content_image/366074.jpg content_image/366073.jpg content_image/366072.jpg content_image/366071.jpg content_image/366070.jpg content_image/366069.jpg content_image/366068.jpg content_image/366064.jpg content_image/366065.jpg
The pressure equation at the surface of the droplet (to first order) is [2] 

<img src='content_image/366074.jpg'>

where F ( t ) is an arbitrary function of t only and φ is the velocity potential [2] 

<img src='content_image/366073.jpg'>

The pressure difference across the surface resulting from the surface tension is [2] 

<img src='content_image/366072.jpg'>

The magnetogravitational potential U at the surface of the drop is (to first order) 

<img src='content_image/366071.jpg'>

<img src='content_image/366070.jpg'>

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 

where 

<img src='content_image/366069.jpg'>

<img src='content_image/366068.jpg'>

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: 

<img src='content_image/366064.jpg'>

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: 

<img src='content_image/366065.jpg'>

