The Collaborative International Dictionary of English v.0.48:

Consequentially \Con`se*quen"tial*ly\, adv.
   1. With just deduction of consequence; with right connection
      of ideas; logically.
      [1913 Webster]

            The faculty of writing consequentially. --Addison.
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   2. By remote consequence; not immediately; eventually; as, to
      do a thing consequentially. --South.
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   3. In a regular series; in the order of cause and effect;
      with logical concatenation; consecutively; continuously.
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   4. With assumed importance; pompously.
      [1913 Webster]

WordNet (r) 3.0 (2006):

consequentially
    adv 1: having consequence [ant: inconsequentially,
           inconsequently]