248 DETERMINATION OF AN ORBIT FROM FOUR OBSERVATIONS. [BoOK II. 



True anomaly for the first place 293 33 43&quot;.7 



True anomaly for the fourth place 343 54 50 .2 



Hence the longitude of the perihelion 249 57 6 .5 



Mean anomaly for the first place 302 33 32 .6 



Mean anomaly for the fourth place 346 32 25 .2 



Mean daily sidereal motion 978&quot;.7216 



Mean anomaly for the beginning of the year 1807 . 278 13 39 .1 



Mean longitude for the same epoch 168 10 45 .6 



Angle of eccentricity y 5 2 58 .1 



Logarithm of the semi-axis major 0.372898 



If the geocentric places of the planet are computed from these elements 

 for the corrected times t, t , t&quot;, t&quot; , the four longitudes agree with a, a , a&quot;, a &quot;, and 

 the two intermediate latitudes with ft , ft&quot;, to the tenth of a second ; but the 

 extreme latitudes come out 12 26 43&quot;.7 and 4 20 40&quot;.l. The former in error 

 22&quot;.4 in defect, the latter 18&quot;.5 in excess. But yet, if the inclination of the 

 orbit is only increased 6&quot;, and the longitude of the node is diminished 4 40&quot;, the 

 other elements remaining the same, the errors distributed among all the latitudes 

 will be reduced to a few seconds, and the longitudes will only be affected by the 

 smallest errors, which will themselves be almost reduced to nothing, if, in addition. 

 2&quot; is taken from the epoch of the longitude. 



