IV. 



Method of Reduction. 



The measured coordinates having been cleared of instrumental 

 errors, it remains to convert them into right ascensions and dec- 

 linations. For this purpose the following constants must be 

 known for each plate: 



1°. The right ascension of the centre of the plate, in this case 

 the central star 15. 



2°. The declination of the same star. 



3°. The scale-value, or the number of seconds corresponding to 

 one space on the scale. 



4°. The orientation correction, or the angle through which we 

 must rotate the coordinate axes in order that they may point 

 respectively in the directions of a parallel of declination and a 

 circle of declination through the central star. 



The first plan that suggested itself for determining these con- 

 stants was to employ the two existing heliometer researches upon 

 the group. In 1856 to 1858 Professor Winnecke of Bonn meas- 

 ured the position angles and distances of forty-four stars from 

 the central star 15 ; and in 1889 to 1892 Professor Schur of Got- 

 tingen triangulated thirty-eight stars and derived the places of 

 seven more by measuring the position angles and distances from 

 stars in the triangulation. The results of both researches were 

 published in one volume by Professor Schur, part IV of the 

 " Astronomische Mittheilungen von der K. Sternwarte zu Gdttin- 

 gen." The stars whose positions are there given include almost 

 all those appearing on the photographs, and consequently very 

 accurate values of the four constants could be obtained by com- 

 paring the measured coordinates of a large number of stars with 

 their heliometer places. Another plan is to determine the con- 

 stants by comparison with meridian observations. While this is 

 not as accurate as the preceding, it has the advantage of being 

 independent of the heliometer results, thus rendering a compari- 

 son with the latter more instructive. 



The course that I have actually pursued is this : the constants 

 were first determined for each plate separately by comparing the 



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