In directions, what does E 1/2 S, and similar notations mean?

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• It's seen a lot in accounts of voyages in the eighteenth century. It isn't Southeast, because in that case they simply say Southeast. They used a system which from East to South goes:
  East
  East by South
  East Southeast
  Southeast by East
  Southeast
  Southeast by South
  South Southeast
  South by East
  South
  
  I'm trying to figure out what they mean by things like E 1/2 S, E 3/4 S, and even E .4 S.+

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  by JimmyG on November 12th, 2009

• The only other thing I can guess is that You go 1/2
  a unit E, then 1 unit South. And the direction is
  the vector from the starting point to the place You
  "walked to".
  Or the other way around if the 1/2 is connected to
  the S not the E.

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  by Anonymous T on November 12th, 2009

• I think I've figured it out, but I sure would like to have an authoritative reference. The compass had/has 32 named points. E 1/2 S would be halfway to the next named point in the easterly direction, or halfway between East and East by South. In a Google book with such directions and a map, NNE 1/4 E looks to be a quarter of the way towards NE by N from NNE. (?)
  
  http://en.wikipedia.org/wiki/File:Compass_Card.png

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  by JimmyG on November 12th, 2009

• Maybe it is, though I'm not that interested to
  look for the answer. Have fun.

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  by Anonymous T on November 12th, 2009