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XXXIV. INVESTIGATION 
OF THE APPARENT MOTION OF THE EARTH VIEWED FROM THE 
MOON, ARISING FROM THE MOON’S LIBRATIONS, 
By JAMES DEAN, a.m. 
Professor of Mathematics and Natural Philosophy in the University of Ver- 
mont, at Burlington. 
neat EE ate 
IF the moon moved uniformly about the earth in the ecliptic, with 
an angular motion exactly equal to that of the moon’s diurnal rotation 
and in the same direction, and the lunar equator coincided with the 
ecliptic, the earth viewed from any part of the moon’s surface would 
always appear in the same situation above the horizon of the spectator, 
or with the same azimuth and altitude. Toa spectator placed on the cen- 
tre of the moon’s disc the earth would appear constantly in the zenith, to 
one situated on the borders of the disc it would appear in a particular 
point of the horizon, and in other points of the disc it would appear at a 
fixed altitude and azimuth, corresponding to the place of the observer. 
‘The inequality of the moon’s motion about the earth, combined with 
the effect of the inclination of the lunar orbit and equator (which cause 
the moon’s librations) produce to a spectator placed on the surface of 
the moon, an apparent motion of the earth about its mean place, sup- 
posed at rest ; to investigate which is the object of the present memoir. 
In Fig. 5, 7, 9, 11, or 13, let Z represent the mean place of the 
earth’s centre, as seen by a spectator placed on the surface of the moon, 
and referred. to the concave surface of the visible hemisphere of the 
spectator, this point being supposed, as above, to be at rest on that 
surface. Through Z draw EZW, representing a portion of the lunar 
celestial equator, or a parallel to it, and SZN perpendicular to it, rep- 
