668 THE POPULAR SCIENCE MONTHLY. 



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 

 ao-e unchanged. To quote Humboldt as a sure guide to the received 

 opinions of scientific men thirty years ago, 1 " 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 con- 

 clusively 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 increas- 

 ing 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 cen- 

 turies. 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 l 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 re- 

 proach, 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 man- 

 ner 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 



"Cosmos," i., 161. 



