  Observations with ground-based telescopes are affected by differential
atmospheric dispersion due to the wavelength-dependent index of refraction of
the atmosphere. The usage of an Atmospheric Dispersion Corrector (ADC) is
fundamental to compensate this effect. Atmospheric dispersion correction
residuals above the level of ~ 100 milli-arcseconds (mas) will affect
astronomical observations, in particular radial velocity and flux losses. The
design of an ADC is based on atmospheric models. To the best of our knowledge,
those models have never been tested on-sky. In this paper, we present a new
method to measure the atmospheric dispersion on-sky in the optical range. We
require an accuracy better than 50 mas that is equal to the difference between
atmospheric models. The method is based on the use of cross-dispersion
spectrographs to determine the position of the centroid of the spatial profile
at each wavelength of each spectral order. The method is validated using
cross-dispersed spectroscopic data acquired with the slit spectrograph UVES. We
measure an instrumental dispersion of 47 mas in the blue arm, 15 mas, and 23
mas in the two ranges of the red arm. We also measure a 4 % deviation in the
pixel scale from the value cited in UVES manual. The accuracy of the method is
~ 17 mas in the range of 315-665 nm. At this level, we can compare and
characterize different atmospheric dispersion models for better future ADC
designs.
