Section IV. ALLIGATION
Alligation is a method used to solve problems that involve mixing two products of
different strengths to form a product having a desired intermediate strength. Alligation
is used to calculate:
a. The amount of diluent that must be added to a given amount of higher
strength preparation to make a desired lower strength.
b. The amounts of active ingredient which must be added to a given amount of
lower strength preparation to make a higher strength.
c. The amount of higher and lower strength preparations that must be combined
to make a desired amount of an intermediate strength.
(1) It is often more practical to dilute a known strength preparation than it
would be to compound an entire preparation. Compounding may involve weighing,
measuring, heating, levitating, and extensive mixing of all the ingredients to achieve the
finished product. Sometimes, a simple calculation using alligation allows us to calculate
the amount of diluent to be added to an already prepared higher strength preparation to
form the strength desired. The job would then be simplified by the combining of the two
(2) Sometimes, it is necessary to increase the strength of a preparation by
adding an active ingredient. If a doctor is treating a patient with 1-percent coal tar
ointment and he decides to increase the strength to 2 percent, it can be accomplished
by adding an unknown amount of coal tar (100 percent). Because this problem involves
the mixing of a higher and a lower strength to form an intermediate strength, the
unknown amount may be found by using alligation.