NOTES. 



455 



tion, fig. 1, the polar diameter N S, and every diameter in the equator q E Q e, 

 are permanent axes of rotation, but the rotation would be unstable about 

 any other. Were the earth to begin to rotate about C a, the angular distance 

 from a to the equator at q would no longer be ninety degrees, which would 

 be immediately detected by the change it would occasion in the latitudes. 



NOTE 146, pp. 50, 80. Let q op Q, and E == e, fig. 11, be the planes 

 of the equator and ecliptic. The angle e op Q, which separates them, 

 called the obliquity of the ecliptic, varies in consequence of the action of 

 the sun and moon upon the protuberant matter at the earth's equator. 

 That action brings the point Q towards e, and tends to make the plane 

 q op Q coincide with the ecliptic E op e, which causes the equinoctial 

 points cyo and == to move slowly backwards on the plane e cyo E, at the 

 rate of 50"'41 annually. This part of the motion, which depends upon 

 the form of the earth, is called luni-solar precession. Another part, 

 totally independent of the form of the earth, arises from the mutual action 

 of the earth, planets, and sun, which, altering the position of the plane of 

 the ecliptic e op E, causes the equinoctial points cyD and := to advance at 

 the rate of 0"'31 annually ; but, as this motion is much less than the former, 

 the equinoctial points recede on the plane of the ecliptic at the rate of 

 50"' 1 annually. This motion is called the precession of the equinoxes. 



NOTE 147, p. 81. Let gcyoQ, ecyoE, fig. 36, be the planes of 

 the equinoctial or celestial equator 



and ecliptic, and p, P, their poles. * 36 - 



Then suppose p, the pole of the equa- 

 tor, to revolve with a tremulous or 

 wavy motion in the little ellipse 

 pcdb in about 19 years, both mo- 

 tions being very small, while the 

 point a is carried round in the circle 

 a A B in 25,868 years. The tremu- 

 lous motion may represent the half- 

 yearly variation, the motion in the 

 ellipse gives an idea of the nutation 

 discovered by Bradley, and the mo- 

 tion in the circle a A B arises from 

 the precession of the equinoxes. The 

 greater axis p d of the small ellipse 

 is 18"'5, its minor axis 6 c is 13"'74. 

 These motions are so small that they 

 have very little effect on the parallelism of the axis of the earth's rotation 

 during its revolution round the sun, as represented in fig. 20. As the 

 stars are fixed, this real motion in the pole of the earth must cause an 

 apparent change in their places. 



NOTE 148, p. 83. By means of a transit instrument, which is a tele- 

 scope mounted so as to revolve only in the plane of 

 the meridian, the instant of the transit or passage of 

 a celestial body across the meridian can be deter- 

 mined. The transits of the principal stars are used to 

 ascertain the time, or, which is the same thing, the 

 amount of the error of clocks. A system of equidistant 

 wires, as represented in the figure, is placed in the 



