2u4 
Example. Suppose a ship from the Lizard in 
the latitude of 50° 00' north, sails SWbW, till 
her difference of longitude is 42° 36': required 
the ship’s place upon the chart. 
Having drawn AE the meridian of the Lizard 
•at L, count from E to F upon the equator 42° 
3G' ; and through F draw the meridian EG ; then 
from I. draw the SWbW line LK, and where 
this meets FG, as at K, will be the ship's place 
required. 
PtiOB. IX. One latitude, course, and depar- 
ture, given ; to find the ship’s place upon the 
chart. 
Example. Suppose a ship at a in the latitude 
•of 20" 00' north, sails north 37“ 20' east, till she 
has made of departure 1 16’ miles : required the 
ship’s place upon the chart. 
Having drawn the meridian of a-, at the dis- 
tance of 1 16 draw parallel to it the meridian kl. 
Draw the rhumb-line ac, which will meet kl in 
some point c ; then through c draw the parallel 
c!>, and ab will be the proper. difference of lati- 
tude, and be the departure, lake ab in your 
compasses, and apply it to the equator or gra- 
duated parallel ; then observe the number of 
degrees it contains, and count so many on the 
graduated meridian from C upwards to b. 
Through h draw the parallel hi, which will meet 
ac produced in some point as e, which is the 
ship’s place upon the chart. 
Proh. X. One latitude, distance, and depar- 
ture, given ; to find the ship’s place upon the 
chart. 
Example. Suppose a ship at a in the latitude 
of 20’ 00' north, sails 191 miles between north 
and east, and then is found to have made of de- 
parture 116 miles: required the ship’s place 
upon the chart. 
Having drawn the meridian and parallel of 
the place a , set off upon the parallel am equal 
to 1 16, and through m draw the meridian kl. 
'Fake the given distance 191 in your compasses; 
setting one foot of them in a, with the other 
cross kl in c. Join ac, and through c draw the 
parallel cb ; so cb will be the departure, and ab 
the proper difference of latitude; then proceed- 
ing with this as in the foregoing problem, you 
will find the ship’s place to be c. 
Prob. XI. The latitude sailed from, difference 
o'f latitude, and departure, given; to find the 
ship’s place upon the chart. 
Example. Suppose a ship from a in the latitude 
of 20" 00 / north, sails between north and east, 
till she is in the latitude of 45” 00 / north, and 
is- then found to have made of departure 1 16 
miles : required the ship’s place upon the chart. 
I laving drawn the meridian of a, set off upon 
it, from to b, 25 degrees, (taken from the 
equator or graduated parallel) the proper dif- 
ference of latitude ; then through b draw the 
parallel be, and make be equal to 116 the depar- 
ture, and join ac. Count from the parallel of a 
on the graduated meridian upwards to d 25 de- 
grees, and through d draw the parallel de, which 
will meet a: produced in some point c, and this 
will be the place of the ship required. 
In the article of Plane Sailing, it is evidentthat 
the terms meridional distance, departure, and 
difference of longitude, were synenimous, con- 
stantly signifying the same thing; which evi- 
dently followed from the supposition of the 
earth’s surface being projected on a plane in 
which the meridians were made parallel, and 
the degrees of latitude equ.fi to one another and 
to .those of the equator. But since it has been 
demonstrated, that if, in the projection of the 
earth’s surface upon a plane, the meridians are 
made 1 parallel, the degrees of latitude must be 
unequal, still increasing the nearer they come 
to the r»ole ; it follows, that these terms must 
denote lines- really different from one another. 
NAVIGATION. 
Of Oblique Sailing. The questions that may be 
proposed on this head being innumerable, we 
shall only give one as a specimen. 
Coasting along- the shore, I saw a cape bear 
front me NNE . then 1 stood away NW4W 20 
miles, and I observed the same cape to bear 
front me NEZE : required the distance of the 
ship from the cape at each station. 
Geometrically. Draw the circle NW SE 
(figure 21,) to represent the compass, NS 
the meridian, and WE the east and west line, 
and let C be the place of the ship in her first 
station : then from C set oil' upon the NW4W 
line, CA 20 miles, and A will be the place of 
the ship in her second station. 
From C draw the NNE line CB, and from A 
draw AB parallel to the NEZE line CD, which 
will meet CB in B, the place of the cape, and 
CB will be the distance of it from the ship in 
its first station, and AB the distance in the" se- 
cond: to find which. 
By Calculation ; 
In the triangle ABC are given AC, equal to 
20 miles ; the angle ACB, equal to 78" 45', the 
distance between the NNE and NW b W lines ; 
also the angle ABC, equal to BCD, equal to 
33° 45', the distance between the NNE and 
NE b E lines ; and consequently the angle A, 
equal to 67° 30'. 
