A surface expressing the optical relations of such crystals is thus an ellipsoid of revolution about the optic axis.
In biaxial crystals there are different coefficients of expansion along three rectangular axes, and a sphere at one temperature will be an ellipsoid at another.
Therefore the surface is an ellipsoid of revolution having A and B as foci.
That this surface should turn out, after precise measurements, to be exactly an ellipsoid of revolution is a priori improbable.
Having now stated the data of the problem, we may seek that oblate ellipsoid (spheroid) which best represents the observations.
For the calculation of an ellipsoid with three unequal axes see Comparison of Standards, preface; and for non-elliptical meridians, Principal Triangulation, p.
Consequently we now generally take the ellipsoid of rotation as a basis, especially so because measurements of gravity have shown that the deviation from it is but trifling.
The theory of the figure of the earth as a rotating ellipsoid has been especially investigated by Laplace in his Mecanique celeste.
For a long time the assumption of an ellipsoid with three unequal axes has been held possible for the figure of the earth, in consequence of an important theorem due to K.
In 1849 Stokes showed that the normal elevations N of the geoid towards the ellipsoid are calculable from the deviations [Delta]g of the acceleration of gravity, i.
Clarke has recalculated the elements of the ellipsoid of the earth; his values, derived in 1880, in which he utilized the measurements of parallel arcs in India, are particularly in practice.
Hayford, executed a calculation of the best ellipsoid of rotation for the United States.
We have first to determine the mode in which electricity distributes itself on a conducting ellipsoid in free space.
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.
C^2 ae In each case we have C = a when e = 0, and theellipsoid thus becomes a sphere.
When the neck was subsequently shaped, these circular markings were drawn out into ellipsoid forms, showing that this part of the vessel was made at a later period.
Oblatum, and see Ellipsoidof revolution, under Ellipsoid.
Since the normals of the ellipsoid of rotation do not in general intersect, there consequently arises an influence of the height on the azimuth.
Three stations, projected on the surface of the sea, give a spherical or spheroidal triangle according to the adoption of the sphere or the ellipsoid as the form of the surface.
The ellipsoid was the shape first worked out, by George Green, in his Research on the Vibration of a Pendulum in a Fluid Medium (1833); the extension to any other surface will form an important step in this subject.
But now while the speed of rotation still increases (The mathematician familiar with Jacobi's ellipsoid will find that this is correct, although in the usual mode of exposition, alluded to above in a footnote, the speed diminishes.
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.
When it is desired to have a uniform magnet with definitely situated poles, it it usual to employ one having the form of an ovoid, or elongated ellipsoid of revolution, instead of a rectangular or cylindrical bar.
An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H0, with its axis of revolution parallel to the lines of force.
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.
Sporangia globose or ovoid to ellipsoid or oblong, erect or sometimes inclined or even nodding.
It has been shown by De Sparre that, owing to the limitation imposed on the possible forms of the momental ellipsoid by the relation B + C > A, the curve has no points of inflexion.
If A = B = C, the momental ellipsoid becomes a sphere; all axes through O are then principal axes, and the moment of inertia is the same for each.
The relation between these axes may be expressed by means of the momental ellipsoid at O.
The method of homogeneous strain can be applied to deduce the corresponding results for an ellipsoid of semi-axes a, b, c.
Proportion of the two axes of the ellipsoid = 5 : 4.
Proportion of the major axis of the ellipsoid to the minor = 4 : 3.
Central capsule { Shell a simple ellipsoid or a ellipsoidal or { cylinder with annular cylindrical.
Both axes of the ellipsoid bear the proportion of 7 : 6.
Proportion of the longer axis of the ellipsoid to the shorter = 5 : 4.
The simple latticed shell is distinguished from that of the three other genera by its typical lentelliptical form, a triaxial ellipsoid with three dimensive axes of unequal length.
Proportion of the longer axis of the ellipsoidto the shorter = 4 : 3.
Proportion of the major axis of the ellipsoid to the minor = 5 : 4.
Round or ellipsoid stones; in the latter the groove may follow either axis.
The basis of geodetic calculations, however, is an ellipsoid of reference for which a gravity formula expresses the value of normal gravity at a point on the ellipsoid as a function of gravity at sea level at the equator, and of latitude.
The plumb line is perpendicular to the geoid, and the components of angle between the perpendiculars to geoid and reference ellipsoid are deflections of the vertical.
The geoid is above the ellipsoid of reference under mountains and it is below the ellipsoid on the oceans, where the geoid coincides with mean sea level.
In 1849, Stokes derived a theorem whereby the distance N of the geoid from the ellipsoid of reference can be obtained from an integration of gravity anomalies over the surface of the earth.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "ellipsoid" in a variety of sentences. We hope that you will now be able to make sentences using this word.
