The necessity for drawing curved lines on flat charts to represent the courses of their ships now began to be understood, for ships do not sail on a flat surface but instead sail on the ever-curving surface of the sea. To the person accustomed, as most of us are, to looking at maps printed on flat pages, this truth becomes evident when he draws a straight line on a flat map, and then transfers the line to a geographical globe, making it pass through the same points. Mariners were troubled, too, by the difficulty of accurately and easily drawing parallel lines on their charts, but this was overcome in 1584 when “parallel rulers” were first used by one Mordente. “Parallel rulers,” which are nothing more than two rulers hinged together so that whether they touch each other or are separated they remain parallel, are a part of every navigator’s equipment to-day. Tables of the tides began to appear in the latter part of the 16th Century, but they were woefully inaccurate, and other information, while increasing, still was liable to be seriously in error. Even points ashore, where observations could be worked out under the best possible conditions, were thought to be from a few minutes to several degrees from what we now know are their positions, and when one realizes that an error of one minute of latitude means an error of one mile, it will be seen that an error of fifteen or twenty minutes might be enough to put a ship in grave danger while her captain thought her safe, and that a position in which there is an error of several degrees is little more than worthless, for each degree of latitude represents 60 miles, and three or four degrees mean one hundred and eighty or two hundred and forty miles. When it is realized, furthermore, that such errors as these were made ashore, where the observations were much more accurate than they could be at sea, one understands why seamen trusted their navigation but little, for they were often faced, no doubt, with errors of three or four hundred miles. And, if anything, their methods of determining latitude were less inaccurate than those used in determining longitude. Truly, navigation in those days left much to be desired. Other instruments were invented from time to time in the struggle to master navigation. The “astronomical ring” was one, but it was little less crude than the astrolabe. [Illustration: A SEXTANT IN USE _Sextants are used to measure the elevation of celestial bodies—the sun, moon, or stars—in working problems in latitude and longitude._ ] [Illustration: A SHIP’S LOG _The mechanism at the top is fastened on the ship’s rail, and a line with the rotator shown below at its end is allowed to trail in the water astern. The passage of the rotator through the water causes it to turn, the line is twisted, and the log is made to register the miles travelled._ ]