2 V I - a /al ' Y' I-a /al ' and the effective inertia of the liquid in the interspace Ao+2A1 W, =1 a13 +2a3W'.
The interspace is filled with a very small quantity of nickel and silver filings, about 95 per cent.
The upward thrust is the same, however thin the metal may be in the interspace between the outer mould and the core inside; and this was formerly considered paradoxical.
Over a concentric cylinder, external or internal, of radius r=b, 4,'=4,+ Uly =[U I - + Ui]y, (4) and 4" is zero if U 1 /U = (a 2 - b2)/b 2; (5) so that the cylinder may swim for an instant in the liquid without distortion, with this velocity Ui; and w in (I) will give the liquid motion in the interspace between the fixed cylinder r =a and the concentric cylinder r=b, moving with velocity U1.
B2' and this, by § 36, is also the ratio of the kinetic energy in the annular 4,1 interspace between the two cylinders to the kinetic energy of the liquid moving bodily inside r = b.
Bdo 7rpb 2 (u, b 2 a2 Uibb +¢z), and the difference X-X 1 is the component momentum of the liquid in the interspace; with similar expressions for Y and Y1.
When the liquid is bounded externally by the fixed ellipsoid A = A I, a slight extension will give the velocity function 4 of the liquid in the interspace as the ellipsoid A=o is passing with velocity U through the confocal position; 4 must now take the formx(1'+N), and will satisfy the conditions in the shape CM abcdX ¢ = Ux - Ux a b x 2+X)P Bo+CoB I - C 1 (A 1 abcdX, I a1b1cl - J o (a2+ A)P and any'confocal ellipsoid defined by A, internal or external to A=A 1, may be supposed to swim with the liquid for an instant, without distortion or rotation, with velocity along Ox BA+CA-B 1 -C1 W'.
= constant, _ ff 00 NdA N BA-AA X - JA (a' +X) (b 2 +A)P - abc' a2 -b2 ' and at the surface A = o, I I N Bo-A 0 N I R - (a2+b2) abc a 2 -b 2 abc a2b2 I /b 2 N = R I /b2 - I /a2 abc I 1 I Bo - AO' a 2 b 2 - a2 b2 a 2 b2 = R (a 2 - b 2) /(a 22 + /b2) 2 - r (B o - Ao) U Bo+Co - B I - CI' Since - Ux is the velocity function for the liquid W' filling the ellipsoid A = o, and moving bodily with it, the effective inertia of the liquid in the interspace is Ao+B1+C1 Bo+Co - B1 - C, If the ellipsoid is of revolution, with b=c, - 2 XBo - - C BI' and the Stokes' current function 4, can be written down (I) is (5) (7) (6) The velocity function of the liquid inside the ellipsoid A=o due to the same angular velocity will be = Rxy (a2 - b2)/(a2 + b2), (7) and on the surface outside _ N Bo -Ao c1)0xy abc 2 62' so that the ratio of the exterior and interior value of at the surface is ?o= Bo-Ao (9) 4)1 (a 2 -6 2)/(a2 + b) - (Bo - Ao)' and this is the ratio of the effective angular inertia of the liquid, outside and inside the ellipsoid X = o.
Hence the electric force E in the interspace 1dRccor the potential V at any point in the interspace is given by varies inversely E = as - the distance distance =A/R from or V the - axis.
R - A, Accordingly var where R is the distance of the point in the interspace from the axis, and A is a constant.
In this calculation we neglect altogether the fact that electric force distributed on curved lines exists outside the interspace between the plates, and these lines in fact extend from the back of one "Edge plate to that of the other.
Constant magnetic field, and in the interspace between the poles is fixed a delicately pivoted coil of wire carried in jewelled bearings.
This distinction is, however, not so important as it appears at first sight, for their connexion with the bone is only of a secondary nature, and, although it happens conveniently that in the great majority of cases the division between the bones coincides with the interspace between the third and fourth tooth of the series, still, when it does not, as in the mole, too much weight must not be given to this fact, if it contravenes other reasons for determining the homologies of the teeth.
- Free medusae with rhopalia of the normal type; the exumbrella is divided by a circular, so-called coronal groove, into two parts, a central portion, which is conical, thimble-shaped, or domed in form, and a peripheral portion, the pedal zone, which bears the marginal lobes, tentacles and rhopalia; the pedal zone is subdivided into areas termed pedalia, from each of which arises a tentacle or rhopaliurn in the interspace between two adjacent lobes of the margin.
The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.