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 

 desig'uate with a, h, c, d, &c. the respective errors in seconds committed 

 in the observations of the different declinations, x 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".31. I find then a ± a' by the 

 formula sin u = cot &> tan 5 and sin a! = cot a tan 5', and call m, n, o, p, &c. 

 the differences between a ± u' 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) = 



x(a + 



x{(N — 2)a + a + b + c + d + }=:m + n + o +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-\-b-\-c-\-d+=0, and a x = 1^ — 9 — lllli^ ^ ^ 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 I 

 cot » 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 j3 Cnicis* and 2 a 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 occa^on inaccuracies in the observations with the small power of the 

 telescope of the repeating circle. 



l2 



