a 



Luinde. 
Lapland 66' 20* 



Fraace 49° it' 



Spatar of 



r=3994,ii; Miles 

/=!, 18 16693 
^=1,4911874 



is=39;8,4 Milet. 
r=i,i6s347» 



' = 3947^2 Milei. 



3.6014097 
o.3s9is»7 
0.3964064 



3-S97S'9S 
0.0664SJ4 
0.1863750 



3.596313* 
0.0000000 



fimi—rTtii 
_ 959-3 ^» _^ 

981.34s 
By LafianJ and Eqiuti'. 

^_ 1198 347 _ «* I 
1310.543 *' f- 



593.604 
'SS«-9S6 



Pttu=3 1 0S.967 
r'//(r»^3090.'3 1 a 



= 251-737 
= 1550.084 



By AvM/and-Sfiu/w. 



" 339-8«69 



Here' 

''»* = 150.134 putting 
fT,^ =588.9685 Lapland 
— ■ Letteri 
(Ittii^o, (or thofe 

»-'//ff*=.3 39.8269 t>{ Fraut. 



Pagi 1]. Thii Author of tic /unt Pnntipla, projcftt tbe Arch of tlie Meiidian Dpon the Tangnt, bf an Eye ac die Eicth't Center, 
pcrhap) with DeSgn to 6nil the maiJIuul Ftrii, If thii wii hii Meaning, then the meiidiaa Line for anji Latitude i> no mote than tUC 
~BmM of that Litiinde : becaufe anj Artb is fnjrHid imt in Ttmini ty am Btt ai tbt Caiur, 

Tiiii Author likewife nprerenii bilii^ by miiidlt iMitudt u not dcrrmng hii Notice or Re(ard: though erery j'feu* kaon, in flioil 
Diflanrei, ir fir ■■ any Ship can run in 14 Houri, that the Diffirate bj thii Mabid from that of Mircaitr, in keeping 1 Ship'a Rec- 
Itoning of LoDgiCude and Latitude, it not Tenfibte j which Method of MidJli-Laliluii-Sailii^ il therefore a Tery ufeful Apfaima- 

Pige ]i. Hefpeakiof a Can^/i, which ii to be mote than 100 Timet ftronger than thoTe of the common Sort, by which, I fupjioTe, tbit 
: intendi to fail 100 TiDn more cofreAljr Chan by the (onitii Mri6tdt in Praflia, 

Page 35. HedocinotreclconDi^aniiMany Element of KavigiTion, or at belonging to K\tt An tf SmSnr, becaufe it cannot be known from 
Obfetvition ; not ii it thought (by thia Authoi) of any real Uf(, being determlncil by CurfajMin ; but feidf (la he thtnki) to Error. But 
doei not every Bodj'of Experience in Navigation know, that all the Eaflings aod }ftJliA[i ate fo many Dipartartt ; and that the Sni of ' 
lying oM ifaj, or DifTEitnce tbe other, it the total Departure, made in 14 Houn-Ron j and exuemcly near the Truth. 

tnPtse j6. He rnikei ufe of Departnte in Calcolaliont, though he had Uii before it wu "JtUfi; who hai here forgot himfelf. He r«- 
folvei all hi] Cafei micktmcallj, by Scale and Compaft, and infleid of a Scale nfca Peftr-Scbaia, from which no Certainty can be eipefted ; 
whicS however, I fubmil to the TWo/of othen. 

Page 4J. He fayi tbe Way of Working on hit Chtrt it the lunt at an any other j he only propofei to b« more 01^.— Why tbeo (In tbe 
Name of WiWom) do«he call them WrtciPrimfiif 

He give* at a T^/( of the Magnitode of the Earth'; Paralleli, at MirrdKi hat done } oorfeenu to fuppoTe them any l^dy diflercnt fhim Ihoft 
ofthc Sphere, for any Thing he batlhewnta the contrary in hia Book of A'lwPn'acifiti. Iffo, be niieht at well fuppofe allthe Deereei of 
the Mendiin m be eifual. 

There is no fuch Thing in thii wioA Bitk at any Correftion of I'f iVnifi or ilM«rii^ I as if they ivere but Tr^i not worthy hii Regard 
bileerety rM^n'oirrJ AWigarir it fcnCble, that there itBoSa'&flf withon^&ch Conxion. But tbtjah ^Aii^HULCail'aU^ADraKmt' 
rmiy make that Corrceion needled, ^HlM«itaMtM4Mi' /C*^ JfT^t*^ BJif ^;>f,»tjt ^Z /^ ^tJS^^ 
Inlhe/fcflH/PdMoflhit new Perrormince, the Author bat given anothtt Table of Meridional Part/lrom Don ^anVBook, quite £fferi^ 
Bm the former he took from Muriccb. * 

Don yiaf makei the Radius of the Equator to tbe Earth'i Ads, U s66 to kSj, and therefore the Zxfji of the Height of the Entier ja 
* Part of th* Radiui ; which it not half To much at the other from Mnftriuii and Mardtei, and ia aot far different from the Rati ' 
tifue JVrtWoB. 

'' finding the great Difference, br fefirm a b'tt/i, and fayt, ttM tiihtr tbt Earth 11 mi a fsrfiff SfttrtiJ, tr ibiriert fimi Emn 



Ji« ibi Mi'furalin : And ii forced tc 



il diffinti n dtltrmti tbt 11 



What then Oi^l 



I Ut/niw Way from Jua* and JIAnM. Hiat if Jumi and t/min ait right, (aiU vbt canjbtw iht cittnrjj tl 



%i 



"7 

,, Google 



■98 r^fROYALASTRONOMER 

or the DIMENSIONS of the EARTH a t SPHEROID. 



•By xbe three Safiti'foanA of thtStixam of the Earths Diuneurt, 

»* 9i9-3S' 'V7f^ . " »98B73' , 

—=«=-„ ■- — — .977S<>9J jj — p~" I Here you m« fee how thii fame Me- 

^ '■*'' . , I thod, by Mr. MirftV* miftaken Radini 

_ "98-347 ,99M937 , » '995??ft I of the Earth's Curvature, giv« the Ratio* 

* = i3to.S*3 ' -*9oo937.^ - , fof the Eanh'i Diusetm, very-difie- 

*"^339.826<) " 1 >99°7*'SSi « | J 

» 26; ^96240 
ITio ^tfft< •? die Etrth** Dtuneten accordiog to Don JUAK, — = — gg" = ■* — j . 

tt HENCE ii JhwM th ERROR, «/ Mr. MARTIN'/ METHOD »/ Altrmmmg lit Jtaiit if tht Bwllfi 
Dumtttri, fy KM huarnS JtaJiiu ^ Ci^vatart, 

OTHKRWISE : AvMiim^ to M. MAUPERTUIS' METHOD of deterfflioing the faid RATIO ; Mr. J&rA^ 

< chufing to depend on hit RULES given, a P. 10. 1 1. in his Nmi Printiflti of NAVIGATION ; who hat 

iberefine Allowed THIS METHOD. 

LET the UMBm of the Eqaater to tlte trntt ««V he ai i to « 1 and A and B the Length of tva» Sffmnt Dip-m, 
DwaAved in dificfeat Laiitodes-} and m and < the ic^Cttve Snw of thofe Luitodei ; then, from thxPrtptn'— -' -- 



» X A— B 

5 X A«»— as^ 



»XA— B , / 



Sfitri it u neartbe tnic Figure of the Birtb uhk/r/l FJgmrt, dnwa TroBi iSttfernai, And thcn&rc tbofie thrt nb fhentri^iM/Pirtifw 
rte ^&<<« wtll cocnc >i uifh the Tiulh 11 thofc who follow hii l^rit Method from Murdotb lod Mti^irtim, 

Wiat theo canbt (lid of ibii £«^n j- Xr^Ttr f Cu thii Jti/jwJ^flv^iM'glTC die cms FipiTeof tbe Eucb fb u to found wif «<miD CotO' 
putitioo) upon it. If nor, ill t)ut be has fiid insert A'uhi^ ti iti Ptrf^, And wbo would not fooncr folkw Ihc fii^ Merhod bf ibe 
Sfitn, Ibm fallow an wnrMi'i AfeW, only for the Sake of hi Noielt* (nd Difficult);, when the DilTetrnce ii itJti^iHi aW u/r/r/i t 

Wheo be comei (0 <ompire ihe dUTerent Meifutn of a Degree oa the Encth'i Suitice, tlii) Atbw it in Ihe aimafl D\fiT!Jt, and ttiei 



would not be taken witbout Dnna^t 
ttnly 



ihttRi^htihtteittbAltOt, vAe villi IrMflf lit Tntlbminlj ft* biil^'aid, wUn Sir {b« 



luder bow be^t ii into hU Connptian, tbu Mr. £■■>/«■ deprciitcd thMDifcoTCFT of the Snherndil FifUfc of the £«th wUcb ti 
,, ..... _....__, r,i..,_,__i.. „_ __,. ..,,_, :. ._ jJi^ Rrfnmuu vihtn applied by P<W«ii to tbe FrtBur if Kavigxin, where 



mike no fennble Diffeience ; and moft create in endleft Deal of Tiouble for no nfeful P^nwfe. Mr. Eatrfa, gai 
lilini it in i^ RifitamiB, Cowardi the latter End ef hii Preface, wichaal Delip [he fiyj of offendlBg any Bodj. And what Ki jhi bii i 
Ian to drfttaut uotber'a Jodgment, for whit be idvancei, unldi bl properly uiwen bun \ ahicb ibe Authoi of the JWne Princifla (!i 
nee difcovtredl nener once it'einptei 

And Mr. Emnfim Kill continiki to iS&tm, thit the tripag tilffirmtt It makea ii nol worth the inucenfe L>b«iir {if mniiig mtriJiiuilfa 
411J una Atba) tbit it eaufei. That u we know nalbin| wbit ^la'ut of a Spfaeioid the Earth i>, or whether it it a Spheroid it all, or nc 
1 hope you will not follow tbit itfined Author'i Slept Of iDfening a T^lt of meridionai Parti fn ibe Spheroid, except it be to tm/nti md n 
ftn with thofe of the Sphere, and coofate itit prtadeJ Mutatap ^ SfteniM aitvt Sfiviail Navigai— by Eiamplci given of both, to fiicw 
Ibe nftlef. /)(/(«««. 

The ReaToD why 5fN«/M't DiSeresce of ibe Meridional Pant ii^thu tbeSphenndai Author'i, it becaule £jii^ afet in Ifaai Nnfa't 

Nnmbert 1*1) to 130. I b»e found'that the Difference se 34iSati, where ie= JVdt. Siu Z-o/. f^i — «■ tssStmi'jItiii/tbeEd'it, 

At to Rehtrtfen't Harigition you mcstioB, it it rather 1 Cturfi if Mttbmaiid ; for it contaioi aloiolt all Btaachei of praAlcal Matbi 

" DTtw it much the ftinc, injfollowt MMrdteb in the Sfbciaid. 

Ip ibe ^gy*^ yau have made ymi obferve, that neither Cwr^ ur i)gSeKt»a fc tnlj ajcrrtaiud. And therefore who doutd go ihoat t* 

Item Immenle Deal of Trouble to ivnd an Emr whifh ii larglved with naibr, tea or iwenry "Qmei a< sicic ; aad which it nnitoUable; 

and yet tttfiEmn, »i tvtil -n at aaibir, way ii all tartiBidfrtm taiiii « Oifavaihm. 

I know no Way of correOing the Zlf^rrsrv but fay finiJing the iJongitnde to every particilar Cnc^i ; yet thit it rroaUelbme, and 
iabtfiH,; and iherefoie In Prafiiceevery Body mifot Dle«f the whole £i4)'VW^!<l''v> imteadofiC. 

MirnoD of finding the DOianan, DiffbeiiCT t£ Laniaidi, Lamadi, &c.ly the £«!«'> CoHPiiTia, Ac. it ^-urt tanlb, and 
wlU be of Ufe in Prdfli"/ Ka^^igtiia,. 

I know of nobody ibac has taken the Trouble 10 compute the Meridional Pliti to ibt Sphereid, but Maidtcb (which it only in vfaiic Di' 
gf€a} and what the Author of the Niw Priuipli! jjittt ii> from yuaw. 
'^ Alto ihe I'A/ii of reputed LflfiVa^r and LuiiWi of Placet, there ti a gKit DifFerance among Authon. 

The tcjl Mribtd to afbertain Ihem nar^ (Once extQ Tnlh Eaanot be hadj ii by cmifarifg feveral Bookt together, niil'whin tbe; iiflrr. 



reckoned fromTheweAermofl Part of T^nVa, ai bu'Dg long fioce cIlablifKed by Canom, uriOugbt ndt to be altered. 
nda are reckoned from ihe firjt Ptimi if Aitt, and ought not lo be altered \ though fome rebhifiial PeiloDl, io 
CootEadiOwD U a bukd CaOam, might taeicaa tbem from Liira, ec any other Paioc of the Beliptie, NaWTOHtaMlU. 



yGoogR" 



and NAVIGATOR. 



099. 



Of the DIMENSIONS of die EARTET u a SPHBROtD. 



Or, (more Omplf ) piiRiiigM = i — *, thinxs: 1 — m, and n* = i — 'ZM+nN where »* bebg Tciy finally iy 

Refped of the other Termi, mar be meBt^t Md a* = 1 — 2n(, and i — »* ss 2m = ' '^ ° , above. 

3X A** — Bi* 

when B ncsrl/ A, 



Then, iif = 



=, as is evident. 



3A X a'—i' 

deot. 

H'btnti, we have B =: A *- 3 Aa'tn, the InjV^ of a Degree of (he Mtridian at the S^tanr. 

EXAMPLE. LET A = $7437,9 ibe Toifci m a Dtgret in Lapland, oai B ^ {fojp Ak Toifei 1* a Dtfru at 
the PMraiMef 45* m Fnncct 

Then, by tbo Equation foregoing, m = o,oo6646= 1 — ft, 

Whence, i —0,00646 =30,99354^*1 

tberifirt, teas >99354 =• '^^ : 364,3 the £0/10 of theEartK'i Dianeteri. 

CONSEQUENTLY, 7i> JmJihtUngtb^ aD^rmattbt Bjmtttrf 



1 a Degree meafured ia Li^lani, and we have \iy the Eqattioa B = A — jAmo* : 
■ f A be taken = 57050 ieifii in a Degree of Latitude in Franci, under the Paraikl 



LET A = 57437.9 T^i/ti 
56501 J Tai^jatcho EqHater: 
ai 45°, ThenB = A-— 3Ajca*= ;64g7,z the 7*^/inii- Degree at (h&EqaMn. 

From both which MilbeJ), of M. Mmuptrtmi, hy a Degree nealbred in Laple'iJ, and another mcafured 
a Degree at the ffud/er Ihould hentarJji 56500 Ti^jj being jI/) chao tbeDegreomcafnrcd there by Don ^k 
Ejua/fr, by abont a68 7'«/>j. 

BUT, admitting the Truth of Don Jiim't MeaGlte of a Degree M die Eqnator, and alfo of the Meafnre of a 
Degree before in iv^ow^. Latitude 45", Then )n:=o 0,003397 ; Whence I : n^=£i ,9967 i: iM : 265,12; accordiiig 
to which Satit, vix. 26610 265, Don yum bujlifj ibo Ratit of the Earth t* equatorial to the polar Diameter ; ai 
on which ^i^/^j he haf computed jif'i TtM of miriJHMai Fkrtt of At Earth, ai a f/irrMV,* which meridional Parti 
We have given with tbofe of the Sphere for the N*vigml§i'iTriaiaadCufit/ily. 

If the two iiclrtmt Dtgrui, meafored in haplmii and at the B^uatar, be taken at true. Then A s: 57437,9 and B 

56767,788. whence m^^-^^ — = 0,004615. 

CtnftquMlj, I : H = 0,99537 :: 266 : 264,731 being ft M«sQ^Mity between z64i3 and 365,12 the Numbers 
before found, aa Mcmbcr^of thei7<K») fromtb&Me&fureofa Dqpres in Ltfiaad uA Fj'tmet, and i'VMwr and at the 



1 According to the Ntw' 
I PriMcifltie/Navigat. 



Frem a Dtgrtt miafiiredi* 
LaplaxatxA FroKCt, 
Frtaa aadatthe £p«t(«r. 



S7 M. Mauftrtuif 

Method. I Vy'Mr'Ma^tig. 

NOW, I to ,99354 f I to ,98873 
( to -,9967 I 1 to ,99839 

I to ,99537 J 1 « ,99533. _ . ... 

WHENCE, it evidently appears, if M; Mauj/trtiai' Method of det<rminiiig the Rtit of die Earth's Dtameten, 
by two diiTcreDt and dilbint Degrees meafured on th»Barth'» Surfhce, be varf twe> as it apntars to be euififie^ 
in the ntar Amcmcnt of the, diffirtU Aofwers, it alfo appears at evident, that the Mttbad, by the ^otv Priariflu 
b/' Gtegraphf trnd Hatngaiian, for determining the Raiit tk thb lajne Earth's Diameten, M arroneoue j &em the 
difiercat Anfwers to the fame Rtjuffitti, deuced as above. For it fiippofes ('•w&M h mn) ib tiS/itit Jrt it it 
tircalar, ffr a Digfti ; and tbt WddU thtrtef, ef circu3» Ctirwtt»n, to ruanalt with ihe- tiJifnie Curvalwa »f th 
Eart^t MmdtM. Tht Rabat 0/ Cur^fitan /iitwi/e af ibt mafmtd. Dtgrii ewfijirtd at « finmtar 4k, tt it -tif. RaJAi 
of Curvature te ibi MiidU of thai Digril ^ tbt elSftit MtrUian. fflicb mftiffafi, it agaefl tbt Hrfetht/ii aiadtiii, 
and DimtMfiem tf ibt Earlb Jei^bt, al a SfhirtiJ, ftmud hf tbt Ratation of tbt Sian-tiUtfU aimt ilt fiorttr 
tr ftlar Diamtftri not " abiut ift laagtr Dia^uur^ as is aflerted ia the Tnlrai^iaiU tbt Sevi Priati^i tf Na- 

t^ HENCE, it necefisrily follows, that the Solutions to the XI Prtblrmi, P, la, 13. 14, of ih\iNci»Nmvhatmt 
ateftOBerrokcoBsPrinciplet, dlfi^g from the 7'ni/:6, \iy ttbtr Mtlb*di t n in ibe ScboUumt P. 14, isfigfufied. 

Q.q a «• 



300 



7be ROYAL ASTRONOMER 



Of the DIMENSIONS of the EARTH m a SPHEROID, 



Tit MEASURE »/ i/t EARTH at <lifferent Timet ij diftrmt PERSONS. 
Ytarifi'a Chrifi. Pbkboni Names meafunur Flacbi Naubi mafitrtJ. GteirapUcal MUu, 

800 . . . • Jtlmmon', Caliph of £«i^&» : . . SahjkK 56, 0757. 

icic . . • • FimtUiu , FraiKi 68. 

SmISus, a Dutch Mathematiciu . between Almatr and Btrgtm''\ Frtntb Tiifti. 
t^Ztom, to 1° 11' 30* . . I yjo*' 
jtlaiuur and LnJai, a MtanQf i in a Decree. 

both J 

M/». 
163; . ; . . KbtvimJ, an Engli^mtoM -: . '. between LaaAn and Twi .... 69J in a Degree. 

= 367196 Feet. 
1654 • ■ ■ . SUfhiuj, hy /tverai MdtitJi hand the EutVt Circamfatace • . 64363 £«&f«>i />«(m. 

0161650 Tofle*. 
XiETrii XIV, , , . M, Picari meifured between Mahtifint and Amtni Ttifii. 

i5?j than MjnoW in a Deg. by 340 ^w/w . . 788500 7«>i to i* ai' SS' • . 57060(0 i". 
1718 . . • , M. Cf^i meuiired the whole Meridian or Frauei. ialfit, 

rFrom Far'u to C^mri S/^P?"} 

4. Paris to Dunkirk 56960 Vto I*. 

Stmt U PieMni . . L Dunkirk U> ColSawt f 7060 J 

Mr. Mu/thenbrtck, corre£ling SiaUm, meafared the Tame Arch, and fband . . . 57033 to 1*. 
•,• 7hiab»vtM.ca.(\iKTaciiubaditiH/»0eieiilforJtterndn:ngtbiEarlb^iDimtnfiamtMaSfben, but Di/putii arifing 
ahtut in Figiirt, aeetrding to Sir Ifaac NcWton, ai a Spheroid, fiirlbir Uta/art vnai madi, t» Jtttrmine tbh impcrlaat 
Trutb, as mar as foJJibU. 

Began 17J6 . . . tAe^tatt C/airaul, Canms, U Maauir, A£u|^.'l meafared a Degree inl T^/es. 
\4tJDec.fiil9toing. tuii, the Abbe OatHtr, of Fraari, M. Ct(/iu,\ LaplanJ, near the > 57437,9 to 1°. 

Profeffor of Aftronomy at ^(/i/ ... .J Ardic Circle ... J 

Pieard'i lefs by . . . 377,9 

AV«r/s corre£led, allowing for ^i«w«/«p« of Light, of the obfervedS(«r,? , , 

thePreccffionof-*jw»MH, Reftaaionof Light, ('V«««'X'^'^'y • 55°9*S>7 » '- 

Lf/s than at the P»iar CircU : . 512,2 

t^ Douiti arifing aboaC the Difference of a Degree in Fnmct, at the Retarn of the AcadmatioM from the North, 

the Arch was remeafured by Cajfini it Tbury (Grandfon to the former) and Di U CaiUe, the Work wat iatitled, 

La Mtrid. it Paris wrifiitt 45° Parallel. 4 , Tai/ti 57050 tO I'. 

The Difierence of a Degree in Lapland and Fraact proved the Figure of the Earth to be nt Sp^rt, but rather 
a SpbtreiJ I the £ii/h of wnicb Diameteri (the Itfi Polar Co the grtatir equatorial) were now to be correftly de. 
termincd. On which Ratie were now to depend the Improrement of Gagrafly and Aftrvaamj, and alfo Viemgatim, 
fo far ai die Eari&s Figari can be applied to the Praaitt aftbat Art. To which End a fiirther Meafute wsi applied 
near the Earth'i Zwattr, 

Set ant ly^e^ . . Doa Giorgt Juan, Don Julnae di U/iia, attending the ^ir«</rm(ci«itj^ 
Set ^aaa'sBttk, fiom France, by whom Ittm Ob/trvattrits were ercQcd in the Plain I 

of Tentqui, one at Pueblo Fiija, and the other at Cutnca, by I 
which, with a great Number of Signali erefted, they formed > 
and,meafared about to Triangles, and obtained a Ba/t Lin* of 
195734,574 Tti/ts, between the Paralleli of Putbh Fie/a and I PatbU Fieja to Caeaca. 

dma : . . . • ■ J Lat.o"3a'45*'N,2''54'7J'S, 

3* +? 



Diff. Latitude . . . Sum 3' 16' 51!'. 

T«/,s T«/e,. 

A* 3» 26' jaj* : 195734,5+7 :: i» •* tbe EpuUtr ; 56767,788. 

a- T.ki.g shJm]- i. . D^ ^^^ piiS:!"? «• N. „ Fr«« }'^ '"*' ^^"l^"[ ««"• •' 

The Earth'* Semi-Axii to the Semidiameter of the Eguetor, at 264,3 ^ i^^- 
Nearer to Sir Ifiuu Ntvitvn . . . Don Juan determines ic to be 2^5 to a66. 
It it known, that 1* : »* (i ton, being the Ratio of the Equatirial t.a the Palar Diameter) :: Ltngtb af a De- 
gree at t he Bf iuOvr : to the Length af a Degree at the Pole, by ibe elliptic Theory, Or, i : » : : 266 : 265. 
T'otrtjare, 265!* :~266|' ; : 56768 Tti/es in a Degree, at tbe Equatar : 57438 Tei/ts in a Degree at the Pole. But, 
they arc the Tai/ei in a Degree ac Lapland near the ArSic Grclt, and much left than in a Degree at tit Pale. 
Htnc*, the Number 265 is a linle tae large (at il is fald by the Rtfiur) in the Ratia of z66 : 265, the Equatarial 
CO the Pelar Diameters of the Earth. And therefore the Matter is flill in Di/putt as to the trae Pigsre of tbe Earth, 
1 whether it !■ an txad SpbertiJ, or not ; and the Daubt U likely to remain, till we can meafurc the Length of a 
JDr^/ at the Pale (nan eft babilahilis Nive). That, upon the tobale ( natviilhftanding tbe lata Aibor's 
T^rettndtd Intfret/tments iy tit elliptic Cbart, cooftraaed from Mtridianal Parts on -wreng Principiei) the Mtrtat^'s Chart, 

' ' ' for 



Old navigator; 



Of the DIMENSIONS of the EARTH u k SPHEROID. 



for praSia^ SailiMg, will prove the Corre^er of ibe r4«v. WluMver mighr be evpeded from a Chart conSrafted 
onj7iMn'»(infteaa of one conftrufled from Murdoch' % ot Mauftrtuii'} Prind^lea. 

That unli/s the Dimenrtona of the Earth be txaSty, or rciy nearly, determined, and what Sort of a Figure it ii, 
the Envrj in Navigation from a wrong Figure of the Garth admitted will, be greater than thofe from fappafing it 
an txaS Sphere, excinfive of the larger Errors in the Ceor/i and Diftanct, that are impraflicable to corre^ bat b^ 
coeleftial Qbftrvaiitn. Nor will the incarrtS Determination of [he Figare of the Earth have a better EffeA, in the 
true Determioadon of the ParailiLxa at the Mosn, Btgimdng, Mi^, and fn/of the £d/iir Eclipfet, their Q,u 
tit/ of Duration, the Sub'i Parallax by the Tnni^f of ''/bhj over bt) Difk, i^fSi, which will all be a little precarioi 
COMPARISON ifUftrtKi SpHiRbiDAL *i'«ii(*c>«*SPKa)ticAL NAVIGATION. 
EXAMPLE. Mr. M<trdi><h (and after him Mr. Martin) fuppafii a SInp fab from a Plact in Ij- LetilmU Stuth 
lo anttbtr i» 30° Latituit N. (the Differmet vf LatituJi ^c") m a Conrfe nf <f,]<r fiftu tbt MiriSan (being a Cafe 
that never happens in the PrafUce of Navigation) rtpdriJ tbt Differintt «/ LoBgitnde md Diftancc run ? 

The Difference of LoDgicnde, by Mn-forsr, it -, i . 3206' 

The Difference of LoDgttnde, by JUsn/iirA't Spheroid, or Figure of th« Earth . . . 3141 

Difference, Iffi 65 

D^MtfV^'/c/ according to the 5/i(rr . . » . 45 1^' 

Di/fsnct fai/tJ by Mvdtei^i SpbtrtiJ , ■ , . , ; . . . . , 442; 



Difference of Ltnptndt according I 
Diftanet JailiJ, according to Tium 
Diffierence of Jifan, from Murdacb, or Martin, 



SphertiJ 



DWereDce, h/t 



in h»ngitudt 
Difimtt foiUd 



. 89 
3148 

44" 

7+ 
,59+ 



Nftiuithfiaa£mr Mr. Martin'; prtttruUd Refinement tf Navigatien /r§nt Error, te, in em Part tf hii IntrtduSim, 
fptakt ihiii, (ai if he had fargat himCclf ) " II it tat otieil tuewn, hnu mtag Errors and Miftaiti »w meft fidl/nl Stamn 
" art llahU ta in ihi DirtSian of ibiir Coarfe, tbiir Diftance ran, yr." — Therefore to agree with M. Manperfuij, 
tien all the Eltmtnti of Navigation are brought to PerfefUon, it will then be feen co what a Degree of PerfefUon 
tbii E/imaii of Sphroidal 'Sivigztioa (being applied to FraAice] will have among the reft, the Errors of the Cma-Ji 
and DiJlMct fiill retnaining, 

TO dtttmdnt (nnrt ttrrtBlj) tit Ratio a/ tit Diamtftrt tf tin Earth, frtm tht Miajurt of MM iBJirtKt Arpw 
af haiititdt n> its Surfati, fuppaJiMg lit Form af tit Earth to hi that af an oblate Spheroid \ 



PUT c= Semi-Axis. 

t= Semidiameter of the Equator. 
M,jw the Mta/itrrs of a Degree of the Meridian 
81 the given Latitudes of the Placts P,p, 

\i t\l^'"A'/: \ of thofe Latitudes. 
o',j' the Cafiaet i 
t' the Cafongent of the Latitude P. 
r:= tabular Radius. 



A=M', * = ».', 



af a Digrtt at differiitl Placts an its Surfa 




iMitaii. 

Ex. Laplaad hd" 1<J 

Praise* 49 zz 

■ Equator o o 
By Lapland 



LapIanJf t 



'\^- 



laifisinDtg. 
mtafurid. 

S6767.8! 



; Roots ofwhidi De' 

Taijiu 

488,67 a = Mi^ 

479,811 aE«^ 
•477.07' 



Vl+*=:^I ,0221723 



,9888 s 



Ejuatar r"J"=v'i+i»^^i— ,00926618 = 

France 1 t 

Ejualer S-^Vi+ji =Vi— ,00321503 = 

*,* Fnm tht ahavt variable Ratios af tht Sarth^t Di- 

amciirs, dtduttd from tmerring Rules (Mpafiug tht Earth 

ta he in tie Form af a Spheroid] it it tviJtnl, thai tifhtr 

' ~ ' ' at a Spheroid, or eiji tit Minfnraliani taien 

tfe Sxpenct and Trtuhle th* French Natita. ham 

ttJdngtht ftviral Menfuratims af Arcbti an lit EarlVi Snrfact, art intirely thratun artuig. And wr fiali al 

laft he farced Ib depend wsere on the Ctmputalitni af Sir Ifaac Newton, ar Mr. Emerfon, fy ihi Laws af Gravitj, While 

tht Afferent Dtnfitiei tf tit Earths Suijanet, nint its Siufacl, oV lav/ardi itt Onttr, (am %ohiti (hat CemptUatia dtftt^s) 

'itaain uncertain. 

And HSKca U riaisn mi AitviDi-tr oi Uhciitaintt or SmiaoiDAL NAvioArtoM I axd cM*a<Ui»itLS or iti 

Far-mn tie irai Figin sf tht Eaitii aad Sea dbfmiW (which mi) lary bf the ZSt& of the MoD&'i Grt*it]F more or lefl at dif- 
ferent rima DB the Sea) hi Difamry rntli bt a gnasr AJvsmtgi u Geognph; lieie ti Ibi PiACTICI i^NatigaTIok 1 Jec^sbt 
Stberitti Strfia af the Eertb «// i«<fiir,d, U fuffiuM n e,f-a,iT lb, EmJ ,/ all niiib Pv^Ja. 

Tbtrtfin Mn. MooKT and Pag. an Tower-Hill, mn c^,iinui ibe Sak if tktir Old MiaCATaA Ciaiti nilbfi^l*r jUveatff 
aity Kiw Sfhiroidal Ohm, ififinaed (fnm Muidoch) doably enonioui, wba camfertd ■arilb tbt Sphen, aad Jaia'i Jufptfid m _ 
Spitmd.~Ftr lit Meridiooit Pirti «f fAcNew SpheroWai Ourt (frtmalunfy » inadnrtntfy taalVJrB. M*rtio^ aWir twice A mMebfitm 
ihefi «f tbt fappored tiuer Sphsraid (laft ncmHvuUd fur Piifiice in NavlgMim, if B. Mutio; ei sb^i traer ^fir fiem tbt Meridianai 
Parti tf the Sphere. . ^^^^_^_ 



"B^ c 



gda 



the RaYAL ASTRONOMER 



y^ eROPfeRTIES. »f a RjglK-wiglfd 1»LANK TRIAMGL.B? 



lacb SiA sf a ri^t multd pUne TiUpgle hi tn^tU E^diqi, and Grdii bt difmM ibtriit /rem $meh £W rf the 
-^ ..henuff, at tin acute An^, at a Centir, t&n tbi taeo SitUt, lying aaligaetu, amdtbirdSii/t lyitigrtmeti te tit famtCnt- 
(4r' •will be thi Natural Secant, Cofine, and Sine ; Cotangent, Secuit, mud Ttmgent, rtfpifli%>ily, of lb* JngU at tbt 



Qialtr, incliultd by tbt Hypoihenufe and one Leg ; taib ef ib^t twa Sidtt btiag ixadt Radini. 

Or, T)x natural 'ievva^, Cofine, KitdSinCi Cotangent^ Scc&dc, W Tangent, ef tm Angle. (-indMifd If i&r Hy- 
pocbcnafe axJ eat, Leg) Kfuiir ^c*, tailHtihi natural Co{ecaBt, Sine, (WCoftnei Tao^nt, Co-fecut, and Co- 
cangeoE, rtj^tBivtly, of tht, aihtr An^lt, ahevt ^, aad ihecaaaity. And therefoie thcle will be pro^oitional to the 
Sfcanti, Sinn, Tangntt, to the Ra^mia tie7ab%. 

Omiiii Propeity c/ r^it-Mnglal fUne I^JuibIm, tii SttMun'i^adj CoaifutentC T. II. IIL trtfimM, hj mtHng Mtib SiA tf t nmti 
jf,U47r;aK[li Rtdia, S3i IQOOO, mW f<t^ «■< »/ (if TVWm jW fi* 3 ™rW Sides, raidc Ridiiu, I. 1. J, 4, 5, 6, 7, S, g TJiviIUdim, 
Qolinc, uJ S«ae ; R^iiui, Secant, tint Tasicnt ; Radiui, Calccinc, mJ ColinEUt, {errijftmliin, /n tit tin jUgkt fnm i n 45 lUfna ; 
^i^iCumfltmniu, btvii^ibe fma Numttn, f'tm\%Uy> Oigna, fervt fir t, », 3, 4* Si *• 7> '• 9 Tmattefamt Cimfltmoat, tr fir all 
tL Attla fn» 4 S « 90 Dtgeta. 

Ct^lir, No, I, 

LET loooo, looac^ jpooo, 40000, joooo, 60000, 70000, 80000, m 90000^ RadHii. Other Sidct. 



Being found ij ISiiltifSttlin of 
nral _ - 

^m nai Si«i. 
TnnpM lad SKtM 

Q^eagaauidCifae 



viuth die oiher wo -^Uti ire let down in Cit^im, 
». Ji 4f i> «. 7. I. 9 '■!» Ni- 



? of «n Z. Xg^ 



«a4*> .... Duutiue 
K Dif. Latitud 

Other SUm. 



Lopgtr (Dif. Lat. . 
Leg. ' {Dcfut. , 

Radjnt. OtlwrSidM. 



.' '! I DiTu 



Lac. 2 Qi'. Lnt. . . . . D^tture 

S-Mtf ?ROPERTlES •/ SINES, TANGENTS, fcCf. 



"' |^**!«-^"! '^'"'- 1>^- }'"^' ^liiSX"' }?r;r.' 



90», fr, a7O*t0 3io«. 



{from JO* tq 180°, from ijo' M 360* 

JAl^matin )frrtno»lo5O",/Toni7p#,(03f»», 
Ne|ttlrc J from jo^ t* S7O9, 






Siail -T ,„ ^ f H.n Itolhofeof 



VtrftlSiim . . Affirnwtin, iupmrtti 

Si. (, 1 A>« 

F«-jrW>'x;f>uttPn«mi'a •/!«>, tut^Mtt. ttt. i»nfi4t Mr. £MBK30N'i TaiGONOMETRy, nA* iai tltri t 
axdUJi— JtMin fit mtf Ftrjm ti mttr Imffivtmnl afiir tin, 

SOME PRQPfiRTS^ eftit $IDBS <uli AKOLES v'PLANB TRIANGLES. 

lJ.fiVjA.'>6!R. ItvriUbf, 

At 5^ -( 35j_ 111; Iljjtirbtiaifi. : Offtfit Sidt tt Ibet Z.t a*»rijv 

|. < bui^bcDcyiwi of the UA Angle, ItwiBb^ 

Ai I I I — — '^ ■ ! ! B/tiili'vfi ■■ •'(p»wi *'■</( ft tiai, £,, wAj. 
4. la ear iltht*nned TriinglE, iatli.ae^\ SoiSida 11 BifiSiin 1 Dift StitMiii Bnfe fy d PrrfmdltnJer, 



f. kiMfright-liaedTriinlle, A»Aim a^ n^ mm Siik 1 MrkkDi^. 11 7>j^pa( { &a.i/ (inr gM^ ^ i To^nrt ) tMr Dij^mm. 
t. In any ritht-lined Tiiin^e, AttalaiittlitBeii^tfiitZtp, j'arJWuf «Z. 1 Stm Siuant^ilii Ltp —SfMorrSafi 11 KmJi'ai 1 C;A 



wmitttz, iiitiuliJIf itf Ltgi. 



yCjOOgIC 



lad NAVIGATOR. 



__^ 303 

ANSWERS <e .]| the CASps pC f L A N E T R I A N'gTrT 



Q^ 1 A 



CASES of Rigbl-Mnikd ^ IJ A ^1 te y fa I A N G L E S. 



QIVEN SOUGHT 



.CA, B 
*BA. C 



CA, B 
BA, C 



Lfg I Sai. :: Hjf. : Sa. f. 4.U lt[. 



/MtbaibtttihyCAtr 



^^. \ffyp. [Find tbi ^1 if Cafe 6. 

BA, CA BC TbaihiHjp. tyCtSc 



fly PROPORTION. 



R«i, 1 Hyp. :: 1. [tvin £_ : ^f. Lig. 



A: Ligsff. : RU, I thp. 
B , CA J! K. : BC. 



C : BA II >. B : CA. 



.« : Jua- 11 "to- : I. If, ^. 
CA :: R : t. B { Cmflmtm, gf 
"' ' '^ ' t. C j o» awijig. 



EACH 4 of the followinj Ttma, is the Omc Rrfiiiljfft at pramr- 
ieaal, lud ftom Left to Right, or from Right to Left : Shewing (he 

•rUi, Ai Rid. 



1 Stm I CiAv f N. B. Jiy net oS tbefe Pnpor- 

1 ratgnt : RtJin Itiondi maybe put intha Room ol 

' 1 RaJiu : Cgf«j^tnr J loy otbcrlwo M( ProportiDiuli. 

a, Ai Rid. : i, given £, " 1 

Ji.Ai See. J t, p.en Z. :: fHyp, : onp.Legtothcgiven 

Cofee. , Ridiui .: 1 



TIie«bove/;fcPr^o.r/„fl/iiniy"be lilb wriei in the Svlaiioii of 
rpberital Tnaogltt fiitiber cm, by Lord Napirr't Fra^ukn, 
UNIVERSALLY, 
IN anj right-lintd Triingle, whofe Sidci are 
rejinrcDtnl bj A, B, C, and oppofiie Anjlei by 
«- *, ', «nyih«eofth«rirTerBiibein8giTtD, 
[ercept the ] Anglct) the Reft ue thut detei. 
mined. 
\c ^V CASEI. Hl>iaibiTiiiaS!JiaiidJ_ef.pva. 

B Then— *-=: — - = -, wheace the 

Tina R(i<i. it h^. <• ■ i. • J. f 

t3» When iiao Side* A, 3, ind aa /. oppofiM to one of theta A ii 
na, if A ii left ibaa B, then i, t, and C hi*e each two ValiMk, If 
u glutei thin B, ihen£,c, and Chave but ontVilne. 
Case II. r™ Sld„.(A the gtuier, B the i-A) <W «■ ^»pC 



Ki 



^A 



A, B, BCA. 
fBC. 



3B TB- l^ A 

CASES c^ Of/ifw y L AN b .'t' R I A W C-L E JT" 



C, CA, A 



Sida ami 
BA, BC 



Bx PROPORTION. 



CA. 



Bt, CA, A(AB (7. A : E^r !, ,.BCA < AB. 

i.« ! CAi! ..BCA : AB. 



W ttrift- Z.< *ft« SfJa : rhS §!f~. 



Which iihA to .ad f^,.>miam 
[the { Suiti jitei The 1 AptLi reauiieV 



<«<ac £ii&, 



ThoB, »!rf 1 Jn, 1;;^ „ iy. £-, 
1 Zh/. £«mn S^i, BD — DA, «A,J, 

= mD, adiled to and fubtraOed from 
half the Safe girei the Scgmenti BD, 
lod DA. 

Whence ^ A it ftund by Gtf ad of 
'JUght-angled Triwiglei.. 



CABK m. 
FROM the J SIDES ^nn, A, B, (ladodfaig i R^ired ^.i -, 
1 "l»i«il Angie, thii Angle nuj be fi»iM] 



ind C ihe Sid* eppoiiie ti 



RULE. AJJ til J SUa Ugabr, aoi t*ti lb, \ Sim ibraj 

fit inn* in CO. Lojanthm, UiJi'- wbiit /» dataw ibt co, Loui 

oftbi DifirtKt itiwanviiet M/S^tmi it, SiJi tpf^t n tbt 
rifind A'^ wi tbr* fu dnei Ibt Loguiaoii tf ,t, Di^nm 
bitiam wbiib Half Sum mwd tit utir two Sidii j rh fitlf jM 
if ^etkk hru Miiilen mllit tbi Logandiik Tin^ent ^ Half Agli, 



ftfiifti. 



B. 



TbeD«= D + E, ud j = D — B. 
Lilce yjle, P ut L. lA + L. iB + iL. j. }( — 



■, and L, denote £((4 Taagtm, RtSn, *ai Li^mthm, 



, Af-B + C 



— C Side oppoCte^ required , 



a.Log. 
l*g. 



4^«S'' Log- Tang, j Sam. 

For, H X H — Ci H — A X H — B ,: ,, (Rjd. *.) (' 
Alb, AB t H — Ak H-i-B :: 1 (Rrt. «, ) t\ \2^' 



U. 



HENCE Iliii RULE. Titbe Loi.Ca^ememu ff ,bt SiJaia 
eluding lb, fitgbt Anglt, aJd lit Logirithma tf lb, Difmna hwran. 
tit Hdf Sum ,faUtU tSiditMJ eiib^ri^miMiirSJdu, ib, 
bdf&A, tfiB^t 4 Nimitrt •uUiit li,lj>f Sine ^ baS lit fmett 

Thii, A, inchidin g Side co. Log. l 

% iiicrdStBk'sne ....,.'. n. ug. I 

H-A Log. 



* (ought Z. ■ 
mbleddte^. 



Lae-Sioe {Sua. 



The ROYAL ASTRONOMER 



RULES for tnfwering aU the CASES of SAILING. 



PROPORTIONS hi die Five CASES of PLAIN SAILING. 

t, AllUJIia i Di^aaetnA it Siml pi, Stt. Ciarfi i Diftaiuirm ii Tan. 7 Or, Cifa, Citrft t DiJlmttTm : 

Cafrfi I D^artfre, J ■ ftw/( \ Drfattm. J «jA« c pfaf 

-1. AiRcdiai I OjS«K« nm 1 1 Cof. J Or, 5«. C»r/, i Djffaw - - ~ - ^ « , .. 



, Ai Ksdms I Dlg.Lailalt i: I Or, Ctf.CurJi : i)/^ Lafir«A : i jfiu { Or, Cor.Ciiiirfi : Diff. LaiiUuk :: 



~ C«r/( I -Oif- L^'nM^ J din : Dig. Laiiitdi. 

J, Ai Eadius I Dig.LailuU i; J Or, df.Curfi i Diff.Laiim . . 

Tang, Cairfi : D^arlurt. ) Ceur/f : Dffariun, J Jtddiin : Dffartun 

PROPORTIONS for the Three CASES of "PARALLEL SAILING, dir«aiy EAST or WEST. 

4. Ai Of. Uliliuk : DiJI. 1 P^Wii in 1 1 Or, ]ta£iii i Difi. 1 P&ni i<i i PtraB.l I Or, Ctf. LAiinJ4 t i)ii(. s F/<m ir i J>s-«Ji;/ 

PoTdAU I : Raiin t Diff. UngiiaJe. J :: Sa.La. ! Diff. I^ixtuit. % : < O^a. Llitmd. : Dif. LmgitaJt. 

^ H£IfCE, The Lcngili of ■ Dcgiee of LosEitudc ia U17 Pinllel of Xdiitude ii u t]ie Cofine of Ae.LitJnide to Kidiui j or, u Radiui 
> Sec. lAtinide ; 01 u Cok to Colec. Latitude. 

PROPORTIONS for the Five CASES of MIDDLE LATITUDE SAILING, where die Lokoituoe is concerned. 

An APPROXIMATION of MERCATOR SAIUNG. 

(. Ai C4, !UiJ. talUvJi : Difrtrrt 1 1 7 Or, KaJiai t Diftrturt 1 : Setam Mid. 7 Or, Ctf. MiJ. LttimU : Htpcrtan : : Cifu. 

Jt^'u I, Dlf. Uag. iHarfy. ) Ltt. ! Dtf. LmgiloJt. { iTid. Lat. : Dif. LmpltJi. 

SINCE the Pnduft of the two Eitrtmii a equal to tiie Produjl of the two middle Termt, in in; Pnipoitioii, thercAKC fubftitotiag in 
5th PieponiDD DiJI.rm x Sine Caift = Rtdiat X Dffanuri, in ill Praponion, indwe hire, 
6. A> Cuf, Mii. Latiiadi : Difi. r«ji : : 7 Again, fublliiuting in the jtb, Dif. Lat. x Ting. Cogrfc ^ Ridiui x Departure, ia 3d Pfo- 

A'nt Canrfi : Dif, Lmitudi, J portion, lod we hare, 

J. Ai Cif. Mid, tatini£ : Dif. LatilaJtl M B. If jon (ike Half the 5m of the natnial Coiinci of the two LatituJu, and nl* the La- 
;l Tt»g,Ctmrft iJDif. LtiritaJe. (-titudi aalweriag thereto, for middlr Idtitiide, the PropoitiaB will (aeuHbtg U Ab^ZmaSoti, 

yp.jitfbiiNrBigiuiimJ be more eiaa. 

PROPORTIONS for the Five CASES of MERCATOR -SAILING, where the LONGITUDE i> concerned. 

8. AtfrtfirDi/.Ljit. t MtridiHul Dtf.Lst.X Bj Sin. &i. By 3d. AiKad. i Tin|. Courle 11 Dif. Lit. 1 DeputuTe. And fnb- 
:i Drfamri : Diff. Lmpnit, {Aituting the/enH- for ifaffn-fiafip, in the Stb, wchite ai followi. 

9. At RmJiut t Mtriiettl Dif. Lti. :i 7>nf . I N.B. TheMotitor-SiilingTiiingte il Bmiluto isd conUina ikepliiin-lailistTriiDgbl 
Cuirji : Cif. Li^tuji, J being both itfreTented by Right-Linei. 

GENERAL PROPORTION. 

10. A« T*w. siojCo* 1 7a„g.Cnrfi :: D!f. Ltt.Ttnan iCtufbmiMt tf LmiiiiJi fnaiibi famt Pdcl f,.r I . 

(efteenung the 3 Uftof 7FiguruDetimiliind ttiereffwhoieNoinben) JJ i^if.""^- 

This PropoKibn, with the iH, mfwer ili the CaTci of Sailing. 

X^ Both Lititudei and the Diftince being ginn to find iheDiScrenct of Loagitnde, thtCmirft muA iiiA be fonod hj f lain Saitng. 
Or, One Latitude being given and the DiSetencC of Lon^ludc re^uitt^ tbe Other Latitude muS fiill be fouiid by f-'aig Sailing, before the 
I.ongitudc [in be found. 

GENERAL EQUATIONS. 

'• <*. **. 
m=sDl/.Aai«lit M = L,r. « j T=£ 
Ltg.tfti N = 3,1984806 ; R = \a.oaa. 
Then, I. R+L = M4-N + T, will 



IF a, t, ixBfitt til Latin/da a/ tmtPlam, tf, V, titir Difianca er Oa^lmamU Jrm ibi fami Fdr ; A, B, tin Lag. 7ar.pnti sf ^af, ^f 
Dif. AanJB; M = Lir.mj T = Ltj. Taig. tf itt Stif'i Ctatfi, trRtuui, c; t=Diffirwia a/ LtnginJi ef iba not Flam; L = 
° " "-' ^ »00. 

be the Rdation between the Laitmia, Diftana 1/ Lemgiindt, lod Biaringt of Ihoft Plicei. 
AUb, Pulling i=bi(lanceof thf two Placet, D = LoK.if j J = Dif. Latitude!, A = Log. ^ 
C= Log. Colinc c ; C, M', N', arithmetical CoDiplementa of C, M, N. 
And, s. D + CsR-{tA. By which two EQUATIOKS all Calei la Sailing are uifwereil, where no Departnreii coaeemcd, 
N. B. KtanaL^. iiiiii fabtiajted, in iti finpiag Sjaatitti, lah itiariibmaicalCiaiplaitmiiiflia^tbtmf aniiiiir. 



The GROUNDS of MERCATOR-SAILING. either by Mari£»»aJ PARTS of tbe SPHERE or SPHEBOID. 

ABCiiif/aV/aiAiirTriin^e liuA ^[ 7E ^.'^.IfihiMn-.FtnifirDif.Lati. 

ADE 1 A(iru/pr-/tiAiw Triangle yyfiKjIar. I / luda A anJB, bt gnatcr than tbt Mrt. 

AB ^ proper Dif, Latitude J BC ^ Departure, A C ^ Difluce run, Bl ' / C farHfat A ; ib€ Laiiindigivm, JiduS 

AD = Metid. Dif. Latitude rf two PUeei A and B. 1 / tbtlih fr. pteiir, fir Mr. Part, ,/B, 

DE, Part of the Equator, = Dif, Longitade /.DAB theConrle. ~-j.— - j- mttttmrary Sidi of Eat — ■"- 



Hence AB 1 BC :: AD i DE, 

Or, Dif. Lit. t DeurtBn n Merld. Dif, LttiMdt i Dif. Longitodc : 

Pot, AD I DE II Red. i Tan. DA" — ' 

Haulba fiBnaingTatUa compoftd. 



aV 



yGoogle 



mi NA V I G ATOR. 



TABULAR RULES for Mlweriog «1I the C A S E S of S A I L I NG. ( 




m WORDS. 1 


Cifti. 


Gi™. 


i«.Kht 


AN.SWER. 




Sought. 




. 


cd 




Rad. ! fin. ( 1: </ ; f . . . . I 


DiflMCl 


Dif. Lit. 
Dep.ttu«_ 


Ai KaJ. It. Ctf. Omrf, f, Difl. l, Dif. Ltt. 

R-d. u jfe. Cturf, fi D\p. » Dt^n. 


. 


»* 




» : < 1: Rid. 1 tu. c . . . ] 
Sin. r : < :: Rid. ; i . . . i 


Diff.Lm. 

Dfpari^ 


Conrfe 

Diftinie 


Dif. Lat. a D^rl. ft Atd. ; r*.. Cikrfi. 
Sim Onrfcn D'P^ri. [, Rediui a, Difl. 


3 


- 




Tu. c < < It Rid. 1 1 ... ] 
Sio. 1 : 1 :: Kii. : J ... 1 


C^rS. 
Diftmrt 


Dilbnre 


Tan. Qm'li It Dipan. f<, Had. n Dif. Lai. 
S;.r C^rfi I, Difart. fi Had. 1, Difl. 


4 


>rf 




i: Rid. :i ) : tat.t . ...» 
Rid. : Sin-C :: d : t . . . 1 


Dif. L-a. 

Diptnct 


Courfe 
Dep.,tu« 


Difianc, t„ Rad. ft Dif. Lai. to Ctf. Coia-f: 
Kad. t>Si^=C«,rfefi Vift. uD^. 


J 


ct 




CoC. c : Ridi. ■.■.t:J...% 
Rid. ■ tin. f :,»..... J 


^^. 


Difbitn 
Depirtuie 


C.f. Cturf, »Rad.f. Dif. Lai. tt Difl. 
Bad. t. Tan. Corf. /= D-f. Ut. 1, D^n, 


6 


d. 




^ : Rid. :: > 1 fin.i . . . i 
W.d. : rf :: eof.c 1 » . ... 


D& 


Dif. Ut, 


Difl. It Sadia. fi Defan. u Sm Ctarf,. 
Rad. ttibifl. Ji Ctf. Omrf.!, Dif. Lat. 


< ^a»K. &.-/<, d i>ij>«<c.r„, » 0,/*r««, /L-rW., < D- 








Cf«. 


Gi™. 


SouKbt 


ANSWER. 




Scosht. 


AMSWER., 


-^ 




.^ 


Rad. ! cof. « :. / < i . . by 4 


Liiiudt 


Dillince. 


R*d. It Ctf. Lai. ft Djf. Lt^. itDifi. 


<<^ 


/ 


Cor. - . Rid. :: ./ 1 / . . . ♦ 


D;ji.n'. 


Longit. 


Of. Lai. t, Rad. ft Difl. It Dif. L«,g. [ 


1 


J/ 


- 


/■ if :i Rid. : car. « . 1.4 


mf.L>,i. 


Lidtgde. 


D,f. L,„g. U Difl. fi Rad. t. Ctf, Lat. 


d the Difttnct ot Iwo Phcn in ihil PiiiUcl. 




A TABLE of the 7 CASES of MLda.i LA flTUDE 3i)4 MKR- 
CATOR SAILING, cDncttning LONGITUDE. 


In WORDS. 


d.. . 


Given. Sanghc 








ANSWKll. 


■ 


-.*,/ 


./ 


t 1 / 11 tor. f. 1 iiQ. . . . , , 7 1 

^ -. R.d. :, n Ui,.t 9 J. 

■uTin-siOiS's" 1! /! Hn,(..iol 

T = M' + l + N' + R{ D:sA + C 

+ R. By EiiuilioM I «ad *. 
CoT. c ! Rid. 11 i : d!CffitpltmS*iS-t. 


t>!f.L«^. 


Conrfe 
DiOuice 


Dif.Lal.uDifU«.fii^.mid.Lai.l,laB.Crft 
lAr.Dif.L.,. itRad.ftDiJ.La. ii To*. Ctmrfi 
Dif. Ltr.Ta^tnlQaipi.Latt. : T«.c|o 

iV 5* :: Dif. Lt^iz- : T*.. G.W1. J 
Ctf.Caarf. It RjU. ft Dif. La,, tti^. 


X 


'.Kc 




B.i. 1 tin. ( 11 X 1 / .... 9 
Tii..ci.:,8'9->t«n."i«>/io 
LsM^N + T—R. Byf«M-Mi. 

^ 11 ibcTR. 


TtMlal,. 
Cmrfi 


Dif, Long. 

DiiUnce 


Ztf.mU.Lai. It taa. C^fifi Dif. La.ttD^.L^. 
Rai.ttTa».Ca^f,ftm.,. Dif.Lai.itDif.hfk 

The Dilt. ii foiind » ibate, tjCitfi ;. pi. Sail. 


3 


•,t,d 


/ 


: found by Caff 4. //arii Smilmg. 


TmLttu 
Dijta,^, 


Dif. Long. 


Courfe f.mnd 11 ibove by Ci/'4- /^"i iilAnr. 


4 


'.'.' 


« 

^ 


which find mia. Lit. lod repcittbaOp^ 

iition for the Dtha UtitDdf. 
Tin.! 1 Rid. II /■ x, Ibbtna or idd which 

Put! from ot 10 ttofe of othf t Latitude fo 

Latitude torterpondrnt. 
Tin. f! /:i tin. ji'iS'g":*... 10 

Which iddnl to Tin. i Comp. ^<ren Lit 

gi.ei the other Lititude. 
M=L+N'+T'+R. HeiCBtiMlJfonad 
rffouodbyC-/,5y*W-i%. 


On, hat. 


Dininte 


Tan.O,urftttc } gi.unL^i.f,D.f.U^.aDif.L^. 

by thl. find n5d. Lit. ind repot the 6^- 

tioD to Rt the olhnr Utitnde. 
r«. Omrfttt Rad.ftDif. I«. It »r. Dif. Lai. 

fubtna ot idd which Pirti fium or to Ibofe 

ofihe other Lit. ud find the Lititude cor- 

Tta. Carfi ,t Dif. Ltm.fi Tn. 51* ii'^ltDit. 

to the tin. ( Comp. gi veo L»t. givej rfw other. 
DM. i. now £id by C-i/f 5- fl''" SaiUn/r. 


5 


.,r, J 


1 


»j.fcu«d»nd*i7C./.i.^:«B-a;.r. 




OtbeiLit. 
Dif. LoDg. 


Dif. Lit. ind other Ut. find by Cafi 1, tl. Sail. 


6 


•-.rf. 


i 


AtTume c, by »hi<h find t, ^ ind t, tiU (ty 
7riM»dEmr}*i >:: \ : 1. 

tnatir th»» ib,J. f^ U>. [Urn, didua tb, 1,/ 
frum Praia fir mirid. Fartt It Ltiiitdi m em 

,rar,%d,./Ep....r. 


On La, 


IDd 

other Ut. 


JUli.meiC«r/<,by»hich6wlDif.LM. i. 
ther Lit. ind Dep. tiU (t, Iriai amd Errtr) 
Di/. Lai^ Difri. fi Mir. Dif. Lat. t, Dif. 

The dirrB Mtibtd of rolTing tfaii afe by one 
R-i»orJt^«, P. 64. P*/. ,7,,, Unottrot 


7 


•<.^, 


t 


Airume a, and theoce find t, till (h trial nA 
£™/l w.i X 1 /. 
(^ The ibore «c ill ea&Iy uAreiH by 




Soththe 
Luhnda 


Affume one Utitode, ind find thence the 
Btber. tm (h Trial a»d Errtr) Dif.Ul.^ 
Df. fi Mb-. Dif. La,. d> Dif. Ltwiiitdi. 


^ dfnotci Middle U 
•Thretb.ndjthC 


ibi iboTC ire oat tikea Notice of bdett by loy 
Kt SehmtiH vnrt mr pvn- It liim. 


MA. *l-(V-of 


[he D^farturi in Mataitr, hereotiilted, miy 
<1 DiAereace of Lidt«d«., liid the SA Pi^ 


Mr. 


*.3&r 


iihuT 




rza^iT^ 





306 



Tht ROYAL ASTRONOMER 



EXAMPLES of anArcrine the PRINCIPAL CASES of MERCAT0R.8AIUMG. Aeconliiic to diffeieBtl 
METHODS. " ' 

I. GIVEN*,*. /j TV jWf.^/HwTw W + N' + L + R; AndD = a + C+R. 

Jtj LOCARJTKMIC EQUATIOMS. Locukhimi. 



EXAMPLE. XtfinJ rbi Banat mJ Di/lmt cf It, 
IJUni e/ Si. Vincmt, (tm rf tkt Cipa it WttiUttit) in 

frim lit tSati Point, in Licituda 4^* jj' S, ' 
50 19' W. «^ CitcBvidi. « 



5 = 3.JJ97' 
d 5= ailV, 



M'=a o.5n*liC 
W=:= e.iai5te4 
L = l.o66i»S5 



Vj DIFFERIITCE of LOGARITHM TANCINTS. 

Ai T)iF. Lof . Tui|eDti { C wapkiu e u a of La* { LoprUbfni, 

Dtodci j6s ■!' and loa »' ]u* ; 3aM,}i7{ . . co. (.jijjlit 

To Dit. LoD|. 3>a 5)' ss 1971' MUa ].o66]«5f 

5oTuii.ca^, ^ 5(* jt'g" * 10.1015104 

To Tu|. Coarfe (jb jV sj* W, 

' ' fmuid « befon. 

Br COHPITTER, Number IL 
Caaift.|Dif. L«t. I Dift. 

I 9°o I 99*-»9 
I 70 I 77.64 



9.6111179 



1971 I 11I6.T] 



Bat tikisg to th* 
•carjtf Ooaifc la id£«!i 
Dctrea wUt be fnffi- 



,177 Milctf ( at «j« jV «j' W a T B 9.4111179 



Br MEUDIONAL PARTS, 
Merid. Pint. .^ Ai Mer. Dif, Lit. ' 
34*6.j 
1019, 



Di^£u. 



6.S ") »4»7.5 • . ■ . I eo, 6. 
9, [To Dif. Lont- iiSc* , , . 1. 

rSo Ridini .... 10. 

7.S 1 

•if.Lat.-'TBTHi.Cavricie'iS' ..a. 



Tb Tn. Covric as* 38' . . 9.61it6«7 

Bj COMPITTEK, NDmber H. 
*4*7>5}i''s(>4'oaiicail7, Qpote, ■sunSwhichuCoCT&si'jt'i 
Mtwriipg to tlu A&romr-TniufS. 

OR, Br COMPOTER, Wombtr If. 
A|tial xS" Cmrfi, ukd 1971 Dif. Lot. 70a nkc Mt 2(91 IIUm 
Di&uK0[ bdnsbat 6 Milei(«B«iu3io ^ P'f, iMitwiti. 



X. GIVEN m,Kt%T»jbai,Jf &r€ L«M+N+T— R t And D b j^ ^-o+R bD. 

B7 LOGAUTKMIC EQUATIONS. 

'\ a =.\T 4'i ^ ;= 7iej6'[ I 
= 49 SSi ** = 40 5M 



BXAMPLE. rnm 



it lqlW.»Si^(tiIintCairf,S. ijo 3i'lj'W. aw//, 
^ Oi/(rM«>'M, /• /«& MUf » Utitudt 170 4' N, It- 



pinditt Luini* <m>^ I> 



t e= ]> 51 ^ *9Z''j ^ " 3.S94Gtt6 
R+Cs: 0.04J01B5 



0.3066117 



Milet. 
z aig6,*77 



I x= J.3J97051 N = 5 S4S4896 

19' T = 9.6811179 

Diff.Loiii. 19 aj =:/s:ii6jMi]ei=sLss ].o663ij9 
Shlp'tLoDj. 14 44 



Br DIFFERENCE of LOGARITHM TANGENTS. 

AiTukconf. ^ ji°3S' 9* CO. a9.S9S4S96 

To Tu. ConrTe 1 j' 18' *]* 9.6Jl«i79 

So D)f. LoE. TaDgcnn | Compi. Utt.' 36° 18' lod ~ 
"I'lo-i 3066,317 



jCOlS'indl 



3.4866114 



Br MERIDIONAL PARTS. 
IMd. Puti. ■ ~ ■■ 
34^-. 

1039. I To Met. Dif. Lit. 1417>J j.itsijs* 
' Tug. Cosrle tj* jf ij' 9.is»t79 



-- 

?.lJ 



DifjLit.lM.Dif.Lit.-' ToDir.Laa|.iiCj'. . . , «.o66377i 
Br COMPtTTER, Number ft. 



SS9-77 ") 
3« J 



,, Google 



tmi NAVIGATOR. 



307 



Bf DIFFERENCE of LOGARJTHM TAHGEI 



Then find the Difirtntt 1/ LtigiitJi u in the rormer Example, I7 
proportioning the DiRerence of Logarithm - Tingeots of the Hi^ 
Complcmeou t>f Liticadei. 



ty prmrlieniitg lbtmr\ ^ ,^ 

jilltlhtr Oifafcurringii Prvaia, (nnpt the 6ih uid 7th} art riitclhb tttht fvtpi^\ ij^ith <£t Dtad-Reckoiiin| 1/ a Stif (1 
oiled) mn it inlj krft, and nmBtd ai filltwiht frijtmt OifirvinitM if lit Lalittule. 

N. B. Ajr fir iliily Couife tfn/ mmJinal DiBmact of Lititudr, fellimiiii fr Lee-'Wtj, VAimtion, Setting of Cumnti, te.) y— ma/ 
tthfiUttiAtilyDiBireBix of Longicnde, /wr Compatcn Number tl. trill, m'f^t reilrn Difanart iwtt tti Rahmi^, txirft ytu ^ff 
mUtOvf»iOtttm»jitrtt4ilyidiHHt frtmibt proper Diftcreoca of Latkitile taiCtarJtpVt*. 



%: GIVEN b, t, d; 7t JbU a. If fifMA=D+C — R, wbencf « and w srefbaDdi And L=aM + N 
+ T— R. 

Br LOGARITHM EQyATIONS. 

1 i ss *i%i,%jj.. D s j.^ioToet 

I Ut. fiiW from 49a ifV. t =8.«5«ji'«3*V. C =3 o.a5«BlS 

W. fnm Greenwich, ■ SM* ran M a Oxafe S. Iff- jy aj' [ VX. Utitodei ]* jt N a ^ 1971 Mile*, ...As i.*u6S66 
V. xili'tijTBilila: B4i«nijrm tbiKtat\AlitmUnif — ' ■ "^ 

Loniitait anivtd it f I Ship'l Latitude 17 4 K. 

= «7'>4'(*'»T»'5*'l f*' = S*'»»' «• A a 9.S«£go4 
4» 5i i*'ss»'> - - » ' - 



49 iSJ *' = 



B = 9.i6»o477 
n ^ 0-106(317 



=/:sIi6jMile>; L s= 3.0663159 



Of eoircaiDg the SHIP'i COURSE 



by the COMPASS. 



ThisVi 



CORRECTIOK of tlw Skip'i Coarie bf th« liLt»iHaa VARIATION. . 

THE Difference between the Sup'i magtiilcol Ainpfiuute, taken by the Compif*, at hit Rifing (or SettiD^aid 
hii apparent Amplitude at Rifing (or Setting) by Vej. /. ao4 fn ]o8) ia the magnetical VariatioD, £, or W. " 
be aUowed for the fame Wa/, or to the Atlg^r or I^of the Coorfa y^«r-(/^/£«C«M^( for the Ship') /nw Guryf. 
' The magattic Variation - u likswife foand by two magoetical Aumutha, taken at eqnal AltJtndeg of the Sao, on 
the famt Day. Thii whole magoetical Arch being bifiaut, the MiMt thereof will nve you the trae Sooth 01 
Meridian rery ntar!] ; which will diew the Di&nsnce, or Variation, £. or W. from the tme Meridian, ~ 
South Point of the Compafi : which is to the Sight or Lift thereof, refpe&ively-i 

The maffitticai Variation ii atbtrwft determined by the .^jMitfA- Com pals, ana z Plumb L/ne with fome^to' coming 

the Meridian at a given Time of the Night, which will flww the Difference between x^eimt vii megmiiica/ Me- 

rid Ian. 

has altered as follows. 
Year ") Variation. T Now (in 1759} it ptoceeds weflerly at LtnJfn, about I Degree in 7 Years, 
I E. I In fome Places it movei Eafiotiarii in others it is wilboat Motion. The 
Changes of Variation is alio different ia di&rent Pllcei. 
&tt Mr, Emerfon'i 7^U ef Variatuu, Pagi ^. tf bii Naviitiitir. 

There are Tables of magnctical Variation in PiiU/, TranJoQimu, and alfewhere, not to be depended ont becanfi 
there is continual Change of Variation in moil Places. 

FURTHER CORRECTION of the SHIP'S COURSE by alhvnng for LEE-WAV. V 

THE Ship falling off from the Ceurfi JIttriJ by tht Cnwtpafs, by fereral Canfes and Impediments to continne that 
Courfe, efpeciaily the Impediment of Let-^ay, her CoorTe by the Compal) mnft therefore be rcAified by allowing 
(oTLtt-ffoj, as follows. 

RuU 1. Seethe Ship's ^4J« by the Ontfd^, and the Angle betwixt it and the Ship's Keei (or right Afv and Jft) 

her Lee- Way, if there is no Cnrrent : for fo mvcb flie fall* off from her Conrfe (fteered) to \keL*tward, or hottt 
the Wind. 

Kuli t- Being within Sight of Land, (he Angle taken betwixt the Ship's Keel (or right Fm-t and 4f*) and thif 
Ptint »f tand always bearing on the fame Point of the Compafr. will be the Lee-way made by the fSiip, or wlut 
"■B falls off fro^l her ParalltJ, while ftte fteers the fame Cenrfc by the Compafr. ' 

REMARK. Different Ships make dhftrent Lu-Waj, canfed by the Difference of their Hailt in Building. Nor, 
as Sbip-BidUm allow, can any two Ships be bmlt to fall alike for Simftiufs: And Experience of Sailing in any -- 



k^ear "l 
1580 I 
16(7 > Northerly. 

•75? J, 'S"W- 



yGo^Ie 



The ROYAL ASTRONOMER 



Of conefUng the SHIP'i COURSE 



by the COMPAS 



$hip will bcA detemine her Lu-IFm ander certjun Clrcumftaaco of Wi»d, Sailt fit, Stai, ftnd Wtmthtr. A high 
Sn, or gnat Swell a-crors the Coarie fiecred bjr the Compafi, produce large £wfiy i requiring fometimc* much 
Skill andExperienGe to determine tti Qnutity : A Ship being out of Trim, or drawing more or left Water, a&a 

■ GENERAL RULES of LEE-WAY from the SAILS /r/. ai f^Ud. 
J Ship t^an a WimJ'uiith lUl SmU fit, i Ptimt In-Ifaf. "I O SOME SroMM make diffeient AlloW' 



ancei, but thefe are the moft common, when, 
in a dark Night, or great Sea, a Ship'i 
. ^Ab cannot be fet. How fiuJiiifi then ii 
'/ihtrdJ^Navitatm, when lo great D^fwEh', 
btuiti, and Difftrtnt* frequeDUy arifc in ad- 
jnfting the true Conrfe of the Ship. 



a. 7^tdLrttftJ, I Paint \. 

3. Hard Wind, imTtffiuliu, 1 PuMti, 

4. HigbSeat harJGidti, htibTtffiiiL fm-Ud, 3 P^m. 
;. On^ Maiiifaii and MixiTi filt 4 Ptinli. 

6. OiJf M^Mfail Mt, c pMMtl. 

7. Only Mixtn fit, tPeintt. 

8. AUSaih furUd, y Ptiitl. 

N. B. Hard Gain and high Seal fetting with or agaioft the Ship's Modon, variei the Lti-Waj, more or left, 
of which Ej^etience can oa\y judge. 

FURTHER CORRECTION of the Ship'i COURSE, and tlfo DISTANCE, by trying the SWIFTNESS 
and Setting of a CURRENT. 

WHEN there ii &ltlt Wind wd a fimtth Sea, a Ship's Oirrtmt ia tried by Ac known Methsdi in PraOice, at 
foUowt. 

Yon /ni (out of a Boat, ata CmaUDiftancefromtheShip, where the Cnrrent it) a lai^ triangnlar Board, leaded 
oji one Side, an/m Pat, or aKttth, below the Cairent, with a L/rw tied properly to either 60,80, 100, or more Fa- 
thom B in Leneth, to be veered ont into the Sea, at one End, to give the Sinier Depth enoagh below the Current i 
and then the End of the Um in Hand ii fafteaed to the Boai^a Sltm, to bring her up, ai if fhe were at Anchor ; and 
keep her u iteidy at poffible upon the Top of the Current. 

NOW, htatnng yoor Log, and turning your HmlfMimitt-GUfi, yon fet the Srift of the Log, upon the Current, 
by the Campafi, when the Length of the Lag-Use ran off the Reel, while the HaJF-Minute-Glart mm out, mil 

f;ive you the Swiftoefi of the Current, or Number of Milct it runt ftr Hour ) if yon add about i, or mere or Ufi, 
or the Drift of die Boat with the Current, iccording to the Diftb, Iftigbt, or Capacity of the Sitilter to keep the 
Boat mtrt or Ufi fteady ) which mnft be jadged. And the Oire^on of the Lint being fet by the Compafi, will fliew 
yon to wbat Paint thereof the Current fett. , 

OR, the Itaded Btard, afore&Jd, being hove into the Ship'i Wake, ai Ihe fails, and fnffered to _fiai bdew the 
Depth of the Cnrrent, the Liu fijlened thereto will fhew you the Cmvtnt't Direaian, And if the Half-Minute 
Glali be turned, when fnficient Lfligth of Liu* 11 veered onl for finking the Baard below the Cnrrent, then, aa many 
Kaat: at (he more mm off, from a A&i io the loofe-Line laftcome in Sight, while the Glifi riaa aut, (meafaring the 
Piai-liru a^crwardi) fo many Miiei the CMrrnt and &iif together move in an Hma; With which Motion, ityan 
compare the Ship'i Motion, meafured by the Logi npon the Top of the CancBt, yev will have the Velocity of the 
Cnrrent, fcparatcly, ai it is -wiib, or ibvMrti, the Skip's Motion. But having the DirefUon and Velocity of taii, 
the s'jfrfr DheAion and Velocity ii net tmnttrd. This Way yon may IbmeTimei lofeyour £««n/or SWn-, andPart 
of your Line. 

The ^an/itj of a Current'i Motion ii determined by keeping the Reckoning of a Ship aaiviardtMd bimtmvd 
bound, as exkft as poffible i the Diftrence of which tun Rteieuiiigt being the CntTent*) Motion : fuppoling it conAanc 

In a furrowed Sea, a Cntrent"! DircAion it a-CTofi the Ridgei of the Wavei raifed by ihc Wind. 

REMARK. /*y^rra/ Strait! tbirt ii aGnnHtabaiM, end aitlber it/aw. In the Straits c/* Gibraltar fir Atlantic 

:ean conliniiali/ tmmj init the Meditenanean, ivbiU oh uadtr Cvrtnt, fivm tbe Mediterranean, nmi lit t»ntr»j W^ it 
the Atlantic. 

tbere ii a Current in tbe Baltic Sound, \vr % Falbwu deep, and anaiber under ii. 

A Curreat Jram the Eoxine Sea fiii tbre^b tbe Strain af Conflaotinople and Propontit. 

Jnd in all olbtr Straits, vibtn then are ra^d nppei Cturents, it it prababU ibirt are iikiwifo under Currents fittii^ 
tbe cenlrarj Ifaj. 

PROPOSITION. If t Sbif be confidered at Stjl in the Sea, while that Sea has a Current letting tovards.fome 
one Point of the Compafi, it ii the fame Thing in £Sed of Computation, ai if there was m Cmrrtut, while the 
Ship failed with the Current's Motion towards ibai Feint. 

HBNCR, iocorrefUng your Courfe fleered by the Compafs, you m^conlider your Ship, failing npon any Conrfe, at 
ifflie:failedopona«rart>r«i&(rf|/{>(n;i, the fame as is that of the Currents Motion, infiead of confideringtlut Modon. 

And, the Dijiaiite on your Canrfi, fittrtd hy tbe Cemfafi, is coneded by the Current's Motion in die SMffi Dirtaivm 
(oimppted from its Motion per Honr in the Angle wuh the Ship's Direoion) by adding that Motioi to the Difii 
biled,. 01 fiibtraSing it therefrom, u it feU lawdrdi, tr emtraiy la, tit Sbip't DireSien. 

,0f 



,y Google 



Of tlie Samm's compass, LOG'UNE, LOG, HALp.MlNUTS GLASS, mni .LOG.BOARD. 

THE common Mmniri Cemfa/i ii well known, and needs no Defcription. Bat the Marinit't Ctmpafi imfravid, 
and recommtnded for iu greatcA Adva&tige to Nungaiion (by its lavtuttr, Mr. Emtrftn) it at follow*. 



Mi NAVIGATOR. 



Of MEASURING tb« SHIFi WAY. 



The Needle i> filed to t mova^ltpJaiii CarJ, under the Camtafi Card, which going iiiff' and bei) _ 

the C»mjiafi-CarJ above It, tbe ¥^ dt Lv* of tEat Card will alwuyi point tO the tmt 



a Staifitr, 

the prefencJ^dnoft'ofi, in the Ctm^i-Card above It, tbe J'Jhtr dt Lart of tEat Card will alwuyi point to the tna 

Nerih and Seatb Points of the Horizon, and likewife each Point of this Compafi to the Irut Ceurfe fleered by tbe Ship. 

By which Meaoi frt^tta Ttonl^ .and MiOakei are prevented in corre£Uiig the fevenl Coorfei fteered by die 

Compafi, 'to the true Conrfe. 

The Z*/' £m, Ltr, and Ha^-Mmtu Ghtfi, m well known, I7 Stama^ for their great U^Uty in fitrin^ tax Skip, 
and mtafiiniig her Wig through the Ocean. 

When the Lig \\ heaved. a> many Am/f and ttuhi of Line at runi off the Rtti, while the Half>Minute GUfi nina 
oat, fo many Milei and Tenthi of a Uile the Ship mna in an Hoar. 

The Ha^-MtBKti Glaffii may be proved by a Thread, and a leaden Ball at the End thereof, hong np 39TV Inchet 
long, from the Point of Sufpenfioo of the Thnad, to the Center of the Btdl. Which Bait being put in Motion, will 
vibrate exaCily in a Seemd of Time ; and if the Gia/i mni ont while 30 Swingt or Vibrations arc made, paft the 
Perpendicular, then ihat Glaft it trne, othcrwife not. Another Proof of Half-Minate Glafles, it by one 
already proved. 

THE 
afniMler agree nearefl wfth the iioth'ParC (the Nurniier of Half-Minotei in an Hour] of the 6oih Part of a' Degree 
of a great Circle of the Earth, or a Mile, by which the Knot-Divifioni are computed. Bat the Log drag^i^ 
(bmewhat after the Ship, tneaforet her Diftance thii Way left than it ia ; and therefore, the Ufi Divifiont of 4; <x 



I Kutii of the Ldf-Siu are judged bell to be 4c or 46 Fm afnnder, betwixt Knot and Emt s though 50 Feet 
agree nearefl with the iioth Part (the Number of Half-Minotei in an Hour] of the 6oih Part of a Degree 



jG Fill, between Knot and Knot, are foond to agree beS mth Pradicc. Some Navigaton, iu our Time of nfing 
by 42 Atf only between theXaotti which yet, by 1 due Correfiion of the DetU' 
ntiont, have fome Timea very nearly agreed witH making the Land, after a Ions 

WajKge. And, in the Sta-Pbraft, it ii alwayt btttf fir tii pdatittg te i* a-htad ef U* Ship, tha» fir thi Ship to ft 



by freqi 
kui, in 
a-btadcf tit Sicimag. 



It with Refpeft to meafming a Shjp't Dillance by the Log, if her Redcooing wat kept by Dtgrtti^and H^drtMh 
Parti, infiead of by D»rut taJ Sixtitlh Barii, ai at prefent, there woald be no Troable of Redoftion (at Mr, 
Emtrfin obfcrvet) of Degrees to Minntei, sad of Minucei to Degree*. And the Knott of fach a Ltg-Siu, 
meafnriag Hondredtht of a Degree in Half. Minntei, woold be, 37 Fiet afusder. In which Cafe of kecpino a Ship'i 
'uinine, nnltiplyine tbefe &i<^ aboveDrgrnj by:6, the Procnfi of the ift Fignre with what it carrieafrom Ue 

wonld give tne Miles above Degreet mtataUf. And cntdng^ff a Fignret to tha Bigbt, front any Number 
of Cra/j, would give the Degroet and Cmtj over, at once. v . i 



of Ships, and other experienced StamtM, cfiimate the Ship*f Diilance failed, in an Hour, at od»r 
wing a C£>> over Board, by the Motion of which along ihti Ship's Side they jodee o:' 
And a Shij^s Way, in the Day-Time, may be nearly cfiimatcd by obferring the Moiioa of tho BAhUi 



Some Mafitr 
Interval,, by throwing : 



of tbeDiilanoc. 
or SM-A4>t 



paffiog by iheShip^t Side from 5rm to f/fn. 

But, for more EicaStttfi and CtrtaiMtj, in ineafiu1ng.the Ship's Way over the Ocean, the L»g ii generally itvt ereij 
two Hoan[andmaybcheaTed every ffoorifNavigatort pleale) when the Difiance, that Way meaforcd, andConrft 
fieercd by the Compafi, are carefidly ciaHid into the Lag^Btard, contrived with Partition for that Pnrpofe, at well a« 
for entering all Rmarki and Ofnrrtntn, that happen in a4 Hoort. At die End of each of which burvm^, the 
Ship's Reckoning for the Day it made up : but nottill after an Obfervation of the Son, at Vbtn, iataken (if t^0l*) 
by which the Dfi^&fifittaf (at it ii callM] la daily ud daly coneAedf or ajiofteau an<^~~''~ — -< " 
at Am, can be had. 



7H 

DigHizcd by VjOOQ IC 



^be R O Y A L A S T R O N DM ER 



M A Y-, the 15th, 1760. 



. Tte L O G - B O A R D. _ 



RtMMIK) anS D<H»i»ci*. 



») from S. to E. ? Left 
1. { or K. to W. { Hud, 
^«d/^ with Run. 

lUrd Gala. 
ime up Willi the Trilii, 

Jfa"" ' 

Lw-Wm, 7To<.k«Jt«/"in out Top- 
'^" ■ I ftiJi. {inCompmr. 



Oo Bwd Hii Maj«fly'> Ship, DREAD-NOUGHT. 



A DAY'i RECKONI 



Cl-Tfit 



t* Cttriat 



TiDer«4Koiin, 7 i-i"'W; J40» 19' N. (By 
14, itNooD. f Utfiiuit 111 35 W, f 00 






L M A N'l COMPASS. 



made good far 14H. 
W. 4° 17'W. 



MiiMlt Liititiide ]9» 41' 



D</. Z. 



,.67 

i 



D^amri. " Dif.UHt. 



lEiimefigHrt <rf Ibt 5aB<m'iCi»f|to/i ii lifrfiTllT phctd irr, 
thefi»r'«» of eierj Lsg-^a/rf, tt'gup in a Stiyiiitiregr, /er 

lOie cetuin reflifying the ftveral Courfei fttertd by the Compafsi- 

trueOnrfcj (nil likewift the fardrto »Bow torLw-Wej, » it 

_ an to be ttM fane Wjy nith, or cotiCtiry to, tbf aagtmasl 

Aiti Item tilt nfattdlriHtU oi c'itst.&\at xbe mtgauiea! iri the n-ir 
Coutlei, for cifling up a Diy'tKeclidalne, uln ihc Etiifif,lt^ts^,_ 
of Che ftreial Couifei rrflifitd, it it feen how much Navigaiia* Cafftn 
in ia baframntaC, foiV/tntott lHarinir'tComfihitiiihti, by ibe 
piefent Variat'iai, fo at for all iti Pajnti to cornrpODJ wjtb the 
' Ntrib and Smb Pointt, and other Painli of (he Htr'tBoH. 

And, in Imiiariem of fo competent i Judge ■> Mr, Emtrfiv, we wouTd 
recommend thii nfifil Imfrtvtmm Co che Attention of the moll ei 
Meiimaiical hfinmrnt-Mahn, in Ladai. And to all Mafiir, 
ntfrmal^ ShipiA>r poHtog.lba Cue in Eia fU e f ! «lpiwu% b^ 
Authority of the Right Hon. cheLoiot of the Admiialtt. 



THE above DIFFERENCES of LATITUDE and DEPARTURES 
for the lertral coneded Ceur/ti and Dlfiaiicu VuD on each Cfjt$ an 
taken out, with great Eafi and RiaMmfi, from Che Stimaa't COM- 
PUTER, Na, I. And being /mw^ up in their reTpeaive Colgmnf, 
the Difteteoce of the Nenbiii and Scthiwg, and alfo Ei^tgini W.fi- 
iiig, will anfwer lo Half of ihe nbt/i (iiittft liij *v aaf*ud bufit 
1% Uiuri inn, ai ft iaan ia ih Ltt) wLich therefore bdngV»liM 
will give the whole JVwriiw or SfUiwf, and whole £,^;W otffWfir, 
ai tfie EXAMPLE (hew.. 

Then, ^iiMiiA'ii:HalfdteDiffotnc«ori.atitvde }g' ftcm th<L«- 
tit«d«4o> i^' itftttaifnita the fgrmer Daji, tht miUli LgrinA j^ 

Aai.iAi Cpf. mi J. Lat, : Red. :: Drfart. 1 Dif.Ltag, vojx 
in fieri Rum i uidditreti buc little from Truth In An^ ffm, 1; 
be proved ; notwilhRanding cbe groundlefi ObjeAion by rhe late jUlbir 
of lit Sphrelial Navigaiia; to Chii afi/ul RULE, or APPROXI- 
MATION. 

Di/.Lal. Dtp. Smll 
BUT, 7«,76)i..j4(,i7Bo, Agalnftwhlch, in COJtfl'UTER N», 
. aoStrCiJ. iDQOo, in C^ Departure, ftandi 15a 31' the Cerrfi, 
S.VH^trAii, DMd(BMd£]ri4Msaca. 

~\Ccm. mid. LtlADifart.Wifi.firDif.Le^. 
A«ain ( co» H' 10'. \*;f.H T The Dill, it alfe 

■j Camtuier S. taken It the i. I i.a; f had cbui, 79.6 by 
N'. (l. I Courte. .J j -39 f Irue Courfe, 

U.3 I •7-51 LMginde nqoictd. 

THUS, all tti DiftmcB ifLtr^tudt I* thi fifareti Ct^rfa, it 
Dttj't Rrciining, mayhf fiartd firiad miJdli tai'<ioif aid Oiparlm 
frflfnjtd, ovriri-mguibttw'hfl&fumKi; lehrrb ,,„ fi, iraKtfn 
meflt iftK Aimitgc, iu a grtmi Dtid if Tr»M le Jbtw that Ivt 
cottcBhH Nt>igBt)on, if limiidmd fcfn*!' Depanura, fti Jntrai 
Hjlmii CmrJ't M a Diy'i Sun, agrtr wiib ibt LagiiuJe taktnfrtm it, 
CeUcSiaer alflrna if ell ib^ D'famru m a Day, accer£Kg lath, 
pvt and aliallfay ef /njlng Hit ZCfgiiudi.fir a Say's Rithfi/ng. 
— -.ncpirt flavigatv may Oioiten Trouble, an^fave hilAKrntlor 
Ta*/o, if he iirradyatufing the GUNTER'i SCALE OF 
PROPORTION, by Meant of extending the COMPASSES there- 
on, in Ibt U/i tf ibnr Tirm, It find a fMi-tb. And here it wiU be, 
AtCcfntmiddliLat. : SheConrfi 11 Difi.ran : Dtff.Ltng. 

Butberein werefcr theiVniforw toMr. EMERSON'i Namga- 
lita, for ample Sitiiradion; wbo hia eiceUedall Che Writen aafbe 
Sab^^ Sai £arigf,.£aaau. ABiL- PrarliVj; Jn i>ba fc hT a.Jga m on 
Cbis Fart of on WORK ia (u we faid before) fapflimaiaL 



yGoogk* 



iwJNAVIGATOR; 



3>« 



Of correCUng a SHIP*i DAILY RECKONING. 



ff. B. Tht Meu of the Kaott fei down etny two Ifouri iii the (/}£■ being taken for the iatermediateHoan, ira 
Rrfiiinmnt of neU/i in Praaici : fineC if it were, tlN Ix>e might be heBTed evtry Hoar. And tiU a i4ilb»J can be 
found of meafuring the Diflance and of fleering the Ship^s Coorfe, wicb lefi Douii and Errvr, heaving the Log cvcrj 
2 Hours 13 faScienc. For, if a Ship'i Way throogh the Water could be mcafured with more Exaaiufi, yet ai there 
will always be Unntiainly in tin Caitrf* made good, efpecially in Utb Stat, trtfi Wimdi, Jfrtia Tiiiti, Oamit, (fc. 

e general A&/WfbfconeCling alt Ship'aReckonidgs, (utteft by tl>Jiroi*gtbt Ltugihidi) mail foSce as foUowk ' 

RULES for CORRECTING a SHIFi RECKONING. 

A Ship'* Reckoaing ii coireOed by t*(pbfer7atiou of the 5ii«, atNon, as often as it can he taken ; by which, 
Doding year Latitnde by Oblervation, yon tSfcoTer the ^ruth or Errer of yoar Latitude by DtaJ'Rrcianing. If thefe 
two agree, then yoor Dtfariurt or LatgimJi are fapipoled to be risht, and require no Corrcf^on. But when they 
differ, yon proportion the CorreSim of Departure and Longitude, by the Error of Latitude, found ia yoar 
Reckoning. 

FIRST, you may examine if yon have rightly allowed for Farlatiott and LuW^, and made doe Correction 
of yoor Ceur/ef, and efpecially by allowing for Currnli, and if after reftifying any Miftikes yoo have committed, 
and again going overtbeO^nAMi, yourl^tudeby Reckoning and Obfervation will not agree, 7OQ may fnfpefts 
Currtal to be the Caufe of the Difference ; a* not knowing its Quaatity of Metiw. But, if yon know iti DiitOUa, 
orCourfe, nfe the fidlowlng 

RULE L For CORRECTION of DEPARTURE. At Ra£u : uTan.M^U */ thiCMnat't Dinaion 

•with ibt MtTl£aii : : /e Errer in LaliiitJt i tt CarriMim in Difarturt. 
If the laiiitJti will not yet agree, and yoni Conrie failed be sfortr the Mendian thantothe Et^arWift, theBrrw 
Itkriy to be in the i>i^». Here find the Difference of tbe lo/iWr and Difarturt fiace the lalt Obfervacion, 
and fay by 



Error im tatittiJt •.•./B6tl,artur* 
.ing ai the Ship 11 before or behind the 



RULE n. For CORRECTION of DEPABtURE. -^-^— Ai Vif 

: ia CMTiQian im Di^ha-e. To be added 01 fubtraSed, accordinj 

Reckoning. 

Bat if yonr Caurfi it nearer to the Baft or Well Poiati (ban ib« Mafidiaa, tlu S**w -U likely tt be in Ut* Cam/t. 
Here take the Difference of LatitaJt vniDipariiire &ftce the laA Obfeiration, a)id fay by 



■ Ai DfjwlMTf : t» Errvr ia LatituJt 1: Ji Difft- 



RULE UI; For CORRECTION of DEPARTURE. 

rtnct af Latitud* : roOTv^fa i« DEPARTURE. 
!!> If the Camrfit in this Cafi, be veiy neat the Eaft or Wifi, this CotreOion tlien, fo very fmall, will be 

KttdUfi. 

WHEN yon Iteer about the Mid^-Wtg, betwixt the £4^, or^<^, and theMr£f<t>, yon may correft either 
Cturf* or Dijtanci, wherein you concave the Error moftly lies : but, if yoa an not con^nced of one being more 
erroneoai than the other, yon may divide the Errw betwixt both and fo correft each, 

RULE IV. For CORRECTION of the LONGITUDE. — As Errnr in UtttaJt : A mtri£ima! Diftrnn 

of LatitvJe bitoaua lb* etmfiiud aad viftr<otd Lai'ttK^ u fi CtrrtBim in Dtfartitrt : H CtrrfSieu in LanptMJt. 
To be uddtd or fabtraatd, according as the Sbif U a-bead of the Reckoning, or RKimi^ a-btad of the Ship. 

ANOTHER RULE. Toknowif the ERROR of die S^j Ji«iMnre be in the COURSE or DISTANCE* 

M B, When the IM&rence of Ladtode is greater than the Departure, and the Error of Btikamg be in the 
Hiftiaet, it may be thus eerreaU. 

As Dif. Lai, 6j Rfchmag : fnu Dif. ef Lat. :: DeparturtbyRMckmimg : le trm D^artan 
(By limilar As tndnded in one another} :: Difiaate bj Uteiuutig : ta mi Difiamet. 

Then, As Ctmatd Dif. Lat. : ttrrtatii Difvtvt :: Ra^ui : Taagua Irmt CskJ*. 

O When the Sbip has 0ll^tDn the Rtcimm^, it is too little, and yon muft add the Difmnu t but the Rtetmn^ 
having ont-rnn the £'&/, it is toomnch, and youmiifi>£/r«?tlie Difierence. 

^ASS 



byCjOOgle 



3« 



nt ROYAL ASTR(5N0MER 



Lai. I Sbip'i Met. tlat. 1 Siifi Mti. 



K. I toward* N. | S. I towttti 



ifs Mil. 1 jj j^^ obferredTp-#«(/rl thuTLtt. by f 5A<> ottt rnn the Jf«i«n»;, 1 + 
f/KtdtS 1 Ltt- l>e Y M j'B.eAoikg.Vftntmw^out-rentbeSi^. r — 



Z^f. j Si,>-jM»/. j Z^/. | gfe^'j<frf. -^if^,^ obferved J"^a/«- "^thaii Lat. hyjRttJbmmi oBt-nmjthe 5^>. \_ 



towardi S. 



towardg N f ** 1 '^ f Reckoning. J Siip out-nrn the Rithamg, 

IF the Emr in the Dillance proceed from the hag, or the incorreflW^of mcaTonQg itt u in general tlie Ship'. 
Difta»ct ig grttatr than ii meafored, then you may take ■ Mile in i^H^^ a great Sea fbllows.the Ship i bnt lefa, 
when alcfsSca fotlowt. And irhrn rhr Taa'iiMnnilJ' '" 't'trar^^o OT^f^aiart '^K^'ti\)^i1A':^o%f ha Ifaf it ^ Hua 
the DiQance meafurcd by the Log. And the Time of Tides and thek Setting will alttr the tnie Meafare of d>e Ship' 
Way, which mall be obferved. 

REMARK on the/#r^i« METHODS of CORRECTING a SHIP'i RECKONING. 

ALL ibe METHODS ef CerreiHon hen givn, art but prtearitmt, vihile ihtrt ttrt m» ttbtrtt iiftudmi Exttft <wiM 
vie hcfoe fitvjn hj thjtr^i»g tht Leirgiliulr, at ntar at it praSkablt. 

The j^^fownf of fcYcral Ship»' Reckoningg, proceediiig together in the fame Voyage, id an Argument of their 
Troth ; ai their Di^ertnct may lerve to corred one another. 

The Retiming (in Loi^itude and Latitude] of a Ship jon meet at Sea, will fometimei be of Vfe to correA 
your own. 

Here you fappofe an Error in the Qwr/f or Dljtance only, whiTe it rtay be in both. Bot if one Error ba] lancet the 
Other, fo as to gire the computed Latitude near that by Obferration, then no Error in either Cearji or Difiaatt will 
^pear t voA yet an Eiror may be in the Laxptmdt, though you are not able to diflingailh it. And if the Errtr in bodi 
(^irjt vaA.DiJianet\\*»tu Waj, foas to make great Difference ID <he Latitude, there may be bnt £(//> Error in Long! 
odei which yet mull be corrcded \n Prspurtim lethi 'Srrtrtf Latiludi, by tkt freadiMg Ralu. 



