438 / 868
N
A
v
1
G
C"tq''''' TRl CA '
LV.
H . ving d ra\\"o ,he compars
NES\V (No ·'7.) let C reprereDt the pi
¿ce
the Chip fai l·
ed from; draw .he SE lioe CA, whi, h make equal tO
.l20;
,heo will A be the place the Chip caped ...
From A draw AB paraJlel to ,he W óN Iioe
cn,
e–
lJ.ual to
40.
the
mOl ion
of
lhe
current in
20 hOU ls.
and
joio CB; theo
B
",iJl be the fl,;p's true place a' .he eod
of 20 hou". CS her "ue elill,oce, ami .he aogle SCB
her (rue courre. T e find which
By
CALCl.t LATl ooN;
lo ,he triaogle ABC, are eiveo CA
,·zo.
AB '40' aod
,he aogle CAB cqual to
34
°
45',
the dlllaoce betweeo
,he EóS . nd SE lines, to Iind tue angles B ao<l C, aod
the Gde CH.
Firfl. For the aogles C and
B,
it \\ iJl be, (by oblique
t rigonometr.y)
As th. fum of ,he Gdcs CA aAd AS 160 -
2.2°4 12
is
10
.heir dilfereoce
80 - 1'90309
fo is ,he tango of half the fum
~
of the angles
B
and C _
5
73°, °7' 10.517 8
3
to the tango of half rheir dilt.
S9 '
4
S 10 .21680
confcqueotly ,he aogle
B
will be 13 1 , 5>, aod the
angle ACB
'4'
23'. Hence ,he true courfe is S 30°,
37' E,
~r
SSE , °.07' eaflerly.
Then for tho true diflance
CH,
it will be,
(by
oblique
trigonome<ry)
AStheGneo(E
13',°,52' -
9 8 71 98
i, .,o AC
1'0
, .07918
ro.i. the .fine o(
A
33 °,45' -
9.744H
to the <rue diflaoce CB
89· 53
1·95 '94
EXAMPLr
I11.
Suppofe a Chipcomiog out from rea in
·the nigb', has fight of SciJly light, bearing NEhN dif·
tance 4 leagues, it beiog then flood lide feuing ENE,
miles an hour
J
and the Ihip running after
lhe
Tate
of 5
",iles an hour. Required upon
wh.aIcourfe and
ho~far
!he mull fail to hit ,he Li-zard, which bear.. (rom 'Scilly
EtS dillaoce 17 leagues.
GEOMETRl CALL.Y.
Havíng drawn (be
compar,
NESW (No. ,8.) Ict A reprefeot ·the Chip's place at fea,
aod draw the NEhN lioe AS, whieh
m.keequal tO 12
",ilcs, fo S \\ill rcprefcot.Seilly.
From S dra", SL equal to 5' mile., and parallcl to ,he
E { S line; thcn L will reprcfeot the L izard.
From L draw Le parallel to the EN E line, equal to
, mile., aoel froll1 C draw CO equal to 5 mil.. mee,iog
AL io D ; theo from A draw AH paralld ' o CO meet·
ing LC produc<d in B ; and AB will be
tlie
reqlÍired dif·
taoce, and SAB the "ue courfe. To fiod wh;ch
By
CA'LCULATION;
In the.triangle ASL are giveo the Gde AS equal to
l'
miles. the Gde SL equal ' o
5' ,
and the angle ASL e–
qual 'o 11 80 07', the diflaoee betweeo the NEbN aod
W{N lineo ; to fi nd the angles SA·L . nd SLA. Cbo–
feq ueotly, (by oblique trjgonornctry,) it will be,
A, ,he fum of the Gde. AS and SL
63
¡,
79934
;. 'othei r dilference
39 I.S9, 06
fo i. the
t~og.
of half.the fum
~
300, 6'
• 6
of 'heangle. SAL aod SLA5
S 9,7,7
3
to the tangoof half ,heir dilf.
