214 DETERMINATION OF AN OKBIT FROM [BoOK II. 



We have, therefore, h = 201 20 39&quot;.03, and so Q= I h = 171 7 48&quot;.73 ; fur 

 ther, ff 192 5 50&quot;.21, and hence, since the true anomaly for the first observa 

 tion is found, in article 97, to be 31055 / 29&quot;.64, the distance of perihelion from 

 the ascending node in the orbit, 241 10 20&quot;.57, the longitude of the perihelion 

 52 18 9&quot;.30; lastly, the inclination of the orbit, 13 6 44&quot;.10. If we prefer to 

 proceed to the same calculation from the third place, we have, 



A&quot;D L&quot;= 2418 35&quot;.25 

 i (/ +&quot;)= 196 24 54 .98 

 i (/ _&quot;) = 5 43 14 .81 



Thence are derived 



i(/_[-A&quot;)= 2H24 32&quot;.45 

 i(/_ A&quot;)= 11 43 48 .48 

 i i 633 22 .05 



and hence the longitude of the ascending node, I&quot; h&quot; = 171 7 48&quot;.72, the lon 

 gitude of the perihelion 52 18 9&quot;.30, the inclination of the orbit 13 6 44&quot;.10, 

 just the same as before. 



The interval of time from the last observation to the beginning of the year 

 1805 is 64.614102 days; the mean heliocentric motion corresponding to which is 

 53293&quot;.66 =14 48 13&quot;.66 ; hence the epoch of the mean anomaly at the begin 

 ning of the year 1805 for the meridian of Paris is 349 34 12&quot;.3S, and the epoch 

 of the mean longitude, 41 52 21&quot;.68. 



155. 



That it may be more clearly manifest what is the accuracy of the elements 

 just found, we will compute from them the middle place. For October 17.415011 

 the mean anomaly is found to be 332 28 54&quot;.77, hence the true is 315 1 23&quot;.02 

 and log r&quot;, 0.3259877, (see the examples of articles 13, 14); this true anomaly 

 ought to be equal to the true anomaly in the first observation increased by the 

 angle 2/&quot;, or to the true anomaly in the third observation diminished by the 

 angle 2/, that is, equal to 315 1 22&quot;.98; and the logarithm of the radius vector 

 should be 0.3259878 : the differences are of no consequence. If the calculation 



