5 6 7 8 9 10 11 0.2 0.3 0.4 0.5 0.6 0.7 0.8 r  (mm) c 0 ′ (ms − 2 ) 3 4 5 6 7 8 9 l FIG. 3: Left panel: Gradient of the magnetogravitational potential trap c ′ 0 obtained from the measured frequencies of two modes, l = 2 and l > 2, of a drop with radius a = r at rest. Error bars show the standard error. Filled circles: data obtained in nitrogen atmosphere. Open squares: data obtained in air atmosphere. Dotted line: c ′ 0 computed from the solenoid geometry. Right panel: dependence of the experimentally-obtained c ′ 0 on the mode number with l > 2 (see text). By using two measured frequencies, ω$_{l}$ and ω$_{n}$ , rather than a single frequency, we obtain a measurement of c ′ 0 independent of the surface tension. Fig. 3 (left panel) shows the values of c ′ 0 that we obtain from the above ‘two-frequency’ method using the lowest order mode n = 2 and a second mode l > 2. We use the n = 2 mode since the corresponding peak in the power spectrum is always clearly resolved. We plot the mean of the values obtained for each mode l > 2. Error bars (standard error) indicate the variation in the measured c ′ 0 obtained from different modes l . Filled circles and open squares show data obtained from a drop in a nitrogen atmosphere at B$_{0}$ = 16 . 5 T, and in air at B$_{0}$ = 16 . 2 T, respectively. The broken line on Fig. 3 shows the value of c ′ $_{0}$( r ) computed from the potential U shown in Fig. 1 (i.e. from the geometry of the solenoid and the current B$_{0}$ ). This line is in reasonably good agreement with the experimentally measured values of c ′ $_{0}$, although the data points fall at slightly higher values. As an additional check of our method, we plot the dependence of the measured c ′ 0 on l (right hand panel). If the trap-induced frequency enhancement that we measure experimentally is accurately given by Eqn. 11, then the c ′ 0 values that we determine by this method should exhibit no dependence on l . Although there is some scatter in the 9