406 



Determination of the Errors of Division 



[Aug. 



In this case to find the true angle subtended by the pairs of cross 

 lines, it is necessary to apply to the mean of A and B the errors al- 

 ready found above for 0° and 180° and for 90°, and 270° and then to 

 interpolate between these corrected readings : from the mean of ten 

 measures in this way the errors come out as follows : 



Error of division. 



At and 180 0.00 This assumed = 0. 



30 210 —0.26 



60 240 —1.00 



90 270 —0.45 found above. 



120 300 —1.57 



150 330 —2.15 



180 360 —0.03 found above. 



To ascertain the error of division at the points intermediate between 

 0° and 30° and between 30° and 60°, &c. I placed the 42-inch telescope 

 by Dollond (already spoken of as the upper telescope) so near to the 

 lower telescope, that the images of the pairs of cross- wires subtended 

 an angle of five degrees nearly, and in a manner similar to that explain- 

 ed above, made the following measures of the angle : 









Mean of 



Mean of 



Microscope A. 



B. 



A and B. 



Pairs. 



o ' 



// 



// 



it 



/, 







0.0 



1.0 



0.50 



1.10 



5 



1.3 



1.2 



1.25 



2.42 



10 



3.0 



3.0 



3.00 



4 85 



15 



6.9 



7.1 



7.00 



8.12 



20 



8.2 



110 



9.60 



10.32 



25 



10.8 



14.0 



12.40 



12.47 



30 



15.1 



14.6 



14.85 



14.85 



25 



11.9 



13.2 



12.55 





20 



9.8 



12.3 



11.05 





15 



9.1 



9.4 



9.25 





10 



6.1 



7.3 



6.70 





5 



3.5 



3.7 



3.60 









1.1 



2.3 



1.70 





True angle. 



Interpolat- 



Error of 





ed. 



division. 



// // 



// 



it 



15.11—1.10 



1.10 



0.00 



6 



3.44 



—1.02 





5.78 



—0.93 





8,11 



+0.01 



// 



10.45 



—0.13 



=2.335 



12.78 

 15.11 



—0.32 

 —0.26 



The above differs from the preceding only that I have here return- 

 ed back to the point of departure in an inverse order, instead of again 

 beginning at 0° 0'. 



In a similar manner the following five series were obtained. 



Microscope A, 



30 

 35 

 40 

 45 

 50 

 55 



0.0 

 3.5 

 6.6 

 9.5 

 12.3 

 14.7 



B. 



Mean of 



Mean of 



A and B. 



Pairs. 



ii 



a 



a 



59.8 



59.90 



0.17 



5.3 



4.40 



4.25 



8.7 



7.65 



7.65 



10.7 



10.10 



10.05 



14.5 



13.40 



13.40 



16.9 



15.80 



15.30 



True angle, 



Interpolat- 

 ed. 



=3.705 



0.43 



3.63 



6.84 



10.04 



13.24 



16.45 



Error of 

 division. 



—0.26 

 +0.62 

 +0.81 

 +0.01 

 +0.16 

 —1.15 



