52 



MICHIGAN ACADEMY OF SCIENCE. 



In position 2 the microscopes are changed 180° from the first position. 

 Evidently the effect of gravity on the circle is considerable. The division 

 errors are to be added to the actual readings to produce the ideal. 



As to the marks 205^^ Od'. 202° ;i8', eh-., the errors were found by com- 

 paring the spaces 205° 04'-06", etc., with the mean of a good many 2' 

 spaces on the circle, this mean being regarded as the true value of a 2' 

 space. For the required 2' spaces we have then the following values, it 

 being understood that 71° 32'-34' for instance, refers to the mean of the 



four spaces 71° 32'-31' 



161° 32'-34', 251° 32'-34', 341° 32'-34'. 



Space 71° 32'-34' 

 Reduction to 

 mean 2' space. 

 —0.47" 

 —0.50 

 +0.01 

 -0.27 

 —0.07 

 —0 33 

 -0.03 

 —0 45 

 —0.51 

 —0.37 



Space 118° 00-02'. 

 Reduction. 



+0.01" 



+0.16 



—0.18 



—0.24 



+0.08 



—0.03 



Space 120= 28'-3b . 

 Reduction. 



+0.37" 



+0.24 



+0.49 



+0.60 



+0.15 



+0.37 



Mean. 



—0.30 



Space 205° 04-06', 

 Reduction. 



+0.26" 



+0.18 



+0.14 



—0.03 



—0.20 



+0.07 



Space 202° 36'-38' 

 Reduction. 



+0.28" 



+0.24 



-0.06 



—0.60 



—0.10 



—0.05 



Finally, for the errors of the divisions employed in this work 



Division. 



205'^ 04' 

 205 06 



IMean. 



Division. 



118° 00' 

 118 02 



Error. 



— 0.46' 

 —0.53 



—0.50 



Error. 



+0.06' 

 +0.09 



+0.08 



+0.25 



9. — Eccentricity of Fine Circle. 



The eccentricity of the fine circle was determined by pointing on the 

 10° lines, first with microscopes I and III, and then with II and lY, the 

 instrument being clamp east. The readings were made so as to eliminate 

 progressive changes proportional to the time. Thus are obtained the fol- 

 lowing values for O and -^, 2 being the direction of the line joining 

 the center of the circle to the center of revolution, e the distance between 

 the centers, and r the radius of the circle: 



