This paper addresses a question that arises while attempting to conceptualize temporal experience, that is, the experience of continuity and transition. The question is how to handle the tension between the unity of the experienced flow on the one hand and the internal variation that it involves on the other. These two features which naturally integrate within the scope of our experience of temporality are incompatible in the framework of a more systematic analysis. It is this gap between experience and analysis which underlies the dispute between Bertrand Russell, William James and Alfred North Whitehead over a theory of continuity. More specifically, the dispute is over the role that our crude feeling of continuous transition should play within the conceptualization of a more general theory of continuity. While Russell thought that the intuitive appeal to our feeling in the formulation of a theory of continuity must be rejected, James' and Whitehead's accounts of temporal continuity are not only consistent with our feeling but actually arise from it. A comparison of their different perspectives reveals the role such concepts as succession, duration, simultaneity, unity and multiplicity in the formation of a theory of continuity.