1S4 



EOGERS AND McLEOI) ON THE 



Equations between 8«, Sc, SaT" for Solution by Least Squakes. 



In order that the results derived from the various methods of solution described 

 may be compared, the fundamental equations, both without and with weights, and 

 the resultino; normal equations for each date are given on the following- pages. The 

 final equation involving SA7'is also given. In the second set of equations given for 

 each date, the value of c adopted in the previous solution is considered as a constant, 



or §c = 0. 



June 1, 1883. 



FUXDAMENTAL EQUATIONS. 



Circle ] 

 East. ] 



Circle ( 

 West, 'i 



+ 7.8 

 +70.4 

 +85.6 L. c. 



-10..5 

 +33.2 

 +73.0 



Without weight.^. 



= +0^020 + 0..57S(( + l.OlSc -tSaT 

 -0.230 - 1.40Sr( + S.OÎiSc +5a7' 

 -0.020 +10..3s3S(( -13.13SC +5A7' 



- +0.010 + 0.81S'( 

 -0.020 + O.lSSft 

 +0.010 - 1.748(1 



1.025c +SAT 

 1.205f' +5Ar 

 3.42Sc- +SaT 



With wti-rhtR. 



= +6!028 +0 80Sr( +1.41SC +1.40SAr 



-0.138 -0.815» +1.79SC +0.605A7' 



-0.002 + 1.045a -1.315c +0.105Ar 



= +0.010 +0.815rt -1.025c +1.O05AÏ' 



-0.028 +0.2.55i( -1.685c +1.405Ar 



+0.024 -1.045(1 -2.055c +0.G05Ar 



Normal Equations. 



Assiinie: ATo = -14". 970 ; c^ = +a200 ; (/„ = +6.380. 



= +0.060 

 -0.540 

 -0.200 



Without wci^lits. 



+113.415(( 



-1.34.r)15ri 



+ 8.775(e 



= - 132 



C. E. andC W. 



-134.615c 

 + 190.54SC 

 - 14.775c 

 +2.437SAr 



+ 8.77SAr 

 -14.775Ar 

 + 6.005Ar 



5Ar = +0.0.54; 5c = +0.017 



5(( = +0.015. 



Witll wtighta. C. 1Î and 0. W. 



+0.112 

 -0.217 



-0.0.50 







+4.236(/ 



-0.855(1 



+1.2()5(( 



= +0.0055 



- 0.855c 

 +14.975C 



- 1.6S15C 

 -0.20415Ar 



M 2C5A7' 



-i.fiosAr 



|5n55A7' 



SAT = -0.0208; 5c = +0.0154; 5(i = -0.025. 



With weights. 



+0'.13G +2.435(1 



-0.205 -1.735(1 



-0.044 +0.72Sn 



= +0.0033 



5Ar = +0 224; 



Sc 



C. E. only. 



-1.735c 

 +6.915C 

 +2.91 5c 

 -0.01475Ar . 



-6.114 ; 5(1 



+0.725Ar 

 +2.91 5Ar 

 +2.-335 AT 



: -6.201. 



With weights. C. ^V. only. 



= -0.024 +1.805(1 +0.885C +0.545Ar 



-0.012 +0.885(1 +8.0C5C -4.f,0SA7' 



-0.015 +0.515(1 -4.G05C +3.325Ay' 



= -0.00071 -1.28105Ar 



.■î. .S-. .^■ 



5Ar = -0.0005 ; 5c - +0.0004 ; 5» = +0.0133. 



Solution for Sc = 0. 



Without weights. C. E. and 0. W. 



= -0.024 +0.6075ir 



.<;. .<:. s. 



5Ar = +0.040; 5c = O.OOO ; 5(t = -0.004. 



With weights. C. E. and C. W. 

 = -0.0733 +4.422G5Ar 



5Ar = +0.0161; 



0.000 ; 



8(1 = -0.027. 



With weights. C. E. only. 



= -0.1171 +2.9398SAr 

 s. .<. s- 



8Ar = +0.040 ; 5c = 0.000 ; 5(i = -0.067. 



With wciglits. C. W. only. 

 = +0 0145 -5.8481 5A 7' 



SAT = +0.0025 ; 5c = 6!000 ; 8(( 



+0.0132. 



