Alligation, from a Latin word signifying 'to bind together,' is a rule in arithmetic which teaches how to solve such questions as the following: 3 lb. of sugar at 6d. are mixed with 5 lb. at 10d.; what is the price of a pound of the mixture? or: In what proportion must sugar at 6d. be mixed with sugar at 10d., to produce a mixture at 8½d.? The solution of the first is d.
In the second, the proportional number for one ingredient is the difference between the price of the other and that of the mixture; the number for the cheap sugar is therefore 1½, and for the dear, 2½, which are as 3:5, so that there must be 3 lb. at 6d. for every 5 lb. at 10d. If there are more than two ingredients, the problem becomes indeterminate—that is, it admits of a variety of answers. Thus: Of three metals, whose specific gravities are 10, 15, and 16, it is required to compose an alloy, whose specific gravity shall be 14. The conditions will be answered by mixing them in any of the following proportions: 1, 2, 1; 2, 2, 3; 6, 2, 11, &c.