REMARKS on B. MARTIN^a NEW NAVIGATION, in a SenwJ LETTER from a C^eJjxMha. dated 
ymu Che i6th, i7S9> 



SIR, 



TO tbe AyniOR «f the ROYAL ASTRONOMER ud NAVICATOR. 



I paxcirc, by the Sbccti TOD lent me, that you bare taken moR Paini vilh ^, Jl£tr«iVi Book thin I think wu worth che Time beftowed 
for 1 UD perliiaded Ibu AU«^ niS mr JMm, kh Siifi (tt Mab^) hj Sa, vbattae- ittfd- if La»d. 

Cootd one nttklun iIk Sw U «BaA^ a) a.MaD cid mearure the L^J, bdiI could he lake the .^^ of the C«r/( ai near ii one can take ■■ 
./Ajfitr on the Orcnind, with en laftmnKnt, thii Hrfinmmi, of fgsbeKudil NavigaiiDn, mighi be of rome ConrequeDct. But finee neicbs the 
CmvA nor 2>i/h>« nn be tiulf known to a aolh Put, lad often moie. It mun be a very idleTblng to intrndiice^r^/rCilnilatiaiu tocDrnQ 
aa£mr, which it no Way feoG hie Vrhro found oat. forwhatruch ■ trifiitr Emr ai thii inMionU to, iniDiy'tRan, ii rwallowed aj 
the other rrMJ Emri, which ate unaicidable. And thii XmU', at well at thore greatei onei, arc all eonefled u fboa ai an OUerral 
canbemiM. 

The only ^^Km that iCMiiIna to be gnrwered it, Wbetbat thia tri^iig and inbuffiiMtt Emr ii worth all that latarim Calcnhdon beAowtd 
,^hbj B. M.iahkFilitBadif I thinlc nf ; and if k, ta HArdieb, Ihinki miirwi/i, I hive Nothing to do with rtir, or they with m 
Aad alTo (wUch llu onanfweiabTe Ar|uinent apioll it) he cannot tell what Sftritt of ■ Spheroid the £uth ii ) the Puti of Ihii Book > 
lo contrKtiflinit, as to mike ihc ^xfoMririry in one Page moit than donble that in anotheij which il thovfore a hfifitl Thnry for 
NAVIGATOR to depfod on. 

the Motive of iBOvdwiog^vrelier AkT? ''*) thl* Henry bgr the Head and -Khoaldeu, ■ FV<9 more than Ufe, that the Pio- 

" " "■ . the RiibiHtnmratktbtL—AiflbiA -j know how well ha if icquuntnl with the 

'' ' Uckki hiaFancy, thai he wonld apply it to mtryTtu^, whtibirit fa' 

But, wbenhehucontmed hiiCemptfi, which ia lobe loo Timei more exad than the conunoa Sort, and hii Iftw titiaktl Drtmemtur, 
by which he can get theCgnr/ftaiiAfiiiiu'f, toA lb4 Difimie u ibe uwi^ Erailafi, it will be TioM enough then to take in the nutaitr Inifa- 
Stiu, fuch ai proceed ftoxa the ffbtrndal Figare of the Earth ; and get an lint v (wn Dtore (hat Way. So that it it to be hoped, froBi all 
thde Improvenenti, there wilt 'be no need, afierwirdi, to coneQ eitherthe Laiimdi or Lngindi, -^ 

' Dull only fortherlake Notice, that, in the Pnfiut is kh Stnmd Part, he fayi " be hai added the Mttbaoc Pnaciflu tf Ittvi^iam, at be 
III not leen them in any olhei Tttatile of thii Kind," which ii g rmlitmbipmu ; for he hai, or night bate, reen them in EMERSON' 
NAVIGATION i except be waa refolnd to OeNothing bnt whnhe did not like. Bot be ii fndi a mm!;! Pra^War of ori^nal invcMian U 
r, thatbeJinotalhanudef M^TS^j^ helayi, mat frotn KiJMa bi tarrvai bii JtUa Mttriali. 

NEWTONIENSIS. 



DniBNSIONS 

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Mi -N A V I G AT OR; 



51-3 



DIMENSIONS KcA WEIGHT of-SHtTT. 

TO Jiltrmrit thi Wdght d/ an Irm-Ball Jram ill Diamuir hting givaii md the DlimHttr /(tm ihe. JFvght ! 

FIRST, Ai 3.i4ifi : to t :: fo li tke Utiafnre roniid ad/ Ball : to lU Diftmcter. 

NOW, Ai 100 : to the Cube of an Iron Bail's Diameter in Inchei :: fo is 14 tothe Weight of thatfiall i 
Poands. 

EXAMPLE. If a Bell mt^urtt \\Imhti rtanJ, rtjmrtditi Wiighit- ... . 



[,eq^. 



42 by too = 4100 

Divided by 14 = 300 Its Log. = (.4771213 

3,1416^ 6.6948 = io.i7750i»e7*/W= .8257071 

*- • IllChes rODDd the Ball. {, Its Na. 6,6948 In- 

■ ' ' [chei Diain. requirtd'. 

^ TheMrthodtf Jirt^liHlaSbip tbroagbSiinAi, iMf a^vhoot, Ot'k\vet'*MaaA,hy Staand Land Marii, (fmcb as 

Buoys, Light-Houfei, Sceeplet, Windmills, ar ofW remarkable O^^ffj, nmri'ueA erfixiden Purfeft) h imivn la 

■n txpcricfjctd Navigator. But fhofi •u.-ie defirt Satifaaim btrtia Si^xas/iiit. Mr. KMERSOH-'j NAVIGATION, 

biandki. iee t.\{o 'O.it Mtihanici (comprehending all Other Books on X^it ^MyeSt) fir eomputing iht Farti rf a 

Ship's Tackle, which he has partly exer; plified in ijj Navigation, ^. 63. making iLt Farct sf thi Hand ta thrWtighi 

in a particular hjlanti. to •wLicb diAinguifhed A\5TiiO^,andiii WORKS, ivi ia'ut/amitiais Inta bibeldm fa 

Judgmtntandlmfrwviminl ie tur Sub/tS: ffb» fam/m/ti alihii Subjefta of Science, in ibe feweft ifardi end Jhortell Mttbed. 

',• THOSE who chafe to fail as near as they can by the Anh 0/ d great Cinh, or to ufe GrtatQ'rc/i.Sai/ing, 
it preferMe to _^btroida/ Saiiing, [fnppo!^ from ihc Cafii of fii^xia to the C<tfl« af Good Hop*, or from the Capt 
' " id Hept to Capt HornJ may compute the Ancjles of Pofition, Length of the Arch betwixt two Places, and 
idea of the Arch, to every e or 1 o Degrees oT Longitude, by Spheiiig Tngonometry ; and then the Courfe and 
Diftance, from one Lutitude to the other on that Arch, by Mircattr Sailing ; pracing [he feveral conftant Courfu and 
Dijlancfi thereon, in a Taitli for putting in PriAice, ai near ai pt£ihU, .For the Anfiseri to all iht Ca/ii y right eaa 
thliqmanikdJpbiricalTriangln.frtJuylbir m; hiing ibt Prindfli, and Ground, fl/Praftical Allronomy in tbifirtgang pari 
oftki Wark. Tt itihich Caft, are addid numtrous Jfiilieni and Proptriitt of TriangUi, in gtniral. 



3. 1416)14. oooo(4.4c6 Inches, 
Cubed = 38 473' 
Multiplied by 14 = 1238 691 lb. az. 
Divided by ico =: iz.jSy^ iz 6,191' 



I/lbt ITtighta/a Bali bt 4a FaumLf njMndHt Din. 



PLACE of TURNING to WINDWARD, and Diftance of a^^-LAND. 

TO eei^ititVl.fiC^a/tiSbip'iTurmngtelVituho»Jfiait«r»atbbtriMieaded?pn, »r 0\iie&, Ij net Tadi 

WHEN a Ship or Veflel is dole btad$d, ihe lies within about $( Points of the Wind, or 61 ■ $z', on eitlicr Side ftfitj 

LET D be the Siftann of the Part, or OlgiB, at the Place failed from 1 

A" the ^ of the Conrfi failed, with the Port or OljiB, on the fame Side of the Wind t 

Then, (a" 52'-«A<=z.of the ^k/ and /■«r/, «t the Place laihKl iron, on the >Mif £i«b ^/jf Wind 

.. .' . . ^. I. . . \ : ' . ■ [-ufHt tit Onrji I 

And z X 61 • s 2' — A> = Z. of the Cmrfi and Pari on the contrary Tack, or Side of the Wind <b ,£. U 

.:•. [the Pa ri or Qjfta ; bct<Jeei(th»Htae' failed from, and rfoi of totnhpgw WindwVd, orTadilag' 

- Alfo, 180" — ix6i»j2'=s 56* 16' = .^'between the Place ^i'j!b!/^<in -and intended P»H, at the Place 

[of Tacking. 

Tbtrtfin, As Sine 56" 16' : to D, the DiKancc of the Rirt ftom thcPlacC of Departure; :: fo Sine uj» 4j.'_ 

[A* : to Diflance between Place ^'jlv/^in, and,that of roffcW, or Turoingjp Win^wWd,, r>ai«'«fl', 

t^ fbtriattff'Tiirm>^um0AuardinaX:iiT't>ahAJ.'ltffitv;ijiA^miHedtrigpinm^^ '• \ ; \- 

Ta etnfVt lit Dijlaiei 9' o HEAD-LVt^JD. ' «r CAPErM-fiEA '•' 

SET the Angle of the Hiad Land, and your Sbip'i Wef, hy the Cnmpafi, and after Sailsug for {arm Time oimikai 
Courfe, fetthe Angle of the Hfad It^tmdmi yoor SJup'i Vlxf t.fiedhJ Tim« -,. Tlieii, Say tqi.PROPOItT10N,.>onl 
the Tables of natural Sinti, 01 by Lagariihmt. 

As tht Sim af the Sgnutindtr aflir tbt Snm «f ihtfi Jngbs ii tahtm from 1 80 Dtgrtn ': ta Diftanct rum iii^etn taiinr ti^ 

ir&mdiecatiA Angle, :: fa ij Sine tf tiibtr Jnglt taiiM : U tte Sbi/i Dtfianei fim lit Hud.Li 

•witb ibe Sbip'i ffttf, -wai taken. 

<S- The Connexion in this Page, and another or two, is at the Copy could come in. 



•Land, luhtn the athtr Aigh, 



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3H 



tht ROYAL ASTRONOMER 



TO mtafw tit TONNAGE. *r BUATKEN tf * SHIP. 

THE Ruletli^Jowii, bj' fercnl Authon, innibllow. 

RULE I. Divide the ProdaA of fccr Bratddi. half Bmdih, awl Ltagtli, lo FMt, by 94, and thcQwMicM will 
pve the Tdiu of her Burthen. 

RULE It. Divide the Prodoa of her Length, Breadth, and Depth, \m Peet, bj 100 for Shipi cpf War. <««; 
for Merchant-Men, dut allow Nothing for Gout, and the QootiQnt wnl give Uw Bnirthen is Turn. 

RULE in. SshtnA two Thirds or her Breadth from her Lengdi (mciiAired JFrom the Stem-Poft to the npper 
Pan of her Stem) and the ProdaA of that Remiinder, the Qreadth, and Half-Breadth, in Feet, being divided bv 
100, or 94, will give the £«;'), or lAre^BMr'iToDDage, refpefUvclx. 

RULE IV. A Ship'* Tonnage, orBonhen, i* eqoal to Half the Weight of Water ihe will hold. 

N. B. Ihtrt is filth a faritty in tit F»nu */ Shift, lh»l m *•( RuGean miafmt thtir Burthtni txaafy \ hat tht ah»vi 
RaJti art tb* mtfiiaitralin PraSkt. 



POSTTFON Of the SAILS and RUDDER, in Working a SHIP. 

Oi/trvalian i . P/adng tht Saih arcsr^ag to diJWtmt F^iata im StfftS tf tht WtoA wiA Ship'a Way, havi more tr 
leli Farce ta irma tht Ship ahng, tr turn her ahaat. 

Z. Thi HiedfaiU kirp tht Ship ^0*3 lad finvt to maki in- wwv. 

3. Main/ai/tiMVithtCtattrtf'Gravitja/lhtShif. 

4. Mis:tii-fiu!t firi/t It itif htr Jraa Stteenag haeivjani and /trviorttt aiutttfiretherStetnttlittWKA. 

5 . Sai/i hmit atri tr kfi Ferct iht Itrttr tr Jlackcr thej an bmfitdi 4 hagpifg Sal/ Jraviiag le/s than out that it 'uitl 
brijitd. 

6. Tht higher a SaiJ it htijkd lit men tPind it rtaiva it ^a^a tht Shif aJtar, tr tara htr aitat. 

J. TTien a Ship giti £n£}fy it/ore the WiaJ, anjeniSml pUud at right Anglii •milb kir If'of dravit viith iht grtalefi 
Ftrtt. Bat finci e»t Saii hindtri tht Wind fralit aSiitg agmafi aaathtr, hiing all plaad tm that Ptfitita, if tbn aifrectivt 
thtUfiadaHut ^g lttftibmtt^Q Dtgrtt t tit j v ri Ht h aw ng ti i t r •witth tit gniat^ Ftm, 

~ WitSaiLdrttvmertthaadrfOaa. 

^ f^ nearer tti «r fiiitberyram, a right Jngli aig Ship'i Sail ii flattd-uiitb tht !Vaj t/ her Cear/i, /£/ lefs «r more 
Lte-IFarJbi m*itj. 

IQ.YhtHtartr thtWi^diiimlh, er farthtr frtm, /A/ Ship'a Way, theXcKxtrnxat^Ltt-Waj flHmaku. 

11. J^/4rPrindpleiof'Mechitti(3, tht ^ii'i^v»tnibt Wind airship's SailM/T bt aitut tftice aimathojtlk 
Jnglt httvJttn the Sail oKd tht Sihif'% Wa;, » Zu/near tiefFiad tuith ti>t griattfi Mtiitn. 

12. If iheVmA ii ahnijl i^tm til Beam, tit Hagli Selvnia the fFiad and tht Sail muA it ah»t oace tni haif lit j/aeU 
iflmiiia til Sail aad Shi^, tfof. 

X. ff" a Ship Jklli atm>/l itfilr* the fflad, tit jitgle^l^utem lit mad oKd^Shifi SaHjMJH Btabtat tjaal f tht 
it iitoDim lit Sail and htr Waj, Ml theft Fejhitni tf tht Saili art ateefaiy It givt ihf S^ li* greateft Modon 

-14.. TPene^ffiaSbifi ta»iit H tht JPiai'ii'i'g ahttt^i.Pfinli.tr ^Dignni.liniagit^iifuitia thiW'mi aiidSiii 
iiaiil/ieaimt^i''f aad tit JagitielwUM tit &tSmdtit ^g't'Vliy^tr K^i ai", er'nearly./* t^ R«tio, it matt 
ier gt fafiiji mWitAwuA. 

ij. ^ /be Wind ii atarfy /^ lit Stan, ibt.Jiarfir tht BMJ-faili art fit ihtf havt tit aurt Pivier U turn tiaSinf\f 
HeadaStat. 

16. If lit ^iHtTi W^ ht luarfy ibi fam atlbt'S^p'iWtfjt thiSul ti^btlo maif ■ 0t- Jiigk V>iih tb* Sbip'* fr<? 
of 54*, It htm htr /atnift aheal. 

17. Themf/lptwrfiiiPffititHeftht Ai4^tefimtirSi^.si»lit,l4tiMwamputd,fitmPriilHftl rf-Muimiiti and 
Flatdtai, at an -^glt •witi lit Keel ef ^a^ Degreii, 

iB. Tbtfi^iraSinf/ailitbiiiUP'^aa^ifibtriitlm. 

tq. fffi>tJaikJ»v,^^U fiaru^./ktr. .Aatbi mift Jbt bttb ^ Itfi Jbt m/iMri btr-Htba, 

See Mt. Bmm^'t Nav^gadon. for further SatitbdioiC 



DigHizcdbvVjOOQlC 



4nd KAVIGATOR. 



a'tf 



Tie PROPERTJES of MAGNETIC VARIATION, 
Ft^trij I. V«riitioiiiii.^MiC{P)«ath«r'£.«rW. Varidcimof A* magnetic htm ^k trMt'HatAtoiau 
t. VariwioD in ^Hoiiitj h tke Number of Degreei (E. or W,} of tbe magnttU from the /rw N«ili Point. 

3. '^lthe*Mf«rtV Ij^Tiriwfr. ASftwIg Iwirawbthe ^^^ Botk » t!ie&^of«Wfaia«fr.P*ta*, 

4. ^^^XAewuiffutie i^'lTarieifr. the *«* ^ g ^ towwdt die |g * Bothtotheijflofthelknw/^wPWw, 

J. AI1thein>^^» ^nV;aTecarriedufitf aitotlie < rj^^<>f^ ''ii>e '''"'^'<*' " i^ ^ Vuiatioiu 

7benfiri, 
6. The tine Paint, jJtdmub, or Ampttti^t, (to which the coiYerponding wuffittic Pttnt is ilwari direOed) being 
reckoned An the Ante m^iuiif Cmtfafi from N. or S. (D the E. or W. lies the fame Way with the variation, to the 

V^^*\Qi±t magnitU Ptiiit, Jxim»ib^ CT Af^Stmlf, ai linch fti the fWuiA* lies Co the ^ ]^|^' | or ^ ^ ofthetr.N. 

Tbele^TOpartieiveeTMetttbya RRCTIPIER, or & nrvMJjb Conpalt dn %jiictimt. Hence the folloidng 

RULE5/#r Jittrmnng lb* ^taliiy and ^uMtiij t/gu^utic VARIATION. 

Ital* 1. The5iVjra/ini of thvtme Aztm. or AmylitadeJ J^V'^T.of tbe roagReiic./&i»t.or5E- ? v W 
(reclconedonthefaH]e««p»*/«C*iV*';beingwtho iiv? 5 ^^. ftiewi iW.J sanation. 



2. The Dyf< 
r. The tna a. 
Or, »/jr«r a , 
^MW K'gwtlic Ctmpafi, 



or DiiTeren^i between the /nvr and magirtiic Azimuth or Amplitude it the ^imntitf of Variation, 



/. The/™«and«tf^*;^Amplitode^J^^^jJ^^°'Jg itheir|^£;^ in Degree, is the Qumtity of Vari: 

Off '/ jwr abuajt nelan tit trvt M«d BOgMlit AmfUtudtt from tbiir n/fiaivt Norlb Paints, and thtn touat tbtm u ibt 



3 . At San-Ri^nf i n/°° tj^ \ AmpJitude being the grtaftr, the Var. ii ^ ^ i But ^ ^ ■ ^ At Sia^tt/m^, 

Or, i/jii ahuajt rtckan tie trui and tnagnttie Aximuthi Jr»m thiir ri/ftSivt N . Paints, and thim ttant ibim ti 
inu magnitic Caatpoji, 

4. IntheFBf«>w«^j[j'" ^jj^ ^Azimuthbeingthegreater.theVar.ii^^ ^Eut 5^ In the45rt-«««. 
N. B. Tht ftfi Hull ii gtn^ai, tmd aa/^trt alt Cafet that tM hifr^ftd. . 

I Mag. AmplTme Anp.l 
15* E. n. |29'£- N.JTrw/tothe/^of «uinr/)f Amptitade. 
6/fecondRnle .... Dif. 14* . . VariatioaW. hy itiRiU. 

Or75^N.£. . . 6i*N.£. Magn. Amp. greater, thercf.Dif. 14^ W. Variat.bys.jfujr. 

SxoBf/t z. At Snn-Setting [ 8* W. S. {14* W. N.l^tw to die Ri^i of magnetic Amplitude. 
By fecosd Rule .... Sum Si" . . Variation B. fay ilt Rule. 

Or, 9g*N. E. . . 76* . . Maga. Arapl.{rf4/?, thcrcf.Dif. 22«E,Var. by 3. fv//, 

IMag.Axim.lTr. Aaim.l 
10" S. S. ]i !<■ £. NlTmeto the Lt/i of magnetic Azimuth. 
BylecondKola .... Som it> ■ . Variation W. by 1 fl Jf»/r. 

Or, 100* N.E. . . 79"N.E. Mag. Aaiin.fre«/»r, tberef. Dif. ai» W. Var.by-4.J?«A. 

Examflt^ Inthe^miMB. ]3O*'40'W.S.|i6*i4'W.S.|7'rM to the Rightct the magnetic Azimnth. 
By fccond Role. .... Dif. 4 ao . . Variatioft E. by tft ff»Zr. 

Or, no«4o'N.W. ii6«i4'N.W. . . Magntiic A3iraai\i gnaur, therefore 01^4" z& E. 

[Variation, by 4. RuU. 



PRACTICAL 

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3i6 



Th* ROYAL ASTRONOMER 



PAACTICAL RULES fi>r finding die LATITUDE of the PLACE of OBSERVATION. 



Tbt Meridian ALTITUDE anJ Declinition »/ Ot SUN or STAR, giwrn, 
CASE h JFhtrtti^OijtaiSUtiot ST AS.) rijii amj fauUaMmiai Riv»Lli*a. 
Rule I . The Digtrtnci. Uiri£mAbifJt andDiiiituUin btth N. «r bttb S, 



Rule I. 



Zenith-DiJUncc 

The Sm». 



^ TlwLttitode {J^ \ N««ofDecIin«ion ^gjJJ^l^l'.nAeZeoid.. 



Mtridian dililMdt atid Dtdinaiian oat N. thi mhtr 3-. 



5 . DiAancc.. 



ZeniA-Diftance 7 TheLatitude j>»r Naac of Dedin.tidD. 
Decimation 5 Z 

N. B. MtridioM Altitude, #r Ztnitb-Df/hnet S. (r N. ««mw ft r^ S. «r N, «/' fib Oifiroir. JmJ Zenilk-DiAaDCe u 
ibe CempitntM of lit Meridian Jttiind*. 

Exam; It I. Oa rbi i6ii tf Miy, 1760, m/ Sm. Q ExampJt i. Ow f^ 18/i {^December,- 1763, «/ Sm. 

To Son'i Zenith Diflance ...... zfi'^S. HFfOm Declinattoit of £jv7'«r . " , . , . 16*13' S. 

Add Son's Declination ..... ^ . 19 16 N. uSabtraCl Zenith Diftancc of it. . .- . .- 10 9S. 



bmn (by Ai^) l^Lat. ofPlaceofObferv. 46 

^Mjuy? a. b»rA« iiiie/}iMe, 1761, 4/S*«. 
from Sun'i Declination ...... , ' 2}'ii'N. 

Subtraft Son'* Zenith DiOanix S 3{.N. 

^if^{hyR*/e I) LaL of the Placa . . . »+ 37 N 

CASE II. »Tm-i thi OBiZCT (SUN or STAB] luilhtrrifiior fttiim a^Mrnal RivtlMiim; tutttwaiii tbtiXE. 
RlpIAN, t^put th4 Herisun, tn ibt ttnlraij StJtt of tb* ilevattiPtlt, t*orce in t^ Haari, 

Role J. The Swn. fZirSUN m- STAR n tbt MtriMan b,l^ tb, POLE. 



o N.OAy. (t^fin&i) Latof tbePlacc- . . . 6148. 

" £x«mplt 4^ Oi,ihtrifi,fJ^wfi, i76^MSn. 

To Zenith Diftance otFtmalbmHt, otirigblifi 7 

of the Southern fiiAci 5ii>ip/N 

•■"'""■ ....... 3. I S. 



Add Star*! 

Swm {by Rmlt a) Lai. of the Place 



Meridian Altitude ? ^^ ^^^j^^jj^ 



Comp. of Dedinat, 
Role 4. The Difftrtnt*. 



of the fame Name wnth the Decliaation, 
7h* STAR M /i» MtriJiM ahavi ib» POLE. 



Meridian Altitude' 7 
clinat. 5 



Comp.ofDeclinat.J * "=""■"""= { 
Exampli I . Om /£« I lib' of Jiine,' 1764, Ktar Spitlber- 
gen, Greenland. , 

To Sun's meridian Altitude below the Pole . . 1 3* 9'N, 
Add Complement of Sun'» Dcclinatioa . . 66 47 N. 

Sum (byJ?>/r3) thoPlace'i Latitude 



The Latitude i of the fame Name with the Declination. 



79 S' N. 

tampU z. On the \oih rf July, 1761, at Sta. 
To SuDi meridian Aitiiadc below the Pole . . 6''i2'N. 
'4 « N. 



Exantpl* 3. On tbt iJ of OAober, 1762, ai Sta. 
From the merid.Aldtade of Northern Pointer? 

ofthe^fM(&«r, above the Pole . . 5'70''i4'N, 
Sabtra^ the Comp. of the Star'i Declination 16 j 1 N, 



Dlf. (by »*&4) the Place's Latitode . . 43 13 N, 
Examtlt^. On tb* liii rf Mxrch, 1763, ^l Sea. 

To nend'iMaAhitu^ of the Fit/ «f tit a^tfiti "" 
belowtbe PoU ........ 

Add Comp. of Star's Declinatioir 



XWiS' S. 
z8 13 S. 



38 4' S. 



Add Comp..of,$up*i Declination 

bun (by RiJtt) thePlacc'i Latitode . . 70 59 N. Skw (by RaU 3) Place's Latitude 
SuotbirRaUi, in praaiialJfirtmm, F:i^, 191. 

RE-MARKS on IL C A « E. 

T. WHEN ihtSineiiiimibtfifmJifhdra, trd a Sttr ama f tin MMriditn if tin Jmi PUi; tat tbim miiJ hdov lit ftmi Ftt, tain 

i^H-mri, lit ItHimdi ef itai Pisa ii «/ riffimc Vime wirifit Dccliutiaii i^rJwSuii (fSnr. AiJ rbi Dxli'MiM ,f ibtSvnirSxa, u 
fucb a Ci'OimftmctBmJi tei^aiA It, ir gntVI tbanltiamnjimnutf lii Pilt'i Hrigit, jtJ ibvffuri, ailbi Swt'lgrMI^ DteKiialiteii t^* iV ^, 
itiCtt^Umnl 11 Geo ji' ^, -Bilhbiilbi lafi LaiXtudi »t iht fame Name wilb tbt Siriii Dallitalia, tuim lit SvD cam caM, It ibi Mlriiiaii, ahev, 
ihtHtrixmatdt'ltalbi fawuPtlatviitfiai^fiiun. An^lbt IteJI Ltlil,^ vbtri a Star can tmn it ibt MrriJita aievi lt< Harix'm, w/lbavt 
■ni below thtj4mi Ptia, Mrlit I- «4 Hiart, ri limfirt tbt Complonent tf ibt Siar'i DkHmiIoo tf lit f-K Ifrmt mlib ibt tItvaitJ Ptk. 
: %, fbiSan, or aSiar, ttmingitibt Miridian \x\o\ii lUPtb, iavlxi il nJ tbt Hariium, ii lia al itilta/l HdiriJuv jibitndt, nd amini Kti, 
/UiriJitam tbt m^riuy Sidi tf ibt Ptit, it titta at iit pvalifi. 

' %, Stmt Sieri {vboU Carnf. of Dcclin. of.tha fiiDie Nwnewitk thaelentgd Polctii IcAdua thi Comp-ordic Lxx.) ami It lit HHridiat hhvt 
ittfilt, btttvixt ii "^ 'bf lltr/'ain, amiabxt ii, JHwijM /<(( Pole mi^ Zeoitb (f but cb* Shb nmr umet). mibib' ptm^ mmiam Abitaia. 

L. Etirrf Star ctmiir II ibt HfiriJiaa bctw etJ ibBvt itiPr/c, ml Ui lia/l' tiU [rulif MiriiitH jtbitMdit, rrfftSivlf, ii aJwffi II lit tfartl. 
■OMrd^Bbwttbt NtrtbPtUiilitvalid, tr alvitni it tbiSaubaarJ, nberi ibt Stmlb Ptit ii iltvaliA. 

c, Him Sttri (wbare Complnnent of Decfiution, of the Ikmc Nune with ch< elcnted Pole, ii gmWr ihan Ike Complonrnl of Latitude) 
nmi It Ibt Mirifua bc]i>w Ibi Piii aeJ la ibt aiautij Si4i rbtntf, h^mdtbtZimlibilvixttbtPtbaiidlbtEjaiiHBitJ, (wbett the Sun comcij 
4> Ibar tr*al^ Mtri£an MinJa. 

r^ For thofe Sttn coming to the Mertdiin bctwiit the Ztniib lai EjniaeBial (eonung alia aadeHtbe Pcl<^ but oem between the Pole and 

Zenhb) tht ift ai Ml %i Rala (in Cjft 1) fttvt to find the PiKt'i Latitude, 

Otpifbicat 



and NAVIGATOR. 



GugrapUtal RULES for finding the ttAular Hifitrtnu of LONCJ'tf UbE. 
7iJ!iiilb4 DlFF£RENCt^ «/ LONGiTl/DE •/ nut Flata, Zatdimg U tbt old Wiy =/ nrhn'mg £. Longitude, frm Ibt Jfisai rfftl 
rmwdtbf Gloii. ' 

Boaiid ft. Idi to peicer Long, 

,»__.■ Jltft J,.„,-_>Diffc«iiceof Un^fl-de . , . )B, 

i«^ \ Re"""!"' J^Mrt J"^''°"'iT.kef™m36o«.em.Dir.LoQg. J W. 

b Long. 



'- 'aPliceia«'(rrfra;(«ri<aewWi)>i/JlMlgjU'i{£. trH^. Lti^iait jnm'ibt Qtiny AtOf, 
tr Mclropolii »f mj Nation, 

r I Dlf. LoD^lude ? ^ } '^"'^ " J E^"* \ t'lgitudc 
B.]thW.Lan^tu<le ' 

O.ieE. Dthcr"' ' 



r W. LoDg, 

N.B. M>. Alkintbn, an jtalhir im'Vopa, btigiva Ra/a It JS-utlbiDif 'f Lai. ti. »r S. frmm Lalitada give*, hiif/.rS. trtniN. a 
imtirrS. Mt u ffdtbi ab^ IM.N. or S. fim — Lat. N. wS. amd D-J.if Lai. N.ir S. mtm. Bui Rxtioa fi-Ji ittlt, mibthtiuA 

klKotion. Wbtnai ihirt ii7mhli le tbt jlitt ' ' ' ' -...—.' ■ . 

tkbittibiaittniafjRiiIti, ii /,riv,iii Miflaii. 

EXAUPLES of finding the DitTcreEce of Lonptiiae bj tht OLD WAY of K: 
LoBgiudM 
Exam. I. From Uavaaiu ij^a 41/ 
To y-BiM jco 6 



Rub I. Diff. Longitude 
Exam. 11. Fromiarfw 



2S W. 



DilF. Longitude tt 

76 37 W. 



• ntLat.N. ctS. aad Oif. ef Lai. IV. tr S. ma. Em RK^oa fii^ Ittit, VHtb li 
I, viht* tbi JUinJ 11 tngapJ, ii fiiiJ iy tie TJiNt v>iitb Ifij ibt Lmgiiiula He, nbta u 

o tbc LONGITUDES E. beta fBBM. 



Loo^Endc* 
I. III. From Cupc tf gtii Hip< jy 



Rale 1. Dif. Lon^tude 
EiAH. IV. From Cr^ Um 



Dilf. Longitade 
J ... ^ . . _ . Emerlbn'i Navigtiii; 

EXAMPLtSoffindiM«ficDif of Long, by the NEW WAY ef Rkcxoh: 
~, Idniitudei 



Dif. L 



Stlt X. Diff. Longitude 
Exam. VI. From LtxJir 
Tli^LimrJ . 

Suli a. . Dif- Loegitadi 

To Giirallilr 
tl„bi. Dif. Long. 
t/Uftm^intf £. IiDHCITUDlt rrci«t^/rtn r .. 

cibe LONGITUDES E,orW. ftomCrmmVi Oul _.., 

LongiUSct 
M. V. Tiomjaaaua 760 37' W. 
to Bariadeu jS. 55 W. 




Ruir ;. Dif. Longilude . . , 
EiAM. IV. VximCtftStm . , 
taCafttfGtUH^ . 



;» 3sj 



..j'.J^J 



U jiaibtri, and mba iba^ 



17 4» E. 



Rub ^. Dif. Longilndt 
ElAH. VI. From Lemba 

ToLixard 5 1$ W. 

KbA^. Dif. Longitude j 14 W. 

Ex.vn. From OmfiaMtiKf/e ig 51 B, 

'toCibraltar . , 4 jB W. 



rt*Ti« eteviA^fvi.riari actrdi-gutbi rt/ 

a*icfrrn<i frtmjMr^ah hj W, Moarti.n, r . <v j. 
AT. S. nb: rrpuiJ Umgiiudn if ihtf, FUca aa JliU iiffert*; la £go 

illhr fxediiumrrmm. B»fc 5. Diff. Longi 

More EXAMPLESofiindlnfichcDiA'ncnccafLiuigitiidet^lbeNEWTAYaf RiccofiKO theLongituJei: 
Longitude Lopgimd* 

EiAM.VIIL From Ci/NT Famuf/^ 46" 50"^. lExAW.JX. Fiora Pm/m loj" j' E.I Eiau.X. From ./«■ 

To Mnirelij Ifit 59 45 E. I , To WUnd Jat» Fcnaidri g» '3 ^-| ^o Pert. 

gtfr <■ Pif. Longitude . ■ . loS j^E. Ign&t. Dif. Longitude 166 ■]i Z.T Rtii 4. Dif. Long! n 



n Cncirwut. 

Lonfiiude 
•dpa 61" 50' W. 
>:SiUt ia 10 W, 






REMARKS 0* ine difterent biciXKiNnt ci tjic trrnftHal LoNCi 

I IT haibeen oblervcd, at^. iqg, bv Nfaamttrfii, thit the rri-rc^ria/LoagitaJdoughC to be reckoned fiom Fern, one of (he Canary lHa, 
:co[dini to ancient Cuflom : and ihiC for tlie lime Reafon tfait tlie tirl^iai Lcngiiudei aie nrclianed from the Beginning of jiriu, ucoiilioB to 
ntient Cofkni. In Trhich (ompuuiion of the teneAiliI Lon^iudcs, if lil NitioDJ agreed, the ConfoGon would be iToidcd new ififiirg 
'om the diJ&Tcnt Beginning) of Longtcudeimongdiflcnnt Nirigaion in the fame and differtal Nation). 

1. The lautudioi eicli Placr, oirihe Globe, beginiit the Eijuinoftial on the Place') Meriitian, andtetiniantKon ibatMeiidiia attheplace 
rbofe La)ii'ide i> fought ; by which, with Refeieiice to the EqainoAlal, the Quin-.itT of cadi puticutat Latitude (of Pla<e«] i> alcerinined, 

J, The (.s.'<^irW<of each Place, aa tbe CT/g^, begins at [bme diHani Mciidiao on the EquInoOial, where it ii interlMled by that Meridian, 
tetinirrJtFsoatheE<iulnaAjaI, wheteit iiinteifrSed by (be Meiidim, of the Place, whofeLongiCudeialbught j.bgi wtucli,. with Reference 
>foineoiher IMeridian. the Quantity of each partitularLonjitude (of Plaeei) it afLeriained. 

4, TliouEh reelioning the Irrrtflrial Lmgil.da roond the Globe ajltrlf, from the Meridian of an OtSavatirj, in aoj one Narlon, would 
equally. ealy, wiili rxi turning hom-Ftrrt, for ^lemiining the DiScnnte of LoDgiiude betwiitany ii»K<«n( yet,.by racluiBiiig.tlicLoD|, 

idei from Fimonly, accordlnj^ta origicaland antient Cuftom eltablilfaed, or from fome otiter Meridian anhvrfalff agriid en, we llioiild be able 
I compare the abfolute/.iii2iiv2i iTcenained by difleient Kanoni, ai wenow coiDpare the Latitadet, and Co arriTe at a flitl nearer and nearer 
nptoTement In botii. And each Nation wnid be able to make the fame Coirparifbs and Improvetncntftir cbemfelva from what ii done bjr 
other N*tion>. 

J. TheI'!^irM</'£«rinM!(ortwoPlKnit<ouiited on the Meridian of one Place, betwixt the Paralleit of bbth Placei. 

6. TheDUieicnceof LonpMdeof tAoPlaeeiiicountedOD the Equinoaiii, bi tnixt tbc Mendiui of botlfPlicei. 

7. Onwhaterer Meridian belwiittwonralleliofLttilade, the Difference of Latitude be reckoned, it it jUlltbifama.iirS'a 

5. By wbateier MetbtdtbeDiflinEeonthe'Eqt^Daia], or DiSerence of Lon^tnde ii reckoned bctwiit twoMetidiaiu, it j 
Jaatti^, which ia the Aflieftion of Longitude chiefly Icioght, and vhat li chiefly wanted, from whaCtrcr Begfnning Lon^to^^ . 

9. The ctl^al Lmitudti are only mnled from the Interleaicnt of the Ecliptic ind ttpino&M, at Aria or Uhra, to which eirer they 
lappeotobcneanfl, lot the PBtpoTe of computing the (*/$((ii/£)t(£wri«o in Aftnnosiyt to wfakb the ttrr^trial LatitMia in Geoenphy ai 
ormpoadenC and fimilir. _^ • . 'o. The 



I>« 



n, ROYAL-ASTRONOMER 



A JOURNAL of a VOYAGE 

1 N THB 

D R E A D-N OUGHT MAN of WAR, 
Captain CONDUCT, Commandir. 

„ ,t,,. .JLjillDd. M>;;'N.7ToAs*.iorMARTI.SL«. ■♦Mj'N. 

'^"""'^""■'il.mgi.^l.s igW.J NlCOta.h.»-;/!.M„ iLo»,6;™W. 6OTier,«wi Ohf»T.L 

D/f.™,™ of LATITUDE jj' u'S; Dipmt of LONCITDDE Js" 41' W. 
Th. c„p^ COURSE S. ;.. =j- J W.^dISTANCE 0. .h« <W/„ ;,£,. Ma«. 


£(ja« ow fffegisn Tborida}'. ti« 8rA d/ May, 1760. 


FnJajf, Afayg, 1 760. 


t>n Kaarrfthe DRE J D NOUGHT. 


Ho 


Courles 
(leered. 


Knob 


Wind. 


Courtei 
ctttTt&ed 


Points 


Dift. 


Kemarxs and Occu«rikcE). 


A Point i V.ri.Tion W. 

n-rfd^, M« S. 17*0, .t Noon, ihtLhrMrJ, by th. Compift, bore 

NN£, Diltince ibout i( Afl/ei. — Hence tire C«r/( fteereil from 

IhenceSSW. Difhnce 16 MiJcf. . . Firlmiu if.' V. Thn^/wt, 

May 8. .t Noon. 

Tr. CodcfelDift.lDif. L«t. S.IDcp.W.l Lit. N. lLo«. ff. 

S.6.tW.l,6'| ts'.g, ) ,'.7+ Ug",,'! s=„' 

At 6 loft Sight of the Llxari, beiring N E h. S I N. 

At lD5fl//<LlCHr-HOUSE bnre Nf £, Uiftinceihoat loLeJcnti. 

Heard > Firinr pf Com to the We»»ird. 


^ 2 


Wb-S 


!-3 


N 


Sw.b.wiw 


fi 


?'.,! 


1 + 


SW 


!■■> 


NNW 


SSW^W 


• s 


H-q 


1 6 




!-4 


N 








< « 




!S 










10 


SWb.S 


(■' 


NWb.* 


Sb.WiW 


■ i 


^7 


IS 


SW 


6.0 


NN W 


SSWfW 


« 1 


18.0 


J * 




?•' 


Nb.W' 








Fell in with ■ rratk Pri»teer, >I 5 thii Uotning, U SKbtUt, of 30 

Cuni, .nd took her. 

The Exftrimat, Drfittt, IlnpiJ, Eutr^lfi, inJ Smcaf,, in Com- 

panj-. 

Flir Weather. 

Pirrd hrthe Ch-sa Indiimin, hmin.l for LvJn. 


> 4 




i-e 










rs .6 




7-i> 


Nb.E 








S 8 


SWb.S 


?•* 




SO.WiW 


I 1 


7-4 


,s .0 


bw 


6., 




SaWiW 


» i 


11.9 


< i» 




,'■♦ 


NS 








Coi]>(M. 


Pltl.. 


Di«. 


N. 




E. 


W." 


■fwency four Houri KECKuhJN.U. 


Sw.b.wiw 
SSW4W 
S b.WlW 


I 


13.1 




13.39 




♦'.67 
.6.30 
4.06 


&»rA. 


Dili. 




Urpacue. lSK.,-.PiAr..| 




S. 




W. 


L«.N. 


Lo.W. 


S..8-17'*. 


'47'.KS 








70' .06 


4T».^ 


,og, 


Coneil" bf Obrerri 
Reck: Head of Ship 








-y.76 


+ 7' 


— 6* 


Co.«aed. 




I.J.IO 




66. 10 


«T-l6' 


7» i* 


Sun'i i;«yii ill//, jo» ji N. 
Sun-i Diiliviim 11 jt N. 


Sun". M*j«r. A^^. ,i" ,7/ E.N. 
Sun'.7™-^«f/. iS .7 E.N, 




:^s 


Sum 




oj.io 




JS-oj 


t«. i,Oi/™t,« 47.36' N. 


NH^IfiVtrialin 160 W. 




Uif 










Thii D»)r, »t Noon, Mirrwi, bon S. sj' 53' W. Dift. 334,' 


Total, doubled] 




l^O.ZO 




7006 


(im (1 " Ltv-Way. flirt vtinbm ii l.te-Viiy, in tljo eUna fi 
Ibc m«i} "t <n^«y Pciiri, Hi/f«t ftMyv' Courfe cor,«fi«J bf V.riitioc 
HENCE a//., -/(ifr*n-.r»-**f»Kl«Ri|!hl«- L«fta/-f*f f™,^P«>f 
»ii. » L«ftii- BlKht, ./ «,rint.nded Coorfc, re !>:<>, tbat Coi.rfcp«^ 
t«tMri> tbt JTtnJ, if lb, Difltmc ,f lb, Sbifi Cm^tjnm it, h^mi tvjil 


«»( .r AsBBJi, ifuiipor.niyoiiilcH It the Center 01 the CompJli) «ir 
C~rJ,fturJtj lhtC,v,pch;f«>h,C^rS.m,i,p-ib,,h.St«f, «£, 

dmil. 


10. Tl««^.*/t«'>»rfBl»v(nBctBrefpond.ntf«-H,Jr«/Affeft»o, or PropCTlr- And Ihrrtfore the /.^s^/rrf C«/rt for lbs Differeon; m 
(ReekoninK) Ihe Btginnmg. of cslcltia) and [cmlliW LongimJej, by ^Jlrutmcr, lai fJ*^£«r., mp.ili.erj, in Ufc, ire rhrfe rwo s 
1, From the Equinofii»l and Ecliptic Imfrfolion, wqHiiing Ihit Beginning for Crmputi-Jon in ^m»/«/ Purpofri. 1. Far ibe PupoTe 
of N.»ig»tiop j requiting the Beginning of Longliude at eich Coontry'. Afrrri^.i. or Olfirv^i^ty, for uljufling the ikI^UI L^MpimJis R. A. 
indDeeliTati««c(MTerpoikieatthertio,lolhoftBnd«r^i^rtitfMffirf;^™j, hiving llie III/; ./Irf-rj. 11 ontepvea, fbr the Purpsfeof Nirigition. 
. WhentHo iaithc Dif. a( LcMf ^"^ bcea > Pn^/Ai, when the Long, ii reckoned accardiag lo ««(/«» CKiSaii. and what »ouU cmbaTraft the 

onU ■> ■ Siit-i IMttiiur. tat Mmp-tng 'he Ship'. Diftaoce rron bn Fort. «kI not conterned in her Longitude from GrKnuiii, which 



•nd NAVIGATOR. 



3 '9 



A JdUftMAL of a voVAdfe from Vw to kJlcfhfiCt> {n the »^i.U«;. i 




Oa i«r^ th« bU^DNOU^lff. 


< 


H. 


;ourte 

ecred. 


ILiion 


Willi 


Cooifei 
correflcd. 


Pointi 


Din*. 


Rbhaiki and OccvKKiiicit. 


s 


S. W. 


6.6 


N N. F. 


SSW AW 


' i 


6'.6 


1 i l^«M Vituthw W. 

S>w>U/Mtli«K. E. 

Spdu «itl> the Afeibr bouin fW i^i,,, /^ i.^. 


♦ 


.s.w. 


6.1 




s.Jw. 


i 


'»•! 


* 




<•■> 










8 


Wb.S 


70 


N t.b.N 


. Sb.WfW 


. t 


70 


10 


S.w; 


7 I 


N.E. 


nSWtW 


'i 


"■4 




ta 




7! 


N.b. E 










o,i«i^; """ — - —\ 


s 

1 


I 




7a 


NNE 








Sqwlly. 1 


4 


Wb.S 


7-S 


NEb.t 


■JSb.WiW 


)i 




OmCIuo 

Spck*. 

A 

Cmmt 




6 


sw 


7-1 


NNE 


SSW|W 


it 


16.2 


A frefli Gilr, ind fi!r Weuher. 
CWmmc fettiag S. E. 5 Honri, a Milei aa Hour. 


8 




7-0 


NE 








10 




6.1 










iJ 




6.0 


ENE 








br tfac Milf Time; only, where the Log. i< doubled. 


^rtb 


Int) 


Dtt. 


1*. 


s. 


-E^ 


W. 


Twentjr-fiwfHonn RECKONING. ' | 


BSEfS 
iJUour 


1 


4'-" 
'S 
70 




47'.ao 

>>.4f 
6.70 

..j6 


441 


■s'ss 
1..3 

1.0J 


CoBtfs 


Dift. 


Uif. L.t. 


DeputuR |SHir'lPLACl| 




S. 


B. 


W. L«.» 


UW. 


S..,..24'W 


.4*'.,. 




Ml'.fc 




48'.l''45'>; 


■•,.' 


CorreaionbjObfc™ 
StUf>He«iorft«kI 




+»s.« 




+ i.« 


1- 


+ !' 


Comacd. 




.,!'.& 




»'.=»4I" 


|,„. 


Zfib DifaKt tj* .3' N ] Wat«f. A*/. lo» 30* 1. N. 






65.JO 


44' 


18.8, 






i-,.fr,o*;«.4,™4s 1 »(|jw»-,»'*«.« .s so"w. 












14.40 




Thii D»7, It W«, MMiMU, b-n* 8. <<•> 54' W. Diautc 1044' 
Miln. 


Total, Doubled | 




i,8'.6c, 1 


48'.8= 


Suni/ay, May il, 1760. 


On Sw-/ the DREADNOUGHT. 


i 

E 

1 


Ho. 


CouMiei 

lleertd 


&.IOt 


. Wiiri 


<orrefted. 


l*iDO 


Oirt. 


RBHAKKI 30^ OcCUftKBIICII. 


z 


^b. W 






Sb.EiE 


■ J 


"'4 


I i Pom yarlfiitM W, i.PoinlL#B-tfV. 
A tn*t:S'M fbllovug u>, S. 

£>fW<v and m-Ar fnun the S. «. 


t 




!6 


Wb.S 








6 


S S K 


SS 


S.w. 


SEJE- 


4» 


"4 


8 




(0 










10 


Nwr^ 


6d 




VWbWlN 


5 » 


=<>-7 


11 




6.8 










.2 

< 


I 




7-4 










S,o.llj-. : 

Spok« wilh the NitUiKgab tnm r.rpmt fw !.«*.. 
Chu «j with the U,:dm.hfertbt,m. la £»/A/ fri'^ar. 

Fiii Wu^her. ( 
A Ckiw* ftiiing N. W. by W. 4 Honri, 3 Mil*. •■ Hour. j 


+ 


SSW 


!.5 


W 


SJE 


* 


,0.6 


6 




';' 










8 


BSE 


4^8 


Sb.W 


EJN 


7 * 


48 


10 


SSW 


I-o 


S. E. 


SSWiS 


1 4 


?.o 


11 


Eb.S 


^.1 


sb.e 


! b. N J N 


6* 


!.1 




TS3>: 


Pan 


T»r 


— R— 


S. 


"E. 


wT* 


-f wCDt>-four Hoori RECKONING. -" 


6b &j 

SEJE 

SWi.Wl 

SJE 

SSWJ 
£b.N J 
W. N V 


E t 

s \ 
N 6 
' 6 


ii'.4 
11.4 
I0.7 
,0.6 
4-! 

1:1 


'lo'.iS4 

I.J5 
'■'9 


.■'.,6 
7.6; 

10.58 

4-7<^. 


>'-77 
8,4; 

4-79 
S->4 


7-7! 


Courfe 


"Dift. 


Dif. Ut. 


Dep.>.««. 


s.„-. ..„|; 




S. 


z. 1 


W. 


L.t.N. 


u.w . 


S.,-.35'* 


V>'M 




„'.=! 


•■•i 


6.60 


«•■!' 


"■..'■; 


Correft" br Obferv" 
Redit Held of Ship 




-,.cc 


...1 


-1.5. 


+ > 


-.'., 


Cot«a«l. 




lo'.oS 1 


.... l5'.o!l« !•! 


•"' , 


>©-i)jr«W«::t8\, --N 




«*»«.. jM, 40° 47' W N 




ijff. 


■4-4! 


U-W 


11.67 


•4-97 


Ljf, *f 0*/fl>ufl/iMi44 j» N 


VtMttVf'uukm 14 10 






I9S4 




?.1= 


TW. Di7, 


«W<U, iiffiJW-bW^.jfc-M' W. Ui».3M9';: 


'l-otal, DoDbl«d 




;,.o8 




6.f 




H 






-- -.— 


















— 


— — 


■"" 




■ftWIll 


ifii ■ 



MC 



,3" 



Tbt ROYAL ASTRONOMER 



Neamefi of SAILING to the WIND, and RefolTing a TRAVERSE Ecometrically. 



t^If a&hipplitt uWmdvmrd, and h cle/t bauUd, it ii nfttid te alhzu i PtinI, frtm the JVinJ, Jir Ln-lVaj ; tcie/t 
/it lit, -witbi^ s I paiHti ef the Wind, via. on litbir Side that Paint of tht Oimpafi frtm •whtnc^ ibi ff'inii hitwi ; 
making a Courft gatd 6 ^ Paiali frtm tb* ffiMd. Bit vii** llitif im Vietd Sea It mail hir fell cff fren htr Ctar/i, 
tht ntartfl fl?t can Ui to the Wind is rtciaatd ahmt c^ Ptints, en tithtr SiJt af it ; thtn mating htr Cear/i gted abtul 6 Piiati 
frtm thi Wind: (Currenli, Hard Galtii and High Situ ixcrpltd) Olhtrviift, fie omj fail large (at 'iit eallid) •u.iib the 
Wind miiri tr Itfs abaft the Beam, 

Whin tht Wind blttvi dirialj eft, a Ship ii then faid tt go right he/ire tie fftmd, ai t» futry ixpirienced SeanuD ii 

IN Imitation of the Ctmrnn Term or Ctifism of Keeping a Sbifi Jeurna!, the Lig i» here heaved but t-vtrj z fftnr 
though on Board mod of our Men ef War and Eaft India Shipi, it is generally heaved tvtrj Hear, for afceniining 
the Dijiancii run on the feveral Courfes as near as poflible. Ai.d therefore one Side of a Pagt in yoor Jturnal Btek, 
being ruled for every Hour, ioftead of every two Hours, To contain one. inftead of z Day> Reckoning in each 
Page, yoor Ship'i Place will be deduced more rircuafiantialiy, though perhaps not mere exaSly ; Siuce iti Place 
derived either from fvtrj Hnir, er z liHirs hta?ving tht Leg, muft he duly corrc&ed by Obferraiion. 

In flying te Windward, you may lay down yourji-verat Courfcs and Dillanccs of the Travaft oa Paper, by Scale 
and Citn^a^ts, and To determine, by the fame Scali and Line oXChtris, the tuhtU Courfe and Dillance, at well as 
•wheli Difierence of Latitude and Departure, from the (cveral Courfea and Diftancet given, at followt. 



RULES /«- laying dtion and Re/ihing a SHIP't TRAVERSE ly ih Line ef CHORDS, 
COMPASSES.. 



>ilh SCALE emd 



Nortbing and Southin 
Rafting and Welting. 



I Meridian, 2 ParaUili. 



[ Meridian, i Paralltl 



Condition of Courfet, 



Add both Cour/ti, 



SuilraS left Irom greater C-.urjr. 



SubtrsQ the Sum of both Cturfei froin i6 Poiois. 



iidd 8 Potnit, the left Courfe, and Supplement of 



£_ between each 2 Courles. 



For the Poiiita or Angje, be- 
tween the DilUoces on each 
two fucceediog Coorfea. 



It? N. and S. are called Meridiam, and E and W. are called Paralleli, in the Courfet. 
Supplement it what a Caurfi wants of 8 Points or i So*. 

TtiVinavi ihe Meridians,: amd Paralleli, Ac Fir/ mi SetfirJ, Steend and Third, Third mi Fenrlh, liC. Courfet, 
:ompared together. '' 



Courfe 
byE. iE. 

.W.byW.iW, 

S. W, i s. 
by N. \ N. 

■.N.W. 



An WoS'CMffif'r'fWPtOJICTIOl 



EXAMPLE. 





N". 




Compared 




S. 


1 and z 




S. 


a and 3 




N 


J and 4 




S. 


4 and ; 


< 




-6 and 7. 








E 


7 and &■ 


8 





PoiUi b. Merid 


1 


4 
5 




7 




6 


6 



Pointi for plan! 
3 by Cafe 4 



Dift. doublcdl ThefefitveralOj/faewbdoglaid 

zz'.S down, or planned, according tothe 

22,8 jfirft Z, 1 } Pointwiththe Meridian, 

41,4 [aod the ^ttienchfuicttding Diftanc* 

zi,2 with the/irmir, as in the zlaftCo 

7,6 lunin>,)-ou wiU find the lahtkCmirfi 

10,0 and Diil. and vihelt Dif. of Lat. and 

10,6 iDepartare ai in the foregoing 

iz,o I Page, 



Diflancet 
AB = ZZ.8 
; Be = az.8 
^D = 4i4 
D£s2i.2 
BF= 9.6 
FG t= 10.0 
GH5S10.6 
Cnrrent, I H ~ 1 2.0 
Whence, rP = 
PA = 
AI = 



of the DTLEADVWGH^i TRAVERSE, 
fertgiing RuLSt. 
Points 
Z SAB = it 
dL. ABC = 11 
£.9CD= I 
d. CDE = 5 
d. DEF = 8 . 
Z.EFG= 6 
Z.FGTr= s 
i GHI = 3 } 
6 6-": Departure W. , 
39.1 = Dif. Lat S. 



iithofAfityt 1760, according to the 



= 39.6= Dift. 
4'S-Ai= 9'3s'W, = theCodrfe. 

N. B.A.S H.|iMT*4aw/SMtrtZ(Mj N.T 
BtTepi S.alSttltm. E tathtHirttty 

J 



yf.jtriilfft. 




yGoogte 



W NAVIGATOR. 



S%t 



Of At TRADE WINDS, «ad MONSOONS. 



PtACiiwhcrethe Winds «re partly r^n^At'. . . Times and Pikiods of blowing. . . . Duecxiohi of blowipg 

tn opeD Seat when Acre u no Interruption from interpofiDg High-Xudi, the Tradr-ff^indi and Muffimt blow • 

nndenteath. 

I. BtttKun tktTrtfititolM. JO" N. and 5. . . . JH tin Ttar cttiflaMify^ Eafttrif Wtud bkvti. 

Wldch Wind, bat for laUn^^dont «f M m u ta JM t and Hii£lr Land on Oie oppofiijg tamtiants, wonkl U«tr qwl4 
roand the Globe. And withonl ihcfe LitdU, which are narroWi thu Wind changet MaHMtsi^. 

t. Frmn to' ti %e» iMt All the Year ffyitrfy m^u/ iUw. 

.^.^Vi»rtktfr^c»fCaaMi AUiheYear H. JE^iJM^ 

4. Kfm- ttrTrtfit ff C ap i imm ..... All the Year S Si^fy, 

t. S)M mar tit Trapie tf Cancir AD Summer . . i . . Wind a Ptiat «r hm mtn SamiiirM 

6. Saa MMT tir Trtpic sf Capricorn .... All Winter Wiai a Paimt or Mtw mrt Nirlherh^ 

t^ The Saa generally fellom tbe DlreCUon of thde Windi. In tbe Pt^fie Omoh, the Windl are ycty fredi 

and regnlaj, fo at to require little Attendance en the Ship's Sailtt find Stornu and TempeSs are fddoa her 
known. 

7. 0« iht (m0 y Pern, th* Jftjl »/ Africa,? 
Lat. S. a»J 100 Ltagim frtm Guinea C»afi\ 

lath* AtlanticeW.£thiopiG Qttaa, '\ 

-Ctafi tf Africa tc %%•> N. and S. Ut. Aai \ 

Oa iht A meric . Caafi/r. 3 1 <> N. fd 4* N :Lat^J 
Ntar tbt Catfi ^ Brafil, i» America , . . . 
Kttt thtCat^rfMAs*^ in/amlaiinUtt •tAett, 



AlllheVear Smittrff It'iaJ ilmu,. 

AUiheY-ear i. Stf/ltrfy WlaJ iU«u. 



All the Year 
All the Year 



"I PWpelMl 



All the Year 



8. OaS. Cx^Q^Gainea,/'. SierredeL«(» 

It St. Thomu's Ifle . . . ; 
Where are frequent Caim and TtnmdQt. 

9. Latiiadi 10' BM Goinca Ct^ . , 

10. Laiitadt 10 «r 30* : . All the Year 

11. Seiwta 4. aaJ 10* H.lmt. sTtadof Sea,"] 
taHtd tbt Rain*'. . , xontr i^oLtagtety Perpetval . 

Jr. Gainea-CtiQt J 

M«r-flrCaribbe-Iflands . . Hacrieaact, 'waA^ . . mad mtttta/Mlf, 
Tfccfe Winds padnally deertaic their Strength, laili^ to Ac Jftjham 

«.O.rf,BrdilO^ Y^Z'S^ 

reSMT^Brafi] AUlhtYMr 

I}. OuthtWtfiCa^tf ^mbAu 



14. it r£( Indian C^tM .... ^.wf^Macral, oieriv-^EduopieMi/ AtloticSM 
Frtm lal. 10' lt$c^Lat. 8. . . /■«rf j* pwiodieal 



^aJ mart Sajlerfy than 

Tit IFimi aitrt Sniitrff, than 

[on the Jmirittat Coaft), 

i mmlStatiif^Mwd^Wtfitrfy, 



. . . »v. 

. . . Ntrtimfi. 

. . ,. Gt&u, attended with Thunder uJ 

[Li^tniog, and freqoeat ft aim 

j,fimlimuV..tr\.ij^hattmmmfjaPtbilt 

'tfiwi. TftM it itmtktMn 

Stiuh.W^WMUtnm. 

Vtrth~&eft. 

muia^Wtfitrh. 

fftjltrlj. 



Ij. Fnm a<> ti lo* LmtitaA S. As hx u-l 



. AUlheYta 



CfVMi Oaober HS Ami 



S.E.lyZ.mMdil^.' 



tiSlfafwiahet , 



Ntrti-WtJI. 



. CUarBnmt Ntrti-BmS. 

. s»ati.^ia tr s.s.rr^, __. 

Raini, and ftrOnger of die two) 
S. 8. fTi/t Wnd ibtei, iut M»M 



\it',Jtcrijm 



A Degreo more, nearyri 
gree Icfi near JUm^V^ar. J 

l6.B«.3'S.i«i/.4*r/J»«* i . . • i>^ April K*oaolo 

rtended' 
Bat thcTe Wlndi anJeftMnftant in the Ga^ of Ame/lfcaB in the Zi^ Sea. 

17, .&KE«M'Hadagafcar«>yAfncanC^,«t/<w7Tr«0i AprilftOfiober . 

^ til Kqninodial 5 

-Sefi^titTta^ . < . . . StUltrfy. 

18. 7<i&t.Baft«rSwnatra,f^CV^CambaiaHM^7Aw«M«reiaber A-tfMay . . Sarti Wiad bt^,. 
■ Cham,4ufi9aiiii?hi\iptmc^a»diaMdJtpaa yFnmliaf iiUO&. trnort ..StmhWrnJ, varying a Punt 01 

[two at Tines! 
iq. Stivtim New Guinea aad Sumatra, Soudi of die EqninoClia], North Wind changes North -weHerly^ ^nth to 
' SDath<eaftcrly(-*a(7li«'i6metiines.$«r6J'Mno. 

try The Tiae Bf tbafeWiwla ohMfieg ia«<liilMUb w 6 WcekiJatn thaa tbiir Time* of blowing on tU 
foieneiitioaed Coaftt. 

...a«».,*,s.£-i,fKM.g.f«,»/,i.si.~]{:~jr'-"«'_"')'-; •_ • '^*^*i.*^"'""'' 



KEMARK. 

yGoOSl 



'g'e. 



B^z 9he ROYAL ASTRONOMER 



Of the T R A D E W I N D S, ud MONSOONS. 



REMARK. Thefe amtrarj Windi Ihtft not Inddcnly. In fomc Placei they chsngc to Calnui in otb 
vafiabl* Winds. 

THE Erid of the Wtfttrlj Mmfim on the CoaA of O-mmW'/i and the two loft M»iitii of the StktbtrJj Uoajaen, in 
At:Chi«tft Sea, are geacrally umptfiMUi ; fo at to nalce the Nsrtgatioit in tliefc Seas vei^ hazardoai, at thc^-eofaa; 
«/ if tht/i Monfoons ; for fo thefe TemptJIi are called. 

t^ In ihi Itmfiratt Zonei, at allTiwiu af thtTtar, thfverUAUWivbhItv} fiamoSPtiattaf lhtCtmf»fi- AaJntat 
lit Sea.Coift), lit ^ndi i/a-ui viitb tfiftrtnt Foues andQvKdiiiiaif iy the Lexd Hfftrtrntlj nfitaing fUat, mdi»ttrrtift- 
inx iht Caurfi af tbaft Wait. . . 

THE Winds, that eenftattlj blow /r»B>, or atari/ /ram, foine certain Pmnt of the CoDif afi, are called 7raJi 
Wimdi : and fuch are the ff^iiidi Ships get into boiiod to the Wrfi lidiu. 

If thefe Tradt IFindi blowing, for a certain Time, in a ConQant Direflian, or near it, fliift their Diieflion, 
firiodicaify, ai a certain Time of the Year, and then blow uatrarj, they are called Mmjiefu: and fuch uexheWimdi 
Ships gEi into bound to the Eaft Indit$. 

Expititiictd Nervigatari,\taitiA to \\ie Weft Udlii, even to the Coaft of Amirua, are more folltcitous to run irito die 
Latitudes where thefe ^radt Windi blow to favour their Paflage through thofe Seal, than to aitetnpt a dirtairCaar/i 
and be retarded in their Voyage by cOnti'bn or adverfe Windi, ai they may happen to blow. And by getting into 
thefe Tradi H^nJi, to command what Codrfe they pleafe, having the Wmd always more or lefi ahtji the Beam, they 
find it (tmmidHus ta Ttin da-wn ihtir Latitvdt, before the Ship comet near the intended /'art or ^W; and then they 
fteer opon a Parallti (direflly E. or W.^ by which they are fure to bit ihtir Pert dtjsgntd. Whereas the Iftand 
of St^adaii, ai well ai other Places lying in the open Ocean, hare fbmttiiDei been ta//?, or over run, by the Inch 
ar Itvt Mari/mti, \\ie hair Jpliltimg mA. diri^ Saviialari ; who, being homeward bound, fometimei Tun their Ship 
on the Recki of Siilfy, inflead of Kttikg tbt Lititrd. 

Far failing iaia /^ Englifli Ch^Kil, in lamtvMvJbaiaiJ f'tjiagtt, fa DirtSieni tf Ca^ainKobcTt'BTimii, tfibiKaiy, 
fwrlbrren, r/nW_/r<M0irr Hiflory of the-IIIandi of Scill^,_^r^Navigatoi'( Pk/^a/^. 

This An of condoOing a Ship in the Tradt 'Wmdi, by a remoter Courfe, to make the qiiiciir Paflage, is known 
(D the experienced Seaman; bnt iia Secret to the La»d littvigatar, (forwhofe Sake we iolett it) that ncrcr made a 
Voyage to prove the tJfe of b'nrf/uudTinritt, -and pat hisic^^j/rLind-Rulei '\aPraSitt. , 

If Shipt, bonnd to, or from, the £«/ iTdiii, arrjve at the Place of. a 7frn[/iw too late for dieir Pafiagc, when that 
Monfetn ii Ihifted the contrary Way of the Voyage, they arc forced to return to the aexxcamitniiiit Port, and there 
wait, ferat Mantbi, for the Retnm of the fatrtcry M»afam, before they can puifoe their .Voyage. Whereas, if Shipt 
righdy tiide their coming to the Place of the fawar^U Maafa«m, they haAen their PafTage through thole Seas, and 
accomptiih their Voyagei in the fierieft Timi. 

Ot tbefe different Sorts of TrtJe Wiads, yon maf obferve, that fome blow from &. to W. feme from S> t 
others from W. to E. — Some are conllant in atu ^'arttr all the Year j fome blow one Half the Vear aat Wirf, and 
the other fix Months quite nalrari. Others blow fix Mpnths one Way, ^nd then Shifting only eight or ten Points] 
continue thtteiix Months more, and then return anin to their former Station*, ai all thefe >&i^(i^ Trade- Winds doi 
and fo, as the Year .comes about, they alternately Tuccecd each other, in their proper Seafona. 

There are other SoHi, called SiaWindt and Laad-Wmdi, diiFeting ranch from any of the former, the one blowing 
by Day, the other by Night, conllattUy and regularly focceeding each other. 

Within the Tarrid Zont alfo ire vh&at Surmt, U fierce, tf not fiercer than any are in ubrr farii of the World 
And as to the SiBfans of the Year, they are diftlnguilhed in thefe Parts only by V'mnd J>rj, (there never being Pro£ 
or Snow) which wrr «nd drj Se^ni do «l fucceffircly follow one another, as the Wtn'tir and Saimnr do \nth as it 
Eaglaad. . . 

Here wt tXto JIr»»g Carrtati, fometimei fetting one Way, fomciimet aiwtheri which ibowh it. is difficult to 
<]e(cribe. With' definbte Accuracy, yet we have attem^ed to give « panicnlai Accoant of thefe (hfattcn, from onr 
own Obierrations, and the Author!^ of othen, further on. 



yAWATIOIf - 

DigHizcd by VjOOQ IC 



ati4 K A V I G A T O R. 



3H 



VAKIATION of tbc COMPASS obferved at different Times and Places. 



Ba§n^i Bay 



Barhan, N. W. Co»ft . 

. — N. E. Coaft . 

Btmhtn 

BrafilCoa&, L«. i8» S. 



It Sea . 



Britl/t a'aaml . 
Canary Tfit . . . 
Caf€ Cuaiffu . , 

Bf Goad Hope 
cue. Weft Coift . 
England, Weftward a 
tranci, W. Coift 

- We&waid ai 
Gtrmttn Ocean . 
Guiuta, S. Coaft 
Gnlph of Batbtua . 
Hudjtn'i Bay . . 

I Coaft . 
Indian Sea 

1:$* See farialiBM Tab 



■ Lai 



S7 W. 



Madaga/t^ 

Madega/tai 



al&C 



S. fr. Lat. 40« 



ines ... 
Malacie . . , • 

?/r«u England CoaA . . . 
Neui/oandJand Coaft 
^nu Guinea Coaft 
JVmo ^g/^aM/, S. and W. Coaft 
Nm> Zealand . , , 

PiTtutai Coaft 

w. s*- 



S(«er (;«ii^ before 

— — Ptati before . . . . 

St. /ffi™ .... 

AW/j, . . . . . . 

SiraitiBj Gibraltar . . . 

— ~- Magellan, E. Entrance 

1 W. Entrance 

MagelJaniea, E. Coaft 



9E. 
9 W. 
6 W. 



13 W: 
II W. 
6 W. 
IS E. 
.3 E. 
19 E. 



N. B. Ai there it a cmti. 
nual Variation of the Vaiia. 
tion of the Compafs, tht 
Magnitie Variations here in- 
ferred, are more for Cu- 
riofity than they are to be 
depended o-a ; being lihe fame 
ai in Mr, EBUr/iin't tfaviga- 
lien. And therefore the ^4- 
•trigalfr (hoald take the Mag- 
netic fariatien every Day, or 
ai often as he finds it conre- 
oientatSea, for deter mining 
his tiue Ctitrfi, and keepiag 
a geod Seeiening. 



S W. 
Pbthfiphiral TrtafaSiM 



REMARO M the Vuliu ERROR, in B«h »/ Niyigician, ef f-pfcfiig Y 
«»rf ./ a fixib qI'AI 



(^ IN iMtpiflg « SiiVi Twrro/, Mtoii'mito AtHnJan'i Epittmy, or Art ef tfav'irflin, the vjhili Depirtnre or Difft 
WfA'cf i« ill <long, in ine diily R«kotun|i, «do<e<l into Drgmitni Miimra, by divic" ' " 
' ni totCe Degnet af Dtfinan ut veiy / " -"-■'— ••- '■■■'- -•--••-■.: 

tptrtiire if. 

Mr. Afdrt/x, in hii SfbtniJal Njv^galiM 
from thit Mcridiin. 



... . of Eafling or 

ividioM the Departure of each duly Recftoaing by 60. 

the Metidioniki Dilliace j being of mother Maiuic to ' - 



illed b; Mr. yilH-fi 

lh« fune 'Ernr, by mtkiag Drfirtare fiom (he Cult Meridian to be the MtriJiiu/'D'if' 



An! V 



Merid 






!n di^mm Cmrfa is ftiHig 
ide of Ihe Perl Jefigeed, toA 



for Meridional Didancr, in long Voyagn, cm produce no Certainty : Since there may be at 

lltletcnt Oiurfa Rtirtd ielviicl them. AeJ ittji Dipurtem nil/ Jifir mere v Wfi, tawrdiar « li 
■a, h niftr u th, MeriiiM, tr lo ei £■ 'r W. Par,.U.I. 

g towardi Ihe P°/<, ifiShtpdiieAiherCaurieN. orS. till Hie iiriTU in the Parallel of Utile 
IbeapuirucianE. orW. CoarTe, till Ihe Mrira at bet Port, duDepaiturt by thefe Coarfei will be Ibe /ujf ^Jib. 

a, ArdifniedtiefltherCourfeE.crW.tn theP<rilkl ofUtitudeof ihePIicedepaitedfroDi, till Ihe aiiives in the DiSereact of Lon^' 
cudeof the Port defigned, md then pnfuea aK. 0[.S, Coorle, (be will matce the rr<4r(/i)^riiir( poflifale. , 

]. Od the contrUT, if a Ship Ijils diteftly S. or ti, [accoidiog ii the Plate luled from it N. or S. Latitude] towarditbe EfuittSiat Da (hi^ 
ie, till Ate arrivea in the Paialle] of Latitude of the Port defigncd, and then purfuei an £. or W. Couife, Ihe will make thtgrtal^ Dar- 
ren pofliblc. 

"lit, if Ac failiE.crW. in the P<r*/iS!/ of Latitude of the Place dtfarUi frai, tomrdt the EquinoAiil, on this Side of It, till the U' 
the Dilfeieqccsf Longitude of the Place defigned, md then parfoea tS. or N, Canrfe, Jhe will nuke the Inji Digtrnct of Depirtnic 

5. Again, in Suling heiwiil one LatiliMe N. and the olhei S. aeroli Ihe EquinoflijI, a Conire diirflly on the Meiidiu betviTt the two 

Lalitudii, andthenanH. or W, Cgurle, '' ~ 

b« the lefa, 

if thi Lalitudc failed ^om ii tb> 
defigned will give the Dtfaritn the Iiii/I, 

7, And tailing from one Lalitude to the E^uuioaial, then the Dif. of Longitude 1 
Latitude, (till I iiftrnt Cearfa) will make the Departure atwaya Ibe gnaeift potlibie. 

InrtklHCi. BiitoneSaiirfe(if/rdAfVsU; betwixt any two Plata on the Clo 
betwixt thegreaujl wd Iraf Depinutea in failing backward ox forwatd by 1 or j d 



of Longitndo, will nuke the EJeparturt the lajl, proiided the Latitude £iil;H front 

l€r, then a W. orE. Courfe, the Dlff. of I.onptude, and iCourfean theM.iidian to thi Place 

Equioodial, and then on the Meiidian'tothc other 

Middle Drparttiri 



Shipt may ^ke at iM«y diBcient Dcpatti 
norei. Q.,E. D, 

The Mature t^ variaUe Deparlun between two Ptam being dinra ai khoi 
lhe/)rrJ£>^i*nof their Meridian*, at Ihe Plate failed to, on a diioa E, 



lill make the fame Drpi 

atCuurfei. So t bat, iroizi nence, it is crear, tnai 
make diSeicnc Courfes bctwTit theft * or ) Courfet, that make the grialrfl and I'ofi De- 



the Mrrldign or MiriJima! D!/a„ti befwwn two Place, will 
i W. Parallel, Which Mirtdlimal Diftance ii alwayi equal 

5m Remark 



til* hil 'Departure, in failing lownrda the Pole, but to the rrroi^ Dnarun In failing from the Pole, Eowardi tVe Eqtiinoflial. 

p.ni^ tlilff^tii. Sre a/f" pagn 6% aid 691/ Mr. Emeribn'j JVaMorivr, (at iht DiftiKaiew ef Meridiaai DifteKit aad Depart, 

(if iHSiaD, The Sum of all ihe Meridional Diltancei, made inSailmg, will be equal to the Sum of all the Depvruree, in wh 



Sailmg, will be equal to the Sum of all the Depanuret, in wbkhSenft only 

DUJanci ud bepattnre are fyaonimoui, or import (ha fame, which Departuie or Meridional Diftance, b, bowercr, proved to be 

wry JiHerent in long Voyagei ; Bea«»fe the ftme Courftaand Diftaniea, all the Way, ate never purfoed. 



M^otMl 



""c 



3*4 



The ROYAL ASTRONOMER 



A T A B L £ fliewing the Miks or Miiaati of the 
Equator, that oair a Degret $^ leupinJt im Mtr 



■Oeg'odMiiiatet. 
Lat. 



S9 99 
S9-97 
59.92 
59-86 
59-77 



S9.6? 
59.56 
S9.41 
59.26 
5:9-08 



58.89 
58.68 
58.46 
58.21 
JISL 



57-^7 
S--37 
57.06 
S673 
56-38 



56.0. 
5563 
SS»3 

S+.8. 

54-3' 



53-93 
53-40 
5*97 
5^47 
5^96 



:a.|Deg' ofiMinn 
I Lai. 



5 '-43 
50.88 
50.32 
49-74- 
49-'i 



48.54 
47-9* 
+7.28 
46.62 
45-95 



45.28 
44-95 
43-88 



4' 43 



4168 
40.92 
40-15 
39.36 
38.57 



37.76 
3694 
36... 
35.26 
34-4' 



33-55 
31.68 
3>-79 
3090 
100 



29.09 
18.17. 
27.34 
a6.3a 
'5-36 
24.41 
43 45 
2248 
21.50 
20.52 



'954 

'855 
'7-S4 
16.53 
'5-5^ 



14-51 
13.50 
U-4J 
"■45 
10.42 



9.38 
8.35 



5.»3 



3-14 
1.05 



DIVISlO^Tofthe OCEAN. 

EA9T»it, m Oritwlal OtoB t WiiTHK, or On' Jrirtir/ j 
KB»T«»i«,ora^Bttr»Mi«/iSonTJii»N,or3to-ji/TOitf/Ote>a. 

Other Sias tike thrir Njnui fVom the Cuniemri or Coun- 
uiei Uwy wiDi i orfroni theiV«(iiHoftholeS«»i. 

A< Ciiatf, S», fnm idjj^nt Cogntij of Ciina. 

JWA'm Su, williing ihc trnJitt Shore. 

Pn-ga Sf, w«Ain( the Frfi"' S^"' 

Arabirn Set, w»(hing the jt'e^tm Shore. 

jEiiKfia* Sa, wifliing the j&iiW( Shore. 

.A^u^ri S", ftmn .At". » liuee Mountiia is j^kt, ipuiB 
•rhichliei JWar Ji' A'wi, Ijiog to the W. of Awic*. 

MariilZnr, lying 10 ibe S. tit AmrUt, or P4tifie Oaam, 
Dm it> Calmnefi. 

OiwTw irjfftHiiui, or Sfmi* i'M, wifting the Coft of 
&«;■ ( aOci life Are t/Bifiih by Ow ««jA;*. 
' £iiWi^ Ci^MiHl, bentein EigliaJ and /'mjiM. 

Irifi £«, or St. C«»i*'i Ciam/, between fnx^W <od £«En^ , 

GirmtM <u £>Iii/^ OfuiT, between Enrla^ ind lUZiW. 

CMlrJuUa Sa, Northvnnl of Snfitiii?, 

Bjpirhtna*, or Fnffln. S«, bejond the Wan* Or^. 
7«r«0T« 5m, or StjibUw Ocum, ft ta&wvi, &e. 

B^kSta, between i)(«ur>, S%M<lm, *nd Otrmmj, wboTe 
BBtnDceu wiled the 5w«^. , . „ . , 

SU£»rtmtam, oi 5(r«i'ri t ^i^'d £(n«l b]> the SfMOMrdi, 

IWu £iwiHtt. M BlMkStM, JMoiat to Pa^i JlfiM-;^ er 

Ott^tei or-Hbi ' 



Divi£oaL of the EaxtL and Ocean. 



DIVISION ef tlwEARTB. 

nt, Aii«, Arai«A, AmaiCA. 



En on Boaaitd. 
T% the Nnth, b; the NDrthun Ocean, or hotca St» ; 
br tk* JUrrinwMM &11 lyiag bctviit it and <^wa j oa tfat 
River Tmm; oatbt Weft ^ the IW^v^.oe.ftJiKiftfeMfc 
Dividod lata Chief Jti^Mai.. . 
Pafaaj; lUtfttmit, Statin, f/truvf, Damtrk, Ctrmtn, Amk 5mk \ 
ytUud, FJt^i, Fntgml, bilf, Btmgtrj, Sitttmit, Gtt~ --■^^^l: 
Umamt, liitl* TvMn, 

Cb>/ nknai. 
CrtJI-Sriltiii, Inttai, Striitia, Sititf, eirfot,CaJi; K^r^iK, CffrMt, 



Oa theHertli b^ tiie Narthera t^TtntriM St i on the Sonihlq' the 
<M-f«<wC«^, or Jiii5u{ aathaSaflby the/tAmiftMat ai^oath 
Wa£bj lb* Bint TMrik 

Dnided lata Clikf Piodocat, 

Tvkj in Jtfit, Jtr^:^ VtHfj, Pb-JU, K^tOa, M^aftuamt, Mrii 
Otilit, Sfrit^j^matia, Pt^fm, Gtrpt, 4Mm, P»Mt, C^vt^I^i 
' Chief IQuai, 

yi4", Samatr*. Btrmc, ia the friote/ Omb.J Medn, in ih* MiJi. 
ttrrttun Sea ; UiutiMt, Sat, Stma, In. ia the Apibifeltp, t^jtmjft 
in the B^-lt^f- ^ 



\c^> 



DMlid'iaio Chief iSpo*incei. 
Mtmrntttft 
pridThl'ttU, CMwtt, MliicfU, 

CUffllhndt, 
TbcCiH^UIe^ e^ Dt yirJ V\ts, lUtt of j^ani, Utiirrt Uttalt 

St. Titmai, Mtdtg*/^'. <a. St. Lat^raa, "-*- '" "-<• — 

St. Btlat. 



DiTiieil ints Akti .dba'h*.. 
* Chitr Provinect. 

JVn> SM/a, TIfitIa, Carplma, t^rgiKt, Bt^fltad. FnifiMiiU, Mw 
Jtr/ij, ifttaTtrl, Nt«i M*ilt*4, NneFmut, Gn^ti, tdiathCTCoa- 
lioeat or Iflaod jiel ubIuxiwd. ; 

- The Chief Iftiodi of JAFtt^AwriM. 
Itdai, Ct^MM, Na»f<m«aa»i, BimOMi. 
i^eaSttthAmrU^i. 
CUtS Pianaeo. 
Mt^Hn, Braaff. OiH, Ae Amanm, GtiMg, iVa, IVaM«t O 
p,4, Ptrtpu^ or Kit itU fl^t- 

Chief JUta^of Salh jimiriet. 

Cmim, Jfmmtum, PtI, Sia, _B»ttm, Str- 



fwrmMratgh BiAautU, Gia. Jamnet, 
aiu, farMa, ami t^Kc* of the Can'Mcf 
KM IlUadk Ja¥a the Cmar, >«* tba , 



>M tba 1^*4 *nl H 



AaOordoa*! gmirtftittl Orm 



AHBCnWi 



««?: N A VXG. ATOa, ^5 



APFSCTI-ONS of^iffw*/ TAIANOLBS in fmrt/,. 

I. BVEKY gitat Cink JMdu tbt GUt hit Am tftai.Htmi^btm. 

i, jiqiv great Qnkt nltmg tatb lirt. mi* tit oppofite J^t tffiah ^ 

Of A N G L Q S. 

Is A N 7 Sjteital T E LA N G L B., 



7. ri«SaDi0/M]'/wfA/A'Wjg»»tcr/^(^S«j|}t*bwtf«/'i^y^&. 

■i. Tbt irtmtijt Jmgkit imfitlU tbtt^tfi SitU, oU tht It^ 4ilk l» ih baft SitU, aMdtttXMOUf^, 



fi* Sam «/«■]> /WW A/A' M greater /wi (/ " "' - " •> ' ' 
, fi# r«tf 9* A^ft (V fMf^r » tbtgrtattfi Sid . 
. Enul Jugh «r* »fp*fiti tt tvud Sidii, Wf4f contrary. , 

S. Tlmtmof hi 3 «?«, w jrf/^ 4fcf^/. 
. A^Mc^e^/ivj A#ib> JcacBlp, mcA f>«^wpiiV^J^'i*> a Qjudrantc 
7. |<'fi(r««vs.oliCaM^4!'r fi«n««/^«M5UrgrcattifAair90*. 

S. r&i^i^f fij»{equ^ /itff^wA^wZfifequal|'fAfrrM)v/r>f(f2^cqiu]atenJ}Wfi(cantnr7;. 
9, jT /wrc «« mt acnte Ju^li, oiu SiJt luiU be lefl thai a ^a^oMt. ' 

■ 0. ff tWJbgh^ ptUtT tbiu, 2riibt.J^lt*, t^Sim*(ibtirtfftfittSifyviitittgrtattr.tkaMi9o'} aMitbtnfirt, 
M tf tbtm U, at leafit mottr tbttm 9o<>t 

IK ff ibt Agki aliht av/t ht gf \i}Lt ASMaaa, fSitb grtMttrtr Itfi tbim 90") tbt ?Krptndiai]v /ai/iiig, /ram the. 
nnical Angle, M/iv Bafc, v^U fallvA&a^thtTriaagU: haifffi^kmaJ^eE^oavaU/iiiioiibma. 
' 12. ^mvAf/H^obtufe, mi/hm jlv^'cutf, ii^SIAt<wiS.btt/like J^taimiviibibiirtj^^iJmUf^, 
Ji, Wbtn*-^..mi tf {Jjj^} Jfimt^^4btSiJtMk4Ub, ^^^.h^sf.tbi 3^^"{«"«- 

16. firSm ./-^ /«» fsiSS"! " {1^}'** ibt.Dif.rtn^bHn.^tbt^dl'^l^li^'.. » 

17. 7J, Sb» ,/th» 5. {^ j « ^ '**• {i£ \»dmr, thu, .Bo'. 

Oa SItQB Sw 

b ANir Spheridi. TRIAN.GtB. 

191 OHB- SiditHtigma/irlhai'ga^ ibatTriM)i^bhatfwtlibta(^A»^9r 

20. ^ tttb^ tbt ifiiii bttnatn tbaa a SsaJraU, »scttf^tif%4fpn-vU(Hobtart*. 

%i.TbiS'mitfa»uivi)tSi£tUfftMttnhm».thiyfSidt. 

31. fit.mtrtDtpin/bm btiM^tmtb8Utihmm*^.*it^mtftbt.A^iKtttdiio*i,atSthaitiit^tm^-/btm 

. %*.Qv^:lbttf»alSi^ftf.attMQM^Ti\iaii^^^ tr.gnuntfbMi ^".tltjhgk of. tb* Safi 

vMli,6e*^ei\iul_tt,\efi,tr.maXatbaM,^'. 

24. £iV^ SuUB/_tm Ilbfcxin Tqan^e » ^ libs AfiUUm imtb-iii a^Jacnit v^tfp^t ^b, . 

th. Jfht»xSiAaarttfiiittMi4iM,MultbtiMdtdUditgUitMcaK, tbt tbMSiAwiilkM-tbMMQf»ir»Mt^ 
vj, WhtM 2. Sidoi <«r ^immttM^Ooit^^aaJtht^iwtlmiidJ^k ho'^oh, lb* ibiii.SUi voiS.bt gn^tr tbm 

: 28. iriw»fA«San;^«!;2A<A»jfequl/i, left, frgre»tfr,/^,.« San'rnrciib /V5«N e^fMr*^ 

k^ cqi^l tt, lefi, . *r greato tbgm a Stmeinlf. 

; 29. H^ia tbtSma »/ aaj twt SUh u e^oalA) Icli» trgreaMr tboMf sStaudnUi tbihittn/li Jh^t, wchM bflb^ 

^nfa, wltittiipiill;_iah.f$num^b^t tbttfitrvii^tff^tJnilt, i^bidtd bf ^ma tf ibrft SUit^ , m/ ih 'i'M^sSk 

'-ttlkmti 

AFMCXlQIMk 

DigHizcd by Vj OOQ IC 



3»6 



nc R O Y A L A S T R 6 N M E ft 



AFFECTIONS of kithi-angUJ Spitrieai T'R I'A N G L E S. 
In k RIGHT-ANQLED Spherical TRIANGLE. 
I . EACH ainju JngU aW itt tfptfilt lig h tf like Affeftnio, 

3. I/htboUiifae^, «■ hli Leg» art e/ <^^j\ jfJiOjaw, iSrHffttl/emifi ii ^^'^^thm^.MJtttcOBXltjy. 

4. IflhiHfp»lhtiiafiii ^jr^rMAwgo', tha tilbtr Lti it i^^^^^tht anneal Z., mU tBt eontniy. 

5. ^ f&r Hyp. iHu/ WW Leg ar» fl/ i ^.^g^JftSit*, ih*»tbtrSidimJ»p. £. io-A^^XthMTfo*,mdtbtQttKUmy. 

6. Tbe Sam 9jf tti 2 ottVimae ^tigltJ it grrater than tue, omJ liji fhan ^riglt jfaglii. 

REMARK. Tticdaubt/uiCajti feldoni arirein afirenBmicaiOmpiiiaihiis, whtieia are commonly ufcd rigtil-angled 
Triangles, whofe Arcs are lefa than 90" : For when there are grtattr Am occur, ic it uTual for the Compater to take 
their Suffltmenti, and work by the nniraiy Ttitagit. 

^U^iiid in Afira»emieii, GngrafhUii, vtl Haatidt, eJUittdum, Trigonomtiri* mitrthtttniam ifi, 

EmerTon'i Navigation, 

TO fail Marly by the ARCH of a GREAT CIRCLE, when s;tw» COURSE can hfm/iad. 

STEER, from thcPIaciof your iJrf«r/w/tothePor/youareboond for, all the Way, by the Angle oi Pofii 

from your laft Place arrived in, each Day, at Natn \ by compating the Difftrenet of Latitude and Longitude for each 

Day's R«jEaxi>; at Noon, and thence compute each fucceJ£ve Angle of Poiitioa; ty ivhUb jtit an ta fiur /n 

Dtrf to Day. 

T» Altrmint tit Angk *f Ptjitiiiit Jram eat eivtn Place la aitollm: 
RULE. Find the Diftanceof each of two Placet from the /mw^si^. Then (by Ca/fjt\t oblique Sfhtrieai Tr 
eonometry) Say, 

By PROPORTION. 
. At Ce/.i Sim: tB Co/, i Diff. •ftbi Diftanct Jrm lit f*mt P«lt, :: fi Cetau, J Di_f. Lng. ittwm the tw, Pltu, 
Ta..c/aMJrciDl^'^^^]tha»^'- ^,/, J«, Polar D,>f. ^^f^^^^/i*, ,80-. 

. A) Siu i Sam : te Sine i Diff, »f thcHifiaiKU fnm tht /am Piltj :: ft ti-e Cslaa. i Dif. Lmgiladt ittvittn ibt Ha* 
Placv, : la 7««y. Arch E le/i thtm 90". 
NOW.g^ll the 1. Of Pofition at the Place of J^*^} Latitude \jZltftfrom \ '*"* /-"•Pole. 



Some P R O P E R T I 

= Rid. r = Tib. ' = CoCk. 
= Sin* T ^ Cotin. v ^ la. Sine 
aCot. /s=St<:.iit V=r«tf.S.Sop.. 
(— 1 = Cover. S. 



Art. 



Tbea, 1. IB ^ I — tt=cl=-- 



f -r^- 



' ■ ■' ' » ' " / 






7.«B 
I. T> 

-+■/ 



-/TTT. 



-•ajl + '/r 



= n + «i»//— f = *ir — rr-E .T n, tf=,» 



:s of 

Oi, If 



/, Taagtnti, Ac, 

r= Lot. Rid. = 10. 7 r^ 

i^Loe. Sine of aa Arc > 

<= Lot. Cor- , jr= 



Log.Ttn.'l/nLot.S 
{Lot-Cot. jr-sLa(.C 



Sine of their .fw sSf + fC -) 

Sineof thtl.flijy; azSf — iC /, 
Cofine of their '^« =Cc — Si f 
CofineoftheitDi/; = Cf + Si J 

■ "■ ' r of 1 equl i 

rtof >ii»U 



ilArc 



«cs. 



Bact, the Sine of fw. . _ ... 

And C^ of iJa^UJat =CiOif.S' 
Alio, if S >n<t C = Slae end Cofine of j £« of a Am, 
And), c = SiocindCofinecf ^'iheirDiflewncc, 
Then, Sc + Ci e= Sine greiter, St — Ci ^ Sioelefi, 
And Cr — St = Cofine tmttr, Cc + %f^ Coliae Mi. 
Agtif, If T and f denote the Tuitentiuftwodiff, Am, Radi: 
T+J _ _ _, T— rf 



Then, - 



-^Tin. Sam) and — 



- ^ Tan. OiK Bu^ 



for TAjMt, Smi, -CjAf, and On^nt of.an AreablHcg«« (fkc fijf 

aa'Aic u niuch twiaw joe, writing ■ aiffiM SigB. 

^ 5u </T«H«n ^i'/.i > niUrDiff. n>SiK ^ ibtSam 

Far iaiinite other Propeitiea, and Proportioni of Anho, Siae^ 
Tangtatt. gf. confalttAi. Brntr^'itrigmimnri. 



and N AV I G A T O R. 



3*7 



ANSWERS to «!i the CASES of RIGHT-ANGLED 5/&c;Vb/TRIAN'GLES. 



,1N m RIGHT-ANGLED fpherical TRIANGLE, 
/^H nprtfmt tbt Hypoihenufe, «■ 
iJiVrr »fpefitt ta tht Right - jingle, 
fi, and P, ibi ithtr Sidfi, Bafe mJ 
FerprnilicuUr, «r L^GSi h aitd 
p tbeir ifpafile AngUi ; then tog IW' 
rf.\b^ I T«nni hang gliinf tht 
Reft 4M fiiutd. ijF.(<b. ANSWERS 
» th* CASES in tht JatleviiHg 
TABLE. 

N. B. Tn tba PROPORTIONS, 

^ repreiCDttt itvmtt I / Stof i r Cofi)ir t t inttgtiti 

, CeiMgtttt I 5^'^^ ? ttiin 90" t be^ufe Jra and tKeir 

Supfl/mtttts have the fane .^wi, C^», Tas^m/i, tod 

Cetangmti. 




OR. thmpug tht SIDES 
e^" u lUght-angUd Spherical T R I- 
ANG LE, /s ANGLES, ii«^ 
ih, ANGLES to SIDES, <^ i» r^ 
-annexed Figure, tbt 'Caf(| ooi/ 
/A*^ ANSWERS, «r* « m /At 
falltwjiig TABLE. 



F^ Bnt here, ioftead of H, 700 maft take its Swf- 
flpatat. And, for lih,pwiailUf, ann the fJ»/r^, where 
'a. Sidt or JMgit ii determined from the Spieiti of H; or 
where H, in SjpeCies, \s i» bt fauei^ 




ANSwidi 



<^^R«!' 



By PROPORTION. 






By FRGI'ORTIOK. 






i.H II t.f\ i.P, £b/. 









Rid. 1 Cof-eLenZ. ■.: T»i..Hyp. t Tin.Legidj. 

: Sine Hyp. :i Sine ima A. •• Sineop. Leg. 

R»d. i Car.Hfp. 11 Taa.p»en^ ! Coc.ihtrZ.- 



-"•"-■■■■■■'*""li{> 

>.H I r :: i.B ■ 1. 1, iVtt B. '' 



:)p/4«-« i- 



Rid. iCel.Hip. ;i TukginnLfj. iCof.^ulj. 
SJK Hjf. 1 lUd, i: S'iDt giv. Lc| ; Siae bpp. ^. 
Car.Le|gir, iCoT.Hyp. 1: Rid. t CoCoiherLcg. 



r : ,.f 1: f<.fi ii'.i, /.'IcB. ' 
r ij,B 11 i.f ! i.i; tiitf. 



Hjfvlhatufc. 



Cof. gU. /. : Rut. 1: Ttn. Uj. Ug t Tao. Hyp. 

RaiiSineVdj. z.!!to''-«4 4^:Co^opi^ 
Rid. I SipcgiT.Lcg II TtD.adj.ji : Tin.op.L(e 



I ../ :;; iab I'. 



