The Collaborative International Dictionary of English v.0.48:

Contrariwise \Con"tra*ri*wise\ (? or ?), adv.
   1. On the contrary; oppositely; on the other hand.
      [1913 Webster]

            Not rendering evil for evil, or railing for railing;
            but contrariwise, blessing.           --1 Pet. iii.
                                                  9.
      [1913 Webster]

   2. In a contrary order; conversely.
      [1913 Webster]

            Everything that acts upon the fluids must, at the
            same time, act upon the solids, and contrariwise.
                                                  --Arbuthnot.
      [1913 Webster]

WordNet (r) 3.0 (2006):

contrariwise
    adv 1: in a contrary disobedient manner [syn: perversely,
           contrarily, contrariwise]
    2: with the order reversed; "she hates him and vice versa" [syn:
       vice versa, the other way around, contrariwise]
    3: contrary to expectations; "he didn't stay home; on the
       contrary, he went out with his friends" [syn: contrarily,
       to the contrary, contrariwise, on the contrary]