Inclusive momentum distributions of charged particles in restricted cones around jet axes were measured in dijet events with invariant dijet masses in the range 80 to 600 GeV/c(2). Events were produced at the Fermilab Tevatron in p (p) over bar collisions with a center of mass energy of 1.8 TeV and recorded by the Collider Detector at Fermilab. The results were compared to perturbative QCD calculations carried out in the framework of the modified leading log approximation (MLLA) and assuming local parton-hadron duality. It was shown that the data follow theoretical predictions quite well over the whole range of the jet energies included in this analysis. We extracted the MLLA cutoff scale Q(eff) and found a value of 230+/-40 MeV. The theoretical prediction of E(jet)sin theta(c) scaling, where theta(c) is the cone opening angle, was experimentally observed for the first time. From the MLLA fits to the data, two more parameters were extracted: the ratio of parton multiplicities in gluon and quark jets, r=N-partons(g-jet)/N-partons(q-jet)=1.9+/-0.5, and the ratio of the number of charged hadrons to the number of predicted partons in a jet, K-LPHD(charged)=N-hadrons(charged)/N-partons=0.56+/-0.10.