The Collaborative International Dictionary of English v.0.48:

Advertence \Ad*vert"ence\, Advertency \Ad*vert"en*cy\, [OF.
   advertence, avertence, LL. advertentia, fr. L. advertens. See
   Advertent.]
   The act of adverting, of the quality of being advertent;
   attention; notice; regard; heedfulness.
   [1913 Webster]

         To this difference it is right that advertence should
         be had in regulating taxation.           --J. S. Mill.
   [1913 Webster]

WordNet (r) 3.0 (2006):

advertence
    n 1: the process of being heedful [syn: advertence,
         advertency]