The Maine Rule vs. The Astronomical Seasons Rule vs. The Sky & Telescope Rule
The Maine Rule
The Maine Rule comes from the Maine Farmers’ Almanac that names each full moon as per its position in a season. The seasons however are derived assuming a circular orbit of the Earth at constant speed so that the seasons or evenly spaced apart and starts spring at the Ecclesiastical Vernal Equinox (March 21). From that, Summer starts on June 22, Autumn starts September 23 and Winter starts December 22 (Yule).
On the rare occurrence that there are four full moons in a season then the third full moon is designated as the Blue Moon.
The Astronomical Seasons Rule
A more contemporary version of the Maine Rule is the Astronomical Season Rule that is the same as the Maine Rule, except the seasons start on the actual Equinoxes and Solstices.
The Blue Moon by the Sky & Telescope Rule
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 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 early 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