NOTES. 415 



real motion in the pole of the earth must cause an apparent change in 

 their places. 



NOT* 145, p. 78. Let N be the pole, fig. 11, cE the ecliptic, and Q,q 

 the equator. Then N n m S being a meridian, and at right angles to the 

 equator, the arc T m is less than the arc T n. 



NOTE 146, p. 80. Heliacal rising of Sirius. When the star appears 

 in the morning, in the horizon, a little before the rising of the sun. 



NOTK 147, p. 82. Let P T A ^ fig. 35, be the apparent orbit or path 

 of the sun, the earth being in E. Its major axis, A P, is at present situate 

 as in the figure, where the solar perigee P is between the solstice of 

 winter and the equinox of spring. So that the time of the sun's passage 

 through the arc T A == is greater than the time he takes to go through 

 the arc =2= P T . The major axis A P coincided with ^= T, the line of the 

 equinoxes, 4000 years before the Christian era ; at that time P was in the 

 point T. In 6468 of the Christian era, the perigee P will coincide with 

 ==. In 1234 A. D. the major axis was perpendicular to T ^, and then P 

 was in the winter solstice. 



NOTE 148, p. 83. jit the solstices, $-c. Since the declination of a celes- 

 tial object is its angular distance from the equinoctial, the declination of 

 the sun at the solstice is equal to the arc Q e, fig. 11, which measures the 

 obliquity of the ecliptic, or angular distance of the plane T e== from the 

 plane T Q:h. 



NOTE 149, p. 83. Zenith distance is the angular distance of a celestial 

 object from the point immediately over the head of an observer. 



NOTE 150, p. 84. Reduced to the lerel of the sea. The force of gravita- 

 tion decreases as the square of the height above the surface of the earth 

 increases, so that a pendulum vibrates slower on high ground ; and in 

 order to have a standard independent of local circumstances, it is neces- 

 sary to reduce it to the length that would exactly make 86,400 vibrations 

 in a mean solar day at the level of the sea. 



NOTE 151, p. 84. A quadrant of the meridian is a fourth part of a 

 meridian, or an arc of a meridian containing 90, as N Q, fig. 11. 



NOTE 152, p. 86. The angular velocity of the earth's rotation is at the 



