III. 



Instrumental Corrections. 



The first step towards turning the foregoing measures into 

 right ascensions and declinations will be to apply the following 

 instrumental corrections, which are here considered in the order 

 of their application. 



i° Division Errors of the Scale. 



Just before beginning the measurement of the Prsesepe plates 

 a thorough examination of the division errors of the scale was 

 completed. The details of this investigation together with the 

 determinations of other constants of the measuring machine are 

 reserved for another publication from this observatory. It will 

 suffice for present purposes to set down merely the final results. 



Previous to the above investigation the scale had also been ex- 

 amined by the Kaiserliche Normal Aichungs Kommission at Ber- 

 lin ; the results of this determination were published in the "An- 

 nals of the New York Academjr of Sciences," Yol. IX, page 206. 

 The two determinations agree quite well, the largest difference 

 for anjr line being o/'n, and usually the agreement is much closer. 

 As the investigation at Columbia was made with the same micro- 

 scope and under the same conditions in which the plates were 

 measured, it was thought Tbest to use only our own results, as 

 given in Table I Y. The coordinates of a star depend upon several 

 divisions for one plate, and the same star usually comes opposite 

 different divisons for different plates. It follows therefore that 

 our final positions will be nearly independent of inaccuracies in 

 the determination of the division errors ; for example, the right 

 ascension of Star i depends upon eighteen different lines of the 

 scale and its declination depends upon thirteen. In Table IY 

 the corrections are given in millimetres, and are always to be 

 added to observed readings. 



2° Corrections for Buns and Screw Errors. 



The screw used in the measurements is of such a pitch that two 

 complete turns of the micrometer head correspond to one space 

 on the scale; the micrometer head is divided into one hundred 

 equal parts and may therefore be read directly to half-microns 



216 



