192 BIGELOW 



The coefficient of cosine flexure found was i".6g^; and of 

 sine flexure, o".ii7. In the case of clamp west tlie circle read- 

 ings increase from the zenith toward the north and the formula 

 for flexure correction is 



C = ^ + o". 163 — I ."694 cos z -f o". r 1 7 sin z — i ."694 



The large cosine flexure was also found b}' Dr. Hall. (See 

 " Reprint from Report of Michigan Academy of Science," 



1904-) 



Corrections for division errors were not applied. Some 



examination of the circle was made to determine its general 

 character. The mean of the 4 divisions, 0°, 90°, iSo°, 270°, 

 was assumed to be without error. In finding the errors of the 

 intermediate divisions, taking also as a division the mean of 4 

 marks 90° apart, 2 microscope arms were set 100° apart, 110° 

 apart, etc. Readings were then made on a number of 100° 

 spaces, for instance, distributed symmetrically around the cir- 

 cle ; these readings were taken forward and back so as to elim- 

 inate progressive changes in the instrument depending on the 

 time. The mean of these readings was assumed to be the correct 

 100° space and was used for obtaining the error of the 100^ 

 mark on the circle. The microscopes were afterward changed 

 180° from their first position and the process repeated. 



The 2 columns of division errors jriven show the changes 

 produced by placing the microscopes in the two positions. 

 Evidently the effect of gravity is considerable as might be 

 expected from the structure of the circle, which is rather frail. 



