The radial dose distribution from delta rays, fundamental to the delta ray theory of track structure, is recalculated. We now include the model of Rudd for the secondary electron spectrum in proton collisions. We include the effects of electron transmission through matter and the angular dependence of secondary electron emission. Empirical formulas for electron range versus electron energy are intercompared in a wide variety of materials in order to extend the track structure theory to arbitrary media. Radial dose calculations for carbon, water, silicon, and gold are discussed. As in the past, effective charge is used to scale to heavier projectiles. ©1996 American Institute of Physics.