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 ??

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