454 PHYSICAL SCIENCES. 



the time included between two consecutive passages of the plauet through 

 the same node N or n : is its periodic time, allowance being made for the 

 recess of the node in the interval. 



NOTE 138, p. 60. Suppose that it were required to find the position of 

 a point in space, as of a planet, and that one observation places it in n, 

 p- VA fig. 34, another observation places it in n', 



another in n", and so on; all the points 



' v n. n', n", n'", &c., being very near to one 



another. The true place of the planet P 

 will not differ much from any of these 

 positions. It is evident, from this view of 

 the subject, that Pn, Pn', P n", &c., are 

 the errors of observation. The true position 

 of the planet P is found by this property, 

 that the squares of the numbers represent- 

 ing the lines P n, P n', &c., when added together, is the least possible. Each 

 line P n, P n', &c., being the whole error in the place of the planet, is made up 

 of the errors of all the elements ; and, when compared with 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 139, p. 61. The true longitude of Uranus was in advance of the 

 tables previous to 1795, and continued to advance till 1822, after which 

 it diminished rapidly till 1830-1, when the observed and calculated 

 longitudes agreed, but then the planet fell behind the calculated place so 

 rapidly that it was clear the tables could no longer represent its motion. 



NOTE 140, p. 65. An axis that, $c. Fig. 20 represents the earth 

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

 everywhere parallel to itself. 



NOTE 141, p. 65. Angular velocities that are sensibly uniform. The 

 earth and planets revolve about their axis 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 142, p. 68. 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 143, p. 73. 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 144, p. 75. Fig. 35 represents the position of the apparent orbit 

 of the sun as it is at present, the earth being 

 fig. 3o. m _ The sun j Bearer to the earth in 



moving through =Cb P cyo than in moving 

 through cya A dQ=, but its motion through 

 == P Of) is more rapid than its motion 

 through op A =Q= ; and, as the swiftness of 

 the motion and the quantity of heat received 

 vary in the same proportion, a compensation 

 takes place. 



w NOTE 145, p. 76. In an ellipsoid of revol it- 



