128 SEE— THE PAST HISTORY OF THE EARTH. [April 23, 



must have an end. In order to improve this notion, and to find with exacti- 

 tude how much the years become shorter in each Century; I am in hopes 

 that a great number of older observations will afford me the necessary 

 succours. 



2. Second Letter: 



XXIII. I am still thoroughly convinced of the truth of what I advanced 

 that the orbs of the planets continue to be contracted, and consequently 

 their periodic times grow less. . . . The late Dr. Halley has also remarked 

 that the revolutions of the moon are quicker at present than they were in 

 the time of the ancient Chaldeans, who have left us some observations of 

 Eclipses. 



Euler then discusses the difficulty of finding the number of days 

 since the time of Ptolemy, and thinks the uncertainty may be a day 

 or two, also raises the question whether the length of the day is 

 constant. 



At present we measure the length of the day by the number of oscilla- 

 tions which a pendulum of given length makes in this space of time ; but 

 the ancients were not acquainted with these experiments, whereby we might 

 have been informed, whether a pendulum of the same length made as many 

 vibrations in a day as now. But even though the Ancients had actually made 

 such experiments, we could draw no inferences from them, without sup- 

 posing, that gravity on which the time of an oscillation depends, has always 

 been of the same force ; but who will ever be in a condition to prove this 

 invariability in gravity? 



He finally concludes that both the lengths of the year and day 

 are diminishing, " so that the same number will answer nearly to 

 a year." 



The views of Euler here set forth that the earth and other planets 

 were at one time farther from the sun than at present are so remark- 

 able that it is scarcely necessary to do more than bring them to the 

 attention of astronomers. 



U. S. Naval Observatory, 

 Mare Island, California, 

 April 24, 1909. 



