[en] It is possible to measure the deep-inelastic spin-dependent structure functions g₁/sup p/(x) and g₁/sup n/(x) for the proton and neutron using internal polarized hydrogen, deuterium, and ³He targets of polarization 50% and thickness 10¹⁴ to 10¹⁵ cm^-2 and the 60 mA longitudinally polarized 30 GeV electron beam in the HERA electron storage ring. The measurement of the deep-inelastic spin-structure of both isospin states of the nucleon at the same kinematics and using the same apparatus allows the Bjorken sum rule to be experimentally checked. In addition, it uniquely constrains the spin distribution of the u and d quarks as a function of x in any model of the nucleon. Possible target and detector configurations are described and an estimate of the accuracy of such a measurement is presented