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Page.
Number of miles in a degree of longitude at every degree of latitude...... 144
Proportional iniles for constructing Mercator's charts...
Table.
LIII.
LIV.
LV.
To find the distance of terrestrial objects at sea
For the manner of computing ditto, see page 149.
LVI.
LVII.
To gauge, or find the content of all circular-headed casks
To reduce French degrees into English degrees, and conversely.....
Respecting the principles &c., see page 151.
145
147
150
... 152
LVIII. Latitudes and longitudes of the principal ports &c. in the known world.. 154
Equation of second differences, for correcting the approximate mean time
Logarithmical radius of the earth, for reducing the moon's horizontal
parallax to the oblate figure of the earth.....
338
A CONCISE SYSTEM OF DECIMAL ARITHMETIC
Addition, and subtraction of decimals
Multiplication, and division of decimals
Reduction of decimals......
The rule of proportion, or rule of three, by decimals
Proportion and properties of numbers....
Given the angles and the hypothenuse, to find the base and the perpendicular
Given the angles and one side, to find the hypothenuse and the other side 172
Given the hypothenuse and one side, to find the angles and the other side 174
To find the side independently of the angles,-See Remark, page 175.
Given the base and the perpendicular, to find the angles and the hypothenuse 175
To find the hypothenuse independently of the angles,-See Remark, page 176
171
SOLUTION OF PROBLEMS IN OBLIQUE ANGLED TRIGONOMEtry.
I.
II.
Given the angles and one side, to find the other two sides
Given two sides and an angle opposite to one of them, to find the other
angles and the third side
III.
Given two sides and the included angle, to find the other two angles and
the third side
Given the hypothenuse and one leg; to find the angles and the other leg.. 184
Given the hypothenuse and one angle; to find the other angle and the
two legs.......
185
Given a leg and its opposite angle; to find the other angle, the other leg,
and the hypothenuse
... 187
IV.
Given a leg and its adjacent angle; to find the other angle, the other leg,
188
V.
VI.
Given the two legs; to find the angles and the hypothenuse
Given the two angles; to find the hypothenuse and the two legs
190
191
SOLUTION OF PROBLEMS IN QUADRANTAL SPHERICS.
Given a quadrantal side, its opposite angle, and an adjacent angle; to find
the remaining angle and the other two sides
Given the quadrantal side and the other two sides; to find the three angles 195
......
.....
193
SOLUTION OF PROBLEMS IN OBLIQUE ANGLED SPHERICS.
Given two sides and an angle opposite to one of them; to find the other
two angles and the third side
198
Given two angles and a side opposite to one of them; to find the remaining
angle and the other two sides
Given two sides and the contained angle; to find the other two angles and
the third side ...
200
202
To find the third side independently of the angles, - See Remark 1, in
page 203, and Remark 2, in page 204.
Given two angles and the comprehended side; to find the remaining angle
and the other two sides
205
To find the remaining angle, independently of the sides,-See Remark 1,
in page 206, and Remark 2, in page 207.
Given the three sides of a spherical triangle; to find the angles
Another method of finding ditto,- See Rule, page 208.
Given the three angles of a spherical triangle; to find the sides
Another method of finding ditto,-See Rule, page 210.
NAVIGATION
....
Definitions, and principles, between pages 211 and 214.
INTRODUCTORY PROBLEMS IN NAVIGATION.
... 207
... 209
211
Given the latitudes of two places; to find the difference of latitude ......
Given the latitude left and the difference of latitude; to find the latitude in
Given the longitudes of two places; to find the difference of longitude....
Given the longitude left and the difference of longitude; to find the longi-
tude in
214
215
216
See Remarks on the preceding Problems
217
SOLUTION OF PROBLEMS IN PARALLEL SAILING
Given the difference of longitude between two places, in the same parallel of
latitude; to find their distance......
218
Given the distance between two places, in the same parallel of latitude; to
find the difference of longitude between those places
Given the difference of longitude and the distance between two places, in
the same parallel of latitude; to find the latitude of that parallel
SOLUTION OF PROBLEMS IN MIDDLE LATITUDE SAILING
221
Definitions, principles, and analogies, between pages 221 and 223.
Given the latitudes and longitudes of two places; to find the course and
distance between them
223
Given the latitude and longitude of the place sailed from, the course and
distance; to find the latitude and longitude of the place come to ......
