DECLINATIONS OF CERTAIN NORTH POLAR STARS I9I 



were obtained by turnino- the telescope over a mercury basin 

 and observing the reflection of the horizontal threads by means 

 of a collimating eye-piece. Four settings were made, the 

 mercur}' basin being turned iSo° in the middle of the set. 

 When successive nadirs differed by more than o".50' ^^ was 

 assumed that the difference was directly proportional to the 

 time ; when the difference was less than o". 50 the straight mean 

 was taken. Occasionally during observations for nadir the 

 instrument seemed to move after a setting had been made, 

 showing either that it was under a strain, or possibly that the 

 surface of the mercury changed slightly. 



The plan was to obtain for each star, both at upper and 

 lower culminations, 2 observations in each of the four following 

 positions: clamp west, direct; clamp west, reflected; clamp 

 east, direct ; clamp east, reflected. This plan was not entirely 

 carried out as the tables show, in part due to the difficulty in 

 obtaining reflected observations. These were often prevented 

 by wind or unsteady seeing. Often, too, reflected observations 

 were prevented by trains on the Michigan Central Railroad, 

 and sometimes by the shutting of a door in another part of the 

 building. Nevertheless, nearly as many reflected observations 

 were obtained as direct. They seem to be quite as consistent 

 among themselves as the direct ; perhaps they are in a sense 

 selected observations. Each night's observing list included at 

 least one of the Berliner Jahrbuch stars. 



Advantage in combining reflected and direct observations is 

 found in the fact that different sets of divisions on the circle are 

 employed, thus largely eliminating division errors, and in the 

 fact that the sign of the sine flexure is reversed. In the mean 

 of the 4 positions : W. D. ; W. R. ; E. D. ; E. R. ; the first 2 

 terms of the cosine flexure and the first term of the sine flexure 

 are eliminated. 



To determine the amount of the flexure the following for- 

 mulas were employed : 



W. D. ■: = z^ + a' cos z + l>' sin z — (iSo° + iV) + a' 



W. R. (iSo° — ':)=z^ — a' cos z + 6' sin z— (180° -f ^) + «' 

 E. D. (360° — :) =z.^ + a' cos z — d' sin z — ( iSo° + JV) -{- a' 

 E. R. (iSo° + :) =z^ — a' cos z — d' sin z — (iSo° + A^) + a' 