Ltg ML Hyfll 



i adjteiKt. 



Sincopp. £_ : Rad. 1: SuicgtT. ^eg : Sifae %p. 
R*d. :T»Q.giT.Leji!.Cot.Dp.Z. : Sine pt|i«rL»g. 
CoC giT. Leg I Rad, i: Cof. op. Jl i Siua ^ tdj. 



: ^.B 1: y>.i /.HjlfBjfJ;,'}p. 
.P I r i< r.B 1 (.*, lii/± '. 



i^*Pf.iUg. 



Rad 1 9ar.aM Le|:; CoT. oilier teg : 1 
Leg.: IM. 1; T*a. othej Leg 1 



.t I r v./.f.: i'.P,^i(>. 



I 



i(r£^f. 



T«a. one ^ 1 Cot. oOui £_ i: li^. i C^f. Hjp. 
Si(ts oiMZ. I Rid- ■: CoCother^ : .Cor.^p.Leg. 



UNIVERSAL ^SXJfQ^VtiiS^. Vi Vr rb^^rW JUvr/Qf/TriziV. tbt Siie 1^ itt'-miiiit P>lt <itr/ lUdini on r«^r4[/^^Mon{>Mi 
taffcT<BVfini/'<ia|ix:reinei|R>DJaa£t,'W'»Fi(Cu£ci«/ tfcEitrtntidiajonQ, ' i ^ 

.W>. KM.X MMWiWl-**— lRefl.nyeCe6neiof&0««oii/«S. J^t*/™; iKingrtckoncd .iM*Pa«i ind tliefw.EO,tiguoui 

. * . 'or rwDOM Ptrtir SxIrO M w y iing, «ni) diijiiiS, 

r^ Tht HlrWthBBiifc, sad tmn^tit Aria, »toiifdltti, imtbi AfVt FAptnim, m Ctrnifytrntmi if ibat rttl jt<i- ; 

COmtmm \ Hjf>cry,[ Ltr .-^Uke RATIOS in Ibr l^ino ! 

J AbUr^ d^ ^\sil ' ( „ «BCTANGI.E, 

EXAMPXX I. tfitudtartpvimtiiJlmdP } Hue (unoag the 5 l>utli( B, f, H, J, P) Sine B it ni'^ Pay, and-ColiDg.U, 
T»og.P, Bjortmei tujna ) ihitki.B X c = «'./ )f '. P^ ffcotc, #*./ : fii.j.B i (.pj Or, r it*.* 11 i.B i ir.P. ' Ttith, (Puttiog 
.- I tfoK' 1 T.) , , i,B „ up I (.P. .1 

EXAMPLE II. IJYmiimmttUfai^i H«te i'.« it Middle Vut.'ind «,# uli'.PEittittiindi^UDfl. !72ii>wVr, i'./ X 
iX ''-Pi ■Wl^«<i«> ' w.* 1! I*.? I i*./.' ; i " 1 



Sil 



tti ROYAL ASTRONOMER 



ANSW8R8 10 111 Ihc CASES of OBLICIUS SfiM,J TRIANOLES. 



IN any tiliM Mgledj^Airir^ 
TRIANGLE, ABC, wliofe 

BC=AT r"=« 

BA=CJ L=' 

jtif 3 tfvtbich 6 Tmu htinr gi- 
wm, ibr^tift arifMaJMi below. 



r«... 



'«•!• 



r*-*- 




'H Let r » X«dw, i « ^hn, 



g^i-^- 'i^}->"^"- tj-^riL-i'^ 




^.A„'.B,„'.D,,..Ei}B,if}Jq:l 

rbta C b: D ±: E, boA tru*. 

But,ifB=A, ors:iSo* — A, or kt bMw. A «( 

tZo' — A.^natRitAiU^f. And 

If A jf^^ } *, tl«>*=»rf±.«Jrt 

ABJC=D±B°iilr- 



OIVEN. SOIKIHT.: 

1-^ IWo-op. ^. 



By PROPORTIOW. 

lneiLcgi9.ittef.^iiS.«th.Leg:S.op,^, 
CoT. Lc| idj. u ^ It Tu. Z.tf**a •■ 
fta. ^ iodudcd bjr *dj,'L«| ud Pop. 
Tin. op. L«g I Tuk. iJj. Lci:i-Ci^. Hj. tot. 
/, I Caf.iith.Ttr.£.iiid.liroth.L«|.*pRp. 

Sid. t Cor.X«>M" " '«*• ■<> W- > T«. 

■4, Scpncat of Bile. 
Cof. kdj.Ui : e^. othc(Lc( i: Ca/,id(.Scg- 

neot : Cm. Mba Scgneit, 



Simap.^ : S. Leg^rai nt.ath.^: S.op.Side. 
■«dim ! Cof, ^ idj, to Lm :i T«n. " 

Tia. kdjiCMt SceMnI sf Bafc, 
«s. ap. Z, td Lif f 1^. idj. ^ ii Uoe >dj. 

Sttneat i Sia* other ScfncBC 
Thai, Bafi: itf < = £n ar JX/: Sctiwak. 

■J. I CoT. Wvm ti rM.*dj. /. t Coc 

adjacent icttiafj^ by Ltgcad Pop. 
(V- Id). ^ t CoT. Z.(*> to Let :i Sine 14. 

vert. £, ' 9in««faeritttia)^. 
IIh, i«i' ^ «= 5Mt tc 2>/> ">*• ^<^ 



'^ 



^_ . ...A 1: i.t 1 i.B 7, bath true. 

"■'■'-'•*'--"'Si,}'{'"'{+ 

r.* J f J I! t.D 1 J.B ^,- boih ine. 
,'.A«U=.'./^^}*,ifAj- 

But, If A = B, W ito« — Jj-orltbetwwo 
B knd ite<r— B, then ' B -aiMi d i end 

1.) <■— d > j.^d-HiihiJ^^^t'^C. 






Other L«|. 






rUfdSdc 



FFI^ 



rt..„ ,. R»d.i,Cof,iiKloded^jiTw.Sid«op.i*ie. 
^ /,:^Tb>. •!><»« SBpn.fcft. 

The Wfaa Se|.B*w Di^ Bde- U« aQ. S^.' 
She tartlet SflM. 1 aa* f i|— rftm d l i ^ . 1: 
Tn^Z.indnded 1 Titi.bn|ht^. 
iMiSunKdetiSMf AtlrW. it Cm. j 

W: I SM-SUei i CoCdtheirZlt/ >^t.|i^ 

■ T*. >«j«ent •= ■ -^ --^ 

^ - -.itBiL 

cVettni 

Rid. t CttC iodadH £. rfTth. oMAcrSUt 
««A. -.^ ■*■■ ■ - * ■ ----* i^i« 



I'^RhA t(.D 






: n C Kf. D. 

r*. J 75^ t A i aI^ 1. 1*, i d 1 1.0 * 
IfA-l-cI^ tlo*. Tb«4 mmSHlB. 
AndCwD— & 
■I /Jii«Jli«J)2*|yjA, ifffe 

CKf.D. 
.'JJ t /.E ti ^.A . I'.B f^ j 1, if *} "^ 














and NAVIGATOR. 


3*9 






ANSWERS to tb« CASES of OBUQUE SpI^rUul TRIANGLES continued. | 






Ca&l. 


iwn. 




ANSWER. 7 . „ . . 


GIVEN. 


OUGHT. 


ANSWER, 






iDU((h 


By PROPORTION. j ^ 


By PROPORTION. 






9 


c,A 

IV. 


B 

Ot, 

Ao4 


= .'.A.,*.*./.^;^^}*.LfAj- 
= / Dif. ^, Then 

!.'.A!i/.*>K.rff^^ t,iSA\- 
= ,Dif.J. . ■ 
......i.r.A.r.B;^^^}e.if.5- 

u\k+,„.ii-,:,,.\A:,.Z- 
I'.iJ+Iif'.i*^ :: /.JAir.D^if 

T+i < rfo». 
rhen, B = D + Ej C=,D-E. 




„. . . Rid, , Cof. included Side j; Tan. *dj. Z. it 
"'^^- Bifc: Cot. «!}. vert. z.. 

Whence the lemote Tett. z. ii known =: Dif. 

»rtiole «rt. Z. «nd adj. vertical Z.. 
Sine adj. : Sine resole ten. z. " Cof. adj. Z. 
at Bate 1 Cof. requiTid Z.. 
«,.,. Rid. : Cof. included Side 11 Tan. adj. Z. it 
*'^"- Bife. Cot. adj. verticil Z.. 

Hence remote verticil Z. s: Diaicence vbole 

and adjacent verticil z.- 
Cof. remote Z. < Cof. idj. vnt. z. n Tan. ajj. 
vert, z. : Tin. Side reauircd. 

Cof. {Sum : Cof. i Dif. Z.> "■ Tan. i adj. 

Side I Tan. adj. Seameot it Bife. 
Then reqoited Side. = Sum ind DiSenncc 

of Scgmeoli il Bale. 








A,B,C 
V. 


t 
Or, 


.iCi. i'A+i-.-.i.l'T-Bxi.odi^ 

Did. PtrftnJ. from lUidd/, of tbe Bife. 
Sow, if Pcrp. within, 

A-— DasDAjV- J ***"• 
Or a X -D s= BD, wUn Perp. withoot, 
.A : Kid. 1. «.BD i Cof. *. Ct/r 4. JHf*. 

i.C X <.A (including Z. les"'"*) i '• si '-i 

B-H>-A X <.l B+A-C . .'. i *. 
[f A + B < J ,800, the Perpend, falli 


3 £j!b. 


Z. It Ihe 
Baft. 

How, 
Ot, 


Tin. i B.Ie : Tan. i Sum Legi :> Tin. t Dif. 
Lep : Tin. i Dif. or i Sum Setmenti of 

OrlSiundoBbdsewh.Bafe: the Pent. witboU. 

Ta». Leg Idj. Z. reqoirea -. Rid. .. T«. a^. 
Segment t CoC Z. >^j- required. 

Has. Z. Sine. Side, (incloding mpund z.) ! 
Rad. Sq. ,: E,a. Z. SImi. of two Difeen- 
ca betw. i Sum ofjS.de., and each Sidt 
inclwlintth« reunited Z. : Squttof Sine { 








VI, 


A 

How, 
Or, 


A.Z....i'-/*-f;;,^}Perp.faIl.}:i;,^„; 

r-.i^+i . r.J-Dif.i .1 !.{(, r.Z. in- 
clBded hf Paf^tJ^r and ^,A bifcOini 
the yertical Z.. Whence Z. BCD i, known. 

Fir, t c + •ai*br Diftince ftom Peipeadien- 

{ (, ci^^bi'^Diltanee fiom Pttpei>di«l> 
tf - + * \0\ 'So". «1« P"P<w>. ^U" 

"fA^ Ai. , 

r.* X W t '•'. ^--t <+H-* X f*. J «T3 
— a:.».iA. 

EeW</-r»"Side,W,j^.«-r™-i.- 

Or, c^uuige the 3 liren Z,> into Sidei, lod Sidei 

trquirtd into /.i, but iuftcad of the jreWeft 

proceed «ioG,f„. 


)Z.<. 


Side. 
Or, 


Cotan. i Sa- Z.« at Bafe 1 Tan. Jth^ir. Dif. 
:: Tan. j vert. Z. • Tan. Z. indtulBl bj 

ticJAngle. , 

Then to f vertical z. •dd «>f^ DiAiaM from 

Perpendicular for f«<.«-^. 
And, Dif. between ^ vertical Z. and annhr 
. Diftuue from PeipeodicoUr s= i,/, ^. 

Tin. adj. vm. z. > Cat.adj. z.atBaIt ::Riid. 

<Co/:adf.Side, bein| Hjpothenufe. 
Reft. Z. Sine, of the Z.I, ioclnding Side re- 
quired : Rad. Squaie :: ReQ. Z-twoCo- 
fine*, of ^ Sum it the 3 Z... and of 4 D.f. be- 
tween the two including ^., and third > 
Sine j,.^of i inclnded Side, «j,tfnrf. 


i 




f 


A,C,* 

HI. 


Or 

Apin 

B 


Ihe 7ih .nd Sili CASES, rtfrimi 

.E.S.D..r.*>r.4';;;j^Ji, lfD|^C. 
,i A+C.J.i"A;^H«'.^*.».E- 
^ \ A+C I •'. i A^ 11 f . i * I r.D^ 
IfA + c| ^ ilo". TbM, asD+B* 
AndcssO — B, 
, *'Jii..a...d^^}a, ifil- 
il = CDif.D. ^ 

/.Di^.E...'.A./.Bf;;;^|E, if*j:j: 


• Si Jit 


CU^Z.'. 

Or 

Again 

TbIrdSiae. 


Rid. . C^. Included Z. := Tan. Side Of. re^d. 

Z. : Tin. idjicent Scgm. Bife. 
The otliar Seg. Bafe -= Dili BiA and adj. Se| 
S'iar litter Segm. : Sine formn found Sef^ 11 

Tin. Z, i^ieladed t Tio.fou^ti'. 
Sine 1 Sum Side. : Sine i .heir Dif.. 1. Cot. J 

incl. z. ! Tan. remote Segment Bife. 
Cy. { £». Side. . Cof.{theirD/. , Cot.jiad. 

■»», otb>rz.itBaft»AwI Bale'.. 
Z. at Veitat = iJ./, JSrgmeatl. 

R.d. 1 Cot Indudod Z. -I Tan. of eithnSiJa 
Tan. of adjacent Segment tf Bafe. 

Wheocs Mher Seg. n Dif. Baft ud that Sw. 

&/. Mlj, S4. ■ Cof. remolt Sej. of UbTr 
Cof.«li.8ide , Crf.mooteSid«. 












U 


ft 




TU 





330 



n* ROYAL ASTRONOMER 



The PROPERTIES of Splmitml TRIANGLES. 



IN an; fpheric«l Triangle, The Simi cfth4 3iAt 
IM PrcfBTtim la tht Sinn *f thi eppeju* Anglti. 

2. Letdng fall a Perpendicular od the Bafe, from the 
venjcal Angie, Tht SImi b/ ihi Sigmnis of thi Sef* art 
rtcipTKollj frap«rtieital H tht teKgaUt »f iht a^aiail 
JtHgla. 

3. 7h* C»finu sf thi famt Sigmmti art Jirtalj prapar- 
H»«atl» ihi Cafina of tht a^actnt SiJti. 

4. Tht Co/bui of ihi iJtrtUal Anglei art ai tht Calangtali 
tf tit rtJ^Si'oi SiAt. 

t. Tbi Siniief tbt^HrticalJngiti «rt M tht Cofintt »f the 
n^taiiH ApgUi al iht Baft. 

6. A> Che Sine of Sum of the Leg* : to Sine of their 
Ptftrence :: fo Cotangent }* Sum of Anglei at Vertex 

to TanccDt ^ [heir Difference. 

7. Alpine Snm of the Sides : to Sine of their Diffe- 
rence. :: fo Cotangent { vertical Aogle : to Tangent 
I Difierence, or j Snm, of the vertical Anglci, accord- 
ibg ai the Perpendicolar ftlli within or without. 

8. Ai Tangent \ Sum of Sidei : to Tangent i their 
Difference v. foTanEentfSomofthc AngleiBt thcBafe, 
l' to Tangent i tlwJr Difference, 

9. At Cotan. of i Som of 2 Sidet : to Tan. | their 
Diference :: fo Cotan. } Bafe : to Tail. Diltance Irom 
qiiddle Bafe to where the Perpendicolar falli ) being Tan. 
} Difference of Scgmesn of Bale. 

10. AtCotangentl SumAneleaattheBafe, : to Tan- 
;nt \ their DifiiErence :i fo Tangent i vertical Angle, 

_ ' \ Sum vertical Angleit : to Tangent \ the Diffcrencet 
or itheSom ofverticalAnglca, at thcPerpondicnlar ialla 
i&n or wiilioni. 

11. Ai Tangent! Sam Segmentaof the Bafe : toTan- 
|cnt I Som Sidei, :: fo Tangedt f Difference of Sidca 
: to Tangent } Difference Segmenti of' Bafe. 

12. A* Taagent \ Bafe 1 to Tangent { SDmr Sidi 

;: fo Tangent i H'lS, Side* 1 to Tangent { alternate Bafe 
fc } Difference or \ Sam Segmenti of the Bafe, aa the 
ferpendicular falli within or without. 

1^ In aright-angled Triangle, the Reflangle of Tnn- 
ent { theHypothenofe + j one Leg, and the Tangent 
. the Uypothenofe — \ tlMi Leg a Tangent Square of j 
the other Leg, 

1 3. Letting UIX a Perpeodicolas oa the Bafe of n iphe- 
al Triaule. 

Ai Stnt Sum Angltt at tht Bafi ; tt Strnt Dijirtmt : : fa 
TantiHi i SmM »/ tht Stgmnts »f tht Bttfi : ia Imgtmt \ 

14. Sint Smi Jngbi at tht Sa/i i Sim Difwmu w Ja 
Tangtwl i B^ 1 ta Tangtnt i ilteniate S^t. 

I J. Sim SamStgmtHtia^ lit B^i : itSimaflhtir Dig*- 
t*c* :: fi Sim Sam jiagttt at tht Vtrttx : ta Sim tf tbeir 
>iff*rmM. 

16. AtSintB^ : la Sint 'otrtieel AagU •.: fa Sin* Diff. 
'a/umli at Baft : ta Sim T>iff. afAKgltt at Vtrttx, vibttt thi 
}trptii£falar faUi 'within i ar Sim af tht Sam a^ Sagmmti 
^ Bafe : M Sim Skm »f vtrHtai -Agbt, <uihtm tht Ptrftn- 
^cfiar faib vitint. 



17. AtC^fimiSam aftbtSida : la C^ti thtir D,Ji 
met •.:fa CBtaagtnt k inehJti Angb ! ta Taagrmt \ Stm 
af affafiti AngUi. 

iS. Al Sim i Sum af tht Sidei : ta Slat i litir Dijirtaa 
" fa Calaiigtal i iaclaJed AagU : ta Taagtat \ DiJItrtnei 
af aff<!fite AagUt. 

19. A» Cifiat { Sam of a Anglet : ta Cafint \ tbeir JUffi 
react :: fa Tangent i iacluded Sid* : ta7aagt*li Sam^ tit 
affiejilt Sidu. 

20. Sim i Sam af ttua Angkt ; /• Siaa \ ihtir DiJ^taet 
:: faTaagtwt i iarladtdSidi : ta Taagtnl { Differma afaf- 
pafitt Sides. 

21. Cofiai i Sam Aagltt at iht Baft : ta Ctfiu t their 
Dijertae, :: faTangintiDifftrtnct afaff^tSidet : laTan- 
giat i Diftrtact ar i £bw, ^ iht StgmaUi tf lb* Bt^t, 
the Pirptndieniar fa& wilhiaar iintbaat. 

22. In any fpheric Triangle, T\i^ Reaang}* efihaSimj 
tfmajt<tM Sidei, X Csjfiw of indaded Angle, + Reftaagle 
af their Cofimi e= Ctfm af third Side. (Kadioi being 1 ,J 

2J. TbeCafint of ma Aagltof a fpbiricalTriangle, s=C*- 
Jim tppafiti Side ~- Keaangii af Cajmi of lie- imUding Sidei, 

tbt luhtie Mwdtd bj tha RiSaagit af tba Simi af tbi iadaOag 

SiJti. [Raditu being 1.) 

24.. 7h* Rtaaagle af Siaei tf 2 Aj^let X Cejme if tht 

iliideJSidi — RratmgU af tbeir C^«« = Cafim of third ' 

Amgle, Radini being 1. 

3;. The Cafiaeafo)^ Side z=Reaaiighaf thi Ce/mi»flbt 

iae/ading Anglei -h Cofim if affafitt Angle, aad tbi •uibaU 
dividtdly SiSaagl* af Siaei afiia imladii^ Ai^ksr Radiu 
~- I. 

26. In ao7 fpherical Triangle, Ai the PraitB af iht 
Stmt af tvia SiJti, inelii£ng a riqairid Angle, : ta tit Prv- 
daaeflbeSimiafl'a)aDiJer*ne*ibilmMalii^Samafihe 3 
Sie/ii, oHdeeubaf ibi IvuSielei, iatiaiBag lb* neairtd Angle, 

:: falbiS^ar* ^ Radikt : t* ibtSfaartaftitSim af \ tb, 
fifmred Angle. 

\ 27. Al ibi Pradaa af lieSiaii efttvaAagliiy iarladiag t. 
[rifaind Sidi, : ta lit ProdaS. of thi Sines ofttuo DiSeren- 
icei, he/njMia ihtha^ Sapplement eflit ihrei given Airglti.^ 
andfbtSappltmtat of each Angli, inibuSng tbi rifnrad Sidi^ 

:: fo the Sjaare aftbe Ra£aj : U lb* Spurt af tit Cifint af^ 
tht njairtd Side, 

Or, taking the Supplement of the greated Angle only^ 
70U mzy proportion, at by Property 26, by changing the 
Sidet intoAoglei. 

Viz. As tb* Ptadaa tf lit Sims af ftut Angles, iacUBng 
lit nqairedSidt, : tt the Predaa of tht Sims of l-u-a Di£, 
remm invitta tie i Sam afthej giiie* Angki (tbt Snppkmet 
if lit grtatefi being anej and tare of the Angles, inclading the 
reqairidSide, - fo is ibi Sjaare of RsuHat^ : lo Ssaeva if lb* 
Sim af \ re^airedSide. 

REMARK, la phat Trigtaameitj, rijjht-angled Tri. 
angle) may be conndercd at fpherical Tnanglet, whofe 
Sideabcine very fmall Aroi may be confidered at Bi ' 
Linei 1 tin Iheitfbre become equal to their Sia*s m '. 
genb. 



yCjOOglC 



end NAVIGATOR. 



The PROPERTIES of Sphtrieat TRIANGLES. 



HENCE, to ftaiu Trigoiumttij, msy be applied, tii 
the Propordoot oi fpbtrical Trigtnamitrj, wherein Cofinti 
uiiCaiatmti Bic not concomeQ, bjr n&tg the Word ^aA, 



uif a Sidi, 
I plu 
itfoU 



the 3 Side* of m pluie Triu 

may be foiind, u follow*, by I'roperty >6. 



iknsle 
by Pro 



SSJr. Por, if 



Ji tit Prubff ^ t SiJn, buUJmg a rtfdnd AngU, 
ihi Fr^JaS §f timDiftrtiKis, hMvatn i Sim »/ ibt tbrtt 
Sidii, animdiif thtSi^tintk^Mgtbtrt^MirtdAiiglt, :: Ja 
ibtSgiurt if R^im : lo lit Sqaart tf tbt Simi of ^ rejainJ 
Angit. 

>8. Ill any Ipbertcsl Triingle, Ai X^aigU tf Sinn 
if 2 SiJes, incaiMgg a nqnirtd Juglt, : U Radiui Sjitari 
;; > vfrftJSit-t Vajt — titr/'dSlnt Diprnu vf ^idii^ : H 
vtrfidSintindaAd A-ngU, required. 

:: And > Ccjint Diprtnet ef Sidii — Caf. Baft : it -vir- 
(edSim ftid incltidtiAnglit re^uifcd, 

19. Alfe, As RtSaitglt ef iht Sinti tf 2 AKgUl,iudu- 
ding artquirtd Side, : ta Radiui Sqiiart, ;• fa verftJ Sim 
Sum of incltuUng ARgUi,— virfid Siat Si^tm. ^djifgit : . ft 

r/ed Sint imthdid Sidt, rei)uired. 

;: And> verfed Siui third AngU — vtr/ed Sim Sufpltm. 
Sum ef iMc/udrng AMgUi, ; to •vtrfidSitu intludid Side, req''. 
And fe &/ Diffrmce af tie including Anglei, + Co/. 
id I. : te njerfed Sine Sufpiemtni ef ittfiided Side, repaired. 

:: Aad fe virfid Sine Suppiem. ^d Angit — wrfid SiM 
Diff. incluimg AMgiei : te verftd Sine Suffltm. included Side, 
reqniTcd, 

:: KttA /i-^>*r/id Sim Snpplrm. D^.incbiding Angltt — 
t vtrfkd Sine ^d Angle : ft veifed Sent Sup. iMciadtd Side, 
reqalted. 

30, If em Are he drinom frtm tit Vertex la lit Middle 
ef lb* Be^e af ^JtiemaiTria,^, ' . \ 



Tken, tie Sawi if . tie •vertical Anghi are rteipraeaUf t 
lie Siitte af the Sidei, and direSfy si tit Sinet ef lit Angltt t 
ihtB^. ' ' ■'■ 

31. If thevtrtical Angle ef It fikerical Triangle ie biftll^ 
td. At twee Celmngent ef (be ii/rSiag Are : tt the Sum 
tf lieCttangetti tf tbt SiJti i: fa Radiiu : ta C^nti ver- 
licai Angle. 

31. A) tkiAh the HaJint : la Tang. irfeSing Arc w f\ 
Stem Cotangtnte af Sidee : la C^/aa { vertical Angit, 

33. A< em 
Circlet v.fel> 
centaiued iein 

34. As 4 right Anglti : te Angle inttreeptid 
great Circlei :: ft Snrfaet ef tie -witle Sfl^re : It Sirfaei 
intercepted bttvietn tbafe t'tat great Grcltt, i 

:: koA fe tbt Selidity af tie S^iere, : tt the Stii£tj ftai 
ttunid btituetn tbt z grteitGrclei. ' 

For the Soliditiei are as the Surface), becaofe the] 
mfiy beicduQtdroPyruBid* of ■qui Height. 



rigbl Angle : te the Angle hit-vietn 2 ^eat 
\ Area ef a great Crcit : la lie liutoltr Arei 
en ihofegreal Crclti. 



3$. In any fpberica] Triangle, A> tw* tight Aii^\ 
: ta tbt Exteftaf % Anglei ahevt MM rirbt Angki, v. fa ihi 
Area af a great 'Cerclt^etSpitre : ta At Area ef liat^ri- 
anglt. 

In any fph erical Pelpgeu, pot » = Nonber «f SaAtt\ 
A = iSo»x«— «, 

Then, Ai a right Anglei, or tSo* : To£n(«f allth^ 
Angle* of the Fafygan — A :: So the Area of a fftn 
Circle of the Si^an : ToArea of that Pa^gn, 



P«Ci 
3*1 • 

Stnt. 

]•« . 



CORRECTIONS /* it wndi la tbt Tt Shm, xtiA tit FEH, Inftrt it U vjtd. 

UlK 



ifr-Top . \ 

■ »♦ 

3fr.BM. 

>6fr.T«p 



^Jthuiil 



tmoK dtir Ifland 
, Divijm; 



Br^Bflliic of I 
7 UolttCi&i, 1 

H.B. >Ds:{ BD— DA, erVKl, s=i Dif. er I Sam, S^mnai ef Ba 
MdtDmrtKUadiidl*, tad Mena,djr^\&,atf7, tr liX, lima ihi' 
nvMSnmJmiUiiibewitleBi^iAntUFert^ia^rJkaiaiamil. 



» D± . . . 

• Sum aad.Kfi t 



. . c = D — E. 
, Sun <r Dif . nr> ^t. 



raarm lln Pofai£tular feOi miitbi 



See Fig. i uid s. Pagt jiS> 



^W>| 



'°?5gk 



ri* ROYAL ASTRONOMER 



SOME GENERAL OBSERVATIONS on the TIDES. 

.. IV ytH^fiTVtthtTimtitftbtfiJiifiHaiijPltut, at'tAt»t4ad?nii.MBtm,Mi iJf»thiir7imnM ibt ^^a^trMtrnt, 
thn i/jv prtpariitn tbi iDtermediate Afftai of ihi Mooa luiib tbt Sunt fi"*" '^fi ^""fi J"" "wii/ hav* tht Timti tf iht 
TiAt ftr tmeb Dtg of tbt Mmp'i Age, in ibat Pltut, very nearly, 

2. AT London tbt Tiiti, at tbt Qaarter-Maoni, htfptM (Kcnerallj) tAmot kw Htm- fiuur tban tbt MndJI* Time, 
bittottM tbt 7iJt Tiimti, at New and Full Maaa. Tbus, ai London, tbt Tidt-Timti, at New aiul Poll, an at ^nt 
Half a» Htar afttr lw» ; tit middle Time bttviixt -uihich Tiatj, ii half an Hoar after eight ; 6m tbt Qoarter Mooq> 
Tides generally haffta, at London, t^aut, tr btfart, half at Uatir afttr Seven. 

3. AT Doblin, it it /aid, tht ^arlir-Maaa TiJti bappen balf um Hfv lattr tjtaa tbt middle Tiae etiMtdfr»m Tide- 
..mtialDeteandFuU. Thiu, aa Ntvj and FuH, at ll>t Cultom-houfe 0/^Doblui, tbtTidti bafpttiabaal II i /ir niddle 
Tim bttweta ti-bieb Timei ii aiant $^fir tbt fimt tftbt (^atntt-lidti : But tbe;f b^fta abaiU half an Hour afttr 5, "titfaid. 

4. THE bigttrlbt Mtoa rijij abfoi (ar farthtr fiedtfctndthtltivi) tbeUorixta »f aitj Tiaci, lit Uglier tbtTidt rifii 
thai Place. _ , 

Therefore, in Nartb Lalitudts, tht Maen baving Narlb Dtilinatim, btivg ahavt tht Horison, and fafi tht Mtridian 
At raifei bigbtr Tidei tbtai inhm Jbe ii midtr tbt Harixm, andpaft tht Mtridiaa. 

(^ The contrary happens in North Latitudes and South Oeclinationt of the Moon. Obferve airo the fame ii 
South Latitudes and South Declinadoni of the Uoon. And the contrary ia South Latitudes and North Declination 
■f the Moon. 

5. CaM/ijutntly, ia Nartb Lalitudti, ia tit Santmu, (lubtn tit Ecliptic at Nam ri/ii UghirlhaM in Vfmttr) ib* E-vtaimg 
art bigbtr lian lit UmiMfTidti, Jad, /« Winter (tuhtn tht Ecliptic, at Naan, ii /ovitr liaa ia Summer] iht Mtraiag 
art bigbtr ibaa lit EvtaingTidtt. 

6. 7it bigiefi Spntig-Tida art aftoafi a /f»ili before 4w/ after /^Eqninoxei, aiaat tit Sfgianiag ^ March, mi 
' Sadif September, eacb Ttar ; Ut iht QnartCr «r Ncap-Tidei, art Itafi at litft •Times, aad ptalefi »f all in June aad 
' December, tAaat tbt Solfticc*. 

7. TitVi^^TidtimahthtlaKueftEhii. 

8. Htatt, /^ highefi 7f dir, «/ New (W Pall A&m, ii aJwofi ftlUwtd by ibelav/t&TidtattbtQpzrUT Mooni, 

9. 7bt bigitfi moaibly Tlda are ^catiiHy thfirvtdia it aiaut the_ficaad Da;/ a/ierFvil or Chxnge,ia Englandj^ttin 
fimt Plaeii airaad,a)at ToR<]mn,a^ New Hoiizad.titiigbt^Spriii^-Tidta art abjirvt J tt it j Da^a/itrifewaMdFiiU. 

10. Tides, la like Circomftances, artUgbt/l alliiVxixatOTi aial bigier in Itfi tban grtaitr Latiiudti. 

1 1 . Tide* are Hgttr ia larger Seal, and lower in kfi Stat, 

1 2. Ildei art higher at tit Sberes af Ctntiaiati, vibtre ibrrt an Riren aad Indraogbtli than in tbt S^Hle »f the See, 
nxibtn thij paft freilj \ tr art bigitr at tbafe Sbani, than they art ahoat Iflands, far frwn tbt Ctatineat, 

ij. jntUMRivtnt&tMAt, thtTideiel>blaiigtrtiantbefJI>m. ' — 

1 4. Tbt Malitn af the Tide it greateft a little a/ier half flttd, and a Rtili hefm half Eth 

15. J little be/iri bigi Wafer ia a River, lit aadtr ffaitr ^ tit Tide rant dtwa, laUlt the apftr Ifaltr raai 1^ 

16. jfy'lbtTapaf iigbir'lawWattr, the Tide bat ittdiriefitfia*. 

17. Siraagff^adi blawiag tbe /ame IPig luitb tit Runaiiig ^tbeTidt, bring it in Jiantr and male it riff Hgitrt iai 
blawiag canlrtvilj, agmtifi tit Tid^i Miliaa, htp it back later, iandmait it ran lower. 



TIME atJ PLACE 
. ODtbeDayofAuVorCJvmofchcMMB, fbrtfacPUcc 

a , „ to which the Time of the Moon't Siutiitr aa the pnuOtj, ind the Sum will be the Time of fegh- Water for dK Tine and 

PUm itqutttU EXAMPLE. Tt /lnJiln^iaiefbigbJf^, at LDndon- Bridge, MMayio, 1760' 
Time af High-Wnar it flftro and Full , . aH 30" 
On My 10, 1760, Moon foatht . , i . g 4 Moraing 

■- 1 So for 

Hiffi-Vfi,ttr ttLendM-BriJgi, thro , . lo jf Hotnjos > the 

Afld ...JO f --. 

Low Water at Graotfind ... j 34 Aftemwi 



yGooglc 



md navigator; 



335 



Ad Alti<.>Mi«i TIDE-TABLE, fnm till bdl AUTHORITIES. Shmiiit the TIME of HIGH.WATEIll 


at the moll remarkable SiA-PoaTa and Sia- 


CoAiT*. when it >■ NEW 


or FULL UOON. For findine thel 


TIMEof Hijh- 


WtKi in thofe Placei at ny AGE of the MOON. 








tWh: ■■ 




TimcH, 




rimcH. 




Tlie-b. 


Pim NAMES. 


Wtter. 


J-iat/i NAMES. 


Water. 


PiofN NAMES. 


Water. 


i>iWi NAMES. 


WMOt, 




h m 




h m 




li in 




h m 


A. 




&j»^«-!, 


64s 


P.»^// 


9 4S 


\i. 




AaiKDBiH, Seal' 




BrvvBgl •uttlbm 


3 4S 


fittBWKi 


9 4S 


Haoui 


8 IS 


1^ 


45 


Bmh^ntf, 


3 






"a^ 


6 ; 


Jt4nuriih 


6 o 
4 30 


BmUmh 


11 
I 


Edam 


1 30 




6 


Jbrtlh 


3 1$ 






E£iitwtb 


4 30 


tUrJUtT 


8 


Africa, Wz/fCV 


3 


C. 




Egmcn. 


4 JO 


Hmla, 


9 


Mli.r«gb 


9 45 


Caeh, Normandy 


9 ° 


Eidtr 





UmkfM 


5 


Amaso?. «.«..<* 


6 


CalJj 


S '5 


Elh 





Hm^h 


11 


/»iMt<^<,rr.Cc»ll 


ii 


Calaii 


11 30 


EmhAm 





H:,f„p 


10 30 


America, W. &,/( 


3 


O^t 


11 15 


Emu 


9 


Hffvrt Ji Grui 


9 


E. &«/> 


4 JO 


Omrvm 


I 30 


Em» Ewtrojui 


7 30 


Si. Bda, 


10 30 


AufiirJam 


3 


Omar/ljltt 


3 


tn^htfiu 





U,r, 





Aah^iSL 


Z i; 


CoHceU 


6 


EagemtUi 


9 


Untr 


Q 


AKfuirf 


6 


Capt Sitae, 


9 45 


y±. 


11 


«.lm 


6 


Jm,, 


It 4S 


CantiH 




6 20 


mijHi^i 


1 30 


Xnutfi.Fi.Coan 


3 15 


CW 


4 30 


IjivMtr 


7 JO 


KmiHrnl 


9 


Mtmil 


6 


/>/fW 


*4S 






ttajtor 


9 


Amtakra 


3 


,fg»cdH>pt 


? 


P. 




Htm 


1 30 


A^ 


I 30 


Si,rr»<uC«, 




Faia laLB 


P 


OJt 


6 


A^,n, Ft. CoaB 


2 IS 


in GuiKttt 


8 IS 


Fair yU SmJi 


II 15 


H-^T M,ul, 


S 'S 


Aur^, Fr. CoaS 


3 4S 


Carmarlbtn Bof 


5 M 


F^nli 


5 30 


Omlif-FM 


3 45 


B. 




OJttli without 


1 i; 


Fn, inE.Chaimcl 


1 30 






Bajadok, iafor. 




CeJUfti within 


9 45 


Fife 


9 45 


I. 




barj 





CMnift 


9 


FiKkmM-k Giaft 


I 30 


|OItltrIIB<LuCI 


10 30 


Baliim(wt, Ireland 


4 30 


Chu^trn./, 


9 45 


4 


hi^S,C,a/l 


5 15 


aar/V./-. F*. Coift 


7 30 


Chirhwrgh 


7 3» 


FlaJmB(M, 


1 


W.C«« 


3 


5*-,«„7A. Pr. C- 


7 


Chili Omfi 


3 ^. 


Florida 


7 30 


JlUU.dIJh 





5^ •witbvui 


3 4S 


Caniarntau, Fr. C. 


3 


'■^t 


1 






Bajinntt Pr. Coafl 


3 30 


CWo^ 




7 30 


K. 




AafAr. Eng Coall 





Cei^Kf/, Fr. Coafl 


* '5 


FoMUiuff Sset 


* 'S 


Kektiib Knock 





Biamioir, Fr. Coall 


3 "S 


a.> ■ 


6 30 


^«-iM^.N. aadS. 


9 45 


SiUivt 


9 


5<///^ 


3 30 


CorpMChriaiPoiDi 


I 30 


F,>n, 


5 '5 


HiU^ 


7 30 


B/r^:-^, HoUsDd 


1 30 


Gt«. 


ip .30 


¥«.buf, 


64s 


Km^, 


3 °i 


B<r»<.^ 


7 » 


Cryl . 


II 151 


F^y 


5 30 


Klw/Mk 


5 '5* 


B.r^«i 


« '5 


Crm*r 


7 


France, W.Os/r 


3 


1. 




lar 


3 


' D. 




Firti 


11 


Lawbxv 


8 i;, 


I 30 


Da»tmootp 


6 JO 


Fri^/UmdCM/i 


7 30 


U.if„^ 


7 30 


B^rr^ 


6 


Da-viit, Mtad 


6 






£An<^ 


^4! 


£/a<i/«;A«M> 


IS 


Dm/ 


10 30 


G. 






4 30 


B/«»iAK«M 




DUigb 


z I; 


Gallicia 


3 


Uiil, 


4 


B^KWf 


3 


VifinP^rf, in J. 




G^»Mdt 


5 


t-m 


9 4S 


Bh 


4 30 


mtrUa 





G^H^MMh 


3 


I^-J 


9 4S 


Biufwilhcut 


z "5 


Ditpp, 


10 30 


GafmmCHiff 
Ciir^BrRml 


3 


&•( 


10 30 




6 


Dart 


3 





Li'o. 


7 


Brajii Ctaft 


rS 


Duver 


II 30 


Gimritt Gia 


1 30 


is«.. 


z 15 


Brimtm 


Do^nt 


' "S 


Gort* 


1 JO 


U^ri 


7 30 


Brte Sound 


+ 30 


DMm B^ 


9 >S 


Gor«iJ 


>> >5 


l^-d.. 


2 30 


Brtft 


3 'S 


0.fim.h«,f» 




Gra»FoilU 


64? 


UmgfaaJHMj 


10 30 


Britan, S.Coaft 


3 ^ 


Dmb» 


z 


Gr0^^wg 
Gravffi^ 


a 


uT 


IS 


Brm*gtan Pi^ 


7 ♦« 


Di»d„ 


1 IS 


1 30 


IMrtlMh 


3 


4 




4 30 


Gr^ 


3 


i-al. 


I'l 


Btm 


.1-30 




9 45 


G-nj^ 


I 30 


i;...NotfcIt 


BHJlol 


6 30 II>ir«i>W 


12 


G«fiM 


10 30 


Lim. «itho»t 


_U1 



/f. B. 0^ o* fignifici laii 0", it Noon, or Midnightt 



Dgnzcd by Google 



334 



Ttt ROTAL ASTRONOMER 





.4**/kJ TIDE-TABLE eoMii«i.i. 1 






rimeH. 




rimsH 




rimcH. 




TimeH. 




Pl^tlJtiiSi.- 


h m 


piMf^yiAUii. 


h m 


J'Jno NAMES. 


Wxar.i 
k n; 


W««NA*ttS.. 


Water, 
h m 








Pt,au, b. CaaJl 


3 


i'..M<i 


11 30 












P^t.BlmJt 


4 IS. 


s™,*,^ 


3 45 








M. 




Portiu 
Piriiand 


3 
8 30 




^ 45 


W. 






Mackwell'i 




P^ardCotli 


3 45. 


s,^,a 


10 JO 


Walm 


S »S 




Castu 


« '! 


PM/iMii 


la 30, 


snn-am 


9 


ir^ji aincoln- 






«^ 


i ° 






SnnUn 


4 30 


fliire) 


630 




M^,, Sound 


815 






StvtrJt muth 


60 


ffaltr/itd 


6 5o 




«./&> 


" 4S 


Q, 




Uni,14,mh 


9 


ffaiani 


I 30 




St.«<ul,, 


6 ; 






Sbarntfl 





ffeOs 


6 




Ma,m 


9 


Qoi.Eci (Ca- 




SkUnJ, 


9 


f^nrnffuib 


7 




SI. »v4 


II IS 


d.) 


6 0. 


SklUit 


3 


e^ 


645 




* 'S 






Sh,..B^,n 


30 


Whith 


3 




St. M.uh^, Piii 


3 45 


Skip,,) 





Shr,i^ 


10 30 


mtrimgh^ 


7 






3 30 






Sim 





Ifieii Mm 







5 'S 






S,mm, U.ui 


II 


Winchdf,» 


II 4; 




UilfirdUiim 


7 30 


R. 




SiumJ ' 


3 45 


m»t€rm • 


8 


' 




3 ° 






Sfaliuw, Coaft 











Mmf.t^ 


+ 30 


RAMESjIMf 


1 30 


3 








Mmi-U, 


*>° 


S£ 


5 IS 
I* 45 


SfUhaJ 


11 JO 


Y\ 










«,ij4«i 


30 


S,„ 


5 IS 


Yxku 


64; 




N. 




Rfc-n 


3 


Slali, 


3 45 


r.«»«(i. Norfolk 


10 








SiMi/ 


II IS 


Staff 


64s 




10 30 




Nabtz Ri«» 


3 "^ 


)M,aKisitJ 


3 


SMbn 


5 '5 


r^ii^ibcime) 


4 30 




»>i> 


II ij 


RatM 


3 45 


Swm 










K«Jk> 


3 IS 


t^. 


4 "5 
45 






z. 






sx^Lrr 







3 45 
5 'S 


T. 




ZeiamdCoajt 


1 30 




Sl^< 


64s 




3 " 






Z^fi-SM 


3 t> 




»m, W. End 




StMm 


« '5 


Tes> Moutb 


3 








«f««m*,Co.« 
!!■»•(* 6/.. il%- 


10 30 


gm^ 


I 30 


t™^/' 


3 








^ 


II IS 


r.»< 


1 30 


JI^.JJ. The abOTC TIDE. 




<"» 


3 « 






witkogt 


o+S 
I 30 


TABL^ u fettled from the 
beft Authoritiei we couU 








S. 




T„p. 


vi 


procure [ yet it i* not im- 




O. 








ttU 


pro^aVe the Timei ofKri- 
&-«/friDfomePkcuATeiiat 








Saiitt Akoeiwi 


« »s 




S " 




OLlMVf 


S »S 


-nir"'""- 




t 39 


^aAIy u Arc here lee down 




Orfiri^l 


10 JO 


7 30 


Tfaami 


60 


— We (h>ll be obliged eo 




0,i^7 


6 


— D<nnf, Hoi 


6 


Ji;|fc, 


6 


PerfoM refiding at the Pl». 




o!Su 


9 


-U.U,; 


10 30 


tfiV 


6 


cei to inform at of un 




OJIml 


SO 


-tl"'^ 


3 30 


Tnfrt 


10 JO 


Miftaket there beiog no 








a IS 






Wey to come M €011111117 
in tbefe Matten, bnt ftom 








— M«t, 


5 3° 








r. 




— Uaiit^iP^nl 


a '5 

"3 45 


V. 




living Aothon. who have 




PiNHII, Fr. C. 


3 45 


— MiAul 


Us 


Vauhe* 


3 4J 


Tim« of higheft Tide, at 




f«»Cda« 


3 


— mv4«i,(Riil!U) 


>W.<. 


4 39 


New and FoU Moon, in 




fu,r Pm 


1 IS 


-PJJ,L«. 


t°. 


I'm! 





differeatSUcet. 




FicarA-QtaSL 


10 30 


— PnJ> 


^WwitUa 


i « 






rimMh 


6 


-r,^ 

^■^ 


11 


4 3* 






pi^^Jt, (RoSa). 


'45 













OISEKVATIONS 

by Google 



«»/ N A V I G A T O R; 335 



OBSBRVATiONS oa tht Oflrtwt BEGINNINGS of LONGITUDES. 

I. THE Diftrmtt of Longitade bctireni the Meridian of m Obfemtory tnd fomc £fiMi Mtri£a», u thit/ff 
wftDMd for deterinii^g the LaagituA, DecliKaiiBK, or right Afcenfion of the Sum, Mmh, or Plaiut aader that ftunJ 
hferidiui, from thttr Datu at ^^fi, oa a given Day and Year, with aUo dieir given dioraal lacreaft or De- 
cneaie. 

3. Ai there iddR be a ^atflian anfK-ercd to determine the DiSereace of Longitade betwixt any two Meridiant, 
wfiofe LoDgitudes, according taantitnt Cujlim, are given from Ftrra, the fame Qaeftion may be at readily anfwered 
from the Longitudei Eaft or Weft, coanted from another given Meridian. But if the Longitude* of Places arc 
liven at once Sam the Mttrtptlh or Ohferv«t»rj of any pariUuiar Nalien, they are ready (without dctermioiog them) 
for the Service of that Nation** Navigation, to afcertain the Longitade, Declination, or right Afccnfion of the 
CKleftial Bodiei nnder a diftant Meridian. And on which Acconnt we have given an cxtmfive SEA-COAST 
TABLE, following, with the Difference of Longitndea from Grttntmeb, according to modem CnSom, at well 
ai the correfpooding tAj§Lt* Longitndei, according to antient Cuftom, from Am, which modern Cufiom has 
ahnoft faperfeded. 

Example* of the eqnal Fadlity of both thefe Wayi of finding the required Difference of Longttnde of Placci, 
areleen in Page 317. 

3. Hence fntore Aftrmaauri and Navigattn may compare the Longitude* of Place* obfervcd with thefe we have 
^Iveu from Fim, or Griimwiib, a* a luar STANDARD of the Tnith ; and may tbAicc make their future Improvc- 
menti, 01 Confirm atSon of our following Namberi, P. ^37, i^c, 

f^ THE Xtvijtr af lb* Seaman'* Calendar newly reAified, al Pm 343, baviBg regrttUd tU Warn of an Oritr 
a/ farUamnI fir caujag AgrtaunI anatg ihaf* canttrnti im JkltUng tbt BigtHning af LtKgilndti af Piaeti (new caiifiuadiiig 
ih* inixprrUnctd Navigalari bj fa vtany diffartmt C^Miagi md BtgiMMJMgi t^naf) •wt bspi aur Eidtavnri her* bav* aau up 
t»hitWifi>*i, andanfiutrtd bitObjiaicm. 



ASTRONOMICAL QJJESTION, of great USE in NAVIGATION. 

^nws Tinf »/ tht Ttaf, in » givta Latiludt, lb* Tmtt itinggivtm ijf a Claei » fFttei, •whtH the Son 
thfirvid la bttvi bit Fartneam tadjf ftt rmt M JitituAi aSIti, la ^tmaat fram tbttui, ihtTimthy tbt film* Clack, af f/Wtb, 
thtn lb* Saafafed lb* MeritSm f 

The A N S W B K. 

Pot L ^ the Laiicnde of the Place, where the two Obfervation* were made. 
D E= Sun's Diitance from the Pole, at Nats. 



T ^ ^ Time (t) between the fun ObJrrvMtiani, in Detreet and Decimal*. 

V = 1 the Variation of the Sod'* Declination, in that Time [t] in Second* of Time. 

M ^ MiddU-Tuat between the Obrervation*, <x k v addfd » the Time of Forenoon-Obfervadoa. 

; Let ;ll2iii. ^ A A like T I wd B -3 D, A/. A. 

Then ''^ ^ ^' J X V ^ N, Second* of Time, the CorraOiOB or bltrval between M, and the tnu Time of Noon. 
.A Xi.D 



And, M ± N ae Time by the Ciack or fFatcb, when the SUN wu on the Meridian, acccording an be i* 
fs, ft, "B; itt, "L /.?defcending7„. 
ly. ST, X. T. 8, n.iafcending ^="8"^ 

SPHERICAL QUESTIONS aAfwcrcd. 

I. Tit B^itmfi, ndSrm tr Diff. •flit Up tf a Hjtt-angAJ 
^trital Trim^li it^t givtn It Smi ibt tr'umfh f 
ANSWER. From iwiee toe Cof. of tBe Hrpoth. fahtnA the 



[laline of Sum or Diff. of Legi, the KemiiadR will be the CdC of 
Arc, which being aiJid to the £iud Sain, or Dlff. ^n* the Dooble 
j^ die greitet Lei, KqBiitd. 

s. QvLtr, tnJtbt Sam, ar DigirtMt ^ita Bjftihmk tad ttt 
WLa,t,Ja!dtb.Hjfmbt>^t 

ANSWER. AiCoCILeg^TO], > taiuTugeiit ii fo the Cot 
[Smof Hj'p.andiHhttXaa, : to Ti^ f thur DUmnn. 



t. Tht^atOaBafi, -dStmtrDif. tf O* thfO i mdi mti BiA, 

givf, t^,<dthtfiAiHcMirrit^iir 

ANSWER. Al CotiDtent {^ pTCB, : toitiTuiemt ii ft Slat 
Sum «r the Hjp. ud *flj. Leg 1 to Sine oT their Diflercncc. 



4. Vha lIff.nd&m^Bif. tf itl haa a^aaat Z.i gi^im, lafiad 

ANSWER. A* Cot, } the HTpothennfe ; to itt TufCnt ti fi> 
Cof. DX, two ^1 1 u Sine of tb* Xm^ al their Sm ibon ■ right 
Angle. 



«B8SRVAT10}ia 



,y Google 



336 r*tf R O Y A L A S T R O N O M E R 



OBSERVATIONS «a the ANSWERS to MARTItTi or MORDOCH") EXAMPLES, ind od Che Simani Ij K 
ROIDAL SAILING, PiiciSj. 
RUM) wWcm SPHEROIDAL SAILING iitfprwmd! WKctStlKif, ingeiien], ttviwmn 
iriJhna! Parn if itt SPHEROID tn itjirtfd u fnve U, tad fiirw tU Earn if in USE, 

OUR ComTpondent Nmttmtn,ii obtain, aa bii Jirfi Remarh, Pip 196, on B. Jlbrfii'i NiiigiCien, bu Mcinin| u, 
7iai 41/ B. Mutin'i Exfmflei an !iki Murdoch'!, in rijpia tf tbtir iring wlti nrmr bepfn im Preffiei, and ibtt fmi ExMnpl* «r( nina 
eafh ibi JaKi eivitilari[ivni tj Miaiio<:ii.~~- Vfhituheeawt ol Oui Brmj, Pige 197, Liae 3. Bottom, DiouM be thii £nf,.—~ W«Br« 
n/i tarOittobCtrttt. — 

WhiL we hil to do *ith til ite/i Examfifn vm odj to fhew tbitthe fennl Cn/o of ^diCii/ might he JJiraify Mntvititi, both iccording 
the Sf tin lai SZ-btrtiJ, \ij tar Cmfaitn, No. I. II. III. morteafily thin bj the common Methodi in P»^/«i it. the fitnc Time we gn 
hfiactr, or mideCom^iiroo, of our comft Anrwcn with the Anrwen ^ren hy B. Mariinto the fime Queftioni or Cifa of Sailing. Wh< 
ther all Mr. A^diYtW'i Eiunplei of the Cain of Siilinj in ibe fame in all RefpfAi with Mr, Mirdxb'i, we had no lartber Regard to, thaa eo 



AljmrUfi or MurdmB, ai 

!AtJjaac Nnuiai't Theory. 

The different fphersittsl 



'dnb, and from Jam 1 tbe Form thereof, by the UJl of wUch Auihara, bdag confidered u mudi ibe marifl u Tmb, ud 



ew how much i;»^gii£]/N»^tk>n bitten Trom itfelf, actotding to the ililiWeDt ffbrnHat Figurei of the Earth, ilTumed hj B. Martin fnmt 

fjimriuii ot Mwiln' '""■ ' " — '"■" " — ' '"" ' ■-- ->-- ■ ~ -•■ ^- < . _■. _. 1 .■ »!..__._. ■. .l_ . . ■.- ., __. 

»'. Tbi 

fphersittil mcridianil Pirtt, iccarding to MariKb and JaaK, ait infetled in etr Wari for the Ntv![aitr to compare thrir Ufe ' 
any Caf^ af Sailing, hr chu!« to make Trial of, and alJb to try tbeit Ufe, rt^aHivilj, with the meridional Firtt ^ the Sfbtrt. By which be 
will ^nd that j^^rrvtb/Niiigition, according to Martin or MarJatb, differ) more fnm Jfbirtitlai Narigation, iccording to ^^m, thin 
Jaam\i>tfaifntn thiNa«gaiion of the Sphere. 

And the only Injiara, wherein the fphuoidal meiiilional Paitt that we bin infcTHd and contraned with thole of the Sphere, areddigiKd tobt 
plied to Practice, fi>r dcieitnlnrng the Sbjp'i Placi, it vba jm art fan itaijeur Courfr aid Difitact, ia a lawj Ran, an iaib virj ciimB. 
'hich Ship') Place Duy then ferte to compare with the Rifult of your feveril daily Reclconings on tbit Courfc, according to the common Ni' 
. jaiion of the Sphen, and thertby to marlc l}ie Dijimm ia Lmgiiaib, according to tbe mofl tant& Fnnn of tbe tencMal Sphemid yer diT- 
covered. Abue ^natim af a fno Number! ormeridionil Parti of the ^ierriif the nwft approved, (bough of afaal Authority with the Treth 
' 1 greater Nomber given, could not have eiinced their Utility or Jatiilay, in the Ejttenl thereof, fo well it by the 6 half Ptpi, to everj 
her Minute of the Quadrant, ind Ltngtb of the^rio to every Dtgree of Latitude, ai we have infcrted. 

{^ REMARK, fiincc tarptiatiag lit 6ih aai yth C^ei ef Mercator-Siiliag, 1M hmii tifirvid, ibfi ibt ttfa Cafe aaJ iri Vaiitdcui 
pri'vffrf in ji«MircrllaneiCuriora, /«■!*( JMWiisf January, FebniatJ, nWMlcch, 17J+, *y Afr. John Turner 0/ York, air ieaajid Ftia 
a/iJ CtrrtJftaJtai i 6tiiiribt yth Quel) ion ibirti li-irb sut frgfafij iaih lUfi Ct[e) viiibaii bmiiiig iifirvtd tbam ilftvAtn ^ war hait wt fitm 
liiber 1/ ikfi Cija frtf^ ima^lVark ^Navigation but tar avin. ibiagb ibtj an tbi^ ffrcalnivt. 



VARIATION (rf' CASE 6tb of MERCATOR SAILING. (See Pap 505.} 

jlSypfmltdfnMePtn!aLaiilaiii\'>V. apu, m aaiaam Ciatfi itimai tbt S.aadtbiVf. till htr Dtfantrt ^ati ^' ^^ Mila, ai 
Diffirati k Lmril»dt ^^'\l7 MAl, naairtd, frva tbtatt, btrCtrfi, DififMi nn, ead Difftrtaa tf Lalimdl f 
' ANSWERED by tbe DIRECT METHOD of Stialita. 

PUT x^fcei^thoftheATchof Lathadcurivedinj ^eo, iccording to Dr, Aa% (in VoL I. PUhf.Traaf.) thi mttidiond Parti of thit 



lod cootequeiitlr — ^ J43S0 Now, to make ill tbe Paiti of &e 'Mtrtatir-VrimgU ililce, multiply tbe Drpirttire and «]fo DiSemice 

of Unytodaby*. Let44'.4SX <=*; wid 74'.i7 x asB4; 4ad Jf «, x 6cix«=:Ji "sajifi^* the merid. Parti fee La j4». 

Theo. ■— M^^''"- -«> — T-«'— -4-«*, V«. ^ nuii^ Diff. Latitude { thepras.DiC LaUesl— x; Siy, b—u:txim— 
« ^ o 14 ^3 ^^' 

^•.^(1— i — xt, tff. .'i} whence (by muliiplyiag Eitreanu ud McaJi*] «e hai«, -^-^^«— « — — «'— — ■'^j-«'——^ 

■», Vt. 

Pot _ sa, ^— «— >i *nd»i — /«riEH— .* — .J-*), flff, Then, by Trmfpolition, n wsi 1— j»'-t~T**-h— x'+T- «'j ^'- 

Pat ■ — ■ = ft • ~f =/> ■"■• Lette n for the kno wn Coefficient! of th e Pow Tti ef j. Then, /« + rg* + "' +W ^ +I**! *'• ■=»< 

Ntw, M, or the Lei^tfa of the Aich being known. The corTefponffit^ Liiitude in Degree* ii that found, by bying, Aa 1,^70! i JO^ : 
... ..r .\.. I-.;....! i_.j ;_ mi 1.. ivi- -t I .. i. C.I . Dsp. ^',q.j :i Mcr.Lil.jii 1 Dif. Loos, 



.} CwHi [by Computer, N". I.] jj-t'IS. 
ij Trial OHrf Enor, (ftePige 505) ir/r^ov, 



t^ TbtiadirtSabtbtd'fStliiiiM, ij Trial mrf Error, (fcePige josJii/V™**. 

CASE ith of MERCATOR-SAILINC. , -a- .-j-^ 

JSb^f^fifiam0PlatliKl<air«lrn9ti. Difiama io> MUi, tuifiKbbtrDif.if Lu^. r« bi ^^^,i^mla, rtfiirti ttrC-afi, D^artwtt, 
fdOimramaflAUiUHltf 

^ ^ : Anfwered by tba DIRKCT METHOD of SaUtiim, . 

' InthitCale, by 47>h-t. (ttWog tbe btnaLettariai In iha former Cafo] Ai(—k proper Dif, Lat. 1 ^'t*— i* + « fa * * 
I a_yJ.«l -x', Vc. Ma. Dif. Ut. : J, Dif. Unptudt. ithtnct, wa bene an fi^nAwi B «/Eyi»tio« »be f^ttaied, andtbea 



the VilMof siihadbjr Vl.ertTliaa tt h/Mit Stria, If any Body chalet to take tbe Tine anld Trouble. 
|:> Tit iafinS afulti^Sabaitii, bj Trial amd Errw (Pa^, 505) ufnfirthb. 



yGoOgk 



mi NAVIGATOR. 



The' MARINER'S SEA-COAST TABLE. 


or Ac ptlncipal Ptrti, Harhttri, HtaJ-LnJi, 3^i, Rivers-Mtmhi. and TflenJ,, lying contifuous round the WORLD 


EiftorW«ft, from GREENWICH OBSERVATORY. Accwding to iha brft AMtbtrilia, and/*».- acc^inf 


to the wtfTtfleft Obfervation*. 




I. TlwC«f9ef EmiLAiiD 




XV. The Qmfl of Ahii ica in lite SMiSu, from" 








G^iA™- to Cdf. ««-■ 






■EUROPB. 


XVr. Bka.ii. In S»,i.A»;«, from 








C>K J/m to CiM Ro<iui 








XVII lU MfJn CoNtiK.WT Of the 

If a Mia 




Vr. TheMAi-CimTiitttiT 


wilhin tha 




VH Th./A«ft 


Strut). 


XVIII. TheGn..i*-, 1, , 

XIX. The ff-«n« I '"■*"" 


AMERI- 






■ CA. 






XX. Camolima, VmoiwiA, Ma.t- 

tANn, PiH.itTABiA, Niw Enolaud, 

Ud KlWrOUNCLAKll 










J[};_J_?£:^KW ["»"" 


■ 




Xli. ^ Tb,&J«i<r» J 




XXI. H«B,oi.-, Bat >od >hr 5/r«« 




Xlll. TlM JMW. COKTIHIB* » in tht f*J«l ASIA 


XXII. 1C.I.AKD.0«»CNI.ANI., No.A 




ZiHiLA, ind (ha AWricr. I>Li( 






XXIII. — . TboSoB»D».idBAi.Trc, EUROPE. 1 


Pilv«;\^»n, 




Pita, Ntma. 


Ut. 


..„ 


fr.'c;"?' 


P/oni A'd>«>. 


Ut. 


l-ong. 
fr. 


(t. Gr. 






ftn. 


B. or w. 




N, 


r™. 


w. 


I, COAST of EMGLAND. 


36. Ry- 


5' » 


■3 to 


o+aE 


7». Linciftsr 


54 4> 


r^ 


441 w 










1. BtlWlcK 


JI*S 


,'1 *; 


ItJw 


37. ««<*7 


so 46 


18 


ao £ 


71- Whiw-H»wn 

74. Ifle of Mb., 


i4 "7 


'4 s 


iisw 


jl '* 


I6 J 


3i " 
















t. Sbtildi 


5S » 


Id I) 


1 »S W 


jt. Shonhun 


" 55 


.7 .8 


a 1* W 


W. End . . . 


S3 45 




s s w 


♦, 8«ni«Iwd 


it S' 


i6ij 


"*ll' 


40! I. /^x^t, New- 


SO 49 


1635 


1 s * 


n- ?*^-?'*' 


53 H 


1* 4i 


4SSW 


,. H«ll«pool 
i. S«x:k<M 
7. Whitbjr 


J4 4J 


is " 


1 t V 








jS. Crlljle 


54 47 


14 10 


1 10 W 


H J3 
54 »* 

J4" 


is Is 

l6 ss 


J JO \V 
OSS W 


41. ^i ' ■ ' 
41. WeynOBtli 
4J. PardiDd 


4» 

JO i* 
4» 

JO 


16 IC 
'5 41 
■+ iS 
•4 5' 


1 30 w 

iii 


[ 


II. COAST of SCOTLAKD. | 










-7-7 


9. Humbra-Hiid 


M s 


'7 46 


6 E 


44. CkHiotk 


ols 


'4 3S 


1 S"! 


N. End . . 


57 45 


II 50 


5 50 * 




54 ( 


'7 43 


" i! 


4S. tin,. 




14 10 


J., w 


t St. Kitd.. 

J. HUndofUni, 

N. Ind . . , 


57 5» 


7 JO 


9 SOW 


... Sj-rn' 


SJ4i 


17 4S 


t £ 


4i. Toflhvn 
47. Tbe .S»]i 


I] 4i 


nix 
























il.if>J7 


13.5* 


17 15 


o.jW 


48. Totfc«y _ 


i» 


'3 56 


344W 


4, Farro-HFK!, or 


















0,6 


'1 57 


3 41 W 


C.Wnth . . 


5* 1* 




n^ 


I,. Orimfti- 


SJ JO 


IS JI 


oji E 


JO, The£«n 


r* 7 


rj4! 


3 5» W 


J. ^*«&.i/,S.EB, 


6c 4 




.t Botton' 


SJ 10 


i> e 


»dB 


;,. Tb^EJ^ift^, 


(o 10 


ij 11 


4.9 W 


6. Fiir-IOe 


59 3° 




>>| w 


;i:^:s. 


5» 55 


■1 7 


*17E 


S*. P4-«* 


JI 


Ij IB 


4 *i w 


7. inei ofOrkntY 


59 10 




I 17 w 


51 1° 


.8js 


OSSE 


JJ. R.IQl>ud 


li 


'J 


44oW 


8. Catlmcfi Poini 


ia+o 


■4 59 


3 41 W 


ij. Bli>kcn]> 


51 8 


il 3o 


O JO E 


S4. Foj 


14 


<J 


440 w 




5? 45 


■ e 17 


r *J W 


.3. Ctonwr' 


5} "0 


l?4» 


I E 


iS. f-i-w* 


n 


u.s 


5 <S W 


10. ^irJ«M 


57 " 




145 W 
1 45 W 


.,. Wintntoo 


i* JT 


■1 57 


• "1 


S*. LiixD* 


H 55 


'* 55 


ilS 


II, Qundee 


6,8 


'4 45 


M. r-r^fi 


i» 4» 


ig 13 


I ji E 


(7, Lind'iEtuI 


e 


" 35 


11. Leitb 


S6 


'4 39 
'4 35 
IJ 30 


3 1 W 


tiSiSit 


J* II 


'!'■ 


:;ii 


5I, C«//-RKlt 


,j6 


11 49 


fi f) w 


IJ, £»IK>I]>OK* 

14. Ciifi«, 


$5 5* 


4 ta W 




J» 10 


lit; 


•lil 


6g. Stvm StoMi 
<l, Hi'tland Poiat 


a 


JO so 


6 JO W 
««* 

4 45 W 










n^J 


;ll! 


10 

JI JC 

SI »o 


"• 55 

13 
'» 55 


III. COAST of IRELAND. | 




,. f*i. Fo»<- 


/ 






»*. IrfMP«M» 


S' V 


■7 SS 


> i w 








440 w 


J. Belf^l 


55 5 


" 5 


6 JS W 


.7. ««l!*' 


51 »8 


i9 1 


ofti E 


51 I» 
5( S3 


" SS 

JJ Q 


55 
54 S9 


II ** 


's^sw 


S:«^?..-». 


5" »7 
SI »7 


It S9 


1 9; 

■ I.; 


5> 4" 
51 3! 


13 10 


J 19 w 


4. Mind-Tora 
J. IQeiQfA'rja 
i. Stap ofSroad 


U I 


'r,! 


9 ^W 


3. •..J.il. 


51 »5 


lit! 


■ >! 


i' 45 




5»0 W 




^1, ThtDowu 


Ji »3 


its! 


IK J 


68. Si. P^ifi 








H»Te, . . , 


54 7 




10 II W 


3,. Jl»(iF««UiiJ 


SI » 


' "! 


BmJ . . 


i* c 


11 iJ 


5 17* 


7. met of ^/« 


54 55 




9 St w 


;,. !li,«l.-S.«l 


)' |} 


ihl 


1.15 


**' riS^' 


5» 44 


n )i 


s iw 


a. Clin. 


SJ 7 




) 4j W 




SI ft 
5° 57 


VM 


n^uvXt 


53 M 

53 3! 


H J5 


4 aj W| He*d 


5* 4° 


s 5 


9 3! « 



y Google 



33« 



fit ROYAL ASTRONOMER 



The MARINER'S SEA-COAST TABLE. 



' 111- COAST of 1K.EI.ANP continiMd. 




»], I dud Uita 

14. Hcr-iinc 

the Middlt 

16. Iltei oJ' Olnoa 

17. J!«W» 
tS. SiwritaaP 
19. St. SebalHu 



HeligbUnd lUi 
J. Hintnrth 
^ Biemta 

J, EmtidtD 
. AmtUiHl-Iflin 
;, Schclini 
.T1k«» 
). TheTeiel 
9. Ahitkbah' 

J. Th« Bri/l 
4. Middkhnrgh b 
Zolud 



■ 3S 3 



15 '° Ji * 
35 8 SS I 
.5 10 7 JO E 
13 SI * 'i S 
»3 33 5 S3 5 
»3 S S "S §^ 

5 s! 

4 sa E 

J ♦*s = 

SS 4 "S ^ 

It 1 Ji E 



C>p« St. Mkta 



?I CO.tST of l^RAtjCE wJ POR Tt'G-AU 



^' sTvdwj 
4. Sitia - Hnd, 
Cape lit^iUih 
. Rmn MmW 

6. CapeBufleuT 

'. CdPcdeUHcaui 

., CaOun 



: ir-^Srt 



', mini ie Soft 

'7' ''!*• . , 
il, CunuiuBax 



49 SO 
*9 S" 
49 33 
49 >S 
48 J9 
♦» 33 
48 5° 
+8 S" 
48 «7 

♦!'* 



»I7W 

i>S w 
.1, w 

> »w 

4 5" 
4 33 " 



47 '>•• , 
4f »»*S- J* 



3ilW 



31. CipePioii 
]i. Ottejil 

33 -Comma 






■ tS w 

I 3» W 
3 5* 
6 (W 
■7 jj.W 

9»S W 
9 45* 

9 3"* 

,., W 



j8 4] »-4s » sfr W 



'35* 
i 7* 

i « vr 



Vi. COAST a r^ A 



4. QucJ'wf 

5. Ai»t, 

>, C^Sii Mar'. 

7. Bmrelh»M* 
S. mrUHa* 

II! Lc«t>ra 

IS. CiriuTeiUa 



»"4» 

3*4* 



[to. ^i** 

1. R<safl 
11. CAIU* 
La Valoni 
P«iitfPltulM 't 



1511 

39 S6 

39 43 
41 40 
4J»5 
+♦ JO 

4» S5 

4*47 



il<a 



*- 4 S> W 

1^ U|w 



- 'S o^ 35 I 
.J » 5 «• ?■ 

ij J7 j J7 ^ 

V 9 •* »» ^ 
]t 10 14 4* E 

34 JO i« 5» E 
jj o 18 o E 
]« 16 iS jf B 

; J4 J5 18 JS H 
I ]i I 14 .1 E 
: *9 45 » s I 



lii^ 



1 37 JO w to E 
I ^o »7 M 47 ■ 

I tf E 



, . Ciryw Cfiloane 
31. SaJoOita 
J]. Capt Moote 

34. GallipotI 

Cafe Barbadof, 
orSiba , . . 

37. Smjr^B* 

1%. CapcBabwiUJi, 
or Bfanc 1 . . 

^9. Epbcfti* 



44, TbrMGl 

Tiipolj 

Jopp.,orJaf. 

fa . . . 
47. Jtr^lm* 
4I. AlaiMMirlt.'*- 
4$. Cap« KoCitsi 
JO. Cape mttan- 



J 5. Baal 

J7. C^=rf 

jg. C^e TUtUU, 

OrDdlya . . 

ia. (^TMa 



■*■* I 
4S iS 



a8 39 

S S4 
»4 3S 

3 JO 

' S3 



^4S?E 



i« MB 

3 JB 

'o 59 E 
<« 14 E 
g 14 B 

6 10 E 

413E 
3 ** ■ 
>1JB 



■ Vlf. ISLANtW wiiUa tbe StRArR. 



J. Ivic 
4. M^rtA 

MitottC\ 






ro» -jE 
' I ' 



3973 

S» so 
34 jc 1 

39 S' 



19 3* 

If 



S »«47 
»» «S 



III 



yGoogle 



ad navigator; 



339 



The MARINER'S SEA-C"OAST TABLE. 






Ut. 
N. 


Long. 


3.Ung.l 




Ut. 

s. 


Loo|. p.Lo»i.| 


P^lAkM. 


ft. 


ft.ffr. 1 


PAwiVkM. 


fr. 


fr. Gr. 1 




F(rr,. 


'•"*■ 




FiFTt. E. or W.J 




J4.-I res, 




/ 






TT 


. > 






Ijn^-i p. 


• IJ 


n 4» »* E 1 


H^C-fW" 


? *i 


>7 JO 


» ^.l\ 




"•I'-hs 


«r 


H >5 


6,jE 


JO. CipcKogra 
,1. RiTcConjo 


6 i 

^1; 


30 « 


> 16 El 


T. Porl *-&«, 






.. - 


il o,s«E 


Minora . , 


19 4> 


11 47 


t35l 




3» *» 


4' 33 


1 !3'= 


J.. AngoU 


33 31 IS 5' '1 


0. C»!itw 


J7 4' 


16 ,9 


57. &i .. Xio 


Ji » 


♦3 47 


i Je 


33. CipeSt. Tho- 










384* 


,647 


s r « 


ji. i>«^ 


37 »° 


*4 30 


«joE 




4 " 


3> 18 


4 j!E 


II, ARctci* 


+1 3 


>6 4S 


, ,E 


J). Zina 


37 15 


43 " 


SI- I 


34. C^ i ^', Se- 








11. ar/«, S.EnJ 








11. Zio, 0( S» 


37 17 


4» IS 


»4 4J E 


(...orSea. . 


19 


31 31 


IJ iiE 


Boniraci, 


♦I »4 


»7 »i 


9 4lE 


fil. Fcfoiiii* 


37 H 


4* 31 


•4 53 E 


15. Cpe of G.a 








Ij, Cbf/«,N. Ewl 








<^ SUuto, orSoT' 








It.^* .... 


34 >5 


3440 


17 oB 


C.p« Corfo 


41 S6 


*7 »J 


14! I 


bat* 


3'S8 


4* 55 


■1 H' 


36. Cip. Apiilku 








14. CoigOBi 

I J. C.p«i.,orOp. 


43 34 


»7 >J 


> 31 E 


6]. UiJlo, MiU.oi 
Mtlo 


3640 






or UeoIIi, . . 34 54 


3>5S 


11 .sE 
















(ii 
r«. LQbi.orZa* 


43 3 
41 4S 


>8 ■ 

»8 J5 


lo i> E 

<» i! ' 


'-. 


End C. St. 
of /.Jib 


35 *i 


41 35 


.3 !!« 






17. Planoft 
il. Vt.Clnifie 


41 JO 


.8.4 


.«44E 


65. E 


Cri-C.So- 








IX. The WESTERN ISLANDS, 


*» '7 


>g ,5 


lOijE 




A*, laroon 


SS ° 


44 43 


.7 SE 




ig. Pi)ln>ro)Ia, or 








66.(1 


bo-- NEk 










"■y 






P.lB.n. . . 


4' 1 


)I IC 


13 30 E 


li.. {SEnJ 


]6«7 


+S .3 


*' 33 E 










■o. Poat 


41 


Ji l» 


ij 31 E 


67. c. •rr4-j»v 


3« ' 


4< 3 


>8 *}£ 


I. Co.*o 


19 5- 


34640 


JI oW 


II. Ifchi. 


40 S4 


j» 5 


14 >s E 


68 


c. B«r- 








». Fion, (4k^,A\* i->\ 


346 41 


JO J9 W 


11, Sfrmitlb 


iB JS 


33 35 


'3 S! E 


SWEnd 


b 


34 57 


4V 58 


11 18 E 


J. Fyii 


38 53^349 ID 


iS -.0 W 


ij. VdIcukUo 


18.7 


3J 8 


IS iS E 


69 E .f 


C. Si. 








4. Pico 


38 46^350 Ii 


17 2J W 


14. Fctliut 


»«S« 


3* SS 


»4 !! E 


S IJ. 


And« 


Ji J» 


5* 15 


34 33 E 


.. St.G«i. 


3> S> 


3CI ji 


16 S w 


^t. AUicur 


jSrt 


1» '7 


"4 37 E 


78 ^ 


Cie 








i. Tercc™ 


38 57|35» ' 


»S19W 


16. fyr«* 


1« j6 


JI 17 


■34;' 


r 


Crt« 


34 3° 


50 4S[t3 5E 


7. Gr«tigr. 


39 "6350 34 


»7 S W 


17. Trep«no, W. 
En^ of Skilj 


17 57 


JC48 


■ J IE 
»»4S^ 








8. WhiltFiDi 

li. St.'Mich»l 
11. formipr, or 


39 37 3S» M- 
}S 43153 47 
J> *3S1 S9 


tS 16 W 
»3J3W 

*3 4rW 


Vni. COASTrfBARBARYMdCtJINEil. 


I. C^» «rA.. 






. 1 


ta. C. P.aim, W. 










35 50 


.14C 


^-! 


HofinigM 


37 4« !S4 4' 


" (» w 


£sd cfS-ti/t 
10. M.J/h...mfialj 


3«1! 


33 >i 


16 IS E 


^ SiUe 


33 5; 




M. auMiry". 


36 i9l353 571*3 41 *■ 


33 r 


31 Si 


3. CaprCuyn 


ji 16 


8 I. 


9 IJ w 








■ 


If. Miiilimo 


18 I. 


34 4J 


1, jE 


4.Qpe-J.G«r 


34 »7 


I'' 


IB 11 W 


1 


,1. «,««;,, ia SI- 








S. CapcBijidcn* 


i< IS 


6 }• 


>l 9 W 


. , ^ 


tllr 


37 I 


11 ta 


■S4"E 


»6 4 


• t> 


■ now 


Z. C«HARy ISLANDS. 


11. C. Udlio. i« 
Sitilf . . . 


36 J« 


33 SI 


*t S> E 


7. Cpe Oknrfo 


M4' 

><• 31 


1*1 


16 oW 
174A W 


■ 




P- 






J4. CpeMfiirO 


33 "S 


iJ ISE 


,. s.«»a 


ii»8 


> S 


iS $3 W 










jj. Pintdni. 


Ifijg 


»9 S5 


,. ■< E 


10. Cpc^yir^ 


•4 43 


30 


■ 7.0W 




]> jg 


' 4' 


'5 19 " 


\i. LinoA 


35 S* 


JO 4* 


., I E 


,u M<iu4>.aflJT*i 








». AfcAr,fl-W.ElM 


J' »3 


9 


>7 ,■ W 


17, Lin.piJof» 


■M 34 


3* SI 


,:„E 


G«<^< . , . 


.3 8 


» 4 


IS36W 


3. S.l»^. 


30 c 


45 


16 55 W 


3i i4 


3» 9 


■»>9E 


11. SuTft LtM 


1 J« 


4>S 


13 . W 


4. Pilna 


»8+c 


3?9 S9 


T7 4« W 


,B. Onnriil. * 








ty Cpc AM^, 








J. F«.o« 


»7 W 




.74c w 


Rock . . 


3! 4» 


34 '■ 


,6 11 E 


or lAiunL . . 


6 »i 


S IS 


t» 3 W 


e. Gomcra 


iS 


30 


.7 10 w 


40. k™/., 01 r. 








14. Msnftado 


• S 


7 J3 


u JW 


7. PicoTeamf 


t8i 


" 7 


i«]3 W 


Unr . . 


M »5 


33 53 


.«.jE 


IS, Ri»r ScOu » 








g. Grind Cnuy 


17 ji 


I »J 


la jl W 


,.. Pbm. 


tJ ic 


33 4» 


16 1 E 


5<ao« .... 


*•* 


>M 


I4. w 


». f^^^ 


19 ic 


5 ■ 


^1. St. Aiidi» 


H " 


34 > 


U >i E 


16. Ope dePWMi 


f »3 


M J» 


«jo W 




>9 


4 jt) 


.. so* 


„. Lrfli 


tj 6 


34 >S 


a ji« 


17. Ki>ciSt.Aiilia 


H 


n «c 


,^yr 


W. r<.n'^«,. 








ivAp.& 


41 iK 


34 M 


,, ,s J 


a. Cpt 3 Point, 


H 


•"S 


] S. W. End 


>B 


3 59 


'3 4« W 


J 5. Co™J» 

+7. CorpSa 
4I, CephaloRla 


43 3 
41 i' 


IS 7 
35 *'■ 


J.7 »7 K 
rf ! E 


^j,^M« 


4 >* 


;a; 








TT r*ADir nt ^mttfi **> A*ma 


'^T 


lS4« 


" ISE 
^ 9 E 


■I. Cft Corb 


l*S5 


■•»9r 


■ «• 


ZI. CAPE DE VERD ISLAMD3« 


>9, Z«it« Ut 46 




tT 


1 




^. S^mft pi 4= 


19 » 


.. ».E 


«.d»«« .. 


i»S!5 




ini 






• ' 




(uJiw-oy na4» 


45 40 


l& o£ 


fj, RmrltniMfa 


7" " 


»4 I! 


t. it, A'MTOwla 


17 14 


1S»3J 

is» i* 


IS 7 W 




»^CH«Fon»& 


♦ "S 


*♦ '5 


S^l 


1 *. St. VlntcM 


'7 4 


444W 


J» 1I1& A&jCUIPELAGti. 




'4 «> 


■s i 


1 J. St. L.at, or 










^ OUOkbuEBt 


4 K 


»r«oi 


r4.E 


\ lonadlhml 


17 


31* S 


»4 4S W 


S».rryj f4o 4(.|^<i. Sfr|*S M E 




I "5 


:fs 


T3JS 


[ 4. St. NJthofu 


16 J 


jlS3 37 


H SW 


fVA<»»» |ja i9[41 i'.\*i J» E 


^Bi^As^ 


.»fO 


I J. tatJiSfi 


16 Jc 


355 »7 


*■ ij W 




1 


1 


t' 








' - 






I 




1 





,, Google 



■Tbc ROYAL ASTRONOMER 



The MARINER'S SEA-COAST TABLE. 


!L.r |I^»*|D-»-"l- 




Ui. 


U-g. 


D.Lon^ , 




Ut. 

N. 


Lone. 


D-Lon*. 


P/«« Ar.wi. r^- ft. fr. C- 


FUmNMm,. 


N. 


fr. 


fr. Cr. 


FkcttNtma. 


fr. 


ix.Gr, 




/■iTTS. 


E. 




r,.T» 


£. 


XI. CAPE DE VERD ISLANDS eonimHB!. 




," / 


' 


' 




, V 


g / 


> / 




14. C«.C!.do 

15. RiytticSimb 






WM 


78. Poiot Rmtmd 

79. Point Or 


1 16 




10, 10 H 
9* 57 E 




> / 






** 51 


\\.l 


110 JO 
116 37 


7- '^•^•f^f 


16 5 


JSS'S 


" "^ 


>6. i>» Hod 
17. StrM* 




87 .5 

90 


,':iil 


80. Sinn JTMrwrn 

8 1. Cunboidif.- 


l+Is 


118 30 


100 50 E 


g. Futgo. wPolgo 


's •* 


3Si 33 


i» 7 W 


a. Dtmui 




91 5 


73 »SE 




10 iS 


>»]5 


■□4 s5 E 


■ 5 g 
.450 


354,39 
153- S4 


»3 I W 


.9. 0W« lOind 
,5. Si. jAn". 


<9 a 

'9 55 


90 4t 

90 is 


7i 'E 
73 'SE 


gi. Ope AilarilU, 
or AnriJli 


'3*i 


.53. 


.07 jJE 


to. Bnm 


14 18 


JS3 33 


*♦ '/^ 


]i. ClMiil, or 








83. CocbiQ,or<:hiij 








II. tutfd 


I 10 


li» S 


•S !S W 


^ Cho.U . . . 


,g ji 


91 11 


73 3»^ 


chc« : . . . 


'4 5 


iij ]i 


'07 S» E 










11 Dibd 


» 3 

IT » 

'i 1 


9" 35 
9" 4S 
91 x% 


73 Ji| 

74 SE 
7345E 


84. JMx-H* 

8j. Toi„«in 
8e. C«M* 




1)1 16 


..,4*E 
lOi 3sE 
"3 3E 


Xli. SOUTHERN ISLAKDS. 


10 jo'iij ij 
»3 *M° 43 




N. 














Ij. CirwiT 


'4 47 


9> IS 


74 5!E 


87. Anoy, or<itt 








1. FttHAMDlPin 




ig s 


10 IS £ 


]«. MwqueloiT 


ft J3 


93 c 


7i«E 


moy lll.od 


=4 35 


'34 "5 


.i6,sE 


1. DePnwt 


I 40 


..5^ 


, tiE 


17. Tdkchnrv 


11 4> 


93 


7S"E 


88. Hockfrw 


=6 l-H'li 55 


..8 liE 




i isC 


18. Cillnut 


II 16 


93 5 


7S »iE 


89. RivCTiSnmtW 


*7 S 


136.5 


.18 4sE 










„. aODUlOO 


10 >i 


93 "0 


7S JoE 


90. Li»mpo.L'ngj«s 










S. 






fo. Cochin 


9 54 


93 30 


TS ioE 


orNi™ 


>9 i9 


.38 10 


»o,oE 


4. St.Ma((he«n 


I 3c 




6 6 W 


4.. Anj.„p _ 


g.9 


94 o 


T6«E 


91. Iflinl ChcCin 


10 


.38 .0 


■ lojoE 






4^, dpc Camcna 


7 5° 




77 10 E 


91. N*iiq.oi«* 




MT 16 


119 j6E 






It a 


7 11 E 


4J. Colo«bo, io 








9j. P,.i»» 


J9 S4j>34 '3 


i.S^jE 










ZM* . . . 
u. Poim dcOiUe 
"^ orGJIOjOnth. 

oa tbc TiiBc 
47. Cr«c Bdliu 


7 7 


97 5 


79 «sE 










6. 4-«->. 

7. St. ttfo«No« 

g. Si. SA^ 
9. Triftuo fc A- 
cuntii , . . 


16 c 

17 5 


4 St 
>S4S 

J 45 


."r^ 


6 10 

6 1 
<4= 

6»3 

9 JO 


97 45 
9l*S 
9> IS 

99 «o 
97 40 

97 3° 


to JE 

go4oE 
gi 15 E 

8. 40E 
go E 




XIV. ISLANDS in the EAST IXDIES. 


6 ,E 


4-iW 

'121- 


I. St. P«d 

1. Ajnflciduullk 
3. Aourai ae Caf 


!l^ 


93 

90 15 


7S»oE 
7«3it 


XIU. Main CONTINENT in ih. tAST 


79 SoE 


tU-Umu 


»<4J 


94 S* 


67 i,E 


INDIES. 




•» 45 


97 'S 

97 >9 


7945E 
79 39 E 


4. Sl.Joan<lEL>/- 


IS 14 


7" J 


6*4e 










I. BAr de Allo- 
CD or DiUiin 


»5 S' 


4840 


,1 =E 


SJ. Fort St. D«id, 


" 54 


S7 S3 


to i3£ 


I:K£' 


11 


2 1 


s. Riv«i Sc. £.>»« 


lUo 


49 S> 


3» 11 E 


orTrfp^n, 


'» 5 


97 «1 


79 4jE 


7. Mnuiciiu 




70 30 


S» SoE 

60 »jE 


,. CiHSt.M«Ao 








(4. Coaftxre 


■> JS 


97 4= 


ge o£ 


8. Miihi 


11 Ij 


7> S 


or Af^ 


11 4c 


5.40 


\i.ll 


JS. Fort 81. Ottrri 








9. est. Ml- End 








4. Ctjt drinta 


1] ^0 


S3 S* 


or34.Jr«ft|M- 








rj, S. of 


4S47 


604s 


4S jE 


J. MoClDDuqlK 


'S 4 


\Ui 


M S E 


'« . ... 


13 Jt 


98 7 


S0.7E 


10. CD-An-Mi- 








e. p. 4c Asiad), 








56. Pullial 


.3 30 


97' 57 


go 17 E 


bR, N. di- 




684^ 




orI>c!C«.J> 


10 17 


$7 4i 


to SE 


j7. Aimtion 


14.6 


97 47 


go 7E 


II. TetndeiMa- 








7, Cjpc de ft/> 


9 ° 


i'ss 


'rs£ 


S8. PCf-lj 


16 6 


9I 17 


So J7E 








g,Tone»» 


4 S« 


s« 34 


15 "1 


S9. D.u Poin., or 








djB.i .... 


1919 


61 10 


44 joE 


,. MM>b.lb 


J S" 


S« 5 


]i »j E 


MhU . . . 


16 8 


P4I 


Si 17 F 


11. St. John dc No- 








10. MdiDdi. or 








So. MifuJipitam 


16 ai 


81 jE 




17 «l 


6a j( 


43 "jE 


Milinde . . 


> 5> 


57 10 


19 3a. E 


61. MUTipon 


16 3° 


99 31 


gi 5>E 


13. S. ChriftoT. 


17 J* 


61 IJ 


43 3S E 


tt. Ri*erLm« 


I 10 


57 4» 


^ g E 


6.. VifH^P...-. 


'7 43 


1 01 31 


»3 S>E 


.4. M.ycto 


13 10 


6j IJ 


45 33 E 


li. Rifet it Fvp 


41 

"nT 


S8S0 


H loE 


63. BintilipMun 
6 J. Iiclrnnit Fa- 


;n; 


101 44 
101 s« 


lt.;l 


17. Cain«TO,orAii. 


i» S 


61 3J 
6. Is 


UsiE 
441SE 


11. M««d<HU 


1 w 


6115 


M 45 E 


e^ 


■ 9 51 


104 17 


%6 ,7E 


E*t«cli. 


u 40 


6.13 


43 45 E 


14. Cipi defidjbi. 








66, Ariipire 


19 II 


'°4S8 


87 ]g£ 


]g. Motfia or Mm- 








oiBoxai , . 


4 ' 


«5 '3 


»7 33 £ 


67. PMUt PaMm 


W) 4* 


10 S 17 


R7 47 E J* 


S 7 


S7 50 


4010E 


■ f. CapeGw<kfb> 


II 44 


6*5 


S. isE 


6%. BaUJm Romd 


*l 16 


lOJ .3 


87 43 K '9- Z«»*^ 


«4l 


57 3» 


J9'5»E 


,«, Aden 


I] 


643s 


^« SSH 


69. PipkT 


>I ij 


;:ii: 


gjSiE 


so. I^nda 


J 10 


57 .0 


39 10 E 


■7. M^Atf 


■4 ■< 


e» »5 


K4i K 


70. Hu^iy 


13 9 


g, oE 




10 30 


U 14 


44 34E 


it. Cope M<ar'>a 


'i *i 


B945 


i» JS 


71. D«c. 


'1 S7 


10130 


II j: J 


». CofiMddo 


10 14 


68 S« 


51 H 


19. Dcfu 


17 


73 It 


55 3" E 


7>. Caliiiibiur 


.s'« 


loS 10 


aj. J«od««™ 


9 30 


70 It 


p 36E 


»o. Cpr Rrfulpt 


11 41 


77 10 


S940E 


73. Ri«r*.^ 


i« 17 


109 56 


91 16 E 


^. Aflortllfc 


9 JS 


7«»J 


iJ4SE 


„, C.P3&«, or 








74. Bi«rAr»aa 


■0 10 




93 35 E 


»S. Agdi^oiCri- 








.Mnft.r. . . 


ij j» 


77 »o 


S9 40 E 


]t'^U^ 


'« JS 


"3 55 


9« "SE 


kp 


9 47 


7« t 


S4«6E 


>i. Boftro 


^ 45 


«ss 


,9ijE 
5*S5E 


1 ll 


'"9 45 


loi cE 


16. Sen* Hv»»- 










17 M 


74 IS 


77.F>n>ob - ■ 


«■ s 


"9 5 


IQI.JE 


DCt ... , . . 


*47 


7S4S 


59 " 



yGoogte 



•Mi NAVIGATOR. 



The MARINER'S SEA-GO AST TABLE. 


, ,, Loa|. lb. LOD^ 




Ut. 
N. 


Uo» 


D. U-i. 


Pin,^*^. ; 


7| 


U.|. 


a.L^av 


PJ<mJV«m>. 


fiT 


ft.G,. 




fr. 


fr.Cr? 




ftr«^(e.<nw. 




■ 


JWa. 


w. 


XIV. ISUANTM io tb* EASF INDIES 




a / 


. ' 


• I 


13. River Cnde 




a ' 


< f ' 


ConiiniKd. , ^ 


74. Cttbet, N End 

75. fcltridiDo, W. 
P»rt . . . . 

76. B«T», N. P«t 


140 


'39 SS 


.».jE 


EotrwKe 

.4^IfUSt.C.(io.i.^ 

15. Cpefri. 

.6. CpeSr.7SM«. 


!" 5S 


335 ■; 
33s *" 


49 $w 


»7. Qo-wlo, Que- 






Si jiE 


7 40 


i]6 so 

I JO 40 


119 10 E 
iij OE 


>3 .0 

11 IO 


bdlo . . ■ • 


3 i] 


70 11 


,'i: T- ??|'' 


11 JO 


'37 45 


119 J E 


.7. V'»&"<«» 


>9 » 


33S 15 


4a leW 


it. Baflii lie Ban- 




«e It 


4»4iE 


,8 ,5 


'37 4° 






336 »s 


4. liW 


hu 


S S 


79. Fw«- s, Pm 11 'o| 


'37 3" 


119 51 E 


19. PtUt^rprw 


it 31 




40+oW 
4> sW, 


19. HnmiBoi 
JO. mCfto 
J I. Padn Banlui 


IE 


83 7 

86 .0 


6j 17 E 


80. /. N.P^ 
Si. PifuiUntBiait 


:ii: 


;!i:: 


..0 40 E 
118 joE 


ij. RjvoSt.VrV 
1>. OfinJti'iaPei- 


11 4^ 


13*35 


34. Th™C«w« 


<ss 


6I40E 




10 y, 


)39 4i 


I7SJW 


XV. COAST of AMERICA /BfitSOUlH- 


S 40 
4 30 


SG c 

io )E 


6S »oE 


SEA, from Cfi/.™;* ro CAPE-HORN. 


Dunbuco 
2]. Cipr!ii.^„f'„dij 


l\\ 


;♦! 30 


35 "W 










,(. ov-uw* 


4 le 


7i4'^ 


j8 oE 


1. Cah St. S«- 


'. ' 


» ' 


• » 


.4. ft.rq.«i^ 


S »o 


141 ]> 




N. 








t»45 


i49 4e 


III oW 


I J. C.peit,« 


s ° 


3414^ 




j6. y- dc Ambn 


70 S 


S»ijE 


i. Cift St. Locu, 


11 »^ 


i6s 49 


III jiW 


16. in^nd )<> diniQ 
do LonnJJi 


1 5° 


34G 2 J 


ii 


57. ^wn, or 






54 oE 
S» 49 E 
7140E 
T»53E 


J. C*/* C«i^^ 


>ls» 


ibj s 


.to JSW 


a;. Pin River 






Zucxon . . 

it. A'jdclou IC ' 
J9- S-btll. . . . 


