Left: period P_z (9) of vertical oscillations of a prominence vs. the currents ratio I/i for different values of the dimensionless parameter a = 2ρgh/k₂. We note that the case a = 1 corresponds to the KR limit (Kuperus & Raadu 1974) when the effect of the photospheric currents is negligibly small. Right: period P_x (13) of horizontal oscillations depending upon the same parameters I/i and a as shown in the left panel. Dashed lines in both panels show a threshold values of I/i where periods (9) and (13) become imaginary, and corresponding instabilities develop.