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for the distortion, which introduces additional significant experimental uncertainty [18–21]. Drops can be bounced on a solid surface or a vibrating liquid bath, the drop and surface being separated by a thin layer of air [22, 23]. In this case, the eigenfrequency spectrum deviates from the Rayleigh spectrum due to the periodic forcing by the oscillating surface [24, 25]. An expression, similar to Rayleigh’s, for the eigenfrequencies of vibrating drops in continuous point-contact with a surface, has been determined [25] but there remains some uncertainty over the spectrum of bouncing drops [25]. Although free-fall can be used to obtain the Rayleigh frequencies directly (for example, in a drop-tower [26]), we have shown how diamagnetic levitation could offer an alternative, accurate method of measuring these frequencies; the levitated droplets are near-spherical at rest and the eigenfrequency spectrum is very close to Rayleigh’s, as shown in Fig. 2. The relatively small shift to higher frequency due to the potential trap can be obtained using a simple spherical-well approximation, Eqn. 11. Diamagnetic levitation can levitate cm-size drops (up to ≈ 3 cm- diameter in our magnet) [3, 4, 27] enabling the droplet volume to be measured easily and precisely. Currently, there is interest in the temperature dependence of the surface tension of supercooled water [28]. The lowest-temperature achieved so far, which used a contact technique, is 245 K [29]; nucleation sites on the container walls trigger freezing before colder temperatures can be reached. We propose that diamagnetic levitation and the oscillating drop technique could be used to obtain measurements of surface tension at temperatures less than 245 K. 

It is interesting to consider an analogue between the oscillations of the levitating droplet and that of an object in a gravitational field. We can consider the magnetogravitational force on a unit mass of water, Γ = −∇ U , as being an effective gravitational field acting on the liquid. Reid has obtained an expression for the eigenfrequencies of a gravitating body composed of a solid spherical core, radius R$_{1}$ and density ρ$_{1}$ covered by an inviscid liquid ‘mantle’ of radius R$_{2}$ , density ρ$_{2}$ [30] (see also Ref. [31]): 

<img src='content_image/334673.jpg'>

where η = R$_{1}$/R$_{2}$ , ¯ ρ = η $^{3}$ρ$_{1}$ + (1 − η $^{3}$) ρ$_{2}$ is the mean density and G is the gravitational constant. Interestingly, Reid’s expression becomes equivalent to Eqn. 11 if we let ρ$_{2}$ → 0 and R$_{1}$ → 0, since this allows the surface effective gravity Γ( a ) to be equated with a fictitious point mass m = (4 / 3) πa $^{3}$¯ ρ = Γ( a ) a $^{2}$/G ∼ 1 × 10 8 kg (approximately the mass of 1 mm 3 of 

