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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 American Journal of Science and Arts

1860 - 982 pages
...these three bodies approached very near to the relation which renders the mean motion of the first, minus three times that of the second, plus twice that of the third, equal to nothing. Then their mutual attraction, rendered this ratio rigorously exact, and it has moreover...
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Papers and Proceedings of the Royal Society of Tasmania

Royal Society of Tasmania - 1864 - 494 pages
...the time of that of the second ; the second half that of the third ; the mean longitude of the first, minus three times that of the second, plus twice that of the third, is always equal to 180°. Or the angular velocity of the first, added to twice that of the third, is equal to three times...
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Descriptive Astronomy

George Frederick Chambers - 1867 - 888 pages
...third, is constantly equal to three times that of the second; and the sidereal longitude of the first, minus three times that of the second, plus twice that of the third, is always eqrtal to 1 80°. From this it follows that for a very long period of time the 3 interior satellites...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Volume 3

William Thomas Brande, George William Cox - 1867 - 1088 pages
...mean motion of the second. Another tqnally singular analogy is, that the mean longitude of the first, minus three times that of the second, plus twice that of the third, is always rery nearly equal to two right angles. These two results subsist equally in respect both of the sidereal...
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On the Connection of the Physical Sciences

Mary Somerville - 1871 - 490 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...right angles. It is proved by theory, that if these Telations had only been approximate when the satellites were first launched into space, their mutual...
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The Analyst, Volumes 1-2

1874 - 490 pages
...first three satellites of Jupiter, and which consists in this, that the mean 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 chance is very small that such a condition should happen at random. Under this hypothesis the comets...
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The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 1-2

1874 - 430 pages
...first three satellites of Jupiter, and which consists in this, that the mean 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 chance is very small that such a condition should happen at random. Under this hypothesis the comets...
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Astronomical Register: A Medium of Communication for Amateur ..., Volume 22

1884 - 332 pages
...and likewise that the mean * See also Mrs. Somervillc's Mechanism of the Heavens, pp. 501 — 608. longitude of the first satellite minus three times...that of the second, plus twice that of the third, is exactly and constantly equal to two right angles. Laplace showed that it suffices to assume these proportions...
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Essays in Astronomy

1900 - 600 pages
...established this relation rigorously, and furthermore has made the mean longitude of the first satellite less three times that of the second plus twice that of the third equal to a semi-circumference. At the same time a periodic inequality has arisen which depended upon...
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The Library of Original Sources: Advance in knowledge, 1650-1800

Oliver Joseph Thatcher - 1907 - 484 pages
...these three bodies approached very near to the relation which renders the mean motion of the first, minus three times that of the second, plus twice that of the third, equal to nothing. Then their mutual attraction rendered this ratio rigorously exact, and it has moreover...
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