414 NOTES. 



revolving in its orbit about the sun S, the axis of rotation Pp being every- 

 where parallel to itself. 



NOTE 138, p. 61. Angular velocities that are sensibly uniform. The 

 earth and planets revolve about their axes with an equable motion, which 

 is never either faster or slower. For example, the length of the day is 

 never more nor less than twenty-four hours. 



NOTE 139, p. 64. If fig. 1 be the moon, her polar diameter NS is the 

 shortest; and of those in the plane of the equator, Q,Ey, that which 

 points to the earth is greater than all the others. 



NOTE 140, p. 69. Inversely proportional, &,-c. That is, the total amount 

 of solar radiation becomes less as the minor axis C C', fig. 20, of the earth's 

 orbit becomes greater. 



NOTE 141, p. 70. Fig. 35 represents the 

 position of the apparent orbit of the sun 

 as it is at present, the earth being in E. 

 The sun is nearer to the earth in moving 

 through =^=P T, than in moving through 

 T A:=, but its motion through =^P T 

 is more rapid than its motion through 

 T A ^= ; and as the swiftness of the mo- 

 tion and the quantity of heat received 

 vary in the same proportion, a compensa- 

 tion takes place. 



NOTE 142, p. 71. In an ellipsoid of revolution, fig. 1, the polar diameter 

 NS and every diameter in the equator qlS>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 equa- 

 tor at q would no longer be ninety degrees, which would be immediately 

 detected^ by the change it would occasion in the latitudes. 



NOTE 143, pp. 50, 75. Let q T Q,, and E T e, fig. 1 1, be the planes of the 

 equator and ecliptic. The angle e If 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 toward e, and tends to make the plane q T a 

 coincide with the ecliptic E T e, which causes the equinoctial points, T 

 and =:, to move slowly backward on the plane e T E at the rate of 50"'4l 

 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 T E, causes the equinoctial points T 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"'l 

 annually. This motion is called the precession of the equinoxes. 



NOTE 144, pp. 61, 76. Let q T Q,, e T E, fig. 36, be the planes of the 

 equinoctial or celestial equator and ecliptic, and p, P, their poles. Then 

 suppose p, the pole of the equator, to revolve with a tremulous or wavy 

 motion in the little ellipse pcdb in about 19 years, both motions being 

 very small, while the point a is carried round in the circle a A B in 25,868 

 years. The tremulous motion may represent the half-yearly variation, 

 the motion in the ellipse gives an idearfif the nutation discovered by Brad- 

 ley, and the motion in the circle a A B arises from the precession of the 

 equinoxes. The greater axis pd of the small ellipse is 18" -5, its minor 

 axis be is 13"-74. These motions are so small, that they have very liltle 

 effect on the parallelism of the axis of the earth's rotation during its revo- 

 lution round the sun, as represented in -fig. 20. As the stars are fixed, this 



