so that the effective inertia of a sphere is increased by half the weight of liquid displaced; and in frictionless air or liquid the sphere, of weight W, will describe a parabola with vertical acceleration

W − W′g.
W + ½W′

(30)

Thus a spherical air bubble, in which W/W′ is insensible, will begin to rise in water with acceleration 2g.

45. When the liquid is bounded externally by the fixed ellipsoid λ = λ1, a slight extension will give the velocity function φ of the liquid in the interspace as the ellipsoid λ = 0 is passing with velocity U through the confocal position; φ must now take the form x(ψ + N), and will satisfy the conditions in the shape

φ = Ux A + B1 + C1= Ux
abc+ ∫λ1λ abcdλ
a1b1c1 (a2 + λ) P
,
B0 + C0 − B1 − C1
1 − abc− ∫λ10 abcdλ
a1b1c1 (a2 + λ) P

(1)

and any confocal ellipsoid defined by λ, internal or external to λ = λ1, may be supposed to swim with the liquid for an instant, without distortion or rotation, with velocity along Ox

U Bλ + Cλ − B1 − C1.
B0 + C0 − B1 − C1