HALL, ABERRATION CONSTANT. 57 



For rofractions liessol's tables were used as prepared by Professor J. 

 K. lOastiiiau for Lite Naval Observatory. The tlierniometer was hung near 

 the object glass of the telescope. For daytime observations of Polaris 

 as much as possible of the open slit was covered with canvas, and a large 

 piece of canvas was })ulled up over most of the roof, which is tin, the 

 canvas being sprea<l some time before observing. However, with any 

 such observing room as ours there must be some uncertainty regarding the 

 refraction, but I did not feel like attempting any reduction for the con- 

 dition of the room. I was careful to air it for several hours before 

 working. 



lJ,.—The 'Nadir. 



This was determined over a shallow basin of iron, the concave part, 

 which holds the mercury, being plated with copper. The basin was turned 

 180° in the middle of any series of observations. As stated, all zenith 

 distance settings were made with the tangent screw, there being no 

 micrometer for that cordinate. To observe the nadir it was necessary to 

 run up two small rods connected with Hooke's joints, and supported by 

 large rods held by the microscope arms of the coarse circle. 



A complete determination of the nadir includes four i-ettiugs, two 

 divisions on the circle being read after each setting. All nadir observa- 

 tions were made facing north. For observations of Polaris the nadir was 

 taken immediately before and immediately after the zenith distance point- 

 ings. If it is assumed that the difference between the nadir at the begin- 

 ning and that at the end of a series is due only to accidental errors, we 

 have for the probable error of a complete nadir determination, four 

 pointings, 



± 0.28", 

 and for the mean of two determinations, 



± 0.20". 



The above results for the probable error of a nadir determination are 

 a little larger than is the case with some instruments. The values as 

 given include the error from the circle readings. The microscopes are of 

 low power, about 16. 



The number of observations examined was 77. The mean of each night's 

 nadir was regarded as the true value. Thus two residuals were formed 

 for each observation. Then for the 77 observations [t;y]=133100, the unit 

 being 0.01". 



A smaller probable error for a nadir determination would be found by 

 comparing among themselves the separate nadir pointings. In this way is 

 obtained [vy] =284942, the unit being 0.01". Then for the probable error 

 of a single nadir pointing including the reading of the circle is found the 

 value ± 0.194", the number of single pointings considered being 646. For 

 the mean of four settings, then, or a complete determination of one nadir, 

 is obtained ± 0.10". These smaller values I think are fictitious. 



15. — IncUnatiou of Horizontal Threads. 



The pointings on Polaris were made symmetrically on each side of the 

 meridian so as to eliminate the inclination of the horizontal threads. 

 These are about 5" apart, the object pointed on being placed midway 

 between them. 



8 



