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CHAP. XIII.

OF THE CALENDAR.

415 lunar month has been resorted to in many instances ; and some nations have, in fact, preferred a lunar to a solar chronology altogether, as the Turks and Jews continue to do to this day, making the year consist of 13 lunar months, or 355 days. * Our own division into twelve unequal months is entirely arbitrary, and often productive of confusion, owing to the equivoque between the lunar and calendar month. The intercalary day na. turally attaches itself to February as the shortest.

* The Metonic cycle, or the fact, discovered by Meton, a Greek mathematician, that 19 solar years contain just 235 lunations (which in fact they do to a very great degree of approximation), was duly appreciated by the Greeks, as ensuring the correspondence of the solar and lunar years, and honours were decreed to its discoverer.

NOTE

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On the Constitution of a Globular Cluster, referred to in page 401.

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hatever might be uld be invariable in event the end of every

If we suppose a globular space filled with equal stars, uniformly dispersed through it, and very numerous, each of them attracting every other with a force inversely as the square of the distance, the resultant force by which any one of them (those at the surface alone excepted) will be urged, in virtue of their joint attractions, will be directed towards the common center of the sphere, and will be directly as the distance therefrom. This follows from what Newton has proved of the internal attraction of a homogeneous sphere. Now, under such a law of force, each particular star would describe a perfect ellipse about the common center of gravity as its center, and that, in whatever plane and whatever direction it might revolve. The condition, therefore, of a rotation of the cluster, as a mass, about a single axis would be unnecessary. Each ellipse, whatever might be the proportion of its axes, or the inclina. tion of its plane to the others, would be invariable in every particular, and all would be described in one common period, so that at the end of every such period, or annus magnus of the system, every star of the cluster (except the superficial ones) would be exactly re-established in its original position, thence to set out afresh, and run the same unvarying round for an indefinite succession of ages. Supposing their motions, therefore, to be so adjusted at any one moment as that the orbits should not intersect each other, and so that the magnitude of each star, and the sphere of its more intense attraction, should bear but a small proportion to the distance separ rating the individuals, such a system, it is obvious, might subsist, and realise, in great measure, that abstract and ideal harmony, which Newton, in the 89th Proposition of the First Book of the Principia, has shown to characterise a law of force directly as the distance. See also Quarterly Review, No. 94. p. 540.- Author.

STYOPTIC TABLE OF THE ELEMENTS OF THE SOLAB STSIES

N. B. – The data for Vesta, Juno, Ceres, and Pallas are for January 1

1820. The rest for January 1 ISOL .

Planet's name.

Mean distance
from Sun, er
Semi-axis.

Mean Sidereal
Period in Mean

Solar Days.

Parts of the
Semi aris.

Mercury Venus Earth Mars Vesta Juno Ceres Pallas Jupiter Saturn Uranus

0-3870981 87.96925800-20551 49
0-7233316 224-7007869 0-0068607
1•0000000 365-2563612 0-0167836
1.5236923 686.9796458 0-0938070
2-3678700 1325-7431000 0-0891300
2-6690090 1592-6608000 0-2578480
2.7672450 | 1681.3931000 0-0784390
2.7728860 | 1686-5388000 0-2416480
5.2027760 4332-5848212 0-0481621

9.5387861 10759-2198174 0-0561505 19.1823900 30686-8208296 0-0466794

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SYNOPTIC TABLE OF THE ELEMENTS OF THE ORBITS
OF THE SATELLITES, SO FAR AS THEY ARE KNOWN.

N. B.- The distances are expressed in equatorial radii of the

primaries. The epoch is Jan. 1. 1801. The periods, &c. are expressed in mean solar days.

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1. The Moon. Mean distance from earth .

29.98217500 Mean sidereal revolution

27d.321661418 Mean synodical ditto

291.530588715 Excentricity of orbit

0.054844200 Mean revolution of nodes .

- 6793*.391080 Mean revolution of apogee

32321.575343 Mean longitude of node at epoch

13° 53' 17"1.7 Mean longitude of perigee at do.

266 10 7.5 Mean inclination of orbit'. .

5 8 47 .9 Mean longitude of moon at epoch - 118 17 8.3 Mass, that of earth being 1,

0.0125172 Diameter in miles -

- 2160

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The excentricities of the 1st and 2d satellite are insensible, that of the 3d and 4th small, but variable in consequence of their mutual perturbations.

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ANO

3.351 01 22" 38" The orbits of the six interior 4.300 1 1 8 53 satellites are nearly circular, 5.284 1 1 21 18 and very nearly in the plane of 6.819 1 2 17 45 of the ring. That of the seventh

9.524 4 12 25 is considerably, inclined to 22:081 | 15 22 41 | the rest, and approaches nearer 64.359 797 55 to coincidence with the ecliptic.

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54 21" 25'n Os | Their orbits are inclined 8. 16 56 5 about 78° 58': to the 10 23 4 0 ecliptic, and their motion 13 11 8 59 is retrograde. The pe

38 148 0 riods of the 2d and 4th | 107 16 · 400 require a trifling correc

tion. The orbits appear to be nearly circles."

Patel

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