' 191. L e t therefore the timekeeper be well-regulated
and let to thè ’time àtj Greenwich, that being the place
-from which vVe rG'ckori{©,ur- IKgftqffe; ; then if the watch
’ïi«itËer;tgÉihs^nor fcfës, -k rwill^wayé fiiow the lime at
-,Greenwich, wherever., you 'he.\._ Now.to' fine!-the ^
tirnè bydhe .clock at any .other place, take the-Itm’ s' altitude,
and-thence & nd\li b y article 61 ;-#W : the
time thus found -is apparent time,"or that founts b'y' the
Lun, which differs fromfthe time Jliown -by th e ^ t t k Ë|gj
:the équation of thne, as me haÿê Æiown^iù ai$jclfe i p : We
miuft therefore apply péréquation o f time to'the.' time
found by " the fun, and we ;fhall get the time by the
.clock ; anefthe difference'between the time b y the ëldck
:fo found, and the time by-t-he^tlme keeper,- o l l i g time
at Greenwich, converted into degrees at the râ|^ÿf 150
dor an hour, gives1 the longitude o f the place from Green-
-w i t h For. example, let the time b y thé time-keeper,
when the fun’s altitude was taken, h e ’6hVhl^^and let
the time deduced from the fun’ s altitude b e jh » 27', ;and 1
Juppdfe at.that time the-equation o f time to be 7V fhdw-.
ing~how much the fun is | that day -behind the clock,
then the time b y the .clock is, 9b. 34', the difference
between,which and 6h. 19' is ÿ jM jf ; ; and this converted
into degrees, at- the rate o f 15'°’ for 1 hour, gives
48°. 45»', 'the longitude o f the place from Greenwich 5
.and as the time is forwarder, .than that 'at Greenwich ■, tlie -
-place lies' to “the edjl■ o f Greenwich. Thus the longitude
-could die very, eafiiy. determined, i f .y ou could depeftd
upon the time-keeper. Butjas; a watch will always gain
o f lofe,ybefore the time-keeper is. fent :dut,,its gaining
or lofing every-day for fome time,;:a m omh-forlnfiance,
is obferved ; .this ..is called the rate o f going o f the watch,
and from thence the mean rate o f going is thus found. 1
i92..Suppofe l e x amine the râte Ipfea watch fear 3 o
-days ^ on fpme o f thofe -days I find it has gained^na
oh £bmèj it haBdpft f^dd‘' t6gethhr alI pt^ quàntities it has
gained, and (uppofe they amount fô~ïy" ; add.-togelher all
has lo ft, an dTuppOfe the y ambhhtto 13.5
then, upon the whole, ithâs gained^." in 30 days, and this
is called îbè'meah rat^;forthatti^e^Bd this divided by 30,
'gives o'Vi.33 for thoztnean daily rate 'ofgaining ; fo that"
i f the watch, had gain ed'’regularly o", 13 3 every- d a y ,a t
the end o f the 30 days it would have gained j lift as much
1Z& it really did gain, b^foj^fimea'gaining-and fométimes
lofing. .Or you may get the mean daily rate thus. T ake
-the difference between what the clocIt was too fârft,' or
tw o üow, o n the vfitf^ and la ft days o f *qb{ervatron, i f it
be too faft, or too flow,' on each day ; but take the
fum? i f it be two faft On one Hay and two flow on the
:otherrand divide by the numbèrbf days between the Ob-
feryations, and4 you get the •fnean daily rate. Thus, if
the watch was too faft on the fir ft day 18", z t$ tofifgft.
