Making it, As 50 feet are to 44 feet, so are 
6.5 knots to 5.72 knots, 1 find that the true 
rate of sailing is 5.72 miles in the hour. 
Again, supposing the distance between 
knot and knot on the log-line to be exactly 
50 feet, but that the glass is not 30 seconds ; 
then, if the glass requires longer time than 30 
seconds, the distance given will be too great, 
if estimated by allowing one mile for every 
knot run in the time the glass runs ; and, on 
the contrary, if the glass requires less time to 
run than 30 seconds, it will give the distance 
sailed too small. Consequently, to find the 
true distance in either case, we must mea- 
sure the time the glass requires to run out 
(by the method in the following article) ; 
then we have the following proportion, viz. 
As the number of seconds the glass runs, 
is to half a minute, or 30 seconds ; so is the 
distance given by the log, to the true distance, 
Example I. Suppose a £hip runs at the rate 
of 7\ knots in the time the glass runs; but 
measuring the glass, I find it runs 34 seconds ; 
.required the true distance sailed. 
Making it, As 34 seconds are to 30 seconds, 
so are 7.5 to 6.6 ; I find that the ship sails at 
the rate of 6.6 miles an hour. 
Example II. Suppose a ship runs at the 
rate of 6 4 knots ; but measuring the glass, I 
find it runs only 25 seconds ; required the 
true rate of sailing. 
Make it, As 25 seconds are to 30 seconds, so 
are 6.5 knots to 7i8 knots ; I find that the true 
rate of sailing is 7.S miles an hour. 
In order to know how many seconds the 
glass runs, you may try it by a watch or 
clock that vibrates seconds; but if neither 
of these is at hand, then take a line, and to 
the one end fastening a plummet, hang the 
other upon a nail or peg so that the dis- 
tance from the peg to the centre of the 
plummet is 39| inches : then this put into 
motion will vibrate seconds; t. c. eveiy time 
it passes the perpendicular, you are to count 
one second ; consequently, by observing the 
number of vibrations that it makes during the 
time the glass is running, we know how 
many seconds the glass runs. 
If there is an error both in the log-line 
and half-minute glass, viz. if the distance be- 
tween knot and knot and the log-line is ei- 
ther greater or less than 50 feet, and the g ass 
runs "either more or less than 30 seconds; 
then the finding out the ship’s true distance 
will be somewhat more complicate, and ad- 
mit of three cases, viz. 
CaseT. If the glass runs more than 30 se- 
conds and the distance between knot and 
knot is less than 50 feet, then the distance 
givenby thelog-line, viz. by allowing 1 mile for 
each knot the ship sails while the glass is run- 
ning, will always be greater than the true 
distance, since either of these errors ; gives 
the distance too great. Consequently, to 
find the true rate of sailing in this case, we 
must first find the distance on the supposition 
that the log-line only is wrong, and then with 
this we shall find the true distance. 
Example. Suppose a ship is found to run 
at the rate of 6 knots; but examining the 
o-lass I find it runs 35 seconds ; and mea- 
suring the log-line, l find the distance be- 
tween knot and knot to be but 46 feet: re- 
NAVIGATION. 
Then, As 35 seconds : 30 seconds : \ 5.52 
knots: 4.73 knots. Consequently the true 
rate of sailing is 4.73 miles an hour. 
Case It. If the glass is less than 30 se- 
conds, and the space between knot and knot 
is more than 50 feet; then the distance 
given by the log will always be less than the 
true distance, since either of these errors less- 
ens that true distance. 
Example. Suppose a ship is found to run at 
the rate of 7 knots ; but examining the glass, 
I find it runs only 25 seconds ; and measuring 
the space between knot and knot on the log- 
line, I rind it is 54 feet: required the true 
rate of sailing. 
First, As" 25 seconds : 30 seconds ; ; 7 
knots : 8 knots. Then, As 50 feet : 54 feet * : 
8, 4 knots: 9.072 knots. Consequently the 
true rate of sailing is 9.072 miles an hour. 
Case HI. If the glass runs more than 30 
seconds, and the space between knot and knot 
is greater than 50 feet ; or if the glass runs 
less than 30 seconds, and the space between 
knot and knot is greater than 50 leet : then, 
since in either of these two cases the elfccts 
of the errors are contrary, it is plain the dis- 
tance will sometimes be too great, and some- 
times too little, according as the greater quan- 
tity of the error lies ; as will be evident from 
the following examples: 
Example I. Suppose a ship is found to run 
at the rate of l)\ knots per glass; but examin- 
ing the glass, it is found to run 36 seconds ; 
and by measuring the space between knot and 
knot/ it is found to be 58 feet ; required the 
true rate of sailing. 