Hence, for CB, the distance of the cape from 
the ship in her first station, it will be, (by ob- 
lique trigonometry,) 
s', abc : ac : : s. bag : cb. 
i. e. As the sine of the angle B 33° 45' 9.74473 
is to the distance run AC 20 — 1.30163 
so is the sine of BAC - 67 30 9.96562 
to CB - - - - 33.26 1.52191 
the distance of the cape fre 
station. Then for AB, it 
trigonometry,) 
S. ABC ; AC ! 
i. e. As the sine of B 
is to AC - 
so is the sine of C 
to AB - 
the distance of the ship f 
second station. 
m the ship at the first j 
will be, (by oblique : 
.ACB : AB. 
33° 45' 9.74474 ! 
20 — 1 30103 j 
78 45 9.99157 j 
35.31 1.54786 j 
m the cape at her 
Of the Lop-line and Compass. The me- 
thod commonly made use of for measuring a 
ship’s way at sea, or how far she runs in a 
given space of time, is by the log-fine and half- 
minute glass. See the article Log. 
The log is generally about a quarter of an 
inch thick, and five or six Inches from the an- 
gular point to the circumference. It is ba- 
lanced by a thin plate of lead, nailed upon the 
arch, so as to swim perpendicularly in the 
water, with about | impressed under the sur- 
face. I he line is fastened to the log b\ means 
ot two legs, one of which passes through a hole 
, at the corner and is knotted on the opposite 
side; while the other leg is attached to the 
arch by a pin fixed in another hole, so as to 
draw out occasionally. By these legs the log 
is hung in equdihrio ; and the line which is 
•united to it, is divided into certain spaces, 
which are in proportion to an equal number 
of geographical miles, as a half-minute or quar- 
ter-minute is to an hour of time. 
These spaces, are called knots, because at the 
end of each ot them there is a piece of twine 
with knots in it, inreeved between the strandsof 
the line, widen shews how many ot these spaces 
or knots are run out during the half-minute. 
They commonly begin to be counted at thedis- 
tatice of about 1 6 fathoms or 60 feet from the log, 
so that the log when it is hove overboard 
may be out of the eddy of the ship’s wake be- 
fore they begin to count; and for the more 
ready discovery of this point of commence- 
3 
merit, there is commonly fastened at it a piece 
ot red rag. 
The log being thus prepared, and hove 
overboard from the poop, and the line veered 
out by help ol a reel that turns easilv, and 
about which it is wound as fast as the log will 
cam it away, or rather as the ship sails from 
it, will shew, according to the time of veering, 
how far the ship has run in a given time, and 
consequently her rate of sailing. 
A degree of a meridian according to the ex- 
ac.test measures contains about 69-545 English 
miles ; and eacli mile by the statute being 5280 
leet, therefore a degree of the meridian will 
be about 7200 feet; whence the -G. of that, 
viz. a minute or nautical mile, must contain 
6120 standard feet ; consequently, since £ is 
ttle TVoP art ot an hour, and each knot is 
the same part of a nautical mile, it follows, that 
each knot will contain the of 6120 feet 
viz. 51 feet. 
I lence it is evident, that whatever number 
of knots the ship runs in half a minute, the 
same number ot miles she will run in one hour, 
supposing her to run with the same degree of 
velocity during that time ; and therefore it is 
the general way to heave the log every hour, 
to know her rale ot sailing : but if the force 
or direction oi the wind varies, and not con- 
tinues the same during the whole hour; or if 
there has been more sail sol, or anv sail handed, 
so that the ship has run swifter or slowei* in any 
I art ol the hour than shediil at the time of heav* 
ing tise log; then there must be an allowance 
made accordingly for it, and this must be 
according to the discretion of the artist. 
Sometimes, when the ship i ; before the wind, 
and there is a great sea setting after her, it 
will bring home the log, and consequently the 
ship will sail faster than is given by the log. 
In this case it is usual, if there is a very great 
sea, to allow one mile in ten; and less in 
proportion, if the sea is not so great. But 
for the generality, the ship’s way is really 
greater than that given by the log; and 
therefore, in order to have the reckoning 
lather before than behind the ship (which is 
the safest way), it will be proper to make the 
space on the log-line between knot and knot 
to consist of 50 feet instead of 51. 
If the space between knot and knot on the 
log-line should happen to lie too great in pro- 
portion to the halt-minute glass, viz. greater 
than 50 feet, then the distance given by the 
log vn ill be too short ; and if that space is too 
small, then the distance run (given by the 
log) will be too great : therefore, to find the 
tiue distance in either case, having mea- 
sured the distance between knot and knot, 
we have the followingproportion, viz. 
As the true distance, 50 feet, is to themea- 
suied distance; so are the miles of distance 
given by the log, to the true distance in miles 
that the ship has run. 
Example 1. Suppose a ship runs at the rate 
of 64- knots ;n half a minute ; but measuring 
the space between knot and knot, I find it to 
be 56 feet: required the true distance in miles. 
Making it, A s 50 feet, are to 56 feet, so are 
6.25 knots, to seven knots ; t find that the true 
rateof sai ling is 7 miles in the hour. 
Example If. Suppose a ship runs at the 
rate of 6^ knots in half a minute ; but mea- 
during the space between knot and knot, I 
find it to be only 44 feet: required the true rate 
the ship is sailing. 
