Now up to the 16th Century navigators were without the one essential instrument necessary to the accurate determination of longitude. That instrument was an accurate timepiece that could be carried to sea. It is not necessary to have a timepiece in order to learn one’s latitude, but longitude is a more difficult problem, and _time_ is an element in it. But the watches of the 16th Century were too inaccurate to be of much service, and, as a matter of fact, it was not until 1607 that it was realized that a day is not necessarily made up of twenty-four hours. If one stays in one place it is true that there are twenty-four complete hours from noon to noon, and clocks were designed to register the time _at one place_. But suppose, as the sun rises to-morrow morning, you board a very fast airplane and fly it at its fastest speed toward the west. Suppose this airplane flies at the rate of 1,000 miles an hour. In twenty-four hours you have flown around the world, and wherever you have been during that time the sun has been just rising behind you. It has been early morning for _you_ all the time. Suppose, on the other hand, you had flown east at the same rate of speed. If you started at six o’clock in the morning, in three hours the sun would be overhead—that is, it would be noon for _you_. In three more it would be evening. In six more it would be morning again, for you would be halfway around the world. Six hours later evening would come _to you_, and in another six hours you would be at your starting point and it would be morning once more—the _second_ morning you had seen after you started, but only the _first_ morning after for the people you had parted from twenty-four hours before. Ships, of course, do not travel at 1,000 miles an hour. But they do travel many miles, perhaps several hundred, in twenty-four hours. Therefore, if you start at Guayaquil, Ecuador (I use that, for it is very nearly on the equator), and sail west for twenty-four hours, making 240 miles, your watch will tell you that it is exactly the same time of day that it was when you left Guayaquil. But that is not true. It _is_ the same time of day _at Guayaquil_, but you are four degrees west of Guayaquil, and the sun must still travel past four degrees of longitude before the time at the spot you have reached will be what your watch suggests. It will take the sun sixteen minutes to cover that distance, and therefore your watch is sixteen minutes fast. Great strides were made during the 16th and 17th centuries and many books were published. Probably the first book entirely about navigation ever published was one entitled “Arte de navigar,” by Pedro de Medina. This appeared in Spain in 1545. The fact, however, that the subject was not really understood is proved by the acceptance at an even later date of the theory that the earth did not move and that the sun revolved about it.