Polarization mode dispersion can be described to first order by principal states of polarization (PSP's) and a differential group delay (DGD), and to second order by wavelength variation of the PSP's and by DGD dispersion (DGDD), the wavelength derivative of DGD. The high accuracy and wavelength resolution of Jones matrix eigenanalysis allows, for the first time, precise measurement of DGDD and PSP variation. A fast, automated system using a tunable laser and an accurate, real-time polarimeter is used to measure DGD, DGDD, and PSP variation by eigenanalysis of Jones matrices measured at a series of discrete wavelengths, and the system accuracy is demonstrated. Measurements at 2-nm intervals of a device whose DGDD is a known function of wavelength yield values of DGDD which differ from theory by less than 13 fs/nm.