APPARENT MOTION OF THE SUN.] 



ASTRONOMY. 



925 



velocity. It would by this appear that its distance from 

 the earth varied. The variable velocity of the sun in 

 its orbit engaged the attention of Hipparchus, who lived 

 about 140 years before our era, and who appears to have 

 been a more accurate observer of the solar motions than 

 his predecessors. This celebrated philosopher, who was 

 of opinion that the motion in a circular orbit was the 

 more natural, invented an eccentric hypotliesis, which ex- 

 plained the greater angular velocity, and the smaller 

 angular velocity, but which failed at the intermediate 

 positions. He considered that the earth was removed 

 some distance from the centre of the sun's motion, as in 

 the annexed diagram. If the earth be supposed to be 

 placed at T (Fig. 13), instead of at 0, the centre of the 

 circle M E N E, it will follow that the equal arcs de- 

 scribed by the sun in equal times will not appear uniform, 



and thus the motion will be slower at N than at M, and 

 will gradually increase from the former to the latter 

 point. Hipparchus explained this change in the angular 

 velocity of tlui sun, by means of the epicycle. Supposing 

 that the earth is placed at T (Fig. 14), with a radius 

 T C, describe the circle C G 1 C". If the sun be 

 fixed at S, in the smaller circle C S (which is 

 called the epicycle), and makes a complete re- 

 volution in the direction of the arrow, in the 

 same time that the circle itself passes round the 

 earth ; it would follow that the sun would 

 always remain at equal distances from the 

 point T, as at a', a", a'". But if the sun 

 be supposed to travel uniformly, and always 

 preserve the same direction C S, C' S', C" S", 

 <fec. , it is plain that its distance will vary from 

 the point T. If we make T O equal to C S, 

 and describe a circle from the centre O, this 

 circle will pass through all the points 

 S S' S" S"'. This agrees with the preceding 

 explanation ; for whilst the sun describes a 

 circle round O, the earth T is placed eccentri- 

 cally in this circle. The amount of this eccen- 

 tricity may be determined by comparing the 

 angular velocities of the sun when at apogee 

 and perigee ; and we thus find T M : T N : : 

 3431-5; 3G70-1 ; whence it would result that 

 the greatest, the mean, and the least, distance, 

 supposing the earth's orbit to be circular and 

 the motion uniform, would be 1 -0338 : 1 -0001) : 

 and G'9662 respectively ; the eccentricity of the 

 earth's orbit would be 0'0338, or .^jth. We may 

 also arrive at a knowledge of the eccentricity 

 , by comparing the diameters of the sun at 

 different epochs. 



Thus, let d be the least diameter, D the 

 greatest diameter, and $ the mean diameter, then 



S S a le Dd 



d = = j i D = , j ,-j = - ; , and t = y. , , 



1 + e 1 e D i + e D + ci 



In this case T) = 1955" '6, d = 1891", and the result- 

 ing eccentricity is 0'0168 ; consequently the greatest and 

 least distances would be 1'0168 and 0'9S32. It would 

 follow from this, that the motion of the sun in its orbit 

 cannot be uniform, but that it must move really more 

 rapid when at perigee than at apogee. The variation of 

 its angular velocity is about twice as great as that of its 

 distance. We may arrive at a knowledge of the true 



orbit of the earth round the sun by marking off the 

 longitudes daily, and the proportional radii (estimated 

 from the observed diameters). It will thus be found 

 that the figure, roughly traced, will differ considerably 

 fron^a circle, and will be an ellipse, having the earth in 

 one of its foci. It was not, however, by these simple 

 means that Kepler made the great discovery of the 

 elliptic motion of the earth and planets, but by a long 

 and laborious discussion of the observations of Mars, 

 made by his master and patron, Tycho Brahe. 



By further consideration on the motions of the planets, 

 Kepler discovered that their angular velocity diminishes 

 in the same proportion as the square of the distance 

 increases, and that the areas described by the radius 

 vector are proportionate to the times of description. If 

 we suppose a planet to pass through M M' (Fig. 15) and 

 Fig. 14. N N' in the same space of time, it 



would follow from this that the areas 

 M, T, M', and N, T, N', are equal, 

 and that the angular velocities are 

 . greatest at perigee and least at apogee. 

 The form of the ellipse which the 

 earth describes about the sun, differs 

 but little from that of a circle, as the 

 distance O T is only one-sixtieth part 

 of the semi-major axis O M ; and if 

 such an ellipse were described of a 

 yard in diameter, the difference be- 

 tween the major and minor axis 

 would be almost invisible. 



The direction of the line of the 

 apsides of the earth being known, its position in 

 respect to the fixed stars has next to be determined. 

 The line to which this is referred is that of D B of 

 the equinoxes. At the present time, the inclination 

 between the major axis M N of the earth's orbit, 



Fi?. 



and the line D B of the solstices, is nearly W, 

 and is gradually increasing the major axis increas- 

 ing in the sam? direction as the sun's motion, at the rate 

 of 62'' annually. The duration of the seasons is cou- 

 saquently unequal, as may be sean by comparing the 

 areas, a T 6, b T c, c T d, and d T a, which being propor- 

 tionate to the times, the sun will consequantly remain 

 longer in the quadrant b T c, than in d T a, ifcc. Whilst, 

 therefore, the length of the year is constant, the dura- 

 tion of the seasons is subject to a slight change from 

 year to year. At the present time, the lengths of the 

 different seasons ara as folio vs : 



