ON THE APPEARANCES OF THE CELESTIAL BODIES. 525 



The sun's apparent diameter is larger by one thirtieth in January than in 

 June; of course the earth is so much nearer to the surt in winter than in 

 summer; and since the revolving radius of the earth's orbit describes equal 

 areas in equal times, the angular motion must increase as the square of the 

 distance diminishes, or about twice as fast as the distance itself diminishes ;~ 

 so that the whole variation of the apparent diurnal motion of the sun is one 

 fifteenth of his mean motion : hence, the srui passes through the vviaiter half 

 of the ecliptic in a time 7 or 8 days shorter than the summer half. Accord- 

 ing to the different situations of the earth, with respect to the plane of the 

 sun's equator, his rotation on his axis causes the paths of his spots to assume 

 different forms; when the earth is in that plane, the paths appear straigiit, 

 but in all other situations, elliptical. 



The rotation of the earth on its axis produces the still more obvious vicis- 

 situdes of day and night; and, in combination with its annual motion, oc- 

 casions the change of seasons. Since the axis remains always parallel to 

 itself, and is inclined to the plane of the ecliptic in an angle of about 66^°, 

 the plane of the equator, which is perpendicular to the axis> must pass twice 

 in the year through the sun. VVhen this happens, the limit of illumination, 

 or the circle which separates the dark portion of the earth from the enlightened 

 part, will then pass through the poles; and as the earth turns on its axis, 

 each point of its surface must remain for an equal length of time in light and 

 in darkness. Hence the points of the ecliptic, in which the sun is situated at 

 such times, are called the equinoctial points. At all other times, one pole of 

 the earth is in the light, and the other in the shadow; and all the points of 

 the earth nearest to the illuminated pole have their day longer than their 

 night, while the parts on the opposite side of the ecjuator, which are conse- 

 quently nearer to the unenlightened pole, have their day sliorter. Tlie parts 

 nearest to the poles have also one of their days and one of their nights pro- 

 tracted to a period of several common days, or even months, whenever they 

 revolve entirely within the limit of illumination. (Plate XXXIV. Fig. 489.) 



The sun appears to describe. every day a circle in the heavens, more or less 

 distant from the plane of the equator, according to the actual situation of the 

 earth's axis ; this distance being always the same as that of the poles from the 

 limit of illumination, and never exceeding £34°; so that by determining the 



