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XXIV. A Eifcourfe concerning the Men - 
flrual Parallax , arifing from the mutual 
Gravitation of the Earth and Moon ; it s 
Influence on the Obfervatiom of the Sun 
and Planets ; with a Method of obferving 
it : By J. Smeaton, F. R, S. 
ReadMay i2,TT is demonftrated by Sir Ifaac Newton 
in the Principia , that it is not the Earth's 
center, but the common center of gravity of the 
Earth and Moon, that defcribes the ecliptic ; and that 
the Earth and Moon revolve in fimilar ellipfes, about 
their common center of gravity. The fame great 
author has alfo inveftigated, from the different rife of 
the tides, when the Moon is in conjun&ionoroppofi- 
tion to the Sun, to thofe which happen when the 
Moon is in her quadratures ; that the quantity of 
matter in the Earth is to that in the Moon, as 39. 7 S 
to 1 ; from whence, and the known diflance of the 
Earth and Moon, it would follow, that the common 
center of gravity of the two bodies falls without the 
lurface of the Earth, by one half of its femidiameter ; 
that is, that the center of the Earth defcribes an epi- 
cycle round the common center of gravity once a 
month, whofe diameter is three femidiameters of the 
Earth. 
Dr. Gregory, in his aflronomy, has laid hold of 
this circumflance, in order to prove the relative gra- 
vity of the Earth and Moon, by obfervation ; which 
is the fubjedt of his 60th proportion of the fourth 
book ; 
