surface at low latitudes or over short distances it can be used for plotting the course of a vehicle, aircraft or ship. Over longer distances and/or at higher latitudes the great circle route is significantly shorter than the rhumb line between the same two points. However the inconvenience of having to continuously change bearings while travelling a great circle route makes rhumb line navigation appealing in certain instances. The point can be illustrated with an east–west passage over 90 degrees of longitude along the equator, for which the great circle and rhumb line distances are the same, at . At 20 degrees north the great circle distance is while the rhumb line distance is , about 1.5% further. But at 60 degrees north the great circle distance is while the rhumb line is , a difference of 8.5%. A more extreme case is the air route between New York City and Hong Kong, for which the rhumb line path is . The great circle route over the North Pole is , or hours less flying time at a typical cruising speed. Some old maps in the Mercator projection have grids composed of lines of latitude and longitude but also show rhumb lines which are oriented directly towards north, at a right angle from the north, or at some angle from the north which is some simple rational fraction of a right angle. These rhumb lines would be drawn so that they would converge at certain points of the map: lines going in every direction would converge at each of these points. See compass rose. Such maps would necessarily have been in the Mercator projection therefore not all old maps would have been capable of showing rhumb line markings. The radial lines on a compass rose are also called rhumbs. The expression "sailing on a rhumb" was used in the 16th–19th centuries to indicate a particular compass heading. Early navigators in the time before the invention of the marine chronometer used rhumb line courses on long ocean passages, because the ship's latitude could be established accurately by sightings of the Sun or stars but there was no accurate way to determine the longitude. The ship would sail north or south until the latitude of the destination was reached, and the ship would then sail east or west along the rhumb line (actually a parallel, which is a special case of the