It is convenient to evaluate the disturbing function,

(B.23) 
in a frame of reference that is instantaneously aligned with the ecliptic plane, as described in Section 4.12.
Let (, , ) and (, , ) be the Cartesian components of and , respectively, in this
standard reference frame. It follows from Equations (4.38), and (4.72)–(4.74), that
as well as
where
Here, , , , , , and
are the orbital true anomaly, major radius, eccentricity, inclination, argument of the perihelion, and
longitude of the ascending node, respectively, of Mercury. Moreover, , , , , , and
are the
corresponding quantities for the perturbing planet.
It is helpful to define
Making use of Equations (B.25)–(B.30), we deduce that
and
Hence,

(B.36) 
which implies that

(B.37) 
and

(B.38) 