An Etymological Dictionary of the German Language/birschen
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birschen, vb., from the equiv. MidHG. birsen, ‘to chase with hounds, to shoot deer’; s after r became sch, as in Arsch, barsch, Dorsche, herrschen, Hirsch, Kirsche, Kürschner, wirsch; from OFr. berser (MidLat. bersare), ‘to pierce with an arrow.’