## Ellipsoidal Sentence Examples

- Some 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. - As 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. - L ' 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. - The quiescent
**ellipsoidal**surface, over which the motion is entirely tangential, is the one for which (a2+X)d? - Clebsch, 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 ?? - A 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. - (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. - 2 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. - The Cassegrain telescope differs from the Gregorian only in the substitution of a convex hyperboloidal mirror for a concave
**ellipsoidal**mirror as the small speculum. **Ellipsoidal**, 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.- By 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. - The bright orangeyellow fruit is round or
**ellipsoidal**, about i in. - The residual force just described is not limited to the case of an
**ellipsoidal**body.