176 THE ORBIT OF URANUS. 



The solution of these equations gives 



j$ = -j- 0".28 + 0".75 a = + 0".54 

 $30 = + 1 .57 + .686a + .2056 = -j- 1".75 

 a = + .35 

 b = 0.28 



These values of a and b indicate that at the epoch 1840 Auwers' equatorial 

 declinations are too great, or his north polar distances are too small by 0".35, and 

 that this error is diminishing at the rate of 0".28 per century. If the older measures 

 in declination had been comparable in precision with those made at the present 

 time, and if the possible periodic error in the reduced right ascensions had been 

 carefully eliminated, I should regard this determination as entitled to considerable 

 weight. In view of the great uncertainty of the declinations previous to 1820, it 

 can be regarded as little more than a rough attempt at a determination. For this 

 reason the first two normal equations have been solved, leaving a and b indeter- 

 minate, so as to show the valves of 5$ and $<50 in terms of these quantities. It 

 will be seen that had we neglected a and b entirely, the value of 5$ would have 

 been smaller by 0". 26, and that of $0 smaller by 0".18 than those actually con- 

 cluded. As the observations with the Washington Transit Circle, and those with 

 the Pulkowa Vertical Circle, both indicate an increase of Auwers' polar distances, 

 I shall take for the definitive corrections to the inclination and node those which 

 follow from the above values of a and Z>, or, 



fy = + 0".54 

 $30 = + 1 .75. 



The following table shows the residuals of the equations, and the mean out- 

 standing corrections to the latitude, (1) when the concluded values of 3$ and q>&0 

 a and b are all used, and (2) when a and b are supposed zero, and the values of 

 <5$ and $60, corresponding to this supposition, are used: 



Tear. Residuals. 5/3 



0) ( 2 ) (1) (2) 



" // ii n 



1783 -0.8 -0.3 0.8 0.3 



1789 +1.2 +1.8 +1.2 +1.8 



1793 +0.7 +1.1 +1.4 +2.2 



1796 +0.3 +0-6 +0.6 +1.2 



1801 0.5 +0.3 0.5 +0.3 



1806 1.2 0.5 1.2 0.5 



1809 +0.5 +1.2 +0.5 +1.2 



1812 +0.9 +1.6 +0.9 +1.6 



1815 0.3 +0.6 0.2 +0.4 



1818 +1.6 +2.5 +1.1 +1.7 



1821 -0.7 -0.1 -0.5 -0.1 



1824 -1.3 -0.7 -1.3 -0.7 



1827 0.6 0.3 0.6 -0.3 