on thb laft day 32", thé dfferenfi I4^divîded-by 3q give3
G,‘ 466. thè; mean daily ' rate ■ o f gaining*. v But if . the
watch was to q faft em the firft day f } and too flow on
the laft day fin i 17" diyidéd by 36 gives o ",y6 f
the mean daily faté d f lôfîn'^. vAft!ëH having thus g o t the
mean daily rate o f gamingpr lofirfg, ah^^mowing how'
much the watch was too• f&ft pr too floW at firft, 'you ill w,k
can tell*, according- to^that-rate p^gpiBg^how much it is
toerfaft,o-l too flow, ths- firftpafé,
for inftance, let ihe watch have been 17" too fafLa-fc
•firft,' and I want ^toÿknow how much it is too" ‘faft 50
day R a fter -that hew-it < ;gàiti4 ©l^>3r';evèry dàÿ,
if this be multiplied by 50 itgives, 6",65 for the Whole
gain-in 50 days ; 1 t h 'e r e f b r ^ ^ a t^ t h è 'that time the
watch would be I '.^ '^ j v t o o - faft.1 This would be
t he e'rrpr,* if -tne-wàteh^côh|in^|'éd up •‘gain at th#abdv.e-
rate ; - and althongh,-from the different temperatures o f
the air, -and, the imperfe&ion o f the workmanfhip, this
cannot be expended, yet the probable error wi'M by this
means be diminifhed^ a w l t ns .'the^beft 'method.we have
to dependƒupon. ' -In watches which-areTmder t-riàl a t ,
-the R'oyarObfervatory ■ at (Greenwich, as: çahdidàtes 'fos;
. the rewards, this . allowance o f amieà'n^rètè'is-admitted,
although' itbis not mentioned in the^a6f .©^parliament ; N
-the commiffioners hoyl^Y&^reJCë^ihdhlgeht^Ifltcofgmn^
it, which is undoubtedly^faybiufable to the watches. „ 1
■ '193. "As the rate;©f/jg©m^of a watch is
vary frora^ Ço'ffi^y eircumftancês,- t î^ bteWër, whenw
ever he goes a'ffore, and has- fufficicnt time, fhould compare
his Watchfdf fevefal daf-s-With -thei^-râe.time found
b y the fun,‘by^ which he ^11 be. .able to find its rate ofT
goirigi" .A n d when he'comes fo/a place whofe longitude
-is known, he may then le t his watch again to Gn?OTwzVÆ'
timé ; For when th<Flb:ngit>üdê^bf%
-know the difference between the * time 'there and ' :at,
Greenwich. For instance,: -if he go^to a place-Jk^^Wm-fb'
feé^o0 :eaft his watefti . fMula
be "2 ^ houfs fl^ ye f|thàmkh€' tî^refa t ’th a tp la c e .. Find,
therefore the trueikme at that place, b y the fun,_and if
th e watch'fe^'^hSufs - floweiy it is■* right |
i t b y the^differenee^ and it, agairigives GmTzwzVÆ time.
• 194. In longjvoyages^ unlcfs you have fometimes an
opportunity o f âdjufting the watch Î -11,,
its error will probably be conifd'cra’ble, and'thc .fongkhdp
■ 'dçd.ücej from-it, wilhbe ïh bjed to/è proportional error.
In fhort voyages; a watch is undoubtedly Very uféful f '
.(aoHjano in ■ long ones, where ybu Bave the means o f cor.
reding it from time to^-time~. | 11-ferves'-tojeanry
longitiidé -ffôjm'' bnè. knp^n^plàc^ _
intervai-'e^tinlè not/ÿët^ilcmg;f%r to.'keëp tKhd^ngi* -
Lpm that - which is deduced from a lunar pbfefyaA
fioSytTll yod h g e t another. „Thus the watch'may pe
rendered o f great fefvice inifayigationV ^
T 0 j in â
Mooh^and of Jupiter’s Satellites.
195^ 'B y an eclipfe o f the mook, - This eclipfeÿpgins
when the umbra o f the eatt-hr firft mtioy sllhe moon, and
ends when it leaves th'e \moon. Having the times calculated
when the eolipfe ‘ begins, and enas"a<G^«WVi6,
'obferye the times when it begins and'ends at'the place
' whëré, you are \ arid','thé difference o f tliefc times7J.'c&--
vértëd inlp;;, ïd ^ ï^ lltg i ves t|je nméréri ce“. pfc p .lprigfl
tude8.t-.'Tfor^ as the pliafes of the moon in an ecliple,,
happen at .the-fame in'ftant àt all places, t^e diffbreh'çù-pf
the times at different places when c e fame phafe is ob-.
