VENUS.] 



ASTRONOMY. 



941 



be, however, examined with the telescope at its various 

 distances from the sun, it will be seen that its diameter 

 varies greatly, and that its disc undergoes a series of 

 changes similar to those of the moon. By observing 

 those in its different positions, it will be perfectly ap- 

 parent that they agree with a motion of the planet round 

 the sun, it being supposed that the planet is an opaque 

 globular body, of which one hemisphere is illuminated 

 by the sun. If the sun S (Fig. 56) be supposed to re- 

 Fig. 56. 



volve round the earth T in the direction of the arrow, 

 and the planet V around the sun, at the point V, where 

 it is in aline with the earth and gun, and the hemisphere 

 turned towards both illumined by the latter body, its 

 disc will appear wholly illuminated by the latter. At 

 the points V' and V", where the angles S V T and 

 S V" T are right angles, the planet will appear as half- 

 full. At the point V* the illuminated portion will be 

 completely turned away from the east, and it will there- 

 fore be invisible, but would appear on the sun as a dark 

 spot, and at its greatest diameter. In the positions be- 

 tween V and V, and V and V". it will appear more 

 or less gibbous ; and between V and \", and V and 

 V", as crescentic. The appearances of the planet, and 

 comparative sizes of its disc, under these circumstances, 

 will be seen in the accompanying representation (Fig. 57). 



Fig. 57. 



between Venus and the earth. The relative distances of 

 Venus and the earth from the sun may therefore be 

 found, as the extreme distances will be in proportion to 

 the extreme diameters, or 



1 + r : 1 r : : 60 : 10, or r = _= = 0'72. 



72 

 The distance of Venus from the sun is therefore r 



of that of the earth. 



Whilst the planets Mercury and Venus can only be 

 separated by a certain distance from the sun, and only 

 perceived in the mornings and evenings, the other planets 

 which are known at the present time can be seen at all 

 parts of the sky, and pass the meridian at midnight 

 when in opposition. The first are called the inferior, 

 the latter the superior planets The apparent course of 

 the latter in the sky is, however, equally irregular as 

 the former ; for the greater part of their revolution they 

 are direct, and for a short time retrograde ; their motion 

 is sometimes slow and sometimes fast, and their latitude 

 is equally variable. Mars returns to the same position 

 in the heavens in 687 days, but preserves its direct 

 motion 707 days ; whilst its retrograde motion varies 

 between 61 days and 81 days ; but the direct motion, 

 combined with the retrograde motion which follows, 

 comprises about 780 days on the average. When in 

 conjunction with the sun, its motion is always direct ; 

 but when in opposition, it becomes retrograde, and the 

 arc of the latter may vary between 10 and 19. Jupiter, 

 fig. 58. 



The magnitude of the illuminated part can readily be 

 obtained for any epoch by the following simple construc- 

 tion : The plane of projection being perpendicular to a 

 line joining the earth and Venus, the boundary of the 

 illuminated hemisphere will be projected into an ellipse 

 more or less eccentric upon it, and the minor axis will bo 

 in the same proportion to the major, as the radius is to 

 the cosine of inclination between the two planes. The 

 inclination is the angle at the centre of Venus, formed by 

 lines drawn to the Run and earth. 



The greatest and least diameters of Venus are about 

 60" and 10", as seen from the earth ; and it follows that 

 if r be the distance between the sun and Venus, that the 

 greatest and least distances will be 1 -(- r, and 1 r 



Saturn, Uranus, etc., are in a similar manner retrograde 

 at opposition, and direct at conjunction. Jupiter's 

 direct motion continues for 278 days, and the 

 retrograde from 11GJ to 122J days, the arc of the 

 latter being constantly at about 10. In a simi- 

 lar manner, the period during which Saturn 

 moves in the order of the signs is 239 days, 

 and the duration of retrogradution may vary 

 between 135i and 138^ days, the arc described 

 varying betw'een 6 40' and 6 55'. The manner 

 in which these various motions were accounted 

 for by the ancients was the same system of epi- 

 cycle already described for Venus, but some 

 slight modification was introduced. The planet 

 M (lig. 58) was supposed to describe an epicycle 

 in such a manner that the radius C M, which joined it 

 to the centre, was parallel to T S at all parts of its 

 orbit, as C' M' to T S', .fee. If the different positions 

 of Mars in reference to direct and retrograde motion be 

 examined, it will be found to agree closely with this 

 explanation. 



It was by this system of epicycle and deferent, that 

 Ptolemy accounted for the apparent motions of the 

 planets in their paths through the heavens ; and ho 

 endeavoured to arrange the radii and motions of the 

 epicycles in such a manner that they would agree with 

 the observed appearances. As, however, new inequali- 

 ties were brought to light, it was found to be impossible 

 to explain them by those single epicycles ; and, in most 



