  Differential cross sections for jet photoproduction in the reaction ep --> e
jet X have been measured with the ZEUS detector at HERA using 82.2 pb^-1 of
integrated luminosity. Inclusive jet cross sections are presented as a function
of the jet transverse energy, E_T^jet, for jets with E_T^jet > 17 GeV and
pseudorapidity -1 < eta^jet < 2.5, in the gamma-p centre-of-mass-energy range
142 < W_gamma-p < 293 GeV. Scaled jet invariant cross sections are presented as
a function of the dimensionless variable x_T = 2 E_T^jet/W_gamma-p for
<W_gamma-p> = 180 and 255 GeV. Next-to-leading-order QCD calculations give a
good description of the measured differential cross sections in both magnitude
and shape. The ratio of scaled jet invariant cross sections at the two
<W_gamma-p> values shows clear non-scaling behaviour. A value for the strong
coupling constant of alpha_s(M_Z) = 0.1224 +- 0.0001 (stat.) + 0.0022 - 0.0019
(exp.) + 0.0054 - 0.0042 (th.) has been extracted from a QCD analysis of the
measured dsigma/dE_T^jet. The variation of alpha_s with E_T^jet is in good
agreement with the running of alpha_s as predicted by QCD.
