OBSERVATIONS WITH THE ZENITH TELESCOPE. 



151 



Employing the weights given in the table preceding and solving our equations by 

 the method of correlates, we find the following normal equations: 



.4760*+. 1458*' 1 .1485*" H .1049/,;'"= | .0050 

 .1458* +.8494*' | .1824 



.1485* +.8897*" =—.0510 



.1040* +.2284*"'=— .0806 



From which 



* .1026 



*' = | .5547 



*" .1273 

 *'"=- 



Also 



!®1 = 



.1453(7;- 



•*' ) 





.0071 



l«l 



,1485(* 



ft" )= 





.0330 



i«a 



.1049(7,; 



*'"): 





.0201 



i "i 



.0828 7; 





- — 



.0084 



«', 



.2041 /,;' 







.1153 



»', 



.1402 7;' 





= + 



.0180 



L®'s = - 



-.1185 /,:'" 



= + 



.0105 



Therefore for the corrected differences 



II— I =—.1836 



III- II ! .0078 



IV— III--— .0847 



I- IV = + .2005 



The algebraic sum should, of course, be zero. 

 From these relations 



1= II +.1836 

 III + .1158 



IV + .2005 



Subtracting 0.1250 from each side of our equations in order to make the sum of the 

 corrections zero, we obtain the following values, which must be applied to the lati- 

 tudes derived from the respective; groups in order to reduce all to a homogeneous system : 



1 — 0.125 

 Hi ,0.059 



III -.0.009 



IV+ 0.075 



A. I'. S. — \'<)L. XX. T. 



