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TYCHO BRAHE.

of the lunar orbit described a circle round the mean pole with a radius of 9′ 30″, so that the inclination reaches its minimum at syzygy and its maximum at quadrature.^[1] He applied corrections separately to the latitude for equation of node and for change of inclination, a form which was retained even by Newton and Euler, until Tobias Mayer showed that the two equations can be combined into one, varying with the double distance of the moon from the sun, less the argument of latitude of the moon.^[2]

It would lead us too far if we were in this place to enter into a description of Tycho's lunar tables, or of his precepts for finding the longitude from his theory.^[3] We shall only mention that he was the first to tabulate the reduction, or the difference between the moon's motion along its orbit, and the same referred to the ecliptic. The table of parallax makes this quantity vary between 66′ 6″ and 56′ 21″, the apparent diameter varying from 32′ to 36′ at full moon, while he believed to have found from his observations of eclipses that the diameter appears less at new moon (25′ 36″ to 28′ 48″), owing to the limb being "extenuated" by the solar rays. He therefore denied the possibility of a total solar eclipse, to some extent also misled by the accounts

↑ Copernicus had employed a similar construction to explain the trepidatio or (imaginary) oscillation of the equinoxes.
↑ In Godfray's Lunar Theory, chap, viii., Tycho's hypothesis is described as if he supposed the lunar pole to move in the small circle with double the synodical velocity of the node. Though this, of course, is the correct representation of the perturbations in latitude, it is not Tycho's idea, as he took no notice whatever of the position of the node with regard to the sun, but let the pole move with double the synodical velocity of the moon. In the well-known term 9′ sin (☾ − 2☉ + ☊), if we, instead of the quantity within the bracket, write 2(☾ − ☉) − (☾ − ☊), we get Tycho's period, as the inclination will vary by − 9′ cos 2 (☾ − ☉). But if we put (☾ − ☊) − 2 (☉ − ☊), the inclination will vary by + 9′ cos 2 (☉ − ☊), and the period is 173 days. That Kepler had remarked the importance of the position of the sun with regard to the node may be seen from Tab. Rudolph., pp. 89–90; Opera, vi. pp. 588 and 648. Of modern authors, Montucla seems to be the only one who has remarked that Tycho paid no attention to the node (Histoire des Math., i. p. 666).
↑ For an account of these, see Delambre, Hist. de l'Astr. mod., i. p. 164.

[1] Copernicus had employed a similar construction to explain the trepidatio or (imaginary) oscillation of the equinoxes.

[2] In Godfray's Lunar Theory, chap, viii., Tycho's hypothesis is described as if he supposed the lunar pole to move in the small circle with double the synodical velocity of the node. Though this, of course, is the correct representation of the perturbations in latitude, it is not Tycho's idea, as he took no notice whatever of the position of the node with regard to the sun, but let the pole move with double the synodical velocity of the moon. In the well-known term 9′ sin (☾ − 2☉ + ☊), if we, instead of the quantity within the bracket, write 2(☾ − ☉) − (☾ − ☊), we get Tycho's period, as the inclination will vary by − 9′ cos 2 (☾ − ☉). But if we put (☾ − ☊) − 2 (☉ − ☊), the inclination will vary by + 9′ cos 2 (☉ − ☊), and the period is 173 days. That Kepler had remarked the importance of the position of the sun with regard to the node may be seen from Tab. Rudolph., pp. 89–90; Opera, vi. pp. 588 and 648. Of modern authors, Montucla seems to be the only one who has remarked that Tycho paid no attention to the node (Histoire des Math., i. p. 666).

[3] For an account of these, see Delambre, Hist. de l'Astr. mod., i. p. 164.

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