80 



'I'lll'', SAYRE OBSERVATORY. 



The proper value of the micrometer screw has proved a troublesome question, as it 

 has been found to be a variable quantity. 8 Ursae Minoris and 51 Cephei were observed 

 on twenty-three nights during the progress of the work, one star being taken at eastern 

 elongation, preceded or followed, as the ease; might be, by the other at western elongation. 

 As the altitude of one would be increasing and that of the oilier diminishing, the mean 

 result should he practically free from errors due to gradual changes of refraction and 

 others of a like character. A preliminary reduction of the latitude observations showed 

 that no one value of the micrometer screw could harmonize the entire series. Evidently 

 the screw had become worn with long service, and the wearing process was still going on at 

 an appreciable rate. A somewhat roughly determined correction for temperature changes 

 removed a part of the difficulty, but not all. 



On July 25, 1894, the micrometer was sent to Stackpole & Brother, of New York, 

 for repairs, including a change in the tension of the springs. This naturally produced a 

 change of value at this point, but it was constant neither before nor after. Finally, the 

 conclusion was reached that the screw value must he deduced from the latitude observa- 

 tions themselves and be treated as a variable quantity. 



In order to have this method of procedure worthy of confidence, more precise values 

 of the star places were required than those before employed, hence the final reduction was 

 postponed until these became available. 



It was observed that the screw was affected by progressive errors of considerable 

 magnitude. An investigation of this matter had formerly been made; by employing a 

 measuring engine designed by Prof. William Earkness, of the United States Naval 

 Observatory; but the results had ceased to be applicable, probably a consequence of the 

 wearing of the screw before referred to. The corrections here used were derived from 

 the above-mentioned transits of 5 Ursa' Minoris and 51 Cephei. 



Let n be any number of revolutions of the screw reckoned from the middle of the 

 scale, the middle in this case being at the twentieth revolution. 



Let R be the mean value of one revolution. 



If the. errors be uniformly progressive, the space S, corresponding to n, will be of 

 the form : 



8 Hi), -J- /> n' 



For a second readins 



8' — IW -\ p n,' 7 ' 



8 — 8> = R («, — »') +p {ri l 



n' 2 ) 



The transits of the stars in. question wen; always observed for each revolution of the 

 screw from scale readings •">:> to 7. The observed times are first corrected for level 

 changes and for curvature of the stars' path. They are then combined by subtracting 