20°, '1 '
S' .s6935
v.oJ.. lll . N',
SS.
2
A
T
1
o
N,
coofequentl y the angle SAL, will be
5'''
1", aoa fo the
di" él bearing of the L rzard froOl ,he .Chip will be N
8S"
02' E, or E óN 6° 17 ' E; and for the dillaoce AL, it
wlII be (by oblique trigooometry,)
AsrhellneofSAL -
S1 o, 17'
is
10
SL
SI
fo is rhe uoe of ASL
118
0 ,
07'
'o
AL
57.6S
rhe diClaoce b<tween ,he Chip and .he L izard.
9. 8 9
22
3
1.
70757
9 -94 54'6
1.7 6080
Ag.io, in .he triangle OLC . aFe giveo the angle Le–
qual
W
17.0 3'" the diflanee be. w«o the ENE and
N
-SSo
o,'
E
lines; the Gde LC, equal to , miles, .he cur–
rc:nCs dri(t in an hour; and [he (ide C O,
~qual
to
S
miles,
,he Chip:s ruo io ,he fat¡le time. H t oce for ,he angle D,
i, wiJl be (by oblique trigonometry,)
As the Chip's ruo iD t hour OC
5
0.69897
i, 'o ,he Gne of L
17°, 3" - 9 ' 4'789t
fo i, ,he curreot's drif, LC
,
0 . 30 t0 3
'o ,he Gne of
D '-- --
6°,
SS' -
908100
coofequently Gnee by coollcullion the angle LAB is cqual
'o .he aogle LOC, the courf. the Chip muClneer is S 880
03'
E.
Then for the diClance AB, i, '\ViII be
(by
oblique tri–
gooometry,)
ASthe
r~oe
of B
155°, 33' -
9.6,689
is to AL
S7·6S
--
1'76080
fois the GoeofL
17 ·3'
94789~
,o
AB
41.96--
1 '~"~5
confequently, Goce the Chip is failing
al
,he ra'e of S mil...
ao hour, it
(011014'$,
.h.. in failiog
8
h
'4"' S 88° 03'
E,
/he will arrive
at
the L ieard .
EXAMPLr
IV. A
Chip from
a
certaio headland in ,he
lati,ude of 34°00' oorth, fail, SEóS " mile. io three
hours. in a current thal Cets berweeD Rorth and
can;
and
then the fame hcadlaod is fouod 'o bear WNW, and ,he
Chip to be io ,he latitude of '33°
S'2'
oOrlh. Required ,he
fcu ing aod drift of .he eurrent.
G EQ METRI CALLY.
Having dra\Vn ,[he
compar,
NESW (No. 29' ) le, A reprdeot the place of the Chip,
and draw the SEhS lioe AB equal
10
1~
miles, alfo the
ESE lioe AC.
Set olffrom A upoo ,he·meridian AO,equal ,o-S miles,
the dilfercnce o( latitude, aDd through O draw OC pa–
ralld
10
the eaCl and.well line W E, mee,ing AC in C .
j oin C aod
n
wi,h the righl line BC; theo C wil: be,he
/hip's .place.•he angle ABC the fetling of ,he curren'
from ,he SE bS line, aod ,he lioe BC will be the drif,
of ,he curreot in 3 hours. To find which
By CALCULATION :
lo the triangle
ADC,
right aoglcd
al
O , are given the
dilteren.ceof latitude AO equaJ
10
6
miles, . he aogle
D AC <qual tD 6:70 30'. Whence (or AC, the dillaoee
the Ihip has faoled, it will be
As radius
8
10.0~OOO
0·9°3°9
is lO"the diff. o( lati,ude AO
fo i, the fe eaDl of the courfe
~
D AC
_
_
5 - 67° , 30' 1°' 4
1
7 16
lO the diflance ruo AC
20.9 - 1.3'°25
Ag.;n, in the triansle ABC,
are
giv~n
AH
<qual
'o
S E
t
1.7