LECT. IX.] THE PARALLACTIC INEQUALITY. 39 



and then 6 5 is given by 



s = + n a. + s 



From these we find 



a 5 =-' 2 x -00595, 3 = '00001,4591, 

 8 



5 5 = fw"x '007 10,3 = '00001,7410. 



8 



These numbers being so small, we see that we may safely ignore, as 

 we have done, their effect in modifying the earlier coefficients. 



To find the effect of these coefficients upon the Moon's coordinates we 



must multiply by the factor X = ^ ^ . 



-- ct 



We shall take in accordance with the results given in Monthly Notices, 

 Vol. 13, p. 177, and Appendix to the Nautical Almanac, 1856, 



,, = 81-5. 

 M 



Constant of Moon's Parallax = 3422"'325. 



Also we shall take in the first place, the Sun's Mean Parallax to be 

 8"'8, and in the next place 8"'9, and we will find the corresponding values 

 of the coefficients of the Parallactic Inequalities. 



We find 



8"-8 8"-9 



X = -00250,9 X = -00253,76 



\a,= --00028,585 X, = -'00028,910 



X6, = - -00060,903 = - 125"'62 X&, = - -00061,596 = - 127"'05 



Xa 3 = -00000,3385 Xa 3 = '00000,3423 



X& 3 = -00000,3580 = 0"7384 \b 3 = '00000,3620 = 0"7468 

 Xa 5 = -00000,00366 Xa 6 = '00000,00370 



X6 5 = '00000,00437= 0"'00901 \b 5 = '00000,00442= 0"'00911. 



These results are very fairly accurate ; but in order to get good values 

 for a,, 6,, we were obliged to discuss a lt &,, a 3 , b 3 simultaneously. Let us 

 consider the peculiarity of the equations from which this difficulty arose. 



Following the method of approximation of Lecture VII, if we neglect 

 at first the products of 81, 80, dUjclt, d8d/dt with the small quantities a,, 

 6 2 , n' 2 , the equations become 



