Art.

Page

300. Expression of the parallax of a star in terms of its maximum

value

231

301. Investigation of the parallax in a line joining the two which

constitute a double star

232

302. Bessel's determination of the constant of parallax for 61

Cygni

233

CHAP. XIV.

TIME.

SIDEREAL, SOLAR, LUNAR, AND PLANETARY DAYS.

-

EQUATION OF

TIME.

REDUCTIONS OF ASTRONOMICAL

ELEMENTS TO THEIR VALUES FOR GIVEN TIMES.-HOUR ANGLES.

EQUINOCTIAL TIME.

303. Value of a sidereal day, and definition of sidereal time

304. Error and rate of a sidereal clock found by the observed

transits of stars

234

235

305. Apparent solar day defined; its length variable

306. Difference between a mean solar, and a mean sidereal day · 236

307. Lengths of a lunar, and of a planetary day

308. Reduction of mean sidereal, to mean solar time, and the

237

converse

-

- 237

309. Reduction of sidereal time at Greenwich mean noon to
sidereal time at mean noon under a different meridian

310. Equation of time defined. Formula for its value

311. Equinoctial time

312. Manner of finding the mean time at which the sun or a
fixed star culminates

313. Manner of finding the time at which a planet or the moon

culminates

314. Manner of finding the angle at the pole between the horary
circles passing through the places of the sun, a fixed star,
the moon and a planet, at two times of observation, the
interval being given in solar time

315. Reduction to solar time, of the angle at the pole between the

meridian of a station and a horary circle passing through

the sun, a fixed star, the moon or a planet; with an

example

CHAP. XV.

244

- 245

INTERPOLATIONS- PRECISION OF OBSERVATIONS.

316. Reduction of astronomical elements in the Nautical Almanac

to their values for a given time, and at a given station, by

simple proportions, or for first differences

317. Investigation of a formula for first, second, and third dif-

ferences; with an example for finding the moon's latitude 249

318. Horary motions found by first and second differences

319. Formula for several interpolations between two values of an

element

323. Formulæ for the limits of probable error in a mean result of

observations

324. Formula for the degree of precision in an average

325. Relation between precision and weight

253

-

253

254

255

255

256

-

256

326. Weight due to the sum or difference of two observed quan-

tities

327. Manner of finding the relative values of instruments or

observations

328. The most probable values of elements are obtained by com-

bining the equations containing the results of many ob-

servations

-

329. Method of grouping equations advantageously for the deter-

mination of correct results

330. Method of least squares

CHAP. XVI.

NAUTICAL ASTRONOMY.

257

PROBLEMS FOR DETERMINING THE GEOGRAPHICAL POSITION OF A

SHIP OR STATION, THE LOCAL TIME, AND THE DECLINATION OF

THE MAGNETIC NEEDLE.

331. Importance of celestial observations at sea

332. The data and objects of research in nautical astronomy

333. Errors which may exist in the observations; with examples

illustrating the manner of correcting the observed altitudes

and the declinations of the sun, moon, &c.

334. (Prob. I.) To find the latitude of a ship or station by means

of an observed altitude of the sun when on the meridian.

—Examples for the sun, the moon, and a planet

335. Method of finding the latitude of a ship by the observed

time in which the sun rises or sets

336. Method of finding the latitude in the arctic regions by

meridional altitudes above and below the pole

337. (Prob. II.) To find the hour of the day by an observed

altitude of the sun; the latitude of the station and the

sun's declination being given

338. Method of determining the hour of the night by a fixed star,

and by a planet, with examples

339. (Prob. III.) To investigate a relation between a small varia-

tion in the altitude of a celestial body and the correspond-

ing variation of the hour angle -

340. (Prob. IV.) By an altitude of the sun, a fixed star or a

planet, to compute its azimuth and determine the variation

or declination of the magnetic needle; the latitude of the

station and the sun's declination being given.- Example,

from an observed altitude of the sun

-

341. Method of finding the direction of a meridian line on the

263

263

264

266

268

269

270

272

276

277

Art.

Page

ground by the azimuths of the sun and of a fixed ter-
restrial object

-

-

-

279

280

342. (Prob. V.) Having the latitude of a station, the day of the

month, &c.; to find the sun's amplitude

343. Method of finding the declination of the needle, and the hour

of sun-rise, by the amplitude of the sun; with an example 281

344. Method of finding the effects of iron on the compass of a
ship. Application of Barlow's plate
345. (Prob. VI.) To determine the hour of the day and the error
of the watch by equal altitudes of the sun

-

-

346. Investigation of the change in the hour angle caused by a
variation of the sun's declination

-

-

-

283

285

287

288

347. Investigation of the change in the sun's azimuth caused by a

variation of his declination; and a method of finding the

direction of a meridian line by equal altitudes of the sun

with the corresponding azimuths. - Example

348. Method of finding the time of apparent noon from equal al-

titudes of the sun, the ship changing its place in the in-

terval between the observations

349. Method of finding the error of a watch by equal altitudes of

a fixed star or planet on the same or on different nights

350. (Prob. VII.) To find the latitude of a station by means of an

altitude of the sun observed in the morning or afternoon,

or by the altitude of a star; with examples

351. Investigation of a formula for the difference between the ob-

served and meridional zenith distances of the sun, the

latter being near the meridian; with an example

352. Formula for determining the latitude of a station by an al-

titude of the pole star; with an example

353. Littrow's formula for finding the latitude of a station by three

altitudes of the sun or a star near the meridian; with an

example

354. (Prob. VIII.) To find the latitude of a station having the al-

titudes of the sun observed at two times in one day; with

an example* -

355. Method of correcting at sea an observed zenith distance of

the sun on account of the change in the ship's place in the

interval between the observations

356. Conditions favourable to the accuracy of the computed

latitude in this problem

357. Methods of determining the latitude by two altitudes of a

celestial body with the interval in azimuth; and by simul-

taneous altitudes of two fixed stars

-

358. (Prob. IX.) To find the altitude of the sun, having the latitude

of the station and the hour of the day; with examples in

illustration when the body observed is the sun, a star, and

the moon

-

359. Principles on which are founded the methods of finding

terrestrial longitudes

* This example has been accidently placed at the end of art. 357.

