(_b_) _Analysis._ Equally important is the part played by mental _analysis_ in the formation of the conceptual space and time system. As we have already seen, successive attention to lesser parts of a presented extension, or a presented lapse, reveals within each lesser part the same structure which belongs to the whole, and thus establishes the _sensible continuity_ of space and time. In actual fact, the process of attending successively to smaller and yet smaller portions of space and time cannot, of course, be carried on indefinitely, but we can conceptually frame to ourselves the thought of the indefinite repetition of the process beyond the limits arbitrarily imposed on it by the span of our own attention. Thus, by an act of mental analysis, we arrive at the concept of space and time as _indefinitely divisible_, or possessed of no ultimately unanalysable last parts, which is an indispensable pre-requisite of Geometry and Dynamics. This indefinite divisibility of conceptual space and time is not of itself enough, as is often supposed, to establish their _continuity_ in the strict mathematical sense of the word; their continuity depends upon the further assumption that whatever divides a series of positions in space or events in time unambiguously into two mutually exclusive classes, is itself a position in the space or event in the time series. This assumption does not seem to be absolutely requisite for all scientific treatment of the problems of space and time,[145] but is demanded for the systematic establishment of the correspondence between the spatial and temporal series and the continuous series of the real numbers. Moreover, it seems impossible to assign any positive content to the notion of a something which should bisect the spatial or temporal order without occupying a position in that order. Hence we seem inevitably led by the same analytical process which conducts us to the conception of the spatial and temporal orders as infinite series to think of them also as continuous series in the strict sense of the term. The alternative conception of them as discontinuous, if not absolutely excluded, does not seem to be called for by any positive motive, and is incompatible with the complete execution of the purposes which demand application of the number-series to a spatial or temporal content.