FIG. 6: Top: Effect on the eigenfrequencies of an a = 7 . 5 mm water droplet of adding a quadrupole harmonic c ′ 2 to the shape of the magnetogravitational potential well ( c ′ 0 = 0 . 36 ms − $^{2}$, all other c ′ j = 0). The thick black lines show the eigenfrequencies (squared) of the m = 0 modes (i.e. the eigenvalues ω 2 of Eqn. 19) corresponding to l = 1 − 5; the eigenvalues of Eqn. 19 were computed using MATLAB. (Note that we have plotted ω $^{2}$− σ 2 T for clarity). The thin lines show the first-order approximation, Eqn. 20, departing from the numerically-computed frequencies at | c ′ 2 | ≳ 1. Long- dash, medium-dash, short-dash, dot-dash and dotted lines show the frequencies of the | m | = 1 − 5 modes, respectively (the treatment of the m = 0 modes is summarized in the Appendix). Bottom: Effect on the eigenfrequencies of an a = 7 . 5 mm water droplet of adding a harmonic c ′ 3 to the shape of the well ( c ′ 0 = 0 . 36 ms − $^{2}$, all other c ′ j = 0). 19 −3 −2 −1 0 1 2 3 −50 0 50 100 150 200 250 300 1 2 3 4 5 c ′$_{2}$ (ms − $^{2}$) ω 2 − σ 2 T (rad 2 s − 2 ) −3 −2 −1 0 1 2 3 −50 0 50 100 150 200 250 300 1 2 3 4 5 c ′$_{3}$ (ms − $^{2}$) ω 2 − σ 2 T (rad 2 s − 2 ) a = 7 . 5 mm, c ′$_{0}$ = 0 . 36ms − 2