'lis 


71 40 


S- Aijiiituico 
6. Gnitimila 


"T 5 

■S»7 
14 IS 


»7S >7 

176 J 5 


loi jW 


it. lfUadS[.i>»/ 
JO'. in.rfaPi'rti 


»o, 30 


3S» 5 

m: 3i 


40. M.l*,« . 


9 < 


»» 33 


7. Puami 


Ijc 


»9S 43 


81 S7W 


3 1.. III. d. M«ti4- 








4t, 0»npe.«wCiip 
4,. Q«Jp«a 


10 4c 
10 c 


,90. 11 
9« 5 


7. j«E 
73«SB 


8. B., B<v>nn< 
ture . , . 


3 S4 


L,,., 


7I-11W 


31.11], St' Mui;de 


19 30 


3S0 V> 


., oW 


43. AndoDUaiii « 
AnUd. , . . 

47. r« J* D..JJ 


11 10 
6 S 


91 7 

98 SO 
93 J7 
90 39 

89 J5 


73 »T E 

li JoE 

,6i7E 
7» S»E 

7> SlE 


9. Ifluid GiUopt' 
1* . . . 

13! U5>r«. 


b 

"sT 


.ij.i 


90 ijW 


13. la Afcci^M 


19 40 548 xs 
7 40 J !• 


»15W 
■4J.W 








7 M 

10 


630 

tg 


»>4S 
100 SI 

J04»5 


iCVll. c6aST rfrt, J<.,>CONTI(feHTl 
wrttWEST INDIES. 1 










4I. l/U«iU 


14 »i 
•9 30 


■]4 41 
"4 Ji 


117 4E 
ioSsjE 


14. It. fuiU'^n^ 


J] IS 


, 


SS >tW 


I. RlTIl Ama- 


N. 


. « 


• / 


CD. >«> NE 


'9 Si 

a J' 


"7 3' 
.58 J 


109 joE 


i£. PortSfmm 


39 1s 
).( 50 


.,;;; 


8. i|w 

8»4iW 


moB'i Mouth 


4»S 


gSil 




1;: teK .-,< 

54. Cocoi . . . • 


!S " 
4 It 


m6 S 

MI 4' 

10! s; 


.iS.jE 
90 S7E 


17., c.p« ria»y 

18. &[« W«Tr, S. 
Pirt Tcm dd 


S» 


:j:.1 


83*sW 


]. Sara urn 


£ ij 


Jio4i 


jsjiW 


Xf^r-::. 


" 3i 

4 5- 


'1 s' 


9. .4E 
..ojoE 


Fucgo 


S6SS 


»97 40 


So oW 


7. MoDtb of (>n- 


s 1 


1»7 39 
319 40 


JO )W 


57. Nimbir ■ - . 


7 11 


III 1; 


93 35* 


XVI. COAST of BRASlLJaiWi.4-m«. 


10 JO 


3'S »i 


i. ijW 


'tod .... 


S" 


111 as 


94 4S^ 


from £if< HORN U 0^ ROQ.UE. 


«»« River 
8, l&.TriniJ,dt 


8 li 


3.8 IP 
3.7 18 


iJSS: 




8. 






S,. B^i. ... 


s. 


r*i 43 


'04 i^ 


I. UM4i«Str.iH 


i4 34 


1.04 J4 


7*3 «W 


10.* U! Curafoe, 01 


irio 


J'4 »S 


'I .sw 










I OpcVirgiDMi- 








Quicafoe , . 




JOJ 40 


tS.ioW 


E«d 


S »» 


■" 4^ 


lOJ J I 


i7crM.tdlu 








.1. Cape Conjoin- 








et. JimU 


. .^ 


no y 


,0. JO E 


Suaiu . . 


S» 


30* 10 


7S loW 


bato . . . 


1140 


joS jj 




«». An(«i 


e *i 


i>] 3, 


.OS JO E 


3. Point of Rira 








11. C.t^.» 


"J 17 


jot 14 


7S 16W 


6]. Stamt 


6 16 


114 »i 


106 41 E 


4. frJy'M« ' 


484^ 


JOJ 1 


74 39^ 


ij. Ddrio, or Sctrii 








64. N»/« llbBd 


» 54 


117 7 


99 »7E 


47 «■ 


J"" 5! 


e6 4JW 


Settlement 


S JO 


191' JO 


78 (oW 


6j. Eniino, er 








I River Omero- 


46 JO 


305,8 


71 l»W 


14. P»nB,a,» 


9 33 


»97 50 


rtioW 


■non^K".. 


i i° 


t>q IB 


.0, 3I E 








I J. IfuartriuEar 








S«.Selui 


S ao 


11948 


101 8 E 




*S J" 


¥>* 35 


73 SW 


trance . . 


II ij 


>93 a° 


8410W 


67. Prince. IIUd* 
fii. y««.E,End 


6 JO 


wi 37 


103 57 E 


7. Paint dclcuLe- 








16. CapeCuuRxi 


.6 u 


■94 S 


8j IJW 


t 31 


•H 5 


113 »jE 




M 


3?« 55 


70 4SW 


17. Cape ifu./w-<i 


16 IS 


Ifll JO 


8+,oW 


6,. Sinittaffo*- 








|:&fH;J 


4a IS 


3»9 35 


jS jW 


iS. Salaniaocha 


16 ,i 


QsU 


891JW 


70. Si,;,; s. lei j 


£ 1 


»3>i 


.OS 4. E 






19. CtjtCtaiU 


ai Um.t 


Sl.fw 


] ao 


i»4»o 


106 4«E 


ditd . . 


,14c 


lU.JC 


6i loW to. cw CondeJe. 






;,. B«r«o, Scth 








10. Rivet K« 


314° 


3*9 59 


S7 41W dT . . . 


10 40 


'^7 a 


St 4sW 


IVunt , . . ; 
7a. Sindi IlhM 


J S4 

4SS 


'44 S* 


.13 J. I 
"7 "E 


11. BafMjhrti'lB 
RinrPblr 


34 3^ 


3<9 35 


J8 jW »»lTriS^Triefl 


1930 


•8s »S 


9* ijW 


;3.Cd.b«,5.En^ 


J IC 


IJ«4« 


1.9 «E 


ll.Cv!8(.M>rf# 


34 JO 


3*055 


S6 4SW lOe. . .. . 


18 10 


iSt IS 


9t ijW 



,, Google 



34J 



Til ROYAL ASTRONOMER 




MARINER'S SEA-COA8T TABtE. 



19. £. Efid of tqf- 
ftl^U . . 

40. St. Damnrt, in 
Hifpuiafi . . 
W.tnlofHir. 

41. HfHEniol]*' 
43, Pail Rojil ia 

4f . . . 

47. WeflEodgfCV- 



* 



il s joi 45 
17 44 ]<M 3 



fr.Gr. 

w. I 



441W 
SSJW 

9 jW 

4 oW 
J oW 



Xl^i 9AVAMA ISLANDS. 



I. Btll|BBA« 

1. Natl) Put o( 




1*3 W 










»6 ^ 












lA 








too 4!! 














i £W.>»>4> 


























l<«.fr 


11. R»e.,fc)P 


H 3 


,c^ g 


... £1«V 


►li 




,l,C5Bpk«dlU,H. 








M ft 




14. LflH". S.»«t 












.7. SkTm 


'IV 


304 


»4 JS 
11 40 


3.0} 44 


H.Hfl«««i 


»sH 


J«» ?» 


.0. ««^, Wdt 








;t? 






i°& 17 


41. C^tt, Hvtk, 








w f: 




»iaj"w 


»Mi 


l"? »7 


jiiS"^' 


iq 10 


]q8.ic 






3: Sfdrftl 




s;r 


}B, G^HOqitW^ 


»4« 


bi 




H^ 


m;i< 



7*40^ 
74 JJW 
76 

r4 '7W 

74 S7W 
7140W 

7> S.^W 
71 4SW. 
74 So^V' 
74. oW 

7?S'*1 

7» »W 

7* »AW 
70 i>, 






ui, ^^ni^^nT 



,, CoiumdlL 
}8. Zau Qetn 



"J 10 IM 1» 

17 10 »f« 7 

■} JO iSS fo 






XX, COAST «rCAR0UHA,VIIt01NIA, 
MARYLAHD, PENSILVANIA, N£W 
8NOLAMD. ind ISVrFOUNDlAKD. 



1. Port Royal 
ofOoAiilarai* 



6. C\f* HttttTM 

7. dpe^**, 
I. ClpcCfwr^ 

orCip* haiqi 
ij. LoDB laud, 

!*<«• . . 
ij.. Uw York 
14. M«B|wkPd»t 



17. EJJMtMth'iiK. 

tect . . . 
It.. Mrrt^-iVwe. 

Iffi- . . . 
19. NwiWckM.U- 

ta. S. l.t.i.oiVt»- ' 

tUClwtShMll 

ai. SoDtk End oTSi, 
CtMBa'iBnok 

1). BoAiin£nnwcs|4« 
14. C«p»C«l 41 

16. «U«*U^^b>. 

17. North V»r- 
WMfh. ■ 

»f^ ^oipi, on Port 
Kertl , . 

30. OpcjSibla 
J I. iAMl^S<U»^ 

]]. CtfbCtarlii,.ot 

J4. 4a(i Qp4iJUI. 



104 1* 

iJ<»3 ♦» 

iBjo,4« 

. _o 306 JS 

1 l» J07 "! 

■ ' 5 lor 37 

)0S M 

30! it 

109 17 



iS I'O V 

30 jql ._ 
II Jo! 40 
*6 307 jp 

■4 J°».S7 



40 

45 f a 

i°t*» S7 
■o Jl8 J4 
4 V>9 " 

H S*i 3J 

4i|iCj« 



7<S»W 

7«mW 
74*sW 
7J.9W 
74MW 
7J44W 

75 iW 

7* 50W 
7>»W 
7«4jW 
TO iW 

«»«4W 

«sjw 

tl Si* 

«9 oW 

t»s»w 

TO 15W 



6(4iW 

« S" 
toffW 



,y Google 



Mi NAVIGAl'dk. 



The MAMNEK'S S'EA-CcyASf TABLB. 



te. COAST ofCAROLlNA, VIRGINIA. 
MARYLAND, PENSri-VANlA. NEW 
ENOLAND, and NEWtOUKULAND, 



3*. TitihnHTk 
«. Btr of flfji . 

4C. rrrjMRMllI 

44. in. St. ivw 

45. Oipc St. LA- 

tfi. PUKmu»tj 
417. Cjjk Si. JM^ 
ffi. Sl.John'tRar- 

49. Bi)' ofStl/i 
;C. Cape Rire 
Jl. Cape St. Fran- 



_ )°7 47 
c !'• 3* 
ic ,ao ,i 
7 !»» « 

S )'* 47 

*»'? SS 
J'9 SJ 
T? '7 



'U^« 



69 J3W 
«7 ftW 

»T »W 
Ji4»W 
j.„W 

li ijV 

S7 45* 

it.iw 
5, Uw 

S>44W 

s- 34W 

51 S7W 



66 15 j: 



Ci/a WalGaf 
bini • . . 9a J5 ago 40 



.in-ifH 1(1. 

' the MUdle 

i. S4eeput''i Mn 

[, Bjkci't 001(1 

Ill« . . 



0. Ifdm't 10. 
,, SoS^mon-iTcm 

plelQuul 
t. Shepbnd'f IH. 

3. DaoSj*! IHand 

4, Chailron't If- 

' Und 

Ic. Rnftit'% Rivei 
61 Fnochmid'a 

Kirct . . 
tf. Point CoBirort 
fS. MonIe&iTet'a 






So 10 196 5, 

S7 56 aje . 

54 '° »94 Si 
i* 5* »?♦ 47 

96 47 
*9J J9 

»>i ij 



»l. OnrHctviiHa 
Mana ... 

if^ Gaf/Gbtrii,!/ 
1(. Sir Thknaa 

Roc't^c/»w 
it. Caft-^MaAr- 

17. SkirlaAiM 

1$. AfiV/i lllti 
]D. Sallftorf Umd 
Jl. SiliaecfUlinJ 

lind . , . , . 
]|. Rerotalloit lit 



m 






jUXIL COrtlT of 1CUAN0. 
LAND, tfOVA tnUBLAi«t»l 
THEKNlSLtl. 




KffliljfiTit 


s,;; 


■ir>; 








tMK* . ,, . 


(ri< 


-4»4C- 


Fiftar-i UhK) 






NtrtbCtft 
SurroT iflaDd 


7. »3 


4037 


Tmtr«tittA, 




ft i 










i9 15 












M >j 


Mt Tf 






•>ri«> . . . 


6Sl< 


»J S 


WW., aifymy 




















i^* 










WsrliPoiM 










-ai ti 








Snif.Ndi, S, 








ii4f 




Hurle IQ, S. 






End 






Bommclji). N. 


60.0 


aj li 


Part 


ifl"( 


»3 IS 






















"" 


19 10 



.o.'st 






"3 J 

■ii'5 

IS JIE 


..«£ 


k* 6B 


.. ^B 


>3 Sii 




>14»B 


WT. 


.> ,B 


S* SB 


)r<i> 


MilB 


« JB 


1. .Si 


sst 


17S!i 


1! »B 


)« i«B 


Ht5}i 


jr .1 


««mb 




li jsB 




.. iSE 


MsI 


»•!! 


7l!l 


».■»£ 




s.r-E 


«J!l 




! JlB 


J JjB 




I'll 


? 19! 


n4»E 



y<o«ogle 



«/ U O Y A t -A S T R O N O M E R 



The MARINER'S SEA-COAST TABLE. , 



1^ VUHer^n 
I, Chr^tmflt 
. Cilncr 

iOt- IS.Soi 
^W jN.EtHl 

I. AboD 

I. aMia 

|! Rnd 

f. X«r«'« 10. 



(« .'» 


.6,. 






S"S4 


.6jc 




>7 ji 


57 P 


19 s< 










,«,. 


3° ; 


ij;; 


30 35 




,64c 


34 " 


,6 I, 




?7« 


14 35 




JJ a 


59 M 


IT ; 










A04C 






44 >' 












46 , 


S9 1: 




S9 3j 


4» J 


"1 


4" 15 



"55E 

16 ]OE 
ijiSE 
.8 55 E 
iS 15 E 
■9 »5E 
II jE 
>i jcE 
»i 5SE 
*«+5E 
.911E 
]o i«E 



30. Oomaocu 

3 1. DcT WlnJi 
33. Der Memel 
33< CoaineltiDrgli 

ll Hid ' 

36. WiAr, iBQot- 



37. Cm/<W. N, Ewt 
3t. G^U»d, S. End 

39. Btnbtlm 

40. Cannlii, oi Hi 



41. jRgtart 

43. ScruUiind 

44. wir™ 

45. Lubeck 

46. Ctfab^ttifl 

47. M/^w, Rud 

S. EIlCDora ' 



oowin. . 
TUSnm 



54 30 

S4 17 
S4 »i 

!+ w 

54 « 

55 M 
s6 JO 



.J.7E 

»S 4»E 



tS 4SE 
1, jE 

.I.5E 

17 40E 
1440E 

14 55^ 

'I "I 

li 3sE 



Bt»it, udm^indfir Rtfitna, H/ma 
ttt SitMMtlsm ttid QrOfnfYij tf Ptaatt im 
Rijfta / met irlv, «i 101^7 « fMr L«>i- 
(■£> mw/L,-tirm4a. mcrm « alrlubc. 
tint T>Ut ^ tU (mm fUen (dbMOtUr of 
Ibc Icb rnnirluhle) btirtfuirii^tvtdam- 
Hi Sm-mia txfUnlhtir SiltaiH*. jimtm- 
fttt •/' vA\th Mf it /m, (/ fit ]!«• M- 
kf f «»/■'■ ti( SilaatHM tf a^ib^htitat 
fliai, M Rab«nCin'i Nan|itiati ] wiwA 
jK pwi « Uw ^ (Mr Coadfoltf. 



BoJia ob'feiTcd mdn ■ ^|jm Miiidlu i All Bfbtmaida, 'In Bookk of HMipcjon, bci(i| pioparl; bhuIb tor lbs frineifal plait of * Nilion' 



. , , comptnnhb what dl other N(tl»)hn« fitcd, nftillfli, tbti 

.^ DificKBci of Lo^ititdn fram Mch Mar^tEt m niodfi OiJirv»nry of cteh Kttlan, ttrptSiwlj) md ihca . . .. 

DiSertnce of Loagltail* wtb* LoDiitBdc Imn Farti ij which Mnu in A g ri nt nt orDiftomct la thi Longiluilci, aoiDBi t^H di^RBi 
DUnrmnocNi^tUcnt wUlbciniBediudffecai ud thtnee tCiruiwi/, or Aifrwaanrf thnon, iMj'llig IboMrbebid. 

AMlmmof Opiirfealhu»UHitiori>aMotdMblilhllKi>cafeAf(10UbTttlaMqi»Ttgrl7, mtntmtUj, uthcfirt mKlt, fonbt Ub ofih* 
I*»i|HM, u htN neatlowd, *ad th* Oood of MukM nftacnl. InBMd of i^cli, wcABd tt» cukftLiI Otfnviri of oat own Bniiji 
NmUm, I^JbAivojusnnttbteDirfoGllonMptiacipkUMf mroMMof, mofCbickwudarmrA, thtqihaft or iny aihcr Njboo, af< — 



Bi6t^ttitiMtQUiitnti»oi(an^tti;ttrtfm4fir U^it thtfMkUm^} Ar tba Ufa of tkaMKiautiUoH, in ptrtWiogihcTactiRT 



IiUwbWUu Guhi, wi J^mmir, (Scim< n S& Iiaac Kivton) tha laH /bwf j uid (MMa>wM>hi« Dr. 



,, Google* 



t,d NAVIGATOR. 



An «A£«««/iVd/TABLB of the LATITUDES oifnm/mm 


and remarkabie PLACES, with their LONGiTUDE.J 


from the lOaad of FBRRO. md Difference of Lou ginde from Grumwtb OB.-ERVATORV. : AjcordinK toj 


the Authority 


of the SiturOESPLACES. in hii£/iv«<tt*/, ftom 1715:0 i7is.- - •' - A 




. 


Ung. 


D. Long. 




Lat. N. 


L..,. 


D Lonj. 




PUotlUmi. 




fi. 


fr. Cr. 


F&m AfflH. 


«S. 


fr. 


St.C. 






■or . 


ftr-.. 


E. orW. 




F«r«. 


E. or W. 


O In the SEA.CO.VSTTA / 

BLE, the i),^r.«< of Longlrui . 

'wy. il tikeo actordinc to Dti 
Haff^, !• 10' E. wbifh t»ke.j 
fromioo, EaftL-ogiWdeoffw,! 
from Pirn IBe, leivn i;" 40' E( 

Longitude of Grmwitb fron^ 


Ao»A. InMotul 
^uaidric, Syria 


«6 4,N 
J63.N 


94 14 
54 ° 


Sill 


MarfelHet 

Mtnixia 


1444N 


3:14! 


5 17 E 
6, 9W 


Ahff,,Srit 


j6 oN 


ss 


37 10 £ 


lAgi^ 


3l"N 


11 5> 


16 .6£ 


^HMfria, JBtyft 


J, ,IN 


47 S4 


10 4 E 


M^i» 


10 oN 


':S.5 

11 JI 

i7 

■9 JO 


.03 joW 


Baraktt 


43 34N 
4t 16 N 


IX 31 

'9 53 


isi! 

+ 4aE 
> ,E 


Mofcow 
Mnnleh, Btwi* 


4S»oN 
43 37N 


8 4SE 
J41E 
J9 loE 
11 40E 


&««,«, Itiditi 


6.5S 


114. 


106 10 £ 


NUM 


47 13 N 


16 7 


14»W 


Berlu. 

Bourtn 
il«fl«, SiUOa 


44 3°N 
44 joN 
47 JN 

s> .3N 

4gi3N 
ji l»N 


JI 7 


ij 17 E 
11 X7 E 
OjsW 
« 13E 

• S7l 


OlmJt, Anerica 
Oftend ■ 
Oxfird, England 


4S42N 
4. sN 
43 4«N 

8 tis 
s. .Jn 

i.4S" 


Jl »o 
»S 4 

J4» 30 

3I3; 


6 7E 
I4 30E 

7 •4E 
3S.CW 

. I hW 


Bi. mth. r*rtpSrt^i^,\u\ 

from Greenwich ta Pirii Oijtrva- 
t.rj >■ taken lo 10' E. only, ac, 
cording 10 the F™m* Aatboritj 
tiS Dila Ctilh, br which the Dif- 
fereoc«ofL.,^,V«/„E.orW. ot 


Cambmy 


50 loJI 


11 JO 
49 3S 
»o 54 


'Pit 


Padn. 

Paiii Oiiikta- 
Toav . , . 


45 J. » 

,!jo» 


19 I 


II ti E 

1 loE 


ingtothe Sieur DESPLACES ) 


Ca^bil' 


SOijN 


19 17 


■ 17 1 


Parw, ItJy 


4444N 


^8.7 


.037E 




Cape BoBOt Efpe- 
iince 

CpedeVerd 
Caithagena 
CMUine, America 
CheftET, England 
C«^«i-^ 

Cncow, Poland 


4S5N 


37 44 
.0 30 
30a 10 
3»4 30 
"4 5' 
4" 33 

!J-| 

16 II 


19 54 E 
17 loW 
,i40W 
51 "W 

■ s'w 

ig-ilE 


PibM, Cbioi 

Perpignan 

PwUB^o 

Indiei . . . 
Prague 

Oint<m, Cbini 


I9S4N 
4» 41 N 
9 33" 

13 8N 
4«SS» 


•34 "6 

10 33 
197 50 

97 30 
31 11 

'JO 43 

VI 47 


116 It E 

79 4= E 
14 31 i 

III 53^ 

70 -jW 


Tht iH^Hnv of Looiinde from 
Lmkn 10 Pirr* in the New £». 
Calindart cwieded, and Mariair't 
Compafi newlj rc£t>ficd, U ,;« 
45' W. which i.i7«so'W.ftom 
Grian^cb, asd aa moci laft from 
Flm, Bgreeing with the Fmct 
ilubsriyi whieh we have cor- 
■refled from ««%'« Aothotity, 
being only 10- Diffe. -e. 


Dublin 
Edinbu^ 

Fkr,«* 
Ftankfbrt 


Jt,0» 

»)47» 
SO ,N 


10 30 
IS 


7 loW 

■;4i 


Redei 

Row 

R tlerdam 

RoMn 

5.401, iBdiel 


4< loN 
4410N 
4. 54" 

ttl 
14 iSN 
i9 3«» 

41 7" 


,«J7 

M 14 
30 10 

%% 

iiS 30 


. ijW 

.Jill 

100 40 E 


Hence, if yoo a M 10' to foint 

the Stt-Ctaft rail., they will 
nearly agree with fome of tbrfc 


Gaadalupe, Ameri- 

Ge««v'»' 

Cm 

Go.ee, CpeVerd 

GaaiKwioa Oi< 


l6»oN 
4« 11 N 
■ illN 
■4 19" 
SI.»N 


116 11 
14 
91 li 

17 JO 


'J ill 
:7'.'!^ 


5-rM 

SuaOiurg 
5i.w, ladlei 


;i.5 

IJ IS 

9a 

>3 3S 

JI 11 


■nil 


tit Then U fliU loMbet *eiy 

vigalim, ai if the 'n-rr^id/Laii- 
Iiidci and Longitude) were ntnr Id 
be iiaed, but ihifted their Placti 
Willi the Utitudai and I^tudci 


«»rf^f» 


S14>» 


.Si, 


10 .J E 


ValpiTairo, South 


Ij 10 




of the Sti i. In out Sa-Cu^ 

Tiik the Latitude, .nd LonEitodJ 


r»ofi1em 

lOeorFfrn 


J. JON 


SJ 30 


35 40 E 
17 joW 


America . . 


'iti 


JOJ it 

34 3' 


71 »iW 

ie4>E 


of Plaeti a e (ccording to the prfr. 


Ifpiliaii, P«r6i 


!»!=N 


70 JO 


j.4"E 


Venice 


tnis 


JO 10 

JO 31 


iiioE 
II4»E 




X,«H, Id?*™ 




»96 4i 


Si sW 












fcipflC 


S; l,K 


30 


11 10 F 












Liflwa 


,!.SN 


9 n 


gjSW 












LOKPOH 


5, ,.N 


»r 4s 


5W 












Mm», Chju 


ti 11 N 


'304* 


IW jS E 












MubfM, Indie* 


^ tiS' 


"9 4S 


10. JSE 












Midiid 


40.iN 


14 v> 


3 3°" 












MalU 


IS 41" 


3» 9 


■41SE 













,, Google 



346 



Tbi KOYAL ASTRONOMER 



Ca^iaifj BROWN'x DIRECTIOtjTS for the Safety of Hom&ward-bound 
SHIPS, comif^ int^rthe £n«^i«h CHAi>WEt. 

FIRST, T recommend that all Shipcand VeflUs, cdming off ' die Omts, be fleered in a Paroililof Latitade, not 
more nor left than 49° 30' i keeping yoor trait going, e nde w onr ro flrilce Ac Grtnnd in looor t to fW^ns Water, 
which I call the oater EJgtof the BHii/b Bani, or StmtJmgs. Steer front thence E. i.S. ^ S. in Order to keep )'Our 
LaiitMdti by the Compafi, tiH by your iw yon have ^iin 80 Leagoei from the tAiore Sending ai looor \zoFaib»i» 
Eaftward, Theti may you h±vii to the JftriWori^and make Land at Pleafgre. fiat, if interrapted by Cloodi, or 
hazy Weather, fo that yon have mifled an Obrervation for feveial Dtyt, whereby yon cannot, with Ceitainty, de- 
termine your Laiitiule, in fmh Ca/it, if you come intb Stmu/ingi from die Wijttrn Ocuh, ottferA, at before, to gel 
Ground, if poffible, in 100 or 120 Fatbmu, which obtained, keep your Ltg and Zray going every Hoar; fteering 
G. ^. S. I S.. tilt, by your Diilance, you have run from the aforefaid SerniJingi 40 or 45 Liagiui, and ihoiiled yonr 
Water ; gradually leffening to 60 fathtmi. Then joa- may find it difEcuTt to deteri&ine wbeclier yon arc to the 
NorlbviorJ, or the Seutb^'arJ of Sdllji for the SaiaJIkgi oa both Sidei I have often found to be pretty ncir alike. 
Tbtriftrt, to rpfolve thi* Donbt, I recomittend fteering a Sauihtrlf Civrfi from the afordaid Difiaaci run, and Depth 
of 60 Faiem i and ai yoafail to the Saulbv:ard yoM mil deepen yonr Water from 6a to 70 and 7j Fathom i which 
having done, von may depend on the Sri.'ijb Chaaiul being open, and clear from the Danger of cither running a- 
Ihore on SciHy,' o! into St. Giirgi'i Cbakml, too often the Fat* and Cafe of Shipt, who, for Want «f fnch tidpt, aft 
fomed met loft, with the Liv» on Board, or daugeroDlly bewildered. 

When you have got the Depth of 7D or 7^ Ftahom, afoirersid, fmmediatel)' alter the Sautberfy Ctarft to E. orE. b. 
S till, by yourDittance, yon are Ih^t wiiJiiii 5i-;//t^.^aflii^ 1 the faid Placet lying abont 62 or % Li^^uti from the 
if'tjlirn Ldge of the Byili^ Soandinft, then may yOu hawl to the NtrtbvwJ, and make the Lad, at yon think 

But, if you come from the Sauib-viard, the Coaft of Sfaiu and Partita], or Bay of Sifiaj, you mnfl be likewife 
careful how yon come in with the Channel, in thick Weather j for at yon fbike GrAund with yotar Ltad, you will 
oheri f^nAirarfiSaimditigi; and, if ncttU/htat, Gravel, with fm all Stones | which Ground it much fteeper than the 
Edge of the Wtfttm Bank. For, if yon come into your Saundingi with the Chinnel aptn, fleering to the Naniviard, 
to make the Land'iEnd, lixard, Wr. in running eight or ten jf^a^w/, yon will go from 100, to 75, or 70 Ftiitm, in 
the faid Difimta. Whereat being to die Wtjhuard, you may nin 20 or 30 Ltagutt, and not make more DiffrertMre in 
your Sottitd'Kg than aforefaid. So that, from what I have advanced, it will be eafy to determine whether yffi have tfce 
Channel open or nut, aAj^/that hit oftm pnzzled the mo& exftrinrad Mariatrt, and fkilfuL Navigators, niing 
ihefe Seat. 

H«v:ivtr, I mnfl obferve, that Tome 'Hmcs, in the aforefaid £'m<ii/(>rp, I have met with t &.ioa% Nan fur Ij Current, 
at the Rate of abont one Mile an Hcmr, wlucb, and about 17 Degrees P'anatioir Wefi, at this Time, (hoaid be duly 
accounted fbr, in Order to keep the true FaraiUlai Latitude, afore-mentioned. At, llkewife, in fome Sta-CAarfi 
the Latitude of the Land'i-End, Lizard, i^c. are laid down, ten Milei to the Nortbiaard of their true Laiitodo. Sv 
that if thefe J/aptdimtnli are not all duly conftdered, and allowed for, I fay, from what I have already obferved, an 
Errer may be caiily contraded, greatly endangering the Loft of a Ship. 

Thefe Dire^lhm being carefully obferved, yonr Latitude and DiAance will be corrected, and a tolerable Enow- 
ledge of the Ship's PoGtion may be inferred. And I would alfo advife all Ships to be carefnl how they deal with the 
FrtB{f> C'ofi, For let the Weather be at it will, after having run the Difiante aforefaid, off the Ifi^Ut of Sdiift then 
make bold with your tnon Ceafi, in Order to fhnn falling in with the Iflandi of Gutrrifij, yerfij, i^t. which (boften 

ds in frightful Circnmflancet of both Shlpi and Lives. 

AND, la/fy, obfervc that in founding a Strtam, and to the Wtfiviari of SclUj, yon will find blMfli, ang GrmmJ . 
fo that when, by your Liad, yoa have mcb Gtoiuad, you may be affured where you are, and therefore Ihapc your 
CourTe accordingly. 



Note, That in nrninguptht Ciamtlvibtn jea i 
Start Point 4 j FatbtM, 



« a-bnap af ihtlAXUt, jtavuBbavt '^oFaihtrnWatir, mtdtf th* 



TbtfraBitalMariatrfniingitdi^ailtlagttGrtiiKJIiiaSlerm, tr bard ilowngf^tatbtr^U lOO or itoFalbtm, tMmng 
inta Cbamul, bt maj ftllavn ibt abav* tUln i getting Grawid at So Fatbtm w if/i, if maiit^ fnftr Jibmrnn*, accmdii^ t* 
tbtDftthafWatir. 



COMMENCSHfiNT 



mi NAVIGATOR. 



MmariaUi jCRAS. 



jmmtnctment of the Jul, Pejod 
he eommon ^ra of Creaiion. T 
Siranhiia. Ncglefting other ( 
lr>d!tiorul^r-Bjofsso!.S'99i 
lod 3955 befoic CA^ifl 
The ^r< of the Delnge . , . 



— 1\i.tGrukOI}ifudt , . 

~~ The Foundition of Saw 

— Naifajir, Kin| ef Saiy/« ' 

— - The SyritaitiACluiliUaiii 

y-/. ti^*r,Corr«. ol Galend 

— Sjsii* J ot S/ani/S JILtx 

— CiriiiT, Ol Cbrijlm-Xra 
The jEibiifitii and ^ijf- : 

fya, called Ma Dltclifin, 
<K^mof M»nr, . . . i 

Kigira, or Tgrlt'i/t and ,*■ ^ 

t^cMra . . . 

- J'fi'i'^^, « Pffiax M'i 



»/p?J{i. 



En. ChT 
^S3 



1 1079 ■"' 5791 ■"' 1078 
158* S.95 158 J 

m^ aiceitained by a ConcorrBice or Cerrt/fmclma dirooiered, in the 



Di. f.. 
Solft.tt 
VfjEnd 



N.B. The difwTaiiconefllydininguiiliet between the anTMt mi cmplitt Jt^'-m Van, before and fince Chrift, (emfujtdly gi 
Cimal^M} and therefore the .>Sr<i heti ^irta ue fitted for the Hidua':m sf Cbrmolegj, or Tor reducing one Account of Time to an 
Which 11 eSeAed by Mtani of TaUei, fuithu on, eftimating the tfumber of Tean and Mnirib-Dnt of any particular RJnd, equivajcr 
girea Number »t jfurun Tan iiti Minfii-Difyi, and the eiiarary. And thef? Tablet arc likewife httcd for determining the Humber of the 
Faiae, or Weeli-Day, correfpandot to a glren Afiiii-/>aT of ditfereni Kindi of Yean. Stif. 141, forthcPormi Lengtri, B(Binniof, 
Boding, of the Jrviip, Eryt-riaa, Aaiic, Tarkijb, and tlfo antient Gnchn Tiar. Any Number of vrhjch, and their Montit-Dayi, are ieda> 
nblctoancquiia!eacNum£>erof >/ia»YeariaadMoath-Dayt} bytbe RULES intBlUJVlPLES henaftcreihibited. 

nj Vtrialion; and each Month of joDayi, with 5 Diyi di/^it the End of the 
fooner than the nHan Julian Year, and gaini i Day of the JuUai Account in 4 Yean. And In 
Ibt^Hof nba Egyft'uiioi'PirfanVcin, the bme Day of the Year and Uonth ceturni. For 14,60 Ytitt Julian mike 1461 Yeart£ry/. 
vrbentbe iftDay of theEgy^m Month nwihappeni on the ift at Janarj Julian %tj\e, a Yaan after whicli the ift of Tbtibhtj. 
in ^e 31ft of DIcmAir, and in 4 more on the jotii Day, &c. ntrnting i Pay in wery 4 Yia:i ?M« Style. Tbetetbre, i D19 te- 
1 or retto(raded every 4. Yean Juliaii li ]t; Dap rettmed in 1460 Julian Van, when the ill of lieib return) to Jaatry i, Jalioi 
gt^, Tbia Egyptian at Pirfiaa Vur, thougb fit for aftmitnmical Computalioni, ii impraper fm the Purpofei of dtil l^e. The mtiegl 
Pirfian, by a CcnoOion of tbnrCi/ra^j at ceifin Periodl, mle their Year to conlift of 36}^ jh ^jn j^a igih, according to the Frntt 
Jabon. 



The if'f f [f— "^ Xurh make tbcir Yean confiQ of 11 fynodical Lnnationi, and ii 
of J54Day», and 1 1 Yeara of jccDayi, via. xd, <■ 8. 10, ij, 16, 19, 10, 14, 1 
■f^: V j*4 Day. ; which Period of Year, conuin 1063 1 " ='- ■^■- > 

iffim, thitiiof i^di*- ■-—- ^- "■■- 



d h m T 

wrYearii J54 S 4* f 

Year about 165 5 49 > 

w- .= .. .J 



JO Year., which i' their Period, the; 
r, andjoth, of ;;jDjy. eachj [he i 
e Ih* Produa of jo Yean, Peiiodi, 
inlind, and waadft) thiou|hiU the Sci 



' reckon 19 Year. 

left. 1(1. J. 4tb 
-r Cycles in Sue. 
ifoni fucceHlvely 



>/!«(Vear *<; 6 M a Mean 

. . . S17 Tio-ti* 

Uake 511 JWm« Yeara, 



f Or 1,5 
\ Make i%% 



rurVp Yeiri 
>/i«ii Year.. 



The^^'^andCrariVfl Year, follow lheirparticu}arForm>udeJcribediaPi';>14i. 

The Vear, leprtfented ty a Siii;, or Sad:!! wi^ the Tai] turned into it. I)faulh, haadiRereat Beginning., and Suec^on. of the fame Parti 
hUfuewKanMi. Same hagintiuii Vear at tlM.£rijilif(j, othera at thq fatinwHi. And, OiFrtw, before the Vear 1564, we Had, bya 
FtOci i^^fOKiw, .tlut their Yetr co;pCi;i)Ced at EdjTri-. But t:£dr/u IX. wc fi^d, in i lie bme Epb/miiii, ordered theCotnraenccmentto be<)n 
the in at Jani^ry, which wai cqiifiimed andallabUflied by Ordrr of the Fnriui CDuaulaniP*rliiirieaCtab«gijltbe I&of ^/''''''O'' ^^7' 
Kj* Tit j<&«BiWwriii^ «in> Iw«r Jan. o, t jffi ef Dtcaabti, ai Hmn, 



Kttxsmwi , 

ibyXjOOgle 



348 



ni ROYAL ASTRONOMER 



DEDUCTION of CHRONOLOGY. 



It 


0.,. cor- 


It 


Kfpon- 


t, 




baa 




'i 






»5567S 




109 S 




191100 


t 




90U 

JOOO 


f^ 




4183 




7JO50O 


lA 




lOOO 


1095750 




UU 








^uoc 


[giCijo 


iS 




60PC 


219.500 



10454 

a. 915 

,317« 



, 3"4' 
33<^03 
350*4 
365IJ 

'=9575 



W. B. There 
bEing 1461 Days 

//fl»Vf.(i,whM 
eithtnft.id.or 
3dV«r(m.rk- 
rd™.h .) ii 

ihe Numtxi of 
J^ayiintbcnfir 
Hjnd Ccluma, 
forih=r™N». 
of D->iiD Suc- 

ill Year, uap- 



TABLE of Che Nnmber of 
DAVS to chc END efuch 
Pajian MONTH. 




rath 1 Making 31 
D.yi. 



CJ..g„ 
pen, givei in Account of 14S| 
bi^lCalhcErut cf fhc liti Ppfitni 
'fonCh .JiflFT, iafleid of 340, 
hich Moalh he ciJli Apnitt 
'Vabak; and dif!«i 5 Days in ihe 
'jilowing Month! ai he doe> in the 
lamt! of fome other of hii 
donthi, u ilfo doet Mr, Frrgafm, 
rom fome of onr Frrjitti and Tar- 
\p Namei of Monthi fiom good | 
Authority, which maket the 
" " I, not !ih Month, inl 
>F 5 Dart i like the 
^'gyfrian Month. 



19 Aug, 
38 Sept. 
iS Oft. 



.6 J,r. 
.5 Frb. 
17 March 
t6 April 
t6 May 



the WEEK-DAVS. 



r A B L E of the Hambn of 
DAYS to the END of the 
Julian MONTHS. 



T A B L £ of tbe Numbn of 
DAYS to the END of the 
7j>rA> or j^aiie Momtbi. 



, 


January 


P' 3' 


DMi 




Februa,, 












9' 




April 






1 


M.y 


r 


'i'^ 




u 




113 






»43 


»44 






«73 


174 




Jflober 










Ws 


lu 


" 


Tectmber 


■N.B.iH*s', 


9-7./i«Yr. 



.«N, 


. 


/lf»i'.^n» 


.5 A.,. 




Safiar 


,;s^.. 






I J oao. 










3iia>iai\ I. 


II Drc. 


J 


(?i.«-^ II, 

?3l 


?ft 


Q Match 






S Asril 




Sdtua/ 






D^OaJaH 








fo'^it" 




In Year iu- 




tercaW 



Moatht. Mi.i»n 



lyGoCfflC'"" 



and NAVIGATOR. 



REDUCTION of CHRONOLOGY. 



Cta/traSita, The Nambcrt ■( the Top of the TtUiAtti^tPrtJaai 
of ]b y«ut in 1 ntngraJi Order. All rbe other Numben ia the T«- 
' ' m tbt Cyclci current froii) i lo jo Yean. The Mmibi tn pliced 
ihe himah, (as*tng the Fm« orWeek-Diy to the Beginning 
ofe«ch Momh, for given Vein, in Ihs fune ColumnJ lofia' ■ 
F,'!». or Week-d.^, » followi. 

t^ Tlf I lo CkiV «/ Yian firai fir %0 ffMt, Mai aafmri li ttt 



S19 

Tnlulb Ye*n 600 



Kl!i 



Rem, 15 Yeari, 

Fn-« lojhefe ij Yeati, bong j, and the 
Firit to the MoDlh Miiimrram he-nf 7, add tfaele togrCber, miking 



Sat, from the Tahli. the Fb-« lojhefe ic Yean, bring j, md the 
'liihurrcm being 7, add thefc toget 
III Diy of Muburram, and the 5i 



which dirideil bjr 7, there will id^iio 4, or the 4.tb fir/a being VU- 
mfjaj, requited. 

OTHERWISE, Tifad tbtJiHa Dati, O. S. nmffmii*l ti ibi 
Stii TuikilhI><Mr 
"tniip Yeuf convicted D>^ 



', See Vart, 



i3'S 
■ ts7 Dayi compltted. 



j4</^, gig Yti. JuL and aoi DaT>. both' m^dhiiL 
Taya/f ittb, 611 Yean tarrat, when the Htpra commence) 
lum, 7ir/. iGtb, t4jo cumnt, and %o% D171 more amflttid \ 
Ir, Fibtaary j, 1451, cuneai, O. S. CJf; Tai/e, ;>. 31.J WhcD the 

NOW, the Damiaital Letter (by Tai, f. 14I.) for 1451, O. 3. ii 
, and Fttnaiy 3, (by Tatll, P. 149) ii evidently on a minijdaj. 



[PLE 11. 7t/^(^TBilcillirM<nrn/>giH6>rr<(i(Juliui 
if xoti ■/" May, ■4n, O. S. CJu'if m « Monday) tain 
U. hum bii Svpt t 

Bi 

1 



[>• mr. Yrt Daya 
515 ^ 1451 + ijo, BiHextSla^ 
197 wliea Hrpra begun. 



Julian Yean Diff. S19 . ji8 completed. 

\rtlMih,Wiih.DajT 
ge6 Yearcumnt 
— !4oCid« 



Oinnadi I. ( 
Daji. 



IbMby . . ■ Reou 

\^UalavtJiBrma»dnJlrila «i«f it Jt— m Ai Ewi tf tia Of 
rminmihiwatCikmM. Sn f. 



GiamaJI I. . . 9 completed. 
Or, 856 Year of th« hrpra, on the toth Daj of CfuMiaEi' I, ai> 

I.e SicarDc^&m, by MiAake, (in the rri/matoWuEfhtmtrida, 
(nm 17 1 5 to 1715, Page jo] biingiDut SjG of Hipra, completed on 
the iS of Sapbar cunent, who Giyt the Twrh reckon it gj7 of Htri- 
rm, OQ the iH of the Month Sapbar, currant, when Mabaait II. be- 
gan bii Reign, which oanBot agrae with the iqlh of Mrt, 14;! 
Maaiaj I The ift of Saptar, in the Sjy of Hipra, en 
a Swirdiy, ai our Table fbregUDg Afwi, according to the 
AiA'giTeo. And the lil of Safbar, in the gj6of Higiia tiitreat, If 

T'^filV 

nJaaag rtt Julian hitt PaBaa it 



/warttfjo- 
amlDaii CO 

i.kib 

!famkri,/r ' . - . . 

ib^t Naaii'i _ 

liwiytrtJatrJitiirfiiBhi ^ ___ 

/bttit/it lain, fir RiJmSim tf m Dale n aaabtr, at djfl'erent Dec*- 
fiona Bull rtfHfT, ibt Hattari ^ miJiaJaar a Bar, ia aattMia* tj Tufi 



Dati aortal, katm ibi Diffn 
. (if faau a, if tb,f, Juliui Tiwi a- 
dactJ itTtariaaiDajitmfUit, ai^ ibtir Difima iba laka, 
" ' '' Tiart larrtM bimg Bifleitile, ir both common ; vt, 4 

__ . - . ^ 

anJriiw Ibi DiifirFnce ar Sui 



dbytjoogle 



ISO 



n* ROYAL ASTRONOMER 



RBDDCTION rf CHRONOLOGY. 



wiii tit xoii tf Mmj 1761, N.S. m M Wcdadasj ; 



Dip 
119150 



. iSi 



! HENCE /I 
£XAM. 



I4JO V'* rompUtc, tad 3] Dift, 
/^. It5l< Fitnarj ], nnrw, u fc/irf. ibe Due 
■ 'of the CbtlJIiM Mra, conv^eodiDg wkh ih* Oite of the fiifira, 

I J5, on tbe ifi D*7 of (he Moath Mt^mmmt 

EXAMPLE IV. T»nAr««*« J»Jk«r.«W »■**» *nw*, /•/!?(/■'*"«* if S.pt*"'*'. »7*'. O, S./K^Cbrift, iit tuntn »rJ 
Mmht tatmat/ tit PcrStn JcClE^d ni< r£t contitrr I 

W.V't.aw)p. D«Tt C^ fifPtriho J««eprd*(f«iIaMi*.r&*j 6j« ./Chri»w 

•' looQ . . . : . I j<s»So ,, ^-'T-*a.j. 

700 , »5567S Jol. Yit. ccmp. D«jt 

lo *«U0 too .... . aigijo 






UJmH, coiapl. . . ij 

Tothc^ifxir^ . . 130639 
COHTRARILT. TeftJ ttt CbriAun Xn, tomjfc^iti tt lit 
BIjl Ictr f/^ Jtfle^td, « (^ lott ■/'Phuimrdiii, arraif 
Agbm Vein Dtji 

■oeg . 



. 36500 
1S150 



1150 Vnnaoisplctc. 



Iijo yean eomplrtt, ud . . . 9 IHt*. 

m^Ai'i of fbtrmovMn. 

n«. In 1151 Ymt of f^t^rJ, on tbi loth of Pic 

_.„._ ^ aid itlht Juliu ActouBt, 

- „ *gF tibtrjumit ^liwtfm^^i, if it* 

/b^'i^Ruln. 




,, Google 



mti NAVIGATOR. 



DEDUCTION of CHRONOLOGY. 



RULE. Divide ths Number of die Dijv complete in tbe Accoudi 
\sy 7, and Jild thereto the Number of ih* Ftria on which the Account 
or ^rm bc^in, then diTiding the Sum by 7, the RciDaiiidei will be the 
Number ol the Frrwcarrerpomllnite the /rat-Cirf, required. 

N. B. 7hi ntupltuhtyfr* »he*ji i ik/i ihta thi D^ anal. 

THtJS, in fxoe^Jf I. The Number tX Daji in the Sj5th Ytii 
of H^ira, on ibe ill or Mabitrrm, ii ]ai6i j, which dirided bj 7, 
leiTct [, to which t being added, the Numbet sf T«« (anfwcripg to 
Frii^} when the vCrv begU, the Sun i* 11, which ^(iiled bf 7, 
tte RemaindR « \i the Piria lUweriut to Jfuimjitiy, leqajnd, aj be- 
fore foaaibfttirlU'lixidi. 

j^ai-, in Exmrnplill. To the Sjfilhytar of Btgirt, on the lotb 
XJiy of Gitimadi I. current, ue 303110 Dajt cisyjrii, which divided 
bf 7 there rcmaini 1, to which if 6 be added, the Number of Fi 
'inrweriog icFriiitf) whin the ^ra began, tbei'iBit 9, whkh' 
ided b; 7, the RiwimltJir i, ii the firi* anfweting to Mniej, «■ bo- 
fore fotuid by otbtr Mittuli. 

A£ti-, in Einmflt III. To the lOlh of May, 1761, N. S. 
(4x968 Dayi dnpltn, which dirlded by 7 there lemiini 4, to which 
adding 7, the Number of Ibe FrrU when the Ch'ijliii^ jSra began fan 
fweiing to Satiajy) the Sam ii 11, which ditided b; 7, the K% 



matnder4, it the Number of the Ttrit uTweting to Wiir.iji^, ai 
' ' fonndbyotberXfeWi. 

^ rnr, in E)i4mfii III. To 1774 Yean of the JJipr; on the i jll, 
Day of 5i«id/ current, are 4i!9ji Dtjttmf/ili, which diiided by 7, 
there remain 5, to wiiich adding 6, the Number of Firit who 
^prd begin (inrweringto frnibf.J the Sum ii 11, which dividi 
7, the Remiindcr 4 ia the Number of Frru, asrwetinglo fTn/^/^d)', 

befon faund, conifpondent to the Dale of the ChnHian JEra, IHi 

; 1761, N. S. 

4lmn, in EMmp!i IV. To . 1511) Year of ^f'!ii'i, on the io< 
o[ Fbtravxjriin corrcnt, ate 4197^9 Diyt cM^rir, which difidtd t 
7, there nmaini4, toiriucfa aiding j, t tie Number of ibe Firia wht 
the Jtfdtiird-Xrm boEio, {v:t.7^fdiy) the Skbi still be 7. t) 
Number of the Foi'tf, or Saturdij, on the Day of the JifitprJ, 11 
quired, coiteffondingco the iiih of i'l^oa^, 17E1, cumai, O. S. 

I7 the tike Mabaiit the R/d:.n;iK of all ./ERAS cf Chconology ■ 



Metlwdi alteid}' Oieini. 

^ (f rifWeck-Dtycinri hi t^/m ra tie arrAotivit Da: 
0/ Chronology, ij Sffaaa MrihcJi tf amfwiii^ lii Wttk-Dej, J 
M«7 U Jurf Ibt StiuSiui if itt Cimu/ifif ii wuJt ri^bi. 



CHRONOLOGICAL SCAL.E of an i£ R A be|iuiin( BEFORE CHRIST. 


. 


ucceflire Ytin complete of the JEII.A b,-fon Chr. Cir\i/l. Sucieffive Yein complete of the iER A fiuce Chr. 




JSIS 


I 


3 


4 


5 


6 


7 


8 


9 


10 


" 


" 13 


'* 


'S 


16 


<7 


I' 


8 7 


« 


i 


4 


3 


» 


. 


« 


« 


3 


4 S 


6 


7 


S 


9 





CHRONOLOGICAL SCALE of an .£RA beiinnicg ! 



[NCE CHRI&T. 



le j^IltA befort Chi. Ctr 



lo^RAfinceChr. 



«|ra 



cfe-k^- 



:, fiom their BeginniBg, onthaLcfl: I 



AXIOMS, 

I. A Yearoarrent, la tbe Year luilning on, Mt yet completed. 

I. Yeiit aaraii are alwayi t nuie than Yean uaflm, in il! Data, 
befoie and fince Chrift. 

]. Dayinm'ataie i more than Dayina^^, Sff. 
4, Yean and Dayi tmfhtt added to, or fubtrailed from, Yeui and 
Day> Of^ti, the Remainder will be Yaaia and Diya tMbu, 

J, Yean and Dayi complete being added to, or fubtrafted fiam. 
Yean and Dayi current, the Sam, or Rima'iMlir, will be Yean and 

Yeari and Dayi larmK being fubtraAed Itmb Vean tad Itayt 
r, tbe lUnulodetwiUbc Yean udDayin^pilMe, 



D.j.« 



Of .£RAS BEGINNING utd DATES, Uih Before 
CHRIST. 

PROPOSITION I. 7* dtttrwmi th* Ni'iAir •/ JuKu 
Yitiri (urrMt »f en Mn, frem >bt Biginniiig It tbt frt/tUt 
Dolt ihtritf. btfart Cirt^, hting I'-vtn, and ibtoct te gitH 
athtr cbnwtUgicil Ruiet f 

RULS, B; the {binier of the ti*0(iniM&/ifa/Snkait iicTident, 
(hat IfytmdtiaB ihe viiilt }u\iiB Tun iarrim iffirr Citift, if iki 
frrftM !iali,fmm itt m*gA Julian TWi rvral, efiit Dtii intn ihi 
Mti it/irt ClriJI, t*[a, both in the lower Column, tti Rem; 



,, Google 



7** ROYAL ASTRONOMER 



REDUCTION of. CHRONOLOGY. 



ill it rir fftmirr e/whoh T/ari coaplett, in tb* upper Col um*, 
(ind alA Ycirs and Dj^i complele, which Ycu) ud Diyi an iu both 
Dicn] Jinattr Coninienctmciit tf ibttJEn. 

"'hich vltli Tan DXKtnact ire nrnfleU Yiart, 1( tub annul Rc- 

of the laaK lUttt-Day, oa which ihc fiid Mn brgin. Tc 

which Drfftrcncc of Deiii cuircnt, or Nunbrt of cEmplrie Yciri, 

' ice the JEn, if i Yeat be added, it will gi*e the Nunbci of Ynr> 

irrnl of ihit .^ra; bec^iifs (u wat before obfet fed) Ihe Nutnbn 

Yeata currcnluc alwiyi i more than ibe Number of Yean 

Oihmnlfi, If Tou fubtrafl i 
II, b«rare CbriA, (to make tl 
Aff thtm ftom the Veaii of lue mnri U'tt at tne j«,ra t nejin- 
ng, brfore Cbr\jl, the Keroajiidci will atfo be the Tta- tf thai Mre, 
ice it btgan. 

PUT A for iht r,aTi «rrw ar ihi ^ra'i Eeainnlug bcfo.c Of j/!. 
P, (or the ^«/«/ Year, curr. " " ' 

T, for the Nun^bei of Y»r> 






before drip. 
not of tliat . 
1= Y 



7 Julian 



EXAMPLE I. Tt ^iJ ibi Nuahet tf ih. Julian rui- current, T, 

Cir'^, ai-fiiinKg ttlbi inib rar, fr,f«,lDtU, P, i,fir,CbH/T 
M ss 471] 
By the ill S^uetim, + 1 



Ttjmi P, (£1 /r^W J>a», i 



r bf/tr, Cbrlfl, 
■I rfib, BuiMin. 



'-^M 



Pier»ql C'ft bcTon Chrill, F :b G61 required. 

EXAMPLE J. rtjini tht D«t. IV., Uftn Ckrift, ,/,i, «^ 
^fmiaf ^ M M't, frtm Y, tbt Tiart rf ihat vEra, ilo current Jkci 
'•< *rr"»> —^ •"» ibifTtfm Pate, in (4r 45/* rear etrrrair bifwt Chtill, 

P a!4i 



J^S 



B)r tbt jJEparin. 



T^jFtm, tbeI>eiithor MxmiltrilcGnit 314 bef. Chr, 

Of >M.AS begioaing BEFORE, an<l DATES SINCE 
CHRIST. 

PROPOSITION II. Tc MtrmiBt tht Y,»,, y, ./«, 
iEra. ,iE. iipliing at a ^iivn, Date. Juljan 5V, h/ort 
Cbrijh a>'/wp'fil>itti>afrtfiniric^,UiVt, V. Julian ^j;^, 
fiiKt Ctrifi i anithtnit « gi'vi sfhtr ghroDological RiUh f 



RULE. By the foimer of the 
dear, thac If i A/i r^x ib rui-i in'-niii >n Ori/I (being the Yean 
tDDipiete) U *Mii n tbt r.an curicnt tf ibtCtrnmiKtrnvn if em Je.i 
btftn CbriJI, lU Sum ihaaf vilU bt ibi Yiati complete •/ liiir <£j 
fait ii trrau, ai Remn if ibi fitu Menib-Dat, 

An.! thtrvroir I being iiici to thofe nmfltl. Yeati (by J^mi) will 
be theYemti.r'*«of ihit *ra. 

OiLir-j.-ile, the Number of ihe ptefent Julian Year cunent. JuKr 
Cfc-M, bei;>g added to the Nombei of Ycjri eurrmr, brfirt Onfl, ai 
liie Ci^miKcimi^i of ihe^'a, the J'lm thereof will be tha Number 
of tlie YeUfurrBir of that jErj, fi nee it begin. 

HENCE, »e ha« 7'' ^±^^^- ?i?'^° 

thefe EQUATiONS. J^; J^ _ f " ^. ^^XZ., 

EXAMPLE 1. Tojfirrf Y, Ibi Numbtr s/rie Julian Tm- jfiir 
Greek Olm,p''it. ■ubtj. £ra, E., btgas in ibt ^^Ub Jullaa r» 
ct'rtabtf^iCirtJI, a'fvterifgltibtfnfHurear, P, 176o,J&k( CSrjS, 

JE s 77« 
By the tJUfualiti. P =; 1760 

Jgtian Year of the CnA Ofynfitdi . . Y s= 1516 
Tef-t! P, (ir prr/«t DMt, 

_. ibi 

ftrtChrlfit 

y = ajo7 
Bj the iJ BptuitM. .E = 74J 

Prefent i)*^ lioce Chtill, P a= 1760 it^nbtd. 

EXAUPLE 3. T«>.J ib, Date, JE, J./*" <:»'6<. V '**- «- 

f™/.it/*.*ra,/r^y, ,i,r««,/,ia,jEra, 18.5, r.™->r, 
(ifcXa.i a«rf P, <b, f>tf,nl Tfur'* Dale, •» ihn-joth T^ir cuttoa, 
*«(Chrift, bthsgi'vaf ' 



Of ^RAS beginning tnd DATES, BOTH SINCE 
CHRIST. 

PROPOSITION m. r»dfe(,rWw/A«n^,. Y, !/■„ 
yEra, JE, foj/nn/B^ 0/ « iiiw, Da/t Julian i/ji, _/£»« 
CAri/?, anfuitraiit i» a givM frejtnl TtOT'i Dan P, Julian 
\Si)it, Juict Cbrifit taui tbtnct ie gkii Btktr chronoloxical 

Kulck 

RULE. By the titter of Ihe two ibtmltpial Siatti, it ii et'ideni 
thai. If jou dediiO th whole 1-(ar., of a Dttt at the BcgiDning 
oran.«£'ii, from the XI i cle Yean of a/rr/.Bi Pan, tha DiftieMt in 
w*a& Yean will be the whole Yeiri coinpltte lince that J^it btgu, 
and coBrrquMtly i Year addtd tbtrttc, will be the whole Yean 
rent of ihat-^flj which arc toiBBlcifid at the Return of the 
MiHib-J^y, fincB Cbrin. 

HENCE, we have l!' ^ T f + ' = ^ W^^" 

theft EQUATIONS, r*' i "*■ V Z « i "L 



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ind K A V I 6 A T O R. 



■iB3 



REDUCTION of CHRONOLOGY. 



EXANfPLE I. Ta /»d itt Iflaniir tf ttt Juliiu Tar arrut, 
if itt Tarkilh Hcpii, tuiffr J£n, S., i^£* i» <*• S»»i Titr mni 
fiMt Chr^. -Jwit-n I* tbt fnfaa DtH, P, «76s '^"'f >" 



JuUn Yew of the T«rfc^ H^j.Vj 



nrnaf fine* Chrift, I 



1760 
>477 



AMPLE ». TafimlP, thi pnfru Dall larrni _fiKt Cb 
aZZZt^ V tf * ^ ^ ill, r.*. |0l»n ./«*. P" 



Prtfcnt Yew y^S** fine* Qh»W, P a i7*> wqoJitd. 
EXAMPLE?. r»JmdiitD^U,B^J^Onf''f'*'^j^ 

CBjnnt HBce kjinn. 

pROPosmoN IV. r. a/*mwm li* joiiui r«ri «»i 

i>«7* complete ht^ixl any /iw ^ro/fl DaWi f 

RIT-E I Tike iheDlffeitnee beWrfit the D*lel la coaipUlt 
Ynii^D;*., bring both bdbre. orboU.Ji«e, ChriB. 

RUl^ II. T»it« the 5»> of ih. Dtu, In Mapleft Ydn t 

BOTH DATES BEFORE CHRIST. 

EXAMPLE I. '*frw^'*'?r^'"?„ - 
In the jjAih Yc« corrent, *ifi" CM. *» >Vri. Di. 

TWw Crr&r reformed tbe C>Anfa> id tli« ■» 

'- . . 344. 



Sja-j . . . . • i_«;_=~.pl«k 

IXIF, 979 . ]I5 MPipIeCe. 
Theitftre, when Jnfiu Cmjtr reformed ih. C.AiJii.', it *w ia the 
doth 7Wim V«r «««« or i79t'' 3*^— *■*" •»' 1' J °*)" **^ 
plM, of thi JEn of i.)IbMiME(r'« Dt>th . 

l7pIlOP.l.efM(.I. *" j»4?cwn«b«fiwChia, 

>79 4- I B alo Yctf mttat. 



ONE DATE BEFORE AND ONE SINCE CHRIST 



EXAMPLE 1. TittFnndttmQiRiimt, 
ia ibaTtjil Yeir euieai, b«roreC6r/^, 
it %tfi ikj tt jttrll 

TiirUjm^irm, beguti in the Slid Ytir 
cwnat, fiQceChriA, aay*fji6 



Ivn. Di. 

J 7 51 . 1J4 complete. 

J611 , 196 complete. 



Sn™ 'S74- *S 

]7;ih YewnrrMf of the BaimK[ tf Am, or on the i]74tfa Yen 
nd a5th Di; thereof, afbu. 

BjPROP.U. £fMt.I. £3 



»]'S 



EXAMPLE]. Tfae^rdOf»ar(*r<,arl 
DiKl^m. becon ID the 114th >A« Year (Ym. Dt. 
euntDtliBce Chrift, tDjIupiflig , , Jitj.s^i « 

The iEnof the RdoelMiioa of^ J^ "l 
Ji4i Cilendar t]> Pope Ci^pry begiD in 15 ti t- 
fioe* Cbriftt «> (>3>^ 5 l>jS)lS7Sc< 



Thmfin, the Crtpnmm 
cnrrcDt of thf An of Hittjrt, 



Dif. ] 



119S . 37 compb 
D the^iggtb JuSai Yen 
the iiQftb Yeu thereof ind 37 



^ mn rlt A71 c—fltt, it my laliiD i>tfft, sv ilrfl ri«r ria/i, 
inandttr fuliu iJcfm It ttkit frm Am. yt m^Jmii^aB I Tmt 
^M ri< AJmri, it vMr Tun twrrat, hit fitm lit Ejumiimt, Jit 
ibt ma wbtU Nmrnitr »f Tun amu. 

X3r Bjtekia|iheYeiniD4Di7iX)r;^nBMni^tf>betwiiluHrAr. 
■r ud fucceeding Oah, jreo my rcdiica the yefio jfc i iw «r ^lue 
to la;^ olhti Accaiuit of Time yoa pleil^ ia Tmn iM Dfpr, ODd the 
anlrtrf i ETpecialJf bj ■ Tiblc of Uie Dni in th» Yeut «d ModAi^ 



Pll.Ot>OSITIOR V. r« riJMti 0^iair'im» 6jfa^i 
Ttan, titbir (imptttt tr camM t 

SVII. SDbtt*aifiaDthenmDtA^*ffai6teth«(MyJb»irDs. 
ber thereof I mnltiplj the JtMutMlirh* 41 ubE^ thereto i bA thu 
tbeNnmbcTof thoodaMjihplcYnncwttetAetlUKMlbe^ of Oe 
Oljnplc Ynin conplete. 

^ icX4s*o 
AMtUtlittith(N*.«fa44CriTnp.Yn. -K 



,y(St1S^Ie 



354 



The ROYAL ASTRONOMER 



R E D U C T I ON of CHRONOLOGY. 



EXAMPLE*. Ittttifiram/rhtiisfbO^fMtK: 



P, itMfTdHt Due, hftn t Sua Ctrift, hy ibt f»> 

iMvkmPtaB, ■■rivl.«fll. PROPOSn-[ONS, 

And P, Yuri cnrnnc glvea bcAin or Ance ChtiA, 1IU7 be ndoced 
to y, Olpifie Yon, from the Olympic iCrM, bc^auag 776 Ycui 
intotirfinCMfii ud then ihofe 0/^ic Yun, Y, may be redDCcd 
lo OfyK^MJi, uti M Ycut emfliti idiI lurriml, hj the Cmvirfi 

of the foRgMDi JIiuEi fa- rcdutng Of/n^ifdi inn Oljmpic Van, u 

fblhnn. 



RULE. Foi niMdnt 
Diride the Olympic Yi 
ibe Olfmpiid), 



OljmpiiTian complete into OLYMPIADS. 



I to the Rimt'mitr for the odd Oljafit Titi ear- 

63 Oljnple Ycut nrmr. 



e'xample }, 



rv^Wi ire rtdncid into Oipt^c Yaxt, Y, ind tbeo into Ynn 
cytHn Ptriti, P, bjconUcriog the .Ai> of Olympiidi, ^, 
bepnDtag itt Xn in the jtjSlh Yetr of (he Vt/iu Petiod } coming 
ider PROPOSITIOK III. ud £fM(>'« a. 

EXAMPLE 4, T, fiti lU fnfiM Titr, P, </ th Jaliin PtriN^, 
B; Prop. ni. SjiiMt. u X = jgjl 



Solftiet, ^i 1 Cjch, MufjBtrimt It im futaffist r«i-i aftU Jolitn P* 
fi^, (^h nmiMcini -aitb juiiurj) ri, /«■■»■ C,f£, 4rt.«» « ,J 

PROPOSITION vn. 7» finiih* Ntmbtr •/■EgyptUa 
Yt»t tarttkt, »f Nabonaflar,- Ai^vtvnar /« «n Julian 7W 
rtiwa/, jjwrt Qhrift, O. S. f 

Rt7LE. Add 747, (the D*H ef Ac JUm Year cohm 
Chritt, when the NA»t^ar-Mr» begin, on the s6th of t 

being on the lA D»f oTthe Sn^o Month, rktd,) to the 

Aafr, Gnce Ouift ; and the 5ii* theicof will pic ni the Naatber 
of JuUtm Teuf fioce that An ) (-»r Pr^. 11. o^ f for, ' 

NOW, 5vi«HfffR>m«bichSni.()ieciu& Ibe 744th Year befon 
Chrifl i) the ad Year after Ji^ifc; and divide the Kenuinier bv 4, 
tn dircovcr the Number of BipxtilB bippeunc lince that jEn 1 tbeo 
add the Namber of Dija e«preffed by the Siaiitmt, [tn i more if No- 
thing reiawi)!) to the pnnding Number af BifftKtiU Ytmt. and tht 
Refult t»eof will pie Ihe Eijftiam Yean npiind \ complete to the 
laA Retnm of the fame Mmlb-bief, on which the jSra bepn 1 when 
tho(« Yean begin to be ciunnL 

BallheP/nDijri, above a Year, orYean, of ^SjDaji, mnD be 
reckihied back from tfaesjlhof Ftdrupji, atNoon, ta Snd IheUonth' 
da;to Xbejmhtn Sljrie, towhkbthcCiiiiiimaiarof tlw£na(/<. Vn 
it DOW fmSn *Mi. Tbl) U Mfilf pcrlarmcd ^ A* Ifelp 
P. ilg. 



tf tht 3Mfr, 



, Can«Dt YCM ^ the JJi^ Period, i«qul(td P as (4*7 



PROPOSITION VI. Tajkd tit Cftlit »f tbi Stm, 
Vtocat, «*^Indiaiop> a^^wtringt* tbt Olympiidt I 

Rm.!. Xcdact the Ohmfitii te the Olympic Yean, mrnf, add 
leicto 17, 4, Md7, aaddjTidc bj 1!, 19, and 15, refpeOiTel/, 
Nuabcn will be thole of the ierpedi*c Cjdo, 



■ . . I leqoired, J 
tbc 1715^1 >£aY» 



I 5H4»»(1 « 
Aafwedflg to tlic 1715^1 J"^ ^**i 



e^j ..6 

For, t49i 4- 17 e sjc 
+ 4e^U! 

Dinntince Chris, 



And. If It, M»4fr *^ (£< Egyptian IW aitf MW&-&. thn^l, 
tfmrnlfirKrfJaiitnMKai-Jajfnadlwi, tr fiM'miiv, Aalmiotiii 
ibi Xre <f NibonalTar^a, you mull deduft, or add, the pm 
of Dayi Ibcicaf, tefpeairdy, from and I-. 
Icb the ^rfl'i Commencement hat fallen bai' 
inlbiiyaAiaa Aceonnt, and yon will haft the Nontbo af tbe£Mff« 
YEanandDaytcottent, njani, certefpoadCnt lo the JutUmUmiA- 
dky and Year giTcn. 

I* If NuUwi rmu,u, tfi» tb, Juliw, rmn, A/r a, m JfwidJh 
4, ibtMimfih»JAdl,lt,^^imi,/wAtln,Nmmia^._fmatf.liitt. 

EXAMPLE. 7r /a/ da JVWJr </ Egyptian nen, Y, ,f it, 
JEn tf Nabnniflar, M, ammmaiig Fcbnuti 16, fa rjv ^A7ti Tit 



Dt/inChrUl, Julian, ar 0. S. ? 
BrPROP.U. ffaar.i. 



1 Tear Sjj/fif . . — iSj 
D*TttobeNckeB«dbadcfi'.nfci6,theAn'tfalU4back, a6i 
JrauMraMijsfi, tojajr ifif (onmd. . Dqn 14a 



3 



Y«(n ajoj EtjpiM, rcqi, ud jCDayt 
fincc that Yeai'a Commeifte- 
ment) being ihe£thi)A|F of iba 
Month P«fi(, concnt. 



t Egjftumytu — j6f 



,y Google 



end NAVIGATOR. 



JS?... 



REDUCTION of CHRONOLOGY. 



But, {bj- T«*. P. m) torAvfry .j . ■ • j6 — ' '" **" 
^ To be reckoned buck i6l in both Yn, 

To btiiekcMJbKtU the preceding Yeir lo; — 



Correfpondlng with the 9A of ^f™. In the' 
Yttt of Chrift 1760, on which the Z- 
wfflUaYetTnov^ai .... 
From wkeoce reckaniiii . 



] 



oaOv «T. 1760, >fi". o, s. . 

■ " , *iA iS, in the ift BrjfHaii 
by bUuii bKk, b the >A« Ac 



, 300, by T«(. P. 119. 

Year of tMauftr, now 

hippeni, by 

N. 1. 7J» »fieb-i*J 'f »7 J""*" I''*-. *5fl" Cinj*. -f7 *• *- 
cnriM/ in (t( /«Mt MMtmr, h udi'ci luy Mwt-^ eftht^ Egyp- 
;iBrMr»/»»booifiiri«/^rtii «^, imfiimiif aiiims-;\-it<!tbtDati 
ti dinatd) fiut Cbrifl, jai lafi imo Juitrta tbt Dale fcflr* Chrift 
•'nm 74J, « fi*i '*• J"'"" ^"^ ""■"" 'f '*' Nibonjflir Aa ; (by 
i>ROP I Eaiul. I-; and iba fabduS x fnm tbt SauinS; v/bicb 
«./iJ>^Sl'*"i"'i«"'^*»4. lifi'i'htNu-iT tf-Bifixlili,; owift, 
fnmJiw " fi*^ ''" EWP'i" ***■ n"T"'. "^'i* MM/i-rf«y 1/ tbi 
JolUtt Bar, «n wifci i« Ci«niiiia«~oir /W/i *«*, » irftn. 



QfTHERWISB. 7* /s//i« Es/pdui 7/<tr andMaaih- 
% nirwi*/ •/ *^ -*« tf' NahoMfliir, ttmminth^ Febrnwy 
'6, 7*7 ?«"■' tVTini htfart drift, anfiwtriiig H fbt Dot* 
./ lit CiriJIiai Mit, tf Jnlj- 16, O. S. 1760, aorm, or 
July «7. i?^' N. 8. 

DATE SINCE CHRIST. 

Jal.Yn.CMDp. Deyt. 

jcoo 1*5*5* 

7«» »J5«7S 

j« . - ; . . »o4S* 

3 *«9S 



iERA BEFORE CHRIST. 

liui Yn comp. Dayi. 

700 . . »J|67I 

44 • ■ ' "w»7i 



1:^ jifr. Fergulani in biu^rumef, hat pva mAvfitti^ 0.5 
M vibiii ihtji'f Day tf tbt Egypliin Mnat Thoth ttpfaU, (iDi 
wbicb webneilliiabrerred) hit bi hn ni pvm n ibt Titr »f Qttifi 
trYtar i/lttJuiitaFeriBd, dkt n^ Ftin 'fTim, win thxt £««• 

RSMARK. The Bepnning of d« ^m of AUx—ia tltGmi 
on N.fnmhtr u, on the ji^ >/,« Veu (gnat, before . Cbiik «u 
on Ihe ift Diy of the f^y^ai Month 7binb ; u xiro wu the Begin- 
DtDg of the fimaiu ^ra of Nmitnsfftr, fo welt known amoog the 
ANTIENT ASTRONOMERS J bccaoA King PTOLEMY, udthe 



jCm, aKOrdiog to 

Like*;! 
IfiJi-Xr,, ., ,. 

Chrift, ftllontheift of the 
Egjftian jGni |i«n ■■ 



JtHMTrtm I7S9 eomplew- „ 

TiBBi compkt* ■ . 
In yrif, Diyi (ur/Aft . . 



itt 



SnaCtrifi, tothe pt»fent JJi 



-r«-r 



t[ffrimY*m »Sfit WB^ttt, ui , . jj D>yt 

3Mf, cotnplete jO— comp. 

rtHfti c Dif 
Ki^ iii>se9&)|f«IaiVan«nmt,«a 8 Day af 



f the Egjflimm Month Tlwi 
by Mr71tW«.J in ^ 

hu aoi^ien m the Juluuduff or Yc~~ " 



if thu 



j^rma^-, thaotk be 



f^ThtftntaanUitim a^Dite, arTitr tf m JBit, hibt Ja- 

\aSlfli, ttfirt irfiHtChnll, r< ibt Yeir «Mf Mondi'day rf ''y 

nhtrMn, f—dtbt conttaiy) McarJiag f* tbi DiSbctKC iiMMi M« 

Juliui tad ifypCiu Ttari, aiy( /sOam ibt Arvn'jif Rolea </' ibt VII. 

PROPOSITION, I'OM^ 1^ CoDTcrrc l2«Vi Miuitii Motudii}. 

THUS luTC we completed THE WTlOLK filTSINESS OF ' 
CHRONOLOOY, (u promiTaJ In fonner Ptpsi lb &r u relitn tc 
JaJtUhHvm^mftfiiiriTti to which the bifitrial ftn Ii hA 

.ag, topeifea the Sobjea, with which wr jjTi awij iib do&Iy 

cnnnoacd. dW&Vir.NewMi'iCinM^. 



IHTRODmnoil 



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35S «< R O Y A L A S T R O N O M E R 






INTRODUCTION 

T O T H E 

COM M E N T 

O N T H E 

M O O N's T H E O R Y. 



I. DEFECT »f ASTRONOMiCAL TABLES. teofirnStdfim OBSERVATIONS. 

^O gtio, froa Ohfirvaiim, fnch * qomplete Knowloige of the /umr Motioiii> ■( to be able from thence to 

franc 7«Jjb/ sccnntely enongh to repreftnC the Moan'i irae Plaef^ or LmgituJr, io every Point of her Orbit, 

dariog an cnrlre Revolotion. «F her Aftigu» and Natb, throDch [he Space of near 19 Yean, hu 

{k failii in hitherto proved iDeffednal Labour. For, thoagh the Immot Tailti framed, from Time to Time, 

V4UII, ftQta focb ioK and ./^(»; Oblervatioiii, at the AAronomeri of the Za^CnUicrj contented them- 

felvei with making, agree fomctimei, even in the Oaaaii and ^luulraiurtt, futpriziogly with the 

Heaveiiif yet, in f^nerai, it hu happened much otherwife. And tbey have been found to deviate, fa mieij, from 

.,, . . J, Obfervation, tha^ no Ufe can be made of ihem /ir aiiamiKr iht LmeituJt n Ot Dtrrtt *f Ex»S- 

*' H'^^JTlT^ "/' Mf^«7 fit- Ibi Piuftfi •/ tiawgatiim 1 Not even the celebrated fsUtt of Dr. iUiia, imper- 

W* '/""Visatiow. f^Q^^ fconded on the Tbwj of the great Sir ISAAC NEWTON. 

II. DEFECT /TABLES /.jyjWi; OBSERVATIONS. 

TBT tbii Deft&i u ihii vjttt Aftrononier, Dr. Haliif, obferven ii not the Fault' of the Jrt, bat of the 

JniJUtr, For, hj obferving the f triad of the limta- IneqoaUtiei, which ii petfarmed in mgbn** 

^.It^iiltB-RiturMi Yean and tbvt« Otyt, or two Hundred and mmtnty-ibrtt LUNATIONS, it it foond thit the 

»f AujMtHtuif im Retnm of ECLIPSES, and other Ph^Hamnm of the 'Moon'i Motion, are very regnlarly per- 

tbt knar ftritJi. formed. That whatever Errtr ii found in ». former PiriaJ, the fame i* ^ain repeated in a 

focceedlng one, under the like Circuafianctii «f the Di^cf of A« Mmt froo). the Sum, 
of the Sun from the Moon'i J^nu- 

Bui, then to gain a ctrtuim and MJliuB Notion of all thefe hrtptbo-Uitt, which, firom Obfervation, tHron|;boat thit 

N her f Ok, '"^i difiurb the luuar Mat'ani, woold not onl^ eitceed. die n>wer of any one PerJon, ia the 

4. Hambtr *j y»~ jij^j^ Duration of hit Exiftence, but would neceflarily be the Work of Agci to pciform j it 

t^a^^^^^T i*l'>'"''g'"> 'ewer than 1 54400 Oi/irvariw* to campjete the Awat-riwr^i beingos36ox6oX9 

t»m**t€tma «- j^jt is to every Minnie in the Zafiof, for gee Bevehition of 'the ^/« jfts. 

^' K> Dr. H^ley, te cwtB tit Cmtpntmitn Jrtn ^> Tablet, hat gram eu Ab8«> ^ tht Smri 

^tmi, tbru^brnt «m PeriaJ, jtintd ta a carriS Seiiei sf Oi/trvaihiu frm vl>fga ihtj an iMiutti* 

UL q/'TABLES cokitevctid $atr£a$ It tit THEORY; 

ON the other Hand, to deduce the Theory of the Moon. Ii feifi, or to fliew, from the Lawt of Graviij and 
AttraSitn, the Manner in which the Motion of a SattlSii, revolving ronnd iti Primary, it di&orhed Inr the SUN, 
the ^auiitj (tf that difturbing Force, and iti Proportion to the utripittU Force, by which it it retained in ita fr^tr 



,, Google' 



tuJ navigator; 



INTRODUCTION to the COMMENT. 



Ortit, with the Nature ud Qamtity of die Emm thence arifing, both in Lnffhidi and LatituJt, ■■ id Attempt, 
which neither the MatbemaHeiaMi of remote Aget, or thofe of more modem Dait, fioce the Reviv^ of Learning in 
the ^tft, hare made the Objcft of their Studies and Inquiries, This wonderful ExtrlieH of the Power* of the Mind, 
greatly beyond what the human Uodcrflanding hu before been thought eqaal to, was referved for NiwtM. Foi 
Him it was deOjned to raife the Snglifi Repotation in the taltjiial Scimea above that of other Nations, and to teach 
the admiring World, the tru Caitfti of the Order and Harmon/ obfeired thiooghoiU our PXiAN£TAB.Y 
SYSTEM. 

*' DifioMiu lane ivtdtai, fia cau/S argmtea Pbetht 
" Paffibm band ^"ii, p-aditar : car JuhSta naUi 
** HaSaau iifhtmam, numiraniM/rtgnartCMfat: 
« Or rmtaU a*di I cKrfia tuigM pngre^mlur," 

Halleim in Newtoinm^ 

Erery ffsfi^&mnwhovalaes his Conntry, and who is emcloas of liaving its Repotation eminently 
rufed in the Opinion of other Nations, fbrthe Proerefttnade in everyBraDchofZiVvro/jirf, and of t.Dl/cfwj and 
Pbiitftfhy in particular, mnll <utmirait the Name otNnalan, for efiabliOiing that Repatation on the Ii»ttuweftbiMaea''t 
moft folid Foundation. And there viftrav)\a will blame this Attempt of making him more Thttrj, Sir llaac 
wd-otrfaUy known aod onderltood opon a Snbjefl, the moll nfefat of any in the. Science of Newtwt'i. 
Aftronomy i though the moft perplexing and difficult to nnderfland I I mean the true Theory of 
che iunar Motions, deduced from the Theory of Grarity by oor^fo^ Malbtmalieian I 

IV. ACCOUNT of ,the SUBSEQUENT COMMENT. 

IN the Pra^i of the fnUeqaeiit CtauKM/, the COMMENT ATOft hu endaaroDred to bb 
clear as well as concife: clofely following Sir .^'om Nnuttu't Argnmenti, He has traced out a. PrintifUt »f tbi 
Trom thence the general Printipki on which the fereral Tltnrtmj are efiablilhed, and firom whence iitmfi TbMiy. 
the different PraBUm are deduced, without entering into the Jkxianarj MUbad in their Srtntion : 
giving only, in zetieral, the RifiJt of the Compncationi, as they are derived from the Prindfiu tf Mitku. To 
have gone fartitr, had been, at once, to copy all that our Anthof haa wrote npon thii 
Sa^tS, who reafoni too c^/tff for his Reafonrng to be obriAtd, nnd too (Uarif forgiving 3. Dtfiga ef th§ 
the Senfe of hii Sii1:qed in fivitr or fitXtr Words. What is here attempud, will, Iliope, CnsMraf atd T. 
anfwer the Purpoft for which it ia given the Public. It ii intended ai a FeamiuitM fir httur hiiit, 
lunar TaiUi than yet have been pi^li&edf foch aa may prepcrly be called TA^ULJEvtri,. 
NEWTONIAN.^. And thefe Tablet ^Miio/r only in very minnte Particulars from the Theory, as 4. TbruSfaa/ia 
Sir 1/aat left itj having but three f adJUifuU Bqnationa 1 except the Bjaatin which correfls the talf eddtd to tbi 
MooB*s Varituitn, according to her Anomaly, may be admitted as addiiioiiaJ alfo 1 which cannot Umu'i Tbtfy, 
entirely be fo efteemed^ as o«i JifthoriaaAM points it out to the Confideration of future Afiro- 
Domerii _ 

s. c.„ 



t Thtfi Ant MUiiitMtl gf*0tit*t art , .. 

StffltmaUl tf tbtfatt. jlnd tUtX., trtitaioa-Ejmimi, 



,y Google 



35« 



rh ROYAL ASTROKOMER 



AN 



Explanatory Comment 

O N T H E 

M O O N's THEORY. 

According to which PRINCIPLES, the Aftronomical TABLES 
at the BEGINNING of this WORK (preceding the SUPPLE- 
MENTAL TABLES) are constructed.. 



I. O/zAr MOON** MOTION. 

IK tRMiQuag Hit Tinty »f tifMiMif from thcLawi of etntri/ttg/FoKn, uhid itnmm At /irjl Swi of At I^i 
cifia, oar Julbor firft confideri the Moon u rcvolring rauiid tke Eartb, in the fame Manocr ii tba Eanh, or txsy 
-. J /■ ■£. oAkt of the friwiaty Planet*, rerolvea ronnd the Sud ; snd from the Phxnemtna, or obferved 
I. M»ui 'V?'™ Metitn, or DiftoKt of theMooo, demonftratei, that the Moon, in revolting ronnd ihe Earth. 
Atai round lb* £«■/* ^jgiciva that efiabliflied Law of Motion, in d(^cribing ^na, frcptriiomsiU ft /At Ti^i. nc 
Miarj^froperlimoM/f |^(.j ^j^^^^ ^^^ primary PUn«» io their refpeaive Rerolotiont round the Sua : neglefling bow- 
ibi iimtt. gyg^ ^Q^ ioconiiderable Enon wUck arife from the Afiion of the Son upon the Moon 

in her Orbit, 
r f I.M ■• ^^ ^'"^'' *^^ obfcnrei, that t]ie Force, by which the Moon it ret^ned in ber Orbit, 
uV" J^fL tend* towards the Earth, agreeable to the i«u af <tntrif€Uinr(u. (B.I.) And alfo, that 
.' Tp ^ the Force ii, rtdprtctilf, m th» Sqparti »f tbt Difiena fim tbt Eartb'i CtrUtr { as is the mere 

ctMtnfttai ecrcf. evident from the very flow Motion of the Moon's jI^u, amonntiDg but to 3" 3' 

Rue in one Rerolntion of the Moon. 

ilt Jurtbtr Jtaui^rtais, that the MooD graTttatet towardt the Earth, and by that Force of Gravity is continnally 
drawn off from a nBiliiuar Motion, and thereby retained in her Orbit This Pr^trij of the Moon's Motion is 
partly to be dednced from the fiftping prtptjitian ; bat more extenfively frvm the following Thttrtm, which Ihcws, 
that the F^a, by which Ihe it retained in her Orbit, it no Other than that which we call Grevitj, and by which all 
Bodiei are m^c to defcend towards the Eanb. 
The corrcCt mean Diftance of the Moon from the Earth, according to Obfervation, is 60 { of the Earth's Stmi- 
j:~—— Let as, faysonr^^, afliime the »wa« Difbace of CoSemidiametert intheS^- 
'P ' " ■ ■ - • -- ■" 

fnm Iht Earth, and in 27* 7" +3' . _ 

htrGrmnt^tn, to 123149000 Parh Peet, aa the Frtxcb hare fbond bv Menfnration. And. now, if we 

imaghie the Moon, deprived of all revolving Motion, M M let go, lb at to defcend towards 

the Eartb, with the ^/w^ of all that Force, by which ihe is retained in her Orbit, lot will, laAe Space t^an^ 



3. Ma9i!tDifitmfi I'm; and fuppofeone Revolndon of tlte Moon, in refpeAof Ait fixtd Siari, to becompleted 
m lit Earth, aid in 27' 7' 43', at Afironomers have determined t and the CtraMj^nr/ of the Earth to beeqnal 
' ' ' oo Parh Peet, aa the Fmcb have fbond bv Menfnration. And, now, if we 

Moon, deprived of all revolving Motion, M M let go, lb at to defcend towardi 



iSt^' 

Spwe (rf' OBC Mboie of Time, would, by i 
iiamutff of the Earth, is < .>.->. 
Earth, increafet in iht 1 



' progreffire Motion, defcribe, at the DiAance of 60 Stmt- 



diamtuft of the Earth, is accmraitlf it Fi ft, 1 ini, and i £m f. Wherefore, fince tbatForcs, in appnadung the 
~ t>vM/^«}i£r«/r/V(/sr/iM^/^Z)ij$««f«, and opon that Account, at tlie Snrftce of the 



DigHizcdbvVjOOQlC 



and NAVIGATOR. 






COMMENT on the MOON'i THEORY. 



J. Giwiff af iM 
BtJiii frevtd. 



vuL 



6, Mmo'i MttitMi 



Einh, is 60 X 60 Timei ETMter tban attbeMoon; iBut/, in our Regions, falling with that Force, ODght, in the 
Space of one JViita/f of Time, to def^ribe 60 X 60 X i ^j Parh-¥ett ; and in the Spsce of 
one SkqwJ of Time ij^ Parh Feet: And, with this Ten' Force, we aftaall^ find Bodiei, 4. DtfiM tfStdit. 
hereopoB Earth, do really defcend. For, a PinJiJum, waWxtivg Sttendi, ia the Latitude of mmr lli Sartift Sm- 
Parii. will be 3 PaHi Feet and 8| Lim in Length, as Hkjgtai has obrerred : And the Space /an, e^liid tr tie 
which a heavy Body defcribei, by falling, in one SntaJ of Time, is to Half the Length of the JMtm^t Grawtj. 
PrnJuiiMi, in the Jitfljtatt Ratit »f tht Ciresm/ertBCi lo ihi Dianuter ef a Circlt, and is there- 
fore I J Fut, I Inch, and I Li*t f . And, therefore, the Forct, by which the Moon ii retained in her Orhit, becomes, 
at the very Surface of the Earth, equal to the Force of Gravity, which we obferve in heavy Bodies there. And 
hence the Force, by which the Moon ii retained in her Orbit, is that very fame Force which we call Gravitf, and no 
other. For, were Gravity another Force, diffisrent fiom that, then Ba£ts would defcead to 
the Earth with the jiint Mptdfi of both Forces, and defcend with double Velocity, and in 
(mtSecaitdof Time defcHbEd 30 1 ParrjFeet, abtgtthtr t^aufl Sxptrimci, 

OUR AUTHOR thus dcmonRratiog, that the Moon is retained in her Orbit by Grteviljt 
and, I>7 Analap of Reafoning, explaining likewise to us, that the fame Sort of Force retains the 
Primariti, ana aU tbek Sfrsna^'w, in ibeir refpefiive Orbits j he refers us, nmt tf all, to 
thofe Prineiplti already laid down, from the thiarj of Gravity, in the fir^ Sack, as the Foun. 
dation on which the lanar Thnrj is built. And obfervea, that all the Motions of the Maoni, 
her Aftgn, and NaJti, are to be derived from thence, as well aa the JitejM/Hiii of thofe Motions from the Adion 
of the Sun upon the fur/^, the Primary, as well as on the Mata, tiic Stindarj P/amf. 

The fereral IntfiaHtitt of the Moon, frofi a Miati Motion, Ihall be coofidercd, w^en we have attended to that 
Profefiiitn, (B. III. 15.) which afflgni the Quxotity of i^it filar Farci on the Moon, tw which her Motion round the 
Eanh is aealrrattdat ratardti. For, havine the Quantity of that Jifiurhinr Farti, and the Pioportion it bears to that 
by which it is retained in it* Orbit, we ftiall know bettei: haw tt (enpuit tbt lunar hijuaJitia, and to find the Agree- 

ent of the C«»i^«fiM with 0^/rnwjc». 

IL 7« FIND thi FORCES ■wiikwHeb lit SUN £^Krtt tit MOTION >/ Ot MOON: 

IN theaBneiedFi;fBr/(ree?r</.a;.B.ni.}letS reprefent the^M ; T, the Earthy P, thcMoonj A,C.B,D,the 
Moon's Orbit: In SP continued take SK, eqaalto ST, and let SL be CO SK, iti the d^fJitate Raiit of SK. to SP t draw 
LM parallel toPTi and if SK or STrepre- " 

fent the Mttkraiive Force or Gravity of the Earth 
towards the Sun f/ir »k Aieimt af the SniaHme/i ef 
lit AngU P 5 T titfi ISnii may it eJleemeJ equal to 
tack aihtr) then S L wiJl reprefent the luciitrativ* 
Force of the Mooniowarda the San, whenatP. 
Bat, that Force is compounded of the Parts S M, 
andLMi of which the Force LM, and that 
Part of SM, Kprefented by TM, dillurb the 

Motion of the Moon. For, as the Forth and J^ are revolved about their common Center ° i . SalmltB »f tie- 
of Gravity, the Motion of the Earth will be atfo diAurbed by the like Forces. But we may Pralkm. 
confider the Sums of both the Ftr<t, and Matitns, u in the Moon, and reprefent the Sam of the 
Forces by the Lines TM and LM. The Force LM in its mean ^antiiy, is to the ctKtrifttal Force, by which the 
Moon it retained in its Orbit, jevolviog round the Earth, fuppofed at Reft, at the Diftance « /_ t- 

PT, » tie AifiUati Proforlhn of tie feriadieat Time af tie Moan about tit Emrti, to the teneJical , '/ ff . ■ .^ 
JimeoftbeEariiahcuttbeSun, that is, in the duplicate Proportion of 27-7" 43'to j^^6» o'; 't^-^Cl^ni- 
rasioooioi787a5, orasitoi78|§. But, the ««^ F«-« LM, is to the Force of. Gri- j'ZJ" J"^ 
ity ofthe Surface of our Eatlh, {aflUmiug the Moon'a mean Diflance to he fiof Semi- ''"™"'"^- 
diameters of the Earth) as 1 x 6o{ to 60 x 60 X 60 X lyacaj, or as i » 6380926 i whenoe, the PrtptrHa 
of TM, LM, TM, isalfopven. A7 ^ '^ 

For, by Praf. IVT B. 3. If itti tie Eaiti anJMetn loere rtvehieJ aiett lith- nwman Ctmter of Gravitj, the mta 
Diftmti of one from tit otier would be nearfy 6o| hum Stvadiameltri of tbt E^b ; axd iht Port* bj wkch tbt Moan may 
it kept Tfu^img in its Orbit lAata til Eartbii\)M{(^CA, at lit Difiaiue, fT, ^ 6oi Stmi^amtt^i ef tie Eartij iitelie 
Fane ij viiicb ilm^it rtvahitd ttt^it famt Timt, at 60 Stmidieomler], Ml x 60^ ft 60 j and lint Forct it It til Firce 
af Gravity tuiti w ^^rj nearly, m i ft 60 x 60. 

ThePtoportioB of the >/iff-An'( to that which rctiini the Mood in her Orbit hemg thus given, the wtxtTUng, to 




Pie.1. 



be inqured into, is the Manner in which this .yMsr fnr/ affeOs die Moon's Motion, and the Owr it produces in thi 
-^.e.L.L ni-. _i.-.i. ___, .1 , ,. t)i^ following fre^rtraj and TJtsww of this T'imffiwi. 



Form ef lie iauirOriiti whjch are included i) 



,, Google 



i6o 



Thf K or AL ASTRONOMER 



III. Tt Jittnmu tbt SOLAR FORCE /ro&nW iht CtJANGES ni IKEQUALITIBS in tbt USViASi 
ORBIT. 

SIR ^aac Ntwttn has demonflrited ^Pro^.XXVI. B. y) thattbe Areai, which id eqail .„ . . ^. 

Timca tre dercrtbcd by the Moon, in the Spagiti and ^MaJraimi, are to each other, rtj^tai-mi- Al^^^'Tf^l^j 

If, 11 11965 to 118651 fuppofing the Earth jwV/ffti/, and the Moon performiDg one Revolncion ^"^ ^j^ HiL 

in 2j* 7" 43'. Bnt the Syni£cel Manth confilli of 29''ii''44', therefofe, the Intrinumu of "f*»''***'f *rw» 

the Moboa mnfl be eolarged Id the fame Proportion ; and the Moment of the Area in the Sjxi- "'"'• 






COMMENT M At MOON's THEORY. 



lolarged in the fame Propoi 
git will be to the Moment of the Area in the ^airaturi, at 1107} to 10973. 

Bat, to DDderAand more fMlij thofe PrineifUi on which thefe PrapaJtMni are eUafaliQied, we mnfl m back to the 
[RSTBOOK of the PRINCIPIA, where, in ^k feand Carsttarj oi thi (,61b PROPOSI- 
TION, Sir ISAAC NEWTON dedacei. that in a SYSTEM of THREE BODIES, T, P, S, ^.Prtp»imtf}U~ 
(fee Fig. I.) If the BCUkroiiiM Attra£lioni sf anj two af ibtm, trwarJt « Third, ie te lach ritu, im aSjfitm tj 3 
tthtr nripracally, ai tht Sjuaru tf ihi DiSantti, tbt BoJf P, rewhrMg rtKitdT, viH/ Jifiriit in M»Jia, txpimntJ, 
dria fwlRer ntar tbt Girgimaiim A, and lit Oppolition B, tbtm it luiUin ibt Qsadratore C, tr D. 

