270 



CATALOGUE OF POLAR STARS. 



a 



Simplifying this equation, we have : 



1.40361 — + 0.53090 — 



0.07105 — + 0.0038194 - 



to 



w 



w 



10 



8 



0.00000944— +0.0000019290 — 



to 



10 



w 



12 



(53) 



[0.16543/*] -^- + [9.72501] — + [8.85156*] — + [7.58200] — + [5.84164;;] — + [4.285341 — . 



W 2 10* W 6 tV* W 10 M? 12 



From equation (53) we derive the following numerical values of the effect 



of the error x for w 



1, w 



8, w 



10, w 



30, and w = 40 : 



to 



1 



w 



1 



w 



8 



to 



8 



IT* 



U 



IV 



u x 



IT 

 U 



u 



VIII 



X 



XII 



-1.4636* 



+ 0.53090a; 

 -0.071049* 



Logarithms. 



[0.16543n]* 



[0.72501]* 



[8.8515Cm> 



• • 



0.022869a; 

 + 0.00012961a; 



0.00000027103a; 

 + 0.00000000022700* 



0.000000000000*064676* 

 + 0.000000000000000028071a; 



Logarithms. 



[8.35925w> 



[6.11264> 



[3.43302»> 



[0.35729]* 



[6\81074»]* 



[3.44820]* 



to 



16 



w 



16 



to 



30 



w 



40 



r n 



U 



IV 



I 



u 



u 



'VI 



VIII 



X 



u xn 



-0.0057173a; 

 + 0.0000081009* 



0.0000000042349a; 

 + 0.00000000000088929* 



0.00( 1000000000000063160a- 



Logarithms. 



[7.75719/>]* 



[4.90853]* 



[1.62684n> 



[7.94904]* 



[3.80044n> 



+ 0.0000000000000000000068534* [9.83591]* 



Logarithms. 



[7.21119w]* 



[3.81C53> 

 [9.98883?*]* 



[5.76503]* 

 [1.07043™]* 



[6.55989]* 



Logarithms. 



[6.96131n]* 



[3.31677]* 

 [S.23920»> 



[4.76552]* 



[9.82104??]* 



[5.06062]* 



We illustrate the computation by assuming 



X 



one unit in the third decimal place of « for 1875.0 



Then, 



assuming 



t 

 t 



t 



t 



t 



t 



t 



10 for to 



40 for v 



40 for ir 



100 for to 



120 for to 



120 for to 



120 for w 



1 



8 

 16 



16 

 16 

 30 



40 



we have for the total effect € of the error x 



