apparent Places of the Grcewwich Stars. 83 



January 0, 1800, being exactly 280°: but, in order to pre- 

 serve uniformity in the arrangement of the tables published 

 by the Astronomical Society, I shall assume the epoch of the 

 sun's mean longitude at mean noon at Greeivwicli on January 

 1, 1800, being exactly 281°: which, in fact, differs very little 

 from the preceding assumption. The mean motion of the 

 sun in a sidereal day is 58' 58",6417; which, in 10 such days, 

 amounts to 9° 49' 46",417 : and it will be seen that the inter- 

 vals of computation may be extended to 10 days, without any 

 risk of error. 



5. This being premised, we shall find that the mean longi- 

 tude of the sun, when any given star culminates, on any given 

 day of the fictitious year, will be equal to 



280° 13' 57",88 + (rf + «) 58' 58",6417 

 where a denotes the right ascension of the given star (in time), 

 expressed in the fractional part of a day (or 24''): and d the 

 number of sidereal days, reckoned from the given epoch to 

 the given day*. Consequently the mean longitude of the sun 

 for the moment of culmination of any given star for every 

 10th day of the fictitious year will bef 



280° 13' 57",88 + « 58' 58",64 + 



The sun's mean longitude for each star, being found in the 

 manner thus described for every tenth sidereal day, we must 

 apply the equation of the centre, in order to determine the 

 corresponding true longitude of the sun at the same periods ; 

 which will be the Argument for finding the aberration. And 

 twice this quantity will be the Argument for finding the solar- 

 nutation. 



6. But we may readily form a table o the true longitude 

 of the sun corresponding to every degree of his mean longi- 

 tude in the fictitious year ; which will last for many years to 



• For those stars, therefore, whose right ascension is between 0'" and 

 18'' 44'", the time oi" cuhnination, will refer to the yjrctec/wig- day. 



•f As an example, take the case of a AquUce, the mean right ascension 

 of which star, for January 1, 1830, is ID" 4!^™ W" = -S^.'l : and the mean 

 longitude of the sun at the time of its culmination on that day is conse- 

 quently 280° i;V 58" + 48' 26" = 281° 2' 24". This value being added 

 to 9° 4!)' 46", and its multiples, will give the mean longitude of the sun at 

 the time of its culmination on every subsequent tenth sidereal day of the 

 year. 



M 2 come. 