ferved, arifes fi'om the difference o f t]ie clocks at' thofe
places, and that diffeicnce (as bef@fb- obfeived) conveit- f
ed into degrees, gives.! the difference1 o f d | f
the beginning o f air eclipfe happen at 6 o’cl-pck at^aa^t,
place, and I t :8;b®?ck ;at ;^^|^7lhe|e-
hours, or 300,, in longitu d e. This ^would he a ’ very *.
ready and accurate method, i f the times (|^&;fipftsandl
laft i contact - o fth e earth’sumbra and"tlie '
accurately'pbferved f bu6 '
continues to f||c^afe'tall it^JmCs to the unibra, fo that
■ un|il 'the ’ um^ra .a^uallv^gefy4 Up on mp lfe it'^isl pot
difcbyeJred. T he umbra1 is' aOT cfeffSelb '
• T he beginning !and'eiid o f a” lunar eclipfe, daifndt'/'in ;
«eral, bl'^e lemB h^ ’ riea'rbr than 1' IohM 6
not} nearer than 2" or 3 ' . Uporvfhe'fe accounts, the
longitude,'thp’s deduced, is Tubjec61o.acpnfiderablc, degree
o f u^cHrtainty..' A'ftronorn'ers* trierefore determine-i
th e lbn^fflMel ‘
pWhmngbBfelylffbns o f buffer ’ ^hafes, ‘thatfffs, when the *
umbra bifedbs1 a-ny fpots upon the ra-fa^e1.1^ A n d 'this-
ckri be"' determined to a greater degree Vf'ltcuTacy,' than
the Beginning and cndL for when'^^p'umbra is’ g o t3
mjon^s furfa'ce, the | obferver- has 1 leifure to'J
cbnfider and fix-u^o'mthe proper line o f termination, in ‘
wliich''\he wi l l af f i f t ed by running ’ his -eye along'
thecircumTerence^oF the' umbra. “ T h u s 'th e coin'd^
dence o f the'umbra with the fpots,' mly“be o#fervpd<|8|
a^febnliderabl^ d^gre^of abcufScyr 1 Thfe
fore fhould have' a ^bpff 'mlp' of'the’'rrifbn at lia‘nd,' that'
^ m a y n^^miftake.* The telefcopW to obferve’ a. lunar'
eclipfe, iliould have b ifra ^ma'll magnifying po*wer w i f lf
a great quantity o f light. The lhadow Co'm;e^{^qn‘ f'he-
moon on^thiC' eaft fide,; and f§bjs- off o f t ^ ^ ■
the t€lefcope invert, tfie ‘appelrah’Ge' V ® 1
tfaryi . :
,*^96*: T he eclipfes ;bfT^itc^s^fellitreA' d^ tffe
re^dieft* method o f determi'hlhg^helllo’ngithdje 'o f places
upon land. I t was alfo hopedi th a t fome method’ might
He invented to bbferve them,at fea^ Vn'd Mr. I rwin made
a . purpofe,/ fo’r' the-obfer'ver to ,
i|t elyn E, in 1 a voya:g^' to Bari>ddoes\'
under the diie£lion 'b rrag
fBu'n'd' i t totally imjira£ficable.fb derive hnfi from’
tt* 9, v ? > f f i ’^jireat^bwef’,
^\')tcl'efc'qpb''?'fdr makirig - smefe? obferva^o'ifs1
wqlj' and tBe^violence,as well’as tn!e' mre|^aritie^^r
'dF the^ mip, I am afraid vth,e. complete mkhage-
m. 5 a On, ftiip 'board',' will always remain'
among^M|^efiderata. However, I would not be und.er-
ftood to^ mean to^Jifeoiurage any attempt, founded on
good pnncijyles,'^o1 get over the difficulty.” The.te-
lefcopes^ proper"■ for making thefe (obfervationss, are com*-
.mjoq refrafling on^sfrom 15 to 20 feety reflefling ones,
o f 1,8 inches or 2 feet • ©r t h ^ 6 inches achromatic. On
account bf, the uncertain^ o f the theory1 o f the fatel-
B H B M as kKl y^e advifes the obferver to be fettled:
a t his telefcope, 3 minutes', before the' expedled- time' o f -
ajnmerfion o f the firft fatbllite j ( f or 81. before that o f
the: feepn(di,©r third; . Ih d a 4uarten b f an hour before
that!.of' the-founth. . And- if.the,longitude o f the place
be;ai£q uncertain, he thuftdook out prdportipnably foon-
ei3u i Thus;1 if the jlongitudeibe^uncertaih tb , 2P, anfwer-
inglto} mu ft begin to look out ft
rmn-ules fbOn'er ^th^n 5a- mentioned'-above. However,
when: be h,asio b fe r v.e d 0 ujsriQ cli p fc and .found! th e error o f
th64aftile$i! he&tnay affbwfthe..ffrne copre^icfn to the calculations:
:of the diphemerisSox fey.erakmahths, which will
a^verfifeyhim^ei^mearly> of.the time o f'.exppflingthe:
eblipfes'bfsfehei lame Ifatellte; and .diFpenfe with bia a t .
