THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 143 
And for the particular case of ¢ = 1, we have 
(1 
(g— q)) = Iu ely — Bi) — OF, % (g — 2H) + 3J, © nin (q¢—3H’) Fete. 
2 (4) 
De ey 0 (g sp Jo" OW Sn (g 55 2H’) an dS, Sia (g aF 3H’) — Cte 
(2) (3) 
(9 +9')) = —Iv B(g— EB) —2Jy & (g — 28 
(4) 
Jy SS (g — 3H’) — ete. 
ye 
(@) 
+ Jy es (g-+ B’) 20, v (9 + 2H") + 8dy sm (9 + 3H’) ete. 
(0) (0) 
Instead of J, , we use (-/,, — 1), as has been noted. 
If we put h’ = + 2, we have 
(0 
0) 
((ig —29")) = $ Jov 23 (ig —E") + Jy SE (ig — 2H") + BJy, 8 (ig — BE") + ete. 
L Joy °° (ig +B’) —2 Joy % (ig + 2B") — ete. 
a (h’—7’) 
In the table giving the values of | tux , we have, under h’ = 2, which applies to 
the equation just given, 
1 : (3) 
for = 1, log. 2 Ji, = 8.38201 log. (4 Jy) = 4.97120: 
(0) (4) 
for? =2, log.( ey —1) = 7.366938n — log. (— 3, ) = 3.85370; 
(1) 
ie 0 == 63 log. (— $ Jo ) = 8.859182 efel sete: 
ete., ete. =a ete 
(3) (4) 
We find the values of — 3 -J,,, — 3, in the table under h’ = —2. We see that 
1 (W—1) 
these are the forms of the function we Vn whens anded.— bh and: 24 == 2) 
In the expansion of the coefficient of (¢g —h’g’) indicated above by ((¢g —h’g’)), 
we have coefficients of angles of the form (7g + 7H’). These can readily be put into 
the form (— 7g — 7H’), but the form employed is convenient in the transformation. 
