IS ASTRONOMY. 
referred by an observer at A to that part of the celestial sphere occupied 
by the star a. From the centre of the earth it would be referred in the 
direction CM to the celestial sphere at 6. The angle AMC, or aMé, will 
represent the difference of the two directions ; and this angle, AMC, is called 
the parallax of the point M, or its horizontal parallaz, since M is situated 
in the horizon. Let the moon now stand higher in the heavens, as at M’, 
then from A she will be seen in the direction AM’c, consequently referred 
to the point c of the heavens; and from C, the centre of the earth, in the 
direction CM’d, referred consequently to the celestial sphere at d. The 
angle CM’A = cM’d will be the difference of the two directions CM’ and 
AM’; and CM’A will be the parallax of M’, more definitely its parallax 
in altitude, because M’ is situated a certain distance above the horizon. 
Let the moon now be situated at M”, or in the direction of the zenith, e, of 
A, then the moon, M’’, will be referred to the heavens at e; the two lines 
of sight will coincide, and they will form no angle, so that for heavenly 
bodies situated in the direction of the zenith, the parallax in altitude 
vanishes or becomes zero. We find, also, by examining the figure that the 
parallax is at its maximum in the horizon, diminishing with the angle of 
elevation until in the zenith it is zero. 
Suppose now a second place of observation, E, lying in the same meri- 
dian, and the moon to be situated at M’; then from A she will be seen in 
the direction AM’c, consequently referred to c, and from E in the direction 
EM’d', and referred to d'.. The angle EM’A gives the difference of the 
two directions EM’, AM’. This angle EM’A, or the corresponding are ed’, 
is called the local parallax of the star at M’ for the two places A and E. 
Hence it is clear, that for the same altitude of the same star, its local 
parallax will be less as the distance of the two places of observation on the 
same meridian is less. 
The Heliocentric and Geocentric place of the Planets ; their Commutation 
and Annual Parallaz. 
20. The motions exhibited by the planets are not so simple as the 
apparent daily motions of the fixed stars, as above considered. This results 
from the fact of their having two motions, of which one is diurnal, in com- 
mon with the fixed stars, from east to west, and the other an orbitual 
motion from west to east. Add to this, that the planets are not, like the fixed 
stars, almost infinitely distant from us, and that therefore it makes a material 
difference whether their revolutions be observed from the sun or the earth. 
The place of a planet, as seen from the sun, is called its heliocentric place ; 
its position as seen from the earth, is the geocentric place. Lig. 14, pl. 6, 
is intended to illustrate these terms. Let S be the centre of the sun, the 
circle described through T the orbit of the earth, that through P the orbit 
of any superior planet, and the extreme circle, the ecliptic ; the exterior and 
interior circles lying, of course, in the same plane, which may be the plane 
of the paper. Furthermore, let the earth be at T, the planet at P, and let 
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