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" ... that the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, is always equal to two right angles. "
Mechanism of the Heavens - Page xviii
by Mary Somerville - 1831 - 621 pages
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The Works of John Playfair ...: With a Memoir of the Author ...

John Playfair - 1822 - 554 pages
...from the theory of the action of the satellites. Another singularity in this secondary system, is, that the mean longitude of the first satellite minus...that of the second, plus twice that of the third, never differs from two right angles, but by a quantity almost insensible. One can hardly suppose that...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - 666 pages
...three times the mean motion of the second. And the mean sidereal or synodical longitude of the first, minus three times that of the second, plus twice that...of the third, is always equal to two right angles. The satellites of Jupiter are liable to be eclipsed by passing through his shadow; and on the other...
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An Elementary Treatise on Astronomy: Adapted to the Present Improved State ...

John Farrar - 1827 - 464 pages
...the absolute mean longitudes are themselves subjected to another law not less remarkable ; namely, that the mean longitude of the first satellite, minus...second, plus twice that of the third, is always equal to 180°. This relation extends equally to the menu synodic and sidereal longitudes. It is demonstrated...
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On the Connexion of the Physical Sciences

Mary Somerville - 1834 - 666 pages
...the values of their masses with considerable accuracy, — a striking proof of the power of analysis. A singular law obtains among the mean motions and...attractions would have established and maintained them, notwithstanding the secular inequalities to which they are liable. They extend to the synodic motions...
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The Connection of the Physical Sciences

Mary Somerville - 1834 - 390 pages
...the values of their masses with considerable accuracy, — a striking proof of the power of analysis. A singular law obtains among the mean motions and...proved by theory, that if these relations had only been appwximate when the satellites were first launched into space, their mutual attractions would have...
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A Popular Grammar of the Elements of Astronomy: Adapted to the Use of ...

Thomas Squire - 1836 - 332 pages
...constantly equal to three times the mean revolution of the second. And, the mean longitude of the Hrst, minus three times that of the second, plus twice that...of the third, is always equal to two right angles. Hence, the first three satellites caunot be eclipsed at the same time : for in the simultaneous eclipses...
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On the Connexion of the Physical Sciences

Mary Somerville - 1840 - 858 pages
...power of analysis. A singular law obtains among the mean motions and mean longitudes of the first three satellites. It appears from observation that the mean...attractions would have established and maintained them, notwithstanding the secular inequalities to which they are liable. They extend to the synodic motions-...
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Recreations in mathematics and natural philosophy, recomposed by m. Montucla ...

Jacques Ozanam - 1840 - 850 pages
...motioti of the third, ia rigorously equal to thrice the mean motion of the second satellite. Stcond. The mean longitude of the first satellite minus three...that of the second, plus twice that of the third, is exactly eijual to a semi-circle or 180 degrees. By following out these laws, we find, 1st. When the...
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On the Connection of the Physical Sciences

Mary Somerville - 1846 - 506 pages
...power of analysis. A singular law obtains among the mean motions and mean longitudes of the first three satellites. It appears from observation that the mean...attractions would have established and maintained them, notwithstanding the secular inequalities to which they are liable. They extend to the synodic motions...
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On the Connection of the Physical Sciences

Mary Somerville - 1846 - 496 pages
...satellite, plus twice that of the third, is equal to three SECT. IV. ECLIPSES OF THE SATELLITES. 29 times that of the second ; and that the mean longitude...attractions would have established and maintained them, notwithstanding the secular inequalities to which they are liable. They extend to the synodic motions...
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