SPHERICAL ASTRONOMY. 81 
The former has consequently retrograded, since, taking the fixed direction of 
the star s as a line of reference, Venus to the observer on the earth appears 
to the right of the star, which is seen in the direction bs, parallel to As. 
It is also evident that Venus has become a morning star, since when the 
observer at b looks towards the sun, he sees the planet on the right of the 
sun. Hence Venus is seen in the eastern horizon before the rising of the 
sun. PI. 6, fig. 21, represents her at this time, crescentic, and with two 
digits illuminated. 
A month and a half after inferior conjunction, the fixed star in whose 
vicinity Venus was seen when the earth was at 0, will be seen in a direction 
parallel to Bd, from the earth at c; consequently Venus will be seen in the 
direction Ce, to the left or eastwardly of this star. Hence, it follows that 
the apparent motion of Venus has again become direct. It will also be seen 
from fig. 24, that the angle scS, formed by lines drawn from the earth to the 
sun and the planet, is larger than the former angle, SOB; we accordingly 
say that the elongation of Venus has increased. The illuminated part of 
her disk has (as seen in fig. 21) increased to about four digits; her apparent 
diameter, however, sensibly diminishes. This elongation must be greatest at 
the time when the earth (jig. 24) is at d, and Venus at D, which is the case 
about 24 months after inferior conjunction ; and this greatest elongation is 
equal to the angle DdS. Venus then (fig. 21), like the moon in her last 
quarter, has half of her disk, or six digits, illuminated. 
Half a year after inferior conjunction, when the earth is at f, Venus 
will have reached F’, consequently the elongation of Venus has again 
become less, since the angle, SfF’, expressing this elongation, is evidently 
less than the angle SdD. Venus, then, during this time has approached the 
sun, has become fuller (fig. 21), but nevertheless smaller, although still the 
morning star (fig. 24). Three months after, the earth is at h, and Venus at 
H ; the latter has therefore reached superior conjunction, that is, is on the 
opposite side of the sun from the earth. Her apparent diameter is now the 
least, and her entire disk (fig. 21) illuminated, although invisible. At a 
later period she appears in the evening sky as the evening star, and exhibits 
the same phases (fig. 21) as before, but in an inverted order. Her apparent 
diameter also increases. 
To illustrate the course of a superior planet, let S (fig. 25) represent the sun 
in the centre of the earth’s orbit, abedefgh. Let that of Marsbe ACEGJLN. 
The earth revolves in twelve, and Mars in about twenty-three months, 
about the sun. If, therefore, the original positions of the earth and Mars 
were at a and A, at the expiration of 1, 2, 3, 4, &c., months, the earth will 
have reached the points 8, ¢, d, e, &c.; and Mars B, C, D, E, &c., respect- 
ively. When the earth was ata, and Marsat A, the latter was in opposition 
to the sun (°°), and the stars in the vicinity of Mars must show themselves 
in the direction az. The motionof all the planets from A to Bis called direct ; 
consequently Mars has a direct motion when advancing from the stars ob- 
served in the direction az, towards the left, and a retrograde motion when 
moving towards the right. Pl. 6, fig. 25, shows also that when the earth goes 
towards b, and Mars towards B, the motion of the latter must be retrograde, 
ICONOGRAPHIC ENCYCLOPZDIA.—VOL. I. 6 81 
