-+- 2.9052 .\ -+- 2.8490 1 -+- 0.2745 = o 

 -+- 2.8490 -+- 2.8292 + 0.2601 = o 



Here again the similarity in coefficients denoted un- 

 certainty in the solution, but as 1' aiipeared to be the more 

 uncertain of the two, x' was expressed in terms of 1' giving 

 (logarithmic coefficients) : 



.v' = 9.99i52„.i'' -H 8.97S44u (D) 



This value for a' substituted into the equations of 

 condition for .v' and v' gave the following series for the 

 determination of j'' (numerical coefficients): 



Check 



'] = 0.1569 



[""■S\ = 0-1570 l" 

 A new unknown y" was introduced such that 

 loj'i'. = >' 

 and the series solved for r" giving 



logj" = 8.40572 



whence 



log.!'' == 9.40572 



The residuals for the normal place.s were found by 

 substituting v' into the above equations of condition. When 

 squared and added 



[?'?'] == 0.1547 



100 



while from the elimination, as a check, 



[;/;/. 6] == 0.1546 



Then by successive substitution of r' into (D), of .v' 

 and 1 ' into (C), and finally of v and y into (B) the most 

 probable values of the unknowns were found to be 



log -v = 1.0167,, 

 logj = 1.6457 

 log= = 1-4584 



log/ = 1. 1 509,1 

 log // = 8.8806 



log 7c' = 9-3244 



Restoring the original unknowns by (A) and reintro- 

 ducing the second of arc as the unit of measurement the 

 following corrections to the elements chosen for the cal- 

 culation were obtained. 



log dtp = 1.9009,, 

 log dX = 9.6306 

 log dj' = 0.1 744 



o) and Qj were derived frotr 



log dx = 1.7967,, 

 logdil/o = 1.7557 

 log d(i = 9.9284 



The corrections to / 

 <ix, dX and dj' by 



d/ ;^ cos at di> -h sin w d^ 



sin i dO, = sin w dt' — cos m dX 



d (Q, -i- w) = dx -+- tg V2 / sin / dU 



d (,Q — m) = — dx -t- ctg '/j / sin / dQ, 



As thus determined the final corrections to Chandler's 

 elements are 



d^/o 



■57-0 



d/i =■ -i-o'.'8479 

 dcp = — 7 9'.'6 

 d/ = -t-o'.'3 



dsi = — 29:'5 



djt = —6 2" 7 



do3 = — 33''2 



dZ = -5'.'7 



whence the definitive osculating elements: 



Epoch 1894 Dec 



iI/„ = 



a 

 ft 



1,0. Osculation 1894 Dec. 10. o. 



8° 22' 58'.'2 + 4'.'2 



345 23 II. I + 4-4 



48 48 23.4 ±27.7 



2 57 558 + 1.4 



34 51 37-3 ± 7-« 

 6o5'.'9999 +o'.'o665 



1900.0 



The ajipended ([uantities are the mean errors an( 



are based upon the standard value for a single observatioi 



of unit weight 



£„ = ±2 ■.■8 



computed I'rom the residuals of the equations of condition 

 To test the accuracy of the least square solution thi 

 definitive corrections were substituted into the origina 

 equations of condition ; the resulting residuals were squared 

 multiplied by the proper weight, and added with the resul 



[rr] = 54'.'o 



The value of [//;/- 6] from the least square solutioi 

 was 0.1546. Expressed in seconds of arc 



[""■6] = 53:'6 