First, As 50 feet: 58 feet : I 9.5 knots: 
1 1.20 knots. Then, As 38 seconds: 30 se- 
conds I I 11.02 knots : 8.7 knots. Conse- 
quently the ship’s true rate of sailing is 8.7 
miles an hour. 
Example II. Suppose a ship runs at the 
rate of 6 knots per glass ; but examining the 
glass, it is found to run only 20 seconds ; 
and by measuring the log-line, the distance 
between knot and knot is found to be but 38 
feet : required the true rate of sailing. 
First, As 50 feet: 38 feet ; : 6 knots: 4.56 
knots. Then, As 20 seconds: 30 seconds: : 
4.56 knots: 6.84 knots. Consequently the 
true rate of sailing is 6.83 miles an hour. 
But if in this case it happens, that the time 
the Mass takes to run, is to the distance be- 
tween knot and knot, as30, the seconds in half 
a minute, is to 50, the true distance between 
knot and knot ; then it is plain, that whatever 
number of seconds the glass consists of, and 
whatever number of feet is contained between 
knot and knot, yet the distance given by the 
log-line will be the true distance in miles. 
The meridian and prime vertical of any 
place cuts the horizon in four points, at 90 
decrees distance from one another, viz. North 
South, East, and West : that part of the me- 
ridian which extends itself from the place to 
the north point of the horizon is called the 
north line ; that which tends to the south 
point of the horizon is called the south line ; 
and that part of the prime vertical which ex- 
tends towards the right hand of the observer 
when his face is turned to the north, is called 
the east-line ; and lastly, that part of the prime 
vertical which tends towards the left hand is 
the four points in which 
are called the 
123.5 
Tn order to determine the course of the wind 
and to discover the various alterations or 
shiftings, each quadrant of the horizon, in- 
tercepted between the meridian and prime 
vertical, is usually divided into eight equal 
parts, and consequently the whole horizon 
into thirty-two ; and the lines drawn from 
the place on which the observer stands, to 
the points of division in his horizon, are 
called rhumb-lines ; the four principal of 
which are those described in the preceding 
paragraph, each of them having its name from 
the cardinal point in the horizon towards 
which it tends : the rest of the rhumb-lines 
have their names compounded of the prin- 
cipal lines on each side of them, as in the 
figure ; and over whichsoever of these lines 
the course of the wind is directed, that wind 
takes its name accordingly. See Magnet- 
ism. 
Hence it follows, that all rhumbs, except 
the four cardinals, must be curves or hemi- 
spherical lines, always tending towards the 
pole, and approaching it by infinite gyrations 
or turnings, but never falling into it. Thus let 
P, Plate Miscel. fig. !72, be the pole, EQ an 
arch of the equator, PE, PA, See. meridians, 
and EFG HKL any rhumb : then because the 
angles PEF, PEG, &c. are by the nature of 
the rhumb-line equal, it is evident that it will 
form a curve-line on the surface of the globe 
always approaching the pole P, but never 
falling into it; for if it were possible for it to 
fall into the pole, then it would follow, that 
the same line could cut an infinite number of 
other lines at equal angles, in the same point; 
which is absurd. 
Because there are 32 rhumbs or points 
in the compass equally distant from one ano- 
ther, therefore the angle contained between 
any two of them adjacent will be 1 1° 15', viz. 
-J T part of 360° ; and so the angle contained 
between the meridian and the N6E will be 
1 1° 15', and between the meridian and the 
NNE will 22° 30' ; and so of the rest. See 
Table of the angles &c. at the beginning of 
the article. 
Concerning currents, and hole to make pro - 
perallowances. 1 . Currents arecertain settings 
of the stream, by which all bodies (as ships, 
&c.) moving therein, are compelled to alter 
their course or velocity, or both ; and submit 
to the motion impressed upon them by the 
current. 
Case I. If the current sets just the course 
of the ship, i. e. moves on the same rhumb 
with it ; then the motion of the ship is in- 
creased, by as much as is the drift or velocity 
of the current. 
Example. Suppose a ship sails SE&S at the 
rate of 6 miles an hour, in a current that sets 
SEftS 2 miles an hour: required her true 
true rate of sailing. 
Here it is evident that the ship’s true rate 
of sailing will be 8 miles an hour. 
Case IF If the current sets directly against 
the ship’s course, then the motion of the 
ship is lessened by as much as is the velocity 
of the current. 
Example. Suppose a ship sails SSW at 
the rate of 10 miles an hour, in a current hat 
sets NNE 6 miles an hour, required the 
ship’s true rate of sailing. 
Here it is evident, that the ship’s true rate 
of sailing will be 4 miles an hour. ' Hence it 
is plain, 
uired the true distance run. 
First we have the following proportion, 
iz. As* 50 feet : 46 ; : 6 knots: 5.52 knots. 
VoL. II. 
ca'led the west line ; 
these lines meet the horizon, 
cardinal points. 
L 1 
