Circular Couette System has served as a paradigm for studying complex transitions to turbulence,the influence of finite geometry on pattern-selection mechanisms.In this paper stability of a circular Couette system with the intermediate radius ratio is investigated through laboratory experiments and computer simulation.The classical Rayleigh centrifugal instability theory is extended to general viscous,incompressible fluid between concentric independently rotating cylinders.A criterion of stability is formulated to quantitatively determine the stability boundary.The laboratory experiments employ the techniques of the laser light scattering and the flow visualization.The apparatus has a radius ratio of η=0.699 and an aspect ratio of Γ=18.A striking feature in phase diagram of flow states is the novel primary instability:when the outer cylinder is at rest,or counterrotating,instability occurs first for nonzero azimuthal wave number.Instead of time-independent Taylor vortex flow,the resulting flow is spiral vortices which are traveling waves in both the axial and azimuthal directions.Preliminary experimental measurements of transition Reynolds numbers presented here are in agreement with those obtained numerically.Laboratory and numerical experiments have revealed the effects of radius ratio on pattern formation,the sequence of transitions.