Practical Astronomy and Geodesy

188. Processes for finding, from the like data, the latitude and
longitude of a celestial body; and the converse

Page

189. Manner of computing the right ascension and declination of
the sun, having his longitude and the obliquity of the
ecliptic; and the converse

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190. Investigation of a formula for computing the difference
between the sun's longitude and right ascension

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191. Manner of obtaining the longitude and latitude of the moon,

a planet, or a star, when the right ascension and declination

are given; and the converse

ITS FIGURE

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CHAP. VIII.

THE ORBIT OF THE EARTH.

147

148

SHOWN TO BE ELLIPTICAL. SITUATION AND MOVE-

MENT OF THE PERIHELION POINT. THE MEAN, TRUE, AND

EXCENTRIC ANOMALIES. EQUATION OF THE CENTRE.

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192. Figure of the earth's orbit about the sun similar to that which

the sun may be supposed to describe about the earth

193. The apparent velocity of the sun when greatest and least;

the least and greatest angles subtended by the sun's

diameter; and the ratio between the least and greatest

distances of the sun from the earth

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194. Approximation to the figure of the earth's orbit by a graphic

construction. The orbit elliptical. The areas described

by the radii vectores proportional to the times

195. The line of apsides

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196. The angular velocity in an ellipse varies inversely with the

square of the distance

152

153

197. Manner of determining the instants when the sun's longitudes

differ by exactly 180 degrees

198. The progression of the perigeum

199. The length of the anomalistic year

200. Method of determining the perihelion point of the earth's

orbit and the instant when the earth is in that point

201. Manner of determining the excentricity approximatively

202. The mean, true, and excentric anomalies

203. Investigation of the mean, in terms of the true anomaly

204. Investigation of the true, in terms of the excentric anomaly

205. Investigation of the radius vector in terms of the excentric

and true anomalies

206. Equation of the centre, and determination of its greatest value

for the earth's orbit

207. Determination of the excentricity of the orbit in terms of the

greatest equation of the centre

208. Nature of the solar tables

158

CHAP. IX.

THE ORBIT OF THE MOON.

THE FIGURE OF THE MOON'S ORBIT.—PERIODICAL TIMES OF HER

REVOLUTIONS.—THE PRINCIPAL INEQUALITIES OF HER MOTION.

HER DISTANCE FROM THE EARTH EMPLOYED TO FIND AP-

PROXIMATIVELY THE DISTANCE OF THE LATTER FROM THE SUN.

Art.

209. Manner of determining by observation the nodes of the

moon's orbit, and its obliquity to the ecliptic

210. Process for determining the obliquity of the moon's orbit,

and the position of the line of nodes, from two observed

right ascensions and declinations

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211. The obliquity of the moon's orbit to the ecliptic is variable,

and her nodes have retrograde motions

212. Manner of determining the angular movement of the moon

in her orbit

213. Indication of the means employed in finding her distances

from the earth, the figure of her orbit, and the equation

of the centre or first inequality

214. Manner of finding the time of a synodical revolution of the

moon by a comparison of eclipses

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215. Her mean motion found to be accelerated

216. Determinations of the moon's sidereal and tropical revolutions 168

217. Time in which her nodes perform a revolution

218. Duration of an anomalistic revolution; and determination of

her mean daily tropical movement

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· 169

- 169

219. The moon's movements subject to considerable inequalities - 170

220. The moon's evection, or second inequality

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221. The moon's variation, or third inequality

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222. The moon's annual equation, or fourth inequality

172

223. Variations of the moon's latitude and radius vector.

224. Elementary method of finding an approximation to the earth's

distance from the sun, that of the moon from the earth

being given

APPARENT DISPLACEMENTS OF THE CELESTIAL BODIES

ARISING FROM THE FIGURE AND MOTION OF THE

EARTH.

THE EFFECTS OF PRECESSION, ABERRATION, AND NUTATION.

