[en] The quaternion field theory of matter in general relativity that was developed by this author was applied earlier to the calculation of the inertial masses of the electron and the muon, as a consequence of their (electromagnetic) coupling to their environment, in accordance with the Mach principle. As a consequence of the axiomatic structure, in this theory, the most primitive matter fields are represented by two-component spinor variables. All other ''particle'' fields must then be built up from these. Thus the high-energy data that are interpreted as referred to massive boson particles must be viewed here in terms of a composite of (electromagnetically) bound spinor particles. In this paper, the general field expression for the inertial mass of a boson is derived as a composite of elementary spinor fields. The neutral pion is a composite of proton and antiproton, the charged pion is a composite of a proton or antiproton with the spinor electromagnetic-field representation of a bound proton-antiproton pair. The theory is applied to a calculation of the mass ratio m(πsup(deg))/m(π^+-)) and it is found to be within o.1% of the experimental ratio