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By the middle of the 18th century, the 32-point system had been further extended by using half- and quarter-points to give a total of 128 directions.
These fractional points are named by appending, for example 1/4east, 1/2east, or 3/4east to the name of one of the 32 points. Each of the 96 fractional points can be named in two ways, depending on which of the two adjoining whole points is used, for example, N3/4E is equivalent to NbE1/4N. Either form is easily understood but alternative conventions as to correct usage developed in different countries and organisations. “It is the custom in the United States Navy to box from north and south toward east and west, with the exception that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point. ” The Royal Navy used the additional “rule that quarter points were never read from a point beginning and ending with the same letter. ”