PRELIMINARY SOLUTIONS. 



cclxxi 



MARS I. 



Normal Equations. 



The solution of the equations derived from the last column gave results so extremely discord- 

 ant from the approximate values already known, that it was found necessary to subject the 

 several individual systems to a preliminary scrutiny, and to deduce their approximate weights 

 by means of equations depending on the equatorial comparisons alone. The three series of 

 meridian observations being provisionally omitted from the sum total, the solution afforded the 

 following values for the unknown quantities and mean errors : 



y = 



z = 



w = 



1".5373 =fc 0".0896 

 + 2".89YO 0".0626 

 + 1".4334 0".1021 



0".1402 0''.0619 



The source of the discordance is thus immediately manifest ; and it is evident that in the 

 new solution the Athens observations may be advantageously omitted. 



The order of the mean errors thus deduced for the two other meridian series being not essen- 

 tially different from that of those derived from star-comparisons, and used for this last solution, 

 the weights given above are clearly still applicable to their respective system of equations, and 

 were adopted. 



