418 LECTURE XLIV. 



of the equinoctial points, and in the situation of the plane of the earth's ' 

 equator with respect to the fixed stars ; and the secular diminution of the 

 obliquity of the ecliptic is discoverable by a comparison of distant obser- 

 vations on the sun's apparent motion, and on the places of the fixed stars 

 with respect to the ecliptic. 



For the phenomena of twilight, we are principally indebted to the light 

 reflected by the atmosphere ; when the sun is at a certain distance only 

 below the horizon, he shines on some part of the air immediately visible 

 to us, which affords us a portion of reflected light. The distance at wlych 

 this may happen, has been variously estimated, and it is perhaps actually 

 different in different climates, being a little greater in countries near tlio 

 poles than in those which are nearer the equator ; there is also sometimes 

 a secondary twilight, when the parts of the atmosphere, which reflect a 

 faint light on the earth, are themselves indebted for this light to an earlier 

 reflection. Some have assigned 18 as the limit of twilight, and on this 

 supposition, allowing for refraction, the atmosphere must be capable of 

 reflecting sensible light at the height of about 40 miles. Mr. Lambert,* on 

 the contrary, makes the limit only about 6. The duration of twilight 

 is greater or less as the sun moves more or less obliquely with respect to 

 the horizon ; it is, therefore, shortest near the time of the equinoxes, since 

 the equinoctial intersects the horizon less obliquely than any lesser circle 

 parallel to it. (Plate XXXIV. Fig. 490, 491.) 



The revolutions of the primary planets, combined with that of the 

 earth, necessarily produce the various relations, in which they are either 

 in opposition or conjunction, with respect to each other or to the sun, and 

 in which the apparent motion is direct or retrograde, or the planet is sta- 

 tionary, according to the directions and the comparative velocities of the 

 real motions. If the earth were at rest, the inferior planets would appear 

 to be stationary when they are at the greatest elongation or angular dis- 

 tance from the sun ; but, on account of the effect of the earth's motion, 

 Venus is stationary at an elongation of about 29, while her greatest 

 elongation is between 45 and 48. The greatest elongation of Mercury, in 

 each revolution, is from 28| to IT^ , according to the position of his orbit, 

 which is very eccentric. All these appearances are precisely the same as 

 if the sun actually revolved round the earth, and the planets accompanied 

 him in his orbit, performing at the same time their several revolutions 

 round him ; and the path which would thus be described in the heavens, 

 and which is of a cycloidal nature, represents correctly the true positions 

 of the planets with respect to the earth. The apparent angular deviation 

 from the ecliptic, or the latitude of the planet, is also greater or less, 

 accordingly as the earth is nearer or remoter to the planet, as well as 

 according to the inclination of its orbit and its distance from the node. 

 (Plate XXXIV. Fig. 492... 494.) 



The various appearances of the illuminated discs, especially of the in- 

 ferior planets, and the transits of these planets over the sunj depend on 



* Photometria, 987. See Lacaille on the Length of Twilight at the Cape, Hi?t. 

 et Mem. 1751, p. 544, H. 158. Bergmann, Schwed. Abhand. 1760, p. 237. Opusc. 

 v. 331; vi.l. 



