  This paper is about the metaphysical debate whether objects persist over time
by the selfsame object existing at different times (nowadays called `endurance'
by metaphysicians), or by different temporal parts, or stages, existing at
different times (called ` perdurance'). I aim to illuminate the debate by using
some elementary kinematics and real analysis: resources which metaphysicians
have, surprisingly, not availed themselves of. There are two main results,
which are of interest to both endurantists and perdurantists.
  (1): I describe a precise formal equivalence between the way that the two
metaphysical positions represent the motion of the objects of classical
mechanics (both point-particles and continua).
  (2): I make precise, and prove a result about, the idea that the persistence
of objects moving in a void is to be analysed in terms of tracking the
continuous curves in spacetime that connect points occupied by matter. The
result is entirely elementary: it is a corollary of the Heine-Borel theorem.
