  One of the methods for studying the highest energy cosmic rays is to measure
the fluorescence light emitted by the extensive air showers induced by them. To
reconstruct a shower cascade curve from measurements of the number of photons
arriving from the subsequent shower track elements it is necessary to take into
account the multiple scatterings that photons undergo on their way from the
shower to the detector. In contrast to the earlier Monte-Carlo work, we present
here an analytical method to treat the Rayleigh and Mie scatterings in the
atmosphere. The method consists in considering separately the consecutive
'generations' of the scattered light. Starting with a point light source in a
uniform medium, we then examine a source in a real atmosphere and finally - a
moving source (shower) in it. We calculate the angular distributions of the
scattered light superimposed on the not scattered light registered from a
shower at a given time. The analytical solutions (although approximate) show
how the exact numerical results should be parametrised what we do for the first
two generations (the contribution of the higher ones being small). Not allowing
for the considered effect may lead to an overestimation of shower primary
energy by ~15% and to an underestimation of the primary particle mass.
