The Reduction of Transit Ohservattons. 193 



m THE EMPLOYMENT OF THE MEfHOD OF LEAST SQUARES 

 m THE REDUCTIOiN OF TRANSIT OBSERVATIONS. 



By Prof. T. H. SAFFORD, Williamstoavn, Mass. 



In longitude work upon the continent of Europe the polar stars employed 

 to find the azimuth and coUination of the transit are usually within a few 

 degrees of the north pole. Each such star gives a value of the azimuth, 

 and three are generally observed each evening, in reversed ijositions of the 

 instrument; while the time-stars are, according to the instructions, twenty 

 or more in number, arranged symmetrically about the polai"s, in such man- 

 ner as to give opportunity for two exchanges of signals. The declinations 

 of these time-stars are arranged at the same zenith distances south, as th, 

 polars are north of the zenith, so as to eliminate pivot-errors. 



This arrangement, for latitudes near 50°, combines the following advan- 

 tages: 



1. The polar stars are slow enough in their apparent motions for a delib 

 erate reversal during each of their transits. 



2. The time-stars are in the declinations most favorable to accurate ob- 

 servation when they are equally distant from the zenith with the polars. 



3. The reduction becomes extremely simple in execution, as the different 

 instrumental corrections are directly determined and equations of condi- 

 tions, to be solved by the method of least squares are not required. 



For the more southern latitudes of Europe, which correspond to those of 

 the northern part of the United States, these three conditions cannot be 

 simultaneously fulfilled. If, for histance, the second condition be insisted 

 upon, the first falls out, for latitude 43", and vice versa. In order to fulfill 

 this second condition the average declination of time stars must be taken at 

 about 20°; and the polar-stars at 66°: which is too far south to accomplish 

 the necessary reversals without hurry during the single transits. 



Certain limitations, however, which are necessary in Europe, are needless 

 in America. For instance, the greater length of the circuits over which 

 very much of our telegrapliic longitude work is done, renders it verj^ diffi- 

 cult to observe the same stars at both stations. As our absolutelj^ definitive 

 reductions are not immediately uecessaiy, the star-places used in any cam- 

 paign can be left open for futui-e improvement; when, for instance, geo- 

 detic measures shall be made over the whole territory. Again, the unsettled 

 country in which much of the work is done renders it necessary for us to 

 IM 



