I've never been quite clear on measures of distance when I heard the words fathom and league. Here is the difference! Its definately a good thing to know!
WHAT IS A FATHOM?A fathom is a unit of length in Standard English that is used to measure ocean depths. It is approximately 6 vertical feet. To get the total depth in feet from fathoms given, just multiply by 6. For example, 500 fathoms = 500 x 6ft. = 3,000 feet.
HOW FAR IS A LEAGUE?A league is also a unit of length (or distance) that is used to measure ocean depths. It is not used in science, but in literature. One league = 3 miles (or 4.8 km).
http://www.extremescience.com/ocean-zones.htm
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