FINAL SOLUTION. 



cclxxv 



13.-FINAL SOLUTION. 



For the attainment of our ultimate results, nothing now remains but the reconstruction of the 

 normal equations, by multiplying them severally by their weights as deduced in the last section, 

 discarding those series which are clearly incapable of increasing the precision of the values 

 sought, and summing the others thus multiplied. The solution of the resultant equations will 

 afford the best values of the unknown quantities which we are entitled to expect. 



The present section contains the multiplied equations for each series, together with their 

 solution and the information thence deduced. 



From the first series of Mars- observations the Athens group is excluded, and the remainder 

 furnish equations as follows : 



MARS I. 



Normal Equations multiplied ~by their weights. 



We hence obtain 



z = 



1&quot;.6688 0&quot;.0938 

 -f 2&quot;.S7550&quot;.0378 

 + 1&quot;. 5885 0&quot;. 0805 



0&quot;.0762 0&quot;.0621 



and, consequently, 



in which P 1 denotes the weight, expressed in terms of the unit used for P. 



