Ellipsoid-of-revolution sentence example

ellipsoid-of-revolution
  • In this he showed that a homogeneous fluid mass revolving uniformly round an axis under the action of gravity ought to assume the form of an ellipsoid of revolution.
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  • The cases of greatest practical importance are those of a sphere (which is an ellipsoid with three equal axes) and an ovoid or prolate ellipsoid of revolution.
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  • An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H o, with its axis of revolution parallel to the lines of force.
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  • Laplace treated the subject from the point of view of the gradual aggregation and cooling of a mass of matter, and demonstrated that the form which such a mass would ultimately assume must be an ellipsoid of revolution whose equator was determined by the primitive plane of maximum areas.
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  • Accordingly the distribution of electricity is such that equal parallel slices of the ellipsoid of revolution taken normal to the axis of revolution carry equal charges on their curved surface.
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  • The capacity C of the ellipsoid of revolution is therefore given by the expression I I dx (7) C 2a ?
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  • (x2+3,2) If the ellipsoid is one of revolution round the major axis a (prolate) and of eccentricity e, then the above formula reduces to I I l og e (I +e) C - tae Whereas if it is an ellipsoid of revolution round the minor axis b (oblate), we have I sin - tae C2 - ae (9).
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