Problems of Rotary Motion Presented By the Gyroscope the Precession of the Equi

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Problems of Rotary Motion Presented By the Gyroscope the Precession of the Equi
J G John Gross Barnard
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Thomson docs not mathematically demonstrate this theorem, but by use of an hypothesis gives an elegant illustration of its truth, for which, though to me it is convincing, I prefer to substitute the following demonstration.
Such a spheroid, all the particles of which revolve about an axis with a common angular velocity n, and attract each other by the law of universal gravitation, would have the form of an ellipsoid of revolution, the ellipticity of its meridional c 2 section being - ' . * (See
... " Figure of the Earth, " Encyc. Metrop. , par. 33, by Prof.
Airy. ) Attracted by the sun, its tides would be expressed by the terms of [2316] Mec. Cel. , Book IV (Bowditch). Of these three terms, the first (a function of the declination wily of the attracting body) and the third (the semi-diurnal oscilla- tion) express tidal elevations symmetrically distributed on each side of the equator, which would, hence, exert no influence through the centrifugal forces of their masses, upon precession. The second therefore, or the diurnal tide, is alone to be considered.


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