Box The Compass Meaning

(idiomatic) To make a complete reversal in stance or opinion.

Example: 1859 September 30, The Times, page 10:
  While in the school-ships the boys would be instructed in the elements of an ordinary education, in addition to being taught to row, heave the lead, box the compass, go aloft, reef, steer, and work the guns.
1892, Arthur Conan Doyle, The Adventure of the Engineer's Thumb:
  (...) I say it is south, for the country is more deserted there." "And I say east," said my patient. "I am for west," remarked the plain-clothes man. (...) "And I am for north," said I (...) "Come," cried the Inspector, laughing, "it's a very pretty diversity of opinion. We have boxed the compass among us."