419 / 868
N
A
1
G
Ihere form certtlin 1ngle! with one anothcr; "<1od fince,
if
'\Ve moVe never fo
litde
tO\V8rds
the ehn
or
well,
from one
pl;¡ce
lo 3nother.
\Ve thereby change
OUr
meridian, and
ift
ever, place the ean and well line being
pe~pendicular
lO
rhe rneridian; ir follows. that {he e;¡¡(l and wefl line in the
lira
place will
DOI
coincide with {he
can
and weU line io
.he Cecond. bur be inclined
t'O
ir
et
a certain angle: and
~onfequently
all ,h e other rho!'llb lines 'a, eaeh place will
be inclined to caeh olber,
tbey alw3ys
form i'ng the Carne
3n·
gte.s
with
{he meridiano Hence
it
follows, that
4111
rJlombs,
"txcept the four cardinals, muO be
curvt:S
or helifphcrical
Jioes, aJways. lending towards the
pole,
and
appro~chi ng
jt
by
infini te gyrations or
tu rning~.
bUI
never
r ...
lling ioto
it. T hus ·Ie,· P (No.
2 )
be the pole, Eq;n areh of ,he
cquator, PE PA,
&c.
meridian., and EFGHKL any
A
T
1
o
1~.
,homb: then bec,ufe ,he ;;ngle5J'EF; PFG, (:;( . ue\,y
the nature
'!lf
the romb Jice equaJ,
it
i,
evident that
lt
will form a curve line on ,he furface of ,he gJobe, alw.y'
.pproaching ,he pole P , but neva fall ing in,o i,; for if
it were pol1i;:.Je for
II [O
fati ¡mo
lhe
pole.
Iheo
it
would
rollow, (hat the
faOle
Jinc could cut
3n
¡nfiche
anmber
of
other lines
al
equal allgks, in the fame
POiOl;
which
is
abfu ,d.
19, Beeaufe there are 32 rumbs (or
PQin~s
in ,he com·.
pafs) equ,lIy dillan' froO! one ano,her, ,h erero,. ,he ongle
contaillcd betwcen any
twO
of thc.m
adj:\ccll t
wil1 be
J
1<'
.5' ,
viz :
, '"
pan of
3600;
and
fo' the aogle
contained
benveen the meridian and the
NhE.
will be
J
,0
J
S'.
and between the meridian and ,he NNE \ViII be
22°
30/ ;
and fo of ,he_rell, as in ,he follo'. :ng ,able.
A 'rabie
oE
the An!;les whieh ev.,y
~
Point of ,he Compafs m, k.. \Vith , he M eridian .
.
-l"'¡---~'I;----~-;-l--·~--¡-l--~--r\----:~· I·!-~-~- \
; \
~
!
~
I
~z
I
~ -J:----~---j!'---';:¡ :~J --~§:-+-J
--Z-!J
~ I
Zl
~I
Zl
~ I
~1 ~1
S eél. 2. Oj'PLAt N SAt LINC .
l .
TH
I S
me,hod of failing fuppofes ,he
e.nh'o be a
plane, and the mcridians paraHeI to one another; and
Jikewife the paralld. of lati,ude
al
equal dillanee from one
.no,her, as ,hey really are upon the elobe. Thoogh ,his
muhod be in i,felf evidently falfe; yet in a Ihort run,
and efpecially near Ihe equator,
an
account
of
the
lhip',
'Way may be kept by i, ,oler>bly well,
2 .
The angle formed by ,he meridi.n and rumb ,hat
• Ihip fail, upon, i. called ,he Ihip's eou,fe. Thus if a Ihi}'
fail, on ,he NNE rhomb, ,heo ber eourf. will be
2 2· 30 ,
aod fo of olbe".
3-
Tbe dinanee be,ween ,wo place, Iying
0 0
,he fame
para.lld counted
in
mile5
of
the equator, or the
diHance
of
one place from the meridiao
()f
another cou nted as a·
bove on ,he paralld palling oyer Iha, place, is caJleJ me·
ridional difiance; which, in plain faiJing, goes llnder_the
n.ulle
of
dep?rture.
4. Le< A (Na 3,) denote a cenain poin, on ,he earth ',
forfaee, AC it's m<ridi, o, and
AD
,he paraUel of lali.
lude palling ,hroogh i,; .nd fuppofe a Ihip 'o fail fróllt
A on ,he NNE rhomb till Ihe. a!'rive a'
~ ;
and 'hroogh
B dr.\V ,he mendrao RD, (whlch .. accordlo'g
10
the prin–
cipie, of plain failing, mull be paralld 'o CA.) aod the
paralle! of lati,ude BC; ,heo ,he leng,h of AB, !liz.
how far ,he Ihip ha, failed upon ,he NNE rhomb, il called
her dillanee; AC or .BD will be her differtoee of ¡.,i.
tude, or nonhing ;
el?
will be
hu
dcp; r'lur~,
or eaning ;
and ,he angle CAB wllI be the eourk H enee
j,
is plain,
,ha! ,he dillaoce failed will a¡\Vays be g,e"e, ,hao ei•
ther the difference
of
Jatilude or depanure ; it being
the
hypolhenufe of a righ, angled triangle, wh.,eof , he al he'
two are lhe
legs:
except the fhip fail, eilher
00
a roeri·
dian, or a parallcl of la,i,ude : fo. if ,he Ihip foil,
0 0
a
meridiano
then
it is plain,
Ihat
her
dill ance
will
be
jan
ec¡uaJ
te
her di{fc::rrnce of Jatilllde, and Ihe
wiJJ
h:ne no
depanure; bu, if Ihe fail on a paraJlel, theo her dinaDee
wiJl
be the {ame with·her departore, and (he will
ha;e
no
difrerenee of la,i,ude.
lt
i, evident alfo from ,he 6gure,
,hal if ,he cou rc' be lef, ,ha n 4 poin.., or 45 degre..,
¡'s compk mea"
!li :,
tbe o,her obli'l0e aDgle, will be
;rcater