Within the past three years a wobbling of the earth's axis has been discovered, which takes place within a circle thirty feet in radius and sixty feet in diameter. Its effect was noticed in astronomical observations many years ago, but the change it produced was so small that men could not find out what the matter was. The exact nature and amount of the wobbling is a work of the exact astronomy of the present time. We cannot measure across oceans from island to island. Until a recent time we have not even measured across the continent, from New York to San Francisco, in the most precise way. Without astronomy we should know nothing of the distance between New York and Liverpool, except by the time which it took steamers to run it, a measure which would be very uncertain indeed. But by the aid of astronomical observations and the Atlantic cables the distance is found within a few hundred yards. Without astronomy we could scarcely make an accurate map of the United States, except at enormous labor and expense, and even then we could not be sure of its correctness. But the practical astronomer being able to determine his latitude and longitude within fifty yards, the positions of the principal points in all great cities of the country are known, and can be laid down on maps. The world has always had to depend on astronomy for all its knowledge concerning times and seasons. The changes of the moon gave us the first month, and the year completes its round as the earth travels in its orbit. The results of astronomical observation are for us condensed into almanacs, which are now in such universal use that we never think of their astronomical origin. But in ancient times people had no almanacs, and they learned the time of year, or the number of days in the year, by observing the time when Sirius or some other bright star rose or set with the sun, or disappeared from view in the sun's rays. At Alexandria, in Egypt, the length of the year was determined yet more exactly by observing when the sun rose exactly in the east and set exactly in the west, a date which fixed the equinox for them as for us. More than seventeen hundred years ago, Ptolemy, the great author of The Almagest, had fixed the length of the year to within a very few minutes. He knew it was a little less than 365 1/2 days. The dates of events in ancient history depend very largely on the chronological cycles of astronomy. Eclipses of the sun and moon sometimes fixed the date of great events, and we learn the relation of ancient calendars to our own through the motions of the earth and moon, and can thus measure out the years for the events in ancient history on the same scale that we measure out our own.