186 ON THE MOTION OF THE MOON'S NODE [24 



15</-35f/ + 8 , , 



COS g77 = COS (777 -! 1 or> ,/ V r^ ~r^r 7~1 T\47"2 i\ "ft 



32<7-( 9 2 -l)- 256(/( 9 2 -l) 4 ((/-4) 



377V/ 1 4 ( / . 2 



rl 



- 1 1 55(/ 8 + 381 5cf - 4705f/ + 1 652r/ - 288 , 

 5 - 2 - 



1 ) 2 (^ 2 - 4) a ( 7 2 - 9) 

 :) 7)iry,y 8 y, 



r , / o "rv\ , . / * i \ / , ^ \ / .! r\\ ' i /* 



Now, if the coefficients of cos Q'TT and sin </77 in this formula be con- 

 verted into numbers, employing the above values of q, q,, &c., we find 



cos gvr = cos (jn [0'99999 ; 97902,01 654] 

 + sin ^[0-00064,77652,06681} 



But, with the above value of q, we find, from Briggs' Tables, 

 cos 977= -0-96424,37306,84295 

 sin qir= -0'26501, 70331,05484. 



Hence cosg7r= -0'96441, 51972,00779. 



Whence, by the same Tables, we find that 



g= 1-08517, 13927,46869, 



and therefore the ratio of the Moon's motion from the node to its sidereal 

 motion is 



g(l -TO) = 1-00399, 91618,46592. 



This is the quantity ordinarily denoted by g in the Lunar Theory. 



Delaunay's value of g, which agrees with that of Plana, is 



3 9 273 9797 199273 6657733 



= ----"--- 58982?^ 



