  We report a value for the $D_2$-line frequency of $^{39}$K with 0.25 ppb
uncertainty. The frequency is measured using an evacuated ring-cavity resonator
whose length is calibrated against a reference laser. The $D_2$ line presents a
problem in identifying the line center because the closely-spaced energy levels
of the excited state are not resolved. We use computer modelling of the
measured spectrum to extract the line center and obtain a value of 391 015
578.040(75) MHz. In conjunction with our previous measurement of the $D_1$
line, we determine the fine-structure interval in the $4P$ state to be 1 729
997.132(90) MHz. The results represent significant improvement over previous
values.
