What is "alligation"

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.]

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.

   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.

n. 1 (context obsolete English) The act of tying together or attaching by some bond. 2 (context obsolete English) The state of being attached. 3 (context obsolete English) An old and practical method of solving arithmetic problems related to mixtures of ingredients. 4 (misspelling of allegation English)

Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity. Alligation medial is merely a matter of finding a weighted mean. Alligation alternate is more complicated and involves organizing the ingredients into high and low pairs which are then traded off.