The expression “to box the compass” means to make a complete turn; also, to adopt successively all possible opinions on a question.
Of course, any mariner would say that is all stuff and nonsense, and in his way of thinking he would be right.
With him the phrase has just one meaning; to recite in order the thirty-two points of the compass, starting from north around through east, south, west, and back to north.
But, of course, in doing so one describes a complete turn.
The figurative sense has been with us since at least the beginning of the nineteenth century.
