16 













Residual 













error. 











II 



II 



1 



= — 0.303 X 



X — 2.700 X 



y -\- 0.333 X 



z + 3.88 



— 0.08 



2 



= + 3.016 



— 3.000 



+ 1 



+ 1.00 



, + 0.49 



3 



= -I- 3..S63 



— 2.400 



+ 1 



— 0.27 



+ 0.19 



4 



= + 3.685 



— 1.800 



+ 1 



— 1.10 



+ 0.22 



5 



= + 4.038 



— 1.000 



+ 1 



— 3.07 



— 1.03 



6 



= + 4.268 



— 0.200 



+ 1 



— 4.12 



— 1.31 



7 



= _i_ 4.594 



+ 1.267 



+ 1 



— 2.44 



+ 1.03 



8 



= + 4.248 



+ 3.950 



+ 1 



— 1.73 



— 0.13 



9 



= + 3.332 



+ 6.133 



+ 1 



+ 1.81 



— 0.16 



Whence the three normal equations, 



= 118.879 X a; + 7.477 X y + 30.443 X z — 45".629 

 0= 7.477 +85.149 + 0.250 + 1".6S7 



0= 30.443 + 0.250 + 8.111 — 8".627 



and — 



a; = + 3".255712 , r = 29".939950 + 

 y = — 0". 272963 , v = ^^^ 



50 



= 30". 005064 



21".65789 



11". 1475 , « = rt + D Sept. 28, 1846= 326° 59' 34". 74 



The values of > and 7t-\-v are the result of a new computation with the new 

 radius vector, 30.005064. The sum of the squares of the errors in longitude of 

 Disturbed Elements I for the 9 equations is 55".96. The sum of the similar 

 quantities for the Disturbed Elements II, is 4".'il, which is the sum of the 

 squares of 9 errors, each comprising the united error of theory and observation. 



In my paper on meteors, in the Memoirs of the American Philosophical So- 

 ciety, are found the well known equations — 



II. 

 III. 



VGauss 



' k) 



e r cos V ■= a cos° f — r=a(l — e°) — r 



In which g is the true angular velocity, in units, of the earth's mean angular 

 velocity. Equation II, by means of r and n in Elements II, gives a= 30.200585. 

 Equation III, gives the value of u for any assumed value of the eccentricity e. 

 It is of the second degree, and gives the value of ^ either in the first or fourth 

 quadrant. It is not possible, from the process above pursued, to decide between 

 the two quadrants of u. By hypothesis, the daily variation of r was neglected. 

 Hence it remains uncertain whether the r of Disturbed Elements II, belongs to 

 a value of w, in the first or fourth quadrant. 



