Marine Collimating-Compass 



187 



Let t/, i/^, i/", and v^^ be the most probable corrections to the independently 

 observed values Aa, Acw, Acn, and A„, respectively, of the scale constants. Placing 



A„ - A„ -R' = n' 

 the equations of condition are 



Aa, — Acu — a 



II 



JI 



A^-A^- R'" = n 



jii 



^'i _ yii + n" = 



v" -r/ + 



J II 



= 



Assigning to A^ one-half the weight of the others, since "scale east" for this particular 

 instrument is sUghtly out of focus, the adjustment gives 



= +0 . 143 n' +0 .429 n" +0 . 714 n"' 

 = +0 . 143 n' +0 .429 n" -0 . 286 n'" 



i/" =+0. 143 ?i^ -0.571 n" -0.286 n"^ 

 v'^ = -0.857 n' -0.571 n" -0.286 n"^ 



The numerical coefficients of n\ n", n"' will always be the same for the above assigned 

 system of weights. 



When equal weights are assigned to the four scales, the adjustment gives 



/ = +0.25 n^ +0.50 n" +0.75 n"^ r"^ = +0.25 n^ -0.50 n^^ -0.25 n"^ 



v" = +0.25 n' +0.50 n" -0.25 n"^ v^^ = -0.75 n^ -0.50 n'' -0.25 n"' 



which are the most probable corrections to the observed values of A^, Acu,, A„, and Ac, 

 on this assumption. 



In Table 49 are tabulated the observed values of Ac during the first and second cruises 

 of the Carnegie and the adjusted values resulting from taking R^ = 90?209, R" = 89?601 , 

 R"' =90?339, and R'' =89?850. These values of R', R" , R'", and R''' were determined 

 at Rio de Janeiro in December 1910, and at Antipolo in February 1912, by using two 

 theodolites. From October 1910 to January 28, 1914, the observers drummed the instru- 

 ment lightly with the fingers, to overcome the frictional resistance of the pivot. 



Table 49. — -Observed and Adjusted Values of Ac- 



'Rejected in mean because of weak statioa-diSerence. 



'Observed value of G scale rejected. 



