The description of deep inelastic scattering as an extrapolation between resonance production and diffractive scattering is extended to give successful quantitative representations for the structure functions of unpolarized electron scattering on protons and neutrons, and of neutrino, antineutrino scattering on nucleons. The same ideas also supply a prediction for the polarization asymmetry in deep inelastic electron-proton scattering (paper no. 2, to be published).