The Collaborative International Dictionary of English v.0.48:

Consecution \Con`se*cu"tion\, n. [L. consecutio. See
   Consequent.]
   1. A following, or sequel; actual or logical dependence.
      --Sir M. Hale.
      [1913 Webster]

   2. A succession or series of any kind. [Obs.] --Sir I.
      Newton.
      [1913 Webster]

   Month of consecution (Astron.), a month as reckoned from
      one conjunction of the moon with the sun to another.
      [1913 Webster]