apparent Places of the Greeii-iS.'ich Stars. 87 



mean motion of the moon's node in a tropical revolution of 

 the sun being — 19°*34'17, we may obtain, by simple addition, 

 the mean place of the moon's node on January 1, of any sub- 

 sequent fictitious year, commencing when the sun's mean 

 longitude at mean noon is 281°. The mean motion of the 

 nodes, in 100 sidereal days, is — 5°*281. But these days 

 should (for each star) be computed from the moment of time 

 when the sun's mean longitude is equal to 



280= 13' 57",88 + « X 58' 58",6417 

 = Jan^ 0''-2194't + a. 



a. denoting, as before, the right ascension of the given star 

 expressed in the fractional part of a day. If therefore ft de- 

 note the mean place of the moon's node, for any given star, 

 computed for the epoch January 0''"21944' + «, we shall have 

 the mean places of the moon's node, for the respective periods 

 as under * : viz. 



for Jan. 1 = ft 



April 11 = ft - 5=-281 

 July 20 = ft - 10 -562 

 Oct. 28 = ft - 15 -84.3 

 Dec. 67 = ft - 21 -124 

 The year in every case being supposed to commence when 

 the mean longitude of the sun at mean noon at Greenwich, on 

 January 1, 1800, is presumed to be exactly 281°. But, it will 

 be found that great accuracy in this resj^ect is not essentially 

 necessary, when it concerns only the lunar-nutation. 



14. The mean place of the moon's node being computed 

 for those periods in any given year, we may readily deduce 

 the place of the node for the same days in any following 

 year, by merely adding — 19°*3417 to each of such values: 

 this being (as I have already observed) the motion of the 

 moon's node in a tropical revolution of the sun. 



15. Having thus determined the mean longitude of the 

 moon's node for every hundredth day of the year, we must 

 enter Mr. Herschel's tables with the Arguments 



(ft -F N') and (2 ft + N'^) 



and having deduced the lunar-nutation for those days, we may 



• As an example, take tlie case of a, Aquilce, whose right ascension, 

 reduced to the fractional part of 24 hours, has been already deduced equal 

 to '82118; consequently we must compute the mean place of the moon's 

 node for January 0-21!)44 -|- -821 18 = January 1-(I40G2. The position of 

 the moon's node for that inoment of time is 172°"!).55 ; which bemjr added 

 to — o°'281, and its nmlti()les, will give the position of the moon's node, 

 at the time of the culmination of the istar, on every subseijuent hundredth 

 xidcreal day of the year. Thus, on the tabular April 11th, it will be 

 167°-674 = 1G7° 40' 2G". 



readily 



