Measurement of Beauty production at HERA using semi-muonic decays ----------------------------------------------------------------- Differential measurements of beauty photoproduction cross sections in ep collisions performed with the H1 detector at HERA are presented. The data were collected at an ep centre-of-mass energy of 319 GeV in the years 1999-2000 and correspond to an integrated luminosity of 48 pb^-1. Events are selected by requiring at least two high-transverse momentum jets, p_t^jet1(2) > 7(6) GeV, jet pseudorapidities |eta^jet| < 2.5, and a muon in the final state. Both the lifetime signature and the large mass of b flavoured hadrons are exploited to determine the fraction of events in the sample containing beauty. Cross sections are measured in the region Q^2<1 GeV^2 with inelasticity 0.2 < y < 0.8 for muons with -0.55 < eta^mu <1.1 and p_t^mu > 2.5 GeV. The visible dijet-muon production cross section is measured to be sigma_{vis} (ep -> e b bbar X e jj mu X) = 42.5 \pm 3.4 (stat.) \pm 8.9 (sys.) pb. Differential measurements are presented as a function of the transverse momentum of the muon, the pseudorapidity of the muon and the quantity x_g^obs. The results are compared with Monte Carlo models based on leading order QCD and with next-to-leading order QCD calculations.