APPEARANCES OF THE CELESTIAL BODIES. 417 



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 sun passes through 

 the winter half of the ecliptic in a time 7 or 8 days shorter than the summer 

 half. According 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 straight, but in all other situations, elliptical. 



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

 vicissitudes of day and night ; and, in combination with its annual motion, 

 occasions 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 

 66f , the plane of the equator, which is perpendicular to the axis, must 

 pass twice in the year through the sun. . When 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 equator, which are consequently nearer to the unenlightened pole, have 

 their day shorter. The parts nearest to the poles have also one of their 

 days and one of their nights protracted 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 23 ; so that 

 by determining the sun's path at the time of the equinoxes, or the apparent 

 place of the equinoctial in the heavens, for any given point on the earth's 

 surface, we may represent the sun's path at any other time by a smaller 

 circle parallel to it. Speaking however, more correctly, the sun's apparent 

 path is a spiral, formed by the continuation of these supposed circles into 

 each other. 



The effect of the centrifugal force, derived from the earth's rotation, is 

 perceptible at the equator, in the retardation of the vibrations of pendu- 

 lums. The whole centrifugal force at the equator is found by computation, 

 to be -g-i-g. of the force of gravity ; but the diminution of the force of gravi- 

 tation appears, by experiments on pendulums, to be -^ ; this diminution 

 being the sum of the centrifugal force, and of the decrease of gravity on 

 account of the oblate figure of the earth, the equatorial parts being further 

 removed from its centre, and the force of gravity being less powerful there. 

 The changes of inclination in the earth's axis are observable in the places 



2 E 



