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Numerous forms of solution for the electro-thermal equations of fuses, together with various methods for establishing the parameters of these equations, have been attempted. Following earlier work on the analytical determination of the characteristics of semi-enclosed oil-immersed fuses and short fuses enclosed in silica or quartz filler, a new method has been established for the solution of long cartridge fuses. This new method is simple and based on a tabular technique derived for the work of Jaeger and Newstead on the transient heating of buried cables. The paper gives a brief treatment of the heat equations for a fuse and indicates the point of departure from the method previously adopted by Guile. The method of solution is indicated and tabular solutions are given for three particular cases of fuse elements of different cross-sections. The predicted and experimentally determined time/current characteristics are shown to be in close agreement.