For, every Ftrct, with which the Body P, ii aded on, and not the Body T, and which dou not a^ in the Direflion 
if the £m-PT, does either accelerate, or retard the Defcription of the jtria, according ai it it direfled in Camfimm- 
ia, or Aittcctitmia : fach ii the Force TM. this Firci, in the PaiTage of the Bedy P, from C to A, it direOed in 
Cmtfifuniiia of iti Motion, and therefore acceleratet it ; then ai far ai D, ill AiilictdntiB, retard) it ; then in Cu^- 
qutktia, at far ai B, the Motion i) again atniiratid. 'And, Ujilf, from B to C, in Anticrieatia, it again retarded. 
Therefore, t^ttrii ^ribai, the Planet P mnft moTe/u^«r in the ConjunAionsthanin the QaadrgtoTci. 

Hence alfo the Orbit of the Body P, (Cer. 4. Pnp, .famt) cattrii faribui, u more curvia at the Qaadratnret 

at the CoDJnnAion and Oppolition ; for the Jkui/ier Bodiei move the lifi they deSeA from a flrait Line. And, 

fidet, the Force K L, or T M, it contrary, at the CaijiMaiviii, to the Force with which the Body T aciraCb the Body 

1 and therefore diminifhet ikat Fartt: But the Body P will be left defleflcd from iu rtSiUntar Courfi the lefs it it 

Slled lowardt the Body T. 
EDce, laflly, ffirCer. 5) taltrii paribus, fnppofiag the Orbit to ^ttircmiar, the Body Precedet ^rtherfrom the 
Body T, in the Quadratarei than in the ConjanAioni : For, if the Orbit it eteiMlrie, iti Ercenaidty will be grtasifi 
(fiiCtr, 9) when the Jffidn are in the Sjxigiii i and then the Body P, at tke higher Apfit, may go farther from the 
Body T, pllced in or near the i»viir Fkmi, uian at the QnadratorN. 

That the Dicrtaf* of the eimripiial Forte, at the Conjunflioha, (honid be the Caofe of the . . j 

Body P, coming, warrr to the Earth ; and the heriaft, of the fame Force, at the Quadraiure* _ '■/" 'JlrmitmK^ii 
the CeBfi of the Body P receding then fartheft from it. Dr. Ratbirferd obfervei, appean to be ""'**"'* 
a Parajex j and tO which he givet the fillnmng SeliUim. 

When the Moon, or Body P, ii at A, the ailaiitieia Force it grealeft of all ; and the Mood, or Body P, is lifi 
impelled towardt the Earth, than the Force of Gravity woold impell it, and, tanftmitiillf, it . . , 

will ran farther from the Earth than if the etntripital Force of the Earth, only, afled upon it, „ ^'^ '" ^ 
and therefore when it bai reached the Quadrature D, will be at a greater DiAauce. ,When, on "'"'''• 
the otlier Hand, it hat arrived there, the ctnttipttal Force ia increafed by the tuUiliiiau Force, cxprefliKl by L M, or 
PT. ^tlkiiCM^, thcCoorfeof theBodyP, it more iiicarw«//^ towardi the Earth; and when it it arrived at B, 
approachei KMTfr to it, than if the /«/4r Fvrffhadnotdiflorbed itt Motion, 

IV. 7> dtttTMnt tbt RATIO >/ ib, DIAMETERS *fth MOOm ORBIT •wiibcMt ECCENTRICITY. 

THE Gttvaian of the Moon'i Orbit, or the ProportioD of the Diamt/tr A B to C D, it dednced from the xSti 
Prep, of the ^Bftt of the Pn'an^'o, wherein Siri/Mf confidcn thcOrbil -uiitbaia Eettntricity ; and laytdown, at 
hu /MMdamtnlM Priaeifif, h^ whicn he folvci thii Prtblim, that the Curvature of the Orbit, defcrlbed by a Body, 
attrafled in Lines perpeadicnlar to it, ii w tbi F*ret ^ JttraSiin, dirtaij, and tbt Sjaart *f tbt Fiiacitj, iwvtr/iij. 
And eOimatn the Curvature of Litut compared with one another, according to the (vm^nt/ Proportion of iho&Wi 
tr Ttigmii */ ibtir Anglti ff CtataS te tftitii Rada, Aippofingtbefe Ai^' to be infinitely diminifhed. 

The.^rA-«A'M of the Moon toward* the Earth in thefiyiuf(M,'ii the fx^c/i of iti Grari^ towardi the Earth, above 
the /i/ar Ftrct, a. PK. by which the Moon tra-mi^t tmon towardi the yan than Ae E^ti 1 and, in the ^Msdratwn 
the AttraAton of the Moi», towardt the Earu, ii the~5«« tfthtGrmvitj tf tbt Mttnttwrdi 
tbiEarib, *r tf?T mi »f tbt filer Ftra^Tf^iaiia firmtrCaft, theExcefiof the Gravity 1. St^tm tf tht 
will be 178795 — uoo n 176715 t in the hitir, the Sam of the Gravitiai will be 178715 + Prtbltm. 

AT+CT 
1000 (* to >79725. For, potti»gW*ti» ■!■ ■ 1 — 178(5, e^oal to the «f »Arvf(«/ Cr«vi(r of the Moon towardt 



,, Google 



#)»rf N A V I G A T O R. 3fii 



COMMENT on ike MOO N't THEORY. 



Ac Euih I At meui Force ML in the Qbtdntoret =s to PT, or T£ = looo. knd the meaa Force, TM, 
hw'fiei, will be equal to tooo t fEOjn which, taking the mean Poice ML, there remaini aooo the Force by which 
■Jitt Moon ii drawn fTom the Eartht and which it^ wu callnl a. P Kt Now, the Vilntitj to the .Moon in Syxjgin 
AaodB, ij tothe Velocit/in theQfjadratntei C aodD, aaCTtoAT. And the Moment of the ^^o defcribed by 
the Mood in the ^«aii«, to thatdefcribcd in the %*fr(U»w/, a* no;* CT, to 10973 AT. j, . , . 

Takinjt thii RatU twice, invtrfiljt and tjie former «■«, diieaiy, and the Curvature of the ni',,„^f,/,, 
Drhit fn SyzigUt wUl be to that in (Wratare, ai 215 1969 AT X CT x N - 14081 AT* o^WfL/F^ 
•" 319137. AT X CT X N + izaf. CT'. Our Aib,r, proceeding, findi, by aljWr,/,V Z.^'^„^-„j"^ 

^nation, the a*//* of the >»*5« Diameter C D, of the lunar Orbit, to be 10 the /mj^^ji AB, "m^ tTs li 
e«clnfive of Eccentricity, ai 99«8i to 10071^, being the Rtoio of the Moon's Di^ce in wl™?- "^ 
Sjmitui, to her Difiance in Siuadralure 1 thatii, in roand Number*, atS^ti 70. 

Mr. Mtuhiii, in bii Trtati/r bm tht Lew *f tht JI&m'j Maim, fabjoined to the EngL^ Tran* 
tlation of the i>Wjtfi>f«, nuJccc the Proportion of the (horter to the longer Axi) of the Moon'g Of* 
bit to be as ^9 to 60. 

But thit Rati*, ai he obferrcs, it ibmewhat larger than the Proportion giTen by Ntvitam ( _ . 

though not fo large at that given from Obfervation by Dr. H^Uj, which ii that of +4I to ^ ^ HaUey 
4ji, oraj 89 (091. '' 

t^ TbeTranTverfeto the conjogate Diameter of the «!£i>rir f/fiyf/t (fo called) of Afoc^w ii a* 2 to 1 j whofe Cen- 
tal he fappofct ia carried to the L^ round a circnlar Orbit, while the Tratk of the Moon't elliptic Orbit i* carried 
round, in the Epicycle's Periphery, to the Right: defaibing eqnal Area* in equal Timet, aboat the Center thereof i 
with the Epicycle'* Tranfrerle Diameter alwayi parallel to the £f«^fjkM(M*iC«^'«ti3iM<M/0//«^/im. The Moon 
ia alwayi at ue remoter End of the (hortet Axis of the elliptic Epicycle when in the ^aartn-i i and at the near End 
( from the Center of the Moon't Of bit J at Niw and Full See the Figie-t and ExplmaMum farther wr. 

Mr. MACHIN /i-mj thif* filhviing SHORT aid READY RULES fir dtiacing tbt/t PROPORTIONS. 
Let Lbe the^mnSfWTimeof the Moou( S, the Period of the Sun from the ^yErn/fror/i M. ' 
the ^Mifo/ Reroluiion of the Moon from the Earth; D, the Dificrenceof the Periodtof the 5. MachinVJTwdj 

M+L fir dtttrminiiig thi 

SMnaBJMaen. Then the i>/^mc/ of the ^Hw<6rr« will be to their ^m, at jLx " to 4 DP fir- 

2 

5S, by the Principlei of Sir J/aac NrwUiti but jLL to 2SS.~LL, according to Miv^Vi PriKciplti: Whence' 

"'} iLLtoSS + LL, it hii Proportion of the i^ to the ;»£/«■ Airii of the Moon't Orbit. 

From the foregoing Data, the Diatntiiri of the Moon't Oibit, and the laejuaHtj of the Momenti of die Arta, which 
ibe Moon, by a RaJiMi drawn to the Earth, defcribet, our grial Malbema/idan next dedncei liat hu^uUity caHed 

V. fbt MOON'* FIRST EQUATION ./ VARIATION *r REFLECTION. 

IT wat htft difcovered by Tjcht Sraitt hat it) true Caufe never afligned, till ear Author nndertooh to fettle i 
from the Prjaclpitt of Gravirj. 

If the Moon (ai hatbita fi^/td} aftually revolved in an ElEpJIi, round the Earth, quie/ctat, pkced in iu Center, 
whofe Oiametett being ai 69 to 70, and the Jnai, by Radii drawn from the Eaitb'i Cen- 
ter, were all proportionable to the Time of Defctiption, then the taxMnt of any Angle of it) i . Mtlbtd »/ dt- 
Motion, in thatOrbit, would be to the TaxgeKt of itt mean Motion from the Quadrature, at ttrmning tht ^aoK- 
6910 70. But, ai our AUTHOR oblervei, tit Dr/iriftiBa tf tht Auat fiam tht ^uadraturt f tilythtrttf. 
lb* C*igMa3i*a,Br0fp*fitiBM, ii atttliraltJ, andtughttB bi i*/iubPrBp*rti»», thai tinMBrntnt Bftbtjrta 
iitSjiagiUi'aaj bile tht Mamnt afibi Artain^iiadraiuri,ainojl /01O973. Which ii readily broaght to Computation, b}^ 
dimioithine the Tangent of thii Angle from the Quadrature, In the>idii/£f^/ Proportion 0^0973 to iioji,that ii, vd 
the AiA'aof68,6877to69. HniM, the Angle ofthetnieMotion,from the C^adratares.will be, inthe0^a*/i, {when the 
Angle of <«a)i Motion it 4;*)= 44* 27'ia'i the Z)/^nv«» between which, and the Angle of >wiis Motion, 450, givBi, 
forthc MEAN VARIATION, at a Mariauuit, ji' 31'. But thu ii, atlfaid, fuppoIW the Earth fiuV^"*. Bniat 
[he Earth mo vet, and the Sun thereby i«, a^partntlj, carried m Canfiqutittia, through the Ecliptic, the Moon, before it 
ovcrtakei the Sun, defcribet an Angle greater than a Right-Angle, in itt Progrefi from the Crtat 3 & 

Quadrature j and Tl-at, m PrtftrtiBii ^ tit ftritdital t* tht /jnaStal RevtitUiou tf tht Mobh, *' fi^^^^^ 

i7*7*+i°« •9'' "*+4"- Whence, it comei to paft, that all the Angle* about the Center /^L' j *'\^ j 
d£ Modon are dilat«Kl in that Rath, and the GREATEST VARIATION, which, in the for- V^f^.'^SSl^ 

vSoppofition, amountsbtttto ja' 31', become* 3s' »o'. «(r «aac newton. 

AccordinE to Mr. JI£uihV* Pnnciple, before laid dowii, the i)i«*sr/*rj of the elliptic Orbit ^ _j- >.m 
beiBgtO each other a* 59 to 60, the VARIATION-EQUATION, at a Maximam, wouTd be ul^ "^ 
bBt23'C3'. which ilKTMcd in Ae^fiiean Rati* ^ ihtftri»ditaJta tht fym*£eaIRtvtlMtim, or "* 
iM.tit Syn^■^i^.^?f7^♦3■'ff ag^ia'' 44.'. giyeifer the GREATEST VARIATION bot^y 45*. 



p. JJ9, L. II, fr. Bat. for 1,000 r. looo ) L. g fr, Bot. fiti 17(711, r. I7>,7ij. U j fr. B«t. Aae P. lUb, fW, « Aij 

(■nw Time, r. m the fun* Time. 

P. jto, L. ifr. Bat. fn, wn to«tid« the San thin the Eat^, r. awi ir A/i this tb« Eutb towiidi tbc Son. 
List ]i fa. Bel. tftet KT, intiodact and i. ^ vhkb tk* Uood >■ lUotttiaSed tswudi the i*tth. 



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36z fii ROYAL ASTRONOMER 

COMMENT OQ the MOON"* THEORY. 



i.AurdngltDr. If Dr. ^.uV^'i Ratio, from Obrervation, of thefhoiterto the longer^//, be take* u 89 
Hill«y. » Qi. it will give the VARIATION at a JVmriinsm, 38' la'. 

Mr. Majer, the Author of the Gattingex Tailti, «flert«, that the VARIATION, at a Maxi- 

K.Atcr^ngnMr. nam, it equafto the«<iii^--^'.|iof EVECTION-EQOATION; thu ii, to 40' 10'. Bathe 

Mayer. giv<> "o Demon ftratioa of thit ; and it appean, by the Cenfin^M af hii T^AIn, that the Cer- 

TiBicn af Evt^ioit, according to Anomaly, and the Correflioti of Anomaly itfelf, accordieg to 

the worinJA Eccentricity, ate, by him, both flung into hii VariatioD-EqnatioB, to raife it to that ^muHij. 

Thig Method of bii ii well adapud for the Ea/e af CamprntatiBn, iut nat to h* aJmilltd ai Ihttry agarnfi tbt Principles 
^tVtoa, faUMdid an thetnuft Giametrj \ •mbieb limits thi ^uantilj, ai abevt, ta JS' ■o'. 



ig into thii ^filan, and proving, for toy own Satjifaflion, the Trnth of Ade 

,. . ^ . . 1 have been led to enqoire what certain Proportion, the greateft mean VARIA- 

parlitHal te ibt Strm- TION, 33'32'(the Eanhaxi^m/^ ai Sir^irhMgiven it, bearstothe 5fMf-^j&of EVEC- 
jHtU af Evi3iaH. TION -EQUATION, at a Maximum, and have found it to be in tbt JnfHtate Raiia aftbt ^^ntdieel 
Rrualuiumaf ibt Maan Jram ibiSiiii, ta tbt fjna£cel Rfoalation ef tht Mam fram htr £ptgtt. And 
Pnforimal It I farther foand, that the Tangent of the Angle of Variation ii to the Tangent or the Angle 
of4C<', in ihe Ratit tf6g /a JO, and the5iiJ'^ii^Var« ^ 10973 /0 1 1073, conjunAIy; fol^etnfc 
the Tangent of the Arg. of EVECTION i* to the Tangent of the Angle of 45', in tlie fermtr 
Rati§ of 6g to JO, and the finiplc Ratio of 10973 to 11073, conjundly. Which Arg. of Eveftion /_ 44' i9'4o'4o*, 
being fubonfted ftom the Angle of 4;*, leaves the Stmi-jf»gJt af KviSioH-Equaijai 40' 19' zo", nearly as before. 

■I: ii well worth obferving, that at there ii ngivn Difference, or Ratio, between the Angle 
8. A Rfmart. ■ of EvtSiaa-Ejuaiim and rariaiian, both being at a Maximom, fo the Sum of thefe Equationt 
Aould be, when txkcn together, equal to the tarria ^aaniiiy af Equatian af tbt SarlVi OrUl, 
a Maximum, I" Cj' 50". 

For the EvtBhn'Efuatiait, 1' 10' 40* + f'»'''«ri«>, 35' lo*, !i equal to I" jj' 50*, the above Equation. So that 
the Faru by •which tbt Citrvalurf af tht MavCi Orbit it changed, and btamri mart ur UJs ucntric than in ill mtaii Stafi, and 
dyaby tubicblht Artai dtfcrihtd artrtnJtrtdmttquai /» ant aaalhtr, putratti an Eouatianaf ihi Mooii'i Longitude propor- 
CionableM thai gntrattd, in tht Snn't Longitude, hj tht EttntHiil} af ibr Earth's Orbit, 

OUR AUTHOR hai here given the mtan Quantity of the Veriatiim only, nnlcOing, ai he fayt, the Difftrrmct 
which may aiife from the Curvature of the Orbit, or the ftionger ACUon of ibc Stat utaii tbt Maen, -j/beu harntd amd 



nrai, than lAihtn full and gibbmu. In oilier Siiuationa of the Earth, that ii, when the 

_ ^ ii rear the Afht&ttt or ptribtlitn, the GREATEST VARIATION ii componndcd ol 

a^^ mtan hi/a^t dufdicatl Pnperlim af tbt Timt af tht £fnadical Rtvolutien, dtreQlj, and tbt trifdicatt Prtft 

»f Mmh frent tbt tf tbt Oifiantt af tbt Earth fram tbt Suninvtrfilj ; and therefore, according to thefe Propoitioiu 

Earth. in the Aj,bi/i»n, the GREATEST VARIATION ii 33' 14': In the PtrihtUon, 37/ 1 1'. 

In thefe C«mpuiat,tm, our duthw hai negle^d to take into Confideration the Change which 
the variable £r»s/riVt9 of the Moon's Orbit mall make in the VARIATION-EQUATION: 
_ .Fariatianeban- leavme it for fulnrt Afiranamtri to determine the Quantity thtrtaf fram Obftr^atiw : For, by the 
gtaiU at 9lbtr Hifi- Moon 1 being mart at Uf removed from the Earth, in her OSar.n, by the variable Eccentricity 
of her Orbit, the Fariatian-Equatian will become mare or Itfi ; the Ratia between the antrifiiai 
and the diftnrbine Force being ii/i orgrtattr in the em Co/t than tbt etbtr. OBSERVATION 
fbewi thu thtj Confidcration ii not wholly to be iiegleAed. For, TatUi formed from thefe Principles are found to 
nwf where thit CorrcfUenof the Fariatian, according to the Maeifi Anamat/, i« greateHi that 19, when [he Moon is 
Qaaniu *nd "<«' ^^ of her Apfidt!. 

It vjiTt much tt ht toijhtj, that Sir Ifaat had not contented himfclf to pafi thit by, ai a 
ARtmari, Rtmark, for otheri to improve on: but had deduced [he Quantity dirtaly frtm thtTbttry 
af G'avitj. However, thii Equatiin of the Moon's mean VaritOian, according ai Ihc ' 
greater or tefs Diftance from the Earth, may be obtained by the foUawinK RuU. 

The centripetal Force in the S^adraturei, is to the accelerating Force in the Sysygiti, as the Sum of the greateft and 
Icall centripetal Forces, to 3 Timea their Dijertnct. 

Again, ue accelerating Force, when the Moon is at a mean DiAance from the Earth, is to the Dii!crencc of the 
greateft and le aft accelerating Force, when the Moon is in the A^tt of her Orbit, as the Radiui is to tlie Sint 
of Half the mean elliptic Equation at a Maximum, or to the mean Eccentricity (Radiui being 1) and the Subd^eati 
of the periodical to the Jytiadical Revolution of the Moon from the Sua conjon^y. 

Therefore, on the Principles of Matbin'% Eqnant, ai the Stun of the greatell and leaA centripetal Forces, is to the 
Kffereoce of the accelerating Forces at each Apfii, To ia the Radius to ttie Sine of this other {^cateA Eqoatioa 
1/39*, -vwi. Ai 357,50 : ,171 :: Radiui : S.j'sg'. 



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NAVIGATOR. 



5^3 



COMMENT on the MOON's THLOR.y. 



VI. Of tbt MOON'/ SECOND EQUATION rf VARIATION. 

BUT there i« Rill a faribtr Ciaage in the imiar Orbit, arifing trom the ftrOnger AfUon of the Son apon the Moon, 
when nnu and /alta/tJ, tban wbtm Jitii ofid giUaai, from whence arilei aootkei Equation, which Sir J/aae c»Ht 
the ficmid VarialUu, 

The ctntripttaJ Force in Cppofiiion being to the fame in ConjuoAion ai l8oto 178 «iarfy, tWMoon recede* fome- 
what farther from the Earth, and moyes fomewhat flower in the Conjan^on than in the Oppofition. This Firtt ge- 
DeTateiawwffMU/va of mean Motion, which luU to it from ^u// to the i/MO Moon, uid /aitraSi kam Nrut toSie 
Au7Moon. Ani Oa Situ ef tMi Ejiuaiam h » AWrni <u ,2 /> 357. Mw. ff^iifitn, for explaining this Equation, erro. 
neoofiy diBinzDifheg between aa ar(/i6jiu/iWPoint of true, and ^wMf/nVd/ Point of mean. Motion; by wliich-he cn- 
deavoun to gire the Lawi of this Equation ; but ai thii Diftinflion sf hii two FointG ii without fenfible Difference, 
hia Reafoniag is incODcloliTe. Sir ^aae Nnutea gives the Maxiiaam of this Equation at 2', as ic is retained in the Ta- 
iUi. But by the foregoing Analogy it cornea out no more than 1' s;6'. 

Bat then Mt/icmJEjiiatitii of fariatim has been obferved, Sir ^<7af- fays, to be liable to Change 
For, when the San ii in Cenfumaieit vihi it* Jpegtan ef ihi Moon, it is, according to nir AatSer, I . Chatigt af tht 

^aottt l* gruutr, and as anu-^/r/i, when in Oppoiilion ; on Acconntof the variable £ccentricity zdVariatieu. 
of Ae Imior Orbit ; "tbt Jciar Faret bang priaitr in «m Sitna/ifM end ie/t in tit »tbtr. 

Dr. Grigyrj, who firft publifhed this fameiu Tb*eij to the World, gives us a veiv perplexed and coofufed Atctuut 
af ibii Efuatien ; nor had Sir (faac Niwlen himfelf Obfervations fuScient to fpeah of this Change with Certainty. 
In his firfl EJimn of the Principia, he fays, that the thiagtahlt ^entity is to be determined 

by the Siluatim af tb* A^gimi cf tbt San aad Maan ; and is grcateft when they are in Con- a. CBntro-oirJitt a. 

juoflion, and leaft when in OppofitioD : It is UnJI alfo when in Qaadratnre with each other, baai tht zd Varitaiaii. 
and greattft alfo when the Moon's Apogeon is in Conjun^on with the Sun ; bat whether Icfs 
in Oppofition to the Sun, Or. Grtgvry, Lt«Jbttier. and others, tell ui, that our jiatiar could not determine, far 
Want ef Ohfert^aihm. But this fuppoled Change, in this Sjuaiisn, i) not from the mutual Situation of the ji^fidtt, 
or of the Sun, in Regard to the higher or lower ^^j of theMoon'iOrbit; but of the Moon in refpe^ to her DiHance 
Irom the Earth ( and is, in Truth, not an Increafe or Decreafe of thisT^nW/Vjafffs, but of the firit only^'and 
from the Principles deduced, in the foregoing Paragraph, to which the Reader is referred back. 

VII. Of tbt MOTION af iht MOON'j APOGEE, or APSIDES. 
PROM tbt ytb mJ Stb Caraiimj af lit 66/i Prapvfitiait ef tht \ft Book. Our Author derives the Motion tff the 

Moon's Apogeon. The /Mfualrtici of which Motion are, at he oblerves, very great, and generate the ^W«a/i>/£;mi- 
» ef Iht Afegtt. 

From what follows, it will appear endent, that the Lim^ /A* .^»iS//f mall have, on the whole, a progreffive Motion : 
bat very irregular. For, when the Meea'i Afegtt is in Coojanflio'n and Oppofition with the Sun, the Apogee goee for- 
ward at the ^i-Mr^ Aa/'; bnt, when in Qaadraturewith the Sun, it evengoeibackward. For, 
in the Qaadrature, the Force by which the Body P. (fie Fig. I.) is urged to the Body T, the i. Irrtgnlar Me- 
Force MT, then vanifhing, ia compounded oF the Force MI., and the centripetal Force with lian ef tht Apfidtt 
which the Body T attratts the Body P. The fi'/i Fe'ce. ML. is increafed, niarlj, as PT. txplaiptd. 
Theother dccreafes in ^dufUcati Proportioo of that Diftance. Therefore the Sum of tbefe 
two Arm decreafe in a lefsPtoportioD than the duplicate. Whence the Li/ir of the Afifij, [hy the 1 . CereH. of the 
4ctb Pn/. of the if Bosk) will recede. In the ConjunAion and Opposition, the nwr/'i/n'ii/FoTceis asthe Difierence 
of the Force KL, and PT; which, bccaufe KL is nearly increafed astbe DinancePr, AezttAfa \a inert than a dupLcete 
Rati* of that Diflancc; and therefore caufes (Car. i. Prep. 45, B. I.J the Apfides to go forward. Bnt, iince the Force 
KL, in the Syzigies, is nearly twice the Force LM, in the Quadratures, the Ejteifi will be on'the Side of the Force 
SL t and, by Confcquence, the Line ef lit A^dei will, on the whole, be carried forward. 
- Sir I/aac Nfwien does not determine the Quantity of this progrciEre Motion of the Moon's A}Jiiti, from die tbtary 
»f Gra-vit), the S«/«/'u« he gives of the PROBLEM, " TO find tbt MOTION ef tht APSl DES (fee Prep. 45 , 
" Prabl. 31. ^. 1.) in OftBITS mar^ CIRCULAR," accounts, when appLed to the Moon's Otbit, but for Hdl 
the Quantity of the progrelhre Motion of the Affii in one Lunaiien, tiix. i> 3 1' aS', nor has Mr. MaMn fuccecded 
belter. He tried what it would do, tonfdtring tbt Caaft ef ibit Malian ai arijing frem tbt Fariatien ef tbt Meen's Graiiily 
ta ibt Earth, ai it rfuelim in tbt eUipttc E^qcit, afareountiantd., for afcertaining its true ^aantitj : the Difference 
of iheFareei being, in that Cafe, doable the former { but it gave not the Quantity of Motion with that F-xaamfs as 
was requijite : Her viai then tag Mtlhedf he ibeagbt, wpen cemaenly rtciititd Prineiplii, fu^dtnt fat tbit Purpeft. 

Neverthetef^ this PrebUm has lately been very Cuisfadorily folved by the Rev. Mr. Patrick PrJ,i~ CJ. J 

Mardacb. (fee Pbi(. Tran/aaieni, V. 47, P. 6a) by which Sijulien he determine* the Quantity ^' g^Tl ^ytL 
io afynodicalMonthtobes' 17' a8*. exceeding the Motion by the 5aAAi bat +'. And he MetiM^tht AtU 
obferres, that the Rtafen, that other Authors have failed in giving the true Quantity of Motion , "". ",, , ^V' 
of the Aptgu^ from Sit I/aact Principles, is, that they all have confidered the Earth as ^V'm^mL 
faitfciM; alihongh the Ca^, ioNatote, and 10 which they mean to apply Sir Ifaac^s Rait, u 



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364- 3-*» ROYAL ASTRONOMER 



COMMENT « dte MOON'i THEORY. 



^ 



^SatBt. For, u thii irwaut Wrllir oUiemi j " Tir fw/A ««/ JMm mwAM rtw/ thdr t*mmm Cnttr tf Gramtj^ 

" thdr Difltuct fitm lubicb bdng iwimfify, <u ibmr Msffti, md tb* Ftrelt fy noUci tmcb it attrnBti. hj tht ttitr, ai aJ/a 

ibi Ftrcti ^ Ih* Sun H iifiarh tUh Mtthf iting in lb* /ami Ruio ; It fMlowi, tbmi tht Em-lb im in Maiim namitit 

(»mmm Cnitr »f Gta-uiij^ luiii faftr ibtfi Difiwiaam tvtri JVaj SmUr tf tbcfi »/ ibt Mtea : md tit ^obti UMaa 

tf tbt Api», rtfultiMg fiim ibt fUM di/hrbiag Ami, viilibt, mmt^, dmbU *f v>baliitbtr *f thtm twM fn^tt fipa- 

rattfy rmaj a fxti Cnttr." — So f«r Uiu ASbor. Aod whoever coofiden tbt S»lati*a of tfait difficult PrtUtm, will 

not oaljr be &tufied of thii Gentteman't great Abilitlci, bat ioin in bit Conclnfion from it : That in thi*, ai !■ tte 

aihxz Pi^MMmati tf ibt talt^iai Mtliiui, lit Prbuifi*i tmJ RjJts it>bieb SirliMcHewtouJ^iJmmtrtJidfytm/bmtd 

aadvtiifitd. 

Mr. Matbia, bowerer, hu dedaced tbe Motioii of tho Jfcgu frosa otber friaafbt, wbkh 
he hai not ezplaiud, but contented himfelf with giving Ruin foonded thereon, fbrofa- 
^aaatitftfyi'i tKranvtbt anaa Hetian tf ihi ^ptgtt, iu Eputit* maJ lit Cbaait tf Ec<imlriatf: which an 
^ (, ia a JjdtrtaJ thefe that follow. 
*l^,aecarSagl»Mr. " Tbal tht auaa Matitn tf tht Mttn, frtm ilt Jptgti, ii It itt mtaa Molka, in ibt fabJt^&tali 
Machin'j Raiti. Freptrtitm of 823c It 8376, «r as [877 It 189$. AccoidiiM to which Proportioa the HtNioa 

4.. AetarUng ttSir of the Apogee, in mfi^rtal Year, ooghi to be 40* 4.0' 40* f. In Sir IJaat"* Theafj the 
Ifiiac'j Tbttiy, Nnrabcn ftud at 40* 40' 43*. Accordii^ to Tjtb^Brait 40* 40' 47'. 

Vm. Tt JtarmiM ibt CHANGE »/ ECCENTRiaTY tf ihi MOON'i ORBIT. 

Sertmlndt, Jt. '^^^ ^"^ '' " '** *'** ^'**''**<J'. "• '** *>&«'« Jt^it tf (*« frh^cal 7fam tf tbe Swft 
joaimnarj at- j^^^/^f^^^ ^ y^ ^^^ fpu^cai Timt tf in Btvimin fitm tbt Mata's AfH," ■' "w^V^ Ratio it 

"lastly, fo/th'e SKCOND EQUATION of the APOGEE — " Tht Siat tf ibt gnaufl 

a. Grtalffi tJ E- Eqaatitn it It tbt Radioi, a» tbe Difftrma tf tht grral^ft and Uaft Ecetnlriritiis art tt ibtir Sam ; 

jaatita tfntMmti diat ii, at jgtt 136. Thii determine* the Jt/Mn'ntwn of thi) Eqaacion at iz' 1 8' 43' 16*. Sir 

Aftpi. .^sf hin dctermiaed it from Obfervation to be 12° 18'. And the ^s/^ I have ureadjr given. 

fcr determining the Simi-Ejaatiti tf EveSita, afligni it the fame Quantitj. 

Mr. Macbin alfo makei Mention of axtfbir RkU, derived from a Jigirtnt Mithti, which 
1. Mr. Machlti'/ prerap^fet the Knowledge of the mean Eccentricity, and which, faefayt, would not on)}' 
JtaZr ftr dutmiming determine Ae •variebU Bettatrinij with greater Exifinefi ; bat would alfo correCl the auJirm 
tbt EretatrlciiUi tf Tbicriti of the Moon in a Particular, wherein their greatsft Error, he t»ys, feemi to cooGll 
tit Mtta'i Orbit, aaJ ibai is, in fiating lit Earti ia tbt Ifoitr Fetui tf tht Elliffc, •aihub ibt Mtm A/rriits ia btr Jt#«» 
ttrrtOfi^ tbt haw buitn remd tbt Eartbt whertM, it oaght; KB SAYS, " tt it im a ciriMa Pttat aurt atsr li^ 
Tbttty. Perigitm.*' What thefe Prindplei were from, whence be derived tliii CorreAion, or how he 

fonnded this atw Hytttiijis, it ii not poffible to colleA from this ^kttti, or dbftraS of a laiga 
Work intended I Tit bmviaggivtatu Dta _^tar GaUt, in bit (iionTriaiiJi tn til Mtea's Gravity, 

IX. CHANGE .//*# INCLINATION «/ '■5* MOON'/ ORBIT ! »^/A*i*RETROGRADATION./*w 

NODES, tstpi^Hii, aad dttirmatd ia » tirtaiar mi elliptii ORBIT. 
BUT, it ii not onlv the Motion of the Moon, ai to Ltmtadt, which ii afiefled bj tbefe difarbiag Fttets : The it- 
rlinatiea-tf btr Orbit likewife (aSen Change hj them, and her NtJii, (or the Ptinli, ivhert ifn Orbit tf ibt Mtta ia- 
irrJiBi tbt Plmi tf ibi Earlb'i Orbit) are carried with a rUrtgradi Motion, through every Point of the Bcliptic. The 
Caitfts of thefeC^a^M are explained in the totb and iiti C^t/l/nia tf tbt 66ii Prtf. B, 1. Principia. TneSi 
of which Explanation ia ■■ followi, 

LET the i^forii*; fff-rM be reprefentcd, ulaFig.l. by the LineiTM, ML. IttievMot. 
Chaagt tf tbt that thU lall Force, aOing in the Plane of the Moon's Orbit, never on diffairb the Modoo at 
OriiPi JntlsaatiM di- ta Latitude j and ^at the former Force, TM, when the titdts are in Sjt^ts, aOing alfo ia the 
fctibid. fame Plane of the Orbit, cannot, at chat Time, afFeathefeMotiom. But, when&eAUuaR 

in Qaadratare, it mult diftorb them very much. For attrafflng the Moon papet u ally, out of ' 
Orbit, it £adiupls tit Inelimalita tf tbt Piaat ihtrttf in lit Paffap tf tbt Mtta frvm tbt ^adratarti la tbt Sjaygiti i 
<nma intrtitfti tbt famt ia htr faffag fnm tbt Sja.jpts tt tbt ^Modrstlirts. Hence, the iDclinatkm i* h^ is all, w 
£e Moon U in Sjp^giit, and retomt to the fii/l Qnantity, nearlv, when tbe Moon urivei at the mm KtA. 

The Mooa being that, ptrytiaali), drawn from the Plant tf itr Orbit, it is manifeft a* Hie continoally reudeil* 

lAt Piaat, in her PaRkge from C, ibat She wilt intcrfeA the Piuit tf tbt EartFs Orbit, not in die ofptAtt Node d1 
u ia JimiPeial laart ntar tt S, which, from thence, becomci a arw PUut of the Node, ia Jattttdtalim t» the fenncn 
Ik*. The Ntdii therefore, when near the ^oA-aturis, recede perpctnally 1 bat, in the Sjtejgits, where w> difitartK 
ingForceiaainthefainePUae, mnfaitfttati and in ix^frnM^^arcHacet, recede with a qmcker or more flow UMionJ 
u the/ areocarer 10 the one Point than tbe other. 



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W NAVIGATOR. 



3^5 



COMMENT on the MOON*i THEORY. 



Oar- Aatbtr Ini cwnptied tkc Q.iwntitici of thefe Irrtgmlaritiu, whkh take no left than pivi (Seey^M Pny. 36 
PaoFoiiTioHi in the III.Booa, II woald be difficult Co render fuch aa ai^ri^5«j;>d dearer t» ^^ tMciKfiv*,) 
than in the Word* of the Author, or to explain the Gnrnndt of hii Compntationi fo, at to give 
fflcne Satiifaaion. Ut it fafficeto U-ace out the Sutg heproceedi in. Ani frfi. He begins with the LEAST VCBfh 
CULT PROBLEM. Ti/W^/i* HORARY MOTION of ibi NODE m « CIRCULAR ORBIT ? 

In which he obfenret, that, of the two Forcci, br which the Moon'i Motion i* diftnrbed, that which it reprefen^ 
•d by the Line MT alone (FiJi Fig. I.) genentei the Motion of the NODES. And that thii Force ii the fasK 
with jPKi which {by Prep. 2j) it to the Force, by which the Moon may be in its piritdicTipu carriid tn a Orclt 
rmaid ibi Earth at Rift, at i?K. to tht RtuSm sf a Gre/t irai/li/'Sid fy ih* Numltr 178,715, eraifK., t» th* Radtui ittrn/ 
maUif£*Jij SQ,i7S' Since, therefore, thefe Forces are the one to the other, aiito 59,57^, this mean honuy Motion 
.of the Moon ociDg32'c6'27'izivf, in refpcA of the fixed Stan, or a periodical Revolution, the 
horary Motion of the Node willbejj' 10' 33iy izT, when the Nodei are in ^aj^f/vfr and the a. Qumtitj if 
Moonin^7j>u. In other Cafes, thehorary Motionof the Nodewill be to ji'io' 33!^ i2V, as ihi baraty Mttim 
the Produft of the £i«/r of the Moon from the Quadrature, of the Moon from the Node, and of ihe */ lb* Moon"! Nodi, 
Node from the Sun, to the Cube of ILtdiut. If therefore the Ntdii went on with that Velocity in a drenlar Oriii 
throt^hoot, which they acquire at firfi, the Moon being in Syxjgit, (for then the Force FK ii at a dtltrmnti. 
Maximiini) ihej •u.-euid difcribt a Sptxi, denbU ta iiilat tht/do, in FaS: but the attui Velocity, bcEweco 
this, their greateft Velodty, and their tttal ^efctKci (when the Moon is in the Quadrature and the 
Force PK vanilhes) beinz half this Qeanticy, their sumt horary Velocity in a circular Orbit will be ■6'i;' 1617367, 
when the Nodes are in ^u*i-a/«Fr/. In all other Pofitions, the (nw» horary Motion oftheNode, will "be to 16* 35* 
i6iT 36T as the Square of the Sim of the Dillance of the Nodes from the Syzygiea, to the Square of Ra£iu, 

Kr.^i^rNnv»*nextconliderswhat the Quantity would he in xatilipiic Orbit whofe Diame- 
ters were to each other as 70 to 69, and the Iinnmiau of the Areas as 10973 to 11073. And he 3. Tht ^uaallp 
finds, that, in {w:h »aOl\iit, ibt hsrarj MetimB/ibt Nf,dri,i» ^lu/rtifiirt.ivi/I hi diaini^dle 16' 16' dtltrmntd in «b 
37iT4iy: To which die mean horary Motion of the Nodes in any other Poliiion is proportional tlUfticOrtit. 
at the Square of fhe &i>it of their Diftance from Syzygy to Square of Radios. But LAEiTLV, 

THE ANNUAL MEAN MOTION of the NODES ii the Sw» of «//'*» HORARY MOTIONS. Andthe 
Motioo in a complete Conrfe of a JydtnaiTear, or of 36;' 6'' 9', amounts to 39<> 38' 7' (O*. But this alfo, fy 
Praf. 33, is tobediminilhedinthe Pioportion of the lUSmiglt ef tbi CircunftriHei numpUtdbj tht^adiui, ta iht Jna 
»/ tbt Greli, »ra/ ttai. So that the annnal Motion of the NaJt, in a fjdatal Year, is half the 



So that the annnal Motion of the Kadt, _ 

above Qoaatity, equal to 190 49' 3' ej*. Which Quantity muft alCo be diminifhed ; it being 
"'"■" Uiat the Son paflea through the whole Circle, - - ' 



ning toi 
The . 



360', from 
again. Whereas by the Fjciji of the JVtA it wilt have paf- 

O 



5. JmauJ Al^ 
tUm of tbt tfth) 
dittrminti. 



ipnted on the Suppoiit 
leaving one i^adt to the rett 
fed through bat 340* 1 1 
tbcrclbre, ftill waua a farther Diminution, 
The Quifntity of this Diminution is afligncdi 
by e» AiitbfT, at 1' 29' 58' 2*, which fub- 
trafied from the above Quantity, leaves i8<> 
19' J* 53', for the luioA Matian tf thi Hade 
tH refpiS of tbt fixid Start bttvjtea Itiit tf iti 
uiJtt CnjmBinuviithihtSitn; which afterwards 
inctcafed in Proporiion of 341' 41' to 360'*, 
mves 19' 18' 1' 23' far tbt mraa Matian »f 

3» Nadt in aai_fydtrtaJTtfir. Obfcrvalioni deter- » ' Fig. III. 

mine it at 19° 21' ai^'so'i but this Difl'eience, eur Autbgr iM^tet W the Eeenitritifj of the/asdr Orbi^ and 
Inclination to the Plane of the Ecliptic. 

Prom thefe Aigmaliiui, in the Motion of the Node, Sir I/aae deduces the PRINCIPAL SEMI-ANNUAL 
EQUATION t/ tbt NODE. Its true Place may be had, in every AfpeA of the Son. About the Center C, defcribe 
the Circle £, E, F, D, produce CD, to A, fo as AB may be to AC, <v tht mtan Metiam af ib* Nidi, u tbt 
bal/a/ thi imt Julian lubtn im ^Ko^-aiiiri iiaih tbt Stai, That is, at 19* 18' i' la* to 19* 49^3* ss'. So that 
BC, be to AC, at tht Dlfiriwe* *f thafi MtUmt, 0° 31' a' 3a*, to tbt iaittr af ibn 




Dljfirti 
Then, 



19° 49' 



;;', orMi f> jSyV* Then, through the Poiot-D, let the retlr/UM ^W Gf. be drawn, x.Miibadtfit' 

toacmng the Circle in D. . Next, if the Angle BCE^ or BCP, is made eqnal to the dnHbh lirmimng lot zd 

Bi^eact of the Son, from the N«di, and the Liat AE, or AF, be drawn, cntung the Tangent Epmtien tf- tbt 

Line G D, in G, and we alfo take another Angle, which fliall be t« the whole of the Motion of Nadi. 

the Node, in the ^«rtWbetween the Spygitt (that is to 9* 1 1' 3'] at the I'mgnt DG, to the 2. Tbt grtattft 

•wbait QrtKmJtrtMct oi the Circle, BED, and we «ii/ the laft Angle, for which Sic Angle DAG ftm-ammal Eqaa- 

may be nfed, to the mean Motion of the Nadu, whilft they are paffiiw from the Qnadratnre* to the tian rf tht . JUms'i 

SjKfgitt, and fi^traS it, whilft they are paffing from the SjKfgia to uc Quadrature, lat^tdl hg/ot Ntdi dttirmiatd. 
tbHftm'I^iHi. Abi ibeEqtialiiirreJii/riiiglbtiiatoi/tht, aTa'Mxximiim, ii>Z9'4/, 



,, Google 



366 



The ROYAL ASTRONOMER 



COMMENT OQ the MOON's THEORY. 



Xr. Ui QUANTITY »/ INCLINATION o//i< MOON-i ORBIT, -wM ih ECLIPTIC, MuceJJhm Btr 

HORAK.Y VARIATION. 

I. Tbi Hwarj 0»- A/iw farther compntei, from the fame Priacipleg, the //«■«»-» rana/ioB of the Orbtfi 

VariaiitH. IncliouioD to the Ecliptic, and girei a Method of computing the Qaandty of Inclinatioa 

at any given Time. 

The Mtm Variatim of the Inclination of the Orbit if givtn It 16^ 23' (i but this U ahftraStd from the Confide- 

ration of the Moon'i Situation in her Orbit. For, if the^vi/M are in Qpadratnre, the Inclination ia awrir by i' 43', 

the Sum of the Horary Incrementa, than when in Sjxigie ; And the whole Mean Variation 16' 23', dhninilhed by 

half that Quantity, = i' z\' 30", becomes ij' i* jo*, when the Moon is la^adraiari : And being increaTed, by th 

lama becomei 17' 44' 30*, when the Moon i* iaSyxigiti. If therefore thcMtranbe io SjtJgiti 

the WHOLE VARIATION, in the PalTageof iheJVa^ffrom tKe Quadratun*, to theSyzigtc!. 

will be 1 7' 44' 30', or rejecting thirds, 17' 45'. And therefore, if the/nc/iiMfiMi, when thcNodei 



Tit Grialtfi 
Variatiw of the In- 
elinalim oflhi Moon'i 
Orbit, dilimiitt^. 



OOQ in'Syzigies : Obrcrration confirming the Anuracy of all thefe Conipi 

Mr. Maihin derives the fame Quantities, ntarlj, by a differiKt Mttbei, ai Sir Jfaac givei 

t as the Proportions, for forming his Elliptic Equant, are the fame with thofe Sir Ifaac ha> 

Dittrtniiuition cf ihi given, it ii unneceflary \a fay more of it here. Our Author thought it worthy of a Place in 

tttarly. the Scio/iiat to thefc Pmfiifitiiaii, ihoDgh the Method of computing from this Elliptic Eqtmi 

wa», at the fame time, found out by Dr, Femhirtim, who made ufe of it for the fame Pnrpofc: 

the IniicJligatiBg the Mwios of the tftilci. I (hall refer the Reader for Jvrthtr litfiruaiim, a« to 

this Method, to Machin'i Thtarj ef Graiiity, which is founded on the known Properties of the 

Figure he applies to that Purpofc. That, where equal Aicas ire,defcribed in equal Timet, 

about the Center of the Elliptic or air/ mhtr Equant, the Rayi, from the Cenier, are atwayi rt- 

cipracalfy in the SuiJuflicafe Ralit ef the Veletit? aheui thi Ceultr. 

: the PRINCIPLES, frpm which our AUTHOR has given the LUNAR THEORY, a 
the IRREGULARITIES, in th« Mvlien if the Me=«, may be derived from PHYSICAL CAU- 
■wattliJ to comf/eaf it, and reJmt thefe IRREGULARITIES to Ciinful alien, a fupplied in th< 



«ill be 4 



59' 35' «'*'<■) '^\^y ' 



n QoadratQ 



, and the 



, Mr. Machin 

fa 

4, The lavejiiga- 
tim »f the Maoni 
NoJti aatrding ' te 
Machin. 

THE Foregoing are 
Prhrii Ihewiogbow ti 
SES. What is farther 
SCHOLIUM to ibi FOREGOING PROBLEMS. 

XII. Of ibt SOLAR FORCES, aaitig on lie MOON, « her ORBIT. 

WE hive bem fufHciencly inftruAed, already, that the ^egalarititi, in the Moon'i Mi 

X.The Sun prsJtttet tion, proceid from the difturbing Forces of the Sun, which increafi and £minifl>, by Turn 

the Ineqaaliliei of the the kmi 'uibiib pie icftribti % and whiih, -were thit iSflurbint Force taken eevie^, wonld, lili 

Moon'4 M^tioni by the Area^ defcribed by the primary Planets, round the Sun, Si equmler priftrtioKol to ihtTime 

Tumi. rf Dtfcriptim. 

k is alfo evident, that the ASioa of the San' upon the Moon's Orbit, muft be increafed Or 
». TbiForctoflbi diminifhcd, according to the lefs or greater Dillance of the Sun from the Earth. And 
H on the Mteift as the Ablatitioni Forces are double thofe of the AJJititioui, nearly, that the Orbit of thi 
Orhit atctrJing lo ibi. Moon mult be inor«, in general, diiated, and its Periodical Revolution round the Earh more 
different Dijiancei. flowly performed, than if thefe ForceihiA not difturbed her Motion at all. Thefe difiarbi _ 

forces increafe and decreafe in the iripliiale Ratio ef the Sun'i apparent Diameter. For they 
are, ai the Square of the Dijiaiiit of the Sun, i/mrrjely, and the Difance of the Moan fram ih 
Earth, dircSlj. In this Proportion, therefore, is the Orbit of the Moon dilated in the Pe- 
rihelion, and cmtrailtd in the Aphelion. The Orbit of the Moon being thus by Turns, di- 
'* lated and ctntraHed, Ihe takes a longer Time to perform her Revolution in the dilated than in 

■ of the the contraSed Orbit. The Quantity of this Irregtjarity, and of the Equation thence generated, 
LniiarOrbit'ixplaind. it determined by Sir Ifaac, from Corol. 6. Prof. 66. B. I. Wherein he dcmonftrate* that 
tbe periodical Time cf the Moon,i>!ilt be inerea/id anddiminijhed, im a Ratio compeunded oj the fif^ipk- 
tateRalio of theinereafinganil diereaftHg RaJii, and of the fubdnplicate of that ^*X\a in tuhicb the Earth' t central Force i\ 
iimiiiifi>id,erintneffed, by tbi Increafe or DtcreafetftheSurCiAHien upon tbi Earlh. From which 

Xni. Ihe Grtatifi Annual EQ\3kT\OH af lb* MOON, 

According to Sir ^^a; Neivton is 11' 40*: The Eccentrifilj of the Orhii Magma, being tt, 

I . Greatcfl .^«fw«i the Radius, as 16)^7 to locooo. But Obfervaiion fltews this to be fomewhat too large; fothai 

EjntUion. if this Equation were fartfier diminifhcd in the fubJup/iceite Ratio alfo of the ^nodical to tiieperio~ 

dicalTiaies,iti Maxiviumwoald be {to the above given Eccentricity 1667)= 1 ('29', with which 

Obfervation more nearly agres. If weaffume a lefs Eccentricity for the Earth's Orbit, «ik. 1685, or as much as (hall 

coirefpon<l to 1' SS' S<^t tor the Equation of the Snn'a C'enier, the mmm/ Equation of ibe Moon will be 1 1' ij' only ; 

by our Tablet) fomewhat great-.r ihan given by Maytrjn the GB»f»fCT Tablei. 

Mr. 



Prtporfienal 
Ciange of the Stlar 
Forces difiarbirig tbt 
Mmsi'i Motion. 



d by Google 



and N A V I G AT O R. 



3^7 



COMMENT OB the M O O N'l THEORY. 



Mr. MatUn, fubftitutiiig ta Equalim which fhall be to the Suift Syvatiea, at tbe mean So- 2. Mr. Macbin' 
lar Force, to the Fotce oftbe Moon'i Gravity, or ai 4.7 to 8400 i and increaling that Epui~ grtatift ^uaiiiij 9/ 
tian, ia the Ralia of the Smtt Ptriod, to the mean Sjnedicai Ptritd aftht MttHfrom Ibi Sua, or of tit Annual Ejaa/in 
99 to 8, compute) /Am £f««/i«i« at 12' j', H»rr»x give* i[) Maxiniam 11' 30'. ef iht Mata. 

But, the Saiar Ferci, on the Moon'a Orbit, which aClt in a Tiiplicalt Satin of Eta Didance from the Earth, /•- 
vir/tif, not only affefti tbe mean Motion of the Moon, bnt generates Equatiem both in the Mean Motion of the Jfpo- 
[It, and ^D^m: Tbey heiag acaltraltd ai tit Miaa Malian »/ tbt Masn ii rtte^Jtd, and rttar^d tubtn that it aectlt. 
rat§J. For, tboogh the Equativa of the Nodes ii to \xfubiraBid, when that of tbe Moon') mean Place i) likewifeyiii- 
traaid, yet it i), in Fa^, an Acceleration of the Motion of the Nadu, which i) Retrograde in Itfclf. For, dcter> 
jnining tbe Quantity of thefe Equation). The MOTION of tbe SUN 19. in tit riciprtcai dupUcalt Balia af in 
DifiDnei fram ibt Earth; This Motion generate), (the Eccentricity oftbe Orbit, being \(i\{ to loooitiM Diam.) an 
Equation of the Center, which, at a Maximum a ss i'- 56' ao'. If tbe Motion of the Sun had been in a Trifiicalt 
Ratia, the Equation thence generated would have been 2° 54'' Jo'. Therefore, the griateji Equation of tbe Apogee 
andNode ii to >• 54' 30', a) the mean iA'wthi/ Motion of the Apogee, and of tbeNode, rcfpectively, iitothcmcan 
lal Motion of tbe Sun, Hence 

XIV. rh, GREATEST EQUATION if tbt MOON') APOGEE, 
19' 43', and the GREATEST EQUATION OF THE NODE 9' 24'. Bat tbe greateft EQUATION 
OF THE SUN being but 1° 55' 50*, the Annual Eqaatieni of tbe Moou's Apgtt and Sadci will be rednced 
19' 38' and 9' *i', TtfpiQi'utfy, u in the Table). 

Mr. ATafAiii's RULE, derived from his J/i'^f/V£j«o»/, ii, that if the Sun's Force is in a \. Mr. Machii 



Machin' 
RuU far dtiirmimng 
thi grtaltfi Equatiati 
af Ibt Apoget 
Node). 



. Mr, MaAin' 



Triplicati Ratia of the Sun'i Didacc'e, the Kayi of the Equant Aiall be in the Se/quipli 

Ratia of tbi Difiantt. ' That, if the Rev.iluiion of the Motion, to be equated, was perform- 

ed in the Time of the Sun'i Revolution, dii Eqaaiicn would be to iht Equation ^ the Sun'j 

Ctnltr, nearly as 3 to z. Or if the Force dccreafed M m, any other Fower o' the Sun') 

Dillancc, the Equation would be to that of the Snn's Center ai n to z. But, if the Motion 

be performed in any other Ptriad, any fmall annual lunar Eqaaiiai, ariling from the difierent 

DiAance of tbe Sun, at difiwent Time) of the Year, would then be mart or Itfi, in the ^aiia griattft Equi 

oi t\ic ^notReal Rtvtlutim df tbt Sun Jrem thr Matieit te bt tqaaiti, la ihi piriodical Revoltiliaa of ihcrtaf. 

that Melian ta b* tquattd. THIS RULE makes the grialtfi Equatitn of the J\W* 8' 56' j of 

the Apogee, 2i' 57'. 

Thefe three 4nnual Equations, according to Nmolan, bear fuch Proportion to the Central Equtaiam of the Earth, 
that when ibat ii greateft, the Refi are (o j and -mbn that ii dimini^fotd, lb* Rtfi iiiil bt d!Mimfl>td prtp^nienablj. 
For the Sun') greateft Equation it to the grca ted Equation of the Moon, Moon') Apogee, and Node, refpefiivety, 
a* theprcfent Eqoation of the Sun to theprefent Fquaiion of the Moot), Apogee, awd Node, refpefUvely. 

XV. A SECOND EQUATION ef ibt MOON'/ ORBIT. 

^yt\itThtory af Gravity, Sir Ifaac Niiuiei fcurd, that the Moon's Orbit was alfo fonie*hat more j^/alid when 

the Sun and Moon's Jpfdn were in Coiijiir.flioi;, than when at Richt Angles with each otber-; which Uiffercuit a- 

fei from the Orbit being the maf Eccentric ac.d Elliptical in the Fa>-iner Sitoation, and teafl of a:i 'in th«. /dir*-. 

From hence the Mtan Mmai requires a farihtr CarrtSiat, ihcMooumovia^/awer'in t di/aitdOtSiT.'^aSjiJif/. 

in the more cotiiraatd one. This Equaiioa our Author determines, from Obreivation, to be .1 

45*, at a mean, when the Sun is in Oi5<iii/i with the Moon't-^dtj: aPothet Times, it is to i.Tbigrtattft^dt- 

thac Qaantity, ai tbtSint of lit doitbltDifanct aftht JpfiJti, from tbt ntarrftSjKfgj tr^adraluri, litj af thit Equalim 

ij to ihi Radiui. Its leaji Quantity in the Aphelion of the Earth is 3' 34' t and ia ^reatt/f, dettrpintd, 

in the Perihelion, 3' j6'' : being in the reciprocal triplicate Ratia of the Sun's Diftance from 

the Eatth, 

Though onr Juttar dedaces thia from ObTervation, alone, yet the Quantity may be de- 
duced from the following Analogy : 7bat it, tht Sim tfihh Equatian ii la iht Sim of tbi grtattfl 
ftcmtdEqmtian aftht Mattel Apagtt, ia thi ditpUcat* Ratio of tht fyneScalJime of tht Maaa front ihi 
'^ ' tht f3na£cel Tinu af tht Sua from tht Monti jlpagit. By thi) RULE the Eqoation 
comes out 3' 46*. 

tS* TheTynodicTimeof theSnnfTom thcMoon's Apogee = 4i2'.7S6i Moon from Son 19'. $3 { Greatcft iccoad 
Eqaationof the Moon'* Apogee = 12° 16'. 

XVI. A THIRD ANNUAL EQUATION af tht MOON. 

From the tewi af Gravitj, our Author has likewife dedaccd a Third Annual Equation of the Moon's Motion from 

the Situation of the Sun with the Nodti. For the Saiar F^ce being fomewhit Greater on the Lunar Orbit, when th«y 



. Wbtnctibiit. 
fuatian dtri%-*d. 



,, Google 



s:$6» 



Th ROYAL ASTRONOMER 



COMMENT on the M 6"0 tf^ THEORY- 



Otbtrvnfi Ji- 
Itrmimtd, 



tM in Coojuoftion with the Son, thao when in Quadrscnre, there aiifet a Jmrnll Eamatitn ham 
.._ gnaltjl thit<liit«rent Dilatativn of the Orbit, at die Son and Nod« are filtnted in rcTpea <^each odier. 
^aaatily tbtlrmMtd. Which Ejua/im tie iiaicom^ted, (/or it h tm /mali ta it drtirmtMMdfyOtfirvmtMm) ubeita 
Maxienm, in AtOSaiits, 47'. At other Timc*i it iito thi* Qnanti^, mi tbiZim tf ih AMi 

mhJ ibtr^t in P»iget 49*, i» Apof^ec ^5', 

The mean Inclinatioa of the Moon'i Orlrit heing t' V 2S', BwI'die half tXSaaxs of the 
neatcfl and leaA Indinatioii 8' 51'^ thi* Equdon wii) he to the Sine of the hdf DiSeresceai 
die Sine of the mean InctinatioD to the R>di«. For the Force bj which the Moon i* dnwn 
froni the Earth being leftned in the Ratio of the Cofine of the Inclination of the Moon'i Orbit to XMhv, thi* Eqoa- 
tion of DCtn Motion, generated by the Inctcafe or Decreafe of that Force, at the Son ii in Conjns^ioB or Qnadratnit 
with the Moon'i Nodei, will be ti the SUti of diat Diftrrnte to the Siiui of the mean Indiiiation, mafctng the FUttmi 
oftheCijxlewbich thcMoon defcribei, acconting to her mean Modon, or while the Siu ii in Otfaaf/ with theNodeti 
equal to I . By which Rule that Equation cornea ont 4S', neari]'. 

Both thefe £qoa{ianl tuU l» tbt man Melin, lubilfi the Smu feffa Jnm tbi ^gju^atnrt, with the Apfidea and Nodn, 
U tlitir CM;wiai»ni, and Juhlraa frtm it, in its Pa//age frem tbt Ctnjmaitni la tbt ^ut^rMvtt; Tht GIVEN CHJAN- 
TITY of thi( /o^, lilce the former Eqnation, \%\a^inan^iim-£imitifl)*iia tbt RMi» tf ibtOdfiff'thtSaJihifaMa 
frtm tbt Earib iaver/ti/. 

XVII. THE SECOND md GREATEST EQUATION b/ ib, MOON'j APOGEE. 

By the fame 7btfij af Gravity, oar Aatbtr dedare* the ficwnd and grtattft Eqaatitit if tbt jfftga. We hare ilteadf 

fpoken of it in cxplainiog the Motion of the Agfidti from 7> S, and 9 Corellarin tf Pref. 66. B. 1. Iti ^eatd 

Qiiantil7, from the Theory of Gravity, ai weU ai from Obfervation, it nearly 1 1" 1 8', aiut ei eU Tiimti ii ii tt ibtt 

^naalit), ei tbt d»»bk Diftantt cf tbt Sua /nm ibt Jpegion ii If tbt RaMai. 

XVni. HORROXV IMPROVEMENT tf the LUNAR THEORY. 

H»rrtx, a* Sir IJoac oblcTvci, wa« the firft Afirooomer, who advanced the Theory of the Mooa moving 

lipfe, ronnd the Eattb placed in its hvitr Ftciu. Dr. HaiJtj improved thii Notion, by fdacing the Center ofthc hJbpfe 

in an EpitjtU, whofc Center aniformly revolved roand tiie Earth. The Metion in this Epicycle, czpreflet the fbrC' 

«ientionnli>^»w!f/wj, in the Pregrtfi anJ lUgrtfi of thi ApjiJtt, and ^aChaagt in the Quantity of the Eccentricity. 

Let the mean Diflancc of the Moon from the Earth, /aju wr Aiuhor, be divided into tcoooo 
I. TbtEcetntriatj Parti; and let T (Fig. l) reprefcnt the Earth; TC, the Moon'i mean Eccentricity = {{05 
•/ lb* Mtmi't Orhit fnch Part*. Prodace TC to B, fo a» CiJ may hi iht Sim tf tbt gnattfi JtMi-amaud Efuititm 
tmd %d fifwon'M tf tf tbt Aftget, 12" t S' » tbt RaJim TC. Then, the Cirde delcribed npon the Center C, witk 
btr Aftitt, iiiutti. the Radiui CB, will be the EPICYCLE mentioned, in which, the Center of the Moon'i Orbit 
it placed, and revel ved to the Lift, according to iheOrnW-ofche Lctten, B, D, A. Sit eff tbt 
dHtk BCD* CQul /« ftWM tht eannal ArgkmtKt, Qt the deubit Difiami tf the Sam'i trai Piatt frem tbt Alttn'i Afagtt, tmn 

twittJ. Then, CTD will be tkc /tciad Epttiitn tf tit 
V , Mtes'iApogufirthtTtKugivtin TD tbt Eectnti' 

tbt Orhit, ttKding It thi Piact tfthi Apogee, mm. 
tjtialidi and CD, Qr CB, tbt Diftraei bttvmi tit\ 
mtan and tbt griatift Etciatrieitj = 1 lyj, of tbt fl^fl 
Parti. N. B. The Radint of the £//c^'& CD, or CB.l 
aa feen from the Moon, at her mean DiHancc ftom thcl 
Earth, fnbtecdt an Angle of ^o'ao',=:thcSemi-Ffiia 
t/EveSiaii. How thii Angle may be obtained, at once,! 
without computing the Angle CTD, or the Eccentricityl 
the Letter to Lord MACCLESFIELD, on die Parai/aSic An^/i, ' 




Kf.ni. 

TD, it fnlly explained ii 

which the Reader is referred. Or you may fee it performed fardier 00, P. 371. 

ir«a Place, the Place of iu ^fegtt, itt Eccmtricitj, thelonga Axit of iti Orbit, zooooo, bcingl 

ivra.' the Moon'i trM Place in her Oibit, with her Dillance ftom the Earth, arc thence detcrmiaed, by the koownl 



uven, the Moon'i /rMPUce in her UiOit, will 
Method of Iblnng die Equation of her Center. 



In toe Cemfuiaiim of the Eqiuitiona of the Aptgttn, and Change of E<cialrititj of the Orbit, 

' -iM^ri.^ which takei Place from the different AAion of the Sun upon it, according to iu di&rcnt Afpe£b,l 

tbt Mfiit I Orbit j^ pefpefl of the lunar Apfidn, no Notice hat hitheito been taken «f tbt Dimipiuita v Kxc^ rfM 

M^dingta thi df- ^^ p^^^ ^^^^ ^j^ji^ ,^yi Cba»g,t in tbt Orhit, acctr^ng a, tbt Stm, u fartbtr frtm, mr nirarir u\ 

ftriKi Uijtancii ^ tbt Eartb. But, aitheSon a£U with greater or lefi Power on the Aaar Orbit, according as ikcj 

c L " Earth ii neareft tq iti Perihelion, or Apbriioa, and ifaat, in tfa* trifUcatt Ratit of itt Diftanae,! 

**"*• invwiely. It ii wtr^arj, diat the Exc^s, or Dimiiuitim, of the Sun's Adioii, qpoa. the Orbk,\ 

Ihould tafcePlace in thefe Ctn^utatiou. — In Order to determine tbii Ejumtltn, Sir ^aat thai proce^. { 

XIX. "THE SECOND EQUATION tf tbt MOON'* CENTER. 

[■ Ae PeiiheUon of the @. when the fotar Fbrce 11 greiteft, and where there ii no fotar Bqitat. the ecmer of 'hH Ortel 

,tt$faftr about the Center C. (fit Fig. 3) than in ^c Aphel. and that in the reciprocal trifi. Ratit of O'a Dift. fr. thd 



ini I? A Vie AT OR. 



COMMENT oi die M O O N'l THEORY. 



■ ^tb*Un>»' 



guth. But, becaafe, in Fig. Ill: tbe EjiMim of the ' ^aCiCtmtn, ftt.other DifUoce*, ii included in tl 
ArpuBtKi, |BCD; the Center of the Orbit thence movM fafter, in i^ Epicycle B£> A, 'm.\Ttfjfto<.i\ iupnrair KmU 
of tbofe Dillances from ^ Enth, Bntthatit Jnight move jtt Mia, roandthe Center C, ia the reciprocal /)»//« 
Rmtit of thofe DiSancei i fron the Point D, tb«^ CeiKer of the Mood'* brbit, fet off the Point F, the lecond 
Center of the Moon'i .Oibit, HUtkiBg DP, fO DC, at liuict tin Secinlridty »f tht Eartb'i Orhit to tbt Sua'i 
mtOH Di^oMci, aaJtht Siati nuan diimal MttitM Jr»m tbt Mtm'i JfWM, tt bii di^Bol mtOM Meliom Jrem bit aniiit Jpsgtt, 
ev^Mnatf: Or, as 33I to 1000, and 52' 27" 16* to 59' 8" 10', cMsunaij, or 3 to 100. 
And tee tb*.^^ CDF U «fWf« Hit Qmplmntml of ih»twii tiat j^nmafy to i6o\ for tit i. GrMifi zj £. 
Timtgpom. ri«iiii*DF<twtfi*/Ar»3s,2>r*P«r//«iTC»««« J50S, or mean Diftanee a^atitn ef iht Maai 
ofdieMowiftointhe'EvthiaDcao; and will fobiend an Angle, feen, at a mean Diftanee, from Ceuir JiiirnumtJ. 
the Mood, at Right.^J«/ with that owtn Ditiance, as i' 12' 30*, io^the matefiBqaationi 
tke Double of which, 2' 2$", accarAiagto oat Author, it tht GraM^a/tUt EjnatiM, which he ca1Uiheyt»a^£;iu- 
riM ^tbi Mtv'i Ctniir. Which Equation ma^ be had, at all other Tiaie*, either by fabtra£Hn2 twice the annual Ai 
nment from di* Snm of the Moon'a equated and San't mean Anomaly, or elfe j^ adding ihi Dijla«<t a/ tbi Maemeut. 
tUfi^ ibt San, t* lit Difimaa 4 tbeJkfagt$fif tbt Utam tfmattdjnm tht Aptgn rflbt Swi, far tbt Argumtnli and f^ng, 
eitbt Radim ii It tbt Sini tf th^Argav\tnt ihm fttetd, /a ii z' 2{" tttbt fictnd Equatiaiitf ihiMtoa'tCnltr. Ttht added 
if tbt jtrgmmul is Ufi than m Stmi-Circli, but te bt fublraaid if grtultr. So Ihatl you bave (cantladit tMr A»tbtrJ tht 
Mood'* true Orbit Place in the Sytjgits 1 in wbkb Cimpucation the f^turiiuim-EjwuitK are excluded. 

Bat diit want* fome farther ExpianatieM, 

lithe prcccdiDgA;;. III. D reprefeDting tke jfr/T Centtr Af the Moftft'i Oii»t, in die Epicycle, according (o the 
AitbU aammml ArguMni BCD) Pa acwCtnter, tranflated out of that Epicjdt, by the Excefi of the Sun'* ACtion upon 
it ( it ii evident, tliat the eorrtS B^nmtmn of the Apogeon i* no longer the Angle CTD, but 
the Angle CTFj and the Erctntrieity of the Orbit, to the Time given, irill be r^refeDCed 2. Expiantaiaa ef 
by the ^'m TP, which, in this Situation, ii greater th» the former Eccentricity, TD. It ibiCait/ieftbt i.d E- 
appear* aJfo, that, the Angle FDC being thKCamplfint of the S«n*s Anomaly to 3660, the tuatiom - • -• ■ 
?xMol F, in tbe iranQited Syftem, muft, in the laft Semi-circle of the Son'* Anomaly, when the Ctalir, 
Snn'i Equation addi to the meam Motion, be in AmttctdiwHa le the Point D, a* in the Figare 
beforem; where the Angle of die Son's ndaj/r Z)/^d«rt( from the Moon's Apogee is no lenger reprefented by DCB, 
but by PC B, led than the farmer by the Angle PCD. So the/^ Center of the Moon's Orbit, D, in the antranllated 
Epic/ch, will, by iAk^Aij the aaniul Ai^MRBt, (in whi^ t^e Son'* Equation ii twice included) for^BCD, becar. 
ried aboDt, out of che>j'j^^V», in the inverfeduplicatei^iuwaf the Sun'* DilUncej and will therefore require aTranfla- 
tlon to P, to move tound G in the fitnpU Rfltis of that Diftanee, invvrfely, corref^nding with our Aatbu^t Thtary,^ ic 
thii RefpeA : which (honld be the AcciitTaiitM of the />raay Center F, of the Orbit, in the retiprocal tripScutt Raiia, 
only, {cxciu&ve of tbe cncreafed Acceleration by the ndoabUd Son'* Equation) every where, a* in the Apfidti ; carried 
' a certain Curve, about the Center C, in the tranflated Syftent, by the Mean* aforefaid. 

BVT BUT Autber, in diii Compnation, bu glren only the £;«d/ia>r which arife* from the difiariin^Ftrei, takaa in th* 
f£n^( ii«"'o of the Sun'*£>iftxiice,inreifety, the Sun'* Equation, he fay*, involved in the ^junrnMra omiwiK, fnpply 
ing tbe reft. But, diii can only bn ondcrliood wboe that Eqoatioa taket Place. For, hi the feribe/ian, and Aphelion, 
of the Earth, or of o, and 6 Sign*, of the Earth'* Anomaly, where the£;r<^, ot Dimimuitn, of the folarPorce^ isal 
iugrraii/t ^aiiitf, there the Line DP fhould be according to the m^/fi-<i<fRd//0 of the difturb ing Force. If wefnp- 
pofe the Center of the f/C^ to be carried about in [he tetipncul dmpiicatt Ratlt of the Sun* Diltaiice,'the£;«a/;«j*. 
dience rerulting, wonld be z'44*; or, a* Sir ^<' ha* determined it, DF would be to DC, at 33I to ^ooe, uid 
VF =3 Ji),?. But, to obtain the Proponson of each in the _finpit Ratio of the Sun'i Dif- 
tanee, he Itffen* thi* ProportiOD, in the' Rath tf tbt Sta't diumal l^tiajt f^em bit tvm 3, A CtrrtaiimtJ 
jhegit to bit i^mmal Mtlitnfnn tht Aptgiim of tbt Mm, »r in thr Ratio of 59' 8' to 52' 27', ibt cemman ad Eqaa- 
ttbicb pvtii>9ws'i^,zaitdanE^atitn ef z* tif', as before'. NOW, in order to fibtain tlli* tion af fhi Mtaift 
Eqaation, in tbe irip£tmtt Ratio of tbe Sun'* Dlfiance, in tbe Apjidti; D F, molt be taken to Cttiitr. 
be, a« 50,85 ttt 1000, which Ptopardo* will give DF 59.63, Intdibejf^r^an ef tbt Matim, 
\n the tranOaied Epicycle, aconrding to the tavMS irifUeatt Ratio, = 4' 6', which ii the true Qjiutity U die 
Ptribrbm or AfbtUan of the Earth. 

In Dtdcr to tednc* THiS EQUATION, at all Tlrafi. to iti tmt ^umtttlj, we mull 
confider it a* con&Aing of two Part*. LET n call thefe Pam P, and Qj The soft of thefe 4. fit frat Rtla 



>e the daublt annual Argamtnt fuhtraStdfrom lbf,Sttpt_^. tit ^1?" '■ '^""l "'^ -<"-'■ 



The Argument for the Equation P, will tian of tbit EfiuUi* 
_ , ... .J.JJIT Sit f-^f yff***' '^"'^ "'^ ■"•"•'• ""- at-oM-Timttt 

.^, The Argameiit for the Equation Q, will be the 6'im'j >^«a>^ (t>/i^i lolbr/bub/t 

aamai Argnmtnt; axi fMroBid from tht Mmift Antmafy a^. Both' Aadnijb the HatA of the Moan, \t their 
refpe&ive ArgumcnU are ineiethan_/Gr &r^, and ineriajk'^ Longitade, if they Ate Ufi. The San, or Difference, 
ofthefeMusj^iinri'rM, will give ^ ^ea/imaj^ii/, with the proper ^iVn caDne£l«dj and tbe Center of t '1 Orbit wtli 
the&be, every where, carried in a Camt abaat tbt Ctnter C, nearly, a tbt O^ oftbtSn^t tajtemffrom tht Earth, iaverfly. 



B bt> 



yGSfctgle 



'370 r^ROTALASTROKOMBR 



COMMENT (A A« MOON*i THEORY. 



XX. EVECIKn^'-EQPATION ^ Ot MOON. 

■ . dmttlirMilM > • 

»ftamt^imgtbt^SMi- OR if, WGordiBg to tkc >()Ar HtfW, laid dowri in the Letter to Lord MACCtESnELD, 

aV>« 9^ r£ /»M J- Tcfened to befi»«, joa compote, M once, the EVECTION-EQUATION, dw refpeeive 

fMatun. . Jrrmmiitt, for both Putt of iiu Ejtmlimi, will he for P, tit^JngU-^ SviSim+Si^i Jmmu^ 

Bnt, the EVECTION-EQUATION ftUl waatf a y&r«(«»- CorrjAin, BMamfidned brtbii 
3. A furihtT Car- ptat Jutiart which iiiCea fioin the OhUfdlj ef tht,Mf»'t Orhit vAtk th* E»*h't OrhU. 
nSitn tf th* S«w- Fiom thii pifititn of the PUne of the Itinu Orbit, it appeari, d»i the QuntitT of tiie Jdmr 
liBwSjMaHn. Fwtt, by which the Motipn of the Uoonji diAntbecl, u to LcngitaA, maft be tS^ni^tJ: 

Tbil Atm requiring to berelblved into /w«/'M'M>i.oiicp>tallel,tbeotherper^)eD<licular,tothc 
DhtStMi ibtrtef. It it plain, that the Utter Force ctUMt afieA the Motion ai to Lngitiuit ; but onlf the fofmer. 
So diat, that f«(Y/ {hall be to the ^vhoU Ftrt*, in the tripiitaM Rmio §/ tSt Cofitiu »f fit Amgitt af lacHmaHam. THE 
EVECTION-EQUATION dioiiniOtcd In AMt.Rati», inll.bc lO 19' 41'. which taken fram i* lo* 4j'-ETcaion- 
Bqnationi, thtffpMOM thrMctn/MHagirill be i'^. according tafmtiu. 

XXI. PRINCIPLES g^fir.THEO&Y agm.mnth OBSERVATION.. 

THUS, from •wf-Moi GmmnrioMJi TVJMt^kortheAiKvT'Wr, the lour Eqnitian may be 

r.TitCtPrtBiufitf dedoced, ifnitri, with a Degree af. ExaSw/i almoft eqaal to . Obfervition. By nKfttmSkf 

rTMti. Tailtt from the forcgoiag Z}^d, theMoon'i Longitade may be fonnd, atrnll Timci^ vxiiia 1 

MumUi tf ih. Trmti, and feldom with- an Errar a/ avrt ibaa Half a Mimme. TUi Tbnij, m 

Sir ^aac gave it the World, tmin.Ma Part.*/ ihr Orbii aimt 6 Mimtai a/ rnDtgrut and the 

X, Th Dafiffi af Method of CaLuhu, to he cftablifiied npon the foregoing Rcrifal of it, (hew* how Anfr ^«. 

nr TaUu. rtUitn it nece&i;, to the maiini TsiUt ftam lUnet la ftrva ib* mfarimaf Pm-^Ja af LamgitMA at 

Sta. That what 11 hetc offered aaan ^MMlNmr, or. Ctrrt&mhf zfoTHEOkY, k«i«inch 

Intewied 1« rifbA Hoiooi 1^ ibii great Man, m U ra*MEr ^^^^tiObX^f ffma^Ufklt-Haaniatimi. . 

XXU; n« SUN. <«/MOON'i.RACK;AL PLACES. 

FOR the ERabliOimeBt of ^ramamital faiitJ, accofdiog n thii Thsorfi by A» Affiftana of Me, fUmiftaai, the 
then Aftronomcr Royal, Sic if»ac Hfunaa fijced thefollowing I^Mgitndn of .the 5 on and Uooo, atthecotreAeft U Ae 
RajaJOi/trvatarj,, Ml GaMawclr, to the lt& Dty of Daftmitr at^aaa .■ ati Stiir, lyoo, Qi t» tba Btginarag q^ lyol : «w. 
The mtaa Langittula eflhtSun, Jtf ao» 43' 40? : Of hu Jfagi—, SB 7" 44' jtj*. Thcmr**. Laaplmd* af tht Maaw, 
S: ij*si/o'. Of btrjffagtmycS* 20'tfi and of htt.afiai£nglUi A, i?" 24' *o^- and the Difference of Men- 
diani, between the Royal 0^/«ma/*r-i/i of .Gtet»aiiti, ,Uii, Paru, ii given, from Obfcrration, at 9' lo'.' On which 
oar eniineat Author obfervcd,^ that the. mean MqtioiLAf'tbBMooot and iu Apogee, were not . then diftoitcnd 
with faficunt Jitmiat;^, 

XXIU. CORI^CTIONm/ IMPROVEMENT ^ th. Lunar NUMBERS m/ IHEORT^ 

THE 0$Sr«H/>Mj (rf. liter ASnmomer«« particniarly, o£,f^/^«^« Sncceflbn, Dn. &%, andDr. Jnt^, h>^ 
CorreAed thefe Nuatarjto the wanted ^ccaracpr. Dt. BraM^f, .oat of the jnoft accurate Obferven that 1 any Natioo 
can boaft of, h'ai.- confirmed, by hil Obfe^Tatlon^ an O)»oion, Batted at firft by Hzz-Matlt^, and lince -porfucd by 
Mr. A£i^> of Ct/ff'afnr,. aadotlicc.-f(treigitAAroBomeEi, /Wj^mmm JH«/iM#/'/i(3£Ma ix mert^ractiLrattd im b» 
Ortit mw liaM in fanner Jget. . The Quaqti^' of tbii ^i/Ar/r-oAMnhat ban lwuly£sed U oat Ra^Oifii iMway, fot 
(he Year 1 750, at 11', for oochoodredYeari before and afiei that ^ra,- and thatihe.&cmf/rof Aeocleratian, from 
that Time, nt ai the j'fyora af thi Ctatuain,.^aKd ttut^auj Pa*n af Ci0/w!i*i^ iafK-t ar afur tkmt JEm^ The mean 
Ixingitodca of the Saa, of 'liii Jfagaa, and tht Maaa, ahd of her jffagtaa, and NcJii, are aJfo made ttrrtA by latei 
Obierrationi ) fo thati now,, in comparing vmy mdat Oi/o^iatiam ■vnib: aac 7^lti, fviatd iy thaji Carrtaiam, 
tk« £rrora an. not greater,., than the Jliidcneu and loaccuiacy of Obfvracioni, ia . tho& . early Agei, will accoow 
for. *■ 



''- NOTI, TlitraibthUEUlE (P. i99..JeM«*.^r.qn>«'VMi''w> '' HT. A'MMMiVPrtih. tw/.i^ MWm.; ' Tfae-MMioa of tbcSn* 
ItihtlntbtmipriKili^/itar^SariDDf btfDilbiiceiiomtbBlar^, withBcDcnkidty t6.|« w MwaDit. looo, gencnM aoZ^BMion !« 5&> 
jKi'} but moring in tkc ruipracil n-'^Arm Rsi* guwfiitci in E^ait.. u a to 3, of Ihc /oTOicrt •>«(■(> t 3 tf i^ j^io* 1 )i* 54-' JO* Eaaat, 

^1inEftatam[iairiiiijtbiSmm'iMtt.iid»id!'iAffsirtrtD&ifflUrKi»Kal piHraring Fantn i/ Ut DiJIaaca fitm tit Eartt 1 rtt 
tn>akilamitiMgl^Jmmi4lhii,fiimtrmai tat if I, £fi^ Tim,, tUBjmatin tifit, f,„^mllb,m,r,,rj^,, a, Tim, J ifi 1. Tim af ti 
—■ Snt wherfaer lMlbolatn»ia4nCrii'nind /■Aoof misrooIgncntiM 



mni NAVIGATOR. 



C O M M B N T on tbe M O O N'l THEORY. 



XXtV.-XUNAR PROPBRTtES mi CONCLUSIONS; 

IN Ae OmUaritU ^C^aucl fton the' ■^ytb Pn^un, Btak III. itUtire to the MOTION tf tht TIDES, 
r ifaai Nmutta givu tb« following Ctmfwtatitns. 

1. TbattbiDnfiijtf tbtMtOH h to fbtHtnJUj'if thtSarth n t^^x ti^OOO, frtu li It g. 

2. Tbai, Jinei ibt tnu J>iamittr ef tbt Man is t» ih* Diaatttf af tbt E*rtb, tu looi*}^, thtlS^i ef ISafl^ imth* 
MmmwiUht tBthtMafiaf Matttr iwtbtEarih, ail r*39,788. 

3 . Tb€ aeetltrmiivt Grvuily, tn til Sm/ati »/ th$ MoMf tvi/l it } Timtt l*fi thm lit acal/mtivt Gr»mtj an lit Sttrfat* 
if tbt Sto-lb. 

4. 7hat tbtDifittiet tf tbt Utttii'i CtHttr, fitm tbtCnitr tf tbt Elinb, luili it it lit DifiaKi rf ti* fern fitm At 

5. •fht wuan Diftaatt tf ibt Mttn Jrtm tit Ctult^ tf tit Earti, it 60 Simi£amtttri, mMd tmt tCRtk, ■■ lit Syaigiei | 
bu, (> f& Quadntwe*, ir6\ SinilJigmtttrt fiibdtJJini »hi lotb Part -, viUcb ii i* Prtftrtitw f^ 6g u jo. 

6. Tbt horizonUl Ptnllay, im tit Mttn'i SjKigitt, SirKuc ghutt at 57' lo*, undtr tbt EqnUor. Ftr, /hm lit 
Euth'f iiing an oblate S[4ieroid, thii ^tiaiitirf JimM^tj, ai ibat m ritidtd /ram i ami tbt Vmi^taiet hibtLaii 
fubt tf yi' 7 38* 7 4s" ? SI- 7 60" 7 , 90* ? 
art . . S7''6'.S!!7*H'-SS7'i^'/S7'><:>' S S?' 8' 5 ,57'+'- i 

7. Tit tman Saai^amittr tf tbt Moan, at fttn fitm lb* Eartb, ii, at at 

tbt Ssa^fraturu el vV 
horisoaul Par&Uax !«'■; 
tras hoiuy Mttitm tf tbt Mean, 



at ailTimii, It litlAtmft iiri±t»l*/ TtTMlUx, a. 

. nearly, ^miili bararj Modoa, rn Sy zigiei, Sir Utc Jtliiit at ji' ji* ^z" ; it 

'bt greateft horizontal Parallax, of aitat 61' ic/i tbt Icaft, «/ 53^30'; tbttim 

IttbtMtam, ia tbt J!mf/i KaiAo tf tit Mattlt Diftantt frtm tht Eartb, inverfely ; ami tbt 

ta MttieHfia tbt duflKKcBiaao*/' tbt triu oa^ Mfna horizonul Parkllaxei. 

I . . S. C, 
■■■ ■ , ' ■. — -■■■ , ii ; 1 ,.■■-, ^ ; , . 



II dctemined it P. 15 4ml 36, in 



OP DETERMINIHO THE EQ.UATION Or ETECno*^. r,J«nJ tola P. j6!, of thii WORK, 
PRINTED L£TT£R to iha £ARL of MACCLESPIZLD. 
THIS ETXCTION-EQyATION, ii tlia Difiraf bctwctn the meui and trn* tntrai Bj*titM of tb* Moon it >J1 l^net. — 
' THUS, (he pettcA £qi»tkiii of tbe Moon** CeDter ^ 7a j^ so* Sbd in jl^Ua 
The Itafl EquMion tfaenof ^ 4 57 58 Sun u theb Qui 
HcBcc, tb* pttRit BvrSfH-FfMriM ii tha.Diffneacc brtwnn the pnteft "J . ■ ■' 

...can, (Bit the patcft iiid lealt me cntrtl Eqiucloai ^ |s to' 41*, vhen (j DiSircDCC a 41 a> 

Ai ill Dihtr Tmtt, (urhtn tbe EcceagldtT ii mere m kfi ihon J59jOi of bcb Parti u the niean Kft. b«ni tha £anh 
Sine of ibii P.'^Ciim-F.^ttiiKi, or at theDlf. between tbepnlcac meaa lad tnic central Eqiutimaf the Maeo, U to the Si 
EveAioa, i> 10' 41*, anrly, u tbe filii of the fun/i of the Mdoo'i aieu AdoouIj, eqaited by 1 meia cenlr^ £qi 
Sign, nboTC (wi» ibe Sun from tbe Moon** Apogee, Ii to ita^N. — Addlof tbit E^oition ~ ■ • • 

chu^SiED^ ind fabtnftlni it tbcfcftaai when tbe AttiUDCDt ii J^j tbu ^ Sijai. 

nn, AiR*dliii i&.ooooodo Or, AiRaJiM 



bQuadritort. 



tbi 



To S. Ar^ Etm. s> «• te (5* • . 
Sc S. 10 V 41' Qt- Ewaion . . . 

To 8. 1" ij' 7* Pttfeat C*eaiaB, »urlf. 



1.3704700 



»-J»774S7 



tmteft 






To S. I" la* S4» . 

Ptdeat EnAiaa iwvjr, Mcotdioi _._ 

OTHIRVISE, EUtfihdftbtUMtTmlEjiiatimiftbtM-mtUagiiMEifKitidtj, Jai^ne tnaiim ZBiffii, whoft SemitnuirTertei 
coMwDiA- of the Moon fttm the I»tb ts looooo, and each rMw thocof dithnt from'the Center s^KaJnt it tha Sfinti ffit F. 
it. 1^£.1|I-) KHiIfof the Dif. of Eh* giaiell lod kaA Eacnlrieitr «t y.i Orbit, asim; aad tht Aij.of nraOiaa fimilu to the 
on AaomdT of the Mooa, TtTol*ia( ibont tlie aff tr /ku. Tbra thets i* alKDi tht Aagft of AifonieBt at -tht tMw Ano^ whoft 
"j iifiBilr ii Ineloded by tvo Slijet of > Triai^e, one the DiSuKt of tlie FiH. ai(d tha odKr ^ dia Ttaafnrfk Dianclti, hoA iaaiaf fmn 
the HMir rent, whoft Amtodfli/'. itaai tb* Apbdion to the Perihctloo Dtnance, tg find the le& Angle ofpoCt^ bj C^ % OUifm Fttat 
Trim^bt. WUEhAn^bdngdoBUedathafMMni-ffMfiMfaoBbt,- T<iy BirlT, 

nu. At Aphelion Di* *..••■ loi'ijj " 

To Perihelion Dift 98127 

So Tao. { Alp tsTuif. j SamoppoEte /,) in th* p>m A ]*°]o' o* 



ToTucflUf thdrDlf. 



i>4lB7j7Tobe 



3" S! 3' I 9-79399<3 



*9Sqti 10 
be xMH,to ,.. 
iTugenCDfHilftbt 
JEveOMn-Eq 



n-E^Bicifo. 



Doobid . . i*ip'44*- Zitfiioa-EuMioa re 
a4, fohe the dliptic EtfiuticD temtHj, bj Xtiimrfl UttM, P. 96. 
> bcioticiMordimiHlMd, in the AnfJeKttio of di« Mooa'thoriv 



K^ If freatei Accunqr h icqatrad, 
D. Cn^^ 4irta* tha laiiatlon to be 
tbe Diff, of tht Cube* tf fteSan'i Dlftiaet JaaerMy, fa glTiej the eogeft centttl 'Eqoitbn, when thii aJ It toaatflta m'tt tht <tI> Put. 



Mooa'* horiioatij ParaBai, anddwAawer^ t< 



Tm 

d by Google 



'37> 



Tit ROYAL ASTRONOMER 



The MOON-i LONGITUDE coaputd fiom ihe TABIES 


, to a 100 


PLACES, ai conpind mh dio 1 


rrfpcffiv. 


OBSERVATIONS.- C. 






WjA., 


Yean EfMlJuwtoi M<»B'»«a»- 


A»m1 






SrrarotCom- 


udwbore 


of 


litiDg the Meridian. 

yt D H li £ ■ 


Argnment. 


mo. 


oMtmd. 


puUtion. 




CMfi. 


■ • ' 


■ • » 


.( e ' » 


' ' 


Moon Eel. 


i6z8 


Janoaiy 10 9 26 31 
Mtrch 19 23 16 11 


1 at a6 


6 « 


a o 27 i6 


4- 42 


Sui . . . 


■66 1 


7 021 


33 


••• II 4 9 


+ 5 


8n . • ■ 


1676 


Miy 31 aa 23 30 


n4 


0. 17 


n 21 26 17 ' 


-^04 


Moon . • 


1681 


Aognft it 15 19 a 


600 


X 6 14. 33 


+ 03; 


Moon . ■ 


i6«s 


February it 11 ^3^19 


: 1 ij j6 


6 e 


' 3 47 33 


+ 05 


Uoon . . 


1685 


NoTember 30 10 3a 35 


S IS 


640 
i 04s 


" 19 39 39 


+ 43 


Ji{ 


i6l9 


Norember 16 11 47 ao 


1 


n 6 12 43 


+ ■ 3 


1690 


April 18 16 23 50 


4 16 4 


8 2. 


V 11 43 l> 


+ 14; 


1690 


Ajril 30 i« 2 32 


t "7 SO 


8,5 1 
II 29, 8 


- • 30 5S. 


, -028 


Son Ed. 


171S 


April tt 20 2 40 

NoTember-a? i 21 ai 


8 11 20 17 




Son Ed. 


1722 


3 i«44 


II 29 40 


i 'S S3 S 


+ I 58 




»7«S- 


December 59*5 


11 2S t9 


5 li 2( 


B IS 42 12 


+ 11 






8 la 19 16 


II 25 11 


= 2 S' S« 


■ .+ 29 




~6 


JiBoaiy 6 12 8 23 


21 2D 


S "! ' ■t' 


— so 






Mareh *l I2 10 1 


, 27 S' 


9 I 4* 


"I ^ i4 $9 


— 16 






2 13 s8 


6 20 29 


"B 26 44 1: 


^ & 15 




'_:_ 


12 16 s6 19 


2 19 24 


» 13 -3 


/ 16 46 53 


■ — 1 10 






April 5 U 20 22 

. '»i.y 9 16 4 IS 


3 10 9 


6 5 30 


m 2, 15 10 


— 4 







4 9 29 


7 2S 54 


2 26 ,1 ,4 


+ . 26 






13 19 3 


4 13 ■> 


9.12 17 


=< IS 49 35 


■ 1 2C_ 


. . . 


— T^ 


June.? »s « 3+ 


till 


■ 7 i« n 


'sr rt iS 50 


+ .35 






>ly 3 " 4? ♦ 


« 7 44 


2; 32 


+ 28 




_ 


10 17 44 7 


8 28 56 


•>• 27 S4. I 


, — 19 




— — 


Aagoft la 21 le 21 


7 026 


10 19 17 


" 19 39 22 


— 15 




— ■ 1 


2» J 7 a. 


7 8 27 


. 2 21 50 


*. 1 40 23 


+ I 18 






SeptcMber 4 'J '3 S" 


7 20 3 


7 2^ 2 


» 16 21 33 


I — 59 




_— 


December 17 3 ^6 48 


10.22. J 


1 25 56 


K 3 10 1 


' — • ij 




1727 


March aj 10 17 43 


? "7 SJ 


5 I 23 


« '4 3S 27 


— 47 






May aa 1 1 3 24 


1 3 9 20 


1 'I*' 
8 26 43 


/ 1. 2 


+ • 3 






June a9 »7 39 » 


411 s5 
6 21 12 


r 14 58 28 


— 24 




— _ 


Stptcwbflf 18 11 34 42 


5 26 21 


r a 25 41 


+ J 


4 




afi 18 10 aa 


6 al ij 


9*2 


• ■« ,2 , 


+ 14 


1728 


March 13 II a5 s 


ia 29 9 


5 19 51 


.» 24. 6 20 


,l\\i 


iC' 




24 ai 17 28 


097 


10 15 li 


'.X . ■! 3'. *> 


& 


. — . 


. Msy 8 8 41 II 


I 1726 


.4 II. SP' 
6 5 19. 


^.19 7 l8 


+ ■ 44 




Jaoe 10 12 17 I 


2 IS ii 


. W 4. « ■» 


4- I 17 




' ' 


OOober 14 18 1.3 17 


6 4I» 
6 ♦ 


9 « 5 


a- ■! ••> *3 


+ 50 




1729 


May 7 >7 47 S+ 


8 22 50 


, = .21 8. 49 


; -'4* 






;. . ■ 94 6. 6 +8 


20 4 


2 29 5« 


■U' 13 47 44 


— 57 




—,~ 


September a8 13 ji 44. 


4 9 7 


7 2 55 


U M. 11 31. 


+ 03, 






Oaober, a 17 n 53 


4 1246 


8 ,3 13 


an 9 M 12 


+ I ", 


'. 


■ — 


a 18 . 3S 
6 20 23 ao 


^iJ ♦■ 


8 20 5) 


9 21 46 46- 


: + 1 si 






4 ifM 


10 6 33 


in $2 10 


+ 1 5 




—■ -- 


Nevfnber s 18 ij 6 


5 ■• '9 


9 J 13 
1& 12 16 


«. S." 23 


+ or 50 




■ '730 


Apra I 20 58 50 
Norcmbei 20 17 ^ iS 


9 24 1! 


