The Collaborative International Dictionary of English v.0.48:

Sedulity \Se*du"li*ty\, n. [L. sedulitas. See Sedulous.]
   The quality or state of being sedulous; diligent and
   assiduous application; constant attention; unremitting
   industry; sedulousness.
   [1913 Webster]

         The industrious bee, by his sedulity in summer, lives
         in honey all the winter.                 --Feltham.
   [1913 Webster]

WordNet (r) 3.0 (2006):

sedulity
    n 1: the quality of being constantly diligent and attentive
         [syn: sedulity, sedulousness]