Why do some Lodges meet on a certain day of the week "following the full moon"? Are Masons some kind of moon worshipers?

The reason is actually simple practicality. Masonic Lodges meet at night, since their membership typically works during the day. Before street lights were available in the 19th century, men walked to Lodge in the dark of night and it was common to schedule Lodge meetings shortly after a full moon to provide maximum illumination for Brothers' walk to and from Lodge.

Obviously, this is no longer an issue, though some Lodges whose history stretches back into the 19th century or earlier still schedule their meetings by the moon's period. These are sometimes referred to as "moon Lodges". More.

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