The pressure equation at the surface of the droplet (to first order) is [2] where F ( t ) is an arbitrary function of t only and φ is the velocity potential [2] The pressure difference across the surface resulting from the surface tension is [2] The magnetogravitational potential U at the surface of the drop is (to first order) where Γ$_{r}$( a, θ ) = − c ′ $_{0}$( a ) for a spherically symmetric well (see Eqn. 4). Inserting Eqns. 9b, 8 and 7 into Eqn. 6, we obtain is the oscillation frequency (squared) of a hypothetical drop with T = 0, held together by the magnetogravitational trap alone. The fact that the square of the measured frequency ω 2 is a simple sum of the square of the Rayleigh frequency σ 2 T and σ 2 0 is due to the fact that l remains a good eigennumber for oscillations in a spherically-symmetric potential well. In Sec. V, we will consider the effect of a non-spherical magnetogravitational well. In a non-spherical well, l is not a good eigennumber in general, but for small deviations from spherical, we can use perturbation theory to obtain corrections to Eqn. 10. We can obtain an experimental measurement of c ′ 0 by examining the difference between the measured frequencies ω of any two of the modes l, n ≥ 2: where h$_{l}$ = l ( l − 1)( l +2). Dividing by ( nh$_{l}$ − lh$_{n}$ ) /a , we obtain an experimental measurement of c ′ $_{0}$( r ) from the oscillations of a drop that has radius a = r at rest: h$_{l}$σ 2 0 ,n − h$_{n}$σ 2 0 ,l = h$_{l}$ω 2 n − h$_{n}$ω 2 l , (12) c ′ $_{0}$( r ) = r h$_{l}$ω 2 n − h$_{n}$ω 2 l nh$_{l}$ lh$_{n}$ . (13) 8 where σ 2 0 = c ′ $_{0}$( a ) l a (11) ω 2 = σ 2 T + σ 2 $_{0}$, (10) = U ( a ) − ϵ Γ$_{r}$( a, θ ) P$_{l}$ (cos θ ) sin( ωt ) , (9b) U ( R ( θ, t )) = U ( a ) − Γ$_{r}$( a, θ )( R − a ) (9a) p ( R ) = T $^{(}$2 a + ζ ( l − 1)( l + 2) a 2 ) . (8) φ ( r, θ ) = − r l la l − $_{1}$ωϵP$_{l}$ (cos θ ) cos ωt. (7) ∂φ ∂t ∣ ∣ r = a = U ( R ) + p ( R ) ρ + F ( t ) , (6)