# Confocal sentence example

Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any

**confocal**ellipsoids.The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the

**confocal**ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area.In a similar way the more general state of motion may be analysed, given by w =r ch2('-y), y =a+, i, (26) as giving a homogeneous strain velocity to the

**confocal**system; to which may be added a circulation, represented by an additional term in w.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'.The extension to the case where the liquid is bounded externally by a fixed ellipsoid X= X is made in a similar manner, by putting 4 = x y (x+ 11), (io) and the ratio of the effective angular inertia in (9) is changed to 2 (B0-A0) (B 1A1) +.a12 - a 2 +b 2 a b1c1 a -b -b12 abc (Bo-Ao)+(B1-A1) a 2 + b 2 a1 2 + b1 2 alblcl Make c= CO for

**confocal**elliptic cylinders; and then _, 2 A? ?AdvertisementThe 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.Legendre shows that Maclaurin's theorem with respect to

**confocal**ellipsoids is true for any position of the external point when the ellipsoids are solids of revolution.The third memoir relates to Laplace's theorem respecting

**confocal**ellipsoids.Now consider the tangent plane w at any point P of a

**confocal**, the tangent plane fii at an adjacent point N, and a plane of through P parallel to of.**Confocal**conics are conics having the same foci.AdvertisementIf one of the foci be at infinity, the conics are

**confocal**parabolas, which may also be regarded as parabolas having a common focus and axis.An important property of

**confocal**systems is that only two confocals can be drawn through a specified point, one being an ellipse, the other a hyperbola, and they intersect orthogonally.To complement genetic approaches we are establishing a

**confocal**based screen for small molecules that interfere with peroxisome biogenesis.The cells aggregate volume texture is acquired using laser

**confocal**microscopy.Keyphrases wave front sensing,

**confocal**microscopy, multiphoton microscopy.Advertisement