DEPARTMENT OF MERIDIAN ASTROMETRY. 193 



but the circle reading at the pole can be formed only from the circle readings 

 on one and the same circumpolar star at both culminations. Because of 

 personal error, the same observer should observe both successive culminations. 



For right-ascensions we also need to observe time stars 12 hours apart and 

 a certain number of stars at successive transits to give the error and rate of 

 the clock, which is the measuring rod in this coordinate. It would also be 

 a distinct advantage to have groups of time stars 6 hours apart. In declina- 

 tion the measuring-rod is the graduated circle, whose errors can be determined. 



Because of the instability of the instrument, some fixed direction of refer- 

 ence should be had, observable at any time, so that not only the observations 

 of circumpolar stars may be compared, but that the result may be compared 

 with the observations of the other stars whose positions are to be determined. 

 In right-ascension the mire mark is usually taken, in declination the nadir. 

 The only requirement is that the instrument shall be corrected by means of 

 a particular, unchanging position. The nadir is fixed by the earth's unvary- 

 ing attraction, but possible movement in the mire mark must be investigated. 



The above is very elementary theory. Observations are subject to a variety 

 of errors. Because the fundamental determinations necessarily hinge upon a 

 pair of observations made 12 hours apart, especial attention must be devoted 

 to those sources of error which vary with the daily meteorological rhythm, 

 and this elimination should begin at the earliest practicable stage in the 

 reductions. 



Such are the terms in differential refraction. The mean of the circle read- 

 ings at two culminations is roughly the circle reading at the pole, but it does 

 not correspond to either time of observation, but to a time when differential 

 refraction is nearly zero. Similar considerations apply to the observations in 

 right-ascension. Even if fundamental methods are used, the reduced places 

 will, if these corrections be omitted, contain many anomalies. These anoma- 

 lies are in the San Luis and Albany observations, lying in great blocks, plus 

 and minus, in both right-ascension and declination. If they are left so, a large 

 part of the possible precision is lost, to say nothing of very probable syste- 

 matic errors, due to the fact that evening observations are most numerous. If 

 they are apparently eliminated by breaking the work into short pieces, each 

 of which is corrected separately, they are not really removed; their effect 

 remains, though hidden. Such a proceeding can either change the system of 

 the observations, as approximately reduced, or it can not. If it can not, there 

 is no gain in systematic value; all the errors of a systematic character produced 

 by the uncorrected errors remain. The only effect is to smooth off individual 

 divergences from the preliminary system. On the other hand, if it can, there 

 is still no guaranty that the change is even in the right direction. 



The attempt should be made to link these anomalies to their cause, or to 

 some concomitantly varying effect of the same cause. The differential refrac- 

 tion term does this for a large part of them. It should therefore be included, 

 and at the most appropriate stage in the reductions, which is at the point when 

 the two observations of the circumpolar star are brought together. In the right- 

 ascensions it can be introduced at a somewhat later stage, since the error made 

 in azimuth can be included in the formula. 



