## VI. DISCUSSION AND CONCLUSION 

Although the forces at the droplet’s surface are dominated by the surface tension, we can clearly observe the influence of the magnetogravitational potential trap on the eigenfre- quencies. We have demonstrated that the effect of the trap on the eigenfrequencies closely approximates that of a spherically-symmetric potential well. Although the potential well has a significant octopole component in additional to the spherically-symmetric component, we have calculated that the effect of the octopole component on the eigenfrequencies is small and verified this experimentally. The small difference between the values of c ′ 0 calculated from the solenoid geometry and the measurement of c ′ 0 from the measured droplet oscil- lations, may be due to a small error in the calculated value: the calculation of the field profile B ( x, z ), performed by numerical integration of the Biot-Savart equation, is based on a thin-shell approximation of the current density in the solenoid coils. We note that the discrepancy cannot be explained by the octopole component of the trap, since this only marginally reduces the eigenfrequencies (Fig. 6), which would only reduce the measured value of c ′ 0 slightly. Experiments have shown that nonlinear effects become significant for oscillation amplitudes greater than approximately 0 . 1 a [16]. In our experiments, however, the oscillation amplitude is smaller than this, and we do not observe these non-linear effects. 

We have shown how to minimize the quadrupole harmonic of the potential trap, by adjusting the solenoid current. This allowed us to use the relatively simple formula Eqn. 11 to calculate the effect of the trap on the eigenfrequencies. This opens up the possibility of using diamagnetic levitation to accurately determine the surface tension of diamagnetic liquids (for example, water, and many water-based and organic solutions): subtracting the contribution of the trap to the eigenfrequencies reveals the Rayleigh-frequency spectrum, from which the surface tension can be obtained directly. A contactless measurement technique has many advantages, for example, the ability to measure highly reactive liquids and to achieve significant supercooling of the liquid, as demonstrated in experiments on electromagnetically levitated liquid metals [17]. Acoustic levitation and the oscillating drop method can be used to measure surface properties of small drops (radius < 2 mm) of water and organic liquids (e.g. [18, 19]). Suspension of small drops in air-flow is also possible [20]. However, since the equilibrium droplet shape is distorted significantly from spherical in both of these techniques, it is necessary to make accurate measurements of the equilibrium shape in order to correct 

