OF ARTS AND SCIENCES. 327 



together, leaving the more refined investigation of the necessary- 

 corrections to a hiter date. At first I employed the standard polars 

 between 10° and 20° polar distance more freely than later. 



Whenever stars beyond 10° of the pole were employed to determine 

 n they received a weight of one half, and those between 5° and 10° a 

 weight of three fourths ; those within 5° (of which the Jahrbuch gives 

 daily ephemerides) represented the unit of weight; the probable error 

 of an n corresponding to this unit bus been, in the mean, not far from 

 ±0''020. This probable error, however, does not include the whole 

 of the errors in the .Jahrbuch places, but is somewhat greater than 

 would be given by perfect standard right ascensions reduced to my 

 method of observing. Omitting those stars beyond 10° of polar dis- 

 tance, for which I have no great number of observations, and elimi- 

 nating errors of star places and personal equation, but making no 

 distinction between observations in different positions of the instru- 

 ment, I obtain ±0^018 for the probable error of a transit, weight 

 = 1. This includes a fair average of the earlier, less precise obser- 

 vations. 



In the tables which follow are given the separate results for each 

 night, as they were derived from the immediate reduction. The calcu- 

 lations were not, strictly speaking, duplicated; but a course was pur- 

 sued which teft very little chance of error. The first thing to be 

 noted is, that only those stars were reduced which have been four or 

 more times observed between July, 1882, and December, 1883. It is 

 intended to observe each star's right ascension eight times, in two 

 different positions ; and to double or quadruple this number for the 

 more important polars. 



All stars within 10° of the pole brighter than the magnitude 7.5 

 (Durchmusteruiig), all in the same region which are fainter but im- 

 portant from proper motion, and all others, wherever situated, which 

 I can find to have been anywhere used as standar-d northern polars, 

 are included in the working list. Each siich star might be observed 

 in eight positions, as the instrument is reversible, and its object-glass 

 and eyepiece interchangeable, if we included observations below the 

 pole. Two of these positions, four observations in each, will suffice 

 for the majority of stars; four positions, for the stars of Professor 

 Albrecht's catalogue, prepared for the European geodetic association -, 

 while the eiglit positions, or 32 observations, will be adopted for stars 

 within 10° of polar distance whose places are given in the ephemerides. 

 The more important standard polars of the Jahrbuch will not be defini- 

 tively determined until the mark is permanently set up : at present 