304

307

- 310

Art.

-

360. (Prob. X.) To find the longitude of a station or ship by means

of an observed angular distance between the moon and

sun, or between the moon and a star; with an example

361. The nature and use of proportional logarithms

362. Method of finding the longitude by the moon's hour angle

363. Employment of chronometers for finding the longitudes of

ships or stations

-

-

Page

311

314

315

- 316

316

-

364. Methods of finding the error and rate of a chronometer

365. Method of finding the longitude of a station by observed

transits of the moon over the meridian

366. Method by observed culminations of the moon and certain

stars

367. Method by fire signals

CHAP. XVII.

ECLIPSES.

318

- 319

320

OUTLINES OF THE METHODS OF COMPUTING THE OCCURRENCE OF

THE PRINCIPAL PHENOMENA RELATING TO AN ECLIPSE OF THE

MOON, AN ECLIPSE OF THE SUN FOR A PARTICULAR PLACE,

THE OCCULTATION OF A STAR OR PLANET BY THE MOON, AND

THE TRANSITS OF MERCURY AND VENUS OVER THE SUN'S DISK.

THE LONGITUDES CF STATIONS FOUND BY ECLIPSES AND OC-

-

CULTATIONS.

368. Formulæ for computing the angular semidiameter of the

earth's shadow and penumbra

369. Method of finding the time of the commencement, the

greatest phase and the end of an eclipse of the moon

370. Method of finding the hour angle of the sun and moon at the

instant of true conjunction in right ascension

371. Process of finding the approximate Greenwich time of the

apparent conjunction of the sun and moon in right as-

cension, at the station. Elements, from the Nautical

Almanac, &c.

326

328

328

331

332

372. Method of finding the difference between the apparent de-

clinations of the sun and moon at the approximate time

of apparent conjunction in right ascension

373. Formulæ for the apparent relative horary motions; and

method of finding the time of commencement, greatest

phase and end of an eclipse of the sun

374. Conditions under which an occultation of a star by the moon

may take place

375. Approximate Greenwich time of apparent conjunction of the

moon and a star in right ascension at the station

376. Formulæ for the horary motions of the moon and a star; and

method of finding the times of the phenomena

377. Elements to be taken from the Nautical Almanac for the

purpose of finding the times at which Mercury and Venus

enter upon, or quit the sun's disk

-

-

Art.

-

378. Process for finding the instants of ingress and egress for a

spectator at the centre of the earth

379. The parallaxes of the sun and planet being given; to compute

the instants of ingress and egress for a spectator at a given

station

-

380. The instants of ingress and egress being given; to compute

the parallaxes of the sun and planet

-

381. Use of observed eclipses of the sun

382. Process for determining the longitude of a station from an

observed eclipse of the sun; with an example

-

383. Process for finding the longitude of a station from an oc-

cultation of a fixed star or planet by the moon

384. Method of finding the longitude of a station by observed im-

mersions or emersions of Jupiter's satellites

CHAP. XVIII.

GEODESY.

Page

337

338

339

340

340

345

METHOD OF CONDUCTING A GEODETICAL SURVEY. MEASUREMENT

OF A BASE. FORMULA FOR VERIFYING THE OBSERVED ANGLES

AND COMPUTING THE SIDES OF THE TRIANGLES. MANNER OF

DETERMINING THE POSITION, AND COMPUTING THE LENGTH OF A

GEODETICAL ARC.

PROPOSITIONS RELATING TO THE VALUES OF

TERRESTRIAL ARCS ON THE SUPPOSITION THAT THE EARTH IS A

SPHEROID OF REVOLUTION. THE EMPLOYMENT OF PENDULUMS

TO DETERMINE THE FIGURE OF THE EARTH.

IN FINDING THE ELEMENTS OF TERRESTRIAL MAGNETISM.

FORMULE FOR COMPUTING THOSE ELEMENTS AND THEIR VARI-

ATIONS. — EQUATIONS OF CONDITION EXEMPLIFIED.

385. Probability that the earth's figure is not that of a regular

solid

386. Certainty that it differs little from a sphere or a spheroid of

revolution

350

387. The geodetic line or arc of shortest distance on the earth

defined

351

388. Terrestrial azimuth defined. The normals passing through

two points near one another may be supposed to be in one

plane

389. The first notions concerning the figure of the earth erroneous 352

390. Brief outline of the method of conducting a geodetical survey,
and of determining the figure of the earth

391. Details of the process employed in measuring a base

392. Reduction of the base to the level of the sea

395. Formula for a reduction to the centre of a station

- 359

396. Formula for verifying the observed angles of a triangle on the

surface of the earth, supposed to be a sphere

b

- 360