Equation 4.26 is not correct, it assumes that averaging over time is equivalent to averaging over longitude. While this is correct to first order in eccentricity, in equation 2.41 there is one term of order e and another term that is being averaged that is of order unity. In the limit where the pericenter does not change over time, upon averaging the two terms exactly cancel (see Burns, Lamy and Soter Icarus 40: 1-48 1977). If the orbit does precess, then the situation is more complicated. Thanks to C. Spalding for finding this error