» 4 »» 54 


— 30 






4 Is 31 


8 23 37 


»« 3 31 30 


41 


. 


1731 


: Juw]! 4 6 ij 8 


5 ■! 4» 


■3 7 38 


» 2 45 27 


+ I Ti 






19 17 $z 20 


6 9 36 


9 39 


Hi 11 44 5 


. — 32 


\ 


— ■ , 


. Febijary a 5 49 14 
Apnl 10 II 39 ID 


6 21 39. 


2 29 52 


« 24 17 15 


— a29 




' — - . 


8 20.49 


. S 26.4s 


. .» .J 6 4„ 


+ a 




17 ji 


January 4 14 56 6 


♦ '5 ! 


7 12 S' 


m a 45 .8 


+ 39 






February 39 la 13 30 


6-5 


6 2 57 


i« 24 47 30 


+ 045 




■ •■■■• 


^pMDber 19 % 55 22 


II 29 IJ 


4 IS 55 


X. 23. 10 Ij 


— 10 






22 II 37 28 


1 57 


. 5 29 2 


V 10 8 27 


— 22 


- 


_. 


aa J7 V 3' 


0. 7 "5 


8.242 


» 9 S6 S9 


+ .3 



,,GoogR» 



mJ NAVIGATOR. 





pued Kith tie refpeaive | 


OBSERVATIONS. C. 










£,h/./a. 


Year. 


E^Ma/ Time of Moon'* tran- 


Annul 




Moon't 


w 


<M'« 


.ffrwofCom- 


.nd whofc 


of 


Cting the Meridian. 


Argoment. 


.' K'^; 


obferreJ. 




pontim. 


ObTervadon 


Cirijf. 


M D H M S 


1 < / 




» « 


' 


' 


/ # 




nil 




I 24 21 


600 


n 10 


" 3 


'7 


1 12 




'733 


April tl 7 18 48 


603; 


3 » 27 


a 2. 


37 


3» 


+ 28 







17 11 47 54 


6 S SS 


S '8 17 


"l 6 


58 


SO 


+ 34 






26 19 8 56 


6 13 I 


9 2 18 


- 18 


S! 


9 


— 1 14 




■ -- 


6 1} s+ 


9 'S 34 


2 ' 




6 


— 14 




■ --- 


Miy 13 9 33 


628 4 


4 17 39 


■=■ 20 


43 


41 


-03. 


t. 


zz 


»7 20 «7 S3 


7 10 21 
10 9 37 


10 9 30 
423 8 


*»* 26 

— 20 


26 
18 


16 

3+ 


+ 011 

— 1 20 




14 13 S3 >2 


■ 14 8 


7 2 10 


43 


IS 


— 10 


6 





18 .7 48 ss 


10 17 46 


8 28 36 


!■' 


33 


34 


+ 027 






21 20 Z5 14 


lo 10 29 


10 7 42 




25 


+ 44 




'7J4 


April 12 16 jj 4j 


4 *o S3 


8 5 18 


" 9 


J* 


4 








December 22 6 1 1 42 


1 12 


3 S 


'»' .8 


5« 


31 


+ 111 




•7JS 


Jtnoary 3 17 24 ij 


12 27 


82.41 


«* .6 


43 


41 


-0 35 






". 7 37 


29 10 


3 H •} 


n 8 


.2 


S« 


— S9 






25 10 38 20 


I 1 58 


5 8 8 


m 2, 


z6 


41 


+ Q41 


Moon Ed. 


■ 


Sertember lo 13 10 10 


7 '7 >3 


800 


T 8 


'9 


48 


+ 032 


Moon . . 


■736 


MarcH 15 11 6 43 
September 8 14 52 


1 5 20 


600 


'^, 6 


3« 


27 


+ 21 


Moon . . 




6 7 7 


600 


X 27 


20 


S7 


+ z8 


Sin Eel. 


— — 


23 4 34 6 


6 19 29 


11 29 49 


t " 


'» 


43 


+ 32 


Sun . . 


1737 


Febrniry 18 2 37 S3 


II 2 10 


J 


^ " 


li 


='3 


— 56 




1741 


September 22 12 ri 36 


9 3 S3 

9 *7 30 


6 4 44 


» ■'" 


■S 




— 7 







Cflober 19 9 59 38 


S ' i* 


Z i 


'1 


'4 


_ 8 






November 9 J 14 33 


10 16 


117 a; 


V .6 




— 44 







December 13 6 25 48 


11 16 43 


3 648 


S 1 


20 


'5 


+ 17 







19 12 I 32 


11 22 30 


S 29 26 


18 


S' 


+ 9 






26 1 8 21 40 


II 2« S' 


969 


*• 22 


30 


40 


— 32 




'744 


March 23 17 38 42 


..6« 


82.48 


W 6 


'♦ 




-036 






April 10 8 4 38 


3 » zo 


3 26 .2 


a 27 


4S 


41 




..?■ 





M«y 13 10 44 


* » 4S 


J 13 31 


n ,7 




S7 


+ 04 


1 


— — 


23 i3 47 21 


4 848 


9 9 49 


X 22 


+7 




— 1 10 


*■ 


— — 


24 19 28 40 


4 10 


9 '• 33 


K '■ 


34 


'7 


— I 18 






26 20 S7 3 


4 11 ij 


to 16 9 


» 2 


20 


3> 


— 044 


a 


—— 


June 2 2 ss 3' 


4 '7 3' 


. 928 


a 2 


SO 


24 


— I 32 






S S 38 *3 
9 8 41 9 


4 20 9 


3 .' 8 


"« 17 


5' 


S9 


— 1 3' 






4 »3 40 


4 '3 !» 

7 26 26 


ni .2 


46 


'7 


— 43 







18 16 2 SI 


S ■ 38 


K S 


4" 


19 


+ 1 * 




—~ 


Joly 12 ti 42 4 


1 1 «9 Jt 


! «3 4S 


U 14 


S3 


5 


— ' '7 






13 '* 3* 40 


e !! 36 

6 !4 2« 


6 4 4« 


= 7 


10 


8 







— _ 


Augull 19 17 56 '7 


9 * 47 


11 10 


42 


18 


— 34 







Sejteoiber 4 4 SS »3 




2 .8 


t 8 


32 





+ 034 






IS IS s' »S 


7 '7 4^ 


8 1 33 


n 6 




S« 




Moon Ed. 


'747 


February 13 17 17 


9 <° 13 


6 . 


"I 6 


'7 


7 


+ 38 


Sun . . . 


'748 


J«ly '4 IS 48 


10 22 


24 


a 3 


9 


37 


+ 0.1 


Moon . . 


17S0 


June 8 8 s8 30 


S |9 .8 


i 29 s8 


f 28 


17 


»4 


— t 26 


15- Nnmber of Obfervations loo ; Difference of the Error!, in Seeondi o 


f n Degree, 4428', wh 


encc the mcao 


Difference of £rnr, ± 44' 17*. 










B«*«| t^. } '""• { :T inr } =*73'4S'Di 


f 








Whence, the 5«bi is nagitire . . — 41' 











N- B. The I 

Motiom, lod '1 ,. ^, 

iodcftodent of thofi: eanSi'i Tailti, 



impotcd bcfon the jttifltritriia-TaUr, P. ]74, fai eomftiiw 



,, Google 



The R O Y A I. A S T R O NO'M E R 



Total CORRECTION of the Mean MOTION of the MOON, 
ji According toCorreaion of the Moon** Mean Motion and Accelekatiohi for any Year of a given Centory 



1400 

I JO* 

1600 
1700 



42 28 


040 8 


37 48 


35 '8 


33 8 


30 48 




d 26 8 


2J 48 


21 28 


IQ 8 


16 48 


14 28 


12 8 


9 48 


7 28 


s 8 


248 




000 


42 


4 "2 


6 32 



1- o S5 11 

+ o 4(^ 18 



+ o 33 36 
+ 0^9 2 
+ o 1+ 48 
+ o 10 54 
+ o 17 20 
+ o 14 6 



614 
4 30 
.56 
' 4i 
0+8 
o ,4 



+ o 



I iS 



+ O 12 44 

+ o 9 10 

+ o 5 s6 
+ 032 

+ o o 28 

— o I 45 

— o 3 40 

— o s 14 

— o 6 18 

— O 7 22 

— o 7 s6 

— o 8 10 
-084 
-^ o 7 38 

— D 6 JI 

— o s 46 

— o 4 zo 



+ o I. 58 
+ o 4 44 
J 7 SO 



5 ?T 

3 34 


3 '4 


» 54 


« 34 


2 14 




1 3+ 


I '4 


54 


34 


rj 


26 


4« 


I 6 


. 26 


;i 


28 


43 


24S 


3 ' 



lotll for. M. Mot. + o 59 50 



EXAMPLE II. 
Radical Vear 1720 
A. C. — goo 



Ceoturieg 8,20 X 2' ao' = 19' 8*. 
jo' X 8,20 □ = 67,24 X 10' = 
Acceleration = + o" 1 1 ' 1 z* 

Corre Aioa of M. Mot. — 19 8 



Total Cor. M. Met —7^6 



EXAMPLE IlL 
Radical Year — 1720 

A. C. 2O0O 

Ceoturie) >,8o X 2' 20' = 6* 

10" X 2,80 O = 7,84 X 1 

Acceleration = + 1' 1 8* 

Corteflion of M, Mot. + 6 32 



Total Cor. M. Mot. + 



7 S° 



t^ The CornQhn of mean Motion of the Moon ii according to 2' 20* for each Century, from the redittd Year . 
— ii/ori, axA + of itr ly 20. And the Acceleration it according to 10' for each fqaare Century, fronn thtrait'rai 
Year i + h^trt and 4>fi*r 1720. Whence, by connefiing thofe Qnantities, the total Cone&ion'of mean Motion; 
and total Ufiercncc in each Century, are detennined, as above. 

fi, B. THE Antltralhitoi the Meuit Jfi^e ii the fame ai that of the Motn ; but with a ttntrarj Sign, or — , 
from the ro/jVo/ Year I and confeqaently, the Aectlmtim of the Moon'i ^mnn^ ii doable the Acceleration of the 
A/ma I with the fame Sign, or +, from the riulical Year, 1720. The Acceleration of the Moon's Node, from the 
(kme rM£fe/Year 1710, it the HiUf'ir \ of diat Half, of the Metait JeetUratien, with the fame Sign, or +, from 
the ra£tttl Year. 



Acceleration \. jAcceleratlon $'*An. 
THUS, + A. I + lA. 



Acceleration li'i'Ap. 
— A. 



Acceleration S 
+ {A+- 



■?■ 



THE ibo*e<4n(AT*rrni-7'<jZiii added to be exunincd b]> future ObrerTiCions ; that it ma; be detcrmiDcd whether the Mood' ■ inMii Mn\tmii 
fnictfria thitAgethanour "SibUtaf meia MdCiod leprcTeot i *i many OblerratioiU of haar EtUffa, Md Othu ObfciratiQiu, wilhoDC tli« 
Sjxjiia, ftemtopraKu^n^ntia*) diSneattonrnit UmMnUiaP. jj. 

A TASLB 



and NAVIGATOR. 



575 



K TABli'lOT wn^mg t'hi S«n g/ ih« V riji >irt ' Vllth BQUATIONS of tbe MOON, »t Hit Beginaiat of ^ TriJti. ~ 



n^ 



BXAMPLES of tb« USZ of tht DtmtJ Umb^n ud L^yOa/ Ligmrirlmu 



IXAUPLE I. 

ILo. La(. 
+ 4' «• >.»«S4 



VI. Eft 
Vlt. £fM 

J 

J10.. .. 



i«9,74 «■ + »')•• Z^Mthw, 



jlO,i<jj. 




RITLE. MohiplT ih* ikii «f thfVI. u4 Til. EqnadoM, cosntaeJ whb IM pnplT Sits, br 
[iK^eciinil X'l carrcfpaBdtDt (o S 1 0> ftl^FnJaS of ^ nnrrW 2fa«/M. Ot add the 
La.i.ag. concrpoodtnt ro B i 0, M tbcLo'Log. of tht Sam «f the Vl.'ud Vlf. Zqutioc 
La. La%, of Hu rtfirtdEfiutitm, to whicb.pMAi-thc JifB of tha^Mcf Equtioni, 



A COMPARISON of it 



I Ktfoi jlfirtnmi 



/jwnmB^, »a< GREATEST ZQjLrATIOMS of th« MOOW. 



AcconJinf m JUiyir. 



Sig.*bcg Gwawft EgmripH p . W*. (jjigri. cwtefpoat" Sit.*Peg. [ Ort»ttB EgT^" 






'"".ES- 



(3*1 M. Aaom. 

deoMM .«HW/. 

©* J'.Ap. 



Mna MvtBiu 
+ ». ) M. A*. 



MoinKvffftn' 

— (t^tM.Ao. 
)'(cactcS>d ABi 
Tf . e*M. orM^nr. 
^{Eq. DVCciic. 



l'+S*+»'»4' 



*..l' of. 



— > Ao.. 

+ J Aa. 
..>*©- 

+ OAB, 

— JA». 






I IIS 
I.w IS 



iu 



.o'sl' 



±:(»ir-44» 

+ .-W43- 



Ap«r« J . . + 19 ij 

O • . — 9 44 

l^ti.QiDAp.i'u'OAp, 

•-Ho4— toji-Hois' 



s-^.>lCH-9Ap40Ap 

4-to6t — toi»^. 

t.A^. I'tAa.h.tfltaitS 
Eq.Ap. D .CMM/£r.acnnll 
^fBewutiaij | Orkuchulf 
101 8 lod 9 ) m lf«)iir'i 1 1 uif 
Vk — bi (• 4.ta i«i ^. 
!i.Ar|..Ji© JPmj'iJ* 

, Jna0«iM tiroi7 II 

7. Donbtfal to AtwWM. 



1. 1 » i> 0(b i a. 
n.|y0->*i 



0+ J An. + .ayCl .. 
.*I. mt thit Atf .owAmV 
^a E'mMu. 



{90 

iii 



D in Orb 1 g. 

..jicr— Jig. 



LL 



±..« so 



1, |M. Aa. li eqoitad. 
IL lllMa£t«a'«< 



I PAR. A LL^ X. 



"sinETFCnalUr 
e ^ & Apogw. 



1. j D COT. Aa. 

IT. i.Biq- - 

III. Ill »q.l( 



DAb 



Atgnneati. 1 

U. .. J i0-JHaM.An. J 3' ^°| rp »<S4' 

in... >i0-OM.An.jj I 

IT. >M.Aii.— ©MjIe. I ' 



iiid Grunft E^aitloBi. 
AtipimaBii irMKffirwi. 
Or Alt, Meu EmUit* + Modb'i H. Aaonul; + Saa'i M, Aao^^t 
Or Arg, Mcu Evt/l!tii + Moob'i M, Aoonulr ^ San'* M, ABondjk 
OiAi|. Iilcu2MflfM + SB»*iU.P]. + &u'iAf. — *.Mocn■•A^ 



^Igl 



374 



The ROYAL A S T R- O NO' M E R 



Total CORRECTION of the Mean MOTION of the MOOhf. 

According to Correflion of the Moon'i Mean MorroN and Accblirationj foran/Vear of a eiven CeDtory 

befmuid fince CHRIST. C. 



jaod after 



— i 3 i8 + 2 3 1 



zoo 

300 
400 

JOO 

600 

700 



- o ;8 4S 
-o 16 18 

- o S4 8 
-OS! 4B 

- o +9 18 
-047 8 

- o 44 48 

- o 41 28 

- o 40 8 

- O 37 48 
-035*8 
-o 33 8 

- o 30 48 

- □ 23 28 

- d z6 8 

- 13 48 

- O Zl 23 

- o 19 8 

- o 16 48 

- o 14 ;!8 



1900 I + 
2000 I + 



o 6 32 



+ I' S4 H' 

+ I 37 36' 

+ I. 29 41 

+ I 22 8 

+ I 14 S4 

+ 1 8 o 

+ I I 26 



+ o 3? 30 
+ o 33 36 
+ 029 2 
+ o 24 48 
+ O 20 S4 
+ o 17 10 
+ o 14 6 

-t- O It II 

+ o 8 38 

+ O 6 24 

+ o 4 30 

+ o t 56 

+ O 1 42 

+ o o 48 



+ o S3 16 
+ o 47 z 
+ o 40 8 
+ o 3s 34 
+ o 30 10 
+ o 25 26 
+ o 20 5a 
+ o 16 38 
+ o 12 44 
+ o 9 10 
+ o s 56 



I 45 
3 40 
I 28 



+ o 



738 
652 
! 46 
4 20 
* 34 



, ..58 
+ o 4 44 
) 7 50 



EXAMPLE I. 
Rtdkal Year 1710 
B. C. + 1000 



Centariei 37,20 X 2^20'= i''3''28* 
lo* X 27,20 O s= 739,84 X 10* = 
Acceleration = + 2° 3'i8' 
ConefiioD of M. Mot. — ■ i 3 28 

Total Cor. M. Mot. + o 99 jo 



Radical Year 
A. C. — 



EXAMPLE U. 



900 



Centoriei 8,20 X z' ao* ^ 19' 8'. 
lo'x 8,20 O =67,24 X 10' 
Acceleration = + o' 1 1' 12' 

Coneaion of M. Mot. — 19 8 



Total Cor. M. Met — 7 56 



EXAMPLE 111. 
Radical Year — 1720 
A. C 2000 



Centuriei 2,80 X 2' 20' = 6' 3 7*. 
10" X 2,80 O = 7,84 X 10' = 
Acceleration = + i'i8« 
Coneaion of M. Mot. + 6 32 



I Total Cor. M, Mot, + 7 ;o 



f3" The CerrlJlim of mean Motion of the Moon it according to 2' 10* for each Century, from the raJiea/ Year : 
— it/ert, *ui + a/iir lyxo. And the Acceleration )■ according to I o* for each fqaate Century, from the r«Jirai 
Year : + %%rr and «/>«r 1720. Whence, by conneAing thofe Qpantities, the toul Correaion'of mean Motion, 
id total Kfieience in each Ceotory, are determined, at above. 

N. B. THE Aatltratitit of the JVf«Mr'f Afogu ii the fame as that of the Mmn ; but with a ecntrarj Sign, or — . 
on therffi//fi/Yeari and confeqaently, ^c J(cikrati«i of the Moon '1 .i^«<i^ i« doable the Acceleraiton of the 
UBm; with the fame Sign, or +, from the radical Yeu, 1720. The Acceleration of the Moon's Node, from the 

Ibme rM!iV<i/Yeari720, ittiheHalf+\ of that Half, oi VHe Moa^i JcetUracm, with the fame Sign, or -f , from 

the radttaiVtax. 



Acceleration }. jAcceleration D'l An. 
THUS, + A + aA. 



Acceleration >'i'Ap. 
— A. 



Acceleration I'« fi. 
iA 

+ iA+ . 

5 



THE than jftii/trMa»'Ttili ii added to be exanuDCi! bj Tutuie OblerTiIioni) thitil mi]r be determined whether the Mood'i mm Miij«ia 

SiEicttrinThiiAgethanour'^bleiaf mean Motion leprebnl i u dudj Obreiratioot of Ariur Edifja, uil Other Oblcintioni, without tlu 
'jy£'"H fcemtopniTeui^in^Ufai, dificicncto whuunBavWoi*. Jj> 

A TABLE 



«ul NAVIGATOR. 



i15 



~A TAbLt'fof mnaing th« S«B tJ tlt« Vltll tmi Vllih IQUATIONS oflt 



JLio^ 



IXAMPLES of tb« USE ef the Dmwl MabifBvt tnd L^iul Ltttritimu 



I' ^ , ■ .6; XT. 



EXAMPLE n. 

U.LOS. 
— I'lo* 



Ib Sccondi, — TO* 
' • ■ •' 'J* ' • -rB XW 



Sj,jo ae — jj* XfrntblB. 



RULK. MahiplT Of Smm <t thi-VI. u4 T 

Iht dcciinil X '■ ccnTefpaDdtiit to ■- ' " ' — 

La. L«t. cMitrpoodtnt (e 1 1 @, i. . 

La. Ls(, of tbtrtfainJEfaiitm, to wbicti.piafiX'ttM JitB of tkcSWaof Equiiani. . 



tha'VI. u4 ril. EfUtion, MnB(<M wtib tti ffOftr Si|n, kj 
I S 1 0, fsr tbe PriJaa of ths rfmd Emmatim, Or *dd tb* 
I, t> thcLixLog. of thiSnnof tbeVI.'ai^VII. Iqouioni, for 



A COMPARISON of tJ 



ij*C2 



i GREATEST EI^IJATIOWS of tin MOOW. 



Ariummt. 5ig.*Drj KinKCtA E^umIom H ■ »o.p<yi!torwfponl.tsig.*Pt|.|Gf«Heft E^. ])" 



AccordiiH 



\iTl 



Hud OKI 



(t}'« M. Anom. 
O* J'. Ap. 



+ S. $U.A«. 

Mtui £«i0iaa 
+ 0-»M. Alu _ 

Mun Eviflin- 
— ©"i M.Alt, 
('icorredcd Ab. 

rr.£««.arMXBfr. 

7lH SVCcat. 



■•-S'S9' = 
:..«'47' 



l' of 



1. tiQ 

— I Ab.. 

+ J An. 






li: 



J— I I'M* 

S'4S' 
±..o'4J» 



( 'AZ- O M,Ab< — 1 

+ >9 43 
«-*1-0«5Ap.j'j4«OAp, 
Q.tS 



SfS. 



•HoW— to)»+toi«" 



. y An. 

I tq. 1 Hw. 



l."»9 
i « 14 

1.4 'i 



±6«i»'-44' 
i:i*»o'4j« 



t-toSt •- to t%* Ai. 

^■jfrt- l'*An.fr,|A(Bdid 
Eq.Ap. s Xttrafff .icucdl 
•pEtaVridtf > ^- iBCJBdt 
)iirS*Bd9{arJf«^'il>ud 
tk — tn (• 4>M i» .At. 
i;.Ar|..|10 iFTrjj'ij' 
, la Camit I Te jj n 
7. Donttfal to A&iww. 



I 









.■I>iO--Ili3.[j| 



,+s' a', i* 
±. .1 s« 



■■O + J An. + u^Con. 
*— ■( that All. rmj^rBV 



I. |M. An. 1) cquii 



+ .6o'»6* fto.»/*»*i — fcO— jAil. 
j> =M«inETFi.E»lljLta. 



I. ]) cor. An. 
ir, i.piQ — JA 
III. p tq. i , 



Argamcatt. 

in... >l©-OM.An.|j I t IT* .» 
iy.tM.AH.— OM.An.|| 3 o|±P4» 



Or Axf, Vaa Evtaht + Moob'i M, Aiionul; + San'i M. Aao^f< 
Or A^ Mein EwBi'a + Moofi'i M, Anonulj — San') M. Anomdjw . 
OtAr|. MuaAi<RiM-)-Sna'iM.PI. + S«i'iAp.— •.Moo»-*Ap.. 



.^4!^glc 



37« 



7he ROYAL ASTRONOMER 



0/ DETERMIHING tU MAXIMA, ad COKSTRUCTIOH »f tti LUNAR iqjUATIONS « »& Bipim-g tf Mi WORK. 



I. FOR >b< p-UH ANNUAL EgfJATfON of die MOOH. 

PatQ,= S, Sun'iEquit. at Eruteft ; i-s the D' of O*' P^°^ i 
r= Mood'i Period to ^li ■«= p'»j>W/(PeriodioSiinj Then, 

. f X 0.= Sine gieat^ innnal Eq. T) ^ ll' ij", 

t..477""7 *■'"*' • - °-3*J479° T 

i»=i7*.l"6 fqmred 1.873011. 1- <= i6i*.is65 U-56.59T9 V 
l=S.l»si'(o" iB.si74775i " = »9''.SS |i-47°'^34 3 



'4n*.7««; 



S»n, 


..J7JS'-9 




S~>>, 


4^3S'140J 


■s's 


,7.5111706 Dif. 






»T 


I,—-- J,'. 


V*.!". 


"0. 




btSun 


Ti». fAi....a. 

■»A,,.,j!. Th.n 


..<,= 


TmtolJy<Hdif 


=s.r 


!,.*.*»' 


),.»«. 


I-x<l>i 


5.r.i,.a- 



9aR4tl«,786] . 



-%i»f^ j.t««9 10.5006344 
t= J4«'';6i97 »-539*S33 
<==*•«• Si' So"|8.j.74T7J. 



t7 » . . .. OitOlOJOO 
1 >f=*79*''j»03 h-»3>194" 
iJ I 



Or, in tTie fiae Korip, 
AiSq.M.dinr.*- 
Tg Sq, M. diur. 



.Mot. D)0,ll•l|'l7■^^,]IB7'lq4.M. 
ir.Mot, O* J)'»Ap. |»l»7»«B3if7"^. 
So Sine gr, id E^un. Ap. ti* 18' 

ToS. }'4S''ul«C>n, iaOOaou 

In Oftinti tlili E<iiij 



o.jisii8a 
*-99S79J4 
9.3184416 



■J9S«li 
kcrctlcd awl Aninikj in die 



Kciprocil IripTicMli Rail's »f the Sun'i piltinca frain the Euth ; anil 
'* 3' 34" """' ''■'*> '"* j' S** "^ pwft*. — Bftt wfien t^c 
Mooa-iAfOgce it nl^ lit Oamt. . ■ 

Ai IIjiA I M jAj. cr 1. ^ ]) 'i ^, ^ ec, iccordini to WmftE, 
NBHr Mvao'i Apa(« from DeiR# SttiQ') :: ]'46*, ur a:ha (laECit 
Equicion in OatKi • pitUat Equtkin, rijuind. 

rtii Et,uiU» K^i f«M«r MoTifJi » ri< P^<^ «/tU Mm't^m€, 
/™. lit ^MtJrmim- tf A. in i, lb, ^aio j iu /Jirjfl, j. In f^, 

III. FOB.tbepMc^fomdSEMIAIlHUALCt^ITA'nOR. 

AiRadiM , ., ., 



O. Sf. 8 4' if Dif, S. 7+34S4" 

. t«'iS So'i ijr.E,. j-.oi i © I iP.rf.Eq.fi 
jCr. Eq. 5| Ap. I Q, 
Sr Ijiuc ffnciai itttmina 11'^" ig'41'' j 9'H' 
Mr.UrwWli&o(iihitPiiiKi(>l«i| 11 j j .*i 57 I > 5^ 

Whni Sir f. MtMnChid found tbe, (jn. £•■ I), he proportioDi, 
Aim.<l!ar, Mot.l, |M.dit)r.Mot.Ap.e'44'' 4«| , |0Eq.I0s6'K 
©S9''e"'9'l iM.diur.Mot.a 3 ,0 38 H * . . s8 " 

■"sr.Eil.a 994 {uibove. J '"+51011 l»"s4'jo* 
_. 7 J r-cWl iniflfi f l/.i.finti.eUft6Sigii,. 

^' ia l«i!<ii©'iMjln.i i/.*.tbdugaieAiiumeai. 

U. SOIL Ux grtaM) firft 9EMUNNDAL EQVATIOH ) . 

Aa.fi>MATimc01 ])'i Ap.4li'<,7Sfil^iiued, Co. 4.77o6;6S 
■Xv ffntJliTiSK D 10 ... igljjj'fauired . , , 1.9405168 
So S. g-. llliau. Mimu'i A#. , , ia> ■S' ... 9.]i844i« 

To S. fT./r^ £»-4>. Eqnat. Iff . j' 4^ in OftuD O 7.0396:51 



6.3638)74 
■ Per. 45" 

Bdai Rclprocally, aiCabeof tlieSun'iDilHDcertointlKEuili. 

In other roGtiont. 

Aa Rad. t S. jfrg. 1. O ^ S (o^i according to Nttntia, to S 
twiuQ, fiom ncireft Sjijg^) 1: J, ^««^ £fM«sjr 47", ertbtrB- 
jtatian in OSami, 1 5. frifiili Bfaaiian, n^uired, oat of Odiali 
uf the Q iL Q, which it tJie AriiaaiU ef tbiiEjaai 

IV, FOR the gidleft of THIS EQUATION. 
fit Ridiui .>..., 



V. FOR the girateft of THIS ECgJATION. 

7rt . 



Ai Sum of Form 3571450 . 

Te 3, Dif. folu Foiec ]| Per, ind Apcf. 

SoRaduu 



■oi-Tiaof*. Eirth'i Orbit looooc 
To 3 Timei Eccentiiciiy 16S5 B 505. 

So S. EveQioD 1° 10* 40' 

To S, Sun E^aitioDt 4' j* tcqnirtd 



ties to DP, iroai the affir Ftau of } 't 
tmdFli.rt.firlbr-. 



ioDift.fr.© t toiDF (fai*.j69.ti»^.*«.^ 
4' **, = /. fibrtjid ^ ipF,.fce(Lfrn«» 



-atd N A V I G A T OR. 



377 



O/DETERMININO (i. MAXIMA, a*f CONiTRUCTfON*/'* I-UKAR EtyiATIOHS tt iht Buhrn^ rf ibli wqRK. 



VI. FORthcgiMWftof THJS EQUATION, 



J.J176J99 
9-9*S'S'3 



Dif. I 41 gmtcftVlI. Equtioa. 
TI. Rsd> I 8iArg.Enc. + Sun'i M. An. it %' i^' i prcr« 

VlX.JiLai. I S. Are.Ene. — San'i M- Ad, )i i'4i'' i prtfti 
Kqiulion. 

N>B. TitTdUaJhtB, h itt A-nmenn, vitai lit Bautliua aJd\ 



i" lo* 40*, tnd CtpnfUai, t 



Kip.1 GREATEST TARIATION-EQyATION 



Mwr/f. w tD 144 Ji It tbc Init iiHl gRaieft Diflmnn of ih 
fnnn the Smn in Coa)tuit]ioa vii Oppofition. — HuKc Ihr p 
condVatiatiiiDszi'. 

Tbe pnCtal ptincipit ind JilTo fecaad Vutition fmin the Ctmftiaii 
^n'iin'«-Equati6n | coD^e£M together with tbeir proper Signi. 

The Tiblni'i genciil (hcvwtacBtbe Equalioni ue to be idded 
rubtnkOed. 

COMPOUND £<^ATIOIirS explaioed. 
' I. Compouod iDniul EqutioB* of the Moon'i Apojee >d<l> 6' 1 
to the licatcft Qwntitjr for eomCting the EvtBim. 

" - ■ ■ ~ ETECTION, It > Mem, it a 



The Mud of tbe Dif, Majanit, \a Oaanli, thence iriJing, will be 
S' j8", tamptnlid Bqwin. The Ca^mfUn, Aj RtJ. iS.lQi J "i 
^P: ■••■ S' jB" i ?'■'/"' ^?""". Again, Al Jtai. I S. Q J J) '1 
yfy, ■.: ^efi 10 aiMhir Ej»*livi. 

X, The HMii ftfrforiu bring 35' 10* + x' 14.", uiil Correfiion 
of mean Anornal)' according la vitiahLe Ecccntricitj ^ i' 6", addei 
make jV 30", camftmuUd Ejuatitn. But ihii Exeifi of Redu£lioi 
betweenliitetniKitind lead, being 14", knAi\viiy»SaiiTa!listtfyti 
riatiai, ibdn^mlabulai VatialiDnli jK' 6" ± 9", funher Correflioii 
of Evt^im, air^or^jng to tbe Moon t Anomaly, «t the Sun ii iq the 
Ipwer, 01 higher .^>, givei^ | j' Inthe ift Ifiil4lh ^Mi^Mf ) and 



II, or id Smi-a-nti. — Tbe ETECT 
Apfii, »± 4'aS'jj IheH-jfa'it*. 
gieiteft, bciai • -" ' • - — --• 

nms/ie linn 1 



Then 



„ HbyTablei, — But the 
tlieBna') Motion fronT the Moan*! Apotee in the 
:l>irf' hcrOrb, being iefi ttnniit thehl^erSuni-eirde, 
(iiiffrMinltdiniiiiilLeilillb. Hutf tlUn MMlher Equation, whieb, 
liketbelecond^<n>nw]>, it greiteA In Quilntom of the San with the 
/^JSJa, indamoatititoibontjo*. It MlnSt^ ialhtStA Stm-Ortb, 



bud iidJ« to the Moon'm 



intheliftSeini-Ciidc, 



o prefeat /tcfad Eqoatio*, 



37' 57"if '" *^ "* jCQmdraot, 

Tbt Cei0nait'i '/ Ibtfi Ejutliau ir, 

4thPtQFartioDal,whl^h^kal>Aoii)4;°IeaTei|]~ 'S I jtrg. Uoob 
" ■Juadratore of the Sio,- 

^«>, AiRad. ! S.^^Jl i®-;: 1 

Theti^aaiToaiatbeOiiiV^ fodcor«4tot Uv ^'daiaffrntccordiiu ct 
tike MooA'i AnamalT, i/ u bcToie 1' 39". But, J>f ObJbrvatioB, ir 
the$iia^'iiriaad Syifgiei, amtnati'ts i' 10" onJj ; fomewhit Eor- 
lefpoodenl to (he Bxc^i of Ntviui'i ktani Ferialim. In Order tt 
accoDii^xlate the Tahiti to thii Cordflion, the Evtain ii AiminUhed 
i^', and ihia E^uat^n t4*> In t^m S^aimiMra. tni Sjicjpn, thi 
Sum of thii I>iinhiuiMn ii »<)', Ind reducn tbii EquuJon to i' 10^. 
lathe QBami, tbe'Ujminolion ii additilioyt't^ tfaii Equation, aiu 
riifei it again to ittWadqiiiiB 1' 39". 

The CitiftiimJ-ytriaiitn it eoiQpnfn'ded of the principal, and fecood 
Vaiiition, and alio the Half of the CorreaioD of Eteaion, 

CONSTRUCnOM of tba RIDVCTION- EQUATION. 

A> Rad. I to Gofrne of the mean Incliaation of the Moon'i 
Orb ;: Tangent of 45* : to a Tangent of an Angle, which, fob' 
duQed from450 leatea AegKaKft mcaaReiltifliOa, required. 



n /xiiWifliofMaon't Orb. 5' S'lS' 9.991149} 



TmTing, 44 53 4 



For MOON'I Mean LATITUDE. 
C^, A> Rid. I S. 50 g' ag' ti S. H a Q : S. prcfent Ut. J) . 
r> 72r wda huttioMalftraUax it iiltrmiiii aatriixg It tbtAl, 
/(w5k»/i; thaTtimciinibttn*l>>rima,t^PmTalUxh]TA. vkfi jirp 

,JfarliernmaiJfyr*b. ■caicji jlrgvmut h y,lrt,PUifr^(r). - S 



For EQUATiON ot MOOWi 
Ctif, At Rad. I S. %i s^i' ;i S. Aig. t 



9.9911493 
in Reduc.Eqtat, 



EQUATIOW of the SUN'i Mei 



EQUATION 0'i M. Mwioa fc 



feq.M,Mo,0.|Eq.lV 



50* I 



Eq.Mc.0Ap.|Ufe < 



<' ;<y I + S' so" 



[■^ MuQWi Mean Plaeet, 




11" I rP aV 



f^i^Yea 



ut Mairarc bigu (or Ximc bach 
0and ]j equted. .— Cutoff 
Van fix the Sacood) for 
ftoai 1700 fae the whole Egu. 



!t,A>rl TbaQuantitii 
Yearind n<aItial*b*theN« of Yfiii H Parti of Centuri 



10 Right. < 
iplf bf the 
I, with ill P'oH» Wga« 



EXPLANATION . 



,y Google 



S7» 



Th ROTAL ASTRONOMER 



EXPLANATION of NEWTON'i LUNAR THEORY. SeePig.tV. 




AP, Tbc j^Ua of the Utaa'i M. OiUr, erir-^imfi Dimmtr = 
loaoooo Pwti, aufirtnlile w die hm» Bccuurldtj s {^50 Pitu 




Dill, or the Imnr Ftni, fmiumi,, it tbc Evth, thtttnt Antic u DF M bcTon,. &ea .(.[he ki< 



ninjm, TN z= leiA EcccDtricJIj Maoa'* (M k 4111a 

TS B patcA Scccacridtj . . k 66782 

TC betoc ^ OKan EcccnIridtT , . ^ ccou 

HcBce, NC (=CD] — Ca.,= TR_TCs .1711 

Df^E .'-... {•« 

NOW, the PoiDl D Ii mixed w the Left ia flUbr'j sJtjd,, (»• 
th* And* RCDnujr Im dmyi cqml ta twin* Sra l- } '• Apega i 
Cjiutcd; ud CTD = AfQ, koDDd E^iucioa of thcMooa'iA- 
po|te. 

Bat Nemrn, fbi fmbet bDenvOMiit of the AnwrThw*. tnof- 
l>m D to F, To thit £_ COP =s OoDiplnocst of the Svs'* tree Aao- 
nuJj' to j6c", tnd DF to DC^ u iwki ihe EcceDtrJcit; of the Einh'i 
Oibk to the Son'i meu Diltintt frmio tba Ejcnh, 1^ tlv Soa-'i meiD 
diurnil MoIioD froai the Moea*i Apogea to tbeSuii!smtu dinml 
Morion [nm iti owo Apogee, nmjwnS/j, vis. ■> jj| to 1000, mi 
Si.'»7"l6* 10 j/ 8* 10", it^mfffy, or « 3 to 100, neuljj 
whcitb/DPss ]jTPcmafEcc«Dtiicit<r, iccordioi to Ah*M. Boi, 
if C[^ tk* MjM/i-t Rtdiiu, bs coBUenl (0 DP u 10000 M »>, 
(for K rutbcT CorrcAioa of tba TIm^J tbco, bj Pnfottiaa, DF^ 
5f6,5Futiof Eccnniciijr. And tfaiiDF, attb* Diltinec of ibr 
Center of the Mooo'i Orb TC, fuknndi tha Aacla u tbm- Einb, 
which tbc 7n«^un* of th* Centci of hdOrbit Iraai D to.E fne- 
ntD initi Uaiioot 

of (be Moon') Orbit inai'tbc^tfa, feeaet'doaUc 

knot Fkh, wbkb AtTrtiifitllm Tmm D to F 

the Diftuce of the Moon from the Earth, iDF it the •fp.r Aiw, in ■ pMiltd 

■■-- TbieAatleljeJleO 



- Ttili. Aai^jtrz*^tiiHdt Gadia( thii Eqmtion MallTinM), {tt^iriiMgto fnMttJ it br aiUint' Ibl Diiaaw af tlw ]|,iSutgtbe 
Uooa'i Apopa ftam the Suii'i Apofcr. 



M Ume, at vtfiaUt Kaikt FC, about ibt Outtr C, vitb 



I Volocitr*! 



ihu a Semi-t^ide, 

ffaUtt'i mon^Foiiil at D, it it made to daTcnbe a. ivttit 1. 

««r<A ai dkc Cnbc of the' S«n't Diftaon from the Earth ) KcoriinK » fim l*m of Hatnrct oUtttcd. 

TBI, Aa^liiftt Ftm, 

AEI, tbaaKM.AMM^Df iheMoon. 

BC >, tbcKTrMTiV^lkiMaAiar tbcMoon. 

BTJf thefratAwHJfof tbaMoon. 

IICO ^ iwict Sua I S'l Ap. ^ 1, Am Arinmtnt. 

TDorTF^pnfen IrrarttionoftbeMaoa'aOib. 

CTD ot CT F ^ (econd EfoatiM of the Moon't Ap^M. 

QQ, ihe HtfeMf^rna of dw 4^:^01 Apofee. {meat at tu 

CfDarCHF, theSemi-ADfk of2M0iM,atKr«tdl (wbeaCI>9«t CF}Kfl>•)«^»'to*'>A }CDor ^CFArta- 
t> MB), Aulc of Con»aiwi of ihe Moui'i meu AmtS, tat ^ABM, the Mooa't correOea mtta Aaomdr, aMoediBs to 



DIFFEREHT 08U<£CnTIU if the ECLIPTIC m al/<rW ia diSuMt ACU of the WO&LD,. hf m 







. • . • 1 »1 « « 






• »j j» • 

»I |0 I? 



m ASTROHOUEM. 



YnBa-Ch, 

14)0 Z)ib/Vkh JCirMAbpiBiw I • 

Ftrrmrii^ , . . J 9} M O 
tji4 Frnma • . t . . s] ai e 
tjTi ^^Brtit . , . , «} ]t a 
1S70 MvfAa . • . , • . ' sj JO M 
■76a P.U^pfi . . . . S]Bt*4 

"75" - . . -^ _- 

l^riebfc alfa acCTTdiag to PI. a y. 



r. MMpn . . . . S] Bl H 
Mr. BwlMrf . . . . at ■• « 
lk.Bt& . . . . «, so • 
Dr.SnaAr . . , . aj aS ]0 



N B. Tlie atiadf^ DSfirmit of dte tbora OUemttooa hat partly aiSci fioB tha Impcif«aion of At Intnneat* wiA wluA A** wtn 



KaMMft rf forwHnwMllyfvaiw. St* J>M^^ Tne^fkOM^ No. 

EXPLANA'nON 



tni NAVIGATOR. 



3?9 



EXPLANATION of MACHIIPi LUNAR THEORY. SeeWg. V. 




OMt Attn the EircH, 

plKCd ia rhe Center T. 

It I mfiD piflMKC) I be 

Moea bi*ia| no other 

Grtriry thin to the 

Eirth. The Diameter 

AT0 diridct the Pan 

of the Moon'i Oib 

ABC lowardi the Sun 

from tb«t Pan ADC, 

offofile to the Sun I 

the Kamettr BTD ti 

IhcUoEeflhcMoca' 

Conjunftioii with or 

Oppofitian to thi Sua. 

The Fit LMNO >> an 

Ellir&t> whole CeoUi 

ii canted rHail the 

Earth in the Orbit AE 

6FCGDH1 InloDgai 

Ai» ^^t ■Ivrayi piral- 

lellD' BD, joinirg the 

Earth tai&mit, TS, i) 

dmble it* fharter Jhai 

tAO. While the V-i. 

LAfNOii carried W the 
frflm A to E, B, 

F.'C. O, D, H,- We, 

the Mtai reiolTCi tt*- 

tnrj, hem M 10 P, N, 

", O, K, L, V, M, 
ircribing Btpul Attt 

In e^ul Tinei >hoH 
'e Center of Hia tUiftic'EficjcIi, butoperro 
. RetolmiDn, \iitixciraliirOrUt. 

The Afna ii alwa3Pi in the remoter Eitrenity of 'm titrir Aiit in Mf ud O, when in her ^Mlen tram tlu5«| ud in the Mtfet Xi< 
rmitr of Mltmpr Axit, at theTinwof JVnBtiMl ra/ZMonn. The Aortei $etni-Axii of tbia EllJpfU MA, ia to the Diftuce of in Centei 
DintbaEanh, AT, ia tht tlufJiult Priferiitm if tti Mtn'i ptrit^ctlTimiaimltbt Earth tt tht Smftfaitdittl TimifUtg ^i^jhS^oo, 



t Jtra^rin therein, kthcbiM TliM thtttbeCmter of tberalde/i^iVfyigrclipeHbtiM 



llie r^ UFNQpRLVM dtftribti ^31 thii conpeand Motion ofthe Moos in the tOiflk Efiitdt, 
the Etrth, mj UuSj I tptrf fta the Tim of the Mooa'i Orbit j rappofini it withoat Eccentridt]r, 1 



<he Plane of tb* Zdiptk } aad lUb tfatt the Sun continacd in the fiiDe PJ 



\, dniiag the Moon'i whole Revolutio 



Of MACHIN*! THEORY of tlis MOON'S MOTION. 



A A^ jfia* 



PROPOSITION. 

fiti Ptimu » ibt BtJj, eami SoMdt ia uu/ ' 
lmtlb,fiadfimdPvm. 

'n.i. — _( r c UKtriftltt Fmo, Knrding to Ktfkr, b, that 

' '- - -'- eqailTiaMC, ibont the finglc Center 






<4 



Tiat patnl .Ltn> of tair^tut Ftna, 
all Bodka dtfciiht mmI Ann in eqwd 1 
of their refpedtJTC tUrolotiaM | hot ii 



lUfiSiv, 



(w iur Ifttt Nram, when a Bod; iratiMM to two 

the fane Time, m every SmMu paiitatci tnraidj . 

mtiy, wUlc it irailtatea alio towarda the Sao, Mr. Uachim, W fuppl]' 
the DtJVI of Kflir'i Ltm, of Cnntation to dm Ccnta oohr, haj 
explained the Motjoni of the Mtn, lad of the other SsttSiltt, ij 
L«w of the abon Pnf»JSth»i accordins to a Onritj teadiu| to : 
different Centen at once. 

. COROLLARY. If * Bt/f inmltuo umtrii tmt fliod Ceat , 

l#>MMa>/, ArnvnfaialifaHpiHi^a^Tm^ m wag «« Plane /wfcf 
rfcvft KM k/(faA died Center*, iht lm,IUl.<«iif li, fiid^lg.,HtSt 
Line jmtiv M tbt Ctitri, tvill v*^ «tariiri It lU Am jifiriiti i 
That te, i7 iti Art* hi abpnented, tbt ItiHiMiai will it JimaiM i 
amiif th€Aftl i\ait^bta, ibibcBmttUm if tin Jad FItM tntt i* 
taimaui\ itM ihtS^lidtAJiriM, aatrjhg it ibtfnfe/im, tuyhi 



of the EeKfi'it | withoat enteiiaf Into the liOrictli CalcaUcieo) 
contained in tbeCurHVAnn toufrif. ofthelU. £••< of thePn'an/w, 
to dctennioe the (reattlt (^ntily of VariMim, when the Lim d 
tftdnii inQuadraturewith t£e Sun) which, ip {^tlicaUl Kninbtn, 
ia fbundte baa' 4]*i or*'4j*, acionUng to Ar^aa. 

Bot in thii CaJi; before nt, we bare t fitin *ti wan*l Halt, frOD 
the foregoing frmdja •. *amilj, that the ptn^ Ytntaim, in the bid 
Pofition of the Moos aOrJiV, ii to the warn la^hmiM of the Plane 
thereof, a> the D}fmwa of the tr^ttS agd leaft Atiu, delcribcd In 
the tame Time, by the }ioiai ahcut the Cvtb, whan in the Dap ~' 
*nd ill the SmtJrgaira, to the yeen .iAm. 

Jlcace, Jf S be to L, ft th( Sun'a to the Mood'i Period { than the 

jrMijfittodif AajtAiea, «• ^SS+jLLtoS, oraiS + ^-^lqS, 

aucrjr- b that the OiWmma of the ^tai, ia to the naaa Atea, sa 
jtLtoSS4-(I.L| !■ which Pioportiosti theJWMa* of tKe In. 
cllMdonaf the ffaa* of the Moon'i OrUt. atthiiTime, totbeaMr 
loclinatiM tiunofj Wteiaf^ auHj, wilh«r J j ta w Al m wa'»<lai- 
patatloBa 



Jc 



380 



g-fc* ROYAL ASTRONOMER 



Of MACHIN's THEORY of tbe HOON'i MOTIOK. 



MOREOVER, tiiot \t t pira/ JUiliid, u Ur. Macbiii obCtrvtt, 
r tBtpiuitiKLani of <iK Motion at k Bcdy lo ind from ihc Ctn- 
r, abfinaedlTCObfiiiendrrominUotloniboutaCciitcr, And tliii 
Motion, to and ftom the Center, i»ali*a bj Krpltr, ibc liira'iirj 
Motion of tl)»t Body, diftinfl from itidrcolir Motion : The Know- 
ledR oT which Molion Mt. ViKiu thinki. necefliiy forde6nin| the 
UwE of the Reiolation of ■ Ik>dy, in RefpcEt af the Motiini of Ihe 
jitfiiaiif ia OtMti which RmiJatiDn, from one jlffii to the other, 
' — ' ■* in the Time of the whole hhrtlarj Motion of the Body j 



the 4 

According Xo' tbiiTbtery, the Motion of ■ Bb^ round tbe CeUir 
of Kerdntion, ii not confidned ■■ ■ continncd Ddkaion from 1 
jSnilUne; but ^tcompotiDded of tcltalatm Motion round the Cen 
tet, (Dd of « riailiiKrr Motion to ind from the Center of Revolution 
i To eiji of "whic^ Motion!, Mr, ifjttiii tSS ffli iu ftoptt Ejatnt. 

Tbegeneril Property of inEquint foi inyMotion, ii t, Curve- Lin 
JitaAtd aSart ih Crrlrr ibtraj, vih,ft Riji m'iricifrKalljir ttejui^- 
detu yi/Miiy at it* Okitr, tr Viluily of Bewlrrfdr. . . 

The ECgJANT for tHe m'ilsry Motion, il m omt-llmJ Figuie. 
the Jrrutf whith iie frtftniiEMl to the Tian whetein the fivtral 
Sfecii of Libralion ire performed ; whkb Flinn 11 deletmined by the 
[jw of Grt.ity, tiwtrdi the Center, being ImowDj For the lil-aUry 
Futi, loiccelenteor reiirdiheMotion, to or rrom the«enier, ii iht 
Difpacc betneen the Gr»iity of the Body towitdi the Center, uid 
•- ■;fi»fl; Force «f«ng/rom ibt arrmHtmy Motion j the Ultei 
wa ji rubjea to iKT flf/f : ficcauff^ ip elltheBkrolationribeDi 
. ..i^u.^f, in»BT Cutre, »h«he[ defcribtd by a centripetal Force, ol 
not, the cenltjftiiil Forw *il be diteOly, i« ibr Jnflicgn Prefcrtit 
„ftbtAna dtfaihid fii a jiVn 77iw, eadruifriiaUj, hibt inf,l:ieii 
Trupettitu »f tU Dlfiaxa; being » inunedtite Con/e^uence of ■ 
known PK^efidon of iby^nft. And the lilu Proportio;i «Hb hold, 
'le centti petal Force, in all o>n/«r UotiowwhltTocter, ftoitii 
_fr^. laSalJaacNivim. And whit tr true of the nnffifaa/ 
Force in Circlei, 1> uti-vtrfallj h of theother Fwca, in Orbitt gene 
ted of iny Fonn. 

MoROier, that by knowing the Grawiy of the Body, ' the otbi 
Fon* being Jwl^i known, the Diftereoce thereof (heiDg the **/•/«* 
Ftra to more the Body to and from the Center) will be alfo know- 
Aad, AomlheaH', the Velodty of the Motion, and Jhe Space dfTii 
bed, Jn a given Time, nay be found ) andilfoibe Hfuar defctibed. 
EttmfU. If the Gtitity be mifrtally si lit 5f«a« 0/ lit Di/hi. 
the Equant for the libtitoiy Molion, will be fouad to be an £iti£fii, 
EmilHia theOtbrt, whofe longer Aii iidoobie the £(rBrfnnfy. Anc 
th* CenUr of the Mrttary Motion, Chat i* the Place where it it Jhvi/r 
^a will be. in tbe Fwt of th(t Otbic, The Time of LiitMitii 
trough the feieral Spicti, will be meifured by the SiBui of the faij 
EWtJ!!, flMtWtO tKofe^ aefcriRdty lhe"Boi!y round the F«bi of ihi 
Oibit. And the Period of the /iJrvtDry Motion will be the iame will 
thePefiodof the Revolution. 

In any other Law of Cniity, tha Ejmmm for the libntory Motion, 
ill be tiihei of a Eqrni different from the Othit, or if of the fame 
Form, will notbealikc divided. 

The Emant, foT At rArttorj Motion of the Moon, ii a CmrBt 
of the ibirJ Kiii, whofc Equation li of fimr Dimt«fim, j but may be 
defcribed by aa EWSfiii the Center of Libation not being in the 

From thil Method of refolnng the Moon'i Motion, it ii not diS- 
talt to Oiew ibe mtralCauJn of the Change of £cr^tridiy, and the 
Xfttaehn of the Motion of the Moon't Afngta. Tor, when the Line 
of .rfj^A* ir moving towarda the J«jv, it it eafy to Ihew, tiuf:"— "- 
ixlernal Fmt in the ^fiia la then ea'rifiigal, It will eont 
lengthen then the Space and Time of Lihraim. By lenglheriipg the 
$pice, it aogmentt the Eccenttidty ; and by lengthening the Time 
Of ^iiraf'Mitalfopioloap the Time of the Revolution to the ..i^l 
canfingwhtt i* iufnftrfy called 1 progreffive Molion of the Affi, 
But when the £nu of .4|^i''B>OTinEm<be J^u^onmi, theeiteinit 
Force in the ^(l^a, h tbtotatrifita/, which Mil cootiibute to Ihortca 
the Space Mid Time of the Lihraiiim. And, by Ibottening the Sgace, 
the Eeeenlrieltj will Iberetnr be leffened j wd by lhortening.tb« Tiioe 
of Libration, the Time of Revoluiioa to tbe .tdi will thotby be 



confnfted j csoGng what ir imfnfirfy called 1 rettopde Motion of tbe 

REMARKS. The Motion of the Mood, in (he before delMbed 
EUngatin of the Moon from the Center 
defciibe an accurate Elliffii, according 
u, the NnuitKiaii ^btay. 

. When the Moon iiJA that Half of ita'Orblt nett to the Son, 
then being nearer than the Earth to the Sun, it will have a greater 
Gravity thin the Earth to tbe Sun j which fxn/i of Gravity, accOTiilDg 
to the A'mwiian Ibiory, confifli of (tog Parti ; oneaaing in tbe Line 
PE, parelm^a thit which joint th^Earib and Sun j and the other aOing 
in thcLiiK £(,dintled toihe Earth. And Iheferuv Krtii being com- 
pounded into Mf, conllitute a Force diteacd in the Line Ft, (fit Fit. 
v.) which ii in Propoitioo to the Force of Gravity, ai that Line 
Pi, ii to Ti, narfy. Hence, •■ there ia a Force connaatlytmpelliag 
"ill Modn fomewhere toward! the Point 1 ; thli Force i) fuppofed to 
■tifiiit the Motion into ■ Carvr. Liu about thai Pifur ; fsrthelime 
Realbn u the Grlrity of it to Ihe Earth ii rapiMfed to tnRe£t itt Mo- 
iMi-iaOt a CurTt-Lrnevboat tbc-Earthi jNot that the Moon can lAn- 
ilty have fo many dtdiaJt Motion! ; bnl that m /m^/f Marin of tbe 
Moon round the Sun it fuppofed lo rtfiiH from a Conipofilion of thei: 
(cvcril Impullea, or Motioni. 

If^ leprifent the Equation of theSun'i Center, S the Sun'tPmiif; 
P, Ihe ^riVVa/ Period ofthe Afgntotbe^uH j L, the Moon'a Period to 
jLL 



the S/*M( Then, 



iFS 



XJE= t 



n of the Momi'i 



If M reprefent At Equation of the Son'i Center; P, the 
cm periodical Time of the ^ptg" "r A'e^r j S, the mean Jjiitiical 
Time of tha Sna'a Revolution to tbe Apogee or Node t Then will 

-^ yi M, = the m«Mal Ejiaiiaa of the Jfcgn of tfiA, Wcord- 

inga>SandPare.de«ned. 

According to Vhich Rr/n, the Equation df the Siiii'i Calir 

fa.-. Squat. •■$ 1 

to J anir. Eauai. j] '1 ^>. S will be in ■ given Proportion, rrffiSivdt. 

l«,..Ejual. r.N^,\ 

f[^ The above general Propofitlona and Propotltom, aauniia* 
latiiii, (arc for ify otbti Salilliii, ai will ai for Hie Miw, 

Mr. fHacbln Iheivt a MithJ of correfting the Angle of mean Ano- 
maly at the upper Rea (by U ilftftic Bnati, fit F. Bi.) fo at to give 
the true Anomaly, acconling to (he Proponi»ni. of Wt^-d"* Hypo- 
thclit. 



A METHOD of findjog (he DIFFERENCjE ttlmtw rU An^e af _ 
Planet or i^ upper Focut famrding n Vtri't Hjpothefia) oi ffa 
inu Auglt tttrrttf Jftm Aphelion.. JaatSmg l».iti ■' ~ 

Moivre, F. R, S. Sit bii ^miljHta. 

IF EPD W 

FJh/tfi,; C, ' ~ 
teriS,F,the£vi) 
DE, OY, the two 

/Inij'andaP^nvr 




ly I s right An- 
gki 1; a* the Am 
PSE 1 to the Area 
DOPE of the Smi-Sa^Jb. 

Tk Mn fU FFQ IS ti« DlSeteuce a/ th, A^la EFP, ZFQ, 
ftUem. 

LetCD=£r, COmr, SP=cb, FPscy, ttc, rhit, bjr At MaboJ 



t/F&.aitm,Cf^^ir-t-tm- 



oy^Googlc 



mid NAVIGATOR. 



381 



Of MACHIN'i THEORY of the MOON'. MOTION. 



THE Aogl* of the Moon'i 'Ehngaiiini fwro tke Catttr, reprefenled 
bj (TP it Cha fanmiM or Kd)c«ion of the MMUf, the PnfirHti 
>r which >ppeufii»n fiJxrrV. 

The Varltiitn-F.fMan iithcSineof ibedoubteDiflanttartheMoon 
^om tKe Q»ii]r»[urr orCorJuntlion with ihe Sun ; it being the Diffe- 
rtttttoS the two Anglrj ^TA jnd PTA, iKiI 1 he Son, vhok Tin- 
pDH, by Conftraflian of the ?igan, ite in » gntn Pn^oKioo. 

The farittif-Efiii' i>> ilt o'her Clicuninincct being (like, in 
the A^««f» Propottion of the ^MrffcWTi 
-'inio the Sua. For (he yariaiitm it in 

iiiDcMr of ihe Ef'cjtll, in the iaplieau 
Ttna of Rtvalnlion. 

The OREATZST VARIATION li en Anfle «hoft Sim lilt 
■ RadiH M ibt DifffHi ^ibtp-ml^iaihafiDifiamaiTKaMtTH 
milhtSam, littiiiAMlUhrirSam. 

Acc«idiBg to which Propiilion of the Limrt defcribtd, lUi Ruli 
Dukeithellwvption neiri^Minoln, which wonid be tha yarUrin, 
riippofing tb« Moon ptifonned iti Reralotjon to the Sun in (he Tim: 
of it* Revohlioa about the Euth. But thii EUajaiio* of 19' being 
iiCTnl*4 in Ihe ihfliitri Proportion of the Tynodical to the ftrioJical 
Tin* of Kertdothn, it wiUgi»eni!»riT 34' ef yin'wiw. •* 

r* Wh>t ii (»i ef tb< E/a'tif' " "p*" Soppofition, that the 
Eitth'i Orhit'itnnJ the Sun ii ■ Cirtlt. Bat if the Erimriciij of tht 
ellipiic innul Otbit he i«nlideied, tbcmcan Diamttm of the £/i- 
»^* mofl incnife ordecTfiJein the fiT(p«M/'i^fiM<»Proportionof the 
Saa'*DUhncc. 

■ Mr. AfBcbim neat ftewi 1 genenl Method of ftndingtlie ItrjuaHiy 
hi an iqtimi. In any Hnotutlon, when the bmlj Motion, or Telo- 
;;'iy of the reenliing Body nriei, in Ref;ca ot ili AfpeS to (omt 
3 her reMlving Body 

That, in ii^ Rewjlution, the ^tta Muiin tai hijiiaHij 
ue to be lAitned by Mum of a nrvtlimiar Fipirt, wherein ijecl 
Artax are defcilbed about the Center in /jnu/ Timei ; the Propeity 
jl' iih'ch fiFurt V, that the fiaji fiom the Center, ire ilwayt in iho 
■tifrtfl frU^, I au P/oportkoD of the haailf Velocity aboot die 

He gi»e«M h^Um 

San'* ftevolutior, u tlie Area of lba(ffi>rfr£fMntothe Areaof thg 
circumlciibing Cintr. 

— "■ Circle be iteferibad, aboot the Center of the cutrilintar 
Figvt, and equiitoiti Aiu, it will cut the Figure in ihe Plm when 
-'ic Sun bt< iIk mein Motion fiora the NtJi. 

Th't, if any druUr Siaf be made, wliich Hi^l conttln in Ana 
tifsi\ (a the Sector in the Figure, drawn through ■ Perpendicular' 
' ""'an of the f i^. let fall from tlw Eiticme'of the Ateh o 
ir SiOw, on ilu Diameter, the Angle of Ihe dradar SaBi 
wilt be the Angle of MM" A*tf/m of the Son from the Nbdt, 

TlMt lh«Ditr«renc«.betwB»nih« Angle of the tiMaler fiffar, repre 
renting the Sno't mean MclJon from the Mdl', . and the Angle of Che 
"■ t'lSiilsr, leprtfenting the true Molion of the Son fiom theNode, 
» [be EfKflm at the Sun') Motion from iIk Node. 
Ill by At fameRtle, an Equation may be dilennincdofllie Moon 
■ - '■---'■--— the Apogeeor Nodf j by ■ tarvi/imar 

!t I the Riiation oi which itriai ftall 



wHl b^ cbi 
That! 
from the . 

^TH-xItlctibcd about the Center | the Riiation oC which Ami ftall 
reprclent the muk and iriu Moiioni ; wbenoe the Ine^silily or Bjaa-i 
' r/Hof ih(leMationi»'illbclhewn. 

That, aa in erery Re*oiulion, ib«K i« ■ cOOin Figure ptoper t« Okw 
thij Inequilit; of Motion, /«(i ■ Flpri any itmtton be ^optrly 
(aOed the fif uM for that Motian or RerdDtiOB. 

That, in every Rerolucion, whFie tbt f fSM hw the Ane Pnftn 
[y the lamaliria or Eatatitai will vary aocorMog to the teM Ruli. 
'example. ]f the Eataat be an EUirf* abnt the Center, ■ ' 
. the Figure of the Moiion ot the Sim ftem A* NtJt, 

1. The nM«D Motion in (be whole RevalDdoii will tea peaat^ 

in prapottiMial between tfae^mv^ Muimi In the Eitiemity-of 

I turtet AiK, and the Ih^ Sbha, in the Extimuty of the Isanr Axia j' 
' htcaafethe SaJUi of the Order which ** eqwl l» am M^Gl^ la 
ui PiopeitioDel betoeen the two J'av'-dCM. 



I, That theTixfuriof theAnile* of thenyinind (rw Motion 1 
In the given Proportion of the two.^if of the Ellipfea ( being u t 
rerpc£ljve Ordinaiis to thofe Moiituu. 

3. The Siai of the Angle orthe,frM'^Ineijuality intbeOSMi^ 
is tolbelW/»»HairiheSum«f thdui to Half their DiUnence, 

Thai the Eaaaai ia an ElliptiiaboaC the Center, ineKryMotloa 
where the Extrfi of Velocity atcu iht Ctniir, abote the lead Velocity 
ii alwayi ia the iupHmtt Proportion of the Si«.of ibe Angle of tbi 
true Motian fiom wheie the Velocity about the Center ii il^. - 

Whence it fotlowi thi't thefe Molioai are leprefanted t^ant^n'i 
Equant, vrs. Tht imlblj Maion tf ibi Matn frtm tit NtJt j iba an- 
Mua/ Maio" •/ ibt'Sm film ibe NkU, and tf ibt Maei fnm lit Sim . 
aialiratid w rttariid, according to the Change of the Atea defcribeii. 
about the Eenh) {ai in NruiimS 16 PrM. III. Bsci.) Alfo the 
e«»a/MoHonof the San frtm ibi Mm' 1 .^tru. 
■ Thua, he jnflantea, in the Motinn of the Nodea, that the Node U 
in iti foifteft icttognde Mo-ton, when the Sua *nii Maea are in Coo- 
junflicn or Oppofition, and in Quadrature with the Li'm t/'flWfi, 

According to ia fjaai Nneiaa'i Method, (et the End of the 11 
Pnf. of Ibe III. Bank} ibe lom of the Sua to pttidoce 1 Motion ii 
the Node, at tbii Tlrtir, iiaual » iTimii tbimanfolarTsm; lia. 
h, ij ConfruBh* 0/ tit dbpnt Eplcjtl*, in Tit, V. aaaal u a Font 
vbiibitt^lhRniffCrBiH, «ijAM M AT, »■ j r;.a«rSf fhottet 
Seail-titii tf ibt rllipiii Epicycle » tbt Diflaaaaf tbt CtaUr tbartaffitm 
ibtCattr^ iki Earth. 

Bat, if the Moon R«ol*ti in en iltipili E^ijfli, 



make a Motion in 



delcribed 



will be to 



Force of Crarityit the Time, ai jBNrsBT, ar iMce lit tangtr Sm\i 
iiij ./ ihf illipik Epicycle, U <*i pmir Sati-aas if lit Wai-'i Oriii 1 
lnlnr(kMi tbt firimr Ftra. But, according to Sir T. NEWTON'l 



thitTime, iatothe Moon'l 
tbtfftJtiita Ihtliri 
Bf Gravitt, And, if the Moon be coDceired leTolring in 1 Chcle! 
with the Velocity of ill Motion from the Node, at Ihii Time, »hed 
the Node ii fwiftell, and the Pb«r of the faid Circle be ftippofed t 
ba'e 1 Rotation npon an j^boiKTpeDdicnbr to the Fbar of tfaeEcliii 
lie, and thecontnryWay to the Moon'i Motion, fo at to prodsce tt 
MnMn of the Node; leiiingthe Moon tO move with iiaRia Mttii 
abont the Earth g the Force to make a Motion in the AMi Item* to h 
the DIHReaee of the firmir Farcet to retain it with the Velocit 
of tti Motion in (henwyeible and inunoteable Plant. But the Veloa 
city of Bodiea, re«ol>iag taCirtlea, •« >■ lit JatJiflicaU Ptafonitt 
tf tbt tatrd Tana, 1 

Tit Malam »f tbt Matt frtm tit Naii, at tiit T!m>, wfan O* NaJi 
atuvtt fai^ijt, iitttbtMtlltm tf AaMtaa, ia tbt f^bJapBcati Tnfir'\ 
rwi */ lit Stm tf Ibt ForcM la lit Ftret ef Otaviiy, at at tit Snuj 
i/TV«W iBN tiTB| liatii, ai tin Sum aftbt Omrter ~ ' 
./■,(- M^. " • -■• ■ "■ » ' " ■ ' - — . .- 



*3 



would be the mrrf^Jtrsriai if ibt NeJi^ pNnidEd that thi 
PImnt of the Moon** Oibil waa nearly coincident wiUi the Plane of thf 
Ecliptic ] but the Inclination tbcr^ bemg confideted, Ch- 
Force for Ihe Node muft be dhmailhad in the Frifvtha tf 



' 59' iS'i ''>* Ctfaa ^ luiici f* SaJiat li at 



SIS »» w 

Force of ih 



4° 59' iS'i ''>* ^J'" !f wUa 
theitJbre the Foice of Gr»ity ii 

thueiirainiftad, la ifac compound Piopoitii .,__ . __ 

to;a5)H9(n«ilru4>tCte-i4i' So ^t ihe p m ^ Motion ofthi 
M*«n frooi.tlM H«dc, ie to the Motionaf dw Bloob, intbeJU. 



ogt ts'47*l bM,, by i\t^aMtln^aa-* Method, it 

- TUe it the Mp4 tvHop^ MmIob ef the Hoi* when th 
Um ef tk« Node* ii ia QutdMuta with the Boo, «BJ the Mwi 
it ia AetrMJI Utkod*, blOeafoaftiM •r-Oppefidoa !• the ju^ 



yGoogle 



382 



ne ROYAt, ASTRONOMER 



or MACHlNi THE,ORr of the MOON'i MOTION. 



Bat tbc EfUti Sot the Kotiao or the M»a fiam the Node 
Moath, when the Ltm of the Nodea u iotbe QeadntanwiA the 
SdD, it u £tliyu&iboottbe-Ceatcr'i ud tbeiefore tb« wai Motian, 
' thuXfMtt, wiUbcfeandb)rtheftill«*iiigRULE. 

•nitmtaMai—^ tbtM-m fi^fbt NtJt, ia lb*t Mtwib it*n tb. 
Line ^ ibt t/tJa 41 IK t Siutirahm nith itt San, ii t Jfiometnal mui 
fr^trtim^ iiMiiuB ibi rrttt^ Mkin af ibi liin JrjK ibt AWr, ah 

Tbii Motion wil! be to the mtm Matioa of tbc Moon, in thcM- 
Jtfliitli Pmfotiion of Ei] (0603, wtrfy *t t»i to Iiti. Ihal 

J... ., f tbe AWr, inthiiMoDth, will be la the Motion of 'hi 

to iiil 1 nikini tb« mUH boarif -Motion iS' ig' f ; 
If to Sir /. JVtwHJi, it*B)ount) to iG'jj"! yet by Cor. 
teftioDi tbithcFDrTuri, it reduce) to iC 16*']. 

The EQUANT tai tbc loniul Motion of the Sun rrom tbc Node 
bdn* lira ID Ellipfil, it fallow! Ibit 

~itmm UtHn tf ibt San frm ibt Neii ii * [nmit-^uai mtm Pr: 
iemtl, iUvKtm 'In Mttim i/iU Ski «W ibi Ktat Mtiin »f rit Sti 
I rbt NiJi, ii Ibt Mmtb win* lit Line tf sit Ncdii 11 ('■ a S^Miira- 
witb tbt Sim, 

'he mem Motion of the Node, when the Liar tf NtJiiitiafha' 
dratare with the Son, it ilteiily IbewD to be, to tit JUmji'i mtu Mt- 
(iM.'ai ion 1*11) v>dtbt Mmitn tf litSmu tt tUMiiim tf lU 
Mmm, at iSo (• 1139} loboKt, lit Main tf Ibt NpJt uii Mmita 
tflbiSnmttitatii^glti^gi. Tbenfore, by the fiid Xvfr, the 
Soit't nKM Uotkm from the Node, i> to the Son i mean Motion, 
ib* JMafliMt fnfrtim tf i^^ti 1395, being aur^ « 9S « 93, 
condpwidiiig witk ObleiTUion I ri6<r( jr'mt 98 XnwAidHi y 
t, lUStitia mUtvtlalimtf >** Sun. — The fubdupliale Pro 
tilcM nOK nculj, ItMltoBgj, wWch will give ij' ii' j*, 
Hotioa of th* Kait fnun the /tW Stan, in ■ fjdeieil Yen, 
Modon oblctied it 19* 11' it*> 

If the Cmmfmiaiiia fnm the iaU hid b«ea men twtSilf Dud*, the 
_jinid/ Motion nodoccd hid b«Bl9<> »l'7"lf whJdi » «♦■ Wt ihir 
the Motiou obArred bf AAtoaomeii. 

Tl^foi«|«iB(Difici«Bce of Motion, probably, miyuile froBtfai 
San'i PartMax j ind if fo, may lucnilh the t^ and moA ceniin Hc< 
tbodof detenmninilhefnuDifliiace of the Buo. FortheSuo't Force 
Wini tMnething molifoa that KoZ/oftbcAMi'i Orb which ii town 
(he Son, ibiD it ii oa the otbec Half, the il/ifiit EfieuU null 
KCOtdiiiE]/ lirfo in the frfi Caft than in the laiitr. And by Com; 
tation, tlie Mwa Motion of the NtiU arifioi (aftci Confideiacioi 
taken »t tiiii Difinwct J iimoie than the m»n Motion from the mi 
Htfidt^e of ibe Efincli, by near »" is a Year, fci enery Mini 
ofuie paraOatHt JUrb of the Moon'i Ortiit. Anil, ' 

-' ", th« Digiratt of i4», ir •>- ' ' 

rife from about i" olFaraHa. 
boK aeODoSeiiiidiiineteri of the Earth. 
Aa n« SfaaM, for the Motion of the Ncda, in that Meath 
Fhaa (he tmof tbe Nodci it in ^naJramn with the Sun, ban 
'./Hi/ht fai in any other Month, it it alio an Elfiffii 1 the Motion 
J&t HtJt bdag dircfl and ietia|Tadc by Tumi, in the Moon'i 
^og Awn the Qoldratare with the Son to the Place of iu Node, 
- -i b^ thtlKC to iti Qnadntture afbrebid. 

The heriaaiin of the Plane of the Mooa't Orhit to the Plane 
of thcEclirticual'bAeirabf ibeleoi^WirfffiuaO, fleeP. »i. 
^ Itt J*-'i Jt***-* *' * t^"^ V 't* ^""•t"' if—Jkui if 

The MtimM tf tit Mata bw Ae 6m, accelerated and retarded by 
the Iirrmtiil of the Area dcfcribcd bgr tbe Moon about the Evth 
faatT^M It i6. Fnh W'. '^ Primhia} it aUb redwid to an 
iftWuffWiff bytakjna tfctAorterto tV loager Axii, in the /n*- 
aa^atSmt f */* Stmt, Fttftrd- of tbi Ffra if rit Mttx'i Craviij 
VXh^mSSmifa^Sktl»■lT,m..,i.,.a»l.larF,»,^ that 
It, li TA {i» Fif. v.) HiiiPfii.wMa FrtftniHai ittmtta TA #»rf 

^ U A» Proponkw f« the .,«« de&rihed by tbe Uoos altcof ibe 
EMh. ahM '» (fcaAratart with the Sua, to the mmattvi Oi, at 
SwMZTw»tk>A(«>Mi>b>d.i> tb*^>n^ HciKSt)>t 



^naatjl Area in the £y«ff»> it Is th* 4|f la the Qg^dramre^ in the 
fiiJajJicati PiopertioB of TA 4- )AM to TA, or u ■*'8] 

But thii it on Svpf^iitt, that the Mooa rerolvei to the &■ in t))e 
ime Time that it rovolvet about the Earth ; which nearly agicct with 
ir I. tirmiat Computalion in tke beliae-ctted PrwptStitm 26 

1. in. '^ 

Jn like Manner, an c/t^ic Bfaam KMy be raDAtnded lo Aew tbi 
tean Motion of the Moon'i Aio|ee, according to Ibe JtuJb (imi by 
iir Ifaac Nrmisn (in Ctrtllariti of ^ ;. Prop, I. Book) for Aaiiitg tite' 
Motion of tkcAftiit; wK. by taking the gteateH retroende Motioii 
of (he Apogee from tbi Ftrti tf ibt Sn atMiie Mttn i» ibt ^aJra. 
aad Ibt gnal^ JUnS SAlM, Jnm On Ftrtt tf lit Sim nftm lit 
wbrw i( Ccajimaitii atd Off^iim j each, antrjiwg it ba Rati 
dtSmridmibt id Ctrtllary It lit faH Pnf^uim. Ami, if in £«^ 
be made, wbofe.,^! are in 1 >M^Var( Piopoitioa of ih* Moon'i 
Motion fronMhey(»w«, when in the faid fwifieft d!iM0tad rOVYwi 
MotioQt, the rain EUiff, will be nearly Ibe E^aam (at the Motiw 
of the Moon from the Apogee, ind b* nearty in the Fotai of thit 
above, lur the lacnami of the Area. Bat tbe Motion of tbc A»«iae, 
by tbia Method, will be fonnd to be no mote ihin i>> ]/ 11', ii tht 
Revolution of Ibe Mood frwi Jgfit to ^ji, which Aould be 30 4' 7' j, 
ling to Ob/trvalim. — By which, then it mote Force oeccfi^ 
mnt for the Motion of the Moon'i Apogee tiua what ariiei 
from tbe fariaiita of the Moon'i Crarily lo th* Sun, in ju Ri 
tion about the Earth. 

Bu^ if the Ciule of tbii Motion be /uppoled ta irilo Am die 

Katiaiitaol the Moon'a Graritj to the Eartb, at it larglvci raood, ia 

'^ - rUifiie Epieydi, thit DiSeience sf Force, nearly tbe AnU of tbe 

mer, willbe jidlulentwiccaiut for thcMctJon c botnMloi ~' 

night be eipe^ed. 

Mt. JI£i(iiaproceedi to laydown aXiiA,(fgoi^edsnMW Piindoiet) 

!cb i>, that 7iw«. MMin ^ ti, Mtta fram inAtvit, iaitit. 

rx Malha tf Ibt Attm, » ,bt fMafHtau Paftnim ^ iitliif.it,- 

» Imu lit mtaa Simi£amilrr, tf ibt EpityU, aad lit Mtm't ma* 

D^. It btr auaa £>yi. ha Fig. V i wiw«AM = 47, AN:S94, 

EXAMPLE. Half the Jhorter Aiit of the Epicycle, it ijl, 
duAed from AT ( = 8400 ) = mean Diftaocc from tbe Cei 
of the Moon't O.b, 8376^ ; the Sam of the Semuxei of ibc 
EpicfcU, 141; the DillneDce of the a^aa DiSance tijCf, ai 
Sum of the raid S«>*B,. of Ihe Epicycle, = lajrj. Wbo< 
fore the Motiatf of the Moon from Ihe Apogee it to the Motk 
of the Moon, •■ tbe S,Jd»t&ai, of Sxjj^ to gj7«|, ai ilTyto 
■Sgj j fo that there ought to be 16 Revolatioiu of tbe Apo^' 
Sj] Renhiiioni of the Moon | aEreeing, is gnat Predfim, wr 
the KHirr* Nainbait obfrrrcd. Wfaeoce tbc mean Motion of tbe 
Apogee, in a fydeietl Year, will be^co 41/ 40* { ; Mcr^ agneing 
' tbc Nnmberi fiom Hitoita't Tbtart, ^at tc/ 4,* u befcci ob- 
il'intbeC»>i.i«i/. t- »i ' 

iie Diein Motion of the jd^twH being ftated, according to the ^iy- 
fcal Roiei afotclaid, tbe billowing ftmli ferret fiir deierminiog Uc 
Viiiatioo of Eccentilcity of the Moon's Oibil. 

RULE. ^btUgfi iilt IbtrntaaEltulricUiiatitJatbtaltPru^t 
^Itt $»'< *MU Mtlitm frtm iht Aftpt tf lit M.t„\ Oriii. n (fc An. _ 
mta* Mtita. Or in Ibi ihifStai, Piiftnitm tf litfcritfieal Timt tf lit 
Saa'tXiMhaaalttiimaMftrit^eaJriait tf iuXtv/adiaitibtliibta-i 

"y the foregoing Rab for the mean Motion of tbe Apagec, ther 
in r6 JlHwAinnof tbcApOgM in 1X9} RffiAi/Mnt/lbe Moim , 
but there bciog a $4 Rcaalutioat of the Mia in 19 Renhtkoe of tbe 
Saa i there matt be about •) Rcrolntiuu of tbe jfyigm ni iboot Ci 
RcTolutiooi of Ihe 3m { or radier iboat ao in 177, 

That the Period of the «n to thefiio-i, aM of tbcSu 
Mom'^ Aporef are, amr^, 11 157 to 1771 tbe D^iliaN of which 
Pr^VOrtioa it, that of wj (o 116 ) wUcb^ Koudinf to the 
tbo^ hi tJtf I^c^Mtioa «f tbe liafi to te iwm Bccentri- 
city. 



,y Google 



tmi NAVIGATOft; 



%H 



or MACHIN't THEORY of the MOGN'i MOTION. 



^11617 i bring mM,h u iJii to la*. 
ccerding CD Nmm, tile mem EcccDiniity 1O5 50J U ii tb( 
mn or SHni-TraDTirilc of the £>nh'i Ocbit ; Half tbc DiS 



HeiKe, by ihii Si/rr, ihcanmEcttiitHtity (or ifajOb* Sam sf the 

gmteflind laOl aofhttD he [be Diftrtnce of the nw ' ~ 
leaft, (a- Half ifc Digirmu tf iroHft rnndli^} u i]fi 

DiftiDce cf Sua. ] j. Half Df^irtmu between pcMcn nad 

r ■ ■ ' . - ~. 

DiOui 

sf gmt^iad lull ,0117}) 

The JtuZi heie hid down i> ealj to be tiCed, for 
ptriaib Eccenlrldty^ wh» the Ececnbicitf of ifac Orbh n fiJlt, 

The gmtrft and l(a& Eceeatrkitj beio| ksovn, [he £f nor foi iba 
MoIioD of the Sun ftom the Apofee laill be ui ElEpJii ; whole grewcr 
^nd IrTt jbdi tm fqul to the |Ratefl lad Idft EcccatriciUae^ .Aad 
tberefore b]r cha PtopcrEy of fiicli u EfttMt, , 

lUDigirBMi ef lit Aui tf thiK^mX ii-tbtir Sbb j- Ihit ii, at fi* 
Diffcrmatf lit [rauft and hafitcnntxtc^Mttttbar.St 

EXAMPLE. The 0\Bmna to the Sam (befon detumined] at 
tq to 136 II Radioe t iia-iS'40*i u bdofe deKiouiu^ in tho 

Hmci kUO). Vlr..AUrti<i gir^ «tn JtiiA, for dstennulBB the Eqni- 
ntof the Apogee In iny Afpefl of lb* Santa the ApocMi 

■narattm >/ ibi AiU •/ itt mtmm Difitmm tf itt Smm fim tU 
Mm't ^^h n(£<TiDgtat tf tit jbgb tf tht ma Difi^Ki ^ iht 
Sum fftm iht jai JfytgH, aitbtptalffi iiu iba kafitMseaai^, tr ai 
i£ctfio7, neirly. 

lAr, Maibia Chen proceed! to &tw thiC 1 Carre nuj be deTctibed 
■bauc a Cents', to leprefeiM-the Imeaaiij of inj Monoa propored, 
whofe Rayi an nafrtraitf » tbt fmUaplkait Pnfniim «/ iti yUKHt 
•^■.1 tit CttJir.. 'i'bit, whne the Inequality ahsat the Center ii 
jmaU, ibete it na Need of ^ttt EiaQnefi in the QoadntBrc of ibt 
...-nFcir Ihewinf obat (he Equation ir Whence all the jiaatfannoal 
kqiatient f'k^tnin^ of the Moon'i MotioB, Biifing ftni the difle- 
rent Diilinre) of the Son, at di&ertnc Tunn of-the Vuf, ire reduced 
to Ml AUf, acat caoagb facitht Pxpofe.. 



— nnii m nan iBirooacM u 10 pi« UM Ke 
of fhjfui ..tfrt-mt f wbk]iSir//H(^nBMif 
Gnce been.impiOTeJ fj frrrnil mmikmtliml ilfl 



That finci tb> Su'i Force to prodan tbefe ^..u.. .wtmrnmrna n 
reciBtooUr la iht trifeaai Pn^wction of hk DiHucet, ibe Re.i 
of the EaaanC, for toch a Motion, will be in the fifymMir- " ' 

(fM of^l INftuwe, »<v attaJwt^criMi who det.,..™, „ 
fauH E^yMkow of ihaJUMi j^tpi, and A'oA, aeeotdingly, u hai 

HeroeeedetoinEaampIeof that^of theEqaaat, infindinithe 
E^uCioiuoflheMooii'iCuiter, by a cmnpUeaced rinr,, (frt tht 
End of MwM'i Primt^, tranOatkl by Mittt) boi u we hale al. 
rtadyiiTeBa Sketch of riii JtaA ta P. Sa. wb need not nneat ic bere 
— Wk.. -« h.- !-«*.-* ia to pK th« Reader the (gnpleter Ida 

'- "■— " '-- - -«ad i a»d hai 

i, DiU Cailb, 

Mr. T. S.. T. R-..S,. the celebrated Anchor of thd^fOwMM Traff, 

diffiofnilhed fer hiaeoiaent AbUidti. baiginn aComaMn •fl«mf| 

Hffwis*'. (« P. 5J »*■ '>>« f»*J TraS.; by Meant of iM, mm, - 

or mote £<|i>aliDni, repRfenling that Mr. JUariia hat gnca «. ot bit 

lee Eauationi ^eff m ; injodidoofiy aflertuo, tbtt iht ImmMi^ 

,h.JLi« ./^FU^taiJ, th,af^T^^%,J^.f7t,!r^^. 

■ A.I if (&yt the TraO Aniho.) the Nal« ef the Sobka admitted 

" «t }n& liai Namhtr, and nomoic| whctcai the Pirta or Eqoationi 

" arifing in the Confidctalion, aiewitbout Koaberi b«aa thaToBit 

" ttinimfiuMSfi'i, wheitin the Eccenltkity it the mtawtmet 

Qpintity. Sir Ifaa, Nnana bti giTen two Teraia of thiaj^ 

which m ngJu i bet .he .^ E,«,ioo ,dd«i by the Cmmmai^ 

(Mr, ifaiha) 11 not fo j the Sifa thenof, ihaC^^mt, " " 

L-m by whiih it incinln uddecreaft^ being aJIdiffer 

what [heywrir-u ' 



. ._ , ._ „.j. u<««B, luB L«un»i, ud the 
icinln ud decreaft^ being all different fnu 



Mottorer, tinP. 54 i/rfcyWrMffj^ theTraft Aathwhaterit 
vmtr for liring the Raili of the Ditneten of tl 



cifcd the lame Cmmafrntr tor giTUig the Raili of the Ditneten of the 
Moon'i Oibit (fmiag afiit tta OMrmum a/Eeeenlrkiiyl at « to 60 . 
iir I/aarfhmu hiring olbenri&/M(«t>pmed it to beat tl to «.! 
-itb which the Traa Aalto'a'^S "Sipitatior wiJIJ^S' 



0/ DE LA CAILLE'f THEORY, and PHYSICAL RULgS, of the MOON'a MOTION 
<Sea thU cdebnted Autkok's Aitkonomy for tbe DcuoiiiTitATioit.)- 



I. THE Miffl f»f 
iralFaratt lia Eailb. 



Vr. mm lit MmaJtim litSj^a, _._ 
lii ttairai Rra, nffamtritf fa til Earth, «^ it 
"■—^atantiBmttitDimim'' ■ ■ - 
u lit ^ma^abira. 



SnmaittmjIIunttim h ioamnUFirti it r^faam tit Eaith, 
Tin. TltPMaAm^iiaMM-'tuwIr^ran: 



ni. ntrtfiH tht fireiaailiratiH[tr raar^^iliSOm^iJI&titaiii thi. ^mrartaimii/itaMi 
in Ortit, it almafi « } if lU Sim «/ twke til Mum'-i Difidta /ram >*»^ '• .(aim hi Oriit InparJi 
lit line j^ lit Spifpii. 



}»eritfia£ttt Mim'i en&ral Firui 
Grmviij, nffiBivify n rir Earth, n « thi Strm,. ir m lia Dlffirm. 
a/Ba^iiaXaJ-M, «id ^ i rf ria Ci/Caa if iwtitt lit JAta'ji^j. 
^^ai rir Lim if lit SjKjpa, 

M til Mum"! Jh 



tbii^gairalKraffititt 
""• '"il mtUiitn i ittpi 
'■■'- ■ 'ttii 



J^w-frwra} mdttulreufi^tii^ainKwtiiitiiSJi 



V. jtU'ti loeqnalide* iaffnaf U til 

-ir-»-r imMt^aaJnlarililii 

Elk laifna/aiit Up* ag^m la lia fami Or^fiamli 
'" iJraan, miart^^i^ U iatiiF^gagiMi 



. . ... SnFtfm 
fhm i^Smty n in wot liaa^anri, an gnda aO f <yWW (* A, 
^M-tPl^^Mt^mtiralmrltllbaiaaSy ' - 



<iir/,^iii„i,lt, Una af thmLatmn. 



/"m'iiSji^ftj'iil'a^t'adraltiri.itMailirmJfiimltaA^A^J, . 
' '^JW. —^ »■«"»> J^««r*,5y«wjr f. iJ« ».«« OftawTaWiw 

>a/-. ., Sr /«rr frtf^rt-, /,« ri^^Saa^ u ,i. fiOm^ «Mih.. 

r.i.It being alwayi in the ««» of. the Sine of twice tS jio«f, 
Diftuce Atm the Syqrgf, Thiilwqaality ii talM thcUoon*!." 



,, Google 



3»4 



rhe R OT A L .A S T R O N O M E R 



Of DE LA CAILLE'i THEORy, kod PHYSICAL RULES, of the MOON'i MOTION.., 



a Rtyjrtm ibe Moon 's itt Eirlh 

, - , r,«, i. . ■ 

Oriii, iht jlrtti an Ufi im Pr^trtun to ibi Timti, 
■ Oaiiitt. 

4> The Mm'i Orjif li>i ben fi^iofed ■ Qn/c g iHRgh it I) in 
?»& u £i%!f I in one of wboA Pod the Einh ii (ilind. Whmce 
the dpluncd i*«H/iri« mi 7 ciufc the EllipGi to be man eonTci In the 
Qnlilnlarei, *Dd more reailineir in the S^ntrgiei. Which InH/naliiia 
malatiuMrmrKHUfinHbtltnW ia the Ualdni- 
eh it In the Syiyrie* j though [be Mom'i cUiplic 
.Orbit it Dot KC7 erceninc And hatt the Moon'i(«<fr«/F(m:edin)i- 
niDwt ia ilieS>i7fiei, irid iicreirei in the ^tdntutc, it if'tvldent 
(fram tai*! iiJnmi^nrtJ iaDtbCailli'i A^rimmj) it malt rome- 
(imei be t« great, lai raneiiB*! tooliitlti to be itrvnfr/f u tbe 
Square of tbe Mooo'i Diflinre froin the Euih. 

TIm Diffoencc in tbe Moon't i)iJ«Kci, thcVtrlrtimof ihcEccep- 
tHeitJM of tbe Gmh and Moon, the Inthiatin of the PUne of the 
Mooa't Orbit to tbit of the Ecliptic, conltitute, tni ut the Ciuf) 
of, GMterr confidirable pnioilinl Inrjiaiiiii in the Moon't Motion. 

I. An Imifmaiitf ia the Titnt of feveral of the Moon'i fucnQwe 
periodic SMoMraa. 

■. Tb« Motion of tbe LiH ^ <^ y^lf/'f. 

], AcontHMulCbangcintheEcceniikityof IbeMoan'tOrbft. ' 

4. Th« SimgrtJMiim of tbe Moon'i Nedet. 

f, ThcCbuipiatkelKlinitioDof [beMoon'tOrbit, 



XIII. tttnitiMM 



I. WbmittMM it >■ itt S^yrici, th hint «/ in Afrits aJ- 
JinCIfy, *rar£ilt In ibt Or£r cf Sigm ; t't mtvti ranfrait 
lit JUon (I u >k ^uaJranim 1 It sivaimi miilb iti ptltft Velo- 
eitf, nba amairTiiigmiilh iht Lim ef Syryjriti ; and rUrapaia v'llb 
tbi [ru^ filictt^ ^atof umarnii viib ibi Une cf HjHJratam ; rtt 
Sam »/ ibiSiHalitiu il gaim, ia Jimmai RivaJatim, madiag tit fitdi- 
tiiiu il rtttttrada daring ibtfi Krvolnihm, caafa an ittirt ttmMatitn 
tf thi\MasJ Affiia, acilrding it ihi Ordtr af Sigat, iaateal igTuft, 

XIY. 7ln eccentricity of ibl Mvm'iOriilvaryii^tvrjln&atiX, 11 
pftufi vtra tbi JJoi |f Jgn-Jf rt!—!J.. guli liaLaf lit Sfmjgii, 
*isdliaft vibiif Ibi Line ef jf^ida ctintidtt v/ilb lial tf ihi Hfednluni. 

ZV. What tbt Mhm i( M flu ^aJralara, tbt t/tdfi tf il, Oriil an 
ihua^ &al\ontiy i iai leaaacah ruri^radc tuhia tic lUn^ ii in ibtSyxy- 
gi^t ia ail lalm^ film laa^aadrMwrfta liaalitri titf anor rtt maft 
mngradt nbm iht Line tf ibi Nodii cmcan viiib ibui pf tbt Qjiadia- 
tertt) tailiafi,'whmiitaiianv>iiblbattf ibt Spypa. 

JIVI, U foiry Kmabtitntf tti Man, ibrAaplref rnellnation rfiti 
'rhil M ibt Plaai 'f tbt Ecliptic, iaenaftt in *r Jaicvai fitai s Sixyg 
I Ibt tan Slaadratan j aad ditriafa in ibi lalrrvalfrtm tbt Sl^cdlm 
■ thefiOtwiat'Sjfayg;,. _ ft i»^'!(»'» ibi SlnaJraturc ' ' ' ' 



XXI. Thi Inciinilioo tf ibi Mttn'i Orbit, tviJtmh cbsira fx 
Inan ia ivrry Kevt/aiim, twin iacrtaJSng and t<inixdiiunifiinr I, ,. 
pi-eiM^n^lfcLiDe »f NcAi naran toiib that tf Ibt &M^™tDia 

.rf Ju/l -abia Ibt Line ./ ibt Nadi, ctindda vriib lUi tf iht Syij gio. 

XXII. 7irMiM.'i perturbitE nne, aad tmftfaaii^ all ittlmeqasT,. 
a, art ftmaaabat greater itviari, lie O/tjaaSitn tbaa iKoard, tL Of- 

XXIII. /■(^Quadntoin, ibtbtrtafi tf lb, }A«m', Gn^^ „ rt- 

:>rtb I. ahv^yta- iS. M«iiV Diftaaa frtm ib. Eanh divididi, lit CdI*! 
f Ibt Eirth-iD^«M fnrn ihtSan. Or (the DiA.ncei being in.erfd, ' 
Jtb«ipp«eBCDi«i>eteti) atiitCaia tfibtSaa', Diaarcnr ftt~ '-- 
rbEuth, druididlytitMm'iDiaamir ftaifremtbi-EatA. 

XXIV. ffUlbtUiintialbt Mtaa-.Inijaahiiiti, r.tt^fi aftdfca. 
■ rt ittSait/Siii tf Jninler aad S»tum. Bot btcaaft tf iS/grtt, 

i>,Uac,tf^l.PlaaHtfrw, tbt Saa, ,bt Iat,aaSiif ,f liiir SariV 
laap if-^fmall; aad, an ft^U, aah i, lit/a atartfi Ibt P/«.,t, 
Jinaat tf ibtir Pnaiamtf, 

XXV. T6f CoBUnitiDn tf ibt MtaaU OrmAf tnoarj, tb, EanV 
,miib. Son, au^ ividtmfy t.r,d^ ,b. famt Effrfl,, «i«t^ ,b, t.nh 

ft f'^'fadl' AS"*"— EllipfiiB*«/B6« Sbq, jfjAv/ia tattfiti T. 
tr wbtlirtbtSattd^iiaaa Ellipfii <^r r«< Eaith, fixnli^ tat ef 
Focti For tUi EfKdt A/>CM^ nwr liM Mtta', Ptfiita and D^la/n 
r^ta tflbi Eanh and Sun ; ud therefor, wheihrr ibt E.rfi •- , 
un iMHi, Ibmt Siiaaiimi nillitlttjam. It tat aatibtr ; aad i«yipnrat.i 
' Ibt Miaa. Ji J 

REMARK. To fettle the JMto.-. Timry, >nd eoofttofl Takk, fer 



nbtalUUiatf tUlitiiict. 



