  The way in which the X-ray photon index, {\Gamma}, varies as a function of
count rate is a strong diagnostic of the emission processes and emission
geometry around accreting compact objects. Here we present the results from a
study using a new, and simple, method designed to improve sensitivity to the
measurement of the variability of {\Gamma} on very short time-scales.
  We have measured {\Gamma} in ~2 million spectra, extracted from observations
with a variety of different accretion rates and spectral states, on time-scales
as short as 16 ms for the high mass X-ray binary Cygnus X-1, and have
cross-correlated these measurements with the source count rate. In the
soft-state cross-correlation functions (CCFs) we find a positive peak at zero
lag, stronger and narrower in the softer observations. Assuming that the X-rays
are produced by Compton scattering of soft seed photons by high energy
electrons in a corona, these results are consistent with Compton cooling of the
corona by seed photons from the inner edge of the accretion disc, the
truncation radius of which increases with increasing hardness ratio.
  The CCFs produced from the hard-state observations, however, show an
anti-correlation which is most easily explained by variation in the energy of
the electrons in the corona rather than in variation of the seed photon flux.
The hard-state CCFs can be decomposed into a narrow anti-correlation at zero
lag, which we tentatively associate with the effects of self-Comptonisation of
cyclo-synchrotron seed photons in either a hot, optically thin accretion flow
or the base of the jet, and a second, asymmetric component which we suggest is
produced as a consequence of a lag between the soft and hard X-ray emission.
The lag may be caused by a radial temperature/energy gradient in the
Comptonising electrons combined with the inward propagation of accretion rate
perturbations.
