41] ON THE GENERAL VALUES OF THE OBLIQUITY OF THE ECLIPTIC. 307 



[k k 



- -(%-%)(<+%- 2) tan A+^- - (a t - a,) cot h 

 yi yj yi ~ Ui 



i ( a i + a ) a i a j) tan h % (a { + ct,j I ) cot h\ 



x y i7j cos {(g { -f/j)t 



Also the value of k in terms of the constant c which, as stated 

 before, is known from the theory of precession is 



k = - c cos h { I - 2 1 (a f - I ) ( 3 a t - 5 ) y{] ; 



h and a are the arbitrary constants which enter into the complete 

 integrals of our equations, and they are determined so as to make 

 the initial values of 6 and (f>, or those of <u and <, equal to the ob- 

 served values. 



It is to be remarked that one of the values of g is 0, and if the 

 invariable plane of the system be taken as the fixed plane of reference, 

 the corresponding value of y will be also zero, so that the expressions 

 for 6, <j), and w will be considerably simplified by this choice of the 

 fixed plane. 



According to Stockwell's determination, in Vol. 18 of the Smithsonian 

 Contributions, the longitude of the ascending node of the invariable plane 

 on the ecliptic of 1850 is 106 14' 18", and the inclination of this plane 

 to the same ecliptic is 1 35' 20". 



Also, as already mentioned, if we make the invariable plane of the 

 system our plane of reference, we have for </ = 0, y c = ; and the re- 

 maining values of g i and those of /3 f and log y t which correspond to 

 them, according to Stockwell's determination, will be the following : 



392 



