Hv THE THEORY OF THE LONG INEQUALITY 



» . 1 Sm'riaM.e , E „ . , 



(a> + ±iy sin 1 e 



6mn i aM x E 

 (w + Hf sin 1 

 Smr?aM x eHt 



+ similar terms with M^eur ' E ' H' for M^eis-EH. 



Taking the values of E and H depending upon the action of Jupiter, Saturn, and 

 Neptune, respectively, 



365-25E = - 0" -006082 - 0"-046049 - 0" -002431, 



= - 0"-054562, 

 365-2517= + l"-234 + l"-188 + 0"'464 = + 2"-886, 



and the values of E', IT depending on the action of Jupiter, Saturn, and Uranus, 

 365'25E'= - 0"-0011 + 0"'0031 + 0"-0093, 



= + 0"-0113, 

 S65-25lT= + 0"-0050 - 0"-1766 + 0"'9504 = + 0"*7788, 



then the corrections of the principal terms for the secular variations will be 



X (nt + e) = (- 55"-58 + o"-010 t) sin X, 



+ (- 12"-32 - 0"-043 t) cosX, 



X(rit + e') = (+ 40"-70 - o"-007 sin X, 



+ (+ 8" -96 + 0"-032 t) cos X, 



t being here the number of Julian years from Jan. 1, 1847. 



The corrections of Se and elur will be, neglecting the terms involving t, 



$e = + 0"-62 sin X + 3"-75 cos X, 

 eS-sr m - s"'53 sin X + 2"-19 cos X, 

 and those of tin, Sri, will be 



S'n = - 0"-0000262 sin X + 0"-0001181 cos X, 

 S"ri= + 0"-0000190 sin X - 0"-0000865 cos X. 



61. If we neglect all those terms in the preceding Articles, the coefficients of which are 

 less than l", we shall have for the inequalities due to the square of the disturbing force, in- 

 cluding the terms depending on the constant corrections of e, tff, e', "&', nri , ad, as well as the 

 correction for the secular variations of e, ■&, e, w' *, 



X (nt + e) = (+ 70"-S3 - o"*010 f) sin (2* - # ) - (149"*25 + o"-043 t) cos (2* - # ) 



- 10"-51 sin 2 (2* - W ) - if '06 cos 2 (2* - # ) 



- 2"'28 sin 3 (2* - $ ) - l"-41 cos 3 (3¥ - $ )• 



" The term depending on the cube of the disturbing force in the note, p. 38, is also included. 



