46 



MICHIGAN ACADEMY OF SCIENCE. 



Taking the mean of the results obtained in the two opposite positions 

 of the circle, we find the following errors : — 



The errors of the lines separated by 5° were determined similarly to 

 those for intervals of 15°, by placing the microscopes on four different 

 days at distances of 85°, 95°, 100° and 110° apart; and thus arcs of 255°, 

 285°, 300° and 330° were each divided into three ecpial parts. Tlie obser- 

 vations commenced successively with the lines 0°, 15°, 30^^. elc and the 

 corrections for the first and last lines of the arc were applied according 

 to the values given above. Thus the error of each line was found on dif- 

 ferent days by comparison with two different lines, so that the small un- 

 certainty remaining in the errors of the lines 15°, 30°, 45°, 60 \ 75°, etc., 

 will have very little influence on the determination of the errors of the 

 lines 5°, 10°, 20°, 25°, 35°, 40°, 50°, 55°, etc. These observations were 

 likewise repeated on four days, with the circle at each time in a position 

 180° distant from the corresponding position in the former series. 



The following table shows the result of all these observations : — 



