AT THE OBSERVATORY AT PARAMATTA. 
33 
= 0, and the reduction to the meridian R = sr A ; but now 
R = a* A + C 
C is too great for a correction whereof the greater part should always be col- 
lected in the first term. 
A = S — S-f-A = S — (S — A); therefore t A = ff S - sr (S — A); and 
R = 7rS — ^(S — A) + ^ (S— • A) + cot A (S— A) sin 1" - cot £ p 2 (S-i) 
=» s - /cot z (S - S) - Scos^+^tM-^Aco^) | (s _ A) sin J» 
L sin 2 J 
omitting cubes and higher powers. 
The last term is almost always insensible, and may be neglected ; and in the 
room of which is unknown, z or the observed zenith distance may be used in 
• 2 sin ~ (z 
the calculation, which together with my having assumed — ~ =*—£=« 
never causes the error to amount to one second of arc in the reduction as long 
as this is not above two degrees. 
Correction of the Hour-angle for change of Equation of Time. 
Biot in his Astronomie, vol. i. p. 451, finds it necessary to correct the hour- 
angle for daily rate of clock, but neglects at the same time a greater source of 
error. In solar observations the observed hour-angle is apparent solar time, 
whilst the interval per clock corrected for sidereal acceleration is mean time, 
and should be diminished in both solstices by a proportional part of the daily 
retardation of apparent solar time upon mean time, given in the Nautical 
Almanac in the column of daily difference of equation of time. This is a 
gaining rate of the clock of 13" in the northern, but of 30" in the southern 
solstice, and more therefore than any clock ought to have. These conside- 
rations are unimportant in the northern parts of Europe ; but nobody will 
dispute their importance where the zenith distance is 10°, when an error of 
1" in the hour-angle of 24 minutes causes an error of 10" in latitude; I have 
therefore annexed a Table showing the correction to be subtracted from the 
hour-angle during the southern solstice. 
Argum. Hour-angle .... 
/ 
6 
/ 
9 
/ 
/ 
/ 
/ 
24 
27 
/ 
3 
12 
15 
18 
21 
30 
Correction subtracted . . 
0.06 
0.12 
0.19 
0.25 
0.31 
0.37 
0.44 
0.50 
0.56 
0.62 
MDCCCXXIX. 
F 
