ORBIT OF THE EARTH. 77 



CHAPTER VII. 



Measurement of Time. 



" The Pilots now their rules of art apply, 

 The mystic needle's devious aim to try; 

 Along the arch the gradual index slides, 

 While Phoebus down the vertic circle glides, 

 Now, seen on ocean's utmost verge to swim, 

 He sweeps it vibrant with his nether limb. 

 Their sage experience thus explores the height 

 And polar distance of the source of light." 



Falconer. 



HITHERTO we have spoken of the earth's orbit as circular, such 

 being its apparent projection upon the celestial sphere, but this is 

 not the actual case, it is elliptical. This is ascertained by the 

 change in the apparent diameter of the sun, viewed from the 

 earth at different seasons. If the orbit of the earth was a great 

 circle, having the sun in its centre, it is obvious that the angle 

 subtended by his disk would at all times be the same, for his dis- 

 tance from the earth would always be the same. On the contrary, 

 the diameter is observed to increase from the summer solstice to 

 the winter solstice, then to again decrease. It is a proposition 

 established in optics, that the apparent diameter of an object, 

 varies inversely as the distance frcyii the spectator, when the angle 

 is small, hence by observing with great accuracy, the apparent 

 diameter of the sun, at different periods of the year, and actually 

 projecting or calculating the orbit of the earth, it is found to be an 

 ellipse, or oval, as represented in the following diagram.' The 

 sun being situated, not in its centre, but nearer one side, in what 

 is called one of the foci of the ellipse. The foci of the ellipse S 

 and C, are so situated on the major, or longer axis, of the ellipse, 

 that the sum of the length of any two lines drawn from the foci to 

 the same point in the circumference of the ellipse is constant. 

 Thus the sum of the lengths C E and S E, are equal to the sum of 



