820 



THE SAYKE OBSEKVATOKY. 



The Micrometer. 



The description of the micrometer and reticle found in the publication of results for 

 L894, '95, before referred to, applies equally to the present series. The methods of 

 observing and of determining the intervals of the micrometer threads being the same in 

 both series. 



At various times transits of circumpolar stars near elongation were observed for the 

 purpose of determining the screw value. Of these 51 Cephei and 8 Ursse Minoris were 

 each observed at live elongations; 43 Cephei at twenty, and Groombridge 750 at fifteen 

 elongations respectively. In comparing the results it became obvious that the effect of 

 constant use in wearing the screw was manifest, and that the value should be treated 

 as a variable quantity. 



The method of procedure adopted, as seeming least objectionable, was to derive the 

 screw value from the latitude observations, as will be explained presently. 



The above-mentioned transits of circumpolar stars were employed for investigating 

 the progressive errors, which were increasing with the increased wearing of the screw. 



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

 scale — the middle in this case is revolution 20. 



K the mean value of one revolution. 



The errors being supposed uniformly progressive, the space s corresponding to n will 

 have the form 



For a second reading 



8 = Bn + pn? 



S' = Bn' + pn" 

 8 — 8' = B {n — n') + p (n? — n rl ) 



The transits are observed, from 33 to 7. The observed times arc corrected for 

 change of level and curvature of the stars' path. They are then combined by subtract- 

 ing 33 from 19, 32 from 18, .... 21 from 7, thus obtaining a series of values for the 

 time required for the star to pass over a space equal to fourteen revolutions of the screw. 

 If no progressive or other errors were present these times should be equal. The 

 difference between any individual value and the mean of all is taken as the correction 

 due to the progressive error expressed in seconds of time. This must then be; reduced 

 to the equivalent in screw revolutions. 



In the following tabular statement is found the mean values of these differences, 

 those for 51 Cephei being reduced to the scale of h Ursa; Minoris and those for 43 

 Cephei to Groombridge 750. 



