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Table.

Page.

LIV. Proportional miles for constructing Mercator's charts...... 145

LV. To find the distance of terrestrial objects at sea ..

147

LVI. To reduce the French centesimal division of the circle into the

English sexagesimal division; or, to reduce French degrees

into English degrees, and conversely

150

LVII. A general table for gauging, or finding the content of all circular

headed casks....

152

LVIII. Latitudes and longitudes of the principal sea-ports, islands, capes,

shoals, &c. in the known world ; with the time of high water,

at the full and change of the moon, at all places where it is

known...

154

Alphabetical reference to the preceding table .

155

Form of a transit table ....

Miscellaneous numbers with their corresponding logarithms

A table showing the true time and degree at which the hour and

minute hands of a well-regulated watch, or clock, should

exactly meet, or be in conjunction, &c. in every revolution.... 155

A concise system of decimal arithmetic

156

METRY

SOLUTION OF PROBLEMS IN PlanE, AND SPHERICAL Trigono-

168

Plane trigonometry, solution of right angled triangles

171

solution of oblique angled triangles.......

.. 177

Spherical trigonometry, solution of right angled triangles., 181 182

solution of quadrantal triangles

193

solution of oblique angled triangles .... 197

NAVIGATION....

211

Solution of problems relative to the difference of latitude and dif-

ference of longitude

214

Solution of problems in parallel sailing

217

middle latitude sailing

221

Mercator's sailing .

236

oblique sailing

255

windward sailing

262

current sailing

266

Solution of problems relative to the errors of the log line and the

half minute glass

272

Solution of a very useful problem in great circle sailing... 276

To find the time of high water at any known place

103 To make out a day's work at sea by inspection....

249

SOLUTION OF PROBLEMS in Nautical AstroNOMY

296

I. To convert longitude, or parts of the equator into time

II. To convert time into longitude or parts of the equator

III. Given the time under any known meridian, to find the corres-

ponding time at Greenwich

297

Problem.

IV. Given the time at Greenwich, to find the corresponding time

under a known meridian......

... 297

V. To reduce the sun's longitude, right ascension, declination, and,

also, the equation of time as given in the Nautical Almanac,

to any other meridian, and to any given time under that

meridian ..

..' 298

VI. To reduce the moon's longitude, latitude, right ascension, declin-

ation, semi-diameter, and horizontal parallax, as given in the

Nautical Almanac, to auy other meridian, and to any given

time under that meridian ..

302

VII. To reduce the right ascension and declination of a planet, as

given in the Nautical Almanac, to any given time under a

known meridian

307

VIII. To compute the apparent time of the moon's transit over the me-

ridian of Greenwich .....

309

IX. Given the apparent time of the moon's transit over the meridian

of Greenwich, to find the apparent time of her transit over any

other meridian....

312

X. To compute the apparent time of a planet's transit over the meri.

dian of Greenwich

313

XI. Given the apparent time of a planet's transit over the meridian of

Greenwich, to find the apparent time of its transit over any

other meridian.....

315

XII. To find the apparent time of a star's transit over the meridian of

any known place.....

317

XIII. To find what stars will be on, or nearest to the meridian at any

given time ..

319

XIV. · Given the observed altitude of the lower or upper limb of the

sun, to find the true altitude of its centre

320

XV. Given the observed altitude of the lower or upper limb of the

moon, to find the true altitude of her centre......

323

XVI. Given the observed central altitude of a planet, to find its true

altitude ...

325

XVII. Given the observed altitude of a fixed star, to find its true

altitude

327

SOLUTION OF PROBLEMS RELATIVE TO THE LATITUDE..

328

1. Given the sun's meridian altitude, to find the latitude of the

place of observation.....

II. Given the moon's meridian altitude, to find the latitude of the

place of observation .....

330

III. Given the meridian altitude of a planet, to find the latitude of

the place of observation ..

333

IV. Given the meridian altitude of a fixed star, to find the latitude of

the place of observation

335

V. Given the meridian altitude of a celestial object observed below

the pole, to find the latitude of the place of observation...... 336

VI. Given the altitude of the north polar star, taken at any hour of

the night ; to find the latitude of the place of observation .... 337

Given the latitude by account, the sun's declination, and two

observed altitudes of its lower or upper limb; the elapsed time,

and the course and distance run between the observations; to

find the latitude of the ship at the time of observation of the

greatest altitude ...

341

VIII. Given the altitudes of two known fixed stars observed at the same

instant, at any time of the night; to find the latitude of the

place of observation, independent of the latitude hy account,

the longitude, or the apparent time of observation .... 347

IX. Given the latitude by account, the altitude of the sun's lower or

upper limb, observed within certain limits of noon, the

apparent time of observation, and the longitude; to find the

true latitude of the place of observation.....

.. 354

X. Given the latitude by account, the altitude of the moon's lower or

upper limb, observed within certain limits of the meridian, the

latitude of the place of observation....

