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"to run rapidly," 1845, frequentative of skite "to dart, run quickly" (1721), perhaps from a Scandinavian source (cf. Old Norse skjota "to shoot, launch, move quickly, avoid (a blow)," or Norwegian dialectal skutla "glide rapidly"); see skittish. As a noun from 1905.
To move about rapidly; scamper: where the poor skitter around the doll's house on the hill like so many rats among garbage (1845+)