The Collaborative International Dictionary of English v.0.48:
Conversely \Con"verse*ly\ (? or ?; 277), adv. In a converse manner; with change of order or relation; reciprocally. --J. S. Mill. [1913 Webster]WordNet (r) 3.0 (2006):
conversely adv 1: with the terms of the relation reversed; "conversely, not all women are mothers"