The Collaborative International Dictionary of English v.0.48:

Alligation \Al`li*ga"tion\, n. [L. alligatio.]
   1. The act of tying together or attaching by some bond, or
      the state of being attached. [R.]
      [1913 Webster]

   2. (Arith.) A rule relating to the solution of questions
      concerning the compounding or mixing of different
      ingredients, or ingredients of different qualities or
      values.
      [1913 Webster]

   Note: The rule is named from the method of connecting
         together the terms by certain ligature-like signs.
         Alligation is of two kinds, medial and alternate;
         medial teaching the method of finding the price or
         quality of a mixture of several simple ingredients
         whose prices and qualities are known; alternate,
         teaching the amount of each of several simple
         ingredients whose prices or qualities are known, which
         will be required to make a mixture of given price or
         quality.
         [1913 Webster]