74 MR. RUMKER'S OBSERVATIONS 



Hence the following Tables may be constructed : 



So that considering how small the influence upon the right ascension is of an 

 error that could possibly exist in an element, such as the obliquity, long esta- 

 blished by innumerable observations, whilst every declination stands by itself 

 with all the errors to which one single observation is liable, we need not hesitate 

 to adopt the obliquity as known, and by using the formula 2 sin \ {pt, — a') = 



— j — ^! —. — ; — rr wc shall havc the advantage of introducing one well- 

 cos I . cos 8' cos ^ (a + a ) ° ° 



known part u in the room of the uncertain divisor sin (S -h ^') wherein the 



errors of observation are doubled. Cos S . cos S' is nearly = 1. The errors of 



so small an angle as ^ is near the equinox, utterly disappear in the cosine ; 



and a ± a' is sufficiently well known, as we shall see presently : but I have 



preferred the following method. 



Besides S and u, whereby a is already determined according to the formula 

 sin a = tan S cot u, there is also given a -|- a' ; and as this can be ascertained 

 with great precision, I have made use thereof in the following manner to cor- 

 rect the former. 



By deducing the errors of the clock, from a comparison of the culminations 

 of the principal fixed stars near the equator with their known right ascen- 

 sions, and applying these errors to the transits of the sun, we obtain the sim's 

 right ascensions at the time of his passing the middle wire, as near as the places 

 of the fixed stars can be depended on ; but the differences of these right ascen- 

 sions a ± a', which is all that we require, are correct to all intents, and 

 independent of a small deviation of the transit, as well as any constant error 

 in the places of the fixed stars. At the same time, for confirmation, a ± a' 

 may be deduced from the Nautical Almanac, which only supposes the sun's 

 motion during the interval correctly known. Thus by the united means of 

 the transit and Nautical Almanac, we shall have a ± a' given independently 

 of the mural circle. 