358

XI. Given the latitude by account, the altitude of a planet's centre

observed within certain limits of the meridian, the apparent

time of observation, and the longitude; to find the true latitude

of the place of observation ....

.. 362

XII. Given the latitude by account, the altitude of a fixed star observed

within certain limits of the meridian, the apparent time of

observation, and the longitude ; to find the true latitude of the

place of observation ......

To find the latitude by an altitude taken near the meridian below

the pole ...

368 369

Captain William Fitzwilliam Owen's general Problem for finding

the latitude ...

371

XIII. Given the interval of time between the rising or setting of the

sun's upper and lower limbs ; to find the latitude..... 373

.... 365

SOLUTION OF PROBLEMS RELATIVE TO THE APPARENT Time...... 375

1. To find the error of a watch by equal altitudes of the sun.... 377

II. To find the error of a watch by equal altitudes of a fixed star .. 380

III. Givea the latitude of a place, and the altitude and declination of

the sun; to find the apparent time of observation, and, thence,

the error of the watch. Method I.....

383

Method II. Of computing the horary distance of a celestial

object from the meridian...

388

Method III. Of computing the horary distance of a celestial

... 390

Method IV. Of computing the horary distance of a celestial

object from the meridian..,,

392

IV.

Given the latitude and longitude of a place, the altitude, right

ascension, and declination of a known fixed star, and the sun's

right ascension; to find the apparent time ..

394

Given the latitude and longitude of a place, and the altitude of a

planet; to find the apparent time of observation...... 397

Given the latitude and longitude of a place, the estimated time

at that place, and the altitude of the moon's limb; to find the

apparent time of observation

400

V.

VI.

Solution of PROBLEMS RELATIVE TO FINDING THE ALTITUDES OP

THE HEAVENLY BODIES., ...,

403

I. Given the latitude and longitude of a place, and the apparent

time at that place; to find the true and the apparent altitude

of the sun's centre

404

II. Given the latitude and longitude of a place, and the apparent

of a fixed star ..

406

III. Given the latitude and longitude of a place, and the apparent

of a planet ...

408

IV. Given the latitude and longitude of a place, and the apparent time

at that place; to find the true and the apparent altitude of the

moon's centre

410

Solution OF PROBLEMS RELATIVE TO THE LONGITUDE

413

1. To convert apparent time into mean time ..

415

II. To convert mean time at Greenwich into apparent time........

416

III. Given the latitude of a place, and the observed altitude of the

sun's limb; to find the longitude of that place by a chrono-

meter or time-keeper

417

IV. Given the latitude of a place, and the observed altitude of a

known fixed star; to find the longitude of that place by a

chronometer or time-keeper...

420

V. Given the latitude of a place, and the observed altitude of a

planet; to find the longitude of the place of observation by a

chronometer or time-keeper....

423

VI. Given the latitude of a place, and the observed altitude of the

moon's limb; to find the longitude of the place of observation

by a chronometer or time-keeper...

426

VII. To find the longitude of a ship or place by celestial observation,

commonly called a LUNAR OBSERVATION

431

Method I. Of reducing the apparent to the true central

distance

433

Method II. Of reducing the apparent to the true central

436

438

.... 442

Method IV. Of reducing the apparent to the true central

439

Method V. Of reducing the apparent to the true central

... 441

Method . VI. Of reducing the apparent to the true central

Method VII. Of reducing the apparent to the true central

.. 443

Method VIII. Of reducing the apparent to the true central

445

Method IX. Of reducing the apparent to the true central

447

Method X. Of reducing the apparent to the true central

448

Method XI. Of reducing the apparent to the true central

450

Method XII. Of reducing the apparent to the true central

451

Method XIII. of reducing the apparent to the true central

453

VIII. Given the apparent time, and the true central distance between

the moon and sun, a fixed star, or planet; to determine the

longitude of the place of observation

454

IX. Given the latitude of a place, its longitude by account, the

observed distance between the moon and sun, a fixed star, or

a planet, and the observed altitudes of these objects ;' to find

the true longitude of the place of observation ....

456

Given the observed distance between the moon and sun, a fixed

star, or planet, the apparent time, with the latitude and longi-

tude by account; to find the true longitude of the place of

observation

.. 470

XI.

To find the longitude of a place by the eclipses of Jupiter's

satellites ...

478

XII. To find the longitude of a place by the eclipses of the moon .... 481

......

Compass

31

SOLUTION OF PROBLEMS RELATIVE

ΤΟ THE VARIATION OF THE

483

I. Given the latitude of a place, and the sun's magnetic amplitude;

to find the variation of the compass.

484

II.

Given the latitude of a place, the sun's altitude, and his magnetic

azimuth; to find the variation of the compass

487

A new method of computing the true azimuth of a celestial

object .....

490

III. To find the variation of the compass by observations of a circum-

492

IV. To find the variation of the compass by the magnetic bearing of

polar star...