5] NEISON'S LUNAR INEQUALITY. 131 



It follows from the equation 



6 = nt + e + 2e sin (nt + e CT) + . . . , 

 that the inequality in longitude 



^7 -A), 



where M, J are the mean longitudes of the Moon and Jupiter, and A 

 is the Moon's mean anomaly. 



Thus the argument of the inequality is analogous to that of the 

 Evection, and the inequality may be considered an Evection produced by 

 Jupiter. From this point of view a very approximate value of its 

 coefficient may be deduced from the coefficient of the solar evection, as 

 follows. 



The Sun makes a complete revolution with respect to the Moon's 

 perigee in about 1-127 years; and the Moon's perigee makes a complete 

 revolution with respect to Jupiter in about 34 '5 32 years. The ratio of 



these is 30'631. The mass of Jupiter is 77717, of that of the Sun; if 



1 UO U 



Jupiter were at his mean distance, the inverse cube of the distance 

 would be about that of the Sun. The average inverse cube of his 



distance is greater than this in the ratio TO 8 8 to 1, and is therefore about 

 1 



129-2 



that of the Sun. 



Therefore the coefficient of the evection being about 4600", that of 

 the analogous inequality due to Jupiter will be 



30-63 4600 4600 



129-2- 1050 = 4430 = 1 ' l """^ 



Also the sign will be opposite to that of the Evection since the 

 Moon's perigee advances faster than Jupiter. 



[A paper probably including among other remarks upon recent advances 

 in Lunar Theory some such matter as the above, was read at the 

 British Association Meeting, 1877. Its title only is published in the 



Report.] 



172 



