One way to look at the use of s is to think of the path of the particle as sitting in space, like the trail left by a skywriter, independent of time. Any position on this path is described by stating its distance s from some starting point on the path. Then an incremental displacement along the path ds is described by: d r ( s ) = [ d x ( s ) , d y ( s ) ] = [ x ′ ( s ) , y ′ ( s ) ] d s , where primes are introduced to denote derivatives with respect to s. The magnitude of this displacement is ds, showing that: