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the effects of parallax, &c. of certain fixed, stars. 
December 1 6 , 1818, and December 28, 1820, must have been 
occasioned by the irregularities of refraction, as the respective 
observations of each day, in both positions of the face of the 
circle, are very consistent with one another. The same 
remark may be made as to the observations of August 17, 
1819, and of September 6 , 1820, &c. &c. 
An illustration of the method of observing, See. is given 
from y and /3 Aquilae in Tables 9 and 10. 
The earlier observations of these stars were made on the 
meridian, and then the mean of the three microscopes, the 
refraction, and the mean zenith distance, January 1, 1819, as 
deduced from each observation, are given. Afterwards, when 
the observations were made off the meridian, the sidereal 
time elapsed between the observation and the passage over 
the meridian, is also given. The coefficients of x and p for 
each observation are also given. 
In regard to the reductions of the observed zenith distance 
to the mean zenith distance : the precessions in N. P. D. 
corrected for proper motion, as given in the Nautical Almanac, 
were used. These annual variations agree so nearly with 
the annual variations deduced by using Mr. Bessel's pre- 
cessions, and the proper motions deduced by a comparison of 
Mr. Bessel's results from Dr. Bradley's observations with 
the modern observations, that no inexactness can arise on 
this account. 
The equation, in polar distance, used for lunar nutation 
was — 8", 28 Sin (TL — 8 ) — 1", 22 Sin (iR-}- 8 ) 
By a comparison of my observations of certain stars made 
1809, 1814, and those made lately, I find this equation of 
lunar nutation — 8", 06 Sin ( Tl — S3 ) — 1", 19 Sin (iR -{- 8 ) 
