This paper studies the free modes of oscillation in a rotating hemispherical basin bounded by a great-circle passing through the pole of rotation. The radius R of the globe, the rate of rotation $\Omega $, the depth of fluid h and the acceleration of gravity g are assumed to be such that h $\ll $ R and R$\Omega $/$\surd $(gh) $\ll $ 1. The waves can then be treated as non-divergent. The problem is solved by two independent methods, and the results are compared with each other and with the $\beta $-plane approximation. It is found that the eight lowest modes of oscillation correspond quite well to simple modes in the $\beta $-plane, the approximate periods being within 20%. Higher modes show no clear correspondence. It is suggested that the peak at 0$\cdot $5 c/d in the spectrum of sea level at Honolulu may correspond to the lowest mode of oscillation in the Pacific Ocean.