tending/ fo,^long., Tj ,ike- oppofitionroji ^npitentb i
the; fun,the-imm-erfions and emerfions 'happen;on.the:
fific o f jupiter ; and after oppofition,i on the eaft
fide j f e t . i f the telefcope i-nvci L, the appearance will be'
' thdribntrIry.,; j Jffpfre'' oppofition,. the imbicrftons: o ily o f
the .firft Satellite J. ares vrfible 7- rarrd j after oppofition,l.the
cn?e;^o«f .only.. T hW S e t j s gefejrallyrlthe cafe in icfpefl:..
and J 1 «
aife frequently observed inctfcH’third and fourth, j
' J97 ’ • V/liefcljfeobfeiT.er is^wartingfoi; an emerfion, as
fS ?^ ^ .bffil4 s^^te lwffce aa !t^it;flie ad d itlonlc at liisi
wat. h ind note the fecond .01 begin .to count t^&beatsj;
, " fofcfe.it is the1 fatemfce,. and then'
lookiat.|the ;dhtek .and. ;fu4t‘ta^Vt]je: nnm.ber:'p£feconds .
yehickhe, has .counted,1'.and he' willihate the time of-
epierfioiM. , K jupiter be' 8° aljove the horizon}rand the
fun; as ranch) belot?, an (eclipfe will he vidbfc may"
beidetermined mear'-enough'ib.y?a fcorhmoit globe. : 1
iia 9.8;:fEhe.ffisneniioiivor'!ammeWon being obierved a c t
cording ,-tb. 3]ipaTseht:time^ t:ht.' longitude o f t,hc.!.piace
i^jc^h djby -taking the diiference be-
; tvveen^that time and the, time let down_ in thzM w ticq l
^/nianaQ rvhich' ^is caleulat'ed for '^ffqrcni,- tim'ei • '
E x . Suppofethc.ejnetljpn jp f a, fateHite.itQbave been
obferyed at t.he t(7^ .»ƒ Goo^ May 9,,',1.767, at
in!fhe-iVah-
. tical .Almanac is gh.' 33'. t a " ; the s}|ffe’rqnfeeJc!f:Which-
QVbsnw^^-timtyfer’-i'y?.11^ '^ ijr'V*** J;‘
199. But 1.0 ^nd the longifu^fe:o f a place from an ob^
b’etter to' commeridiah,
than1 with thevcycifetjons in' t® 'Ejibeniefit,
i becaufe of the imperfeSidnrbftte theory; rb:iit: where!
- a correfponding dbferzatibn ;canifbt be obtained, A d
what correftion the calcmatifehsiri tfieEphemeris require}'
by the neareft obferyations to.tl^e^iven time that can be'
obtained ; and this ’eorreflibh' applied’ to-: tlie calculation ’
1 the eclipfe n t h l ( ' ' » f n , tenders it almolt equivalent
to an aS.uaf'^ffirqi vacion. The' obferver mull be
careful to..regulate his cloeli'or wateh to- apparent*time,
dr 'at le'aft to know the difference, f
. - . apo. In' order the better to know the difference o f
£pem correlponding obferva-
tions, the obferver fhould be furnilhed with the fame
kind o f teleicopes. For at an immerlion, as the Satellite
enters the Ihadow,’ it grows fainter and fainter, till
a t laft the quantity o f light is fo frnall that 'it becomes
g ' ; ■ inyifibie,