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It is proposed that etchable damage is produced in dielectrics by energetic charged particles when a critical dosage of ionization energy is deposited at a critical distance from the ion's path by secondary electrons. Within the critical cylinder, molecular fragments more soluble than the parent molecule are formed. The radius of the critical cylinder is taken to be approximately 20 Å, as is appropriate to the passage of the etchant along the track and the diffusion of reaction products back to the surface. At the critical radius the dosage approximates doses producing bulk damage under γ irradiation. The proposed criterion predicts the formation or nonformation of etchable tracks in Lexan polycarbonate, cellulose nitrate, and mica, in agreement with published data. The calculations have been extended to magnetic monopoles to establish criteria for their detection in dielectric track detectors.