FIG. 4: Values of the j = 0 (spherically-symmetric) and j = 2 , 3 (quadrupole and octopole) coeffi- cients c ′ j in a multipole expansion of the potential well gradient, Eqn. 4, at B$_{0}$ = 16 . 5 T (in nitrogen atmosphere). Note, c ′ 1 = 0 (see text). The values were determined from the magnetogravitational potential (Eqn. 2) shown in Fig. 1. The c ′ 0 line is the same as that shown by the dotted line on Fig. 3. data due to experimental error, there is no clear dependence on l . In the previous section, we assumed that the potential well was spherically symmetric around L$_{0}$ . However, whilst we have chosen the field B$_{0}$ to minimize the quadrupole com- ponent of the trap, the octopole component remains significant, as can be seen clearly in Fig. 1. Thus it initially appears surprising that we can treat the well as if it were spherical, in order to calculate its effect on the vibrations of the droplet’s shape. (Had we determined an unphysical dependence of our measured c ′ 0 on l in the previous section, it would also have followed that the spherical-well approximation was inadequate.) We now consider the effect on the eigenfrequencies of the drop of additional harmonic components c ′ j of the potential trap, and consider why, if the trap has a significant octopole component, the spherical well approximation is so effective at reproducing the measured frequencies of the droplet. We first discuss how close to spherical it is possible to make the potential trap; that is, how small the coefficients c ′ $_{j}$, j > 0 can be made. Lorin and Mailfert have considered the relationship between the coil geometry (the distribution of the current density) and the shape of the potential trap [14]. Although we cannot alter the coil geometry, we can alter the coefficients c ′ j by adjusting the current flowing in the solenoid. The magnitude of the 10 V. NON-SPHERICAL POTENTIAL 0 2 4 6 8 10 12 −0.1 0 0.1 0.2 0.3 0.4 0.5 c ′$_{0}$ c ′$_{3}$ c ′$_{2}$ r (mm) c ′ j (ms − 2 )