NAVIGATION. 
<823 
the diftance, AB the difference of latitude, and BC the 
departure. 
In conftrufling a figure relating to a fhip’s courfe, let 
the upper part of what the figure is to be drawn on re¬ 
present the north, then the lower part will be fouth, the 
right-hand fide eaft, and the left-hand fid t.iuejl. 
A north-and-fouth line is to be drawn to reprefent the 
meridian of the place from which the fhip failed ; and the 
upper or lower part of this line, according as the courfe 
is Southerly or northerly, is to be marked as the pofition 
of that place. From this point as a centre, with the chord 
of 6o°, an arch is to be defcribed from the meridian to¬ 
wards the right or left, according as the courfe is eafterly 
or wefterty ; and the courfe, taken from the line of chords 
if given in degrees, but from the line of rhumbs if ex- 
preffed in paints of the compafs, is to be laid upon this 
arch, beginning at the meridian. A line drawn through 
this point and that failed from, will reprefent the diftance, 
which if given muft be laid thereon, beginning at the 
point failed from. A line is to be drawn from the ex¬ 
tremity of the diftance perpendicular to the meridian ; 
and hence the difference of latitude and departure will 
be obtained. 
If the difference of latitude is given, it is to be laid upon 
the meridian, beginning at the point reprefenting the 
place the lhip left; and a line drawn from the extremity 
of the difference of latitude perpendicular to the meri¬ 
dian, till it meets the diltance produced, will limit the 
figure. 
If the departure is given, it is to be laid off on a parallel, 
and a line drawn through its extremity will limit the 
diftance. When either the diftance and difference of la¬ 
titude, diftance and departure, or difference of latitude 
and departure, are given, the meafure of each is to be 
taken from a fcale of equal parts, and laid off on its 
refpedtive line, and the extremities connedted. Hence the 
figure will be formed. 
Prob. I. Given the courfe and diftance, to find the 
difference of latitude and departure. 
Ex. A fhip from St. Helena, in latitude 15 0 55' S. failed 
S.W. by S. 158 miles. Required the latitude come to, 
and departure ? 
By ConftruBion .— Draw the meridian AB (fig. 2.), and 
with the chord of 6o° defcrihe the arch in n, and make it 
equal to the rhumb of 3 points, and through n draw AC 
equal to 158 miles; from C, draw CB perpendicular to 
AB; then AB applied to the fcale from which AC was 
taken will be found to meafure 131-4, and BC 87-8. 
By Calculation. 
To find the Difference of Latitude. 
As radius ------ io-ooooo 
is to the co-fme of the courfe 3 points 9-91985 
So is the diftance - - 138 - - 2-19866 
to the difference of latitude 131-4 
2-11851 
and the correfponding diftances in the fecond, column ; 
the third and fourth columns are to contain the diffe¬ 
rences of latitude, and the two laft the departures. 
Now, the feveral courfes and their correfponding dif¬ 
tances being properly arranged in the table, find the dif¬ 
ference of latitude and departure anfwering to each in 
the traverfe-table ; (fee Mackay on the Longitude, vol. ii.) 
remembering that the difference of latitude is to be put 
in a north or fouth column, according as the courfe is in 
the northernror fouthern hemifphere; and that the de¬ 
parture is to be put in an eaft column if the courfe is 
eafterly, but in a weft column if the courfe is wefterly. 
Obferving, alfo, that the departure is lefs than the diffe¬ 
rence of latitude when the courfe is lefs than 4 points, 
br 45 0 ; otherwife greater. 
Add up the columns northing, fouthing, eafting, and 
wefting, and fet down the turn ~f each at its bottom 5 
then the difference between the fums of the north and 
fouth columns will be the difference of latitude made 
good, of the fame name with the greater ; and the diffe¬ 
rence between the fums of the eaft and weft columns is 
the departure made good, of the fame name with the 
greater fum. 
Now leek in the traverfe-table tii! a difference of lati¬ 
tude- and departure are found to agree as nearly as poffi- 
ble with thofe above; then the diftances will be found on 
the fame line, and the courfe at the top or bottom of the 
page, according as the difference of latitude is greater or 
lefs than the departure. 
In order to relolve a traverfe by conftruftion, deferibe 
a circle with a chord of 6o°, in which draw two diameters 
at right triangles to each other, at whofe extremities are 
to be marked the initials of the cardinal points, north 
being uppermoft. 
Lay oft’ each courfe on the circumference, reckoned 
from its proper meridia-n ; and from the centre to each 
point draw lines, which are to be marked with the proper 
number of the courfe. 
On the firft radius lay off’ the firft diftance from the 
centre; and through its extremity, and parallel to the 
fecond radius, draw the fecond diftance of its proper 
length ; through the extremity of the fecond diftance, and 
parallel to the third radius, drawn the third diftance of 
its proper length ; and thus proceed until all the diftances 
are drawn. 
A line drawn from the extremity of the laft diftance to 
the centre of the circle will reprefent the diftance made 
good ; and a line drawn from the fame point perpendicu¬ 
lar to the meridian, produced, if neceflary, will reprefent 
the departure ; and the portion, of the meridian inter¬ 
cepted between the centre and departure will be the diffe¬ 
rence of latitude made good. 
Ex. A fhip from Fyal, in lat. 38° 32' N. failed as 
follows: E.S.E. 163 miles, S.W.-JW. no miles, S.E.jS. 180 
miles, and N. byE. 68 miles. Required the latitude come 
to, the courfe, and diftance made good ? 
To find the Departure. 
As radius ------ 10-00000 
is to the fine of the courfe - 3 points - 9-74474 
So is the diftance - - 158 - 219866 
to the departure - - 87-8 - 1-94340 
Of TRAVERSE SAILING. 
If a fhip fail upon two or more courfes in a given time, 
the irregular track ftie deferibes is called a traverfe; and 
to refolve a traverfe, is the method of reducing thefe fe¬ 
veral courfes, and the diftances run, intoafingle courfe 
and diftance. The method chiefly ufed for this purpofe 
at fea is by infpedtion, which (hall therefore be princi¬ 
pally adhered to ; and is as follows: 
Make a table of a breadth and depth fufficient to con¬ 
tain the feveral courfes, &c. This table is to be divided 
into fix columns ; the courfes are to be put in the firft, 
By InfpeSlion. 
Courfe. 
Dift. 
Diff of Latitude. 
Departure. 1 
N. 
S. 
E. 
w. | 
E.S.E. 
163 
— 
62-4 
1 506 
— I 
S.W.fW. 
I IO 
— 
69-8 ‘ 
— 
p 
00 
S.E.fS. 
180 
— 
1 44‘5 
107*2 
— 1 
N.&E. 
68 
66-7 
— 
13-3 
— 1 
66-7 
276-7 
27I*I 
85-0 
66-7 
85-0 
I S-4i|E. 
281 
2 I O'O 
186-1 
Latitude left 
- 
38° 32' N. 
I Difference of latitude 
- 
3 21 
S. 
jl Latitude come to 
- 
35 11 
N. j 1 
By 
