9 
obtained may be examined. For the other stars, the principal 
results are only given. * 
The observed zenith distances are reduced to the mean zenith 
distance, Jan. 1, 1819, by applying the usual equations with the 
contrary sign. 
1, The precession in N. P. D. the annual value of which is—3”,00 
9. The aberration, the constant of which is 20”,25 
3. The solar nutation = 0”,48 sin(2 © Long.—A.R) 
4, The lunar nutation = 8”,28 sin (A.R —9)—1",22 sin 
(AR+ og) 
5. The refraction has been computed by my Table given in vol. 12. 
The sum of these five equations, according to their signs, is called 
the sum of the equations. 
A mean of a considerable number of observations, made through- 
out the year, and reduced to January ], 1819, gives the zenith 
distance = 14°. 41’. 56”, 41. This must be nearly equal to the mean 
zenith distance. 
Let the correct mean zenith distance = 14°. 45’.56”,41—e 
p= semi-parallax 
90,25 +2= constant of aberration 
z— the constant of solar nutation, the coefficient of which is 
above given. 
Hence, if m be the mean zenith distance determined by the ob- 
gervation of any one day, reduced by the sum of four equations, 
omitting the solar nutation, and supposing its quantity unknown, we 
obtain an equation of the form 
m+fr+ gpt+hz = 14°. 45’, 56”,41—e 
or, making m—14’. 45’ 56”, 41=k 
e+fe+ gp+hz+k-0 
We thus obtain an equation of condition for each day. 
VOL. XIV. c 
