HALL, ABIlRRATIO.V CONSTANT. 59 



tions, we obtain for the probable error of tlie eorrespondiug zenith dis- 

 tance ± 0.24:". This ((uantity is to be combined with the probable erroj- of 

 the refraction tables, wliich for Polaris may be taken asiCS''. So that 

 for one observation of 7 pointinj?s the total probable error is ± 0.38". 



Tn ordinary observations the nncertainty of the division marks should 

 be included as well as that of the flexure. 



/7. — Observations of Polaris. 



At first the conditions imposed on the observations were too severe. I 

 attempted to obtain always successive culminations, and at each culmina- 

 tion both direct and reflected observations. On account of the Aveather 

 and duties of instruction it was necessary to give up the idea of observing 

 only successive culminations, and being for most of the time without a 

 recorder T could not make observations both direct and reflected without 

 working rather near to the edge of the field. 



Since the direct observations above and below x)ole extend over about 

 the same periods of time, the latitude variation will be eliminated from 

 the determination of the aberration constant, as well as other disturb- 

 ances of a like nature, including changes in the flexure. 



It is planned to take more of these observations and with some assist- 

 ance the necessar}' frequent reversals could be made, in order to determine 

 the latitude variation with accuracy. 



The following are the observations of Polaris corrected for refraction 

 and reduced to the meridian. For each observation seven pointings were 

 usually taken, though sometimes five or nine. However, each observation 

 has been given the same weight. 



For reduction to the meridian has been used the expression 



sin 5 1/2 (T— m) 



sin 2 6. 



sin 1" 



In this, 8 is the apparent declination as taken from the ephemeris, and 

 the single term is sufficient. 



All the declinations of Polaris have been taken from the Berliner 

 Jahrbuch. An account of the terms included in the computation of ap- 

 parent jilaces is given in the Jahrbuch for 1884. 



The reduction to 1900.0 is given in order that the observations may be 

 comx)ared among 'themselves. 



The nadirs for any observations were interpolated when they differed 

 more than 0.3". 



The images and steadiness are marked on the scale 1-5, 1 being perfect. 



