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It can be shown that uniform magnetization is possible only when the form of the body is ellipsoidal.

00Some importance attaches to the form of the pollen grains; the two principal forms are ellipsoidal with longitudinal bands forming the Convolvulus-type, and a spherical form with a spiny surface known as the Ipomaea-type.

00As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.

00l ' so that over the surface of an ellipsoid where X and ¢ are constant, the normal velocity is the same as that of the ellipsoid itself, moving as a solid with velocity parallel to Ox U = -q, - 2 (a2+X) dtP, and so the boundary condition is satisfied; moreover, any ellipsoidal surface X may be supposed moving as if rigid with the velocity in (I I), without disturbing the liquid motion for the moment.

00The quiescent ellipsoidal surface, over which the motion is entirely tangential, is the one for which (a2+X)d?

00A torsion of the ellipsoidal surface will give rise to a velocity function of the form 4)--- where SZ can be expressed by the elliptic integrals in a similar manner, since dX/P3.

00(9) c 2 Ci If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan S = ird/nd = 2 d p/u, (10) '°If a denotes the density of the metal, and if the shell has a cavity homothetic with the external ellipsoidal shape, a fraction f of the linear scale; then the volume of a round shot being sird 3, and sird 3 x of a shot x calibres long W =*ird 3 x(I -f 3)v, (20) 2 Wki 2= 61rd 3 xo(I-f 5)Q, (21) Wk22=67rd3x 2 2+0 2(I - f5)Q.

002 Consider then an ellipsoidal shell the axes of whose bounding surfaces are (a, b, c) and (a+da), (b+db), (c+dc), where da/a =db b =dc/c =,u.

00The potential of such a shell at any internal point is constant, and the equi-potential surfaces for external space are ellipsoids confocal with the ellipsoidal shell.

00The Cassegrain telescope differs from the Gregorian only in the substitution of a convex hyperboloidal mirror for a concave ellipsoidal mirror as the small speculum.

00Ellipsoidal, pear-shaped or hour-glassshaped stars would all give rise to the phenomena of a short-period variable, and doubtless examples of these intermediate forms exist.

00By its aid, for example, the whole of the properties a elliptical arches, whether square or skew, whether level or sloping in their span, are at once deduced by projection from those of symmetrical circular arches, and the properties of ellipsoidal and ellipticconoidal domes from those of hemispherical and circular-conoidal domes; and the figures of arches fitted to resist the thrust of earth, which is less horizontally than vertically in a certain given ratio, can be deduced by a projection from those of arches fitted to resist the thrust of a liquid, which is of equal intensity, horizontally and vertically.

00The bright orangeyellow fruit is round or ellipsoidal, about i in.

00The residual force just described is not limited to the case of an ellipsoidal body.

00The most common form of grain is ellipsoidal, more or less narrow at the extremities, which are called its poles, in contradistinction to a line equidistant from the extremities, which is its equator.

00moniliform nucleus of ellipsoidal beds is shown.

00Under the microscope, an anther can be seen to have many spherical to ellipsoidal pollen grains on its surface.

00Max Reess distinguished the species according to the appearance of the cells thus, the ellipsoidal cells were designated Saccharomyces ellipsoideus, the sausage-shaped Saccharomyces Pasteurianus, and so on.

00He as well as Artemidorus and others accepted a circular or ellipsoidal shape of the world and a circumfluent ocean; Strabo alone adhered to the scientific theories of Eratosthenes.

00It can be shown that uniform magnetization is possible only when the form of the body is ellipsoidal.

00Some importance attaches to the form of the pollen grains; the two principal forms are ellipsoidal with longitudinal bands forming the Convolvulus-type, and a spherical form with a spiny surface known as the Ipomaea-type.

00As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.

00l ' so that over the surface of an ellipsoid where X and ¢ are constant, the normal velocity is the same as that of the ellipsoid itself, moving as a solid with velocity parallel to Ox U = -q, - 2 (a2+X) dtP, and so the boundary condition is satisfied; moreover, any ellipsoidal surface X may be supposed moving as if rigid with the velocity in (I I), without disturbing the liquid motion for the moment.

00The quiescent ellipsoidal surface, over which the motion is entirely tangential, is the one for which (a2+X)d?

00Clebsch, by taking a velocity function 4,=xyx (I) for a rotation R about Oz; and a similar procedure shows that an ellipsoidal surface A may be in rotation about Oz without disturbing the motion if I I dx + _ a2'-A) x 2 a R t i/(b2+A)- i/(a2+A) and that the continuity of the liquid is secured if (a 2 _ I -A) 3/2 (b 2 4 A)3f2(C2 -+- A) 2 ??

00A torsion of the ellipsoidal surface will give rise to a velocity function of the form 4)--- where SZ can be expressed by the elliptic integrals in a similar manner, since dX/P3.

00(9) c 2 Ci If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan S = ird/nd = 2 d p/u, (10) 'Ã‚°If a denotes the density of the metal, and if the shell has a cavity homothetic with the external ellipsoidal shape, a fraction f of the linear scale; then the volume of a round shot being sird 3, and sird 3 x of a shot x calibres long W =*ird 3 x(I -f 3)v, (20) 2 Wki 2= 61rd 3 xo(I-f 5)Q, (21) Wk22=67rd3x 2 2+0 2(I - f5)Q.

002 Consider then an ellipsoidal shell the axes of whose bounding surfaces are (a, b, c) and (a+da), (b+db), (c+dc), where da/a =db b =dc/c =,u.

00The potential of such a shell at any internal point is constant, and the equi-potential surfaces for external space are ellipsoids confocal with the ellipsoidal shell.

00The Cassegrain telescope differs from the Gregorian only in the substitution of a convex hyperboloidal mirror for a concave ellipsoidal mirror as the small speculum.

00Ellipsoidal, pear-shaped or hour-glassshaped stars would all give rise to the phenomena of a short-period variable, and doubtless examples of these intermediate forms exist.

00By its aid, for example, the whole of the properties a elliptical arches, whether square or skew, whether level or sloping in their span, are at once deduced by projection from those of symmetrical circular arches, and the properties of ellipsoidal and ellipticconoidal domes from those of hemispherical and circular-conoidal domes; and the figures of arches fitted to resist the thrust of earth, which is less horizontally than vertically in a certain given ratio, can be deduced by a projection from those of arches fitted to resist the thrust of a liquid, which is of equal intensity, horizontally and vertically.

00The bright orangeyellow fruit is round or ellipsoidal, about i in.

00The residual force just described is not limited to the case of an ellipsoidal body.

00The most common form of grain is ellipsoidal, more or less narrow at the extremities, which are called its poles, in contradistinction to a line equidistant from the extremities, which is its equator.

00Under the microscope, an anther can be seen to have many spherical to ellipsoidal pollen grains on its surface.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.