74 
MR. RUMKER’S OBSERVATIONS 
Hence the following- Tables may be constructed : 
Argument Right Ascension 
0° 
2° 
3° 
4° 
5° 
6° 
7° 
8° 
9° 
10° 
Cor. of a. for 1" increase of Declination... 
2".305 
2".307 
2".308 
2".313 
2".317 
2".322 
2".328 
2".332 
2".340 
Argument Right Ascension 
1° 
2° 
3° 
4° 
5° 
6° 
7° 
8° 
9° 
10° 
Cor. of a. for 1" increase of Obliquity 
0".04 
0".08 
0".101 
0".161 
0".202 
0".242 
0".282 
0".324 
0"365 
0"406 
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 ^ (a — a') = 
— Mn ( s O cot co — we s } ia n have the advantage of introducing one well- 
known part u in the room of the uncertain divisor sin (c5 -f l') wherein the 
errors of observation are doubled. Cos h . cos 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 1 and u, whereby a is already determined according to the formula 
sin a = tan ci cot co, 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 sun’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. 
