324 Secular Acceleration of the Moon^s Mean Motion. 



Art. IX. — Secular Acceleration of the Moon's Mean Motion; 

 by James H. Coffin, late Tutor in Williams College. 



It is one of the discoveries of modern astronomy, that the 

 moon is slowly gaining time ; that is, that it performs its revolu- 

 tions now in less time than formerly. It is not two hundred 

 years since Dr. Halley wishing to know the precise length of a 

 lunation, went back to the ancient Chaldean observations, intend- 

 ing to ascertain how many new moons had occurred between that 

 time and his own, and then to divide the time by this number, 

 which would give the average length of each. But he was sur- 

 prised to find that a lunation in those days was considerably 

 longer than now. By comparing the Chaldean, Alexandrian, 

 Arabian, and present observations, he found that the lunar period 

 grew successively shorter. 



When incredulity in regard to the fact was succeeded by con- 

 viction of its truth in the minds of astronomers, it became an in- 

 teresting question to account for it. The most plausible theory, 

 and one which was generally adopted for about a century, was 

 that the moon revolved in a resisting medium, which would 

 cause it gradually to fall toward the earth, and thus by reducing 

 the size of the orbit, make the periodic time less. But the fact 

 that bodies so extremely tenuous and vapory as comets are proved 

 to be, pass through this medium with little or no resistance, 

 seemed and was truly an objection to the theory. 



It was reserved for La Place, about sixty years ago, to explain 

 the true cause of the acceleration, and by a refined and skillful 

 analysis to calculate its amount theoretically. I propose in this 

 article to investigate the cause, and arrive at the result by a dif- 

 ferent and perhaps more simple process, though I believe equally 

 rigid. 



Owing to the attraction of the other planets, the earth's orbit 

 is gradually becoming less and less elliptical, or nearer and nearer 

 to a circle ; so that the sun is every year about 39^ miles nearer 

 to the centre of the ellipse than it was on the year before. At 

 this rate the orbit would become a circle in 40315 years ; an 

 event however that can never take place, for long before such a 

 period of time shall elapse, the change in the shape, which is 

 only an inequality of long period, will have reached its limit, 

 and the eccentricity of the orbit will again increase. 



