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Latitude of the Moon.

125. That the moon's orbit is inclined to the ecliptic was known to the earliest astronomers, from the non-recurrence of eclipses at every new and full moon; and it was also known, since the eclipses did not always take place in the same part of the heavens, that the line of nodes represented by Nn, in the preceding figure, has a retrograde motion on the ecliptic, N moving towards T.

Hipparchus fixed the inclination of the moon's orbit to the ecliptic at 5°, which value he obtained by observing the greatest distance at which she passes to the north or south of some star known to be in or very near the ecliptic, as for instance the bright star Regulus; and by comparing the recorded eclipses from the times of the Chaldean astronomers down to his own, he found that the line of nodes goes round the ecliptic in a retrograde direction in about 183 years.

This result is indicated in our expression for the value of the latitude by the term k sin (g0 − y), as we have shewn Art. (78).

126. Tycho Brahé further discovered that the inclination of the lunar orbit to the ecliptic was not a constant quantity of 5° as Hipparchus had supposed, but that it had a mean value of 5° 8', and ranged through 9′ 30′′ on each side of this, the least inclination 4° 58' occurring when the node was in quadrature, and the greatest 5° 17' being attained when the node was in syzygy. *

* Ebn Jounis, an Arabian astronomer (died A.D. 1008), whose works were translated about 30 years since by Mons. Sedillot, states that the inclination of the moon's orbit had been often observed by Aboul-HassanAly-ben-Amajour about the year 918, and that the results he had obtained were generally greater than the 5° of Hipparchus, but that they varied considerably.

He also found that the retrograde motion of the node was not uniform: the mean and true position of the node agreed very well when they were in syzygy or quadrature, but they were 1° 46′ apart in the octants.

By referring to Art. (80), we shall see that these corrections, introduced by Tycho Brahé, correspond to the second term of our expression for s.

Since Hipparchus could observe the moon with accuracy only in the eclipses, at which time the node is in or near syzygy, we see why he was unable to detect the want of uniformity in the motion of the node.

127. To represent these changes in the position of the moon's orbit, Tycho made the following hypothesis. Let ENF be the ecliptic, K its pole, BAC a small circle,

N

B

Ebn Jounis adds, however, that he himself had observed the inclination several times and found it 5° 3′, which leads us to infer that he always observed in similar circumstances, for otherwise a variation of nearly 23' could scarcely have escaped him. See Delambre, Hist. de l'Ast, du Moyen Age, p. 139.

The mean value of the inclination is 5° 8′ 55.46",-the extreme values are 4° 57′ 22′′ and 5° 20′ 6′′.

The mean daily motion of the line of nodes is 3' 10.64", or one revolution in 6793-39 days, or 18 y. 218 d. 21 h. 22 m. 46 s.

having also K for pole and at a distance from it equal to 5° 8'. Then, if we suppose A the pole of the moon's orbit to move uniformly in the small circle and in the direction BAC, the node N, which is at 90° from both A and K, will retrograde uniformly on the ecliptic, and the inclination of the two orbits will be constant and equal to AK.

But instead of supposing the pole of the moon's orbit to be at A, let a small circle abcd be described with A as pole and a radius of 9′ 30′′; and suppose the pole of the moon's orbit to describe this small circle with double the velocity of the node in its synodical revolution which is accomplished in about 346 days, in such a manner that when the node is in quadrature the pole may be at a, the nearest point to K, and at c the most distant point when the node comes to syzygy, at d in the first and third octants, and at b in the second and fourth, so as to describe the small circle in about 173 days, the centre A of the small circle retrograding meanwhile with its uniform motion.

By this method of representing the motion, we see that

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Again with respect to the motion of the node, since N is the pole of KaAc, it follows that when in syzygy and quadrature, the node occupied its mean place, in the first and third octants, the pole being at d, the node was before its mean place by the angle dKA= (9′ 30′′) cosec 5° 8′ = 1° 46′, nearly, and it was as much behind its true place in the second and fourth octants.

So that the whole motion of the node, and the correction which Tycho had discovered, were properly represented by this hypothesis, which is exactly similar to that which Copernicus had imagined to explain the precession of the Equinox.

THE END.

W. METCALFE, PRINTER, GREEN STREET, CAMBRIDGE.

BY THE SAME AUTHOR.

I.

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With a paper from Part II., Vol. X. of the Cambridge Philosophical Transactions.

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These diagrams have been engraved by the Hydrographic Office, Admiralty. Published by J. D. POTTER, 31, Poultry, London, Agent for the Admiralty Charts.

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