Historian Oscar G. Darlington asserts that Gerbert's division by 60 degrees instead of 360 allowed the lateral lines of his sphere to equal to six degrees. By this account, the polar circle on Gerbert's sphere was located at 54 degrees, several degrees off from the actual 66° 33'. His positioning of the Tropic of Cancer at 24 degree was nearly exact, while his positioning of the equator was correct by definition. Richer also revealed how Gerbert made the planets more easily observable in his armillary sphere: