Methods of Astronomical Observation. 187 



seconds, n the number of observations, and I their effect 

 when applied to the zenith distance. 



^ = '^^' («) 



The sign must be changed when applied to the altitude. 



III. When three or more verniers are applied to a circle, 

 and the observations are repeated and read each time, the 

 mean result will be readily determined by the following 

 formula in which S r is the sum of the readings of all the 

 verniers or microscopes, n the number of observations, 

 V the number of vierniers, and m the mean value of the 

 whole. 



m = ^ (7) 



nv 



These formulae will apply with ease and certainty to any 

 case likely to occur in practice, and are more simple than 

 any I have seen. 



IV. The case to which they are now to be applied is one 

 of a series of observations made by a small circle of Captain 

 Kater's construction, to determine the obliquity of the 

 ecliptic at the late summer solstice, at Edinburgh, in 

 latitude 55° 57' 15"-67 N. 



It may seem to be an attempt much beyond the powers 

 of so small an instrument, one of six inches diameter, fur- 

 nished with three verniers, each showing 15" and a level, 

 indicating by each division only to the accuracy of b'-b. 

 Yet, the correctness of the final result, which differs from 

 Bessel's by about 2'^, and from mine, obtained by a com- 

 parison of the late observations made at Greenwich, with 

 those of Bradley, reduced with the best tables by 1"^, 

 shows how much may be accomplished with moderate 

 means. With what pleasure would modern astronomers 

 have contemplated the observations of Hipparchus and 

 Ptolemy had they been made with such precision ! 



To determine the obliquity of the ecliptic in the most 

 accurate manner, the sun's declination (daily if possible), 

 near the solstices, must, it is well known, be observed 

 carefully for some time, and the results, by means of 

 appropriate formulae or tables, are reduced correctly to the 

 moment of the solstice computed from the best solar tables, 

 or obtained from corresponding observations. 