225. Annual increase in the longitudes of fixed stars, and move-

226. Investigation of a formula for the precession in declination

227. Investigation of a formula for the precession in right as-

a

229. Manner in which the phenomenon takes place

230. Maximum value of the aberration depending on the motion

231. Explanation of aberration in longitude and latitude

232. Investigation of a formula for aberration in longitude

233. Formula for aberration in latitude

234. Formula for aberration in right ascension

235. Formula for aberration in declination

236. Effect of aberration on the apparent place of the sun

237. The diurnal aberration of light

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- 183

- 184

239. Explanation of the phenomenon so called: its apparent de-

pendence on the place of the moon's node

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240. Nature of the path described by the revolving pole -

241. Investigation of a formula for the lunar equation of preces-

sion, and of obliquity -

242. Formula for the equation of the equinoctial points in right

ascension

243. Formula for the lunar nutation in polar distance

244. Formula for the lunar nutation in right ascension

THE ELEMENTS OF PLANETARY ORBITS. VARIABILITY OF THE

ELEMENTS. .KEPLER'S THREE LAWS. . PROCESSES FOR FINDING

THE TIME OF A PLANET'S REVOLUTION ABOUT THE SUN.-FOR-

MULÆ FOR THE MEAN MOTIONS, ANGULAR VELOCITIES AND TIMES

OF DESCRIBING SECTORAL AREAS IN ELLIPTICAL ORBITS.MODI-

FICATIONS OF KEPLER'S LAWS FOR BODIES MOVING IN PARA-

BOLICAL ORBITS. MOTIONS OF THE SATELLITES OF JUPITER,

SATURN, AND URANUS. IMMERSIONS ETC. OF JUPITER'S SATEL-

LITES. -

THE ORBITS OF SATELLITES ARE INCLINED TO THE

246. Method of finding approximatively the distance of a planet

from the earth

247. Manner of determining the trace of a planet's visible path

248. The elements of a planet's orbit

249. Method of finding the longitude of a planet's node. - Proof

that the sun is near the centre of a planet's orbit

250. Manner of finding the inclination of a planet's orbit to the

251. Manner of finding a planet's mean motion by observation

252. Manner of determining, by rectangular co-ordinates, a planet's

radius vector, its heliocentric distance from a node, and

its heliocentric latitude

253. Manner of determining the same elements from observations

at conjunction and opposition

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194

Art.

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254. Kepler's three laws stated as results of observation

255. The semi-transverse axis of a planet's orbit found from those

laws, the time of a sidereal revolution about the sun being

given

256. The time of a revolution about the sun found by successive
approximations, from two or more longitudes of the sun
and as many geocentric longitudes of the planet -
257. The place of the perihelion, the semi-transverse axis and the
excentricity found by means of three given radii vectores
with the heliocentric distances from a node

258. Method of finding the mean diurnal motion of a planet in an

259. The angular velocity in different parts of the same orbit

varies inversely as the square of the radius vector

260. Investigation of the sectoral area described about the focus

by the radius vector of an ellipse

261. Time in which the radius vector of a planet describes about
the sun an angle equal to a given anomaly
262. The laws of Kepler require modification for bodies moving
in parabolical orbits
263. In parabolical orbits the squares of the times of describing
equal angles, reckoned from the perihelion, vary as the
cubes of the perihelion distances

264. In elliptical orbits the sectoral areas described in equal times

vary as the square roots of the parameters; and in para-

bolical orbits such areas vary as the square roots of the

perihelion distances

265. The sectoral areas described in equal times in a circle and in

a parabola (the perihelion distance in the latter being

equal to the radius of the circle) are to one another as

1 to √/2

266. Investigation of the sectoral area described about the focus

by the radius vector of a parabola

267. Time in which the radius vector of a parabola describes about
the focus a sectoral area corresponding to a given anomaly 2014
268. In any parabola the angular velocity varies inversely as the
square as the radius vector

269. Nature of the observations to be made for determining the
elements of a comet's orbit

270. The satellites of Jupiter, Saturn, and Uranus

271. Visible motions of Jupiter's satellites

272. Their disappearances behind the planet, or in its shadow,

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- 206

· 206

273. The satellites of Jupiter and Saturn revolve about their

primaries from west to east. Their orbits inclined to

the ecliptic

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208

274. Manner of finding the times of revolution about the primary

planet

208

275. Manner of finding the inclinations of the orbits, and the

276. Manner of finding the inequalities of their motions
277. The satellites of the planets revolve on their axes in the
time of one revolution about their primaries

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278. Uncertainty in estimating the instants of immersion and

emersion

279. Saturn's ring, its figure and position: times when it becomes

280. Manner of finding the inclination of the ring

281. Manner of finding the positions of its line of nodes

282. Römer's hypothesis concerning the progressive motion of