484 NOTES. 



the errors obtained from theory, it. affords the means of finding each. The 

 principle of least squares is of very general application; its demonstration 

 cannot find a place here; but the reader is referred to Biot's Astronomy, 

 vol. ii. p. 203. 



NOTE 137, P- 74. An axis that, $c. Fig. 20 represents the earth revolving 

 in its orbit about the sun in S, the axis of rotation P p being everywhere 

 parallel to itself. 



NOTE 138, p. 74. 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. 78. If fig. 1 be the moon, her polar diameter N S is the 

 shortest; and of those in the plane of the equator, Q E q, that which points to 

 the earth is greater than all the others. 



NOTE 140, p. 83. 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. 84. Fig. 35 represents the Fig. 35. 



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 sQ: P fy 1 , than in moving through 

 ry 1 A -rv.. but its motion through -TU p cy> 

 is more rapid than its motion through 

 Y* A :h ; and, as the swiftness of the mo- 

 tion and the quantity of heat received vary 

 in the same proportion, a compensation 

 takes place. 



NOTE 142, p. 86. In an ellipsoid of revolution, 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 143, pp. 57, 90. Let q <Y> Q and E == e, fig. 11, be the planes of the 

 equator and ecliptic. The angle e <Y> 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 <Y> Q coincide with the 

 ecliptic E <Y> e, which causes the equinoctial points ^Y 1 and =Cb to move slowly 

 backwards on the plane e <V> 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 posi- 

 tion of the plane of the ecliptic e <V E, causes the equinoctial points <Y> and -^- 



