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Using gas targets, $K$ x-ray cross sections have been measured as a function of projectile charge state in nearly symmetric collisions for highly ionized S and Cl ions at a velocity comparable to that of the $K$-shell electrons. For bare nuclei, the projectile cross sections are accurately described by the cross section for capture to excited states calculated in a Brinkman-Kramers approximation and normalized by a single scaling factor. With lower-charge-state incident ions, the total $K$-vacancy cross section is in good agreement with the $2p\ensuremath{\pi}\ensuremath{-}2p\ensuremath{\sigma}$ cross section for rotational coupling.