>Chandler discovered the earth's polar wobble in 1891. Scientists knew right away that there was a seasonal wobble that was easily explained by a forced factor. But why couldn't they determine the lunar factor?

I don't quite understand why you got the impression that this lunar forcing wasn't taken into account:

From Wikipedia:

>In the case of the Earth, the principal sources of tidal force are the Sun and Moon, which continuously change location relative to each other and thus cause nutation in Earth's axis. The largest component of Earth's nutation has a period of 18.6 years, the same as that of the precession of the Moon's orbital nodes.[1] However, there are other significant periodic terms that must be accounted for depending upon the desired accuracy of the result. A mathematical description (set of equations) that represents nutation is called a "theory of nutation".