Page:Popular Science Monthly Volume 9.djvu/696

668 may be ascertained from the "Nautical Almanac" to-day, and it will be found true within one-hundredth of a second. But that throws no light on the question, What is the absolute length of an hour or a second? They are both definite fractions of a day; and a day is a revolution of the earth on its axis; no artificial measurement of such an interval can prove whether the interval itself remains from age to age unchanged. To quote Humboldt as a sure guide to the received opinions of scientific men thirty years ago, "The comparison of the secular inequalities in the moon's motion, with eclipses observed by Hipparchus, or during an interval of two thousand years, shows conclusively the length of the day has certainly not been diminished by one-hundredth part of a second."

The assertion is derived from Laplace, and even now is mentioned as an unquestioned fact in the most recent astronomical text-books. Halley, it is true, in 1695, discovered that the average velocity with which the moon revolves round the earth had apparently been increasing from year to year, and this acceleration remained unexplained during more than a century. Halley compared the records of the most ancient lunar eclipses of the Chaldean astronomers with those of modern times. He likewise compared both sets of observations with those of the Arabian astronomers of the eighth and ninth centuries. The result was an unexplained discrepancy, which set all theory at defiance for a century or more. It appeared that the moon's mean motion increases at the rate of eleven seconds in a century; and that quantity, small in itself, becomes considerable by accumulation during a succession of ages. In 2,500 years the moon is before her calculated place by l½°—enough to make a very material difference in place of visibility of a solar eclipse. Laplace at last, as Sir John Herschel says, stepped in to rescue physical astronomy from its reproach, by pointing out the real cause of the phenomenon. Laplace accounted for the apparent acceleration by showing that the motion of the earth in her orbit was disturbed by the other planets, in a manner before insufficiently appreciated, and the explanation was accepted for many years as complete and satisfactory. The acceleration was calculated to the utmost point of precision attainable in mathematics by MM. Damoiseau and Plana. Using the formulas of Laplace, and the numbers deduced from them, it was found that the circumstances and places of ancient eclipses, as recorded by historians, were brought into strict accordance with the times and circumstances as they ought to have been if the theory were true. Laplace's explanation rests upon the fact that for many thousands of years past the orbit of the earth has been tending more and more to a perfect circle—that is, the minor axis is increasing while the major axis remains unchanged. The result is, that the average distance of the moon from the sun is greater than it was in past ages. But in proportion as the moon