Given both latitudes and the course; to find the distance, and the longi-
224
226
the departure to find the distance sailed, and the latitude and longitude
of the place come to
.... 227
229
Given both latitudes and the distance sailed; to find the course and dif-
ference of longitude
Problem.
VII.
Given one latitude, distance, and departure; to find the other latitude,
the course, and the difference of longitude..
Given both latitudes and the departure; to find the course, distance, and
difference of longitude
... 232
VIII. Given one latitude, departure, and difference of longitude; to find the
other latitude, the course, and the distance
IX.
Given the distance, difference of longitude, and middle latitude; to find
the course, and both latitudes
235
MERCATOR'S SAILING
236
Definitions, principles, and analogies, between pages 236 and 238.
PROBLEMS IN MERCATOR'S SAILING.
Given the latitudes and longitudes of two places; to find the course, and
the distance between them
Given the latitude and longitude of the place sailed from, the course, and
distance; to find the latitude and longitude of the place come to
the departure, to find the distance sailed, and the latitude and longitude
239
240
242
Given both latitudes and the distance; to find the course, and the longi-
tude come to........
243
Given one latitude, distance, and departure; to find the other latitude, the
course, and the difference of longitude
244
VII. Given both latitudes, and the departure; to find the course, distance, and
246
VIII. Given one latitude, course, and difference of longitude; to find the dis-
tance, and the other latitude.....
248
To find the course, distance, difference of latitude, and difference of longi-
tude, made good upon compound courses; and also the bearing and
distance from the ship to her intended port
Solution of problems relative to the errors of the log. sine and the half-
minute glass.....
272
Solution of a very useful problem in great circle sailing
276
Spherical route from the Cape of Good Hope to the north point of King's
Island, at Bass' Strait.....
285
Spherical route from Port Jackson, in New South Wales, to Valparaiso,
on the coast of Chili
294
A compendium of practical navigation, for the use of such as are un-
acquainted with the elements of trigonometry
689
To make out a day's work at sea, by calculation
701
Of the log.-book, and particulars relating thereto...
706
Correction of the course steered on account of the variation of the compass 708
Correction of the course steered on account of lee-way
Allowance for lee-way under particular circumstances.
Setting and drift of currents, and heave of the sea.....
A general rule for correcting the dead reckoning
Form of a log-book
Of the measure of a knot on the log. line, and the spherical figure of the
earth
716
How to find the true length of a knot on the log. line
720
Errors of the log. line and half-minute glass, between pages 272 and 276.
To find the time of high water at any known place
To find the course steered by a ship seen at a distance
103
636
5.
The recession of the equinoctial points
301
6.
The number of revolutions that the earth takes to complete the solar and
the sidereal years
304
7.
An apparent solar day
305
11.
Arc which the earth mást describe beyond one diurnal revolution on its axis
to bring the sun upon the same meridian
A lunar day, and arc of excess which the earth must describe to bring the
35.
Illustration of apparent time, mean time, and the equation of time, by a
diagram
310
36.
Signs of the equation of time to be marked contrary in relation to mean
time
313
42.
43.
The mean sun's right ascension, or the "sidereal time," in page II. of
the month in the Ephemeris, and the "mean time of transit of the
first point of Aries" may be deduced from each other......
Equation of time expressed by the difference between the mean sun's right
ascension and the true sun's right ascension......
315
44.
"Sidereal time," page II. of the month in the Ephemeris, called the mean
sun's right ascension, and why
45, 46.
47.
The adjustment and use of nautical instruments
316
48.
49.
50.
To set the index-glass perpendicular to the plane of the sextant, &c.
To set the horizon-glass perpendicular to the plane of the sextant, &c.
To set the horizon-glass by means of the sun's image..
To set the horizon-glass parallel to the index-glass
51.
To set the horizon-glass by means of the sun's image...
319
52.
53.
To make the line of collimation parallel to the plane of the sextant..
To make the line of collimation &c., by another method
320
A more correct method of finding ditto, and how to read off to the right-
hand of zero, or off the arch
322
58.
On the elasticity or spring of the index bar
323
59.
The true method of finding the index error of a sextant, so as to guard
against the errors arising from the flexibility and friction of the index-