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The thermal analysis, by hand calculation and computer, of the experimental data of fine-wire fuse "sealed" (in air) in tiny tube shows that the heat transfer through the air around the fine wire is the dominant heat loss mechanism. Even at the melting point of nickel, 1454°C, the radiation loss from a fine wire amounts to about ten percent of the total power loss and becomes comparable to the thermal conduction loss along the wire toward both cold ends. Results of the analysis also indicate the importance of three-dimensional effects, i.e., axial heat transfer in the air around the fine wire, especially for short wires at high temperatures. Experimentally, based on the comparison between his data on "sealed" (in air) and "vented" (in vacuum) fine-wire fuses, J. L. Olson has recommended a 40 percent derating in the threshold current, where the hot resistance of the fuse starts to rise fast. Based on the resistance versus current data of "sealed" and "vented" fuse made of 2.5 x 10-3cm diameter nickel wire measured by F. X. DeCurio and similar data by Kyte eta!. on 7.8 X 10-3cm diameter platinum wire at 66°C, we recommend that the blow power, where the fuse melts, of the vented (in vacuum) fuse should be derated by a factor of 11. Mathematically, the insignificance of the radiation loss at temperatures below 1400 K lends the heat equation, which includes the positive temperature coefficient of the thermal conductivity of the air and that of the electrical resistivity of the wire, solvable in terms of elliptical integral of the first kind.