NavList:

Lars Bergman, of "boxing the compass", you wrote:
"I think it is quite easy, once you understand the system. But it is seldom described in text books in any great detail."

It is indeed easy ...with two caveats. First, it's easy if you find someone who can explain it plainly. As you say, the textbooks seldom do so in any comprehensible way. It's maybe the sort of thing that a sailor was expected to learn aboard, at sea, and not from a book. So you rarely find it in books. Also, there is a spectrum of "boxing" that can be taken to extremes and made more difficult. The problem here is that the extreme end of the spectrum could be seen as compass directions in the sense of "helmsman, follow these directions" (directions as 'orders') rather than directions as in "steer N-by-E" (where north-by-east is a direction on the plane).

Wrangel, in the document you translated, speaks of ENE¼E as a direction used in Swedish navigation culture and compares it with E-by-N¾N in English navigation culture. But these are identical directions on the plane. The difference in naming arises simply because they are not really necessary as often, and they are more like sailing 'orders' --directions in that sense of the word.

Boxing the compass if we ignore the little quarter points is indeed easy. I've discussed this in earlier years, and I like to sell it by pointing out that the "by" in the finer compass points can be read as "and a bit" where "a bit" here is that small-ish 11.25° angle (an eighth of a 90° angle) that we call a "point". So the direction NbE or N-by-E could be read as "north" (meaning "primarily north") and "a bit" towards the east (meaning a point towards the east from the primary direction. With these by directions, we fill in the spots between the more well-known compass directions.

The primary compass points, of course, are N, E, S, W. Every can fill in up to the three-letter secondary directions (and we can limit ourselves to the single quadrant from N to E with the others completely analogous):
N, NNE, NE, ENE, E.
We can now fill in points between these as listed. Here we have some ambiguity. We could start at N and then just run through the list adding "and a bit east" to each of them, as follows:
N, NbE, NNE, NNEbE, NE, NEbE, ENE, ENEbE, E.
Notice how each "by" direction is created by taken the preceding "simple" compass direction and rotating "a bit" (a point) towards east, and the name is the simple name plus "bE" or "by east". That works, and formally there's nothing wrong with it, but it gives us some rather long names. We could equally well start at E and fill in the missing "by" points by adding "and a bit north" to each. That would give (reversing the order and starting the list at N to match above):
N, NNEbN, NNE, NEbN, NE, ENEbN, ENE, EbN, E.
This also works, but now we can see that we have some redundancy --two different names for the same direction. NbE is identical to NNEbN. They both refer to a direction that is halfway (11.25°) between north and north-northeast. This redundancy is eliminated by sticking to the shorter option. The shorter option always begins with one of the single or two-letter compass directions. The final standardized list in the northeast quadrant is then:
N, NbE, NNE, NEbN, NE, NEbE, ENE, EbN, E.
A more general way to think about it: start at any of the "45°" directions, either a single-letter primary compass direction, or a double-letter direction in between. Then to pick up the "by" directions, rotate left or right to the primary compass point. The by directions will always have the form AbP or ABbP --the part before the b or by is always one or two letters and the direction after the b or by is always a primary direction. So, picking another quadrant, if I'm starting at SW and I want the compass point to the right from there, it has to be SWbW. Continuing in order to the right, the next is WSW. Then the next after that is a point to the left of due W. So that one is labeled WbS.

This standard set of directions, with redundancies removed, is (or was) an international standard. There was nothing really "wrong" with a compass direction like NNE-by-N (this naming implies that we start at NNE and rotate 11.25° to the left towards N), but it's non-standard. We stick with the shorter version which is NbE (this naming implies that we start at N and rotate 11.25° to the right towards E).

We can fill in still finer divisions of the compass by adding a quarter point, or a half point, or three-quarters of a point. But this was a more arbitrary system, and it seems to have varied culturally. For example, suppose I want to steer a quarter of the way between NbE and NNE. I can give that direction as NbE and a quarter point E (which as a shorthand is written NbE¼E), or I can give it as NNE and three-quarters of a point towards N (which as a shorthand would be NNE¾N). These directions have that same redundant naming problem, but it was not a problem. We can pick as we please. They both work.

Frank Reed