The Blue Moon
If we understand the Blue Moon is used to identify the occasional extra full moon that occurs in the seasonal cycle and is part of the “Named Moons” system, the apparent obscure Maine Rule makes sense. However due to some error in interpretation in 1946 a new definition of the Blue Moon became popularized and that is the Sky & Telescope Rule.
The Maine Rule
By the Maine Rule, the Blue Moon is the third Full Moon in a season with four Full Moons. The Maine Rule defines the season by the motion of a Fictitious Mean Sun starting with Spring on the Ecclesiastical Vernal Equinox (March 21). From that, Summer starts on June 22, Autumn starts September 23 and Winter starts December 22 (Yule).
The Astronomical Season Rule
The Astronomical Season Rule is a contemporary version of the Maine Rule. It is the same as the Maine Rule, except it uses the actual Equinoxes and Solstices to mark the beginning of the seasons.
The Sky & Telescope Rule
The Sky & Telescope Rule defines a Blue Moon as the second Full Moon in a calendar month. It was deduced in a 1946 Sky and Telescope article which incorrectly interpreted an earlier 1943 Sky and Telescope article that was referencing the Maine Farmers’ Almanac. The error was not caught for 55 years and by that time the Sky & Telescope Rule became popular. The original Maine Rule at that time had to be deduced from old editions of the Almanac.
For more information on the history of the Sky & Telescope Rule please refer to http://skyandtelescope.com/observing/objects/moon/article_127_1.asp