112 A NEW METHOD OF DETERMINING 
To find k, and &,, we derive from the preceding 
k, [ cos g —e-+ 7) cos2 g + 7 cos 3 g + ote. | aL fh, [ sin g + 7° sin 2g + ete. | 
d 
—3 44+ 6(v),+4 fe (ndz)) = O 
k, [ sin g +27 sin 29+8 7° sin 38 g + ete. | — k, [ cos g + 27° cos2g + ete. | 
The value of JV is found further on. 
Having &, we find i, from 
ch, 84, +3" (nbz), + 6 (rp = 0. 
ko 
We have » 
hb=—el, N= —2h—Zh—3Z, 
where Z% is the constant of W. 
Let us find the expressions for the constants WV and K, A being the constant of 
: : c ° : h 
integration in the expression for 3 ; 6 
The equation (22) we can put in the form 
dz hy : a hy hy 
fo ee ee 
Rae ay + (3p 4y* + ete.) = 27 (5 
The differentiation of nz relative to the time gives 
- =1+h+4+ Z,+ periodic terms, 
where Fh, = — 32.7162, in the case of Althea, and 7, the part to be added when 
terms of the second order of the disturbing force are taken into account. 
