44 



MICHIGAN ACADEMY OF SCIENCE. 



The mean errors of the seven lines, resulting from the two series of 

 observations, are therefore: — 



Error.. 



315° 



-0.48' 



In order to find the errors of the intermediate lines for intervals of 15°, 

 I placed two microscopes exactly 105° apart: by means of these positions 

 I divided arcs of 315° into three equal parts, beginning successively with 

 the lines 0°, 45°, 90°, etc., and applying always the corrections for the 

 seven principal lines found before. These observations were made on four 

 days in one position of the circle, and on four other days in positions 

 always 180° different. The same errors were found also by another series, 

 with two microscopes placed 75° apart, arcs of 225° being divided into 

 three equal parts: these observation ere likewise made on four days, and 

 repeated on four other days in positions of the circle which differed always 

 180° from those in the former series. The following tables show the re- 

 sults found for the different errors on the different days: — 



MICROSCOPES 105° APART. 



CIRCLE 180° FROM ITS FIRST POSITIONS. 



