AT THE OBSERVATORY AT PARAMATTA. 
75 
Allowing now that the polar point of the mural circle is well established by 
superior and inferior culminations of circumpolar stars, as well as by observa- 
tions of the principal zodiacal stars, and that by observing alternately the 
upper and lower limb of the sun any vicious habit in observing is obviated, I 
designate w r ith a, b, c, d, &c. the respective errors in seconds committed 
in the observations of the different declinations, a being as above the effect upon 
the right ascensions arising from an error of one second in declination, which 
during the equinox is a constant quantity of 2".3 1 . I find then a ± a! by the 
formula sin a = cot a tan h and sin a! = cot co tan l', and call m, n, o, p, &c. 
the differences between a ± a! thus calculated from the mural circle, and that 
known from observation with the transit and Nautical Almanac as above ; 
then is 
x {a + b) = m 
x [a + c) — n 
x [a + d) — o 
oc[a + 
jt{(N — 2 )a + a + b + c + d + }= m + n + o -f p 
N being the number of observations ; or if these are not all brought in account, 
then is N — 1 the number of equations used. 
But if no constant error exists in the observations with the mural circle, 
then isa-{-&-j-c-f-c?+=0, and a x = m + n ^ ^ + ' a x being the 
required correction of the sun’s distance from the equinox. 
Thus each distance from the equinox found by the formula sin a — tan h 
cot co is successively corrected by a comparison with their observed sums or 
differences. I shall omit here the particulars, which are long and tedious, 
and simply give a short abstract of the results. During the equinox of Sep- 
tember 1827; the following observations were made for determining the right 
ascensions of (3 Crucis* and 2 u Centauri. 
* I have preferred /3 Crucis to a Crucis, which latter star also culminated with the sun during this 
equinox. But a. Crucis consists of two stars of equal magnitude, as near to each other as those of 
Castor, which I feared might occasion inaccuracies in the observations with the small power of the 
telescope of the repeating circle. 
