The construction of a third-order secular analytical J-S-U-N theory by the Hori-Lie technique: Part II: Determination of (F 1s ,F 2s ,F 3s ) and (F 1c ,F 2c )

We expand both parts, the principal and indirect, of the Hamiltonian function up to the third order in the masses for the four major planets Jupiter-Saturn-Uranus-Neptune. Accordingly we write down the secular terms of F 1 , F 2 , F 3 and the critical terms of F 1 , F 2 in terms of the canonical variables of H. Poincare neglecting powers higher than the second in H, K, P, Q