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4

the positions of the nodes are determined at distant epochs of time, and referred to the ecliptic, they are found to have experienced variations, and to have a very slow retrograde motion. These variations, as well as those which take place in the inclination of the orbit, are denominated secular inequalities, and are necessary consequences of universal gravitation; which modern analysis not only establishes, but also furnishes the means of calculating their effects on the planetary motions.

When the position of the orbit is thus determined, the law of the planets motion, and the nature of the curve it describes, are then the objects of research; and these would be known if the length of the radius vector and the angle it makes with a fixed right line situated in the plane of its orbit, and passing through the centre of the Sun, were assigned at every instant. The first object is therefore to ascer. tain the duration of one complete sidereal revolution of the planet; the most simple means of accomplishing this is, to observe two consecutive passages through the same node. This being found, the mean angular motions of the planet about the Sun are easily deduced, and the variations in its distance from the Sun determined. For these purposes, observations at the time of conjunctions and oppositions are favourable, as these take place in different points of their orbits. Thus a series of similar obseryations gives different angles and different radii vectores; and as these radii are known in terms of the radius of the solar orbit, and their true directions from the centre of the system ascertained, the figure of the planetary orbit becomes known.

The eccentricities of the planetary orbits experience very slow variations, both the law and extent of which have been determined by theory. The eccentricities of Mercury, Mars, and Jupiter increase, but those of all the other planets diminish. .

The Perihelia, or the points of the planet's greatest distance from the Sun, are not fixed; but have a slow motion in the plane of their orbits, in the same manner as the perigeon of the solar orbit moves along the plane of the ecliptic. For all the planets, except Venus, these movements are direct, or in the same direction as that of the Sun ; but for Venus this motion is retrograde. The observations relative to those small variations that can be depended upon, are still of too recent a date to give them with certainty : the theory of attraction is therefore the most accurate.

From a consideration of these principles, it may be perceived that the knowledge of the elliptical movement of each planet depends upon seven elements; and as there are eleven planets, seventy-seven elements must be determined in order to have a complete knowledge of our planetary system, in the present state of astronomy.

It would much exceed the limits, as well as be foreign to the nature, of the present work, to enter into a particular explanation of the methods, and give the formula which the improvements of modern analysis have established for ascertaining these several elements. We must therefore rest satisfied with giving the results that have been obtained by the most eminent astronomers, and refer the readers to their works for the methods by which they have been fonnd.

We have already given the sidereal revolutions and mean distances of the planets from the Sun in our Occurrences for March, inserted in a preceding part of this volume; to which we must therefore refer for these elements. It is also necessary to remark, that the recent discovery of the four new telescopic planets, Ceres, Pallas, Vesta, and Juno, and the small number of observations that astronomers have yet been able to make upon them for the purpose, are not sufficient to determine their secular inequalities with the desirable accuracy : those which are given in the following tables must therefore be regarded as only approximations to the truth. The subsequent

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results are extracted from Laplace's Exposition du
Systême du Monde.
Eccentricities of the Planetary Orbits, at the Commence-
ment of 1801, expressed in Parts of their semitransverse
Ares.

Mercury - - - - - - - - 0.205514
Venus - - -

0.006853
The Earth .

0.016853 Mars -

0.093134 Ceres -

0·078349 Pallas - - - - - - - - - 0.245384 Vesta

0.254944
Juno - -

0·093220
Jupiter - - - - - - - - 0.048178
Saturn - - - - - - - - 0:056168
Uranus -

• - 0.046670 Secular Variations to which the preceding Eccentricities are

subject. The Sign denotes Diminution.
Mercury - - , - - - - - 0.000003867
Venus - - - - - - - - - 0.000062711
The Earth - - - -'-'- - - 0.000041632
Mars - - - - - - - - - 0.000090176
Ceres
Vesta

Not yet ascertained
Juno
Jupiter - - - - - • - -' 0.000159350
Saturn - - - - - - - - - 0.000312402.

Uranus - - - - - - - - - 0.000025072 Longitudes of the Planets at the Commencement of 1801;

reckoned from the Vernal Equinox.

Pallas

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Mercury - - . . . . . . 163 56 27
Vepus - • •

44 35
The Earth

• 100 9 13 Mars • - - - . - -

64 7 2 Ceres -

264

45 '5 Pallas - ..

252 37.2 Vesta -

290 30 - 52 Juno

267 25 1 Jupiter -

.. 102 12 36 Saturn

- - 135 20 32 Vranus

••• 177 47 18

Longitudes of the Periheliu at the same Epoch.
Mercury - - - - .. 4 1 4
Venus -.-

128 37 1
The Earth -

99 30 Mars -..

332 24. Ceres -

146 39 Pallas . .

121 14 1 Vesta -

53 18 41 Juno -

249 43 0 Jupiter - - - - - - - -

11 - 8 3 Saturn - - - - - - - - - 88 8 58 Uranus . .

- - - 167 21 42

Sidereal and secular Motion of the Perihelia. The nega.

Sign indicates a retrograde Motion.

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Inclination of the Planetary Orbits to the Ecliptic, at the

Commencement of 1801.

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The above inclinations of the four new planets are those determined by M. Gauss, of Gottingen, and are the means of a great number of results.

The

Secular Variation in the Inclination to the Ecliptic.

negative Sign indicates as before.

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Mercury - - - - - - - - 18:18
Venus - - - - - - - - - 4:55
The Earth - - - - - - - - 0:00
Mars - - - - - - - - - 0:15
Jupiter - - - - - - - - 22.61
Saturn - - - - - - - - - 15:51

Uranus - - - - - - - - - 3:13 Longitude of the ascending Node, at the Commencement of

1801. ,
Mercury - - - - - - . 45 52 31
Venus - - - - - - - - 74 52 40
The Earth - - - - - -. - 0 0 0
Mars - -'- - - - - - 48 1 28
Ceres - -

- - - - - - - 80 53 41
Pallas - -

172
Vesta - - - - - - - - 103 10 41
Juno - -

171 9 13
Jupiter . . . . . . . . 98 25 34.
n. -

- - - - - - 111 55 47 Uranus - - - - - - - - 72 51 14 ' The above elements of the new planets were determined by M. Gauss. Sidereal and secular Motion of the Node on the Ecliptic,

the Sign - being used as before. Mercury -

- - 782.27 Venus

- - - - - - - 1869.80 The Earth

0.00 Mars -

2328.47 Jupiter -

1577.57 Saturn -

2266.46 Uranus -

3597.96

The Naturalist's Diary

For JUNE 1818.
Short is the reign of night, and almost blends

The evening twilight with the morning dawn. WARM weather is generally established in June, yet the heat is rarely excessive :-showers of rain

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