' ibtSaairaluru 



XVTI. Vbtlntttajt tf litteatii] Tira, lalU^dranm, ititli 

ra ^mt apn tbt Mttw'i Plant, at thi Caht tf Sadin, U 1, ibi trip 

Sim tf ibt Mfa'tDi/laait from tbt SJifadrarim, mibipVrd ij ibi Si 

tf Ibt NtdnD^li f^-^ibt ^ijg^f andtyibi Sinitftbi Uiliaui. 

tf lit Mta'i Oriil. 



jat, IttgenUit, TluAAoi^f MA *»it« ttnYlli^g It i}it.Ord,r ^ 
JUpn, amd Ti S^imuj ^^ V}bnt ibi'Mttii 11 li Qqidrinire, fr vibtn 
JSiBm Lalitadt. ia all tiitr Ci^, il atnnr^igtiukitinb a ythtiiy 
lertafJ ia tbt Prtptrliaa tc ibt AfWi Pnximity It lit Sf ifgj, and " 

t laiilaili it griattr. . . 



ical Oifn 



computing Jior.true f^ap'f*^. 
will benecefEwTiodotenoine, t 
Elenwati, fall q wing. 

I. TitcMona-i total* fmiidUtlTimt. 

». Tbe m=in ftritdical -Tiau of the Moon'. Afttii. 

y 'i:\ittnttafiTitdiiainmi a( \<atiittBiiaillUt. 

4. An Eptxba of the Maon'i mcin Hljte. 

S- An Epeiba of the nl»n Pljce of the Jlptgu, 

*, 4 n S/ a t ba a i t ho aaan P l ai».»f thaAM^. - 

Jhefi^rKiw.omheNooopf 3iftO«n.t(r, 174J, u.S mcu 
Time, wetej for tbe Mt<m o« I^'li'to"; for lhe..4i.:'i 
o" B* l»U9*i fortheiWufriHiyo j/o". 

7. Tkc g naitfl Equation of the Moon'i mem Pkee. 

8.-TI111 of Ttie nuj^ Plate of tht Moon'i A pogfc, 

9. Thit of the mcu Place of the Moon'i Node, 

Theft three /«^M/;f.«rerTe to n-^BW ihe loequ^Iitie. of tht 
periodical Re vol utiODi, icconlingai the Eatih it in itii>(riK- 
liinotjfybtlitai aod iR proplrtioKil to the Eqnition of ik 
Siv'iCtalir. The/5). for the Mt>e, ii 11' JO*; iaithf^ 
fcgitio' of f and foi the Kcdtg' jo*. 

>o. The^«(fl Equation of the Mooa''i Apogee, whith ii no li 

II. ITie nKoa Eccentricity of the Moon's Orbit ; which ii c,o 
fuch Parti u the Moon'* .MirDilt. from the Earth contain! loooio. 

'M.Eilaiita between lb* greateft and kill Eccaatrtciiiii - 
being ai 6677 104333. 

By thefe Kilalima thr EqaaHon of tbe Mo«n'( Center H fo< 
all Ca^. 
Ij.The MfoiCtatfan Variation ia OrTauB, being 3 ^ ic". 
14. The Biltiini between the groateit and !e»ft Vaiiallon : heiia 
■™37'»!'"33'4*, 

(S- Thep«*,/firondE«iiu[.o*Moon'iA'aA, being \a i^' ^c^, 
iG. The MM India, of the Moon'i Orbit j bring about ca 8' to*. 
17. The Proportion of the grtUifi to the Itafi Inciinauon ^iagi 

50 ijf 30" to +» re' JO*. 

.iB. rba miaa PnUn of the Mom, behif 5/ c'. 
1 19. The Rata of the Parallu <• tb« Maen'rOim 

55' 40" 10 jC. atarlf. 
Befiika «tii4 Slmetfi tti'cn «r« othtri gin^m bsU Bqi 



, being u 



Mi. 



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M NAVIGAtbR. 



3«S 



MEAN ViMe 0/ ri- FIRST iftAN WfcW ml 


g't/tni, tni Sun from the Jlf»«'i Ntji, torrarpondhig, ■ , , | 


Of 
Chrirt 




AKBIfllty. 


R1»d\' A^. 


Siatrotam 


of 

chttn 


Moon in >-, 
d b m r 


a™™i,. 


Moon-. Arc. 


SunftomS 


J h A f 










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1700 


9 '4 4> 44 

* 5 .5' 17. 


6 11 43 S3 

7 10 6 5 
6 t9 II 56 

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9 6 17 36 


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7 6 S9 S9 
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6 'S 31 4 

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s .1 31 i 
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9 '9 33 3» 
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10.11 ji 31 
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9 I 11 57 


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the Ne* 

hUIuri 


•I Qmvcnkncy of CompUciuon, the fDmputrr njuft ipdute 
unA Fun Moon, of .h/OM/'to .lieDiy. of N.w Stvii, ^ 
e NBmber of D.v. Di(r<:«D« of S^le. 


^AJmbeIC> UAYSinibc MUNTHlV R£V0LUT1UN& oC tht M 
MtinAnomilT, AehuJ AtpimqiK, vt. 




3r. 


Mi 


+ Diyi fiom 


JVfotioli Sun'i 
M. ADOmilT. 


M.*7i'pAf»g. 


f™»a 


No. 
D.. 


Mt. 


4- Diji from 
jinuiry p. 


Motion Son'! 
M.Anomdj. 


Mo.SDDliom 
M»>i<Apo(. 


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1* SO 9 JI 
II T9 tj 51 


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" |"33 
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liafflbtc, biitClkeoiit>tliir«ni«M'otiDn. 1 


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b(Ti£line ftHHjr ■ Rei'olution fiern At Time ind PItea injmny O. S. will tiit die 
•^D ib« Diji on .hich A N.» M<m bOTm Rceid (^ <)r dH iM ATkbh H <Mfi)T Ttdk: 


.Weed, f^L^T^ur., ^\i'tci^-iS^J^ 
r»iM and PIicnAk tbc |>r«edii>B FoU Moon j 












D d 


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EVoLuf 


OHS of the MOON 


to .he S V ti. n«t HFT 


>A«"cTTrfuR[ES cooiplcted. "I 






fiou of lA New Mooa af- 








Moatlu. 


J»)i«. 
Ccmoriet. 


ter ful. Cent! tomplcted. 


Snn'i Mem Aaomilf. 


SoBlimMoon'i Apogee. 


Son froB Node. 




• / » 




• • r jr 


K37 


100 


4 8 - S* 
i 16 »^ 4S 


« I >9 44 
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8 15 »' 59 


4 19 »7 17 


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4948 


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8 *] I* 48 




148,, 




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10 (O 3, 


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S .. 47 IS 


l6cSo 


1300 


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14 10 19 
II l8 ,3 44 


I .3 S6 4« 


■ .1 » 14 31 


17316 


1400 


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19790 




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9 IS so 4*. 




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1100 


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1 5 5? +1 


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37106 


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Sun'i Mean Aoenuly. 


Sun fiom Moon'i Apofee. 


Sub ^m ^Mle. 


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Vllj t>t t> prfnu tf »yn'( Vie- » K, l«ft tlwr 



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Iwhr.Lsliir^ri will nfuAitiiUkiiiuK •mill .ikf.»l»...> 



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ni ROYAL ASTRONOMER 



R»lCAi. Moo PLACES uHl UO-noNSof tUHOONfkoDi^SUN, »>.fMfctemiBincili*fe1»TlMror(Lc_«..MitWi> tbd 


t™ NEW indFULL MOONS, with (cr wirhdgt) 4 


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6 I. 5, 17 


7 '« 44 Si 


I ao 7«( 




6 la a4 


8 '5 9 55 






i66o 




6 IJ 17 IJ 


6. 41 It 


a .0 IS 8 


171a 


I 17 1 J 


* "1 7 44 


7 IJ 8 la 


.1 .* as .- 




6i 


3 •? 47 »9 
* 7 »4 51 






a, M 31 


»1 


5 a« 4- a* 


« la 5a a4 




IS .4 ji 










3 >» »5 55 


'4 




6 ta 57 I 








»1 


17 a 17 




lai o+o 


4.7 J. .i. 


■5 


« "I JS '1 


6 la i> 4j 










5 1 5 ■ * 


* >J 35 S 


17 5> iV 


4 >7 39 


.716 


7 744 1 


* 'J S «7 


a a »1 51 






*^ 




6 I] 19 45 








11 17 ai aS 




ai a, 4! 








6 IJ 4 »4 


9 1< 10 J7 
1 ij >6 U 


J 3S 49 47 




1 a6 !< 49 






1 a> 1 




67 


6 7 4J .6 


6 " 49 4 


6 a* S5 "° 


"9 




6 ,a .9 afi 


9 t9 41 a7 


4 M I aq 




>6it 


.0 ., 3. 6 


« IJ J» 4I 


7 S "4 4J 


7 «S » 5* 


17»o 


oaSas 3 


6 IJ J 10 


8 19 39 44 






•9 






S 14 »o 33 


B 4 1 15 






6 la 47 50 


1 " " n 










4 .1 a6 aj 


1 aj IJ 19 




9 '7 19 49 


6 la ja 19 






7" 




6 |i 46 ^7 


3 . la .. 


9 la 19 a 




I a7 .7 ., 


6 la 17 9 


4.«S7.1 






.67. 


+ «.J 6 


6 IJ JO ji 




10 a i« 14 


'7*4 


«i. 4 a 


6 IJ 54 


3 eisj-i 








8 >9 so ij 


6 IJ »S "' 




to ai 31 7 


ai 


10 ai 41 as 


* " 45 14 




t 74a.: 








« 12 jg JO 






3 lao48 






8 afl 47 JI 




75 


J 19 S '* 


« " 44 10 


9 19 47 58 


■I as 4> 54 


>7 


7 17 S> » 


( la 14 « 


(I 4 ij c 






,.T' 


la .0 S4 i 
I 10 31 aS 


6 IJ il 15 


g a 46 i« 


: 1 i? ^: 


.718 


947 a 


6 .. SB 17 


9 M " 17 








6 13 »» 55 




»9 


tiS^il 


6 la 41 17 


8 13 17 , 






7l 


7 Si. 


6 " S7 14 


S J7 57 5« 


laB I a* 


JO 


i " "' ^\ 








79 


II 946 li 


6 la 43 14 


4 7 3 4S 




1' 


4 >i 48 49 




5 a. aS 4« 


3 '7 S 




,6ln 


4 ' IS S 


6 IJ as S* 




J 7 «4 »9 


I7J1 




6 ,a j6 ac 


4 11 a? 3 






Si 




6 1] IQ j8 


»6 7 ji 


3 a6 19 SI 


13 




« la 41 










10 49 S> 






4 >S »S '6 


34 


a 19 4a 48 










«! 


S »7 "S 


< " J9 57 


10 4 I, JI 


5 4 JO 19 

5 24 j8 la 

6 "1 43 45 


3! 




e la-io iq 


844,, 


ii"^*.i 




.6.4 


,«,( 4 




» M >7 49 


1736 




;;:;5,' 


10 11 4a JC 




u 










4 46 *4 










6 la S3 " 


fi a 99 ai] 


7 » 49 9 








» 6 54 1= 






•l 




ti la 17 4' 


4 " 35 ■* 


7 ai S4 Ji 


19 






6,6 0.9 


5 « 4ii 




" .Ml 


J •» S7 4 


6 13 «• »S 


1 " 33 3S 


Si. a 14 


1340 


J II SO 1 


6 l» 51 47 


5 «S 58 3» 


i;;"ii 




N 


7 »* 34 *7 




a a 19 as 


9 » 7 J7 




9 »• >7 «4 


6 ,a 36 a? 


4 i 4 »« 










19 45 >S 

11 i J. 4 




4» 






a 14 ifi 16 


7. 6111c 






4 II 49 H 


• » 1! H 


.0 9 .1 a* 


♦3 




« la s 46 


I ij .6 s 


7 »5 »> 4i 




»» 




\ •! i9 « 


J aS 49 ai 
t 17 Si II 


II iS JI a. 


1744 




6 tl 49 JO 


J 14 aa 


8.SJ6.5 








Sij ,4> 


<% 








9 4 4i*B 












7 J6 53 




7 »S 45 47 




9 II 16 . 






9! 


M a JO 14 


C la 33 7 






47 


1 ai It 


6 la 3 a; 


1 0,1 51 


10 la sa Ji 




>^< 


a>4 >9 4 


« 11 i« ji 


416 s 7 


. ifi 49 S« 


174I 


4>3 » I 


5 » 47 ij 


6 ao 30 g 






?5 








» J SI «i 


4! 
















» »4 !« 4J 




50 












« 


1 M 11 '4 


6 la 10 so 


I, aa ,6 






S " 4 ti 




» '7 47 35 






*7» 


».i 04 

■+ 37 >7 


6 I] 14 J4 
6 la s» 14 


Il aj ao jj 
10 la .» 43 


4 4 "3 50 
4 »1 >9 »1 


175* 


■0 n ^^ 


» «44 ^7 


' 7 45 55 


I ao 14 11 












J 4 »4 SO 


6 1* 4j J, 


9 « 1» 31 


i l» J4 J7 


Nrw irxl Full Mooni 


F cbe QU to ihe D.. of N« St,!,, ta yd 




! 


9 *l s> '4 


6 la at 11 7 10 js 111 6 1 JO 


ing tbe Kimbu of Dan Difficnoce of the Style. 




Mm MU 1 ION Hi lh< MOON tran 








e 


M«. J i C 


hlot. An., M. 1 A 


M.Qia 


e 


|Mot. > 1 


M.QA.. 


M. 01 HAP 


U.QJQ 




. • * 




• » ' 




. . " 






. . ' • 




l«0 




;:3J 


Bi. 34< 
4 «1 » J 


4 >4 56 47 


IJOO 




.1 17 39 «6 




to .4 11 11 




«» 




» H S3 M 




.1 9 >» 










J<* 


6 »i 14 1 


II a? 9 


I 44»S 


I 14 s" »' 


r 


9 It .3 IS 


II IS 4! 1° 

1. 14 48 3» 


s »I3+ ': 


7 >♦ " 4! 






4 il 19 3 






,5 »T 47 » 










3 5 »4 > 


II as IJ 1 

11 14 iS I 


» 5 a7 S« » 


5 I" '4 43 55 


17c* 


6 oaa ^ 


11 11 SI 34 


vAr^n 






r 1. >, . 


• 9 »S ^ 


1 » »9 40 4» 




4 7 »7 54 


.1 la S4 3* 


la, 1 1 




9« 


11 19 34 1 




» ao 59 s 
6 7 » J4 ' 


1 7 14 17 »! 


l9oe 


» H J» 47 


II II j7 It 




to I, 58 53 
S »8 Jio 




11 aa»4 ' 


* " »9 ?4 >* 


aoot 


11 17 40 


(I It * 40 


II ai aj 40 




1 14J S 


II al 17 I 


i ] 14 S 1 


1 4 '4 JI J 




lo aB 4> 13 

9 I 47 »» 


It »o 3 4, 


» « 59 57 


» » J S> >7 
7 "2 , 








11 ao 10 a 


D II as 4a • 






;; 8 h 


;21^ 




no 




;:;!|u 


a 8 , 17 


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«JO« 






■»~'»H-iL3. 


, 4 i> 51 H> S»9 "' X 


vr' ^" " " 




9 7 4" 4** '« •! 4a 4' 





and NAVIGATOR. 



389 



UuM HOnON of the MOON fton the SUN, Ac. for MONTHS. 


Mm MOTION of } from 0> Ac. f« 


H^M 


«/«, >i>d Sutt^. 1 




J' 

S9 


i 




M.QIDAP 


M.&miS 










4p. 






lll'i 


Mbe. ItSo 


Wut. Am 


• ' i. 




H » 


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W*-. 0.1 19 15 ■ 


, as , 


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7.« I 10 48 10 4 i3 « 33 4 " •> 3« ! 6 44 44 
5^4, I 16 31 li s «S »J 3" i ! "4 '4 6 7 S9 '4 
Ai, a a 4 »6 (9 6 »B s» 5< " j »o n 7 10 11 1 


1 

1 


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13 
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17 


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HI 

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304 
114 


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D«. * ri 4* 1 


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7lS.a9 4 

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7 aa6a4H.aaa47 

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8 »5 4fi 7-0 IS 44 « 
S»'i9_4yil llstJ! 


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M.Sa-'tAi.. 


M.OiJAp. 


l^.S»aia 












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14 13 53 

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a I a 19 




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9 39 4 
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4' 53 


Q j7 9 
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41 3> 
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* J' S' 
"5+3" 
57 7 




I 


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; a aj ao 7 


4 55 41 

S S4 49 
6 S3 S7 
7 5i fi 


4 aa 16 

: rjn 

6 S9 3! 




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JO 40 1 
11 10 *9 
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1% If »7 


5' 4i 

5+ '3 
s6 40 
S9 8 




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3 19 41 

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4 "4 S S4 
4 :.6 17 «° 


8 JJ 14 
0. 9 S" >' 
10 JO JO 


7 i* S 
844 33 

9 37 


^.j:;;; 
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la 4' 55 
IJ Ii 14 
>1 4» 53 


I I 36 

: «,: 

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59 


38 
49 


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1 Ii 41' 




'3 
14 

>9 


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5 ao 40 >4 
i 1 51 40 

6 >S J 7 


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.4 47 3 
.5 46 11 


II ai 54 
la 1+ «a 

1] 6 49 


ij 30 7 

,, 3, »6 

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,6 37 3 


»9 

JO 

3' 


'4 43 S<> 
IS 14 18 
'1 44 47 
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1 II aS 
■" 'J 55 

1 il aj 

« »8 JI 


" 3 
» 5 

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33 


I i| 17 
' 'T 53 
I 1* a9 




6 aj .4 ,4 

7 9 16 


0,64s "S 

17 44 a? 
18 4] ]S 


"+ 5' 44 

Ifi Ja |b 

17 as s 


*, ,9 » 
.8 4- 4" 

1944 
ao 4* .9 


33 
34 


16 45 44 

17 16 IJ 
•7 46 4' 

>> 17 10 


t at 19 
I a8 4» 


i is 
1 18 


iS 

•9 
40 


a JO jx 

■ 33 »B 




»4 


8 16 II 

8 a! .> 47 

9 to 13 .4 
9 " 34 4' 


ai 39 '6 


iS ai JJ 

19 14 
ao 6 a7 


al ,48 38 
ij JO s7 
H ja .6 


39 

40 


iS 49 39 
19 18 7 
■9 4< J6 


ilii 

I 3» 34 


I as 
• '5 


5" 

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-. ,! ,9 

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10 19 9 I 

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a, j8 ,4 
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ai 16 4. 
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ai 51 IX 

oaa4J 49 

a4 i3 43 


iS S7 S4 
a9 4 51 


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4* 
43 
44 


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at s<» SO 
** *' 59 


1 41 » 
r 43 30 
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1 39 

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53 


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: I 51 3> 




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18 34 S7 
aag 34 5 


I \\ \\ Is 

017 g , 


I 7 10 


8 


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>j at 56 
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H « 5? 


I so JJ 

1 JJ ai 

> SS 49 
. sS -7 


I 4« 

I 44 


3" 

4» 
54 


. 56-49 
• 59 H 

: • 4 37 








■ USE ./ (i.F0R.EG01NC TABLES ^ MOON /■«. tfa a.*. 

COLLECT >lw Moo ?!««.• (from ihe Ridinl Pl.«. .aJ 
Man Motiotu conncAed) for ihe bi^ioning of ih>t Mo.ib, io 
mlitk xif Mod Time of ibe Mtin or true New or F.U JHoon ii re- 

M. M«b0D lad AccelBition of Ibe Moon, (/n. 7^. «. ,7. fo„u- 
iDt)tiidtlnJIr/.iIi»jJ]gipethicoRea«lw irut Mun Place of 1] I 
'0, >t (he B^'nnini of the bid Month ; connejling il/o the Vi'i.. 
tHHiofihe J'tAp. .ode. toirefpondingtothefiidw^/CWrf/H, 
fofcBiUMrTSiEn>)i>'ith (he Plicei of Q J D'lAp. lodQ jQ (st- 
cTftrgi^f. 374) '"r Pl»ee "f the Sun', M. Ao. I«lng/ni«.«r, 1. it. 
MotioDii dtam'i \o b> Innriible. — Now dedaa du linil PIi« of 
J iSuiifn>mii<(ifJVfw3f«B„/«^h)or*oM6>ori8S (iiJf.fl 
iim»ti7D«r, «->■«, WiW««Mid&««iM«nbededua«d: Forwb 
An. Sunl ]| Ap.jiDd>loi>n > Sun. B7 which /«/ Plia., yon n 
proraSi^n. ufweriag, ia MoL ]) 1 Sun, totbeSaoi of thr SaD*i£: 

Uoon nquind. Stt Examfl,, fmlm- m. 


49 
50 


«4 JJ " 
»5 «J S' 

:3 1* :i 


» ° 44 

I in 


< 49 




» H a4 




S3 
54 


a6 is .6 

»7 aj 45 
a? sf "4 
a8' a6 43 


• to 3« 
» 13 4 
a IS 3» 


P! 


49 


» >• 47 






>8 57 t, 
'9 »7 40 
.9 s> t 

30 »8 37 


; » « IS 

. » "S «3 

' » »7 5» 


I t 

a 1 

» II 


J* 

7 


» »7 J9 
'» 3«. J4 
" 33 10 

« « 4fi 




cbl>._v,;^ 

uilob^n 
p«r«, tud 
snof tluS 


if) and then like from the R. 
«n, Jkc. you niaft idd the con 
ndfobjoin to Ihe Time of M 
oftbeSatnof^Moon'iiiiD 
umof S'lEqnitiaiii) for the 


■wi'-xfrr, in Ma 

■trpondtntMoi 

nc TioM of 


. SiSu,.. for 

0D.tort«S.ll', 

7i», «ith in 
J«jW.rr.,I 

^nOOQ 












/ 


» 








)r: /CLl 


r.,. 





«o 






«» R T A t. 


A 


ST 


U 


t QN M E R 


















lh<7rt.»J6thSappleo«nI,IEqMlioM0flhiMQdN, (tl«6tht<. bi douUrd) /. 6., 6i .bJ 74. .nd S.nS fepHttn,, p. ,,. 




Arfmii". SUN tram the Af«.'i Apog« 1 tquUr d, at A™ , ind + Si- Sign. »i ^W/ MOON. 




^UD 1 


»,.. 




SI,. ,. 




%. .. 




Mj. 3- 




Si;. 4. 




Sig. s- 


^ 1*"* 






















— 




— 




»Ap. 









/ * 


« 1 1 




a ( a 




a / " 


f ' 






> ' « 


/ 4 




a 




a 
1 
4 
J 


16 47 


5 IS 
S JS 
5 J3 


% J8S3 

\V\ 

% S» 4* 
* 57 I" 


4 33 

:n 

4 «» 

4 IJ 
4 14 


4 »7 45 
4 1* * 
4 3»«' 

4 34 Ji 
4 j6 35 


" IS 

» 4 
I 59 

\i 

I 41 

1 J7 
I J" 
1 >S 


4 57 4* 
4 S7 »^ 
4 56 4i 
4SS I' 
4 5i »9 
4 5»^' 


oaG 
31 

37 

"41 

047 

1 4 


4 i« 

4 S 3' 
4 asS 
3 59 41 
3 S» 39 
3 51 IS 


»49 
* SJ 

» 57 

1 a 
1, 4 

3 7 
1 II 


2 19 .7 
1 I! 7 

a \ 57 


♦ »7 

4 aa 

4 ai 

:n 

4 29 - 

431 


ii 




« 


:!ri 


i,l5l 


4 40 »; 


4 51 5° 


3 so »5i 
3 47 I* 


I -'3 » 


a4 






04418 


S 1« 
S J" 

IS 


3 '4 JO 


443 58 


4 SI 4k 


J 44 1 




I 41 S« 


* SI 
4 34 

'.IS ■ 






9 


so 9 




4 i 


4 4S 3S 


4 50 4C 


'" "9 

"1 


3 40 4» 
3 37 "R 


3 a4 
3 •* 

3 33 


I 1* W 


;! 




[J 


; J,! 


3«^45 


4 48 3i 
4 45 J" 


r.i.; 


3 11 S> 
J 30 *» 


'l n h 




>9 


1 17 JO 


S »3 

S '8 
5 17 
S 1? 
S >3 


3 34 33 
3 38 " 
1 41 I 


3 47 

3 4» 

3 39 
3 34 

3 »9 


4 S' S 
4 S» 13 


si; 


4 45 '*> 
4 4J 41 


I 5* 

I 57 


3 1649 
3 »3 '4 

3 >9 36 


3 35 
1 J3 

3 4» 


;;:is 


4 4'> 
4 41 


;; 




I 2» .3 

■.Hi; 

' 44 ! 


3 45 40 
J 4» 14 
3 i»43 
3 56 6 


+ 54 '3 
4 51 5 

>! 55 S' 
4 5* 3- 


4<?' 
4 j! 33 
4 3»4t 

4 )4 44 


1 IS 54 


I '^55 

I a 13 

57 JO 

524 

48 


4 4* 

*4S 

4 4S 


•4 

>3 

la 

»o 




•1 


I S*»7 
I u 36 
3 441 
* f 43 


5 » 
S J 

s » 

s « 
4S> 
4 S4 

:s 

4 41 


4 .-37 
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4 849 
4 " 47 


3 9 

» 53 
» 47 

:;^ 


4 57 3t' 
4 57 SJ 
45J ,6 
4 S> »9 
4 5*3S 


»3 

17 
ij 
t 

i 
9 
IS 
ai 


4 30 3 

4 »j 5° 


• IJ 

1 19 
a as 
a 19 

» 11 
a 37 

a 4S 




4 4 

4 J 
4 • 

'■1 




4*7 

1*4 


1 
i 






1 19 4' 
» M 35 
»»»»4 

> ]4 10 
» 1»1J 


4 »S ' 

4»7 4 


4 5< J6 
4S»3' 
4S<»» 
4 Si 7 
4 ?7 4 


♦ 13 ** 




\l% *-!9 






4-*^ 


Dirr. 


+ 


Diff. 


+ 








+ 


, Diff. 


+ ■ 


- 


suni 

DAp. 




Sig.'n 


Sig. IG 


S<«. a. 












'" ' »>» MobN-. a-nTtTD 


In'ciIinXtION ««i REDUCTluS .. r^, ECMPTi- , :- N<» ,nd r-rMVON; '"■" 






■jp,»« 


5an'if),/)4'wfremth»MOON'.me»BNODE, or Ar^iir, em . M... .1^,.. ' 






Sic.oN. 












Sig. , «. 


■ ' 










lW«c- 








from 
Nod*. 


Si(. 6 S. 


DiA^. 


tia". 


Oiff. 


er 


Diif. 


i.i 7 s. 




i.P". 


UiH 




»ift; 




Uiff 


S-ndt 




Uiiofc, 


Lit»u'^« 


— ■■ 







« ' • 


-/ ■ ./- 


/ > 


« 






. 1" J 


/ " 


( /. 




»■ 1 .- 


/ • 






■ 






5 ■ 
V 10 j= 


5 IS 

5 IS 
J U 
J >5 
J "4 
5 >3 
J IJ 


« 14 
19 


15 

14 


5 17 10 

J '6 5h 


3 
9 
14 


» y> V- 
• 34 41 
2 39 <■ 


436 

4 »? 

4 "5 
4 1" 

4 19 


« 1 
6 .E 


s 


4 19 39 

4i» •; 
4 14 *-■ 


a 31 

a (9 
a M 


S SI 
3 41 


8 

1 
1 


50 




4 
6 


0>O Jj 


° . 


14 


?n'i 


t> 17 


*47 56 
• 5* 3" 


6 ;G 




4 M as 
4 3' ft" 


* "J 
» 9 

a 4' 
1 59 


sa*- 


9 


14 




0". 


'1' 16 ■ 










p 1* } 


" 4« 




J >4 Si 


04* 


3 4» 


**° 


4 35 S; 


4 3 




»1 


































» 


47 




» » 




J 13 »' 


f Si 

> T 


3 >S* 


4 » 

3 5« 
3 l\ 
3 51 
3 47 
MS 
3 39 
J JS 


64ft 




4 39 47 




4 37 










5» ' 


V\ 


• 49 


13 


S " »^ 




« J* 




441 31 


I 4* 

I 39 


"4 '5 


li 


:s 




JJ • 


5 II »t 

J l» i» 


3 li' 5* 
9 »« SI 


4 43 »■ 
443 
4 4; 34 






' J3 
» « 4^ 

1 »» T 


i i 

5 5 

5 3 


S »9 


'3 

IJ 


5 4 S> 


1 19 
' •S 

in 

» 4' 
1 4fi 
' (3 
I iS 


3 »4 4> 

31819 
3 3^ " 


SIS 

• 1! 




I *9 
I S3 
1 IS 
I '3 
I T 


3S' 
1 39 

1 14 


11 


>4 




J 4' 


3 SS 5; 


4 S=44 




:; 




4 37 
4 J5 

M 

4 4j 
4 41 

j;i 

«>♦ 

oir. 








3 19 »' 


















4 i 




J I 35 


3 4J 57 




• !1 




4 51 < 


aiH 




If 




"9 


f J? J 

1474 


Vii 


" 


4 5949 
4 57 (« 


J43^ 

3 S3 7 
3 S»" 


3 M 
3 i» 


^ 






" sr 
j» 

047 


a k 


"4 

13 

'4 

i^ 
'4 
'4 
»S 
IS 
'4 
<I 
'4 


11 
IP 

1 






4iS jS 




w 


' 5» J 


« i» 




4 51 %\ 


\ \ 




'41 




45641 


I 54 




»1 


I iT » 


J p 




4^1 47 




J J9 s; 








4 JT-a; 


= IS 

29 

• 44 

e ig 
9 14 

e 1 

Diff. 




9 




»4 




% 'P 




4 49 3! 




4 • n 








4 ST l' 










a *i 


s »2 

5 J* 


> 

r 


*4? (' 


% 14 
■ J» 


4 « 40 


\% 

a 44 

• 39 




Dlff 


4S*Si 
4 SB I" 
4 S9 >4 
4 19 3* 


• 14 


-J- 

6w 




4 4* » 
4 39 4) 
4 V 1 

4 14 V 


411 as 

4 '4 I* 
4 17 • 




Una.. 


s,ri-,i 


Dur. 


[ftCUHt, 

V.K.' 


Diff, 


Diir. 




Sli. 4N. 


>'■'•)!. 


, 















«rrf NAVIGATOR. 



M KMTly MOTIONS, DIAMETERS, uid PARALLAXES of tbc SUN uid MOON, inECUPSES. 
N.B. Ib Eclrpruof tbc Moon, add 6 Sigiu to tbe Arf . ,,4ini>ini, or Q ) ]) Ap, i cquitcd. 



I « 




,s 




11 




1" 




IV 




4'> 




4" 


J" 


4> 



rrbtTIMESbetwKnth 
acucA DiA.of tkcIrO 
MiihUc of [hi EclEpfc. 



Sun from 



L'uHJ' 



34 4J 
JS < 
JS S« 



Horiiont, 



31 34 

13 36 
33 36 



S| il ii 

5« to ,, 

56 JO 

i* 49 



58 47 



itt.i.Xv^\\(.C»i^aimoiOfftfitine,( ih.t%iiii ind Moon, uid thtlUiJJbi 
n. Hiifof wtkhTimo, «i.h ihe f«ne S^iu, -wiU be oWlj ihoQii 



naccbeHMcB tbt OrbitSfifgy u 



t6 16 



* 


11 


i 


to 










tt 


;; 


'3 










4» 


t6 




17 


48 



i'i 






N.B. AlmrtfMH. i !t Of : 6a M... „/r,mt ,: Rt,i„ll. 



.1 16 



i_4i 



N.B. AlmrtfMH. i !t Of : 6a M... „fT,wti: Rtii-ll.n „ E,lit,k m 
w«r«> tU Redugimhm, EiLpiU C«r>..?,« «• f^/«j((;« « J^U> ./ Ey»/i , 



i^l 



•4. ' s« 



I it 



clifiK i» Ml*, tad S41. tfD^.. I 



^ 



lii 



I" -•- 



*.. «rf irt, «/ TiW. jhif rh 









Thi ROYAL ASTROJNOMER 



•» n 

l4 iJ 

fa n 



Tnit *«Br/r MOTIOH of the MOON 



t^TtaCi- 
plniKst of 

theft AdbIci 
(0 90* Ibewt 
'ttc Jbgia thit 
[he Wa; of the 
Moon frai 



84 j6 
*4 »9 



xith 



84 
8« 36 



EZAMPU.I. 7»/i»Jthima»Timi»fibtmiMiiJinuOiiilli%wKoiijifiTlbiMmb'fHfj, ialht t,lpkrctraimmU/TiCb>iftt 

Bj thsNituiyarCu!#nieiH«r tbcr«i/(i, t Yni eiirrtnt bofoK Oi^U repideiiteil by O, 101 }xfon Chri/I, by 100. in the Tablet, ff.. 
ueh current Yur bcJbie Cbrill by i liji in tht Tabla, ■■ wc hare naticed in our fttregoing InproveinenU of Chrooology ; eonfe^uenUy ibe 
jg^ChYtarcurrentbcfonClirifliinprelentedby 584111 xYMtttla. And, fince jil^ before, +i7iGGnce Chilli = 13 compleie &vi 

or 1300 Yuri, bj tbt Tablei, fiom Ihc Beginnii^ nf the jSjth YcM coitcnl bef»"'^'',jB .n .k. a.^n..;«. ^ •>.. ...1.1. v 

Goct Ouifi. ThocfM, by r.i. P. jSj. 



lotbe Bc|iiuiiD| of Ihi lyiGtb Yeai 



XWb, *e. 
i7i6liiKeChc.O.S. Jin. 
Sab.i]o6 YiiMn. 



BfT*. P.jffo, Jilt. N. 

V JutiiTimtm f^i „ , 
ftt « £W M lit Bmii tbtn J^fltfKi ttt^ 




s—iyijf. 



Eg. Sun 



43 



SnJQ. 



Ef*mi**t tf lit Mum tulri tuur^ 



I Equal. P. 61. 
6Eqwlt. doubJeil, P. 74. 
.UN.tadF. >,? 
590. . ■ - J 






41 



J ,48 5» 

TmeSunia. 1 'q 

So, the Sur'i ec 
ipMLimiM.tbetef 
ihc O " thltTinei 
greatly ecliplcd. 
bcin<o]Yeubtr.Chr. Maj it, 8<> 31 



1 + 


814 


+ 


9>8 
• 4! 


D.+ 


7 4J 

57 


,..tf, 



Fercooon, fttaAir-Meri^uO >t Tn 



ElBffi tf lit Sum tuMiwH/, itti ,.,-,. 
m jf^»t ttlivHK iht Medei aud True Arg. of 
l.ydiaol,*Ji«iUcii'ia«aVi«A— '>^'i"E<:'>Ff<)i*PP«"<>i<x"'t liJ^i ' 
» Hoon Uln at the Meiicliln where the Battle w»» foogbl, f— 
DCtitbeltiTer fifi^t, the Boundary betwixt Afn^ii and LyiQa, 
iik>41uMiiMr,intire4.thTearofthe4Sth OAn^aJ, accordioj 
to»n<te>i,upRdi£lad(>yTi«&i, ol Mi&as, ar SarJii '^ 
jifit. -~ But Rrpiflm't Jlfir. P. iflS, wilt have tfaii Eeli|il 
Iboner. TheSonwaithen ibow 4 Degrm from the Ma 

rbiDmmtalLmtnfathn rtsr (Bipniile) inrgFE, vtrJiivH T^tt^fO^mthp, P. 148, May aS, in tbi it^ibTfr 
Ckifi, ittJln — m/bitiltii Br/rf^lnffmJ tea- in a Wtiotaif. Im totiti Tar ibt CjA tf tin 5» 1M1 I}, Gi^da Krmtv 6, 
iiait*^\ iti*ti'il' ^t%g>i Tar •fibi]aV\taetr!id. And 1716, Gncc Chrift, being In ttke tflgth Ybu oftheJv/Ma PnW, the DiAbtace 
iwoYeenafcrilaidi 

IT.. „- .„_-... ,~__.._j «_. 1 -...-.I.. _B.L .* w_ ..i-u J.T. --,..r- 1. J •-■---- «W«, inflead 

«■*,.> Arit 
0- It, D^'uni 
,. _^. . „ . . .^. ■" iwEeli^ii 

(be jlfth Yieu cuntnc betee Chrilt, on ACn iB, vthen t!iRDomiD>c)1 Letter wu O and Cyeie of Sun it, (hii Rnle, P- *4>> Ctmpad.jt/I, 
br talinttbeSon'iC^Jf, not true) lb it mti ft' be on the atlh of Mbj, in the jgitb Year current, bafMVCbrid, eB.xWwi»ildiij, accordln. 
Do JVnf ■»*> ClKDDolqy) when thri EtHpfe hajiKned { at the Cm/iwWim prove* above i and ai hji own Comoatilian prora ('A J40. Cm^T 
i«Jr J of i«o Yeen compleled back from M^ I. ijjfi, fincc ChiiS, toM^ i, jSj, before ChTiftj who hai the fame HiDaiCe. P. - 

fcr the litb of Jl^^^> ■■> ^« S'li V«*'' *'/'" '^s'- 



\idiyf the Dominical LcKcn BA [thoDfhnot Letf .l^t)l 
Lm^ <*»■> W Haeii alfUiri^itpaatijht&iEihiatibCtmitrj, P. 3<t I 



Digitized by 



Googfr* 



and N A V I G A TO R. 



393 



EXAMPLE II. To find the true PlacM of the I'm ud ATim it the Time of (he iate|Miig Eclipfi of the Sn,. Mcordtni to Ae Mooo'i 
Oibit-Conianflion ? , , . , . , ^. ,„ ,, , 

RULE. (W-f( '** 5b«'i ^^j< « !■*< TIiDt iflUmumwrK Mt; and mojibl lb, Uhtrmun Plact,, >^«»£, » K*« Tiw, Ttasiitb, 
Uijff Mifofiu '• tl" EqiuBon of Time, i/ riar miii ( or /aiwwfl, (/ ihn fuiiraBi f /« ri* mmh Picu, 
Suii'tApoE«»ndAiiom»ljfoi theSun'i nw»nPlice, /nmi which tikiog theflmfi fi^*. aiulSinfit 
FlaiBlJliiMlim'tjtfttuiadNixii. AiJlbtSiai ilUm'ijIftglr adJiduMs "" ' 



jffigitaid 

(j^iM maiSid wilt til 



, h!f,rtfi^ 

The METHOD of COMPUTATION below u 



I7tf Gnce Cb. M^ 18 
»»o Y»ui Motion — 
j!5lief.Ch.M5»8'l7 

Aiidfor It* . . . '. 
EijMtiaoi. { M. i]S.>] 
jgj, M^ i!* 4" o" 3»» 
Pull, — 1 »i 



it 1 59 II 
Coma meui 
Time of ihe Nra 
MoBi, leqaind, or 
Oibil-CoBJunaioa. 



Sun't M. An. 
Sun'.Ap. + 
Son'i U. Place 



i Jul wDVfi'w rb M» 
nm'i inu Plaa. Tbi S 

irely NEW. 



i», (I r^ Tii 

«b imSjrxjn. Tlien idd the 
■ Nfde, ihtrt vlll rmti* thi 
>. The S*m if lobub lai 
act tail badfrm tbt Sim't 



Ap.8 ij s» J6 



Aig. 6 Eqi. P. 74, 

'i E * ^al 
CoDJunAion, = i> 
1 be dedufted. 



O I 



[Arg. jIUc. 
lEq.P. 61 . . +0 
6 Eq. doubled, P. 74. ~ o 
Eq. It New and FnU — I 



PROPOSITION. 



,f1m 



Sum *f ite Mcurn't EaUnivu m Sjiygin (mirflcJ^ii currtf^ 5ijii nrirdii £■■*! Ejntuiim, mni ill prtftr Sign, vu'Hitlit Dljll 
ifH/fy, It man Mtiiai, iflhi MtK/rai it* Sn, fa ibii Sidt, tr irftiKi, ■ rru ConjunftiDn sr OppoCtkin g/ ibi Su* aiJMxm,/ 



DEMONSTRATION, I^t J i 

or Orpofi[ion of the Maeti ioA 5™. 
Efttiiv, ami ± M denoie tl 



IQrtpi 



rfent the Sua 
) will be the I 
jn-i EqoMion 



n'l mein Placei, refpedlTcly, at the Tine of a trae Orbii-Conj 
_ bnce of ihe Moon from the Sun at ihat Time, Let ± S denote tl 

if iheMoon'i Equation!, il the Tin» of a mean Srcj^^. Arnv becaufe there it but /iw^ Difin 
for the Son and Moon't mean Placei, it the Time of a mean and (rue Siaygy (efperially when the Interval ia linall.) 
t( ±Mmin. 0±S = o, or 6 Signi, bbu-Ji it the tiue Syiygy. CuKJi^amily, MeinDinancf = J — Oi=±3^M + 
by Tranfpifiitn. Thai ii, ihe mean Difltnu of the Moon from the Sun, at the rmr Syiygy neatly = Sum of, the Sun't Equation 
S, with its ptoeerSign, and the Moon') Equation M, vith * tarirtrj Sita, + o> 01 6 5i£U, at mean Conjiui£tjon ot OppoBtion, RlpeOiTely. 
[Iierefore, ihatSeareduad to 7i>»> iamcan Motion of the Moonfioro tbeSun, reckoned fiom o. Or G* ^ from Q it iheaein SyxjrEyj 
il ofTimeaAMordtalbfWto or from Ihe Time* of mean Sjxjgj, accotdioe aithe Moon '1 true Place iilhoit of, or beyond, the 



Theterote 






lePlice.-otiiiOppofiie, as the Sign oFthofe Equationa inoooSura direSj, will ^ve the lacin Tfw t/'iiv rriif fyztfji, req 
AndiheiBsrcneitly ibe/f/i itt IiUrrval htpfCat to U{ bccaufe then the Moon and Sua'i Equationa at mean in! me Syj 



Q. E.D. 
If greater Atararj be r 
, :rue Sy^,%3, and the Dif- 
luf Ihe Moon from theSun, 
I foimer, taken fri 



iygy ire the 



ed, the Equitioni of the ^arfi and Mim may be again found from the Argumenii to Ihe laft near Time of the 
between the Sum of thore, and the Sum of Che former Equationi liken, and reduced to Time, in Motioi 
I addti to, 01 JvbduStd from the lal) near Time, according u tlie Sign of the DiHcrence of the Sum of thr 
lie Sumo!' the latter of thore Equiijooi, <ire£ti, will give thenrnAv Time of the inie S/s;^, and To od. Or Che Sun 
CI may be found to the nwly imeSyxjgji, iod tht Diftrtna of thofe Placet, reduced to Time, io mean Motian ]) ti. 
id added to, or fubtrafledfrom, the Time of the nearly true SyKy|^, according at the Moon't true Place it j<£iin/ or f(^rt the Suo'i 
will give iho ttrrefltr Time, required. 



PRECEPTS for fioding ihe TIMES ind PLACES of ORBIT NEW &nd PULL MOONS. 

TO/x^titwMiTIME •flbt ,ariy uiu ORBIT CONJUNCTION «r OPPOSITION tf tbf SUN «u/ MOON f 
FromTsU, (P. 3S5) of Che lil'meinJVrro Af«« in ^auMr;, according Co Sjitf AyA, eoUeA the Dayt, and Putt of 1 Diy, ufwiting to 
e y«r iDd Month (talcini out a Day /(/i In Leap-year after f'r^Ti'ani; and colled alio the Di^tei and Porri of 1 Degree of the Sun't {neu 
nomily, niein Diftance of the Sun frnm the Moon't j^fw, and Ntdt\ which are the fame /or Lop ai for common Yeart. Or, if the 
Time of the iK« following or foregoing Fu//Mkiii, in any Month, ia reqUred, you matt add 01 fuitrtB, to or from ihe Time, and PUcei, 
f the mean IVro Afcgi, lefpefllvely, the Time and Motion for Half a ^'wfr»/ Month, Co befoun) at tneBoctou of the Monthl. 

TroiaTaili, I. Equiilon J), (P. 61 and 61I take out the Eqoationi of the Mm, Apegn, and iW', «nfwering to the ^m'l ibmb yftwwfc, 
'hich iWply to the former Placea, with a unirtry Sign to that direfled in the TMii, •nd yon vrill h»iT ths «un'« Dliiance f^om the jtftvit 
nd NtAi, once equated. Add to thefe, or (uhttifl therefrom, {according to iu Title) tint Sui'i Efialiin, and you will haie the true Dirt. © 
Ifrom » 'a' Apogee, and true Dlft. Q from H I. equa'ed. 

The nnan DiAance of Ihe Sun from tbe Moon'i Apogee i equated, being fublrafted from the Sun'i mean Anomaly, the Rauindtr will be 
tboArBUmontof the VI. Equation >/ffa»««/, P. 74, xt Nrv lUtH; bat at Tall Mam, ihit Artoment, and ilfu that of the Sun from the 
Moon'a Apogee, for«he leaii*! Eqaationin Sji^ypa, mull be increafcd by 6 SigMimldidnHitbi becaufe the Arj, 6 Equal, it O^ofitian, =1 
D i O + B Ap-'— G Ap. = 6» + 5 Ap. — ©Ap. And Atg, ttmiriil Equation, at Oppofition, s; J Anom. + 6 Signt ^ ©from 
J>', Ap.+6Signi. 

In P. 61 and 6x, find iff, or anattal Equation ef tbe Moon, with t tnurtrj Sign, iccordingtci the Snu'i mean Anoinily, In P. 74, fkA 6. 
Eautif^ fufflauititl, anfweriiag to tbe praper Argument ; which Eqoation }ou ntnit Jmili, andconncfl iCi tatrarj Sign. In V.^go, find the 
central Equation, at Nrtii or Full, from iti proper Argument, with ■ nwrery Sicn, the Sum of thefe 3 Equitioni with their conCraty Sign, (r' 
Khich amouitit to the fame Thing, tbe Sum of chefe ] prapa knar EquMioni with ■ aararj Si|n) comicfteil with che EfaMia tf li, Sr. 
Tenrtr [which joumnfiilfo find) wich itipnfiT Sign, will gire the mean Diftiiire of tbe Moon from the Sun, vay nearly, at 1 true Conjuofti 
>r Dppofrtion 1 which, reduced to Time, [by Tai. P. 389, of H. Mot. D 6. Q) vrljl be nsvl; tbe tru Efnatm »f wan Timt, miiit ii'fr,ftr 
iigH, for tlie /iW(r«a/of Time, to be added to, or fubtraSed from, the Time of chemean Kfvi or FallMooa, it t> or 6 Signt mean Dilt,!) i 
^, for the mean Time of che neirly true OibiC Conjuoaion or Oppofition. rifiund. 



• ImF. AS Hilley'i^fnn. Taila, hii Fnafi-mil. 
•Tiim*. in mHuHn. ]) /©) IHtiTimi " ' 
t »f liitrmSjr/fi frtuMifgibtmi 



fpba Itti 



S7»jgyi 



rEquitiu 



id Sam tf ibi Moon'i Equitiona, (rcimad 






39^ 



fbt ROYAL ASTRONOMER 



PRECBPTS for fiodiog the TIMES and PLACES of ORBIT NEW aad FULL MOONS. 






id her Ptacc in tbe Zcliplic^ bj X 



The Place of tU fj fabtnaeJ irem the Son'itnit Pli«, in Conjnnaii 

theMoon'iUuiod*, in5;«xr"i bj which, and T-S. P. 390, the J 
fiom bn Orbit-PU«. both whith Orbit and Ecliptic Pli«« in tbtSjxjgH 

BuCtbcTime brtwecn Ecliptic ConjunJhon or Oppoficion, and Ote Middle of Eclipft*, ii&MoibjTti. P. ^gi. Half of whidi Tape u t|t 
Diffireacebetwetn an OtbitSy.jw and Middle o/aaEclipfe. • 

Tb Jiurmimiln Sm mJ Mm*' • Irue PLACES, nrri^tmliiil It lit 



«r,mo/tt<martr Inu Ortii CONJUNCTION a/ OPPOSITION ? 



Compute the Sdd'i Apogee rfrotnTo^d at the BeginnJnKof thii ^ir*; to the Time of the mean ATmr or rs// Moo 
neap Placet alreadj found to that Time ; with ill which Placet^ {of Sun'i M. Anom. Sun from i, 



it refpefli^f 

"lenAUth 
>om Moa 
>m Q, will B've t 
e t/^Ihe Moon io 



ot6>] coDoeQ th 
.. the fn^Sign. Then *Uthe Sun'i Apogee j 
Apogee, and alfo Sun from Moan'i 8, (bsre will re 
Apogee, added to Jl from (Tf, will B've tbe Mkh'i - 



./71«, t 



and aonn the other 

Ap- and Q, and Moan fnnn Sna, 

leirly true Orhic Sj^gf, acmdiDg 

<m. ]) , for the Sun'i mean Place, from which talcing the Sua from the Moon'i 

iwaa Placet of tbe Moon'i Apogee and Node, An* the Sub fr<im the Mooo'i 

ilj. The Sum of which Moon'i Anomaly, and Hooa'i Apogee (itfrr Jtmad) 

Place of the Moon ia her Oi-*ir, with which if you now conneft hei fn^rr Eqaatiooa 1, 6, ind the «nliil in Sjjypti, 

Iten out from the tmeorequitedAigumeBU, (inP. 61,74, and 390) jou will haw the Moon'i nealymitPUce in her Orbii, 
Tbe Sun'i Irnt Plact being here alfo had from the EquuioB of hie Center, the Diftuce of the Moon'* fnni the Sud'i true Place, i. t. ibc 
Remainder after thtSuniiultenfromtheMoon'tPlaee (beingi /w//.,*!-; turned into Tim* (by Ta*. wrJn JMjr. \, i Gj) and aJJtJ to 
ir /.*ir«a(J from the former Time nf the Orbit ^iey^y, according «• the Moos't tnie Plan it, by the Leaglh of that Ate, iMnJmitfifiibe 
Sun'i PUce, willgiTethets/i'aflrrT'imof the Ottit S^e»m, required, 
r- ..... ,jf,;„_ V Full Mi<", y" mtfi iM t Sii<uiiihi Smh fioKtbi Mibii'i Afii£H, fi,ribi Jrgtmai if ih MkiTi ciuril Epuitu 



tt. A /■ Orhit Opfsfisim, er full Mici, yiiu mtfl rid 6 iif « /o Ibt Stn Jrtm tbt Mum 1 A 
a Ibal Tim, ; mmiaffiS Sip, mufl U addU /or <l» Jn^mal =f iht 6. Ef«aluM, in Off^i«, 



S.EMARK. In Dt. Hel/a't Afumulffiii Tai/«, for compHiiog the ^Ifm'i Placi, at her Oi.V-Conjunflio 
mmon Tableute not left eipeditioui) the zft or aiauel Efuaii<m of the Moon,' Apogee, anJ 3, being 
loan') mmn Motion, Apogee, and B, anfwering 10 the Sun'i ««» A»m^. 
And in Imitation of Dr. Hallff, we hue alfo ai u(efully compounded the ift fimiaitiuial Zjuarlon of the Mnon, with the Moon'i mtnl 
pationinffwio} having both the fame ylr{. nwiM. (See P. 390) Which iM<>-«/£i]iutian iicomputed by fioding the mean from Ihi 
Domilyof the Moon, and talcing Iheii Difference. 



iw tuai if itc mttii tnJ imrffir 



<NneM, 



I, tr Orbh-CmJMHaiim, in (** Af«.i -/ Aoril 1764, fi^ieClnf 



EXAMPLE III. Tejindlbm 

New Siyle » 

r*- II Dayimufteithei beadded to theDay of OM57&, injannary, for the Day of A'nci Sif /r, eorrefponilent, among the j;#,i«j 
Month muft be folalien, that when 11 Daji are added to itfDiyi cocrefponding, the Sum may come out in jfjinl, or ihc Month wh 

New or Full Moon ii rtfuind, the •iterijl pofiWe to the _firjl Day of ihtt Month. 



By P.iSc- i764r.ii.Ch.O.S. 

Bir.r{A.[addingiiD')fl«r 



M. Time OrHi N. J, Jfrl!, 
1764, N. S. rifmr.J. 

Aicording to Ffju/ta'i j^'. 



,am.H. J> 



,'iM.A 



Sy i JMIhi'j Af. 



Si«ia. 



4 14 »| 



Eijuir. l),P.6i.+o" 

Eq.d^*W,P,74. + o 
Ei;.atA'.li,P. . — i 






t/ rht >«»» enT4 at- 



in'i Eqiiit. P. ta. -f- I 
i0,inSyi>gy. I + 



EXAT^Ptt IV. 7>/hidlUt»aOrtiiPl. 
larh ina ConjunAloo i 

Son-. At>iit. 

I7«4, Mar<b\U N.S- 

Add for Eq. M. ;5 S. ■ 



[764,-^. 0* a 



•/ ibt Sun lid Mood, . 
Sun'i M. Am 



the Sun tc'-ipjid confi. 



( Ac TImi ef fi, fwigiiii Eclipfe «/" 1*1 3up, aotrjing u iht Mm 
Snn i {}. 
o S 34 57 



sotE4.Ap.+ ig 59 



9 it 10 

Afg. 6. tif 



*9 



1 7 3J » 

[ArB.l)*.L«t. 

!>. prop. P. «i. 

«UE4.JttM<P-T4- 

Cent. Eq. atN. ]). 



4» 44l>'iM.Pl. 

-II 4« 

- 4 "B 



gr^ l/ynifiiidtbfS'aaaiiJMooB'4iTtHPiiialfJl»TimtfaHdaSjiysj, *<u[rtJitttwl>MthiK<>on nturttf, tr h^md, tCi^nBiUwOf. 
j^$i\s!iim Time, i<tmumM.tt, } J0> thmtlni'limit^l aJJid it tr'jiiitr»at4 film lit Timi ^-witrSfrny, iiwiBgimyni mtHftb^^im 

^ " " ' EXAMPLE 



and NAVIGATOR. 



SX AMPLE V. Tofindt** 
1764. 



Mild OppoGtioo, Afril 
Eq. bft. M. mil) Irae Oppn 

M. Tim: Imc OppoEttoa,^. 
1764, N, S. required , , 

AetordiDB to Ftrgafiin'i ^, 
P. 199 



■.J Apr 
'39 J 



gr Futl Mood, in ibi lUonib s^April, 1764 ? 



S46 }4 



Arf.ti.EqDit. P. 

74. at Full ). 



tilbt^an, fjlitmaiia tte Samara/; ciamgrug ibi Sigi, 
aiit lit EfuMiutf lit Sub' I Cmrir, fit ihi mat Difi. £ iQ, 
nit iMrmiim* Tiim, and xftd at aMv, otuaBid, in iiifrifir 



Q^q- +r . , 44- 57 



S 34 S7 



I c/ rii XfiM wifi ten- 
. ]),1>. 61 +oO|i'i9' 

rob'', P. 74. — O I 14 

Ccn£ii.»tFiifl,p. 390+0 30 5 



the (3, here hifpent 
noBclipfe of tbe ]), 
u near the ep^Gu 



•WEqmt, I 



,6t 



3 8 49 M 

By 7i*. p' 389 



w iht T\iiu sftbi finguMg m 



Ejtai. M/KvTM/'of Time, .f. 
« Oriit OppoGtuMi tftbiSwMtad lUn t 



* 1 £ but + 6> It Fall Mood. 



5 a4 o . 
Arg.cnt.Eq«l. 

fn// Moon. 



iS 48 



[Ar|, Lat 
I Eqnit. J . . . 

6 Eq. S doubM 
Eq.Centciit Full 

True Orb. PL p 
Moon' I Lit. 
Sun ■ D Ap. 



1716 finitChiiji, 
1300 Yrart UotioD — 
5lf brf. fir. current 
«:«;<rdf. ACoi.M. Mat.P.3;4. 
CorreOid . 
May . 



[n 58 i:, M. 



7''44' 3" 



fli; 



finnnin ijoo Yctrt Juliii 



.. 10 It' jK 

o i< a 31 



I 6 It »7 
lAp. + 1 18 10* 



(r> To iirbV£ Tinu lit 5n mj 3i™'i imtFUut may i, ctmfnuJ, i h BxtB^b II. 
Rf<6n;. })MEiliftic, iyreh. F.-^gx. JntTagiti • and" far ll£<i. mdSu.Mtt.Ti 



sbd i a. 



. Eg, a con. — 7 



Tme Snn from Node, 
grutlj etlipfed. 



B; thit Mubid* thejiatlirf 



Brginl of ia)r Yni, fin.Clir, 
AcceL Ap. (nd 8 conHfiid 
[wilb 1 atOrarj Sign, 

The Mot. of-Sun'iM.An. 
San a } Ap. and {J an tddid 
hTDl.llr,:mir.^e. Hb 
DsyiaS, n>. 0, Af.sf, 5.10. 
Mean Placet corrcfpondtnl 
EjumtUus 9f Moan iibu 
lEq, pprop.P.fii.+o" 0*10* 
SEq. Jdoob.I'.74.— o "l 4 
Cea.Eq.N. >p.39Q — _ i 1 4; 
f. .. Sbh,-! ti7 
»•. B,u,t. — o I j6 

■i- Sig. B Eq. > 

changed, Suml+i i i 
Mean Oift. ]) a Sun, in Syiigj, 

JW01.0, &r.^ . . . . 4 
SfiMT, or llaomi/or^uDe; -f , 



,y Google 



39« 



til ROYAL ASTR^ONOMER 



lilFiTpfm'lAftrettBmy, (ind ilfo ia * JVns fFH-ib(wiaghiiKiuiieiiK hinlccD itCheOUcrTMorfiit Crunn'ct, \a ^UmtfiTif^, cmnimiii 
tbt Timet «t MMtitlEtSf fa, irfemAloDr. Br^iy'tinCfrSiomniAfprabttioa) «i find * >hijd' Method lo tbit ibon, ferdctmiDiBi tb< 
Time af tlie man ind true Orbit Conjunftion ind OppolidoD of the Son did Moon. But Ihii Autha (irrimtfy) timchc Sum of [he 



1664 fincc Cir. O, S. 
4-I0O Yetn Mot. . . 
Mtftt 



N r<Mi, P. jSS uid ]t9. 

'iM. Aoon. SuiMMs'iAp, 

*! -11 



r" 



>[g,6.£q. P.7 



Arg, Ceol. £q. at Ful 



[| Sun'tl 



II ij 17 16 
I'm* SuD a Nod*. 
Where Moon 7° from 
>ppo£u {3. ThuE' 
Tote } icAjt/W beii^ 
b/ithiaifaO- 



Or^tfi, Uoiioai 



Miiaaa 17, £«nn^4a 

P^fi oornTpoDd. la } iSmi^i 

I E^oat. S, P. 61, -^ o«ii'3 
6 E^. donUed. P. 74. 4- o 43 
Cent, El. } ■( Full — «»jj 



Siui'i Equn 



4-£I|.SEi.chaiigcd^nr4-4 ». 47 
Mean Dill. Moon i. Son, in Srzin. 






lirx &iMr BnMin Taila atJ Si 

mi ud Eiliffa, aifollowi. 
AoTtTug - Ferpiro 



of the Son and Moon. 

the San'i Eauation with iufro^Sign, leduced 

Efnaiim 7ailt, litre riin-id n ^imi. tvima) iatttii of redu 

intaa Motion of the Mna frtm itr Smu. Who therefore ii 



1761 XCfT 4 S 4 New Moon, 

tt i« 24 Full Moon. 

I7E4 Mtrtb 31 » 15 ticw Moooi 

^il I 10 li Eflipfe. 

4frU 15 10 j6 Pull Moon. 

. itoi AUrii ij g I] Man New, 

^t^M^rtb g 10 19 NewMooni 

jal Marth i 7 36 Full Moon. 



,a<ur£-[ M De la Caille't utBnrnmj. 
*^ 4' s"" J7* <■' _Nf" Moon. 



Afrilt. 



> J7« C New Moon. 1 , , 

.1 o Foil Moon. jEtL Jj",'?* 

19 51 Ne«M«B. iMenHui 

jS o Full Moon. J «"'*■ 



«? i: 0^- 



If Dr. BnUtj bti —1 ituBid iht ffrgarg Mijiaki im Ja^mm, 
•ifirvt if, ibl Mr. Fergufon'i Cn^ualiau, priti»l, gr li SJt- 

Hr. fapijm deduQ) a Day In lui ] and 4th Eiui^'a aboie | tfaoagh he propofei to avoid that Imsmaiinai, bj be^nning hii Compo- 
t Manb, infleadof ymmiarj, where the<r will admit of it ; which appear no Advantage to ui j but rathet the Eontrary. — He fm, 
of hit Aflnnom^ " Oar Savitar «<i itrti ia a hi^ }«tr," though the ift Yeat tarrral of Cbtift (at the Beginning of which out 

ml born] witcbe ifl Year after Leap- Year, or afta the Leip Year which wa* thciflmient beforeChrillg oi whrii i Vearditeaed 

bo be deduced out of the Vesn befoacChiill (bcfcit a Di(i6on of the ReBuindar bj 4) tothew the 1, a, 3, 01 o Year Gnce Lcap.Year, or 
' ' Bifleitik) acxordint ai 3, a, t, or o, nmuoi } 



PRECEPTS for ficdiog the TIMES and PLACES of EcUptic NEW aad FULL MOONS. 

rtfiadlbi mam TlM^cf lb, irai Ecnftii* CONJUNCTION «■ OPPOSITION ./ lU SUN aaJ MOON t 



KULE. To the mean Time of a 
Moon'a true PUcei, in the Ecliptic. 
Moon iidifcoTCred. If tbey differ, 
tr afar lU Tiau, for which you ha»i 
Edipti 



thalof a nearly true Mw or FatfMoon (fbanl bj the foregoing flulei} compote the Su and 
And if thejace era.?^ the fame, ot oppofite, (vibich JtUambefUia} the Time of the true A'rv or JU 
lOte that Difftraa, and compute, again, the Sun and Uoon'i Placet in the Ecliptic, for an Htmt hifmt 
their Placet ahead j compoted j whrnbj jroa vrill gain the tnie iwr^ Motion of the Moon ficoi ihcSoi 

bi Mean film lb, Sm 1 11 tat Hmr tr 60m af Tmt ti fi U tb, Di/laaa rf li, Ki»a fin, It, Sa. m, 

^ 'iJ'BBK,,/ibarPlaaiiefirtii,l«l} ; Itlbtlottrw^-rfTimittBiHaibtmaa, m^aiar liJ^HtKevir..^ 

KfgfM. which Time Ixing o^i'lo, ot frinvClfdSmm, the Time of the mean, or neariy trae Coajanftlon or Oppo6tton, according ai tk 
"Mn't computed Place ii fliort of, or beyosd theSnu'i coropotsd Place, or In Oppolite, at diat Time, and jfou will have the mean ~ 

'irly) of fhernKEtlipticConjanOion or Oppofitian of the JSaii and JMen, ft^mred, , When grcatei £xa5iir/i hwantid, compBleafi 
Sun and Uoon'a true Plicei to the lafl found Time of ConjnnAioa and Oppolitioa, and if the) are pctdlelf tba laaie, or opfii£^ ym 
fOurDe&ej if otheiwile, ; icportion for tha Diffeiesc*, to get the exaft Time of Ectiplic Coigiuiaiaa «r Ofpofition. 



d by Google 



mnd NAVIGATOR. 



PRECEPTS for finding th« TIMES xxA PLACES of EcUpdc NEW and FULL MOONS. 



EXAMPLE XI. ttfinitbtS— aai Uttm'! ma Plia, tlitir 
EcCtfiic Offifbi«., ('■ lb, r,mr X764, Mtnb I7<l \\^ 5]>> imartf. Set 
EntnplcVin. P. 396. 

Sdh'i tnie Plice It tbit Time bj fiift TaAAi , . lt>«TOj)' 5S" 
Mooo'itnic PUce bj 1, %, g, ia,Mai 11 BfUt. C S *7 i' 4' 



S *9 4+ 4' 

II 17 jfi »7 
S «! 16 n 



Moon i Sua M ihtt Tinw , • 

MMa piftin Oppofition or£> ..,,.,. 
Houily Moiioaaf cheSua .... 

HouiIt Motion of ihc Moan . < , . . 
Hourlj Motion of the Mood a San 

S«y 3s' 10* 11 6o" 1: 15* !»■ 
A£>r(A 17* I 

HeaM, the tr.£cA/KieC»;. will be 1764, Jlfar. 17' (1 

BfM. £>(£tC*;7Zf')£phc[n. 1764, M^r. 



37 49 

3S »* 
■ »5" 49' 



ik iS=49i 



EXAMPLE X. 7i jW ibt fingMig Ediptk Oppofition •/■ _. 
Stu *iiJ Mptn, MMuch 17, ^ ri< SvppleoujiMl EquatioD T>bJe> 

J, o/M-.M»yer, P. 97, »i. 
Siio'itnie Pl«ce, 1764, Mar, ij* lib jjm, «i before, 

]| u.EdiplicPI. by 1,11, II, 13,10(14 E;. JUTS', 

Moon J San at thit Time 
Short of Ecliptic Oppofitioo or 6 Sipu hf 
San'i ttne Plice for en Hmir litei u bEfore 
Mnon'i tnie Plice f<a tluc Time , . , 



J <9 4> I 



MooB pilt OppoCtioaoifii . . 
Houriy Motioa of Oie Sun . 
Hotulr Motion of the Moon . 
Hourly Motion of tb* Moon t Sun 



S»r3i'i' 1 6o» :: 11' .o- 1 19" S9' 

Jtfri-fi I7< lib j3 o + 



Ecliptic 10 4] Dif. 
^ Thi Timt a/ ibh Ecliptic Offtfiim ^ lb, Sm» rnnf Mm m^ i. 
,lftmm»itrljamfiittdbyefiii[alliA. Mijer't i^. ToWs, P. 97, Wi 



TO ^«nMMf ffo NUMBER ^ECLIPSES utm^ YEAR, ai:d on inhal OkYS »f ibtYAOSTli tbij bafptwf 

^jT^A, P. 385, t*ke outtbe PUce of the Son from tb< Node hr the Beginaingind Month-da; of uj Year in the iStb Omirj, 
yoo BU7 lednce 10 the Beginaiog ood MoDlh-daji of (ot otber Yor, in imaH Century, bj a<Uin[ at lU^ahg ibe Diyi ' -- - 



■ndPli 



. . Motion of the 

if the Sun from tbe Nod*. Then a^ 

Node, at Nmi and Full, come within the 



Limil, of a filtr or /wutr Ediple, for la maov Mooch] at poffible, (which ia done by Inrpeflion of Motion of Sun ftoa Node) 

iSo Sun from Node; at Nov ; and 11°, at FmS Moon. 

i en nhtf D^Hb^ t^ifa in ttmtT,*r f 

All the ECLIPSES that tm happen, ia ]7<4. 



1764 3-". 



AU I 



» 59 
•44 J 



4 14 »9 
o 40 14 



j^ain, O. S. 1764, 'Itmafj 1 

N.S. ... Add I 

,.4^^, BilT. 1 



o 4 14 49 
% 5 .1 SI 



Moon too >^( of South Node. fcA/^ Ji. I. 
Son 50} ^JfN. Node. £cA>/< Sun. II. 

. t:^ jnntbiSimfhmlhiMitM', NkU U jufl wUbnt, f iittr lit Lim'm if 

felarir-lKiiarEeliffi, nmmuft atimint til QramfiMncti cl^iljuntijmljfwra 
EJifft. 



SuD94^/S.Node. £(%VSiia. IV. 
Moon Go jfcm of S. Node. ItHffi ]). III. 



PRECEPTS for compodiig ECLIPSES of the SUN ud MOON. 
WHAT AN ECLIPSE OP THE MOON IS: 

M dark Saiiit, itiMr t/fafal 1, ibt Sm, cafi a StsJpv MiMdlbm, hii^Bafti*[ lit Sun'iS^i, nd biaJainfib, iffafit Spa,, frim hin 
tanibltmJ, jbi tb, tartb, iiiif m dirk BtJy, ajit a SbaJm imt lb, SUmu ^f^i it tbt Sun, wbirmi if lb, Mttx fiaU emu, i* Iw Cttrjt 
ibnuibbirOrhii.PimifiUd^nvidif lUSmi Ugbfai hi Jt Ji/pthfid frm aUibtm-i lU EarA, ig RijUftim if bir bti-reni,d Liglt, at 
le tccafimibei Appearance vbiib ;i catUdax Edipfe of the Moon, 



ibai Sfoa tier, tr Itfi, Miadimg m lb, Plaa i. 



\t Spta iiibicb 
, r/biutb,'Rayinmh£fnmfim,Pana/bilBtdjet 
ir It trJimiirfiKiiIbi lilaJfy Jttk Sbadttai IHifftitlff dark SbeJra it 1 



,, Google 



398 TAfROYALASTRpNOMER 

PRECEPTS for compntiot ECLIPSES of the S U N and H O O N. 



TOcM^MfMECLIPSEf/rfc MOONj 
-...ifrt. AtlbeTiDw of trnc OppoGtinn ef tbc San *nd Moan 
(hvdat iifinj tnA (he jingle vbici lit /Fh t/ itt Mm frtm ibi 
StwmttnwBitCirdf tf Ltindi (tj Tai. P. rf) fnm the Argi- 
nnit of Ltilnir, ind baud; Motioa of ibc Moon tioin the Sun. 
Thing /ijr, 

Ai itW. : S.Moh'xLsi. :: S. falJ ^ Mpu i Sim i S. man/I 
Affniaik if Ibt Ceniri^ ihi Mini aai Earth-i SbmJm. 

Pnr. 1. From the Tiblc (P, 391J of ihi bimrly MmrnnmiSim- 
£amtifi tf rbSn, with the ArEumeni of the Sun'i nie.o Ajwnu)]>, 
Uke out hiiSemidiimeter. Ani, from ihe r*me Tibk. with the pn>- 
pjr ArgDinein in Eclipfei, uke out Ihe Moon'i hoiiumtil finllu imt 
* midiimetct. 

Then from the ««■ of the horinnul Puilliiei of the San lud 

Mean, fthrma iIk StmHiimeter of the Sua, ind the Rtmtimjir will 

he Ihe ipp.renl Semiiiime-ef of the EmUi'i Siafl!«.. — To be U- 

,M b. jo" for Ihe Eirihl Almofphtrt. 

.'rtc. J. To Ihe Semidiiinetei of the Earfb'i Shadow, that in- 

crecfed, idd the Scmidiuneter of Ihe Mood ; and if the ifnof which 

lite than the ntar^ Approach 01 ibeit Centcn, (foond at before) 

Mooo uin'Geedipfcd lit tbatlinic J but 

'fk. 4. The Moon beinf: found ccJipfed 



AfpTOach of tbeii Centen, and ih* XoMiiiii 

' aI SrmJl»m.\/ Mi.n« ! 6 Dit'i' " ISC' ■•■ P' 
icSffiJ. 



>l) be tl 



Prt. J; Fjom Tai. (P. 391) with ^g. Li. and hmmAj Ifot. 
Hooa fr. Sob, cake ont the Time bctweea itic im Oppofioon u^ 
thi raean Celipfc^ or rrrmi^ OUaraiis* j which b^i^ added to, or 
fabtraSed fnim, the Time of ibe irtt EclipiK OppiHhiiia, arconlutE 
ai die Moon it yti Aoii of, orpaS, the dcil f/ijr, will pic job the 
Tin* of the gRatcB DbJcnntiaa, 

Prtc. 6. From theSquanof ihe5«wof the SemUamttai of the 
Moon isd latth'f Shadow, n Secondi, dedoA the Sqaac of the 
■Mrjf Appioach of their Centen in Secnadi of a Dtgrtt, the Sjtj^t 
R-ict what reiBaiai will be Motion of fof^arwriin, inSecaodiofa 

Frit. J. U the Ecif ft be iiCeomrd tc btaiivi 11 01^ foi total; 
Von the Square of the DiSoeoce of the SemidimKtETa of the Moon 
ind Eirtb't SbtJmr. is Sccoruk of a Dicnx, inima the Sq. an 
of the mianfi Approjth of their Centen, in Secoodi of a Decree, the 

Root of whit cemiini will be ibe Motion of ScmidBaiioo, ' 
total Diticoeb, in Se<on<!i of a f)cgt«. t.'ow %, 

jIi bcurjj Mat, Mtcit i ^it^ ik bar Ori (referred in fiodini the tr 
OpjBfitioO : iirg I Hnrarbo'Tau :: ft ii ibt Mmiim of S^Om, 

iu iMtl Dtrhuft : ntht 
1 i*ir wf aanaiTBi'snim iBiMi uarmji, >v nich bciait rrj^^ive^ fch- 
IraAed from, and addtd ro, the TicDC of the [tralifi Obfrwrjiirw, wi!! 
giM jFOy the Tim of tba Bmiaitr and fmrf erf' the Moo*') Ediric. 
»d alfo of ilu ,MDu\Loc£i. 



WHAT AN ECLIPSE OF THE SUN IS. 



(•paimer, uSrJan'Ec'lifStef tlte Sao, mithi frtptrly U , 

vtdif tht Sms'i htght, vibilt lit S«ir bmfdf It^girt w DtJ 

m ErUpfi •/ ibt Son, tiviitl irttU tie Mtufi Mallyiuk 
■ " ■ ■ ■ " " ' ■-■■■-■-- -"rr Penunihr»,/B/i«wr (i^Mm'i 
Bn'i Penumbi a fiilli -pe* ibe Etn 
■lb. jind iDbite iti Eartb Jinrin, 



IU Afpteraier, talUd an Xclipic of the Su 
■Jjalrtci™/!/' -'-'■--■- ■--■■• -'■;'--'-*■- 

lalia an E<Ut, , 

~ lit Eartb fut lit Eanb'i dalle Shadow, aiut . 
/, ibM ibt Sao il ftn iiliffiinbeK fly ibt Moor 
>f /.//. /w= Ibe totally dark Sifl^™ =/-■"-■ 



.cf/flSui; 



.JXOWM. 






1 D.^ «■ Fan 



. mjl,>e^JI,„rfrm 
lfe, frei paly ib^ Eanh't eih-baxid Htmjphire, be viM jte Platei 
iuht„ ,h, f,bJ>i'aMI. effucb Piatel if Ibe Eartb fie -b. Su, rif, aod » 



,, , , - ibmtTimiintt 

DefiaefL:gt,. lfmmJidira&f*etmipl^tdallb,M««i„,k.nm,>Jnlm 
' Shadow, anJbirPtaambn, fafietm-ibtt:artb'iDifir faer, UUnambba' 

„ ..t. !_«.._._ ^.. -^w, inanEcIiffe ef tbe-Mean. Htmaiii. 

Ibe Mnm II UHT /«,-, tr faii t, k,, vMei, 
lit, a sLaaar at tba Maaa ta«; la 



Dift, . »- 

rfo Mm fm Ibe Edp 0/* Pe^mira Imib b-jjf Plati up,', <« i=.ni. , 
■bifid. X 

TO ampaiia genetal^nd central ECLIPSE efibi SUN. 

Preufi I. At the Tiitte.of the true Cfjmain of ibe Siirt and 

Moon (f-aiad « btfsre diiinii) fum the horiioifial Panllat of the 

Mtm, fnbirafiihe heriiooial PuilUxof theSiiir, the Rnnainder will 

the SemidiuMtet of the Etinb'i Difk. Likewlfe, to the Semi- 

meier of Ihe Sun add the'Scmidiameler of the Moon, the Sum 

at which wiH be the SemidiaaMier of the Meon*t Pt-umbra. 

. To Ibe SemidianMUi of the Earlh't Di/, add ihe Scau- 
of Ibe Hoon'i Fnumira, and if the Sum ixcetdi the nior^ 
Approach of their Ccnien (fi"d r,ke rbt manf 
,f ,bt Bi«m fd Earib'i Sbadne. ia an EilifJ. 



fome Fait of the firl 



>ft^frcach,flt.Cea>r, 
' >f fbi ltl*,t) the Sun 



I but oihernile 



■: 



wUl be feen edipfed in fome Fait c 
Ecliefe of theVitftan then happen. 

Prii. J. The Shn bein| found eiUpfcd in 
Sfpinniv, M'iddit, andjEnrftf Ihcf^ntri/imi jiiotmrair.Ciipic iwim 
Refpcn to Ihe whole Earth) fnij' be found in like Manner al ii hfart 
iirtaei, for fiodiai the Bi^kiti'i, Middle, and E«d of an EFlipfc 
gf the Moon. 

But to find the Placea on the Earth wheic ibe ^i«i*pi>f ir fanimlar 
AAeirancm of an Eclipfe of the Sua haiipcn, mij' be done bv an aribe- 
rratie Projeaion of the Sphere, or fuch >■ would befeea bj a Sfiffa- 
ut placed at a teey (rutDiSance, in a tight Line j joining the Ctn- 
1(11 of ihe Sun and Earth. 

The Biginiig, gcealell Otfiuratini, and End of an Eilipfe ol tUc 

ID, in any patticolai Place on the Earin, are alfo determined by an 
loalyde Computation from cooTetglng Serie;, pounded 00 a gennK- 
ttical Prqeaioa : (SeeCi'jMiinH'i PiaflicalAltroDonir of the Moon, 
infciibtd 10 Dr. iM-t of Camlridti} being ■ FIlOLiX METHOD. 



ri if ibai Place n tit Eanb mU 

TO ruafaie 1 paniiatjr «■ panial ECLIPSE if tbt SUV, h PA. 

KALLAXes, aeardmgisibi COMMON METHOD 

Pniepi 1. To theappaiencTimeof the (raa CMi»fliH of the Su 

and Moon, (f-tiJaiiipredirrBid} compuIeihePs-iAwof the Moai 

from the Son, in Lungitnde, 

Pret. 1. To Half an Hout, an Hont or mote (ai the Aid PraBai 
icfmatlotEreai) btfiri or afiir Xia true Conjurtfiiari, accordini: 
Moon il in ihc t^em or v/e/lirii Quadrant of tha Ecliptic, coi 
igaintheP«H/(aj(of the Moon from ihe Sun in Loii(i>Iudei bf which 
Meinj (from the m,.J yoo will have the -LJJSii half bourlj, hourly, 
itc. Motion of Ihe Moon from the Sun. Now fiy, 

funWrMjicRo^ Moon i Sun 1 i'iM7)Wr*tn a fi !i tin Paral- 

if Ibt Moon f rem Ibt San in Laigitade, allberime cf Itst Caxjtal- 

I n Ibe Inlemil if li. Irac aiul vifible Otjanflin. — Which aUti 

or fublraHed iiam, ihe rime of the (,-iu Conjunftion, atCMdia| 

he Moon ii in the lajfim or m/ira Quadrant of the Ecliptic^ wil 

■ y£u the Time of (he TJW-Conjunflion of the Sun and Moon. 

'ret. J, To which Time, compote apin the irae Placea of Ihi 

Sun and Moo->, with the Parallaa of the Moon ftam the Sun in Lei 

gilude and Liirtude, and fo find bet apparent or vifiilt Plac^ in Kt: 

peA of the Sun, 

''■vr.4. ToanHourUfara iheTim?of mmCo/^unflion, con 

thec^i/( Longilode of the Moon from the Sun, iajfUKidnti 

I her vWi Lalltudei and alfo to an Hour after the vi^ Coi 

junttion, compute the rillble Lfingiiude of the Moon fion; the Sus i 

CnJi^niKi I with her vifible Latitude. Now lay, 

Al S;<,i tf lb, vifihlt Muim if tit Moon frun tin Sun U t-rinde 
imbifeliat Hiarl : ii It Madiai il fiii Ibi Taijim tf ihl Dijirtaa 



yGoogle 



and NAVIGATOR. 



399 



PRECEPTS for coDpating ECLIPSES of the SUN utd MOON. 



efib, vijtlr Utitadt •/ iht Moon « 

rit Tim •/ tbt vifiili Ctujiiaffitii nji it lit Sine ^ At Angli if ibi 
mStbl^tj tf lU Wooa mirb ri( Ecliptic Ml tba Time : iilhtSim 
1/ ihi Maim, fun /nm tbt r'lMt Cit/imSiui li lit gtuteft OiJmrM- 

And :: ft it lit CoGoc if tbtt jlvh : U lit Sim sf ibi Vilible 
DllUta ^ tbt OiaiTt tf tbiSnita»i Mwin 1 lit Tim 'f Ibt ^esafi 
M/etralin, thilii, thtir ndrjS liCble Diftinu. 

iribidHKincebe/c/ithin cbe Semidianwlcr ef the Moon't Pi 
niirt IfiKmliitrftnJiriatJJ ihc 5u wiU be eclipftd in that P/a, 
if the EiiCh ; hut othcrwiTe not, 

IF tilt Sun be foand edipM, from tbe Semldii meter oF ibe Pi- 
■'iimhra liibtnA che nnrelt vifiili DlOince oT tbe Ceutert of the Sun 
ini Moon, the Rinuindir will be tbe Piit Jifiiieiit. — Fiom which 
t\ic Digia ct]ipM miy U (avni, tt \it!ote UrtBiJ'ia P. ]$8, 

Pm. c. Now fiy. At tbi Tifibk Maim pf ibt M»m J^em iti 
Sun frm en Itx-r b, f^rt U -it Hwr ,ft,r tbt Tmi ./ C5.>»fl;« : /. « 

" , V iia" :: ft ii tbt Mtiiaa fia fitm lit tiSbie C<":ji.^.lh^ ii 
.. ..,,9 Oifcaraiiiai ■ ra (tdnterril /■ TiW. — Which being adHft/ 
to, •>! ftbiraBid from, the Time of ihe vi/hli Conlnnflion (ii ihe 
Moon'i vifible Latitude ii decreaAn| or increifing) tivei the Time 
' ■ paufiCifivrtiiea, 



Prtc. a. From tbe Sjiitn of the Stmidiii .. 
n Secondi, fubtna itie Saman of the neinfl vifible DiHuice of the 
I Cenlen of the Sun and Moon in Sccondi, tbe Spmi Slit af the Re- 
mundcT will be the vifible Motion of Semidurttion in Secondi of ■ 
Degree. 

Pnt, J. Now fiy, Ai Si if ibi viJUt Mitif if thi Moon i Eaa 
in Lanpnit firm Himr kiftn ibtVffiUiCniiunaim i i, n Ra^a aft 
U III TengiM t/tbtD'Jinwa i/vifiiriUillyJiinAtiT.mi i tiibt 
TnpM tf ibi jtngli tf tbe -nifilli Waj if ibt Mm viHb tbt Eii^ 
-■-, Jhm Ibt Rtpiaing if itt Kinp/i li ibt vjfib/i Cimjt*/fii*. 

And, ^ Rd£iii I /( 10 liiSine ^ tbt vifii/i JUeliiK if SmiJtir»li» 

fi it tbt C«*K tf ibtt jttgU : II lit Sine ,/ ibt wfiiU Mn'-m 

... , i-Lw- 

giiuJi, it ibi Hnr it/in lie vifiil, CnyutHi 

;: fi it Ibe Muicn in tsrji>i,«&, /(rt/rm fA. Beginning if ibtEeUfSi 
u Ibt ptaxijl Obfcuntion i ii ibi Tmr if Incidence — Which fat 
trsdled froir the Time of grtatei Obfcurktion, gitei the Time of the 
B(f-Ww of the Fclipfe. 

^ Bjibe Hit Prifinim (fern ibt vifile LtwrinJi if lit MmkJSbb 
Ibt S:.A w Confequence, ■with hr iii/H/e LalilnJt fir « Hitr aflir ibi 
Tilible Cw>e/?i3i>J ii.77w=/ Emergence »^ fit End if Edi/ff may 
btJtitnmnt^i -a-iri fi^iniUi«,raHjA-- " 



To find the PLACES, on the EARTH, of the ptincip>l APPEARANCES of Solar ECLIPSES, byPaojicTiOH. 




„.„ iptlt^«*H, Cit» Pole, P ihe Projeflion of the Earth. Pole; 

mi SIK tbe Pith of the Moon'i SiaJnv, or her Wiy Iran Ihe Sun 
rojeftnlontheUiVit. 
NOW, in the righl-Jngleii tfbiriciil Triangle, CMP, we hare 
^Jveofbefiilci the right Ansle at M; theSideCP, tbe Dirtsnceof the 
Polei of Ecliptic and Equator, and ^ PCM s= Son's Uillance ffom 
Ihe etjuinodial Pom' i from whence the Side CM, the Meafore of itae 

II Z. CEM (the Inclination ol the Eaith'i and Ecliptic't AtnJ ■« de- 
lennined. 
t3» tltriir ii II bttnled, iLtltvbt*lbt Sya ii in rhr i(ctniillf Signi 
yf.SS, X.r. ti.-a.>l>'P«':<V.lbtP.lt.f,btE^.^,ir,n,i.Proj«. 
tin falU II Ibt Right if tbe Ecliptic Aii) ; *ei wi™ ibt Sun i. in Ibt 
dercendinE Sim, ag, gi, ng, &, m, t, ibi P«ni F ftl/, u ,h 
L*f* •/■ lb* EtTiptie Atit ; amra-j » lit tffj it ftllt vim lit Pnjtt- 
tier, ii f-pffii M *< mtit M * Piu* fartlU t, ibt Etrif, Difi, »i ibt 
j Moon J Oriii. 



of the Angle, which the Waj of the Moon frooi the Sun 
l^iakei with a Circle of Latitude, Bat )aa inuft oblenre that ihii Per- 
pendicular faUi to (he Ltji of the £clip(ie Axii when the Moon it 
Renter to her afcendlng than defcendiDg Node j but to the Rigbi 
jttiercof vehenffaiineHerteherdefcendim thanafcending Node. 



The ^.CEM .odCEI, being, i 
fthtit Sum or Diflirtnce) the Pile 
louched bj Ihe Ptnambrt, ai 
inhi./v^j«- 

SIE, ate Kite 
Eirth'i 



before, determined, the^IEM 
i-iiu F on tbe Eirth'i Surface ' ~ 
there the rifing Sun be^M to be eclipfed 
f.r.,H luuji., iit iiMwifedetertnined, airollowt, 
theMeiidjjn PF; then, in the right angled Plane Triingle 
■- giien the Sidei SE, (he Sum of the Semidiasietert of tlie 
Difi ind Moon'i Penimiia, and JE, (he ftarift j^tatb 
oi meirCenteii; ftotn whence the ^SEI is detemiined j and br add- 
inE or deduaing the /.lEM known, the ^SEM wiU be alfoknown. 
NOW, in the /Atrr/o,/ Triangle PMF, oo the Earth'i Surf.ce, 
right angled it M, the Sidei PM, e<,ual (o (he Sun'i Dvlinalion, and 
FM, the Meiforeof (he ^SEM, aie given. Henet, joumivfind 
the Side PF, (he Complement of Laiiiudi of the Place >, and the ^ 
MPF; which ^, er in Suppteroencio iSo" (at theeloited Po' 
the Place F, ii aaitened er enlightened) a the Anfle laintaiiM 
tweeo (be Meridian of (he Place F, and the Meridian of the PJaci: 
where the Sun ii, at ihi( Time, t-rriical. Bat the Loogiinde oi \\k 
Place where (he Sun ii I'crThj/ ii knnwn bj ihc Time j and th:<tfar. 
(he longitude of the PUte F, will be known, — And hadng deter- 
mined both Lj/.rWf and LmgiinJt, the Place ttfelf will beknown. 

By the like Method you may find (he Place on tbe Earth, where tl>i 
Center of the Pmmbn enten (lit Farth'i [)ifi, and the Sun rifei in. 
— i/^eclipfedi :• likewife thole Plat ei vibiixxhectnrtil Pciiffi, am 






■efair 



Mcti 



:, ,-cii 


ni* the PW n, ui"n 
•.■xt, =1 the Tin-.,-.,' <hei 
cd in Ihe iwBa£,yj-,.3/Di£i 


meter 


Le m,ide ffj,/jki, then G 



Eaith'i Su'rface, undertbei', 
Ci*iii*(7lim, when the Sun ii cei '-j 
or higheft Point of the Eclipiir. 

For, if EC, Ihe Difi't Semidf 
the Moon'i Latitude, will be the 
I'.rtu of Ihf Place Q, Thetefore, in the _(>ifrira/ Triangle CEP.'on 
the Earth '• Surftte, tbt Siiin PE, the Sun'i DiOance from the 7 ' 
andCE, hiiDillaRce from the yiiiix, ind the ^ QEP are ci 
from whence are found the Side GP, the Ccmplemcnt of Lai 
of tbe Place C, and the Z.GPE, the DM'ereDCe of Metidiina of the 
Place G, anS where (he Sun it then Teitical i from which the Place O 
itCdf will, ai before, be alfo knows. 

In like Manner, the Place of the Earth may be'foand, under the 
Center of (he Ptnumirt at any ^Kn InlHnt of Time. 

The Place K, upon tbe Earlb'i Surface, where (he Sun it n 
lelifftdta the Meiidian, may be found by onlj lelblting the right 
Triangle EIH, whetein are yten ill the Anglei, and (he Sidi 



Digilizcd by VjOOQ IC 



The ROYAL ASTRONOMER 



To find the PLACES, on tbe EARTH, of the principal APPEARANCES of Solar ECLIPSES, byPiojicTicx, 

^ Mr. Fergarsa, a, P. i6S e/" ii. AftrononiT, wx trnuf (m 
t Dif/BK, g^MMi-m ,/ tbf S.I- from iti NiJ.. a -b. Tmlif laif. 
Ct^tmaiai MmJ O^Jtiin, to&« Etlipfei ef SuBmrfMooniMn /lit 
f'm lb, T.mi o/ibi S«,', Pt£i,gi By it. Ncdf} ^«iii,)n. 
llai/nfir-lttNumiirift.cyip{altalcaiijffaiiwar,v. BMbitiik 
~^amfU .^^Birfi in bii mcnrtti Drtugba, ard jfcaiM sfdbo Sm^ 



find the otha two SiJa ; viz. IH JiviJiJ hy ibt Moon'i bmirif M*- . 
riM frtm lb. Sun mill rivt lb, Diffttnci if lb, Tnu /■<■■ tbt MidJlt 
if li, EcSfiji, V7ba tbt Cain- ff lb, Sbnbv h ufna tbi UNIVERSAL 
M ERIDIAN, V Uai HPE, wbaiiw lb, Enrlb'i Acii (i fnj,3tll. Il 

ii ealicil VnirtiM Meridian tianj, ■aibcii aSye&uai plaa^ iiiibitAoBo 
tifirvnmPka, h lit Ee' it' iSnr/accma mitmbibii Lint (by the 
Eulb't dwriM] RotitiDii) ii -uria bt Mii-iiy it tbthbaiiiaUi ef ibat 
Hence, the Longitude of the P/at H will be kaowa j being 
to the Longiiude of [he Plan where the Sun ii Tcnical, when 
rninof the SiAl!iiiupoathE fiid laivtrjal Maidita i And the 
SHcHEIi the J'iMOf theSuD'iDiltuicerronilbeVRtexofthe 
Plice H [nuking the Seniiiliun«er of the Didc, Raii.i) whaeby the 



Uiitu 



» PUci ' 



: alfo knd 



a EcUpfe 
miamiud by 
•ufical Pr.«c. 



13- 7b, Br£ii«h{, grreuji Ob/iuraiiim, ni EtJ, ef 
jfxteSan, fur aiy farlialtr PUa tf Ibt Etilb, mttht-di. 
itgrbraicCa^lelK*, Bnditfiiiu S,ria, gnafJrdi 
tea, fimiiar It ibt fwtfsing (atmayiifim iuDuntnoioe • Aitipnoroj'.j 
Bui, ailtii lUilbKi il vajttiiout ami fnii\x, and filltr far Sftculitiia 
ibaaPitaict, ■at tbtrifot, imil ii. Jixi vit km, it t, lb, Csmfultr', 
PRACTICE Mrf EXPERIENCE wajW/r (i<pUin«d etTy RULES 
ttrat diSvcrti, fur €7,i^<,uxg ECLIPSES of lie SUN and UOOii 

;nav/. See P. 160, foi the Applicilion. 



NUMBER of ECUPSES of the SUN and MOON ihit un hippen 

in ONE YEAR. 

THE Numbw of Eclipfei of the Sin ind Moon in »ny Yen onnol 

be left chin (w not above /ivffl. The ufual Number ii/urbutvcry 

feMom above fx. 

t> Su P. J97i /-■ finding Ibt Numia^ ,f EcHpfa in an Tiar. 
Ifattbe fitft A'oo Moon in 7«i.b/,, before the uili Day, (the 
Number of Djiyl Difference belvMCn tbe lunar and foUr Year) the Sun 
' nnr iS Drgrai Ihort of tbe Node, the Sun will be then edipfed, 
■nd the next FuU Moon, and tlCa following New Moon, will be 
ecliplcdi Wk, lEclipfn of the Sun and i of the JUvm will hippen 
before the 91I1 of February, that Year. And ai many will happen in 
the 6tb Lunation after, in the fame Order, before ^^ 5, w'x.-i 
:f the Sun, f^of tbe Moon, and inoihcr of Ihe Son, In 177 Dtyt 
from [be foimer ; beini ibe Time of 6 mean Lanilioni. And i Ec- 
nore of the Sun will happen at ihc End of 11 Lunaiioni tVom 
ft, being the grcatefl Niunber of EtUpfa, v.s. 5 of the Sari, 
: of the IHaa, thai can bapjien in a Year, incluiling 13 New 



Before y<-. 



