To find his position at sea a navigator needs to know his longitude and latitude. For both determinations he must measure the altitude of the sun or a star above the horizon, and from the 15th to the early 18th centuries he employed simple instruments known as the 'cross-staff' and the 'backstaff'. A much more accurate instrument, the octant, was invented by John Hadley in London and, independently, by Thomas Godfrey of Philadelphia in the 1730s. In this instrument the horizon was sighted directly through a glass half silvered and half clear, and the image of the sun brought on to the silvered portion from the observer's side by reflection in a rotatable plane mirror. When the sun is on the horizon the two mirrors are parallel; under other conditions the angle through which the rotatable mirror must be turned to bring the two views of the sun into coincidence is half its altitude above the horizon. The sextant is a modified form of octant.