3 mote Ed^iff. ^s 
i Liuuliooa + 6 



e Edipfe 



Ed. Moon. 
Nctt Fn/I. 



NeitA'm 



O J G O II Q ©■ 'n OfJ"- 

Hot It on'thefirft Fa// Moon bcfiire Ihe iitb of Janiiary, the Sun 
from the Node be near iS Digrai, aa at ihe firfl Ntta Moon, in Iba[ 
MoDlb, and changing Edipfet of the Sun to thafc of the Moon, in 
theiiiw£»a^, then theie can only happen 1 Eitipf; rflbiSsw, 
in that Year, being the lufi Ktmitr. And two Eclipfei of the Sun 
can only happen in a Year, when, at the fiift A'en Meat in Janarj, 
tbe Sun ia Tcty near the Moon't Kode ; To that the mean or di/tereni 
Nianbetof Eclipfei happen (between the gtcateft aodleafl Numben, 7 
and »} when at the fitD New Moon Jn7.iiiM'^, [he Sun a S ii in che 
oiiddleoTatdiltcrentDiiia[ice, betwiit iheSun'aeclipfed Limiti, ofc 
■ad it DeEieei, Sua t (ij> at >ppcara from above. 



=,7oyt. 



Of the PLINIAN PERIOD of ECLIPSES, aitd tieir RETUilHS 

THE Pmod •/ Etfifji, of 1.J Jy^tdUal Month, (d.fccmti bj tb 

CbaU,api, and caUed by them SartI, and alfo called the ritawFeriM 

ifed by P/iity; conGAiof 18 Yean, iiDaJj, 7 Houn, a, PKlnWB! 
uid 10 Seconda, when 4 Uap-Yean atecDniained { buiwhencUu- 
Yeara intervene, it coniifti of 1 Daj lefi, or of 18 Yearj, lafijp,, 
HDan,4,] Min, and jo Secondij ve^ necelTary to btnoteiin iul'fe 

The Addi[ian of the odd Houn in thii Period ma; fliift 1 J^k 
lipfe into Night, and a lunar one into Day j fo ai both to btramii 
Tifible, afnt a Period or two. The Sun i Q, aitheConckSHiofo; 
Number of Period!, wilUhew ithether an Edipfe of theSi-iet.Me 
retumi, within the Limitj of iS or 11 Degieei n/f^ivrki *bi:; 
doei not agree with Mr. Firgufin't jlcanni of no Eclipli oi' ibiS,' 
repeated, ifrer joo Yeara; nor yet with-hii 11 TiMjiaJYeinRoi 
luiion, on their Return from travelling in tbe Etfitti, dunct tki 
/.(.™./. For .47o<3''of«Deg, iiwhatSunaQgoeibittiooi 
Pttiodj hy which dividing igo, tlieQuotieal^ jS.ii? ibiNmli 
of Periodi, when the Moon'i Sbadno quiti the Earthj »h:ili nii 
l8Yri,4ii inQnePeriod = 705Yn,5i, S'c. Yn. (ini an 5K 
when the Moon'i Sbadivr quIii che Ejnh, and Irivelt in [be Eipiu 
Now, jSo"-^ i8<> = xoi tberefoie 705,31 X 10 s= i+iot Von 
the Period of Reiarni of lolar Eclipfei ; and not i a Uttfad, uoid 
ing [D Mt. Firja/i,. _ Again, 11" -r ,47011" = Ji.jiiiPoiai, 
when the Eatrh'i Shadow qniti tlie Moon, which x d by il " 
.7ortt,ii7, when the £aith'ii:bd.fen> wholly traveli in 

- But, 360" -^ iio^ JO, which xd into 470,117 ,... 

before, thepttiod of inw Edipfn, travelling in the Iipiii. 

Tbe falling back of the Sun aod Mood frecn the S in ever, FoM, 
il the Caufe of thele Bclipfea about the afiailiagiioie hapficoiii « 
fmbirlj, at each Retom j and of Ibofe abr.ut the d«cendiJi( fi bu- 
pening more northerly till they vnar oft' the Earth ind Mooi'iSii' 
facei, aod travel in the Eipan fe. 

Of Antlrnt ECLIPSE!. 

THE pre lent ^nKHnid/Ta^u ace found tadiraimuiihtbttiMi 
of aniient Eclipfei, on Account of the Moon't Aurlirtiia of ~ ~ 
Motion, requiring a confiderable Addition to her aniieai meis F 
at wahaveilluflrireil. Therefore, the Edipfeof thcSuifrc^clEtbi 
7Wii, inthe4>b Vearof the4g0^i>f ju', puitingin EndleibiBii' 
tie betwixt tbcHfAliiind Lydiant, might very well lorierponl villi 'b^ 
Time of that Edipfe by Computation j without goiiqfsfarbicliitt 
Mr. Feixo/{<i, 11 a Plm-'ai, or CbaUaa Period, lo make [ht Tim, I; 
peannce, and Event, agree. On which Principle of Aci<Juiu«,ie 
nootber, Ihe7imuofantJeatEc1ipf<.a, iogencral, ire to be cuud 
and reconciled with Oblct*atioa. 

PLURALITY of ECLIPSES, 

MOREEitiifei happen of [he Sun than aftfaeM»r; btu»l!< 
Sun'i aEfJid Limiii are greater than that of Che Uooo'i, 11 iJ' ' 
ia<.SuD/romQ. 

But more vi Able Edipfei of the Moon than of theStuib]|^; ^ 
caufe Eclipfei of the Moan ire ^likc (eco from all Pirti of ibrbi 
placed next che Moon. But Eclipfei of the Sua ate nulj vifiblctiiit 
fmaU Part of Che Eanh (placed neat (be Son) whetHD Ibt lb,' 
Sbadra filli. And at the tithed DiAancei of tbe Ueoi ivB ^ 
Earth, her Sbadru lerminatei before it reuhei ihe Einb, iiKn 
Moon i and the Sun'i g-auft Edipfe ii then called aiWff, 
bright Ring appearing round die Moon'i Edge. *" 



J8S May »» 

''^/^^ I* 
+9" '*'■■ »S 

46J J^. JO 

43« ■*?- 3 



HISTORICAL ECLIPSES of the SUN and MOON. TobeaawiW. From RICCIOLUS. 

idar, an Edipfe of the Sun. lisaH be^in lo be built. 
The jtjiyrian Empire ended, and BaiyUniaB eftabliftied, . 

Eciipfeof theSun, ptedifled by TAa/a,. Peace enfued beiwiit Che AftJu aad i«(i«i. 
Edipfe of the Moon. Followed by the Death of Ca-ig/i,. 

Eclipftof IbeMaon. Followed by the Slaughter of th&Ji'»«, and Death rf yalriat PnUiuU. 
Eclipfe of the Moon, Followed by a great Fimine at Sen, and Begioning of the PtlM^am/Saa War.* 
Edipfe of Ihe Sun, War with Prr/aat, filling off from EgyfiiaM.. -r- -v— 

TotalEdipfeof theSoo. ACttmetand Plague at .*iB...f 



f m, Edipfe ewi ia lb, ifi f, 



h PelopoEinefianWA-, aearditgrt Fergafen'i j jf i «*i» f» 



mgl 



and NAVIGATOR. 



401 




TduI Eclipfc or iht Moon. Mrui and hii Ship deftroj-ed it Syruiift. ■ 

Edjpft of the Sun. Pirfiant bc*l Camji in i Sea-Engigiment. 

Toul Ecliple of (he Moan. NeiC Diy, Ptrfm. King of Maitd/mte, conquered by Faulni EaiUiai. 

Edipfe of the Sun. A Piodigy for (he Dnth of j1gr!pfiiai by Nm. 

Total Eelipfe of the Sun. Reign of the GtrdiMi ftioit. Perfetution of Chriflijni. 

Eelipreof the Sun. Stan are feea, and Emperoi Csi^difiai died. 

Gnal Eelipfe oT the Sun. Lmiit ihe Pioui diod 6 Monchi afier. 

Edipfe of the' Sua, 7<i-a/d/^Uken by the^amfim. 

G[e»t Eelipfe of the Sun. Sun ire feen. A Scii/m In Che Churth by tvro Pcff al once. 

Eclipfeof theSun. CbhJIoptrr-CclinniiiiAcovc on tbclttuii of Jtmaici, where he wai rerurul Proiilioni ; but he if- 
frightnj thelnhibitaatibyPrediQian of tbiiEclipfc ; Ibrcatcning them with a P/«^(, of which i^ wat to be (he 
~ ■ led fo gotfopplicd. 



RED" 



EQ. 



Solac TABLES re4uced to othei ! 



Htl/n't 1^,a«.^4r{jM, orGrm 
Tibi. in f Maytf't, for Parii I 

reduced to {Majit't,totGrttimiiib 

See^uo.J j^rtmr 

j1/lr.jicii'f Mryir'tTih' for Ptrii' 

a Tib". iMryir'l htCrawraiib 

r ed, to ) SeeF. ]t7. foe fa^ti 



M A. cu 

Yta.n Motio 
multiply lb> 


toffiF.g'tothcM 
nforSeeoudifor 1 Yt 
Number by the Yeirtl 


£(i 


Lunu TABLES reduce 


to other L 



HilUj't ~)/lflnii. Arce^, or ?rM 
Tabi. are ( JM«o-'i, for Para K 
reduced to \MBytr \, (or Grmau'et 
See/.iii.J /ifirat^ 

" - a-lAfayii-'lTibi forpBi-i. 
it. iHaye-t for Crumviib 



N.B, Cutoff » Fig* to 
feui Motion for Second! loi i 1 
nultiply that Numbet by the Yea 



.ein^w Moon 
VrivMQon'i M. 



itfooj 



' thin Ma%'i New 



r Ml lit _ 
Sua Ir.MoDn'iv^fH, it hii M. JVfwMoon, redaceatoain 
' Sunfr.Mooo'i J3, libit me*a New Moon, redacei to eari, 
. Sunfr. Mdoo'i Apoge^ rejucei tooun, at the fame Time, 

■ Sun fr. Moon'i Node, redocet lo onii, icibe fame Time, by 

■ Other Pltca reduce to eiirt, u by Equitioni ibore ; iiix. Sun'i mean An< 
WHENCE, I'rii » htoHrtlly jkibI, if e,y pariiimlar TMiir,J„a u ftvrral tlinriifirMiniicirahla, 



lor TittK frosf 1700, Id be allowed, 
by— 5'is'' withEq.Mot. 

Mot. 



Hm Moon, by . . .+36"* witlKHii 
New Moon, 1^ ■ . -^15 1 £q. Mol 
+ 3 'o f fram 

— I oj 1700. 

om. and alfo Mot. from 1700. 

WHENCE, iliiliibriiKrtlJyiKiid, if any partimtar 7aiJii nJna u fivrra/ tlitr tflr^tmiral Tai/n, httimrtnPlMa, iyaruiHgivn'Eqat^ 

tinat, vubtbdr r^iaivtS'im, ibaiaiytni cf tttUTablaieillridiucttairf tttrtf ihtTablamtiiiiexd, ky ebaaghf iti Sigm if ihi Tmaiitni 

if Iti ta^la «** r.dui,d. amlcm^Klini lb.fi £»«„«, -wiik Ibe 5.f .. an/n^ualia, <f ibt Tail« yia ™uUr*J.« I,, i. o»e Sum, fir lit Sip,. 

■' ^r-_..„';.„i..-i..-,i,i.i.^.,/i;„. .- ,i( requited Taiii, ij« it ™A. -' « 

rni Tibiciind chtir Equaiieni (malta lbffamiTailiiJti]at) to one inc 

one Side of that Equiiion, and Tablei reqiiired to be reduced to, on th( 



and EauaiiMiity ^utiib lie Reduflioi 

Tbii you may prim!, by maltini ditftient Ti 
Tablet and Equitic 

SnPalkiiim 1759, P. 7*, L.l. Hallry, fr — 71 1^' E^. J) im,aa/a. ano -r o' 1 
EXAMPLES of ib« REDUCTION 

T« nJati M Mljtt'i KttiiJi Platt$ ef tbt Sun fir Piiii Ot/h 



EX. I 

t^aitivn of Maim 39. Vttn 



San'i PI. 



9°*^s6"|: 



Sun-i Ap. 



Miyer't mean PI. Sun, req*, »739( N.S. 9 9 40 54 Ij K 15 1 
for P«f )i ObCerTa<ory. 

- ■ ■ ' ■ OK Plata if ih Moon > 



i*'i''3*'"4' 

ill 



+ 41 



[X.».^.*».i7M,N.S. 

Equ.t, 01 IMace 
Equat. ofMot, 39 Years 
Maye>;i m. PI. D, iTjq 
for Barii Obferv. reqJ, n. a. 
En.Mo.©+ls''''o"ooYn=,i5"foriY^, ..Eq.Mo.Ap.+i'30«io*. 



i-.30.7'37 
+ o 51 



Alb t\. Ma. } 
StfwthtB^. 



•^i'-filoiVfai^Yn. _?? 

+58'',5 for 
,' js'fot looVrtei j'lijferi Yr, 



of TABLES. 



hen tranfpoling the 



EX, 



.. 3. , 



HaUy, Sun-i mem Pla. 
' Equit. Ph. 

Equat, Mot. forT " 
ngto^!,. 
I, N.S. Sun'imcinPl. 



+ 4 18 




E^.Mot. foiSi Yean 
Jlll.jbamm, tySt, N.S, 
fotGrainmibObiav. 



KJ" THUS, 



■ HX32 



Tfe ROYAL ASTRONOMER 



isisr: 



■r TcSiid'Wih Baft tt lit mnn Pl«m fte th*t Thwv 
tiod it nmftfiv TtOin, *tt^hg la iiftrful warn r^iOtMl 
ItdMu'-Mmiijllrauimdviivlrftlfyhfr " - - - 
iimpftoinr, rtmraBi»i, nd nma'tmr, iki UAvt eAXantt 'Efntiimr; (vivitpr. _ 
lin) tin PERPETUAL AND CORRECT TABLES OF THE SUN ANP MCX>N 



^^d » . Mam 0? iiiiving >t fe dtfinbU in Af«f&i«, it ii lititby pra»U, *« (he OrriS/w jf £jm(im ^ »■ PUct, iOmi 
/la^fr*i<m if mUM Muiit, anittfmfibiEqaiiiitiut/ibiiKMKn rtc imi Placa, (hi U bt pub Wired from Time lo Time, n the)- ire .dale 
mi found conTinuilly Co ipprOKlj nejier wd neiret to ObfttvatioB, in all Circa ind Circumftuun, by the indcf*Iigablc uid p 
Jt/trmilr. WhoDuehltopi'Plit' (indnoirecm) iheObfemtinni p.M forwiththe public Money, for the [Jfe w.»ff.f. 



tf> THUS, ,btmumtUMfirtmjT,wu, tictrdixg 
,^„g I, nj uhaEIamiat if mm Ttt, - ' 

•lata ati Moti—i, h rvadtd. Hmci a, 
, -Barpi lit KjmaioHt tf Pliet« attd ^ 
^difirit, Accel««inn if ibt Mm' 
• -■hBida*JiM''fi^- 



■ tfttrrrff 



Sttof correflTnhS 



GEOMKTRICA L f K Q j ii CT t O N 



t C L I i" S E. 



"foTAL ECLIPSE of the M U U^, tbr Crutniib OB8ERVA 



I Ill 



LLl. 



''Scitc ol MiD> o( Deg. 



Si£l«<i't I 31 401 
Immtrfn 9 3! 41 1 
JUi'd!i/> 10 IS a VAppuent 
Emrfm 11 11 j6 I 

Z>'i«» 17.16'. wNorthw«rd. 



Ptiiliifib, 

fsn ifihmtSiBitwnh'atbt tt.fi. 
5. HtMiffttrB,d^da ty tbi EiUplii 
(tbtTfFtntfihtOahtii K.amiit 
Bnnm S.) _ Afr. Fertufon, n P. lai 
tij..^frM. jap, tbt B "i Weftetn tiW 
(■ fill EiJifJi, iffiir bir ImmerfioD, i« 
lin /if Ifki tidilbumd! ~" 



J' 



ttma^'t ktiminal PartBau . , ; , 
SatCtbinMnial ParaOan .... 

of *«t .' ^ ' 

. . 1 which Uke Sun'i Sm.Diam. 
KM. Sem. Dun. Euth'ifiubn, 



S^'44"|SicniidiuiiM«of the Moon ....,, it'w" 
13 Sum 5n>.A'Mi. Moon (irfA'i 5^0^. d ti 

j£ -54 Im«>ui'i2^. M. >i(. c 

>5 ji Real, P4rti r^i/«>« <( 



i» KtfftS af ibi Ui- 

anj/rjlrt«^^,fr„, 
lit Earth' 1 Sia^n, 



Mona'l iturff Mili** J<''44' 

Sun'i tti'fr Mtiim, fubt^a . . . a ly 
Rem, Moon'i ^hpA Aftr. /ram Sun . . ■> 17 
Dif. Ji'fSmid. indScniid^'iSludow ij 41 
Hoon't true Litiiod; . . • . . >o 11 



CinloAERXCOA. Then with the Smidiuneter of Ae Eatfa'tShidoi 
Dif. Moon't Snnidtnn. ued Semid. Moon'i Sbi- 
Dn'w the Edipcit, XC, )hron|b B ; and pvtpeadknlir iherttc^ dn* 



sCii*, with which ExHnc, on the Ceniw _, ,.™^i,w.„^.»„^,n,« 

,' X-, definb. the inner Circle MN, for the Ewent of Che Euth'. Sbido. , ind nnt wi 
- "■ Vi',,> «/"'- -""""""""ftCirelePa on the fane Center B. Dnw the E(lipt« 
AX, the Ecliptic • Axii. ' 

S.tolftheAD»koftheMoon'iTilibleW.ywiththeltIiptic, e* 4,', ftiwiK toR, (otbeZjfl, (hee.tif«theMoon'tLitlt«d.M*eleeodinf, 
itrtieRilbtofJt when the MoBn'iL»tinidei,N.rfcendiii|toirJ ind dmw R80 for Ihe A»i of tbe^ Moon'. Orbit. Whenthe J'l LM. is 
H.ife'.l '■"''"'"^ '•"O'W'lwtntheXififof lEie ZeUptic'l .Jni. 

When h« Utiwde ii 5/ J^^'' J the Ai< of her Oibii li» to the I</( of the IcUflie'i Au. 

Set Bff the Mooa'i true Lttiude laf it," from B to r, on the Axit of the Moon't Orto, bdng M, of ihs Idlpt^f, {bui lb* COBtniy Wiy, 
from B towirdiO, whan the Moon'i Licitude ii S. of the Ecliptic.} Then throiq^h r, pcrpeDdlculiria [ha.Orhit't,4nt It(( dnvc, J, t, 
b, a, f<» the MooB't Orbit, or Wiy to the Ufi through the E»rth'i Sbidow. 

WhentheM«>n'iL»t.ii^|^'|.|._| fliei.4iw(th«EdipUc, But Moo»'« Lit. beloj |'^; llheiiic&w the Ecliptic^ 

With the MooD't tiue'&Mr^ Mocion fivm the Sua tS' 17" fet off' the Honri on riie Moon'i Otbil, to the Left, in (oA Mmnef tint the 

iineof Fii//MH>byaur3UJ/a, may be placed in the Middle between c isd j, in the Uoon'i Orbit ; thit ii, MtMle W tb« laxeftakm 
«r tbeMooa'iOrfaitby the^ui of the Ecliptic and^Aii of hetOibii, Or lb h the Time of the fmr^ (W^«tn^ ^ HiMIe of Dm EcEffe, 
nw ba placed in c. ^ 

Idt/Of, with the UooE 
Z and T jult touch the Earth' 
OreU She In the Middle of ' 




Thijk fivtral Timti art marhd n lit iff 



._ i^^bw/f^rwu the Middle of tbt Eelipl^ c ond p tpdiin alfe to the 

AlliCodeof Ike BqulnoOial of the P/m(, and cnlminatlDf Point of the £c£fn[. And mark the MiMa'i LKitudein^mrdPnioDiu, Bt BMr- 
-w£, MiJJIt, andJWoTibtBclipfri.bTwlilchtheAfaM'rilfiUeffVitinaQn-M-Zj'H, totbe Lef^ tbrensh the Earth'i Sb«knr. 
ff.S. If the Parte aQfciau be more tbu ibc Mm'i J)uwiv, thi Edipla (aitAtm) witl be tnai with Cnntjntwacc } ii afmal 
COUl withoatCoBtiBuneej bnt if Y>> it wiH only be a/wrtu/ f (Jij^ of the bfnon. 

Xy Ji UUr EtBfft, atfttnframitiBartt, m*f li tUliuaUd, InPleno, ia ria fimt BOtatr vhilit OtPtPr^U^^ALwitrllmj anqM 

li^liaJ tf lU S m i d i a m t U r if lii Barit'iSbadmyaa m^ mfi Hi in'i Saddiaamtri and iha Mtia'i vipU LtHimb, ii^hud if ibt (w. And 

iTatDedrawahoriioatilLine to comfpond with the Allien^ of oonigefimal Degree at the Time of Middle of the Ecli|tle, eorR^oadin(illb tr 

bhi Equinoaial'i Hei^t, and Eclipdc'imeridiio Altitude, and let off the Moon't TifibleLatiCtHle in fneral PofitioUf "' " ' ' .-...- 

^Eadof thcEdiple, Ihewing the. Moon'i TJfiUe Wiy in a en md Liae. ' ' 



mi NAVIGATOR. 



♦01 



£iJiptic,arviJ 
Conj. tpOrbi 
CoDJ. ot Midd 
Ed.0. 



AWOLK of the BOUR CIRCLE (pifliag AtoBih ft* SUM w MOON ) 

«itb tke ECLIPTIC. For finding iha ParalUait Antle of tbt Sun 
Uood, in ECLIPSES] and alio inallUtilDdeaof (he Moon, 



ArtntMni. Rltht AlcmBon of the SUIT or MOON. 



" * ^HouiCiTcl Dif. ^ HourCii 



3J JJ 
3i * 



R.A^ 

Sua 
12 



Sis. 



?y 



Dcg. 



> ST i9 , 

» 4« SO 
3 .o 5< 



S^t 



!°°°^kf» 



78 30 40 

78 51 5» 

79 13 '7 
79 J4 5' 

79 jS 3S 

°' i8 »s 



80 4* J» 



84 s" J» 

!s ■* " 

U j8 »7 
86 s I 



is u 18 
89 n II 

gg 36 i 



»J 54 

>1 SI 

>J 54 



.?>«■ 



■ ij"' 



OjAwAs. Ai Kadlnt : S. Sclipiic Obliqnitj :; Cof. R. A. ftom 
nal E^in. Point, 11 C«r. ^ Hdot dele with the EdIptM. 

Eumpte. Ta find lb* jtnUtfHiiir CirtUiaitliliit Eelipiu n it' R^A. 
' - ■ - ip,iMT 

Loprilhm. ~ 



frtm d> nM ipimaMrta 



AiRadioi 



Of the MOON'S PARALLAXES. 

T. If AtDlftiBceor tII(M«iAan thcPofat 
ilWn Ag or dcTetodiai of the Ecliptic, be lefi 
that) her Altitude, Ae bn dm no Pmtln in 
LMitnde, which Berer happeni bat in fndi Lati- 
tDdei where the JUwa'a Oib or Edipifc ue nni- 
cilardea. 

s. If the Mci'i Oiftiflce ftmn tli« Poiat tf- 
teBdhig otdeftradiai bejuAgoo, then iTCrtica] 
Circle iPtrrfacti tbt Scnplic at ri|ht Angki, tad 
thin IE DO PicidUiof Lon^tudebutonlj of I«- 

]. If Ibe Verticil pafeRg Aronth th* Mm** 

Center f.11 oo the Ecliptic, at oUiqne ^fa. 

e ii Panlln in Longitude ind Lali' 

^ifUi CnpnA'iv of Stm tadHtmi, n feen fnm the Eiiih'i Superftdet, alwija 
from iheTioieof rru(>t(in?»>, M Inn tism the Entb'i Center, except wbca ibej trcR 4. To itlPIimoB the Eanh hiring above 
coi^ncd in the noniice<iniil D^ree I vhen tbe tnc and nfibte or ipinmrtTinie iitbe{nl> 46'io'' NiirthLatitsdc, the JHin'i PtnUax 
hmt. — 'HaK*, if thettne Coajunflion fiHi to TbcSujhtunf of rliE Bea;rfinialDeEne,l|iiJnf£(r1^, ml n dcprdled bdov her Ine F 
the Mrta't Place ii adviiBCed b; her Parelln tf LsupBuk, when (he tifiUe Co^nnflion iilliccording M One n taft or Weft of tbe 90' 
hefcTCttolrae. Bat if ibe tnwCenJiinAion fini to the^^thuWofthv im>i{{ini'/^>vr,r|7)(/e FtrtOmi tnmc^rj - • • 
tbe lffMll\ Flue if Teiarded hf i^par»/ini n LmpaiTtf tai tbe rMMe or appumt UM-jICHyrncrin ^ filrr B^Ja. 
iunaioa of &•• and Afna, then followi the Tiipe ot the »«( CfjimBim, *f T QCcelliiji *-■ ' 
Ittowtti eanputiHB ^li Eclipftb 



ToCof. go'il'ig* g.uSaiig 
^ ffcar Circle Teqniml . 




.C'.Vif.Ut. ) 



./.Conj. 
1 Mid. 
Ed.Q. 



Ut, « _ DM. 



■A 



PRINCIPLES of PROJECTION ttf 

% Stiar ECLIPSE, Gttmttrinillj, 

A Pimm being coDCciTCd to (ooeh the Mttn't 
Dibit JD a Poiat where ■ Liik (it right Angln (0 
the faid Plant) inteifecting the laid Ortii, rsn- 
nectithe Ceaten of the EarAind Sum e"^ "■ 
itfiiiiii Nomber of ftraigbt Unci being fuppofed 
to pih from the Sun't Cinter, throo^ the faid 
PIm of ibe EirHi't Peripherr, to the Aait 
theitot, ud likewift to the jixit of tbe EcHpiic, 
and the Pith of tnjFirlKt, tbe faid flnight 
'" ' vnfbie»Dj, prq'f tt the Emi'i 

, . . it jlxk tf ibi EiOflic, taiPsti 

ibt Viria, on tbe iforefod Plane. 

Stirimlitt^iDtBrimt/tii9fbtn, P. *7. 

If the Sdd be in tbe Z^inoctial, At P»tba 
of the^A-licri fdelcribed by the RoutioB «f the 
Eanh'i Seiface) wUl be prdened mfim'gtr Liaa \ 
upon the laid Plane; but >f thc^iahM Decli- 
nation, thofe PKhawiO be nn^ed is £%/«, 
upon tbe fiidPboe. 

The TranfvetA- Diameter of the EtlipGi, re- 
prefendng anf Pith, is equal to double Uie right 
Liae of ibeDiflance of the laid Firtrx fnai tbe 
Pole { that ii equal to twice the Cofiue of the 
Place' I Latitude. Sut theConji^ate u equal [o 
the Diltinence of the ri^i Sinei of the SwD and 
Difference of the Diftancei of the Path and Sun 
from the Pole. Thatii equal to the Sine Compi. 
of the SMt'% Declination added to tbe Co-litltude 
>f Ibe Place leTitbeRlght Sine of the Diffeieace 
>f the Complement of the Sun'a DetliMtkii 
and Co-Utitude of the Place, 

Tb* TnnlVerfe Diameter liea at right Aiula 
to the Eaiib'a jM; M< the Clojogatt coiodde* 



EXAMPLES 

Digitized Dv 



BXAMPLBS , 

ov Google 



rht ROTAL ASTRONOMER 



ZXAHPLES •r«MM%lte PA&ALLACTIC ANOLX, 
BtD. CQWPEK. 



M DIPFEEENT METHODS. 



fti(lHA£xafi»a 
Time rRioiN'iDaiiiDc(i, 
ft. Ale. Mii. CmB 
Maon'i LADr. in Eiiftic 

LuiisJf S. 

Dfduu'ioa N. 

^— Rifbt Alic(n£oa 

Hcni'i Zni^-Diftta 

AatlcafPafitMD, II ],*t 

CbUr, « ^P1,Z 

Circ. D«J, ^PhL, 
tbrleri 
^ Z.f J) L SappUmni 

('■■■B.flK^.Of^PJL 



17' 9* J»" io*, ffyvn/ 



•»» »4 57 
«« 35 o 

D i J> o 

4 ji ij 

16 41 IS 
*4 J4 )» 

»* J* 3i 
71 JJ s« 



99 SO 50 
Co >9 14 



P, ibeW^iPii, 
Z, (be Z>»ii. 
HH. the atriam. 
SJL. ibc £;>iU.r. 
EC, ihr I*>«H, 
LL, P»i;!cl Lu/nir. 
O >0, Uoo'i <V*.i, 
J. Meon'i Orii-yiaa m\-\ 

4' jg' S. t«»v*. 
PZ, Cunp. Ul. if iV o*, 
P>, Mmn't t>R.Bcc>M 

/■<47j»i7'45-. 
Z>, Moon-> C<^. Ab. 




z. z<c. fviOiak ^ 1 

- A.^rf.«tk.:z; 

jO wrh tV EcTidc EC. 

C ^z>L, p.d3iua.c^ 

»'• A=ck.ri«nn.Z> 

HwiT^iPmlcIo^'Z^]. 



Bjr tbe VmivtrU METHOD. 
MaUUaAatk ..... 

Altindi JW. C*J! 

Moos'i Atimaih fran N. vr ^ PZ > . 
inlliaic i:. ZiC 



Ti find Ih, faralUaii jImtU m lU Mtm, ( 
TtnaSit A^ili ttitt Eihfiit Z/C 1 

At Of. i Ut.tf\%'yi' I Had. I 
•o* jl'i4"fl*mr I Ctf.io^ i\' ^\', fart 



^ZjL,/n- /ir ^. 



,, Bj the 9<;ih DEGREE. 

Vh' *^y M<A* C-£ in EdJpdc 
-^( j6 }4 n jibitui, foth D-grcc . . . . 

.7 a( >j 11 f.u^rnfr 9oih Drgiee 
to }S 14 II Mson from go'b Dtfree , , 



AiarJint (o D. COWPER'i Aon METHOD. |/*ar,/ij^ id UNIVERSAL ME- 

'7J7» PA ll''l*iS"9''^-'ni»f, BepooiDE. Sun Etlip. cbrciwdl THOD. 

— Fitrijirta. I For fi 



—~ R. AlecBfion ] 4* }4 4S 
l^nie fr. Noon '- ' 

K.Af.AU.Ci 



J« 17 *5 
tt j> 3 



HMn'^liptKLoa|. K'> lo 44 
LwilDdc N. o J7 40 

DcdinatiMiS- 6 4I 11 



^ II Uk Pole -li iS 7 lAIlitnilc AT. CWA' 

Mom'* Zeaitb DiS. 



36 «8 7 I 
S« 7 4' I 

*3 S* 54 I 



lod Ci«. D«l. J •T 4' 
X.fat^lsa<tAu^ 4 J 4I 



AzatSn^ to ^ 



For bme Tin. 



DEGREE. 



«../. Crr/i 
Allinde 40lh Dig. 
lADgrtude <}odi Deg. 
"inrr, 9orbDej. 

in'iZiHiiDifl, 



50 S4 >« 
. .0 « ,5 

4J 4> <» 



EXPLANATION of the i 



I DIFFERENT PARALLACTIC ANCLES. 



[^ WtiM (ha Mmd ii in 01 

._ar the Etr}piic, or neir a or 1^, 
riib LalitDde, Ibe fartlltSit As' 
|le 01 tU f'/i^iV ZtiH will b* Tuf- 
ficidit te uifwer tbc Fuftjt. 

Bet ir Ibabe oetr >V>or Athe 
iirtUiSIc Angle it tbe Moon mnS 
je afed ) th« Diffrraa btmta 
botb wbicb ADglei bcioi (b«n con- 

For, AtC^.Ltt.C-i : Rti. 
|oifed, according to the ibofc" 



P, the H, Pole of tbc 

World. 
E, Pole of th* Ecliptic. 
Z, tbc Zenltb. 
CN, Put oflhcEclindc. 
C},Ut. } SooOk. 
H, the Pl>« of 90th 

Deg. Ediptic. ' 

L]|L,4Pan]ielofLat. 
Pn, the Mnidiin. 
^PmN, Ibe Mciidiao 

An,lc. 




ZS = Altitaik 90th Dec 
M Dift. of Zenith d. Pole 
of Ediptie. 

Z. C>^ ■») de Moid. 

Z.Z,., otCe}, the^. 

ralttair £_ »1 the Ec^it. 

I Z-Cfr, the CinpLo^ 

p /«f«flifljt i It tbe Moon, 

EJ. 



ti.-ACtf.fartlUaUAKiUatEtlitAc,Ciy % Caf- f»«*8it Aith at tt-lAn, oF Z JiL, v/z. toC}>, re- 
PrcnoTtionibjD.Crvttr.— Tbe true ^a/ibAV Angle, it (It Timei, being the Angle of i Verticil uid Pvallel 
nt at the Angle tbitaVntical mikci with ■atde.ofDccliiuiiaa, vis. Complanent of ^E)Z being /.<>!.; 
I Eeaurkin bit ^^nmamj, F, 6]. 

. QUIRE. If E}, 1 Circle of Lititadc, cot the Ecliptic CN, ind Pmllel of Latitude LL, both u right As^, 

whjboaU not the •Itemitc Angk) Z(N, Z I)L, refpcSiog (he Dune Piiallela, cut bj the vtrtittl Circle Zp be tlie faow, or tbc pmllaOii 
AdtteetE^/tioodit ibeJUfM, bcthelwic? 

•^ ir (iMi^'rw'^avf^iivCBirgfMiii^^ I'd vn />£«N>i Matbeaiaticiui «nJ AAroMmcr} thtt U nvtt ma vtth nj Aaitr mht ua^ 
thitnt Mtibtdtf rifriftMhrr iht jHpurauatf Eclitfii, ftc. titr nirr Jtm ihtm tnfy Jrjcribid im a^ Almuic tr J.f'baaem, Jw tbe Biiulb 
/)Mv'ii«M, txc^l I* fi* jten Wciirer I Ephemcrfa, 

Thit&nvAudW cominted the fsn^Sie jl^li, and dw Moon'a rlfibk LatiCnde, Id feraiJ Pafitioni, it the Bigimdi^, Middk, Mai EmJ 
' tome Eillfja, fbtlhe IHind of jtuiraM, tliat ha might trulj iJJ!jh«( the Minner of their ..Iji^wfiiiv ibcn which (by RafonofthcEcliptii 
.. tisfiiiit the Z«Dith once in ererj 14 Tfonrt] ii cjuite dlAerent to what h^feu here in Eti£UiiJ, both with Rdpta to the PfMw of thi 
Moon'i Face, and tlw vifiilt Cairtw fte de&iibta. 



,, Google 



<»«/ NAVIGATOR. 



Ethe igth ol FiirnMry, 17J7, bu been compnud bj ihc ^urtft Mabti itXlitttHntitAttv'tViwt^api*, 
nling the Mtridin Antic, (luWiulur Point, golh Dtt<^> Vr, in the Mtn't Otiii. And liktwib that 
EiMy/M'tempaii, for the Tune Pbw, with llufc Xiraif/nia the Edi^tic ; Init tbejift Campalition came much ncueft to the Obrervilioii. 
And roa miy obferTC in the Extmfln ef the Ufe of Dr. H*liif't TMa, (d lod i s) that the goth Decree, and frailMaic Angle at (be Mono, 
both tikco ia the Btlipiit ; thoagb the MOi>ii bad alrooH jo of Lai'iituU, 

[[iililtFwiic evident, that ai the £Jf^ic .t a jbcaJ C>>t/', (not chao^iiti Jw/iHriW, and Place of rarf/fflin with the EqmndOiat, like the 

•on'i Orbit] in which [he Sun trnjlailli ippeari, and ii that Circle to which all the Lef^litdu and Lsiiinda of the Plaaeli are cocnputed, and 

;tred {being the £aiiiar>J for determining ihe iAoan' ivlfibli\aa%a*it and Ljlitudt) thctefoie Ibt fbtr Mabtd of compatiug tbc/wrwJUlic 

Angle Oiaie bjlhe InKtfcaioo of a yiniaUni the Afm-iOriii, ii tejefled ; aa being both tcAioui - ■ 



PRECEPTS oflonM COMPUTATION. 



70/mlibi Abia'i im PUa, fnm iht mam Timr givtK, -aha 
,fba Uwtta ftga -ht MiriJia,:, ttr tijfveJ Rigbi ^(ogfn df ( 
Timi, (hrvltg Ht PMraUaxJ miDxfaoa tf irr Umr (tr opfu) Litii 
fhm ibtVtnxt. ' 

' In Ihe Year 171;. DKmtn^ ;, the tr,Jlnt Lirab of the Moon wta 
iblcrved by Dr. i/d/A7 to pafi the Af(ri.Ji« of the Ro^alOhfervatotT 
It Gtatviitt, at gt 8" s», tnean Time, iti obferved Bight Aftenlion 
idng 41° if/ t J*, and DiAtnce of (he Imtr Limi fiom the ftrtix 
14B9' i;') RijuirtJ fnmibrmtiibe U—»'i mi ylan im lit Stlifiic, 
ad a^t lnr UiiimJi r 

EXAMPLE, 
Bj HmlUj'i Tablei of the Moon"i Ecliptic Longitude H >!»4*' J4" 
[SceP. e. I.) Het Latitude North' I 39 J7 

Br fune rehln. Mocn'i hori 
Which Patallai, al anj Time, ii a 
Half + Vfi of that Half It the Moon't bu 
The obferved Dill, of the Moon'i lower 1 



Ap.nn. Jt'alower Limbfi' JViW, cUtrofHiJnai 
I- Com. Lag. 
Kow, AiRidim . 



f,.ytr,« 34 9 'J 
Refraftion +36 

34 9 S> 



8.3]9T9oi loo»t Lo,Log. 
9.7494008 1*506 Ar.Com.L.S. 



Al'.'' 
i o jj 31 



ToS. T) Par.inAlr. _ _ 

Tbit PataDai fubtraftcih fr. ap. Difl. D' 

from Ihe r«r,x, clear of Refiaflinn , ^ 

Remaini true Dill. Moon't lower Limh fr Vertex 33 jj 

Subtr. from which the horitontalSem. > — 16 ij 

Rem. the true Difl-Mooa'i Center fioroKtriM j^ 19 J4 

The Compl.of Lat, o( Obrerratm;, added to which 38 31 jo 

Sim, TheimeDift. 5 'i Center from N. Pole 71 51 34 

Now, AtSifK H'ltrueDilt.i IjCom.Logi, 

Polejio ji'14' CO. J 0.0M1481 577StogJiQ. 
To Radim lo.oocoaoo f 

So S. hot. Dtim. J),J»'so" 7-9>ooj4j [ 1617 L, L. 

a: S, )*ihot.Di«ro.iiiR.A.}4'3]*l g.aaiiSifi ]'i.i]95 L.L. 



fy- 'When the Moon" 
/"/^ J he, Semi, 



ff^B 



I Limb J 



Limb \ touchet the Meridian, 



To the obferred R. A. 
Add the Moon'i hoiimntal Scmi-Diametei 
Sn, it the tjae R. A. of the Moon 
Now, Fiom the Mi 
And her Diflince from' 
Her £(/i>fi'c Longitude wilJ be tf Ij 41 



rnter 4* 4.. 3 
'.R,A. 4a''43'3l*7QiK8.X]Ot. 
N.Pole 71 51 14 I P. iii. 



- - " i ^ 

Laliiode North i 38 37 iOifirvtitn. 
Lon^tode J j.f, ^^ ^^ j,y^ ( o' 11* J the Error of Com- 
LitilDde J "'■ ""° -^ ' a«" 2, JO J putition, 
Th« hoiiiontal Diameter of the Moob ii toberDiimelei in Loo^' 
4e, aif^KiMOf theMDon*>LatitD^ta Jl^i^u, 
Aad her horfiantal Diameter ia to bcr Diameter in ri|hl ArcenGoD, 
f he C^mt of her D^Iination ia to KtJiti. 

The Skkk/i of a Degree (in Tab. P. 391) anfweiing to the Moon'l 
Diflmnce from the Vertti, and ilfo to her Diftance from her J^ifa, 
being added to tbeMooa'a ^vrfaMiTd/ Diameter, will givE her apparent 
Diameter, which, increaled in the refpcdiie Aregoing Proponiona, 
will B>*<herapptreDtIHanietcninj;,«^(iiAind')^fc.4^ftQti«, 



igbt AfcenGon orLoag, j-' fber 
right Afceniion or Longrtude of the Limb obferTed, (n the tight Af- 
ceofion or Longitude of her Center. 
R.BMARK, on Dr. Hf/Vt TABLES. SeetheEND of hiiiVv^n- 

Wri'rr-t PREFACE. 

•' II mffttti fnm Dr. Halleji'i Fnfiri, ibai ttti it computing tbt 
•• right Afceolian t/'f^M'mr'j Limi, imd jimdim[ltm Ltrnplndt^b^ 
" Cimttr frmm Oiftrvatim, bl ntfianlh mfej tix affmrtml, imSimd tf tbt 
• ' trm,, SrmiJiMmttir d/ ibt Afon ; and tufifmtmllj /ram tbt Baiimmg 
" ifibt T'UrtanX Meridiinc, &e. ti lit Imiiir Emd tf tbt Yfar 
" I7*J, fnm Ibt New it tU Full Mimt, wbilr lit Weaem IJmt «- 
" tifirotd, tti ampaiid riibi AJremfitmt tf ibat Limi art fit draii 1, 
•' bickwild; amddm-iiiitbt Rimtimda-ff iht Mimib, vibiktbt'Zi^i . 
" Limb iiMu lijcTvid, ibt computed riibt j^amfimt if ibti Limb «rt 
<< /(I Jewrrto forward. 

" /tud/rtmrbiT/ar 1715, ii« Longiwdei a/iii* Afcaa'j CiiUir A- 
" dmcidfrtm tbt Obfir«mimt if lb, Weflein Limb «r< /a drmm itt {oi- 
•• ward, and ibtfi frtm lit Olfavaiimi tf ibt Eafietn Limi it back< 
" ward. 

<■ Tbii Btror It mt fmfidii^Ji, amd fildim txcidi tt,*; tbtrtfwtia 
'< ttmmm Cefa it mn bt migSeatd. — But if at} ft naJinaJM Ii arriB 
" tbt Mata'i mta* Mttitm, tr It ann mtdil ibt EjmHitm, il vlUbtmf 
" fjjary tt atrta tbt Errort >■ tbt Abacui, ar labU, bj tbt Eiceft 
" tfihe Bttam'i tpparal Simiiiitmna- it rigbl AJaafit*, tr Lmiitade, 
" aiaw lir horitoatMi Simidia»air tf tbt liki Deaomioatios." 

Ttfti, amrJimrtt HALLEY'i METHOD, tbt Timi nt/a tbt 
Mmn'i Eai!ernZ.ni4 paffid ibclAaiAitt tf Gtteaiiich-Otfirvatny, ta 
December i3, 174$ ? 

EKAMPLE. 

Take a PJltiam Period back, which to Ditrmitr 1 
Year), 10 Day., (becaufe it conlaini j Leap- Yean) 
in the 7abi. Lttm Mttuliam*, the Mooo'i Eaflcra Lit 
to pifi thcMetidianat i3>>4;aii>, n 

But 18 Yn. 10 Da. went 7I' 4j«i 1 
which Time the Moon'i mean Motion 
And the Meridian paOei otct an Arc of the Equator 7 

eqail totbitAicof mcanMotion, In . . . J 
SmbtraS which therefore from the Time of Obftrva- I 

fiw, and there remaina . , . ) 13^ iga lii 

Tbe-ne ai Time of the PalTige of the Moon't Eajlirm Limb orer tbe 

Meridian of CrrmRsici Obfemeor;, rtgairid. 

But, the Moon'l computed Long, to thii Timeii SI, 4° 4]' 
Her Latitude N. 1 40 

la the laft Column of Ha!lr,'tAbani, Tab, Laatrmiti£ti 
Errar of CampalJtion fee flfWfar iS, 1717 it ~' i' 

Tbarefbce, aid which to the computed Longitndo, lod 

]roa bate Ihe coneS Longitude fat the Time £t '° 4^ 

Hence, the tight Afceniion of the Moon it found ijo ~ 
Whkh rixrtayUbf her trae Semidiamcler in R. A. 
GlTca the R> A. of the Mooti'i f^fm Limb ijo 
To Sun'a mean Z^iv. at the gifeu Time zSg°*5' 3" 
.,«U«n AreanTwenbletotheaboTaM. I, < 

Time i3»3S-*6' .... f'"* ^° 
Sam, ia tha light Aleanfioa of 



a complete Period | 



. '*■"' 



'.r 



le Mtridiam 130 



Whichrjght ATceflfisnii^thtMooii'alWbjMAtcof j jt 



CS* 71(SappltmentalZfDtfioB-TaUti, atStpamnrtfibii'Weik, afidwitblbtKtaalritiljtftbt Mata'iOriit, trtiEjvaiitaU 



w tdEauaiitaiifbtr Jlf^tt, 



.*)Oglc 



4o6 



Tht ROTAL ASTRONOMER 



Difierent MBTHODS of eMerriiig the U>NGITUDE. 



Tmutof €niuinmiB| dct unmifE inn la* amn. 

To aU«w for vUch mU ^ M Ik* Are of Ditonn *ad 

iibccomn . . . o" l' ^ 

Which Arc tbcMnidJHipafla over in 7'T> 

Striirtil wMch Ihnnthe^Tiiiic gtfni . Ij' if at' 

TbcRraMi'ntbeitwanTiincamd, «f tbcMoon'i 
EmJIirn Limb p>fliu| Cfmiwffr Merfdin, tCEOrd- 

ioE to TMtt i Ij tl 19 

Obferied bf Dr. £»^ . . . t] *t 1( 



tBtdltom tb> Tina ^rcn, *oaM Awr dw TTm* of thcMwoi) 
- - ~ - " ■■■ ' ' ■-'--■■- Mwn, IBO — ' 



^riMSisMTtet, cFTcr (hi HtridiiB (n[bt, but f« ibe Mood, iDcna- 
liai ber rifht ArcraleB Aa ber Limb fUcd tbe Haridiu, ud 






ng bcT OithBfc 6«al tk« fine. 



». ?ra obEcTMi tlie tDOti Time of AppnKfc of the Moon'i Limli 
Tbe mnn Time, lod intDln- DUtioce of tbi Moon'i Limb fioo 



(he Snn't nut Limb ia bcr Erft md till Qui 

AJI obfeirid aodet tJiJlMidMtiHiaa framCttiraitt Obfcnalory. 
And b; affiiniiDi ■ mean Time at Griaru'ch Meridian, to wbich 
hii o^rMw/cri/ Tablet areadjuRed, (bj npcited 7nab} till if eorre 
pondt with tbe refpefiire mean Time of tbe ippatrnt ObfemtiDn 
made onder a diflmt Merifan, be detrtiidaei \ht Diffiraci of Loi 
^tudc : Being the Dtpm lofwetaUe to the Difttaa between Ibe 
egiimmtman Time at Crwrwici Obfer*»tory, and the meaa Tinit 
nodcr the diflmi Meridian, obere and vhea ihe tefpeairePA^aMMm, 
ft Appeuioce, it obfeived. 

Tbii be rfeBi (ai mij' be feen at rht BetioniDC of hi> Tiblci) bT 
rompvtiDi the Snn'i LasgitDde and the Moon'i Lopgiiude lorreficd, 
md L^titu^ to the aObmed Time at Crumpicb «ith tile Moon'i htri 
tuittl PlnJlti to that Time. 

Tfcen the mean Time, in Dt[rta, whentleObfertalion wai iriadt. 
bting added to ihe Sun'i mean Lon^tode, it Gutmict, will gire 
the ri{bt AfMlifian of chediftint Meridian, novty. 

Awl by tbe Moon'i Parallel, he pini tbeftrtlitSic A^k 1 
Whence from the Moon'i irue Diftince from ihcPrria {her apparen 
Sonidiimettr beii>| giten] he deteminea her Pa-allax in Minii, 
LawruiJ; tat LMiiUi, (aceoidiii| to failtiiD P. XJ4) nsdthencahei 
Ti&ble Diflaice and alio of the Srtr, from ibc Vtnet, (itloitioc fc- 
HifraSim) and apparent Place of her Limb or Ceatei, in LmgiinJr 
fo ai to comfporid with tbe mjtli or apparent CtniaB, 01 aKgnk 
Diftuce, of tbe iUMK and Sitr ] or I^flaoce of ihe Moon aod Sn 
Ertlljicn. 



TWi wte b ta tai fntA AMnimaur, pronedi accord lug w the Rr*trfi 
of Dt. tUOif* lU-itdi from the appeieM er fifibfc to tb ■ 
-«Mm of iheObfeSi, oWtrrad, 

He afie, for fala Aid, FAImamtc iwafifH, wbcreia arc comnittd the 
DtftMNU of dM Moon'i Limb from > iiTCn dbntf Sitr at Pari,, t* 
even Hoar of ibe Nifbi for each aOMMnueil Di^ of (krTMr, mrfei 
that Meiidian ) ftofli Whence tbe ttve ailgalir Dltomcet-of the Moon 
A«mth«&>ne&ar, toMi)>otlKrnM-HidlHnTineari'«4;^ are had by 
a^h^^fiopatioo. 

To •hich Ihin ii ananiW the In* Tine ef tbe Mmi'i ^aOaie by 
thcMntdin af rtra, aaCtbt Lag. of her koriMBtal ParalJai ' 
Stendt of a DegMe, at that TiOK. 

Alfo the tmeDiSajKC of tha Mmb'i Ui* ftoav fh^ Saa't aftt 
£M are let doM, fwe*«ifHoui of the Day; *ipi tKc Sn'i Dif. 
tMMe data (Mb V«t», mi Lo^ of «b« Mooa'i f*Mlk)i Ar («cb Day, 

ftltB, hthe iid Almmtc Mwinf. — With the Lvtriibmi for pro- 

ntonlng ih^MiMaeT af rii* M«M «>< ^Wr •' ■'mo Md^ S>nv fci 

met bilwwi the Hson ; with odier maaBmy Taila, for ficilita- 



liDg tbe Or««aBa j aa may be leu ia Dtli CtiOft FfhmtrUn, fraoi 
t75S «» n's- 

" Jipiiiiiirtilm,tf0^in>mita>miTti^mHI6ri£mmfrm 
tm Jlniadtrf a Sru, a-d Dififa •/ lit Xytfitm ik Etrtf. 
Swrfaci (allovini far RdtadMa) fir (nu I>ifaaa «/ iii Star fimm (fc 
Pth taag alfo [ivta, tn a ttrtarr Dmf, via tti trmt tan tf ki F^^t 
iyiir Mfuliamif Pmi ii ti^, aaJltii neariy jl j a ^/ jjr < ^ T a 
MtriJuu, amd lir contrary. 

1. He rtHm lit vi/ati /ailmit 1/ tU g&m amtSUr, atJirmaJai 
a difami Mtridi^Hf u lit irrni jUiiimda, at tht JUboi ^ liar aBgi 
Di/lamiflail*. 

]. BinmSiibf^mi, trm^iatplar Di^amiatfli* ilbm 
Slat fi tti Irm Bi)Uma f Utr aa Errtr taafid h tafiaHimL 

4. H-amHitiaiiifiUiDijiamatJavd M tbt irat mpilm- I^/Um* 
tf lit Mai amd Star, aSraiar fir lie EfiB af litMmaTt FmraUa*. 
— Oa-ahicb it rtmarki tm a fan,ailar Captf iba Ma^md Sur itrng 
ia til fun Ftnkai. 

5. 7bm film ihaXcMi if titftOfirmim; ttJlitdilia-lrttDi^mn 
tf tir Moon aad Star, ai y« fimm Hi Earti'i Court A <*< P^a 

tf OUtroatim, and trai llaftma; rbim /nftrtimiat fir lia ' 

r«, n til JiM tru DifiaMtt tf tit Mma ami Star miJir Pttit I 
iiaa, til DiffirHKi •/ ibi Time if Oifirvatim, andn^MPm*, fi 
rbi M-m aadSiar bavt tbt (ami trm Dif rati) rwdaOt f Depwa, 
t* rte DiSercnre of Longitude, retailed; iiag a mm^HiSa, i 

• -~ ■■ Mahod ihaal>. NalleT'i] MKmiilfiamJii 



amdiawtti 
• D^aMB 



U. DELACA1LLE takei Notice, in tbe 
EPKEMERiDES, from 17551° I7<s, thai tbe Mood aod SDr'i^ 
/itiAi, and their D'^mt from each ochei, are with Doabt, or IXi 
culty, taken near enough for UA. Th)^ u (be Moon'a Motim 
but 130 ± in 14 Ho«n, affoiding aa Arch of aboat a' of a Oqp«, 
BOTM orei by the Moon iii 4 Minutei of Time to a Degree DAmm 
of Lon^tude, an Emr of 3' of a Degree tefuUing ftam tbe C" 
nlion, and Compatation of Ihe Moon'i Irt Plan, audcr ■ c 
Meridian, will create an Error of about 1 Degree M>d a Half 
DifFcrenct of ^firvul LcrimJi. Who thinka we cannot be < 
of ihe Longitude nearer t£n to I Degrcca, on Account of tbe 
contingent Obltadet in the Obfemlioa j hoHeier IkiUfnl the Obb- 
Ter and howeter accurately and well contriecd hii Jn&iwmMita nay 
with which be oblervei. 

Me alfo idviiKea thit in tbe fereral Oraw^lawai eBtamg intoAl 
OtfimitiiiM and Curptratiia of the Lon^tudE at Sea, that the Sow 
of the ateviiMte Ernr, thereby are not Icfi than 5'af aD^m; 
Who aniunerata fcHnl Cat/rt of Error, in taking aa ObfanOM 
of the AltiiudeiaDdDiftance of thcMoonand fame Star, by a (^ 
diant of A^ieffiM. 1. 7bi dtfiHrui Draifiim if ibi Imfnmrti 
1. TbtDIBa-ltyifiafanahimrib.emallA^fmifiU G!^ im IliVft 
if lb Iigramnl. 3. 16, Di^in 1/ ajarlaimmg ib, Caalaa W" m- 
eefaij Imaca ami Pa,aUelifia. hj lU Diamami rf ObUBi, im a CI4 
magaifyng m imr, ibaa 3 ir 4 Time,. 4, Ibi Digaby if a^,^ 
ibitaiagn^Oijt/h win m maid mrafiriibtir angular IT, Difi. {.n 
Abtim if tbiSUf iairr,ptiagim-jtriatt,M II duOijrBi. 6. .<«•« r 
ifaDip-aErr»,fimni.fylaaarTable,, tbm^nB^ifOtfm* 
tim, in umfniiai tit Idna't inn Piatt. Whe futher iddi, that Per 
feai, biving bceirat Sea, nuy ban le«a, that two OUencn tikial 
the Sna'i Aldtnife at Naea. with a good Qaadtant of RcfleSin, 
wall i«aified, OuJldiSei (, S, 7, or H Uinntn of a Depea, iwvi) 
Weather. That in the fa^ Weather and tahuf Sea, oo two Pf> 
loni will apee in arccitainint tbe w^Laiitnde} bntwiBdiflBa 
leaft, J or 4 Hiuulei of a Degfee, which are the Xa _ 

Obfemiioai made at Sea, wbentbt greaWft Caaait lah e aa w J thetd 
IsfinmeoM arc of 



,, Google 



NAVIGATOR. 



407 



Of obferririg the LONGITUDE «t SEA. b/ the MOON'j THEORY. 



OS WHICH WE REMARK: 

TH*T if » Mon of the UriitiJii, Mi'tJ.; &c. wlten by kn- 

nl Obttrntt, of the fune, at the fuM Time, be iaamlnei, it will 

KtrtDTrmib. Fortheagh it ii poffible one Obfirrer miy 

[ doct DM follow thai be mull do fo i Iccaufe It u bjiown, 

ihai ftvml unatoiJable Etroii, lyinf 1 differtal Wajr, comprnfaw 

rather than encreafe one another. And hy 1 Repeji 

in, bj one, or more ObrcTvert, iifln| the fj — ' 



on of Obfem- 

ethodi, we may 
the Truth h) taking* Mean" of two or more LongitmlM 
I. Aod htncithe DiffHence of LaipaJi, bytheMowi'i 

PJate, obferrtd undn 1 diftant Meridian, at s giien ot d< ■■ 

Time, compaiad- wiih the com 

the famt Plan under 1 fitft Mi 



Guefi) in the tame Virtual wi[h 1 fad Sitr, taken by two ObTerra- 
lon, will] the Altitude of a fecond fiatdSlar, taken at the fame 
Time, by a liirdOtfirtiattT ; fium whence tha Mooo't £e/i^K f ^an 
and Lalilidivat determined, ti^ethervith ibcl^rindaof die Placci 
and Time e( Oifiroaiia* rbut without any Allowance for ParaBaat 
aod RifraSi'K, wlwieby the Operatlaa became altc^ther irrfvia.} 
To which DbTerretf Time and Plioe of the Af«a>, the Time cotmf- 
IKindent was ilfo found in the Tablet to the /on Plan, in i blondotot 
ffay, andtbeoce, irrautmfy, the DillereBce of Lomitude hi r>u« the 
Meridian of theTiiMri, andMeridiui of Otfin-atin. 



i^Ttme, when the Uoon hii 
from coirea Tibin, will be 
^Crtiiini for corteaing ■ Ship'i 
uSgitodeinlongVoyiBea. ,,.,,.„ 

•Ttaefiri itt D\jct«trj •/ tbt DifftriiKi •/ LnpifJt, ittmxt Green- 
vicb a^Jlif Flau of 6ifi-*an«i, h N„hit -•" '*•■ '*< D'/*"" 
tfTimi lumd in" Dignn, ("affawiBf 15' 4f a Dtpm n 1 ift 
irr.mt} iitwal ilir.mil -fiUMo^ bailing ih, f«m cmp^ud Plact 
ii Creinwith, ai itat li/irvtd minltr a iliftiwi Miriiiam \ aBtrmai Jar 
-parillaxau'Rerraaion, mfht Plaa •/ Oifirvaim, fpr rriniirg 1' 
jUm't effaiiM (• Ur im Plact, 

It ii obIei*ed ibit the Jlf»a'i Aliiioit in the Night tin be bat ti 
Krfoaiy taken, though the Sky be then TCty clear ; beciufc the Hoti- 
of the Sea ii then fecn but mj awfuji^j ; unlcA the Moon be 11 
the HotitOD. Tb^ arifea from the Uoon't reflcfled Light 



le Siirfact 



in] ti 



ill puhfliedClaflViirakiog the Eflfca unequal, A Truni of I- 

Eare painted in the Vinicmlof the Mron, where Light hia:!ento 
juifttheHoriicnof theSia beycnd ii| •hithhoweier italwayi 
^near the End of that Tuir, artft when the Moon ii near the Zt- 
nith. But when the Moon ia lery /«v, or neat the Horieon, fie. 
i^/tit>^J thiirrflcjled Light ii confonnded with 

,„._ .. Sea, aod then ii the Time yoo may lake her 

altitude the ih^ Bualj and fit for the Parftfi 1/ ihi Lamgittdi, 
' t<«i\ni to DilaU,tU\Mah»i. 

A fmall CkriUrrfi or Thickncft at the Horiwia l> rtckooed tnoAer 
_ bAicle (o tak-iig the Moon'i tne /t&iliiJi ; btcanfe we thereby lee 
(he Eitremity of the Horiion but »eiy " 
■ f the Moon. 

he Moon fiSii to the Meridi 
RifiDg. DrbcFore l^ii Setting, her Ii^jr ii then too feeble 



OUR METHOD of .Abrsiaw the MOON'a tni« PLACE vain 
^JfiMMERIDIAK. 
f:^' Bj latiai rbf AUicaie >/ thi Mmk'i ^ffir ar/anwrUmh, tmtlt 
fam Vertical -witb a mud liied Si&r, mitft AlliuJf 11 ita laia (al- 
Irw'mgfir Pittila^tm am tfhaurii, and Refi^flian) at a nwu 
TnH, it a gima Latitude, yn airfy, fitm lima, Jairjiini lit J^h'i 
true Lon^tude A^Lattttide, vtitbniB It 'fOft i* dairmiuM 1' 
Difiata if lit MiriAan, UtwHn thi PU» tf Oifitvaim aadti 
Medium, fit wiM'c^fvrrfi aflronomicat Tableig/r£< lunar PUta. 
aiifitJ. Ft' fit DiprOKt if Tim, i* Dirrat, ttnaair lit Tim 1/ 
Ataam'i trat Pita aSfavi anJn- a iHjlami Afiniia*, anJ lit Tlmt 1/ 
CtmettuefiiCtHmpiaiJfiimTaila/wittJu ibi fitfl Mtri£n, nil! 
it Ibi Difference e/ Longitude between thore two Merldiana, 

Bcr ibi Mtri£Bn Aliiiaii tf m •/ ibt Mini's Limbi, aMiTiwu vibei 

timcta Iht AteriiiaK itrng lelta, (mllrwiiit fir Rifraflion •»/ Paral- 

lai) aijitt Turn itftncr afiimkitt a jiWfaied Star iranflii tbi fnu 

" '" ', vibtJtMtHJitn aiiU*it ii irml, afctnaneJ, wi/l rltit ibi 

■HI Piece, at fita frm lit Earth '1 CcWr, fiai btr ■mSih PU 

---- -•■ ' ■ ' Milt, 



fimfimittBanfii 



:, rtt fotufS if a> 



ytiibtd /itcatji 'bai i 



'. tilcatji 'tt 
"MPitiihx in ritbl jlfrn-fea tf lit Mm, m'ibt Mtridlaa) and ll 
jta mllhavi ibt Digirtna tf Longitude _^nni tbi taa^Mi Timi It ttt 
'ami mi lunar Place. 

EXAMPLE of a 



•"•Fr!'"'£ '"" '" "■ ■■■■■'--I" •• i.^.j-j..", .~ I— J .^- 1- .-— 
iw ibt Mtriitr, n6i, tnal Tnu, ibt M<m'i ina Plata (at fita frcm 
lb. Eirib'. Ctntir) Ufmni frm tir -vi/iUi Plaa (ai fta fitm 



ibtEarlb-i Surfaa) ; 
- ■ ie film Green 



4> W : Required, frtm tbtati, Ibi P'la 

. •■mbnlbatObfimt 

-' Xt>GnfwitK 



nine, e.aflly. her Meridian Altitude. And when the M.>on i> By D< /i Cfl'/i'i E,'i-ir. ' J "t PL reduced to <7«m 
ered wi!h Cloo*., in the Tim. ,f her P.ffage to the Metwii.n. ',,5. j,,', i-^Noon U?eW»8' „■<■ • . / 
r.i.Ko.hirgtnbe,ioneth.tDaT. All which /««™«««,muft be ' * "^ "^ ,L Koon 7 Sit °'f- >*' Si'. 



Kcd to the proper e^Stj-rmiVyof obferving the Long! luie, 
._/ render the Rt/ali of tlie Oblertalion eitremrty doobtfol. 

Id ihii JHfttrJ, befidet the Moon'i Altitude, it ii nrerfliuy to haie, 
ai eȣt at poAiblr, the DiAance of' the Moon &nm a near Star, that 
we mayfucceed without hating 3 or 4' Errrrf and we mud ilfo haie 
aieiaftlyaipoffible the AltiiuHeofiher»«5rrir, one of the brighten, 
MI i, lb, rirlical if Ibt Mta, for aioiding the locDuirettieRdei of iti 
RiJbSin, ihicfrtqaentlyDccarioniittabereenDnthe Horizon of the 
Sea. In taking an Ob<«valiDn of itaAllilude 7 or S Minla of Errm 
thciein. viill not be of much Coocetn in finding the Htar /trjit, or 
Time uf Obrertitlon. There are but /lepCe/ri wherein an ^or in 
;he Stir't Allitttde of 7 or 8 Mi-min of a Degree will caufe an Ei 
of 1 J Minutet of Time in the Har A-tli, or jDegreei and } ' 



feenently ROt«b< 



IN the Year 1710 there wm a fmall Pamphlet, (which It hllei 
bito oar Handa) printaj for O. MAnnfp, at t he tt we Cmrai in Si 
PtaPt Cbanb-rarir intitled A ATne and Eaff METHOD to find 'hi 
LOHGITUDE at 5m. Which waa Irom the Ohterfaiion of the Alti' 
tndetW thtMaoa (tboagbDM of her Limb, but of her Center by 



diuTsal Mot. 

Tljn ''''■ '" "'■ ^^' '*• •*' SS' 

iS^ firl, from the Noon of the ijth. 

Hence it ii iS)> i>i^ Noon, itCrumoiib on thrtjtli ftfranauVj/ 
Day oF Julf, or at 6 in the Morning, on the 141b civil Day, 1764, 
when the Moon hai Longitude ZX ^" 39', nearly. 

But to determine the Difference of LoagiCude comflly, compnl« the 
Hson'i troe Place for 17G4, ftlj ijil, ■£'<, at Grmuiii, and repeat 
the Operation, till the »tfa/Time>t CrwnviVi i< found comfpondent 
to sr 4' 39' Long. B ; then the Dii^ffrirrf between thecomputed Time 
It TrBiwiiiand^^ 13't ii'< ao°> Time of the Obfetiation, \iaiti 
the diflanl Meridian, turned Into Dcgreet, will giie the nrrvff DiSe- 
rence of Weft Luifiiuili trnm Gmimitb, leqaiied. 
By firft XI. EquB. marked C, and ttmainr Tab. 17*4. 7"i' '1* '8b 

Crtnpixeb, Moon'i Placi . SS i'i^ 6* 

1764, July 1%* i]^ iqb under dift. Moid, obrened ^43) 



Moon'a PI. at Gmwvlcb Ihort of Place Dbferrcd 39 54 

17C4, Jatf Ijd igl', (r/wnBicir Moon'a PI. computed ^ 4 ]) 4.3 

Hourly Motion of the Moon 34 yj 
S»r, »' 37" ' •* " SB's*" ' •" 9"° "*! '**" '**' " 

17S4. "J 'J »o o Tune under djlbnl ^^^ „., ""' 

— ■ — — — — Meridian J "• -J » is • 

'"'.fimr 5 49 10 under dift. Meridian. 



Anfweiing 1 



■■ ! 49 
>*7">7 



i7'3o'W.Lon. &,Cr«»aoK*,i«q. SifiribiRill 



db.Google* 



r 



408 



The ROrAL ASTRONOMER 



A NEW METHOD of making c LUNAR EPHEMERIS. 



7i,/™ 



ibi MOON*! PLACE, —J tf »ul:i«i th.**r EPHE- 
MERIS. 

LET (he Moon'l Place be loniputed 4. Tjnin in * Mmlh, it Ittfi, 
{ihoojh 6 Timei will be btttei) mi.on the Hoon of the Syitypa, 
id S^iaJraiura, being iht ijrrrBB L/nri of heijoo. 
If 41 |o j' be <^'^ to th< Moon'l Fn*F/<wc, fottajamOij, it 
illpn bet inic Leiipi*A fai my other Dir, wiibin 11 or 15' it 
art, after 4]i6 D*}t Ibaat 11 Yeiti, 309 Da;), or i> Yean 
waotiag ei Daji] ire elaprcd, 

Tkeniorc, look ioto > »i-riA I^pfnvrfi for 1 1 Vein befote. And 
if H» vronld know the Moan'i Inc Plicc on the ifi cf J^mrj, M 

' " ^--■^< ■„ ..-r-.j. ,0 which add 

th.I^ /)-,./>. 

looni 11 or 15' (la miflj 

of lur compaled Place br pod tftgatmicti TiUa. But on foiDe Daji 

of the Year, «rtci4ii6 DaiieWed, ibei>i#imM will bcNolhiD|. 

EXAMPLE. 

D PI. Noon.] Lat. ^ )'tPl. I 
i7S»,H.i6,O.S.or»7,N S.SLtt'ty'U' S»' / Oi/s 
+ 4 ' 5 y ^•"'- 
I Koon. Lat, 

J'.P1..7«4.7"»-'^'-«™'-/"S 3"l , J/ 'S'+rU-Ss' 

Procecdiog tbot, from Dif to Djji, with tbe Placci found in an tU 
Eftamii, Dill adding 4* 1° 5', and wriiing a|aliiftthe5iiau, theref- 
pe«i« D*J« anfwerloi thereto, tuatSinly, you will baTS ■ m 
Efiimirhof laurPltta, anfmring nearljto the Tnab. 

Ptrta't Efhaurii hu been the ^ for thii Punore ; becanfe Dr. 
HALLEY coodefnnddl, •nniiajl]', to iffift tbit ifbtmaidijl in hii 
Campotationii efpeclillf in the lonar Placa ; ii the late Mr. Bmj 
Bti^iM, F. R.S. then Aoihorof theL(A(iO'J'/, obferved in 1738, 
ibo wai peironillf acquaiotcd with both thofe GentltoieD. 

Ai IbE Moon'l Irue Place mi; differ from thit compoled, for the 
D171 oF the uns ysai, ^wanm, Sfc. (bme few Minuiei, ma; pro- 
porlisnibtr be *dj/d 10, ot frilraHtJ from, the computed PUcei, 
foand after tiub Imirvtl, iccordioE ai the Cafi mij reijuire, which 
will detetmioe the Mim'i Plm to • defiied Accuncj, wiibout a mem 
CBmftlailm. 

N. B. The forepiiag Mrlhod (coramDnklled b; a FriaJJ of eSi- 
mating ibe Mooa'i Place ii ptBpoJcd for Trial, aad making a fanher 
ImprotcsKnt. 
'tiy Sm PalladiDin 17CI, P. tS, fir t Method e/ Jmrminii 
fwi'i rrii(Fi^(B/r(r<Fliai«afBW (^ l%Tt*rt, xt Dtji, 
tmda^obirlAliCait. 



■'•'g itf 



i< fl&«'i Rl/,-^, („ , PUmtt',) ,-, , 






with the 



It AlcnilioD 



I the eftimaie R.fing, 1 
more or left 6 Hoon, (ucotding it i> ii len or m 
will be the near Time of Moon', (ot a Phnet',) RifinViB the Mor 



r*/iuffie 

Enter the rdJ/(ofobli<)aeArcenfioai in Time, ■« in Ci-di, 
Vol of jtfinmmf, (proper to the Liliruife of the Place) ind 
Moon'l or Planet*! Longi'ude and Ljiitnitr, a the eftiinii. 

lherf/,>«^/™/« in Time, ft,™ «hid.teloa thiTo?! 
-"'- ■ the Remainder 

iug, required. 

J^^.rfA-«rr«r ./ri*M«',^„.PWV S«,irt. „a^. 

Enter the r^ of ^,„^„./„,, i„ Tin«, (proper to .be Lati- 
tude of the Place) with .he ,»./„ Sigo.»I DegriTof /„rt^. ,^ 
™...r7 L#r,ttAlo*b.t .h= Moon [or Planet) hj, at the^me of ia. 
.,af, and lake o-t the M,j.. Defceofioo io T™ Mreeinr thfrT^ 
from which t^e Ae Snn'. .ight Afcenfion inTime, a^7-he'R^' 
ia, DHueorlefifiHouri, {"cording nit 1) iehorm«( than 6 H^u,.l 
will be the Titae of the Moon', (o. Planet'.) Setting after Noor 
<)Bired. 

Since the DiBerente of tilitai .ffinfiai of 1 Derree (in our 
tudei) iniSignofAiif A&eofiDn, .1 jc, fl , np, ^i. ti * ,,^, 
6- of Time, at moft, if the Moon", Lii^-Jde be withfi *' Z , ' 
of Tn«^ which it will /(^Meneei*, andfcr themofl Pan bo lefs it 
«mS4« bot .boot ,- Errw in ,he Time of R,>^ i^d S„,;„. Xni 

:iStUlo'::i^f'.tt^v^,-;er^^^ 

Eot, if Ihe be in Ibe Sign, of >6.,, Afr^fi„ „ i„ y" '"J""^''- 
B. n, the Difference of ,*/.,CJU. of , D^;„7;^'^' 
fometiinei, amoont 10 iMurriin T,me. G.,/™«,i/. Hould ha 
Longitude raryaiaboK, tbete will not {b; (*/■ M«W of Comouii 
d«)^b.if-f a Minor, Difl™« (a,L}) fr^ ,he ^ I'iJ^^'''^;^ 

In Compntationi ot thie Klsd, it ii ne ceffar, to be cirefiil in rtdi 
ig the_Moon'i Plato and right A'e.nfion. lod^Son'. tight Afcenfioi, 
if her Xi/njiDd 



for the Time (iren, to thofe fa 
Smi-^i ot(in 

f^ It iht firtpini OftrMi 



Operu 



n) for t 



Of the MOTION of COMETS. 



TR£ Rererend STEPHEN BOLTON, MA. tni Ilia » of Sla I- 
irii^r, DrftlAI'i, h» oblittd ul with fiviral of hit curiau Rcmtrh 
tailmfitvimtm, on the Motion of dwrri. TheDASlSoo which 
be found! hit IrriproTementi, inil to which he refrit all hi Compala- 
■ on the mii/'T Motion of the Earth roand the Sun, 
from the'liirt to the lift ObfiTvation of the Comet. To awmfJifii 
- - - -- . (,fti„f,„-t 



which, 
ouad the Sun, 
Hi, Umtti 

^ ,arfri.S.,,, 



of the angulii Motion 

ia diffi:rent Poitioni of dlfterent Cometi obfetied. 
iiiit. MiTROD ,f fubnaa'at f adiixg tht Atla, 
n. H a.Jfrm mttr ^gla -uibkb rti tarit JifitOt, 
■iJftJnUh lir^ila t>ifx-i,tJinJiffm.l P,J. 



Mofconr, if the pariMIe Trryatrf of a Comet be fo 
Eirly, toanfwer tht Obfertitioni at the Earth, it U nr; 1 
I conclode f if/nt,; that the frAviff of ihatCoiael, In tti tnie«/&Mj( 
.f^ir. In and about the PmWiH, iVd Peri he lion •/)«(««( itielf, will 
ba'M7 KUrh the lame, aiiq the iOi^mat farmMUCmt, 

And, if fo, then Nothing more inBunar {be fifi) battofindhcfa 
Smt-Trdtftntfi to the Cimet'i elliptic Orbit, {or p^eiitTimt, the 
ooe (ifiBt the otlur) u guj aoBljf coirefpond With ill the Ohfena- 
rioni of the Comet tikn [ tai which (be Oft) nay be eficAtd by 
Tritl. 



«/r- 



|> Sh t^ tafy a,J fiirt *f«b:j tf fi„dhi Ii, 
Anomaly/aPlioetw Comet. P. 96. 

In taking Obrcmtioni of the Ahiiode of a Omit, and &uj Slai 
in the fame V^nkal, rither above or below the Caaca, Mi 
»**wprfyeaiiheLlgbtfiom a dark Lai,\hon\ up a im JL'vtrtfh 



playing 

The^i'wifrof the Cmui. (al]< 
ferfation, and Latiiode of the Plai 
Diflanct ^m the Meridian ii alfo gitrn. Who 
Sran Aaimulh from the Notih, the Sii'i Angle 
«nin«/andCire!eofCetliniti:n, iheStar'iAltiiudt 
the Diftienee of Altiturt 1, the Diffr.e'ce of ti jhtAfanllon V Co' 
met and Star, and Ca-Dedination of the Comet j and the LoDiitndc 
and Latitude of that Comet, ire found. 

M (Jm >«r AunnA, wHjffantbt/irtgthii innaomiaiCfZ 



IT RefnfliDn) Time of Ob- 
<E gi*fn. the S'u'. aogulir 
ct the Comet and 
of PoGlioo, b) 
-' ft,. ' 



_ 0*/™«m, lailaw the MiiaJ, «/ li. Comet, ami fiied 

Star, M ibt fm Vettjea', ntlir ahret v JtAeo tht Comet, ar ittj^ 



yOwigle 



tni NAVIGATOR. 



40J 



EXAMPLE oflBUf COMPUTATION. Acconliog to D. C. 


hjtt^'ittUa. 


SUN ud MOOJT. PLACES conpnted. C. 


ARGUMSHTa of EOyATIQNS ud CONCLU- 
SIONS. 

MonAnotnilTof tb«)' 6 I J «. 
x,yitn Arf. Anil, or 1. meui Long. 

a. Qi J'.ApogM . 7 J? la 


S<i*->£f«"^ 
Swi-it«el«yinrdf 


i •; '^ n 


6 11 5* ji 

6 8 I4 ;« 


6 10 jfi 4( 
6 1 1* tfi 


^ «. S6 46 
3 4 4" 37 


3 S8 36 

An. Aig.tomeM 
Long. Sun. 


1 « 30 

4,n.Arg.tot.ue 
Ung. Sua. 


MeinEviSi'Mi 5 »3 8 10 
1 Man EW''«* of the S '1 Center + 

K*. 6Equ.tion. , . +47 




B'.Longiwdej^ 


J'.Apogte,^ 


J-.Ndde.^ 


Atg. of fvrSiM, cantEt, htati Suo'i 

maaPiicc . . . j ij u t? 


I73» 
17" • • »*• 


3 ai 40 j9 
S Tl 44 41 
*° 34 


5 9 45 M 


8 V 47 49 


. . sg 


31 S3 


. 14 » 
.... I »7 


E»ffi'«*-X^MA'ii to tUi Argument — a 9 40 
£K««iBP-i:f«rr«tDArg.ETee.(fn>mO ■ 

trt.>!Pl.)s.i,0 4'»,» . . — 4 11 










Diff. e= Equiulon of Ew«(m from qui- 

' dtupliuilc Ruh of Sua'i Dili. . 5 18 
tilint(ia-ipaxs&J,cudivnX.<>l D'iCenter — ■ 15 


MMdMotiom 


• 4 1; :s 


'4^;: 


1 11 44 '7 
+ 9 *o 


J I. cquitcd 
Apo(« I. tquattd — 


°> IS ;s 


e S 54 '« 
J-.Ap.,.e,.md. 


!o " V^ 


GnaltBI'swrm of ^'i CeaMr, Ihun 

rri»/, JIj()VDfSDn'il>ift.rtruliSng i . ■ 3 
According to Mt". 3<> + 4<t>E4"«'>» • . J * 

E-Mairm-EMiimf irfpwtinlj at a Hfximi^. u 1. E(- 

P- 31M 

C:^ 72f*ic«/t</tfrn4<ua PROOF, ital li. Sum 
tf ihi 6 ni 7 £f«t»», « fit Ar»ur OF THIS 
WORK, » s:4' e', « . M«gm>m, i^.4fr>m A. 

pliuu cr 4tbPtm»r ofibt Smm', Diftma imtth- — For, 
u the gcncntcd Equiiout ire difeftlr >i the Indim of 
the redprocd geaenting Powert of tJM Sun'i DiAuo, 
S.7, 
A) , Index i 4'6'Ei'at. -.i 4 Inda i ^tft- 


6 Equ,ri<.n. 


6 . S .. 


6 I i M 
4 S 


3 >« 3 1< 
[.flAr.li?. 
a. An. Arg., 
Eme.fr.Oii, PI. 

Aig. of Etcc. fr. 
» [t.Pi: 

Eqnitioiu. 


AaoDi. 7 £i;w(. 

Elliptic E,u.tion 


< . i .7 
+ 7 « 


S .7 o- >• 

+ 047 


Anooi. a EsDit. 
. £«cd»a Eqiution 


- P » " 


S »7 4 «9 


Anon.. qequiUd 
Vitfation-Eqintion 


« 1 5 .0 
— 1 14 


N». 


S »9 'o 


True Amamljr 
Apog. 1 equted + 


« . 7 S« 
« > M .6 


II. 
III. 
IV. 
V, 

vr. 

VI I. 


16 


047 
1 40 


s p-iOib. Long. 


° + J 1; 




T 10 8 5 


Error 


- = » 


OniittiDgth«7thIi]intkiii>_^ , 

By Hallr/'t Taila, Emn — 5' i-,' 


An.B. 
An.Ar. 


6. .Vlt 
lajo 


ikSE,. 


.3 6 


JiO 


S»?6 4<' 


+<'S 


^^MmMI* Pe^as-. Or tbc Siipplownul ASTRONOMER ind NAVIGATOR, complecug th« |[9«/4r™,wr W JKm^<r.- 

'GoDOiBing tbe«r»n>jtiwj Pm', TABLES i}Mt, KqiLtd) of tbt Ridiol Man FAm ind Xfixtm of dM SON ud MOOM. 
CORRECT TABLES of the R«lkJ Man Pi«fl ud Ww 0/ th, PLANETS «d SATELLITES > ud £f>«i« for comuitia. thdr 

W^th uEPHBMERIS, fi>r 6 yanfnMtlM I><«/of Publiati«), 
CcmeiBfalltbe&Ma'jCi&KbnaMot; ud TibUi fitted for obforing the ^w^nfa&tmtbcftsplCl^nitfMjitO/iMnBfat. 

B7 lb AUTH(Ht oftbc ROYAL ASTROIfOlUR uA NAVIGATOR. 


- ' ■ 




Sim , 
MUt. Pit. 


Loft. B. 


rf. 1.JS4. 



Ggg 



yCoogle 



rhe ROYAL ASTRONOMER 



EXAMPLE of COMPUTATION. According lo Mr. MAYER's fupplemeDUl EQUATIONS. S*t P. gj. 



IB Time, («tb«Xfeiduflf 



«7» 



Tt. Lone- O f'- ^' 



8 SS 



J* 

3 48 



1 38 49 



o .4 .< ! 
— I SS 

OM. Aboo. 



Long. ) ft. Eq. 



>j ll iS 
4 47 »* 



I. B g JO 40 



XI. 56 q 

xir. 4- 38 

XIII. — 10 



«^:li 


)T 


Eqii.t. Prwf. Equinoi — 


14 


Lmb. SoDfrmn Equina. - ,j- „' 

Long. J fVooi IqBinm qp » 17 

Laritu*e J) Smith 4 ,6 


T 


Ung. ]) obr«™i ty 10 .7 
Latitude obfc^fd . ;6 





CntriaiaDof ihe Longfiudc of the SUN mnd SUN'i DiftiDcc ftom cbc EARTH. According to Mi.MAYER. 



i JTCH^hl 



,, Google 



mi NAVIGATOR. 



A TABLE ard EXAMPLE mwmtdttUi. for USE. (the TRUTH of Jnvt/i^aMn and On/^i-A-SB being proved.) 


According to MiGciLLANEOui Tkacts. Wberebyyon may reduce a COM&T's Longitude frcm ihe Perihe- 


lion in a parebalk Oibit, to the Loneitade from the PeiihelioD in an tlUfiU Oibit ; by ihe Oift'ccence of Moiion 
in tbofe Orbit*. 


(^ " 


M.;.. 




For Log. 


^^ 


M.n. 




For Log. 




Mm. 


co>»rp. 


tor Log. 






C,„r=1p 


IcrUp. 


ftodi 


of 




of C»»( 


from 


of 




of&«« 


from 


of 




of Cm,, 




of' 




of C-ml, 


ptt. 


Deg. 


Log. 


fr. Sun. 


Per. 


Deg. 


Lo,. 


ft. Sun. 


Per. 


Deg. 


Log. 


fr. Sun- 


Per. 


nrg. 


Lci. 


(r. Sun. 


- 


— 




— 





— 


— 


— 


1 


+ 


+ 


_ 


'^ 


-t- 


+ 


— 


■ 


r; 


"■4770 


j.Sioo 


4' 


B36' 


1,9110 


9.0006 


Si 


151' 


1.IB17 


9-4777 


,11 


3<47' 


3-!499 


9.75.6 




1.7770 


6.4,1a 


4> 


8j6 


1-9119 


9.019s 


81 


106 


1-3139 


9.435, 




367s 


3-5653 


9.7601 


] 


90 


•■9S33 


6-77)5 


43 


836 


1.9131 


9.0378 


83 


161 


14170 


9.4914 


113 


jSoS 


3.5S05 


9.7690 


4 


119 


1.0778 


7.0141 




S36 


1.9123 


9-osSS 


84 


3.8 


1.5011 


9.4996 




3941 


3-5956 


9-77E1 


_L 


149 


1. 1740 


7.1 17« 




Hs 


1.91.7 


9.0717 


ss 


376 


*i75° 


9 S067 


■1; 


4120 


3.6.05 


9-7874 


6 


'79 


..ijii 


7'»759 


76" 


8ji 


1.9100 


9.0894 


86 


435 


2.6386 


9.513S 


lib 


3-6153 


9-797' 




Id 


M'78 


7.5C95 




817 


1.9.76 


9.,os6 


37 


496 


2.«9;i 


9.51^7 




4364 


3-63<,9 


9*070 


S 


157 


»-374S 


7.6150 


48 


811 


1.9145 


9.111! 


88 


518 




9-S»7S 


IZb 


45'3 


1-6S4> 


9-8,71 . 


9 


166 




7.7169 


49 


814 


1.9107 


9 1369 


89 


611 


1:7936 


9-5341 


119 


4H7 


3.665c- 


9>«i78 




>94 


I'tlt] 


7.8.78 




Ba6 


1.9061 


9.1510 


_£0_ 


_m 


1-S371 


9.5^09 


J}^ 


4^25 


..0Ri5 


98,87 ; 


~J^ 


3" 


1.5074 


7.S998 


V 


796 


1.9007 


9.1666 


9' 


7 Si 


.8776 


9-S475 


'V 


49S9 


3.6980 


9.8 (to . 




349 


1.J4J1 


7-9747 


S» 


784 


1.I045 


9..B08 


91 


823 


1.9151 


9-5S40 


'3' 


S.5K 


J-7'=5 


9.86)3 . 


'3 


176 


..5760 


J.0437 


53 




i.!i74 


9.1947 


93 


891 


1.9506 


9,560; 


'33 


S33* 


3.7^69 


9.8740 . 


'4 


40J 


1.60(3 


8..C74 


54 


7S» 


1-879 S 


9.1Q83 


94 


963 


1.9*37 


9-5670 


■34 


SSit 


3-74>3 


9.SB66- ! 


.'S 


43° 


t..6,i. 


8,1666 5s 


743 


1.8708 


9:'»;5 


95 


1036 


3 °'i4 


9-!7'4 


'35 


_56c,« 


3-7';57 


o.?9- , . 


^T 


*i* 


..6583 


8.1117 


iS 


7.6 


i.!i6io 


91344 


96 


IIIO 


3-°45S 


9-5797 


'36 


1^'^ 


3.7701 


9.9.31 


'7 


4S0 


J.6S16 


S:i73S 


57 


708 




9.1469 


97 


I1S6 


30741 


95860 


'37 


60SS 


1-7845 


9-9>71 


iS 


JO 5 


1.7031 


!-3'" 


JS 


688 


1.8378 


9.1591 


98 


.164 


3.10,6 


9-,S9il 


>3S 


6197 


3.7991 


9-9419 


'9 


i»9 


»'7i33 


8.3681 


II 


667 


1.8243 


9.1711 


99 


'343 


3.1179 


9.5,86 


139 


65,3 


3.8.38 


9-95-" ■ 








8.4. r8 


645 


1.809 s 


a.1819 




141J 


3'51i 


q.eo50 




6739 


1.8286 




|Ti~ 


57' 


»-7S94 


8.4518 


61 


611 


1.7931 


9-»9+3 


ioi" 


1505 




9.61.3 


T4V 


6974 


'■M' 


9.98,3 . 




.S96 


»-775S 


8.491, 


61 


556 


'■77S4 


93°S5 




.5lig 


ll^i 


9.6,76 




72,9 


3-»sSi 


10.0064 


»J 


6,7 


,.7906 


B.J29S 


6, 


57" 


1-7 S!7 


93163 


lOJ 


.673 


3.2136 


9.6139 


'43 


747 S 


3-«73« 


10 0141 


»4 


«37 


1.S046 


8.5651 


«4 


541 


1.7338 


9.317° 


,04 


1761 


3>457 


9.6301 


'44 


7743 


3.8889 


10.C417 




657 
676 




8. sqg.i 


6; 




i.-,C95 


9-3374 


'o.i 


.850 


1.167, 


9.6,66 




So^ 


,.-9t44 


10.C610 


1.8^97 


8,6,20 


66 


43. 


1.6827 


9-3477 


■06 


1941 


3-1879 


9 6430 


"^6 


3,,6 


3.9199 




17 


694 


18,10 


8.6634 


67 


450 


1.6526 


9'3576 


107 


1033 


,io8. 


9-649r 




8630 


3.9360 


10.J031 


i! 


7.0 


..a,.4 


8.6934 


68 


4.6 


1.6.87 


9-3674 


log 


iiJ7 


3-3178 


9.6560 


Its 


^S96l 


3-9514 


10-115, 




716 


iE6io 


8.7114 


"o 


38. 


1.580s 


9 3769 


109 


1113 


3.3469 


9.6617 


149 


93.1 


3.9690 


,o,,4Si 




741 


iS»,3 


B.711D1 




3M 


...361 


9.386. 




1311 


3-3656 


9.6694 


JJ^ 


963, 


3-'8;9 




3' 


7^; 


'■sz-' 


B.7770 


~ 


J06 


1-4857 


9-3954 


iTi~ 


1411 


3.3840 


9.676, 


'S' 


10071 


4.0051 


10.1^0 


j» 


7fi3 


i.|Bij 


H°r 




167 


1.4158 


9.4044 




IS13 


3.4019 


9-68,1 


'5= 


10491 


4,oic3 


10.1131 




7S0 


1.I920 


8.B2S0 


73 


116 


"■3537 


9.4131 


"J 


1617 


3-4'9i 


9 6901 


'53 


10540 


4.0390 


10.1504 


%i> 


791 




8 8,11 


74 


184 


1.1639 


9.4118 




1734 


3-4,68 


96971 


'SI 


11416 


4-OS7! 


10.1791 




Soi 


j.gou 


8.8755 


75 


14° 


1.1+58 


9-4303 




'V3 


3-4538 




'5< 


■ 1529 


4.0766 


.0.3094 


"Tfi" 


8c5 


1.908. 


K.8,80 


76 


9S 


-.9767 


9-«86 


m6~ 


=9S4 


3-4704 


9.7.19 


T^t 


114B, 


4-0963 


io.i4,i 


37 


K>7 


1.9121 


89198 


77 


48 


1.6840 


9 44t8 


117 


30tB 


3.486S 


9-7195 




.30B6 


4i568 


.0.37*6 


33 


813 


i.9,s6 


89409 


78 


+ 


+ 


9.4546 


118 


J.84 


35030 


9-7171 


153 


'3:4= 


4-1 iSo 


.0.4098 


39 


B»9 


1.9184 


!5^'4 


S' 


49 


..69,0 


94614 


119 


3301 


3.S.E8 


9-73!i 


'S9 


14455 


4.1600 


10.4469 


*o 


8?1 


l.qiO< 


S.atl<3 


80 




l.Of 06 


9.4701 




J4" 


i-'%i-: 


9-741 ^ 


l6t 




4- 'Sit 


lo.iSfii 


USE. In the ifl Column find .he CwKf'. tc»;H»^. from ibe PtrihcUon the rimeai that gi>ca iccordiiig to ihl Hvpothtfis of t^rjfofe Ortit 


n,»Hoft/i, DilaCaim>,««btr7»ki>,) agjinlt which LonEilod', !fl iheirfC./rt™, jou hivt the Loa"ilhin anf»e.inr to 1 NLtrbrr of Mi- 


aucei in W C«iiiir«. From which Logititbm /.fafsfl the Loprithm of the r™/«- Af divided by the TniMxn DifliT,i of the C.ir,. 1'. elliptic 


Orbit, ind the Rtmtinlir will be the Lagtrithm of , Number of Minuici to be idded or fuhitaOed to ot from the Ijid tdn«it>ide, » the TbUi 


ibove diwa., for Ihe aw^l't t™ Longitude in the rWfricOrtil 


yiievvife. f.cmiheLoB)rilhmi<>theiiiCg/.>»>, cnriefpanl^ to Ihe fiid Longiiude, fubtrjA the Loganthm of the fiid Sgi!i,„r, >nd the 


Reiminie-, wneaed with loii/ntn, will bclhe Logaijthm of » J^irnw/iiito be deduacd, fiom ihe Lopriiho of iheCcmet'i Did-nief.tm 


the San. in ihef4«i«fif lljfcil>ij!i, for the Logiiithm of the &»rt',Di(lince f,om the St'N, iccorjing (0 the imptUOrhii. 


EXAMPLE. Let ibintiiir jtxi «/ ft(£i/i/(l'i*«= 35,717, txd Firxbtbtn Dxftana ^ o,':%i% (hri-t !hi Crhii ^.f lit Ctird fur, h ihi Yfr 
t6Si) a'dlaik'Vot^im'tfrMptriMi-Mardmiuihifcrtitn, Orhii, « i)'. HiUey'i Tjblc, it 440 3' 10", w(Vi (i</.-f. c.sCiHjg ^f dr 


Oiw'j Oi«e-(« >«>"4' S". t*^//*^*- 


TheLog-of ■'■—-= I-7S77— • • • 1.7877 — 


°-S*»S ..jiiSinT*!.. . . 9.05SS 'B'iofl 44» Lonsi""!'. 




Subma J3'39'= ij',65 . . i.ijst tog. 7-»678 


Cmi J Ptrlb. 44' J JO ID pir. Orb. 


— 10 




Rem. Long. 4* 49 41 ftomPnih. req. 


Or Log. 3.a«7B..N» 


eorrefp. ,1-0185, — 


iDe%-0>l>. _ J Lof. Com. i in pm 


.o.b. ,065838 




Log. of Comei'i DiAince ftom the Sun, requ 


"■-.f^X: 




C5> The foteeoing T.kle no! only reduce. tl;e Comel'i Unginde ftcm . MraW/r to an elliptic Oibjt, by the DKTttenc- nf Mniioi in thofe 




made thenon differ eSentially from the computed PUcei by ihepanboHc Hjf-abijb. 



































COMPUTATION 



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